S O P A

Transcription

S O P A

SUMMARY OF PROFESSIONAL
ACCOMPLISHMENTS
JOANNA JAŁOCHA-BRATEK
— GENERAL INFORMATIONS —
I
Held diploma, scientific/academic degrees
MASTER OF SCIENCE DEGREE IN PHYSICS (2001)
Institute of Physics of Jagellonian University in Cracow, Dept. of Theory
of Relativity and Astrophysics
Supervisor: Prof. dr hab. Marek Kutschera
Title of graduate dissertation: Quark stars.
DOCTOR OF PHILOSOPHY DEGREE IN PHYSICS (2006)
Institute of Physics of Jagellonian University in Cracow, Dept. of Theory
of Relativity and Astrophysics
Supervisor: Prof. dr hab. Marek Kutschera
Title of PhD Thesis: Physical mechanisms shaping rotation curves of
spiral galaxies.
II
Informations concerning previous employment in scientific institutions
2001-2002, INTERNSHIP
Institute of Nuclear Physics, Department of Theoretical Astrophysics
Tutor: Prof. dr hab. Marek Kutschera
since December 2006 UNPAID WORKER
since April 2007 RESEARCH ASSISTANT
since April 2008 ASSISTANT PROFESSOR
Institute of Nuclear Physics, Department of Theoretical Astrophysics (at
present - Department of Mathematical Physics and Theoretical Astrophysics)
III
Specification/Indication of the scientific achievement pursuant to/in accordance with the instruction/act art. 16 $ 2 on the academic degrees
and the academic title as well as on the degrees and the title within the
scope of art /as indicated in/ Dz. U. nr 65, poz. 595:
My scientific achievement in the sense of the instruction/act mentioned
above is a monographic series consisting of 7 published co-authored
scientific papers listed below.
1
III.A PAPERS BEING THE SUBJECT OF THE SCIENTIFIC ACHIEVEMENT
(listed in the order of appearance in the text )
[h01] J. JAŁOCHA, Ł. BRATEK, M. KUTSCHERA
Is dark matter present in NGC4736? An iterative spectral method for
finding mass distribution in spiral galaxies
2008 ApJ 679 373J
I want to stress the discovery that the disk model, when properly used, may
satisfactorily explain the rotation of galaxies without the need of invoking a
massive halo of nonbaryonic dark matter and leading to low galactic masses at
the same time, is my own solitary achievement. Without it none of the works
mentioned below would have ever appeared.
As to the details, my contribution to this work involved the analysis of the available measurement data – in particular, the rotation curve (bringing forth and
applying the sphericity test) – the idea of using neutral hydrogen to eliminate
an underestimation of mass, the disk model leads to. Apart from that I applied the disk model to obtain surface density by using a formula in form of a
series of Bessel functions that I found and which relates the rotation velocity
and the surface density (these calculations became the basis for later works)
and obtaining mass-to-light ratios dependent on the radius. I also essentially
contributed to writting down the results, drawing conclusions, and I was taking
part in discussions with the referees.
Estimation of my individual contribution 50%.
IF in the publication year 6.331, present IF 6.28
[h02] J. JAŁOCHA, Ł. BRATEK, M. KUTSCHERA, P. SKINDZIER
Global disc models for galaxies NGC 1365, 6946, 7793 and UGC 6446
2010 MNRAS.406.2805J
My contribution to this paper involved taking part in the analysis of the measurement data available in the literature, independently finding surface densities
based on the available rotation curves, and calculating the resulting mass-tolight ratios as functions of the radius. This approach is different from that
commonly adopted in modeling spiral galaxies, where the mass-to-light ratios
are customarily assumed in advance. My contribution consisted also of writting down the essential parts of the results, drawing conclusions, and taking
part in discussions with the referees.
Transverse gradients of azimuthal velocity in a global disc model of
the Milky Way
2010 MNRAS.407.1689J
2
My contribution to this paper involved taking part in the analysis of the measurement data available in the literature that concerned the Milky Way rotation
curve and the vertical gradient in azimuthal velocity. Based on the rotation
curve I calculated a surface density for this galaxy which I then used to determine the vertical gradient in azimuthal velocity. I introduced and used two
methods for determining the gradient. I calculated the gradient for the Milky
Way also in three-component models. I also substantially contributed to writing
down the results and conclusions, and to the discussion with the referees.
Estimation of my individual contribution 50 %.
Vertical gradients of azimuthal velocity in a global thin disk model of
spiral galaxies NGC 2403, NGC 4559, NGC 4302 and NGC 5775
2011 MNRAS 412: 331-336
My contribution to this paper involved taking part in the analysis of the measurement data available in the literature and concerning the galaxies NGC 2403,
NGC 4559, NGC 4302 i NGC 5775. Based on the rotation curves I independently
calculated surface densities and vertical gradients in azimuthal velocity. The
methods I had introduced earlier were used here. I also contributed substantially to writing down the results and conclusions, and to the discussion with
the referees.
[h05] J. JAŁOCHA, Ł. BRATEK, M. KUTSCHERA, J. PĘKALA
The role of large-scale magnetic fields in galaxy NGC 891: can magnetic fields help to reduce the local mass-to-light ratio in the galactic
outskirts?
2012 MNRAS 421 2155J (Erratum: 2014MNRAS.443.2436J)
I contributed to this paper by analyzing the measurement data available in the
literature, by noticing the possibility how, with the help of magnetic fields, one
could try to explain both the behavior of the mass-to-light ratio at the galactic
outskirts (namely, its growth), as well as the anomalous behavior of the vertical
gradient in azimuthal velocity. I carried out most of calculations (both analytical – e.g. a derivation of the fluid equilibrum equations in the gravitational and
magnetic field – as well as numerical), I also contributed substantially to writing
down the results and conclusions, and in the discussion with the referees.
[h06] J. JAŁOCHA, Ł. BRATEK, M. KUTSCHERA, J. PĘKALA
A possible influence of magnetic fields on the rotation of gas in NGC
253
3
2012 MNRAS 427 393J (Erratum: 2014MNRAS.441.3502J)
My contribution to this paper involved the analysis of the measurement data
available in the literature, putting forth an idea of how one could try to reduce
the mass-to-light ratio in the galactic outskirts with the help of a magnetic field
(this is a novel idea, not used so far). I also carried out most of calculations
(both analytical and numerical), I also contributed substantially to writing down
the results and conclusions, and in the discussion with the referees.
[h07] J. JAŁOCHA, SZ. SIKORA Ł. BRATEK, M. KUTSCHERA
Constraining the vertical structure of the Milky Way rotation by microlensing in a finite-width global disk model
2014 A&A. 566A 87J
My contribution to this paper involved the analysis of the measurement data
available in the literature and concerning the rotation curve of our Galaxy. I
contributed substantially to calculating the density in a finite-width disk model
and the determining the vertical gradient in azimuthal velocity resulting from
the rotation curve. I also contributed much to preaparing essential parts of the
publication and to the discussion with the referees.
IF in the publication year 4.479
III.B TITLE OF THE SCIENTIFIC ACHIEVEMENT
INVESTIGATIONS OF THE POSSIBILITY OF DESCRIBING THE SPIRAL GALAXIES BY MEANS OF THE USE OF INFINITESIMALLY THIN–
AND FINITE-WIDTH DISK MODELS.
III.C DISCUSSION OF THE AIM, OF THE MEANING AND OF A
POSSIBLE USE OF THE WORKS MENTIONED ABOVE.
Introduction
My interest in astrophysics began in the fourth year of my graduate studies. I
studied physics at the Jagiellonian University, I chose astrophysics as the main
subject of my studies. I wrote my master thesis devoted to quark stars under the
supervision of prof. Marek Kutschera. In my PhD thesis, also supervised by prof.
Marek Kutschera, I was investigating spiral galaxies, more precisely, my research
concerned studying the distribution of mass in these galaxies. I was particularly
interested in the question whether they possessed a massive, spherically symmetric halo consisting of nonbaryonic cold dark matter (CDM) or, maybe, they were
4
disk-like objects. Having had defended my PhD thesis, I was still working on spiral
galaxies, as I consider this topic important and promising. Moreover, I was successful (together with prof. Kutschera) in making several other persons interested
and I encouraged them to cooperate. A dozen of papers had appeared during a 6
years-long period, among which most had been published in respected journals,
and 7 of them are the subject of this dissertation. Apart from that, 2 PhD theses
and 2 Master theses have been the result of works within our research group.
Today, nonbaryonic dark matter is a basic notion in many branches of science, including astrophysics. The beginnings of the dark matter notion should
be linked with the investigations of galaxies and with the person of Fritz Zwicky.
The proper motions of galaxies in galactic clusters had been pointing to higher
masses of these clusters, than estimated based on their brightness. Obviously,
nobody had been using the dark matter notion at that time, and simply some
matter difficult to detect, invisible in the spectrum band-width available to observations, had been understood under this notion. The other astrophysical objects,
important for the discussions on nonbaryonic dark matter, are spiral galaxies. By
measuring the rotation curves of spiral galaxies, and then by attempting to reconstruct them based on the observed brightness of those galaxies, an excess of the
dynamical mass over the luminous mass was ascertained. The dark matter forming a spherically symmetric halo encircling spiral galaxies also turned out very
useful in stabilizing these galaxies. As it seems, the branch of knowledge requiring today the nonbaryonic dark matter most, is cosmology. The contemporary
cosmological model, being a consistent framework of theoretical assumptions and
observations, states that the baryonic matter contributes only a tiny ingredient to
the matter-energy content of the Universe, essentially built of dark energy and
nonbaryonic dark matter, about the nature of which nothing can be said with certainty, and a measure of this lack of knowledge is the fact that the predicted value
of the cosmological constant is tens of orders of magnitudes greater than that
observed. This is a serious epistemological problem. According to the currently
reigning paradigm, the nonbaryonic dark matter constitutes a predominating part
of the galactic clusters’ masses, and of separate spiral galaxies (also dwarf elliptical
galaxies, which are especially abundant with it). The presence of dark matter is
also a factor stabilizing spiral galaxies and enabling the formation of structures in
the Universe. Saying it shortly, nonbaryonic dark matter is currently one of the
basic and indispensable notions and entities.
Thin disk model
Only a few years ago, both the author of this dissertation and her collaborators,
belonged to a group of persons convinced about the ubiquity of nonbaryonic dark
matter, in general, and its indispensability in solving the problem of rotation of
5
spiral galaxies, in particular. But these viewpoints underwent a complete change
during the period of last few years. This change was prompted by the investigations taking its origin in my doctorial thesis and now being the subject of this
dissertation.
—1—
The first paper devoted to this subject and being the part of this dissertation, was
published in 2008. The work is concerned with galaxy NGC 4736 (M94) [h01].
I introductorily studied this galaxy already during the preparation of my
&
%'()&
!'*&
"' "&
)'(+&
#'*"&
$' +&
+'""&
% '*+&
,
PhD thesis. This was when I rec!
ognized it as particularly suspected
of not containing large amounts of
%#
,
CDM. This opinion arose from sev,
eral facts. Firstly, its rotation curve
%!
decreases with the radius for large
distances from the center (Fig.1).
$
This fact shows that the mass function saturates quickly with the dis"
tance from the center, in contrast to
what one would expect if the galaxy
!
"
#
$
%
%!
%"
%#
possessed a massive spherically symmetric halo (as predicted by modFigure 1 – The observed rotation curve of NGC 4736 /circles/ els of galactic evolution), for which
and the rotation curve obtained in our model (thick line v4 corresponding to a surface density σ4 found in the fourth iteration the mass function would keep on inbased
on equation Eq.6)The thin line vk is a the Keplerian curve
p
creasing further, almost linearly with
GMTOT /ρ, where MTOT ≈ 3.4 × 1010 M⊙ is the total galactic
mass obtained from density σ4 . The thin line vm is the rotation the distance, dominating the convelocity obtained for a spherically symmetric matter distribution
tribution to the total galactic mass.
with the same mass function as for σ4 .
Moreover, the rotation curve of this
galaxy breaks a very simple sphericity test suggested by me, see Fig.2:
)*+ ,-./
-
.
, !"&'(%
"
!"#$%
v 2 (ρ1 )ρ1 ≤ v 2 (ρ2 )ρ2 ,
if
ρ1 ≤ ρ2 ,
Breaking this test means as much as that, for a spherically-symmetric distributed
matter to explain the rotation of this galaxy, fairly peculiar properties of this galaxy
would have to be assumed, namely, regions with negatively-definite mass. Other
important facts at our disposal are the surface brightness measurements for several filters (I, V, B), and the distribution of neutral hydrogen reaching out further
than the rotation curve.
As it will be shown below, these facts are crucial for the accurate study of a
galaxy. In my approach, a spiral galaxy (here, M94) is modelled as an infinitesimally thin disk. With such a model one has to solve the Poison equation first,
6
under the assumption that there is no matter present outside the disk plane (in
this approximation matter is distributed entirely within the plane z = 0).
A solution can be searched for in a form of a series of Bessel functions defined
on a finite disk, or by means of an integral representation:
Z∞
ρ
|z|
2
Φ(ρ, z) = −2πvR σ̂(ω) J0 ω
e−ω R dω.
(1)
R
0
*
By convention, I introduce the characteristic constants R and vR on the
dimensional grounds: R – is the cutoff radius, that is, the outermost point
of the measured rotation curve of a
galaxy, and vR = v(R) is the velocity
in that point. A discontinuity of the
potential in the direction normal to
the disk plane is the source of disk
mass, which according to the Gauss
theorem gives an expression for the
disk surface density (being close to
a column density of a flattened mass
distribution the model approximates):
Z∞
ρ
vR2
dω, (2)
σ(ρ) =
ω σ̂(ω) J0 ω
GR
R
*
*-./0/1.2*345.61/7*028*/94*:4;54-102*<0==*>?26/1.2*
@0-A1/-0-7*?21/=B*
'()*#+,$
!
!"
!#
!$
!%
&!
81=/0264*@12*?21/=*.>*/94*6?/.>>*-081?=B
Figure 2 – A negative result of a sphericity test for the spiral
galaxy NGC 4736. The figure shows an observationally determined rotation curve (continuous line) and a corresponding to it
Keplerian mass function defined as MK (ρ) = G −1 ρ v 2 (ρ) (dashed
line). The Keplerian mass function is not an increasing one
for all galactocentric distances, which excludes a domination of
a spherical component and points to a disk-like distribution of
matter, for which the global disk model is a more suitable description than the spherical model.
tion of the density
GR
σ̂(ω) = 2
vR
Z∞
0
where σ̂(ω) is a spectral representa-
x σ(Rx) J0 (ωx)dx.
(3)
0
In order to find a surface density distribution, we make use of the rotation curve
(we are looking for such a density distribution
in the disk plane which would
2
precisely account for the rotation curve) v (ρ)z=0 = ρ ∂ρ Φ(ρ, 0). Thus we get:
2
u (x) = 2π x
Z∞
ω σ̂(ω)J1 (ωx)dω,
(4)
0
and from this the inverse relation resulting from the Fourier-Bessel transforms
is easily seen:
Z∞
1
u2 (x) J1 (ωx)dx,
(5)
σ̂(ω) =
2π
0
7
where we have used the notation: u(x) ≡ v(xR)/vR , x ≡ ρ/R. The above formulas
are analogous to those known from the handbooks discussing the astrophysics
of galactic disks (eg.[19]). What is interesting, having substituted Eq.3 to Eq.4 and
Eq.5 to Eq.2 we obtain expressions that can be integrated with respect to ω. The
results of these calculations are the following integrals, expressing the relations
between the rotation velocity and the disk surface density, which are mutually
inverse transforms:
!
ρ
∞
χ
ρ
2E ρ
R
R
χE
χ
K
)
)
)
(
(
(
v 2 (ρ) = 4 G ρ · V.p.
σ(χ) ρ2 −χρ 2 dχ − σ(χ) ρ χ2 −ρχ 2 − ρχ dχ ,
(6)
)
(
ρ
0
χ
!
ρ
∞
ρ
χ
R
R
E
E
K
)
)
)
(
(
(
ρ
χ
ρ
ρ
σ(ρ) = π 21G V.p.
v 2 (χ) χ2 −ρ2 dχ + v 2 (χ) ρ χ − χ ρ2 −χ2 dχ ,
(7)
ρ
0
where the V.p. sign denotes the principal value of an integral, and K and E are
complete elliptic integrals. Owing to the [7] (B&T) handbook, popularized in the
literature is a formula involving a derivative of the velocity. It is rather astonishing,
that the relation Eq.5 is commonly integrated by parts, in the result of which a
velocity derivative appears in the final equation analogous to Eq.7 (which can only
be understood that authors do not trouble themselves, but copy original Toomre’s
formulas, who had done so for other reasons). The derivatives of the rotation are
difficult to be determined observationally, which the B&T handbook considers a
central disadvantage of the disk model. As it can be seen, our formula does not
involve any velocity derivatives! In this context it is interesting that in a new edition
of the B&T handbook published after 2010, this problem is not discussed at all,
neither is given there a formula analogous to Eq.7 devoid of this deficiency.
The above relations between the rotation velocity and the distribution of mass
possess a feature that is qualitatively distinct from a spherical mass distribution, namely, the disk-like solutions for the mass distribution, unlike sphericallysymmetric, depend at each point on the entire rotation curve, not only below a
radius delineating the region in which we are looking for a solution. And it is
obvious that any measured rotation curve ends somewhere.
Such a property of the disk model (and of flattened mass distributions in general, which the Newton’s theorem on the homeoids does not apply to) always
leads to an uncontrolled disturbance in the disk mass due to cutting off the integration region, which is a real problem left untouched in handbooks, maybe
because known profiles of matter distribution had been assumed in the modelling
of rotation curves (e.g., exponential, Gaussian), for which a global relation could be
derived in an analytical way. But an attempt to reconstruct the observed shape of
a rotation curve, without assuming any known mass profiles, becomes a difficult
task.
To overcome this difficulty one can use the fact, that for some galaxies (including M94), neutral hydrogen distribution is known reaching out further than
8
the rotation curve. Using this fact, we are looking for such a surface density distribution, which will result in a rotation curve agreeing with the measurements,
and moreover, above the cutoff radius, it will go over into the gas distribution.
In practice, this aim is achieved by
applying an iteration method pro$%
posed in our modelling of rotation
curves. This method, starting from
the measured rotation curve, by us$%
ing the relation between the ro$
tation curve and the surface density derived above, first finds a ze&
(
roth approximation to the surface
'
)
$%
density. Next, based on this density a corresponding rotation is being reconstructed. It is then seen,
!
"
#
$%
that the rotation is lower than that
we started with.
Now, we are
3 – A fragment of a surface density distribution obtained
looking for a difference between Figure
in the result of applying an iteration method (solid lines σ1 , σ2 ,
the squares of the original veloc- σ3 , σ4 ), and the observed surface density of gas (points).
ity and that obtained as the zeroth approximation, and next we find a correction to the surface density corresponding to that difference.
We repeat these calculations until
a satisfactory agreement between the measured rotation velocity and that
obtained in a given step is reached.
!
This procedure is depicted in Fig.3
%$
and in Fig.4. Then, using the cal(
%#
culated surface density and the mea(
sured surface luminosities we deter%'
mine a mass-to-light ratio as a function of the radius which is shown in
Fig.5.
%&
(
A low mass-to-light ratio (of the
order of a few) suggests a lack of
(
nonbaryonic dark matter in a galaxy,
%!
or an insignificant amount of it, because it shows, that the matter con!
"
#
$
%
%%
tained in stars suffices to explain the
galaxy rotation. In this case, the Figure 4 – v1 , v2 , v3 , v4 are rotation velocities of galaxy NGC 4736
mass-to-light ratio should be decreas- calculated based on Eq.6 and corresponding to surface densities
obtained by means of applying an iteration method. The v4 line
ing for higher radii, for it is assumed was
extended beyond the measurement region (the measurein general that the central galactic re- ment points are marked with circles).
),- ./01
&
!&
'()
+
*#$ %
$
%
!"#$%
)*+ ,-./
!
( !"&'(%
%
"
&
!"#$%
9
gions are dominated by low-mass stars with higher mass-to-light ratios. In contrast,
were the mass-to-light ratio high, particularly for several various filters, this would
point to a possible presence of CDM.
In the classical approach to modelling
spiral galaxies one proceeds
'
in the opposite direction – based on
the measured luminosity curve a con"
stant mass-to-light ratio is most often
+
assumed (although, usually different
&
ones for the central bulge and for
*
the disk) and then, based on this, a
!
density distribution is inferred [20]. If
(
such a density distribution does not
%
lead to predictions that agree with the
galactic rotation, the missing dynamical mass is recovered by introducing
!
"
#
$
%
a dark halo. In contrast, I start with
a rotation curve and then I obtain
Figure 5 – The mass-to-light ratio for galaxy NGC 4736 pre- the mass-to-light ratio as the result of
dicted based on the calculated surface density. A correction for
the extinction has been taken into account. B-filter (triangles), V - the modelling process and when the
filter (squares), I-filter (circles) and, additionally, an I-filter with ratio is low I conclude that the disk
a correction for the extinction taken into account (stars).
model accounts for the galaxy properties very well.
I have to stress, that several years ago rejecting the constant mass-to-light ratio
assumption was not a standard approach. At the present time, also other authors
lean towards giving up this too stiff a restriction more often [10]. As can be seen,
our approach is characterized by a minimum number of assumptions: I make
use of the observational evidences, such as the rotation curve, density of gas, and
the assumption of a disk-like distribution of matter. Then I carry out an analysis
of the results, and judge if they are leading to a consistent picture of a galaxy
(if it is disk-like, it does not contain a massive spherically-symmetric CDM halo,
then we should obtain low mass-to-light ratios). The most important conclusions
following from my research on NGC 4736 is the fact, that the rotation curve of this
galaxy can be perfectly accounted for by a disk-like matter distribution, without
invoking any assumptions about a nonbaryonic dark halo. It can be even said that
a disk-like distribution is preferred here, since, as I have already mentioned, the
rotation curve of M94 breaks the sphericity test. In addition, the surface density
distribution obtained with the use of our method goes over smoothly into the gas
distribution Fig.6.
What is important, in the result of the modelling, low local and global mass-tolight ratios for this galaxy were obtained (of the order of 0.5-0.4) in three filters:
)
&'( )*+,
!"#$%
10
blue, visible and near-infrared, which for large distances decrease with the radius.
*23!4567
Our work concerning galaxy M94
raised some interest in the media [5].
%
That is not strange, since this galaxy
is a model galaxy for which the in%
troduction of a dark halo is not only
unnecessary, but it would cause trou%
bles.
"
%
I came back to galaxy M94 in
a next paper (which is included in
(
%
this dissertation) because new data
had appeared concerning the rota%
tion and luminosity measurements in
!
"
#
$
%
%!
%"
%#
a 3.6-micrometer band-width. But
!"#$%&
the conclusion that this was a galaxy
6 – Global distribution of surface density for NGC 4736
devoid of dark matter did not change Figure
found in the 4th iteration step (thick solid line σ4 ). The matand even strengthened.
ter distribution perfectly accounts for the rotation curve. To
'
%
&%
—2—
compare with, a surface density obtained in [30] is shown. The
gas distribution (neutral hydrogen) is marked with points. The
I-band-width luminosity takes into account a correction for te
intrinsic extinction (stars).
In [h02], together with the co-authors, I compared the mass-to-light ratio predictions for the 3.6-micrometer band-width, obtained as a result of studying a J − K
color difference in NGC 4736 galaxy [10] with that of ours, and we obtained a
satisfactory agreement, see Fig.7.
This work, apart from NGC 4736 galaxy, is devoted also to four other spiral
galaxies: NGC 7793, NGC 6946, NGC 1365 and UGC 6446. An infinitesimally thin
disk model discussed above was used to model these galaxies, and the conclusions that CDM in unnecessary were based on: the obtained low mass-to-light
ratios, a possible agreement of these ratios with the predictions based on the
color difference, and a smooth overlapping of the disk model surface density
with the measured distribution of hydrogen and helium. For all galaxies but
UGC 6446 with single rotation curve, the analyses were based on several independently determined rotation curves. Rotation curves of these galaxies are
characterized by high diversity: the NGC 4736 and NGC 7793 galaxies have rotation curves that definitely decrease and breake the sphericity test (this concerns all of the measurements). As for the NGC 1365 and NGC 6946 galaxies,
the results are not unique and differ depending on the rotation curve used: NGC
1365 has a slightly decreasing rotation curve (seen for all the measurements),
while breaking of the sphericity test depends on which particular rotation curve
is studied. Galaxy NGC 6946 has a rotation curve which is flat for most of
radii, but some of the analyzed curves were locally breaking the sphericity test.
11
!
!
0
0
!"'()*+,+-+./$% &+!! !"1()*/$% &
"
2.0
NGC 4736
M/L
1.5
1.0
0.5
0.0
0
3
6
9
12
15
R [kpc]
2.5
NGC 6946
2.0
M/L
1.5
1.0
0.5
0.0
0
3
6
9
12
15
18
21
24
27
2.5
NGC 7793
2.0
M/L
1.5
1.0
0.5
0.0
0
3
6
9
12
R [kpc]
Figure 7 – The comparison of mass-to-light ratios for
galaxies NGC 4736, NGC 6946 i NGC 7793. [dotted line] –
the mass-to-light ratio calculated based on the 3.6 µm bandwidth luminosity and the surface density corresponding to
the THINGS rotation curve; [thick solid line] – the same
as before but with the HI+He component discarded. For
comparison, [thin solid line] – the mass-to-light ratio found
in [10] based on the J-K color difference.
At the same time, galaxy UGC 6446 has
a rather flattened rotation curve that
does not break the sphericity test. For
galaxies NGC 4736, NGC 6946 and NGC
7793, we additionally used the predictions on the mass-to-light ratios in the
3.6-micrometer band-width based on the
measured J − K color difference. In
the case of NGC 4736, NGC 1365 and
NGC 7793 we inferred that these galaxies can be modelled very well as thin
disks without nonbaryonic dark matter:
we obtained surface density distributions
smoothly converging to the gas (hydrogen and helium) distribution and low
mass-to-light ratios. In addition, the very
character of the rotation curves excludes
the possibility of domination of a spherical component. As for NGC 4736, as it
has been already said, we obtained a
good agreement between the mass-tolight ratio in the 3.6 micrometer bandwidth: predicted based on the color difference, and that obtained based on the
disk model, see Fig.7. A higher divergence between this prediction and our
results occurred in the case of galaxy
NGC 7793 (see Fig.7) but on account that
the galaxy satisfies in a perfect way all
other criteria ”of a galaxy without CD”
we accepted this fact as being rather an
anomaly in this respect. Problematic in
the case of NGC 6946 were the discrepancies between the rotation curves, and
consequently, non-uniqueness of the results concerning the mass-to-light ratios.
Nonetheless, it is worth of emphasizing
that even the highest value did not exceed 7. At the same time we obtained
a very nice consistency between our results and the modelled prediction for the
12
mass-to-light ratio in the 3.6-micrometer band width, see Fig.7.
Finally, we concluded that NGC 6946 is a good example of a galaxy not requiring
CDM, at least in large amounts. Anyhow, the galaxy UGC 6446 turned out to be the
most interesting. The mass-to-light ratio for this galaxy (in the blue band-width)
attains a value of as much as 30 at the disk boundary, which would indicate the
nonbaryonic dark matter presence. At the same time, the surface density turns
smoothly into the measured distribution of gas (hydrogen and helium), while the
global mass-to-light ratio is low, reaching 4.89 in the blue band-width. These are
arguments against large amounts of CDM. It is also worth emphasizing that the
galaxy is very reach in gas – the measured abundance of the neutral hydrogen and
the corresponding helium abundance amount to nearly 1/3 of the galaxy mass we
obtain in disk model. Finally, we were concluding that responsible for the increase
in the mass-to-light ratio might be a so far undetected component of this galaxy:
baryonic or, maybe a gaseous, or that connected with the compact objects.
The vertical gradient in azimuthal velocity
Matter in spiral galaxies rotates not only in the disk plane but also above/below it.
When a galaxy is appropriately aligned with respect to the observer (has a high
inclination angle) then the rotational velocity can be measured not only within
the disk, but also at the altitudes of a few kpc above its mid-plane. The rotational
velocity decreases linearly with the altitude above the disk, and the vertical gradient
in azimuthal velocity attains a value up to about -30 km/s/kpc, depending on a
galaxy. The other gradient feature is its weak dependence on the radius.
—3—
The work [h03] is devoted mainly to the Milky Way’s vertical gradient in azimuthal
velocity, therein also a fragment can be found discussing the gradient in the galaxy
NGC 891. The values of the vertical gradient for our galaxy are high, reaching
−22 ± 6 km/s/kpc. It is measured for very low altitudes (below 100 pc above the
mid-plane), in the region of the radial variable ranging from 3 to 8 kpc [21].
The starting point to calculating the gradient is the assumption that the matter
above the mid-plane moves on orbits allowing for the use of only the following
relation between the radial component of the gravitational acceleration and the
rotational velocity
vφ2 (r, z)
(8)
≈ −gr (r, z),
r
where gr (r, z) is the radial component of the gravitational acceleration. If it is so
(and the circular orbit approximation is reasonable and commonly adopted), then
the relation between the rotation velocity (considered as a function of the radius
13
r and the altitude z above the mid-plane) and the surface density σ(r) in the disk
reads:
Z∞
2 Gσ (χ) χdχ
χ 2 − r 2 + z2
2
vφ (r, z) = q
E [X] ,
K [X] −
2
2
(r + χ) + z2
2
−
χ)
+
z
(r
0
s
4rχ
X=−
< 0,
(9)
2
(r − χ) + z2
%
&'()*+,
where E and K are complete elliptic integrals. Thus, the central role is played
%
here by knowing the rotation curve.
Using a rotation curve, we ob$
tain the corresponding surface den#!
sity with the help of a method described in the previous paragraph.
#
In the case of our Galaxy the rotation curve for radii ranging from the
"!
Galactic center to the Sun position
has been determined very well on ac"
count that the measurement of the
!
rotation curve is done from within
the galactic interior, while it is much
harder to determine the curve for
!
"
"!
#
-%'(./,
higher radii. This is well illustrated
Figure 8 – Rotation of our Galaxy. Measurement points and two in Fig.8, where shown are the meabest fit model rotation curves A) [solid line] [28] and B) [dashed surement points as well as two rotaline] [29] resulting from various model assumptions.
tion curves (both accounting for the
measurement data), which agree with each other for lower radii, where the rotation is well known, and for higher radii there are differences between them.
It is difficult to state which rotation curve is the correct one. In this work we
determined the density based on rotation curve A. I also would like to remark
that the gradient is measured in the internal regions of the Milky Way (for radii
inside the Solar circle), therefore the choice of the particular rotation curve is not
so important – the differences between them concern only the external regions.
Knowing a rotation curve, and the relation between the rotational velocity
and the surface density, we can calculate the gradient in two ways. With the
method I we first calculate the rotational velocity at a given altitude above the
mid-plane for various radial variables, and next we average these values out obtaining a mean value for a given z. With these data we determine the rotation
velocity dependence on the altitude above the disk in a given range of radii, and
with the help of a linear regression method we compute the gradient, see Fig.9.
14
Of course, this method performs best
when the rotation curve is approximately flat in the radial range of in200
terest.
In the method II one first com180
putes the gradient values for various
radii and then takes their average. Of
160
course, we can also calculate the gradient by differentiating with respect
to z the formula Eq.9 describing the
140
relation between the rotation and the
surface density; the result of this pro120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
cedure is shown in Fig.10.
z [kpc]
Apart from these methods the paFigure 9 – The azimuthal velocity on quasi-circular orbits ob- per includes the results of a numertained in disk model of the Milky Way, shown as a function of
ical simulation modelling the motion
the height above the mid-plane. The points represent the velocity mean value obtained based on Eq.9 in a region r ∈ (3, 8) kpc. of matter above the disk mid-plane.
The dashed lines show a standard deviation,
h
i the linear regres- Test particles were moving in a thin
km
sion gives a gradient of −21.3 ± 4.2 s·kpc
.
disk potential with a surface density
accounting for the observed rotation curve. Next, we checked how the dependence
of the azimuthal component on the altitude above the mid-plane looks like.
Using these methods, each time
-35
me and my colleagues were obtain-30
ing high gradient values, consistent
r=3 [kpc]
with the measurement within their
-25
accuracy. In addition, we found out
-20
that the gradient is to a good degree
of approximation constant in z and
-15
depends weakly on r.
-10
The model of the Milky Way rer=8 [kpc]
-5
garded as a thin disk without a CDM
halo accounted both for the mea0
0.1
0.4
0.7
1.0
1.3
1.6
1.9
2.2
2.5
2.8
sured values as well as other propz
[kpc]
erties of the vertical gradient in azimuthal velocity. Additionally, investi- Figure 10 – Vertical gradient of azimuthal velocity for quasigated in this work were models of circular orbits as predicted for our Galaxy in: thin-disk model
(thick solid line), a three-component model with light dark halo
the Milky Way involving three com- (dashed line) and with heavy dark halo (dotted line). Maxihalo model (thin solid line). The radial variable range:
ponents: a central bulge, a disk, and mal
r ∈ (3, 8) kpc with a step size ∆r = 0.5 kpc.
a CDM halo with a small and a large
mass compared to that of the disk. Finally, we investigated a single-component
Galaxy model in which the whole matter had a spherically symmetric distribution.
-1
-1
vertical gradient [km s kpc ]
azimuthal velocity [km/sek]
220
15
The conclusion is that the larger is the contribution of the spherical component,
the lower gradient magnitudes we obtain (see Fig.10). This is especially seen for
low altitudes above the mid-plane, since only in a thin disk model the gradient can
be high for arbitrarily small z. Therefore, the high gradient magnitudes obtained
by measurements in such a proximity to the mid-plane strongly support the disk
model of the Galaxy.
The last part of this work was devoted to the spiral galaxy NGC 891. In fact, the
results could provide a material for a separate paper, but we thought that such an
overproduction of papers was not justified and that similar research concerning
distinct galaxies ought rather to be included in a single paper. In NGC 891 galaxy,
the measurements of the gradient also give high values: -15km/s/kpc [26] and
-17.5+/-5.9 km/s/kpc, for r in a range from 4.02 kpc to 7.03 kpc and for z in
a range between 1.2 kpc to 4.8 kpc [14]. As it can be seen, the measurement
for this galaxy is made high above the disk. It is interesting that high gradient
values concern only a single (north-east) galaxy quadrant, in the other quadrant the
gradient is vanishing (I dealt with explaining this peculiarity in one of subsequent
works devoted to magnetic fields and their possible influence on galactic rotation
curves). In the case of galaxy NGC 891 the disk model also accounts well both for
the values as well as the properties of the gradient (the obtained gradient values
were -19.9+/-3 km/s/kpc and -19.7+/-1.7 km/s/kpc, respectively for the method I
and II).
—4—
Because the first results in disk model concerning the studies of the value and
the behavior of the vertical gradient in azimuthal velocity were very encouraging
for the Milky Way and NGC 891 galaxy, the subsequent paper [h04] included in
this dissertation was devoted to 4 other spiral galaxies, for which the gradient was
measured. These galaxies are: NGC 5775, NGC 4559, NGC 2403, NGC 4302.
It is worth remarking that the galaxy NGC 4302 possesses a record-high measured gradient, which is -31+/-19.8 km/s/kpc [15], whereas galaxy NGC 5775 has
a low gradient value of -8+/-4 km/s/kpc [13]. We determined the vertical gradient
in azimuthal velocity with the help of methods I and II, and by differentiating a
formula relating the rotational velocity and the surface density (9). No simulations
were carried out this time, because we had already shown on the example of the
Milky Way galaxy, that the analytical methods were efficient and led to results
agreeing with the simulation. In the case of any of these spiral galaxies, and independently of the method used, the obtained gradient values were in agreement
to within error limits with the measurements, and they also accounted for the
observed gradient properties, such as a weak dependence on the radius and its
constancy with the increasing altitude above the disk.
16
In my opinion, it is particularly worth to emphasize, that in disk model we
obtained a high gradient value for galaxy NGC 4302 – the values obtained by us
are -22.7+/-8.4 km/s/kpc and -22.3+/-4 km/s/kpc, respectively, for the methods
I and II. This is very important, on account that the alternative modelling of
the behavior and the value of the gradient, assuming the presence of a massive,
spherical halo (e.g., a ballistic model [15]) have problems with reconstructing high
gradient values. Therefore, I consider this fact as quite a success.
To compare with, I calculated also the vertical gradient of azimuthal velocity
in galaxy NGC 4302 in a model consisting of two components: a disk and a spherical halo. The value of -14.8+/-4.1 km/s/kpc (obtained with the help of method
II) is substantially lower than for a ’maximal’ thin disk model. If we translate the
region in which we calculate the gradient by 1 kpc in the direction towards the
galactic boundary, then the gradient in a disk+halo model will drop to -10.4+/-4.2
km/s/pkc (that is, by about 30%), while the gradient in the disk model will still
remain high – with this change of the radius the gradient will drop only by about
5% (to -21.1+/-6 km/s/kpc). This perfectly illustrates the fact that the variability
in the vertical gradient of azimuthal velocity with the radial variable grows with
the increasing contribution from the spherical component (I stress that the measurements show that the observed gradient is weakly dependent on the radial
variable). In addition it is seen, that the difference between the ’maximal’ thin disk
model and the disk+halo model becomes more pronounced with the increasing
galactocentric distance. This is clear, for small distances from the galactic center
the contribution from the disk in the disk+halo model is substantial. The closer
we are to the galactic boundary (the disk edge), the more important becomes the
influence of the spherical component connected with the halo. Therefore, it would
be worthy to cover as large galactic region with the measurements as possible.
Summarizing, based of this one can conclude that starting from the simplest
and most natural assumptions in disk model we are able to easily obtain any
observed properties of the vertical gradient of azimuthal velocity. In disk model we
obtain both low and high gradient values. At the same time the three-component
models of spiral galaxies have trouble with reconstructing high gradient values,
the greater the more massive is the spherically symmetric CDM halo. This fact,
known earlier of course (e.g. [15]), has been confirmed by my and that of my
colleagues’ research.
Large-scale magnetic fields in spiral galaxies and rotation of matter.
Magnetic fields can have an effect on the rotation curves of spiral galaxies. For
the first time this idea appeared in [4]. Of course, magnetic field can only influence the motion of gas which is at least partially ionized. However, among
other things, rotation curves are based on the measurements of the rotation of
17
such gaseous clouds, sometimes (e.g. in the outer galactic parts) they are the only
measurements.
—5—
*+,
1
ÊÏ
ÊÏ
((▽ × B ) × B )
(ÊÏ
v ▽)ÊÏ
v =−▽Φ+
4πρ
18
(10)
)
)
In [h05], together with my colleagues,
#
I presented the results on a pos(
sible influence of large-scale mag"
netic fields on the motion of gas
'
in the spiral galaxy NGC 891. We
used the fact that there are very
!
good measurements available for this
&
galaxy, including rotation curve, surface brightness in the 3.6 micrometer band-width [12] and the neutral
$
hydrogen distribution [26]. Using the
%
disk model we obtained (based on
!
"
#
$%
$
$!
$"
-./012
the rotation curve) the surface density distribution, and we found out Figure 11 – Local mass-to-light ratio for NGC 891 (H and He
that the mass-to-light ratio, although have been subtracted). Quadrant NE – dashed line, quadrant SW
low (within a range 1-2) in a prevail- – dotted line, mean value – solid line.
ing part of that galaxy, it increases in the outer parts, attaining a maximal value
of 8 (Fig.11). Such a behavior may indicate that there is dark matter present in
the outer parts of that galaxy, maybe nonbaryonic one. Nevertheless, we decided
to find out if there could be other factors responsible for this behavior.
The first observation in [h05] emphasized the fact that even a slight change
in the outer parts of the rotation curve (to within the measurement errors) is
capable to noticeably reduce the mass-to-light ratio in the vicinity of the galactic
edge. Next, we established by what amount the velocity of rotation would have
to be lower so that the mass-to-light ratio would seize to grow and even become
decreasing at the galactic outskirts (see, Fig.12 and Fig.13).
Next, I decided to find out what would happen if we assumed that it was the
gravity in this galaxy, which was responsible for such low rotation values, and that
it was the magnetic field which was responsible for the rotation increase in the
outer galactic parts. I wanted to find out what intensity and character such a field
would have to have, and to what extent these findings would correspond to the
observational facts [18],[11],[2].
The starting point for the calculations is the stationary Navier-Stokes equation
(that neglects viscosity and pressure):
A bulk density ρ in (10) is the hydrogen density, which can be obtained from
the measured surface density. When we are interested only in the azimuthal
component of the magnetic field, then we obtain from the Navier-Stokes equation
the following correspondence, linking the magnetic field and the rotational velocity
this field supports:
1
∂
(11)
(δvφ )2 =
Bφ (rBφ )
4πρ ∂r
'
Using (11) we find the numerical
value of the magnetic field and we
can finally ascertain that for the ve!
locity excess we assume to occur, a
magnetic field of the order of a few
%&
microgauss would suffice. It is typical
for spiral galaxies and such is mea%
sured also in galaxy NGC 891. Figure
Fig.14 shows the field dependence in
&
function of the radius. In this figure
I show two components of the mag!
"
#
$
%
%!
%"
%#
netic field – the azimuthal and the
/)*01.
vertical, but the vertical component is
Figure 12 – The measured rotation curve of NGC 891 [12] most probably vanishing in the mid(points) an a rotation curve modified so that the local mass-toplane (on account of the field symlight ratio was a non-increasing function of the radius (solid line).
metry with respect to the mid-plane
z = 0) and therefore only the azimuthal component plays a role.
(
As it was mentioned earlier,
"
the galaxy NGC 891 exhibits some
'
anomaly in the vertical gradient of azimuthal velocity: the gradient, being
!
high in the NE quadrant, is vanishing
in the SW quadrant. The large-scale
&
structure magnetic field in galaxy
NGC 891 is measured both in the disk
and above it. I decided to find out,
$
how strong the field should be to influence the rotation at altitudes in the
%
range from 1.2 kpc to 4.8 kpc, and for
!
"
#
$%
$
$!
$"
,-./01
radii in the range from 4.02 kpc to
7.03 kpc, in such a way that the gra- Figure 13 – A non-increasing local mass-to-light ratio corredient would be reduced to zero. At the sponding to a modified rotation curve shown in Fig.12.
same time I assumed that the gas density decreases in an exponential fashion in
the vertical direction off the mid-plane. I obtained field values up to 13 microgauss,
19
(
)*+
'
()*+,-.
!&
+
, '+,-+. /0
(see Fig.15). These are quite high values. However, the observations [18, 2] show
that the magnetic field in NGC 891 is nonsymmetric, and that it can be aligned in
a particular way in the +SW quadrant, reaching high intensity.
I have to mention, that a numer*'!
ical error had crept in the numeri)'%
cal integration procedure in this pa)'!
per and later it has been corrected in
('%
an erratum to this paper. However,
('!
this error was inconsequential for
&'%
the final conclusion of the paper,the
&'!
correction introduced only a slight
%'%
change in the magnetic field values
and their dependence as a function
%'!
of the radius.
$'%
!
"
#
$
%
&
1.2340
—6—
Figure 14 – Magnetic field needed to reduce the rotation of
galaxy NGC 891 so that the local mass-to-light ratio is a nonincreasing function of the radius: the vertical component of Bz
– dotted line; the azimuthal component Bφ – solid line.
)
* )+ ,-
The spiral galaxy NGC 253 was another galaxy for which, together with
my colleagues, I studied the possible influence of magnetic fields on the motion of
gas, and this became the subject of paper [h06]. Professor Reiner Beck from Max
Planck Institute für Radioastronomie suggested to study this galaxy because on
account of its exceptionally strong magnetic field, (see e.g.[16]), attaining values
from 7 to 18 microgauss,
which can be even stronger in the central part.
)
The other reason why this par&
ticular galaxy was worth to study,
were the measurements of the rota#
tion of the ionized gas clouds extend$
ing far away beyond the earlier rotation measurements [17]. The mea(
surements confirmed that the rota'
tion curve is decreasing for higher
distances from the center, which fact
&
alone makes this galaxy suspected
#
of not containing large amounts of
!"
#!$
#!"
%!$
%!"
&!$
&!"
nonbaryonic dark matter. In addi.)+/01tion, the fact that the measurements
Figure 15 – Magnetic field in NGC 891 needed to reduce the concerned the ionized gas, suggested
vertical gradient of azimuthal velocity to zero, shown for r = that a magnetic field could have ef4.0 kpc (solid line) and for r = 7.0 kpc (dotted line).
fect on its motion, the more that, as I
have already mentioned, the field in this galaxy is exceptionally strong. Using the
20
21
)
)
*+,-./0
,-.
disk model and a K-band-width brightness we obtained a mass-to-light
ratio
)
which, what should be emphasized,
"&
*%+
was low, not exceeding a value of
(&'
3.5 (see curve 1 in Fig.16). But the
(&
dependence of the mass-to-light ra!&'
tio on the radius was increasing in
the prevailing part of galaxy, which
!&
*!+
in turn could have suggested a dark
%&'
*(+
matter presence. Similarly as for
%&
galaxy NGC 891, a slight correction
&'
of the rotation was performed (curve
2 in Fig.17),which changed the mass&
!
"
#
$
%
%!
to-light ratio profile in such a way, so
/01234
that it became decreasing with the radius in the vicinity of the galaxy edge Figure 16 – The solid line (curve 1) shows the mass-to-light
ratio for NGC 253. The dotted line (curve 2) shows a change in
(curve 2 in Fig.16).
the mass-to-light ratio resulting from a small modification of the
Now, it is the right moment for in- rotation curve. The dashed line (curve 3) shows the mass-to-light
ratio corresponding to rotation curve 3 in Fig.17.
cluding a magnetic field into our con)
siderations.
!#
!"
We modified the rotation curve in
!!
such a way (curve 3 in Fig.17), that
!
the mass-to-light ratio did not exceed
%$
a value of 2 and be decreasing in
&%(
%#
%"
&'(
the prevailing galaxy part (curve 3 in
&!(
%!
Fig.16). Next I found out what proper%
ties the magnetic fields should have
$
had in order to exert such a change
#
"
in the rotation. I studied only the az!
imuthal component of the field (using
Eq.11); the vertical component of the
!
"
#
$
%
%!
%"
%#
1)+,230
field in the disk should be vanishing
(from the symmetry argument of the Figure 17 – Rotation curve of NGC 253. The points with the
magnetic field with respect to the z=0 error bars are the measurement data. The solid line (curve 1) is
a rotation curve corresponding to these data in the disk model.
plane). It turned out that the required The dotted line (curve 2) shows a small change in the rotation
field intensity should be of about 11 curve (used to show that small variations in the rotation curve
may have a significant influence on a change of the mass-to-light
microgauss, and we know, that a field ratio). The dashed line (curve 3) shows a rotation curve modified
such a way so as to make the mass-to-light ratio small, and to
with this intensity is present in this in
make the ratio a non-decreasing function for large radii.
galaxy (Fig.18).
Similarly, as in the case of the publication concerning NGC 891, a numerical
error crept into the integration procedure which resulted in an erratum to this
paper (both papers used the same numerical routine). The error was inconse-
)
* + ,-
quential for the final conclusion of the paper, and its correction introduced only a
slight change in the strength of the magnetic field values and into the dependence
on the radial variable. )
#%
In the summary of the two above
works devoted to problems of mag##
netic fields in spiral galaxies, I would
like to emphasize that they both
#$
showed that magnetic fields may
have effect on the rotation of matter
"
in spiral galaxies, and thus also on
!
their rotation curves and the massto-light ratios. For this influence to
occur, the gas must be at least partially ionized. This influence will be
(
!
"
#$
##
#%
#&
#'
the greater, the less concentrated is
.+/01the gas and the higher is the magFigure 18 – The azimuthal component of magnetic field needed netic field. Therefore, the magnetic
for such a change in the rotation curve of galaxy NGC 253, so
as to make the mass-to-light ratio small and decreasing with the field influence should be expected eiradius for large distances from the center.
ther at the galactic boundary, where
matter is less dense (then the magnetic field will have a significant effect on the
mass-to-light ratio), or high above he disk, since the matter density also decreases
with the increasing altitude above the mid-plane (then the magnetic field may
influence the behavior of the vertical gradient of azimuthal velocity).
An additional fact which the two works show clearly, is a very high sensitivity
of the mass-to-light ratio close to the galactic edge, even to tiny changes in the
rotation curves close to the galactic boundary. Of course, our works should be
regarded as presenting certain possibilities. We do not know, if the character
of the magnetic field both in galaxy NGC 891, as well as in galaxy NGC 253,
is such (the field dependence on the radius) that it could cause the effects we
postulated. However, our works show that this is possible, thus magnetic fields
have to be taken into account as those factors, which by increasing the mass-tolight ratio, may cause an overestimation in the postulated amounts of nonbaryonic
dark matter in spiral galaxies.
Finite-thickness disk model
—7—
The last paper this dissertation includes appeared in 2014 and it essentially extended the disk model [h07]. Again, in this work I dealt (together with my colleagues) with the Milky Way, but the way of its modelling changed. Previous
22
works had modelled galaxies as infinitesimally thin disks. Of course, this accelerated much all calculations, this model also worked well, but I wanted to find out
what changes taking into account the disk thickness would bring.
The density of a thick disk in our model depends both on the distance from the
galactic center and on the height above the mid-plane, and is given by the relation
ρ(r, z) = σ(r)f(z), where σ(r) is a surface density, and function f(z) describes the
vertical density fall-off with the height above the mid-plane. We considered two
vertical profiles in our work:
1
1
|z|
2 z
exp
−
,
f(z)
=
.
(12)
sech
f(z) =
2h′
h′
2h
h
The exponential fall-off is the simplest one to impose on, while the second profile,
so called Mexican hat, is grounded in the observations concerning the distribution
of stars and matter in our Galaxy in the Sun vicinity (it is also a solution of the
Jeans equation under appropriate symmetry).
As we can see, crucial for the construction of a finite-thickness disk model
is finding a surface density in this model. Our method to find this density was
applying iterations. Based on a given rotation curve in the zeroth step we find a
surface density in the infinitesimally thin disk model. This time we make use of
the rotation curve B seen in Fig.8. With the surface density and a given vertical
density fall-off profile, we can calculate the rotation velocity at any point above the
mid-plane, by making use of the following relation between the rotation and the
density:
Z∞ Z∞
vφ2 (R, Z) = 2G dr dz ρ(r, z) ·
0
0
· [J(r, R, z − Z) + J(r, R, z + Z)] ,
where
r 2 −R2 +ζ 2
r · K(κ) − (r−R)
E(κ)
2 +ζ 2
p
,
J(r, R, ζ) =
(R + r)2 + ζ 2
κ=
s
(13)
4rR
.
(R + r)2 + ζ 2
Had one to calculate the rotational velocity in the z = 0 plane in a finite-thickness
disk model based on a surface density obtained in an infinitesimally thin disk
model, then it would turn out that the rotational velocity would be underestimated
and thus diverging from the measured rotation curve. Now, one has to calculate
a correction to the surface density corresponding to a difference of squares of the
calculated velocity and that measured. We proceed with this procedure iteratively
until a rotation in the z = 0 plane is obtained that agrees with the rotation curve.
The iteration procedure enables one to find a surface density in a finite-thickness
23
disk model, which, together with the assumed vertical profile (and a given scale
parameter), will allow one to reconstruct the volume density.
Now, one can proceed to making use of the observational facts, in order to
check how does the finite-thickness disk work, what are the differences between
the predictions made based on this model and that of infinitesimally thin disk, and
finally, based on this model and the observations, if something could be said about
certain parameters of the galaxy, e.g., about the disk thickness.
First the observations concerning microlensing in the Galaxy had been used.
An earlier work, of which I am a co-author, was devoted to this topic and it concerned microlensing in an infinitesimally thin disk model [P14]. A crucial notion
we have to do with while considering microlensing, is the notion of an optical depth
- it describes a probability of finding a gravitational lens in between an observer
and an object, whose image is being subject to a distortion arising in consequence
of light passing through a neighborhood of that lens. What is very important,
only a compact object (star, planet) can be a lens, and so, the microlensing is sensitive only to baryonic matter. Nonbaryonic dark matter is not detectable through
this phenomenon. The optical depth is being determined based on microlensing
observations in the Milky Way (observed are changes in the brightness of objects
due to lenses passing between us and those objects), but it can also be calculated
theoretically if we assume that we know density of matter in the Galaxy at least
for radii ranging from the Galactic center to the Sun. Accordingly, we computed
optical depths corresponding to matter densities in the finite-thickness disk model,
both for the exponential and for the Mexican-hat vertical density profile.
The first important fact, I want to stress, is that the theoretically computed
optical depths for both density profiles (in the range of the thickness parameter
h from 117 pc to 180 pc for the Mexican-hat profile, and h′ from 88 pc to 325 pc for
the exponential profile) well correspond with the optical depth determined based
on the observations. This is an exceptionally important fact, because it shows that
whole matter that is needed to account for the Galaxy rotation (inside the Solar
circle) is seen through the gravitational microlensing, therefore, this is a baryonic
matter! Next, for both of these density profiles there were found such thicknessparameters h and h’ for which the theoretically computed optical depth fitted best
the optical depth determined based on the microlensing observations. It turned
out that the thickness-scale parameter for the Mexican-hat profile is h = 117 pc,
and for the exponential profile it is h′ = 88 pc.
It is now the right time for making use of the measurements of the vertical
gradient in azimuthal velocity. As I already pointed out earlier in this dissertation,
the gradient magnitude measured in the Galaxy is, firstly, high (22 ± 6 km/s/kpc)
and, secondly, it is measured very low above the mid-plane (out to 100 pc off the
mid-plane) for radii ranging from 3 kpc to 8 kpc [21]. As it turns out, both the
gradient properties and the part of the Galaxy which has been covered by the
24
,
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1*23,4-5,6'&,-./'&7
measurements, is very important. As I stressed this in the section devoted to magnetic fields, such a field may have an effect on the rotation of matter in galaxies.
,
Since the gradient in the Milky Way
is measured so close the mid-plane,
')
that is, where the density of matter is high, we can be sure that the
'&
*+%,-./
influence of the magnetic field can
'&)
*+0,-./
be neglected there completely. As it
*+$,-./
has also turned out, the fact that the
'"
*+),-./
gradient magnitude attains high val*+#,-./
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ues, despite that it is measured at
so low altitudes, allows one to draw
*+(,-./
'(
conclusions about the thickness-scale
!
!"
!#
!$
!%
&!
&!"
&!#
&!$
&!%
parameter of our Galaxy. The ver8,4-./7
tical gradient in azimuthal velocity
was computed based on the formula Figure 19 – Vertical gradient of azimuthal velocity for the Milky
Way calculated in finite-thickness disk model, as a function of
(13). It turned out, that for altitudes altitude above the disk plane, shown for various radii: solid line
exceeding a value of about 0.4 kpc, – gradient for the model with a Mexican-hat vertical density profile (h = 117pc), dashed line – gradient for the model with exthere is no difference in the gradi- ponential density vertical fall-off (h′ = 88pc). For comparizon,
gradient in the infinitesimally thin disk model (with the same
ent behavior, neither between finite- amass
as that of the finite-thickness disk with Mexican-hat profile)
thickness disk model differing from is shown – dotted line.
each other in density profiles and the thickness-scales, nor is there a difference
between these models and an infinitesimally thin disk model, what
is illustrated in
,
Fig.19.
The calculations were carried
)%
out for various radii r, for various
)$
thickness-scale parameters, both for
the exponential as well as for the
)$%
Mexican-hat density profile. This is
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an important conclusion, because it
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shows that the infinitesimally thin
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ple, and therefore it can be safely ap!
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!#
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plied in a number of cases. However,
9,45./8
with the decreasing altitude above
20 – Vertical gradient of azimuthal velocity for Galaxy
the mid-plane, substantial differences Figure
as a function of the altitude above the plane z = 0 calculated
appear between the finite-thickness in a finite-thickness disk model with a vertical density fall-off of
the Mexican-hat type, shown for a radius of r = 4 kpc and for
disk model and that of infinitesimally various parameters h. For comparison, the dotted line shows the
behavior of the gradient in the infinitesimally thin disk model.
thin disk.
While the gradient magnitude can reach high values arbitrarily close to the
mid-plane in the case of the thin disk model, the gradient approaches 0 in a finitethickness disk model at the altitude close to zero. With the increasing altitude
above the z = 0 plane, the gradient magnitude quickly increases until it gets
saturated, and then only weakly depends on the altitude, similarly as for the thin
disk. And then, the lower value is assigned to the thickness-scale h or h’, the closer
to the mid-plane the gradient magnitude attains high values, see Fig.20.
Based on the microlensing two values for the thickness-scale parameter were
singled out: h = 117 pc for the Mexican-hat profile and h′ = 88 pc for the exponential profile. It was very important question, whether the gradient magnitude
would attain high values with these parameters, in agreement with the measurements of the values for altitudes above the mid-plane not exceeding 100 pc. It
turned out, it was so. This is another very important fact, because it shows that
a finite-thickness disk model, but without the massive spherical halo, successfully
passes two tests based on the observations. Both these tests resulting in the same
value for the thickness-scale parameter, crucial in describing the disk properties.
It should also be noted that there were no important differences between models
with the exponential density profile and with the Mexican-hat density profile.
An important part of the [h07] work is a discussion of the factors which could
have had an impact on the results we obtained. Namely, it can be stated that the
assumed value of the rotational velocity of the Sun may have a significant impact
on the determination of the disk thickness-scale. The rotational velocity of the
Sun (as well as its position) is a parameter indispensable to determine the Galactic
rotation curve, the shape of which and values are dependent on that parameter.
In this work, a value of 200 km/s for the rotational velocity of the Sun was taken.
However, this value could be greater (e.g., [8] gives a value of 239 km/s). Increasing
the rotation value will increase the disk mass calculated based on it, and hence
also will increase the vertical gradient magnitude. This in turn will result in the
increase of the thickness-scale parameter of the disk.
Another thing tackled with in this work, was a comparison of the surface
density obtained in the finite-thickness disk model in the Sun vicinity (140 M⊙ /pc2 ),
with a value obtained as a result of measurements (about 70 M⊙ /pc2 ). As it is seen,
a discrepancy appears here that calls for an explanation. The first possibility arises
from a fact already mentioned above that, as far as it can be said that the shape
of the Galactic rotation curve has been well established in the region within the
Solar circle, much worse is the case for larger radii, where the uncertainty as to
what the rotation curve looks like is significant. This situation is caused by the
specificity of the rotation measurement.
We thus performed a little experiment: we have shown that the rotation curve
of the Milky Way exterior to the Solar circle can be modified in such a way as to
keep the circular velocity of the Sun to be equal 200 km/s, and to make the rotation
curve well fitted to the measurement data, and at the same time, that the surface
26
density at the Sun vicinity would be reduced down to 70 M⊙ /pc2 . Additionally, this
modification do not substantially influence the behavior of the vertical gradient
in azimuthal velocity (because the modification concerned the regions beyond the
Solar circle, while the gradient is being measured and computed inside that circle).
There is also another way of explaining the discrepancy between the modelled
and observed matter density in the Sun vicinity: we have to remember, that the
rotation curve and the matter density derived from it as a function of the radial
variable is a kind of an average, in a global circularly-symmetric sense. As to
the surface measurement of interest here, it is a local measurement, concerning
a region of 1 kpc in size. Therefore, it is not strange that lower densities were
obtained than those resulting from the use of a global model. It is obvious, that
even for the same radius in Galaxy there have to be regions with higher and
lower density, whereas a global disk model yields an averaged out density value
at a given radius.
The paper [h07] was thus another work devoted to our Galaxy, which introduced a substantial modification to the disk model – taking into account a finite
thickness of the disk. This work showed, that a finite-thickness disk model well
describes our Galaxy (at least its internal part), which was demonstrated by two
tests – the one making use of the microlensing, the other making use of the vertical gradient in azimuthal velocity. This work gave also a constraint on the disk
thickness-scale. The obtained value is small, pointing towards a thin disk (with
the rotation curve we dealt with the thickness-scale parameter should not exceed
150 pc). We also discussed possible factors that might have affected the thicknessscale magnitude. This work was also discussing the local matter density in the
Sun vicinity.
I can say, that thanks to the works on this paper which is closing this dissertation, both myself an my colleagues have understood many essential problems
connected with the disk model in general (which nobody had been paying due
attention to) and with our Galaxy in particular.
Summary
The research results presented in the papers discussed above justify the doubts, as
to whether all spiral galaxies (our Galaxy, in particular) possessed a massive dark
halo consisting of CDM. Apart from the papers being the basis of this dissertation,
I have to mention here other research papers devoted to spiral galaxies and the
disk model, which are the result of work of the research team of which I am the
member. These papers provide an additional confirmation, that the disk model
use in describing spiral galaxies is legitimate.
Paper [P12] from 2008 is a more theoretical study concerned with disk-like
matter distributions. Although these distributions were of course considered many
27
times in the past (e.g.,[7]), the view-point presented in this paper gets rid of several
of the troubles of this approach, as for example the already mentioned „boundary”
problem resulting in under- or overestimating the mass. Additionally, in [P12] we
studied galaxy M101 which presented itself a model example of a galaxy which
needs no dark matter - modelling this galaxy as a thin disk resulted in a density
distribution smoothly passes into the distribution of gas, while the (B and K bandwidth) mass-to-light ratios turned out low and decreasing with the radius.
In the already mentioned paper [P14], a microlensing method was used to study
the amount and distribution of matter in a region within the Solar circle. We compared the optical depth obtained as a result of an observation, with that obtained
in a theoretical way from the surface density obtained under the assumption, that
our Galaxy has a disk-like geometry (and can be modelled as an infinitesimally
thin disk), and we obtained an agreement between them. Putting this differently,
we demonstrated that the whole matter needed to account for the Milky Way rotation within the Solar circle is seen through the gravitational microlensing, thus
it is certainly a baryonic matter.
As one of the most important papers concerning the problem of dark matter
in galaxies I consider the paper[P15], in which we deal with the motion of the
baryonic halo objects around the Milky Way. Objects which contribute to such a
halo are, among other things, dwarf galaxies, globular clusters and isolated stars.
It was standard approach to analyze the motion of these objects in a dark matter
potential, which was used many times for estimating the Galaxy mass. (e.g., [4]).
But we applied a method different from that commonly used: its novelty was
in releasing the constraints imposed on the phase space, and in considering a
gravitational potential of a compact mass, thus corresponding to a Galaxy without
dominating dark matter. Constraints arise by conditions imposed on in advance,
by the assumed profiles of the secondary quantities, derived from the phase-space
distribution function, such as the flattening of the velocity dispersion ellipsoid. It
is standard to assume it in the form of an anisotropy parameter independent of
the distance, which makes the models of motions of halo objects more stiff. In the
case of a central mass potential, which should well approximate a compact mass
potential for large distances, this means adopting a model of the phase space
equivalent to a system of confocal elliptic orbits, with an arbitrary number density
defined over the space of energies and ellipticity. Following this, we are able to
model the dispersion anisotropy as almost arbitrary function of the distance. In
the result of this, the expected value for the ellipticity of orbits crossing a sphere
of a given radius, can depend in a complicated way on the distance. Despite the
formidability of this problem, we succeeded in developing a general procedure
reconstructing the distribution function in the phase space, consistent with the
observed profile of the radial velocity dispersion. Finally, we showed that the
observed motion of the halo objects is fully consistent with the assumption that
28
our Galaxy mass is low (of the order of 2.4 × 1011 M⊙ ), that is, such as one should
expect based on the rotation curve of the Galactic disk, if the Galaxy mass is not
dominated by nonbaryonic dark matter. Then only a few of the observed halo
objects would not be gravitationally linked to the Galaxy. The radial dispersion
profile of the motion of the baryonic halo objects alone does not give the upper
bound on the Galaxy mass. However, this approach allows us to estimate the far
more important lower bound for the Galaxy mass, consistent with the observed
motion of halo objects.
The problem of the motion of halo objects is also the subject of one of our
recent works. We carry out there numerical simulations of halo objects in the
gravitational potential of the Milky Way, modelled as a system consisting of a thin
disk immersed in a spherically-symmetric shell of hot gas, that was detected encircling our Galaxy ([23]). The gas mass can be 6 × 1010 M⊙ out to 200 kpc. Our
simulations were performed in a potential corresponding to a minimal mass of
1.8 × 1011 M⊙ , and then re-scaled so that the simulated radial velocity dispersion
profile fitted to the observed profile as good as possible, which finally gives a mass
of 2.4 × 1011 M⊙ . To determine the initial conditions for the simulation we used
our phase space model from the paper [P15]. The simulations showed two very
important facts: the phase space model with a central mass found in [P15] is stable (the simulated dispersion slightly oscillates, still remaining high, consistently
with the dispersion profile), and that the point mass approximation of the Galactic
potential applied in [P15] is sufficient to study the motions of the baryonic halo
objects. The model is thus structurally stable (that means, by modifying the potential a little bit one obtains similar results). The work [P17] confirmed that the
observed motion of halo objects is consistent with the assumption that our Galaxy
is a disk-like object of a small mass.
There is also a recent paper [R24] that is being considered for publication
and a second one [P16] that has been just accepted for publication in MNRAS.
The first is a mathematically-oriented paper devoted to disk transforms. The
results have an important practical meaning - they allow to simplify and shorten
the numerical computations. The other work is devoted to the vertical gradient
of azimuthal velocity in the galaxy NGC 4244. This is another in the sequence
of our papers confirming the effectiveness of the disk model in modelling of the
magnitude and behavior of the gradient. The results obtained in thin disk model
agree with those obtained based on the measurements of rotation in this galaxy.
Me and my co-workers are not the only ones who express doubts about the
current paradigm of CDM presence in spiral galaxies. Here we can mention the
work [24], that proposes to explain the problems with the rotation curves of spiral
galaxies not with the help of assumptions made about the nonbaryonic dark halo,
but by modifying the theory of gravity. It is also worth to mention Kroupa works
(in particular [9]), who shows, among other things, how to solve the problem of the
29
dynamical mass excess over the luminous mass in dwarf elliptical galaxies, or the
paper [1] announcing the lack of nonbaryonic dark matter signals in the Galactic
center. Recently, a paper appeared [6], the authors of which give arguments for
the absence of CDM in the region within the Solar circle.
The arguments for CDM presence in spiral galaxies (and in the Universe in
general) are very strong, of course, and the most important comes from the cosmological model. However, we should remember that the cosmological model
is the effect of mutual agreement of model assumptions and observational facts,
which are not independent, but the latter have to be interpreted based on a model
which they are to confirm. It is possible that there is another cosmological model,
which would also lead to such an agreement. That we have not found it yet may be
the result of the fact that the model is much more complicated from that currently
used, as it would require getting rid of the Universe’s homogeneity or isotropy assumptions, and hence to introduce essential problems of computational nature.
It is also worth to mention that the problem of the nature of the gravitation on
larger scales is still open. The equations of the gravitational field and their Newtonian limit are based on the Hilbert-Einstein Lagrangian with a cosmological term,
but it is not the only possibility presently considered.
Other important arguments come from the observations of galaxy clusters –
most importantly, from the fact that the clusters’ mass estimates based on the
observations of motions of galaxies that are members of the clusters, is higher
than the mass estimated based on the brightness. But w have to remember that
the first way of estimating the mass is possible only when a cluster is virialized,
and the latter condition might not be satisfied.
Another weighty argument is the issue of the stability of spiral galaxies – the
massive CDM halo role is to stabilize a galaxy [27]. Here, I can recall the example
of NGC 4736 galaxy, to which I devoted much attention above. As I was writing,
its rotation curve, its observed brightness and the predictions about the mass-tolight ratio based on the color difference, do not allow to introduce a spherically
symmetric halo of a large mass. Such a halo can be introduced, but its mass must
be lower than that assigned to the disk component (see [10]), and then the halo
would not suffice to stabilize the galaxy. Therefore, if we have a spiral galaxy,
as to which there is presently a consensus that it is CDM poor (the controversy
concerns only whether the word „poor” should be replaced with „free”), and at the
same time it is stable (it does not even exhibit any instability, which the presence
of bar would be a signature of), then this points to stabilizing mechanisms being
in action other than a halo.
Thus, as it seems, although the arguments for the ubiquitous presence of nonbaryonic dark matter are strong enough, they are not incontestable. Of course,
in physics as in any scientific discipline, decisive is an empirical argument – and
here we have to stress that in our opinion the most important fact for seriously
30
considering arguments „against dark matter” is, that in spite of the intense experimental efforts to search for dark matter, it has not been directly detected,
and the recent LUX experiment reports [22] strongly narrowed down the region
worth searching through, and it did not confirm earlier findings. In the Standard
Model of Particles – recently so spectacularly confirmed by the discovery of the
Higgs Boson – there is a lack of natural candidates with suitable properties, while
neutrinos turned out to be insufficient. Only an extended model, predicting new
families of particles, would give us any hope for the carriers of nonbaryonic dark
matter.
My research (and those of my co-workers) concern absolutely fundamental
issues for the understanding of how our Universe had come to existence and how
is it built. If it turned out that the real amount of nonbaryonic dark matter diverged
strongly from the amount required by the cosmological model, this would mean
a serious blow to that model. I do not hesitate to say that this would mean a
true revolution in science, as it would undermine our present knowledge on the
Universe as a whole.
Of course, even proving that spiral galaxies are in general poor in nonbaryonic
dark matter would not automatically mean that there is no such matter present
in large amounts in space. Since the beginning of our research we have been
bringing to attention the fact that a higher clusterization scale of dark matter is
another possibility – the scale might be of the size of galaxy clusters, not of the size
of single galaxies. But such a scenario would have deep consequences, too. Now,
CDM is needed for the separate galaxies to come to existence, and showing that
spiral galaxies do not comprise large amounts of CDM (all or only some of them),
would force us to revise such a scenario of galaxy formation. Besides, showing
that the Milky Way does not comprise large amounts of dark matter (at least in
the central part within the Solar circle), explains the so far null results of the direct
dark matter searchers, and puts into question the rationality of continuing with
these experiments further.
Of course, it may equally well be, that our model of disk-like galaxies does not
correspond with the reality. Dark matter may be discovered by a direct detection
of a dark matter particle (the LUX experiment still gives a chance, the data will
have been collected until autumn of 2014).
However, what I have to stress, the papers which are the part of this dissertation
have their meaning as such, independent of the nonbaryonic dark matter problem:
they have extended our knowledge on disk-like objects, they have shown how the
microlensing measurements, or those of the vertical gradient in azimuthal velocity,
can be used in studying galaxies. Similarly, the works concerning the influence of
magnetic fields on the rotation of matter in galaxies have a universal meaning, not
necessarily connected with the dark matter problem. In searching for the truth
behind the reality surrounding us, it is always important to explore and follow not
31
only the paths of the main stream of research, sometimes it is worth to give this
path up.
In conclusion I would like to emphasize, that 8 years ago, at the end of my
PhD studies, when I started my investigations of the CDM matter presence in
spiral galaxies, this was a new branch of research not only for me but also for
my supervisor, and for all of whom I was working with. In addition, me an my
colleagues’ results were in opposition to the main stream of research and the
reigning paradigm. Our research group is small. Despite that, we managed to
publish a series of works in the leading astrophysical journals, which always was
a result of a several-month-long, or in the case of our work on the halo even
more than a year-long, extended discussions with many referees. I think that this
proves the scientific maturity and large creative potential of the research team I
am the member of and one of its pillars.
Future research plans. The research subject concerning the presence of nonbaryonic dark matter in spiral galaxies is very important, therefore my research
plans for the nearest future are connected with these problems. Together with my
colleagues I intend to tackle the problem of stability of spiral galaxies, modelled
as disks without the spherically-symmetric halo. We have developed several ideas
of how this problems could be solved, in principle we have already started our
research. I think I will devote myself to studying this topic in the nearest future.
Further reading
[1] Abramowski et al. 2013, Physical Review Letters, 110, 041301
[2] Allen R. J., Sukumar S., 1991, in H. Bloemen ed. Vol. 144 pp 287–294
[3] Battaglia G. et al., 2005, MNRAS, 364, 433
[4] Battaner E., Garrido J. L., Membrado M., Florido E., 1992, Nature, 360,652
[5] Battersby S.
February 2008
NewScientist
http://www.newscientist.com/article/dn13280,
[6] Bidin Moni, Carraro C., Mendez G., Smith, R.A. 2012, ApJ, 751, 30
[7] Binney J., Tremaine S., 1987, Galactic Dynamics. Princeton Univ. Press, Princeton
[8] Bovy J., Hogg D. W., Rix H.-W., 2009, ApJ, 704, 1704
[9] Casas R. A., Arias V., Pena Ramirez K., Kroupa P. 2012, MNRAS, 424, 1941
32
[10] de Blok et al, 2008, AJ, 136, 2648
[11] Dumke M., Krause M., Wielebinski R., Klein U., 1995, A&A, 302, 691
[12] Fraternali F., Sancisi R., Kamphuis P., 2011, A&A, 531, A64
[13] Heald et al . 2006, ApJ, 636 181
[14] Heald et al . 2006, ApJ, 647, 1018
[15] Heald et al . 2007, ApJ, 663, 933
[16] Heesen V., Krause M., Beck R., Dettmar R.-J., 2005, in Chyzy K. T.,
Otmianowska-Mazur K., SoidaM., Dettmar R.-J., eds. pp 156–161
[17] Hlavacek-Larrondo J., Carignan C., Daigle O., de Denus- BaillargeonM.M.,MarcelinM., Epinat B.,Hernandez O., 2011, MNRAS, 411, 71
[18] Hummel E., Dahlem M., van der Hulst J. M., Sukumar S., 1991, A&A, 246, 10
[19] Jaroszyński Michał Galaktyki i budowa Wszechświata
[20] Kent, S. M. 1987, AJ, 93, 816
[21] Levine E. S., Heiles C. , Blitz L. 2008, ApJ, 679, 1288
[22] LUX Collaboration 2013, ArXiv e-prints 1310.8214
[23] Miller, M. J. Bregman, J. N. 2013, ApJ, 770, 118
[24] Moffat, J. W. Brownstein, J. R., 2006, ApJ, 636, 721
[25] Munoz-Tunon, C., Prieto, M., Beckman, J., and Cepa, J., 1989, APSS 156, 3001
[26] Oosterloo T., Fraternali F., Sancisi R., 2007, AJ, 134, 1019
[27] Ostriker J.P., Peebles P.J.E. 1973 ApJ186: 467-480
[28] Sofue Y., Honma M., Omodaka T., 2009, PASJ, 61, 227
[29] Sofue Y., Tutui Y., Honma M., Tomita A., Takamiya T., Koda J., Takeda Y., 1999,
ApJ, 523, 136
[30] T.Takamiya, and Y.Sofue 2000, ApJ, 534, 670
IV The other scientific achievements:
IV.A Discussion
33
For the 8 years since defending my PhD degree I have been concentrating on
studying galaxies. But also other papers appeared, of which I am a co-author
and which did not concerned with this topic directly.
• The paper [P09] was written in reply to the F.Cooperstock & S. Tieu work
”General Relativity Resolves Galactic Rotation Without Exotic Dark Matter”,
introducing a relativistic model of spiral galaxies which allegedly had solved
the problem of their rotation without invoking the nonbaryonic dark matter.
This model turned out to have been defective as a model of galaxies. However, thanks to it we had investigated stationary, axi-symmetric and asymptotically flat dust-matter space-times. The matter rotates rigidly with the rotation
being differential at the same time. Such a situation would be impossible in
the Newtonian gravitation, where rigid rotation cannot be differential, thus
the considered motion of matter is entirely a relativistic effect, despite that the
matter travels with the velocities lower than the speed of light. This rotation
is possible, owing to the effect of dragging of inertial reference frames in a
space-time filled with matter endowed with an angular momentum. Although
the angular velocity with respect to distant reference systems connected with
„fixed stars” is vanishing (rigid rotation), the vorticity vector is nonzero. In
this kind of motion, matter appears to be rigidly and motionless hovering in
space, while the motion on circular orbits is still present, owing to the inertial
frames dragging effect. In our work we showed that such space-times (apart
from not having the Newtonian limit) are characterized by pathologies and
singularities. There are present singularities of a measure zero and negative mass, balancing the regular positive mass distribution, so that the nett
mass of asymptotically flat space-times is zero. We called these space-times
the ”van Stockum-Bonnor space-times”, as we have found general classes of
solutions which include, as particular examples, the earlier known solutions
found by van Stockum and Bonnor.
In the result of this research it became clear to us that the differential motion
which we have alluded to above, cannot be identified with the rotation curve
of a galaxy. It is strange, anyhow, that such an identification leads to quite
reasonable masses of galaxies. A comprehensive description of this issue
can be found in the work [I21] which I co-authored. Methods employed in
this model resemble an approach used in the disk model, and these are the
low-mass results for galaxies, that prompted me to study rotation curves in
a newtonian global disk model.
• The work [P10] is concerned with a similar topic. It discusses a different
kind of a space-time, in which a motion of dust-matter is considered to be
connected with locally non-rotating (locally inertial) observers. In contrast to
van Stockuma-Bonnor space-times, this motion is non-rigid, while the vor34
ticity vector is vanishing. Here, we have to deal with a differential rotation
of matter with respect to distant fixed stars. Braking the energy conditions
in regions with regular mass distribution may be considered as a deficiency
of this type of models. Positive mass singularities are located on a measurezero regions. Similarly as for van Stockum-Bonnor space-times, the total
mass of asymptotically flat solutions is equal to zero, and the mass of the
regions with regular mass distribution is balanced by the opposite-sign mass
localized in the singularities of the curvature.
• Meanwhile, during the 8 year period since my PhD degree, I came back
also to the compact stars issue, more precisely, quark stars. In result of this,
a paper [I22] appeared in which we consider a hypothesis that Wolszczan’s
planets may be miniature quark stars. This paper has not been yet accepted
for publication.
IV.B Index of other published scientific papers
Scientific papers in Journal Citation Reports (JRC) not being a part of a
scientific achievement in the light of Sec. III
[P08] M.KUTSCHERA, J.JAŁOCHA
Rotation curves of spiral galaxies: influence of magnetic fields and energy
flows
Acta Phys.Pol.B 35 2004
My contribution involved putting forward the idea that magnetic field can influence
rotation of matter in spiral galaxies, and to perform computations concerning this
problem. This prompted my interests in magnetic fields in galaxies. I have to stress
that this was my orgiginal idea to use magnetic fields in explaining roation of spiral
galaxies, only later I found out that earlier this idea had been put forward by Battaner,
who had published his paper in Nature. This is the same author who later quotes our
works devoted to this problem, which proves the importance of these papers.
[P09] Ł. BRATEK, J. JAŁOCHA, AND M. KUTSCHERA
Van Stockum-Bonnor spacetimes of rigidly rotating dust
Phys Rev D, 75(10):107502, May 2007
My contribution to this work involved taking part in analytical computations, as well
as in a reflection over an appropriate interpretation of the obtained results. I was
also taking part in writing down the results and conclusions.
35
[P10] Ł. BRATEK, J. JAŁOCHA, AND M. KUTSCHERA
A Class of Spacetimes of Non-Rigidly Rotating Dust
Acta Physica Polonica B, 38:2513, August 2007
My contribution to this work involved taking part in analytical computations as well
as in a reflection over an appropriate interpretation of the obtained results.
[P11] J. JAŁOCHA, Ł. BRATEK, M. KUTSCHERA, AND M. KOLONKO
Clustering Scale of Dark Matter.
Acta Physica Polonica B, 38:3859, December 2007.
My contribution to this work consisted of an analysis of the measurements data
available in the literature. My contribution was dominating in the computational part
of this work (calculation of surface densities in disk model and of mass-to-light ratios),
and in writing down the results and conclusions.
[P12] Ł. BRATEK, J. JAŁOCHA, AND M. KUTSCHERA.
On the axisymmetric thin disc model of flattened galaxies.
Month. Not. Royal Astron. Soc., 391:1373–1383, December 2008.
My contribution to preparing this paper involved taking part in the analytical and
numerical computations concerning the disk model and the example galaxy M101
(in this case I carried out most of the computational work), and I took part also in
writting down the results and conclusions.
[P13] J. JAŁOCHA, Ł. BRATEK, AND M. KUTSCHERA.
Disk Model with Central Bulge for Galaxy M94.
Acta Physica Polonica B, 41:1383, June 2010.
I carried out most of the computational work (finding the volume density of the
Galactic central bulge and the surface density of the whole Galaxy), I had the dominating contribution to writting down the results and conclusions.
[P14] S. SIKORA,Ł. BRATEK, J. JAŁOCHA, M. KUTSCHERA
Gravitational microlensing as a test of a finite-thickness disk model of the
Galaxy
2012, A&A, 546, A126
In preparing this paper I carried out computations, leading to the surface density
36
of the Galaxy (in various models), with the disk alone, and with a disk and a central
bulge. I computed also the local mass-to-light ratio in the Sun vicinity, and compared
it with the measurements. I took part in writing down the results and conclusions,
and in a discussion with the referees.
[P15] Ł. BRATEK, S. SIKORA, J. JAŁOCHA, M. KUTSCHERA
A lower bound on the Milky Way mass from general distribution function
models,
2014 A&A 62A.134B
My contribution to this paper consisted of taking part in the analysis of the available
measurements data, and processing them in such a way, that they were suitable for
further calculations. I calculated Milky Way mass in the disk model, and I also contributed to writing down the results and conclusions, and I took part in a discussion
with the referees.
IF 4.479
[P16] JOANNA JAŁOCHA, ŁUKASZ BRATEK, SZYMON SIKORA, MAREK KUTSCHERA
Modeling vertical structure in circular velocity of spiral galaxy NGC 4244
2015 MNRAS !"#$%&'() "# *+&, -./01/0021/-3450
!%%+()+6 78& (#*9'%!)'8" '" -.5:; <=01 -!> 0?
(&+(&'"), @))(,AA!&B'C48&DA!*$A01=E4=1F=G
H@+ IJ "# *+& K$)C002GK '$ (!&) 87 )@+ 7#99 JLI
I put forward the idea of this paper, I carried out most of the calculations and had a
dominating contribution in writing down the results.
IF 5.226
[P17] SZYMON SIKORA, ŁUKASZ BRATEK, JOANNA JAŁOCHA, MAREK KUTSCHERA
Motion of halo compact objects in the gravitational potential of a low-mass
model of the Galaxy
2014arXiv1410.1051S !"#$%&'() "# *+&, "& &+74 ::A<=01A<20?F
!%%+()+6 78& (#*9'%!)'8" '" :M: <=01 -!> <2
In this paper I was one of the co-authors of the idea of the simulation, I computed
the Galactic surface density distribution, which is the source of the potential in which
the motion of halo objects takes place. I took part in the discussion with the referees
and in writing down the results.
Estimation of my individual contribution 20%. IF 4.479
37
Conference proceedings
[K18] P.SKINDZIER, J.JAŁOCHA-BRATEK, Ł.BRATEK, AND M.KUTSCHERA.
Do Spiral Galaxies Need So Much Dark Matter?
in V. Y. Choliy and G. Ivashchenko, editors, Young Scientists 15th Proceedings, pages 25–28, December 2008.
My contribution to this paper involved taking part in the analysis of the measurements data available in the literature, independently finding the surface density based
on the available rotation curves, and in computation of the resulting mass-to-light ratio.
[K19] Ł.BRATEK, J.JAŁOCHA, M.KUTSCHERA, AND P.SKINDZIER.
Spiral galaxies without CDM halo?
in „Very High Energy Phenomena in the Universe” XLIV Rencontres de
Moriond, La Thuile, Italy, February 2009.
My contribution to this paper involved taking part in the analysis of the measurements data available in the literature, finding the surface density based on the available
rotation curves, and in computation of the resulting mass-to-light ratio. I also took
part in writing down the results and conclusions.
[K20] Ł.BRATEK, J.JAŁOCHA, AND M.KUTSCHERA.
Mass distribution in flattened galaxies,
in „The Role of Disk-Halo Interaction in Galaxy Evolution: Outflow vs
Infall?”, ed. M. A. de Avillez, European Astron. Society Publications Series, 2009
My contribution to this paper involved taking part in the analysis of the measurements data available in the literature, finding the surface density based on the available rotation curves, and in coputation of the resulting mass-to-light ratio. I was also
taking part in writing down the results and conclusions.
Other papers
[I21] Ł.BRATEK, J.JAŁOCHA, AND M.KUTSCHERA.
Relativistic model of spiral galaxies.
Prace Komisji Astrofizyki PAU, 11:79, 2007.
I took part in the analytical and numerical computations, which revealed the failures
in the relativistic model of spiral galaxies. I carried out also a comparison of the
relativistic and the non-relativistic model. I also took part in writing down the results
and conclusions.
38
[I22] M.KUTSCHERA, J.JAŁOCHA, S.KUBIS, AND Ł.BRATEK.
SQM stars around pulsar PSR B1257+12.
ArXiv e-prints astro-ph 1010.2056, October 2010.
My contribution to this work consisted of computing masses, radii and densities of
the quark stars which might be candidates for the Wolszczan’s planets. I was also
taking part in writing down the results and conclusions.
Estimation of my individual contribution 30 %.
[I23] J.JAŁOCHA,
Searching for life in the Universe,
Foton 111 Zima 2010
This is a popular science treatise on the possibility of life in the Universe beyond
Earth, and on searching for life.
Papers submitted for consideration
[R24] ŁUKASZ BRATEK, SZYMON SIKORA, JOANNA JAŁOCHA, MAREK KUTSCHERA
Velocity-density twin transforms in thin disk model
2014arXiv1411.0197B
My contribution involved discussing the idea and the results as well as taking part in
the calculations.
My individual contribution estimation 20%.
V Indicators of scientific achievements:
• Overall impact factor according to Journal Citation Reports (JCR)
– in the publication year: 68.467
– at present: 69.634
• Number of citations according to Web of Science (WoS)
– total: 65
– without self-citations: 29
• Hirsch index according to Web of Science (WoS)
H=5
VI Scientific conference talks
1. IX 2007 Kielce XXXIII Assembly of The Polish Astronomical Society, Speech
title: Matter distribution in spiral galaxies.
39
2. October 2007 Conference: Prospects of the Astro-particle Physics, Kraków,
Speech title: Dark matter: clusterization scale.
3. VIII 2008 conference poster ( with Ł.Bratek) Ascertaining the mass distribution in spiral galaxies, The Role of Disk-Halo Interaction in Galaxy Evolution:
Outflow vs. Infall?, Espinho Portugal, Aug 18-22, 2008
VII Didactic teaching/works and popularization of science
⋆ As part of my job responsibilities as a PhD student, I taught the following
courses:
- computational exercises in introductory mechanics
- exercises: physics students’ Labs 1
⋆I was an associate supervisor of two Master Theses and one PhD thesis
• MSc Thesis: Investigation of the influence of molecular hydrogen
mass on the shape of rotation curves of spiral galaxies,
Alicja Grochowalska, Jagellonian University 2008
• Msc Thesis: Investigation of rotation curves of spiral galaxies,
Piotr Skindzier, Jagellonian University 2007
• PhD Thesis: Investigation of the dynamics of spiral galaxies,
Piotr Skindzier, Jagellonian University 2014
⋆ In 2013 I was supervising a student in its Practical Training Programme
⋆ I regard the popularization of science as a privilege and duty of a scientist,
therefore I strongly engage myself into this type of activity. Many times I
gave lectures to the groups visiting The Institute of Nuclear Physics (initially,
together with Marcin Kolonko, and then alone) concerning astrophysical
issues (most often, the lectures concerned the evolution of stars). I was also
actively taking part in The Open Days of The Institute of Nuclear Physics
In Cracow and several times in The Days of Science held in Cracow and
Warsaw.
selected lectures within the popularization activity
• IV 2008 a lecture given in Osieczna (as part of the Physician Conference)
„Scales of distances in the universe”
• IX 2008 a lecture given in Żywiec (together with Marcin Kolonko) „Scales
of distances in the universe"
40
• IV 2013 a lecture given for a Discussion Society in a village next to
Cieszyn ”Evolution of Stars”.
⋆ Seminars
1. January 2000
Evolution of massive stars
Astrophysical Seminar PAU, IFJ, UJ
2. January 2001
Do strange stars exist in the Universe?
3. Deceber 2001
Mili-second phenomena in Roentgen low-mass binary systems .
4. December 2002
How to weigh strange stars – kHz QPO
5. April 2003
Non-relativistic accretion
Seminar of the Department of the Theory of Relativity and Astrophysics
6. March 2004
Magnetohydrodynamics
7. December 2004
Accretion onto a black hole – a model of Arpa S quasar
8. May 2005
Viscosity of the Universe
9. November 2005
Generally-relativistic model of spiral galaxies
10. March 2006
Models of spiral galaxies without dark matter
11. October 2006
What do rotation curves of spiral galaxies tell us about?
41
12. October 2006
Mass distribution in spiral galaxies
Seminar of the Institute of Nuclear Physics PAN
13. December 2006
Rotation curves of spiral galaxies and the dark matter problem
Friday Seminar of the Astronomical Observatory UJ
14. November 2007
What replace dark matter with in spiral galaxies?
15. April 2008
Condensation scale of Dark Matter
The Mikołaj Kopernik Astronomical Center PAN
16. October 2008
Life in the Universe
17. November 2008
Quark stars
18. March 2009
Rencontres de Moriond luty 2009, La Thuile: Very High Energy Phenomena in the Universe
19. October 2009
Tests for absence of a massive, spherically symmetric CDM halo in
spiral galaxies
20. December 2009
Argentina - a good place to tackle with science?
21. May 2010
What for is dark matter needed in spiral galaxies?
22. October 2010
A mysterious influence of the Sun on the radiative decay in earthbased laboratories
23. December 2010
Dark matter in galaxies
J.Kochanowski University in Kielce
42
24. December 2010
Do all spiral galaxies need nonbaryonic dark matter?
Friday Seminar of The Astronomical Observatory UJ
25. March 2011
Weight-lossing the Milky Way
26. December 2011
The role of a large-scale magnetic field in galaxy NGC 891
27. April 2012
The methods of determining the mass of our Galaxy
Seminar of The Institute of Nuclear Research PAN
28. April 2012
Determining the mass of the Milky Way
29. October 2012
The role of a large-scale magnetic field in spiral galaxies. Galaxy NGC
253.
30. November 2012
Large-scale fields in spiral galaxies and their rotation curves
Friday Seminar of The Astronomical Observatory UJ
31. May 2013
What does astrophysics need nonbaryonic dark matter for and is it
indispensable indeed?
Seminar of the Field Theory Department IF UJ
32. November 2014
On magnetic fields that can disguise themselves as dark matter in
spiral galaxies
IF UJ
33. November 2014
Influence of magnetic fields on the rotation of matter in spiral galaxies.
IFJ PAN Seminar
VIII Awards
• In 2011 I was awarded The Henryk Niewodniczański Prize for A series of
five papers devoted to the conceiving and the analysis of the properties
43

S O P A

Transcription

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