The Lowest-Luminosity Dwarf Galaxies

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A type of matter hypothesized in astronomy and cosmology to account for effects
that appear to be the result of mass where no such mass can be seen. Dark matter
cannot be seen directly with telescopes; evidently it neither emits nor absorbs light
or other electromagnetic radiation at any significant level. It is otherwise
hypothesized to simply be matter that is not reactant to light. Instead, the existence
and properties of dark matter are inferred from its gravitational effects on visible
matter, radiation, and the large-scale structure of the universe. Found due to things
like abnormally high velocity dispersions of dwarf galaxies, unexplained rotational
speeds of galaxies found by Vera Rubin in the 1960’s, gravitational lensing and the
pattern of anisotropies in the cosmic microwave background
According to the Planck mission team, and based on the standard model of
cosmology, the total mass–energy of the known universe contains 4.9% ordinary
matter, 26.8% dark matter and 68.3% dark energy. Thus, dark matter is estimated to
constitute 84.5% of the total matter in the universe, while dark energy plus dark
matter constitute 95.1% of the total content of the universe.
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The missing satellites problem, arises from the fact that the Lambda Cold Dark Matter
cosmological model predicts that dark matter should to cluster hierarchically and in ever
increasing number counts for smaller and smaller sized halos. However, while there seems to
be enough observed normal-sized galaxies to account for this distribution, the number
of dwarf galaxies is a full order of magnitude lower than expected from simulation. For
comparison, there were observed to be around 38 dwarf galaxies in the Local Group, yet one
dark matter simulation predicted around 500 Milky Way dwarf satellites.
This problem has a few potential solutions. One is that the smaller halos do exist but only a
few of them are visible to us at the moment because they are faint enough to evade our
current instruments, but as our surveys become more complete, the problem might become
less severe. Another solution may be that dwarf galaxies tend to be gobbled up
or tidally stripped apart by larger galaxies due to complex interactions. This tidal stripping has
been part of the problem in identifying dwarf galaxies in the first place, which is an extremely
difficult task since these objects have low surface brightness and are highly diffused, so much
that they are virtually unnoticeable even in our own backyard. Another solution is the
hypothesis that reionization could suppress the formation of dwarf galaxies by preventing
low-mass dark matter halos from acquiring enough gas to form stars after z ~ 10
There are also Cosmological solutions include modifying the power spectrum at small scales
and changing the properties of the dark matter particles, such as by making them warm or
invoking a late decay from a non-relativistic particle, but I won’t be talking about those
proposed solutions today.
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Data from the then-new SDSS (Sloan Digital Sky Survey) led to the discovery of 10
new Milky Way satellites in quick succession.
Location of different classes of objects in the plane of absolute magnitude vs. halflight radius. Lines of constant surface brightness are marked. Filled circles are the
SDSS discoveries including the 10 Milky Way satellites, as well as And IX and X. Open
circles are eight previously known Milky Way dSphs with Sgr omitted, squares are the
M31 dSphs, bold squares are three new M31 dSphs recently discovered by, and
triangles are the Galactic globular clusters. The SDSS discoveries are larger and
somewhat less luminous than typical Milky Way globular clusters, and as a group,
they are much fainter than the previously known Milky Way and M31 dSphs
A variety of other extragalactic objects are also plotted: asterisks are the extended
M31 globular clusters discovered by Huxor et al. (2005), plus signs and crosses are
UCDs in Fornax, respectively, diamonds are the so-called Virgo dwarf-globular
transition objects, and filled stars and inverted triangles are globular clusters from the
nearby giant elliptical NGC 5128, respectively. Different measurements of the same
object are connected by straight lines. The straight line connecting the Earth symbols
refer to measurements by Mieske et al. (2002) and Drinkwater et al. (2003) of UCD3
in Fornax.
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Also apparent in the figure is the fact that the data points fall into a number of clumps. The
Milky Way globular clusters form one obvious grouping. Separating the globular clusters from
the dwarf galaxies is a sparsely populated vertical band corresponding to half-light radii
between 40 and 100 pc. However, this gap is suggestive and not conclusive, as the survey
was nowhere near complete when this paper was published (only 20% covered)
At the moment, all objects to the left of the gap show no evidence of dynamically significant
dark matter. All the objects to the right with measured kinematics are consistent with
substantial amounts of dark matter. So far, only two of the galaxies have kinematic data. the
velocities of seven UMa I stars were measured and obtained a velocity dispersion of 9 km/s
and a mass-to-light ratio of ~500. They measured the radial velocities of seven Boo stars and
obtained a velocity dispersion of 7 km/s and a mass-to-light ratio of between 130 and 680.
Based on these results, UMa I and Boo would be the two most dark matter dominated
objects known in the universe.
The implication is that the SDSS discoveries may well be members of the missing population
of low stellar mass, dark matter dominated galaxies originally predicted by CDM. Only when a
complete census of these objects has been obtained will we be able to assess whether the
properties of the population are consistent with the predictions of the simulations. A number
of unusual objects, such as the extended M31 clusters and the UCDs in Fornax and Virgo, all
lie in regions abutting the globular clusters in the plane of absolute magnitude and half-light
radius. For example, UCDs are brighter than Galactic globular clusters, but they could be the
bright tail of the globular cluster systems in the Fornax and Virgo Clusters.
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This paper did similar studies on 7 other ultra-faint dwarfs.
a) Color-magnitude diagram of observed stars in Hercules. The large black circles
represent stars identified as radial velocity members of the galaxy, the small black
dots represent stars identified as non-members, and the blue crosses are
spectroscopically confirmed background galaxies and quasars. The red curve shows
the location of the RGB, subgiant branch, and main-sequence turnoff populations and
the blue curve shows the location of the horizontal branch, corrected for Galactic
extinction
b) Spatial distribution of observed stars in Hercules. Symbols are the same as in (a)
(the figure legend applies to both panels), and the ellipse represents the half-light
radius of Hercules
c) Velocity histogram of observed stars in Hercules. Velocities are corrected to the
heliocentric rest frame. The filled red histogram represents stars classified as
members, and the hatched black-and-white histogram represents nonmembers. The
velocity bins are 2 km/s wide.
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Looking at velocity dispersions, Mass, Mass-to-Luminosity ratios, metallicities.
The authors of this paper do note that the likely presence of unresolved binary stars in our
stellar velocity sample may increase the measured velocity dispersion of our target galaxies
due to binary orbital motion, but that the correction due to binary motions is negligible when
compared to their uncertainties.
The process of determining the total mass of a dwarf spheroidal galaxy from the velocities of
a relatively modest sample of stars that are probably located well inside the virial radius of
the galaxy’s dark matter halo is fraught with difficulty. The standard technique in the
literature is to assume that (1) the galaxy is spherical; (2) the galaxy is in dynamical
equilibrium; (3) the galaxy has an isotropic velocity dispersion; and (4) the light distribution of
the galaxy traces its mass distribution. All four of these assumptions may be false in reality,
especially for the ultra-faint dwarfs that are the subject of this paper (most of the studied
galaxies are elongated and irregular). These dwarf galaxies have incredibly high Mass-to-Light
ratios, but also have incredibly high uncertainties.
The function to estimate the total masses of the galaxies, where Beta is a parameter that
depends on the concentration of the system and is generally assumed to be 8 for dSphs
(Mateo 1998), rc is the King (1962) profile core radius, and sigma is the observed central
velocity dispersion.
These are incredibly high Mass to Light ratios (normal numbers are from 1 to 30), implying
that more of the mass must be made up of dark matter than in most galaxies. Hence: dark
matter dominated
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(a) Velocity dispersion as a function of absolute magnitude for the ultra-faint dwarfs.
The filled black symbols represent the gravitationally bound dwarfs and the open
gray symbol represents UMa II, which is thought to be tidally disrupted (talk about
that more later). Circles are ultra-faint dwarfs in this sample and the triangle is the
Bootes dSph
There is a significant correlation of velocity dispersion with absolute magnitude, with
the more luminous galaxies (MV < -6) having larger dispersions of ~7-8 km/s and the
fainter galaxies (MV > -6) exhibiting smaller dispersions of ~4-5 km/s. The four lowluminosity galaxies Coma Berenices, Canes Venatici II, Hercules, and Leo IV are the
first galaxies to break the velocity dispersion ‘‘barrier’’ at 7 km/s that observations of
the previously known dSphs had suggested. The unprecedentedly low velocity
dispersions of these galaxies and the correlation with absolute magnitude down to
such low luminosities demonstrate that if there is a floor on the masses of dSphs, it
does not appear to have been reached yet
(b) Dynamical mass as a function of total V-band luminosity. The ultra-faint dwarf
galaxies clearly display a trend in which the more luminous galaxies have larger
velocity dispersions and correspondingly larger masses. Perhaps surprisingly, there
appears to be a simple power-law relationship between mass and luminosity.
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This is the Metallicity-luminosity relationship for dwarf galaxies in the Local Group.
The new ultra-faint galaxies (red circles) follow the trend of decreasing metallicity
with luminosity set by more luminous dwarf galaxies (black squares). The two lowestluminosity objects (UMa II and Coma) show possible evidence of tidal stripping. In
comparison, Galactic globular clusters (blue triangles) do not follow any luminositymetallicity relationship. The smaller horizontal bars on our galaxy measurements
represent the uncertainty in the mean metallicity; internal metallicity spreads are
indicated by the larger vertical bars. The ultra-low luminosity dwarfs are among the
most metal-poor stellar systems in the known universe
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Coma Berenices has the lowest luminosity of the new Milky Way satellites (-3.7).
Coma is unique among the ultra-faint dwarfs in that its member stars span a wide
range of g - i colors near the main-sequence. The photometric uncertainties are not
large enough to account for this spread. The stars on the blue side of the MSTO could
be blue stragglers, but the presence of a few similarly situated stars on the red side
suggests that we might instead be seeing the effects of multiple stellar populations
with different ages (and hence MSTO luminosities and colors) in Coma.
It also has a location near the Milky Way (44 kpc instead of 32 kpc), and an
unexpectedly high stellar metallicity. As with UMa II, we find a modest correlation of
velocity with position in the galaxy. Dividing the galaxy in half along the minor axis,
found a difference of 5.5 km/s in the mean velocity from east to west. This velocity
difference is significant at the 4 sigma level. It is not expected that galaxies of this size
are rotationally supported, so if this velocity gradient is real it suggests that Coma
Berenices, may be distorted by tidal forces. On the other hand, there are no known
tidal streams that are plausibly associated with Coma, its velocity dispersion is
approximately what would be expected given its luminosity, and its stellar
distribution is not noticeably more irregular than those of the other ultra-faint
dwarfs. With a smaller half-light radius (and larger central density) than any other
Local Group dwarf, Coma may be more robust to disruption than some of its
counterparts. While the available evidence is suggestive of the possibility that Coma
Berenices could be tidally disrupting, these and subsequent authors therefore treated
Coma as a bound, dark matter dominated object.
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Ursa Major II is one of the hardest galaxies to identify based on its signature in the velocity
histogram (c), but a clear peak at -117 km/s emerges once the foreground dwarf stars are
screened out. They identify 20 member stars in UMa II out of 236 targeted sources, which
represents our lowest detection rate for any of the galaxies. There is a star that the authors
suspect is an cepheid variable, and future observations of this star could provide improved
constraints on the distance of UMa II. UMa II is a clear outlier from the magnitude – velocity
dispersion trend defined by the other galaxies, with a dispersion of 6.7 km/s despite its
incredibly low luminosity.
Ursa Major II is located very close to the Milky Way, second only to Sagittarius (which is the
archetype of tidally disrupting dwarfs) among the known dSphs. UMa II appears irregular and
that its stars are broken up into several subclumps. The Orphan Stream lies along a great
circle intersecting the position of UMa II, so it’s possible that UMa II is associated with the
Orphan Stream. The found strong evidence for a difference in the mean velocity between the
eastern and western halves of the galaxy, with the stars on the eastern side having a velocity
8.4 +- 1.4 km/s larger than those on the western side. It is highly unlikely that a galaxy as
small as UMa II would show significant coherent rotation, so this velocity gradient strongly
suggests that UMa II is distorted by tidal forces. As noted previously, UMa II is also a clear
outlier from the magnitude – velocity dispersion trend shown earlier. This galaxy therefore
either has a mass-to-light ratio several times larger than any other, or its velocity dispersion
has been inflated by the tidal field of the Milky Way. Finally, UMa II has a metallicity >0.5
higher than would be expected from the luminosity-metallicity relationship shown in the
previous figure. Its metallicity is more appropriate for a system with magnitude = -10 (250
times more luminous than UMa II ). Taken together, all of these independent results make a
strong case for the imminent tidal disruption of UMa II, and we are not aware of any
observational evidence suggesting that UMa II is bound.
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So far, we’ve seen that with the likely exception of UMa II, the ultra-faint dwarfs seem
to be dark matter dominated systems, with masses lower than those of the
previously known dSphs and very large mass-to-light ratios. These galaxies are
currently the darkest known stellar systems in the universe. Going back to the Missing
Satellites Problem, the addition of the new dwarfs, combined with the correction for
the sky area that has yet to be observed with sufficient sensitivity, substantially
changes the appearance of the substructure problem.
The solid line with diamonds represents the subhalo abundance within the virial
radius of the Via Lactea N-body (234 million particles) simulation (Diemand et al.
2007a). The open gray squares show the observed distribution without the new ultrafaint dwarfs. These previously known Milky Way satellite galaxies have a nearly flat
circular velocity function below v = 15 km/s, causing a discrepancy with the
predictions that worsens with decreasing mass and reaches well over an order of
magnitude below v = 10 km/s. The filled black squares include the new circular
velocity estimates from this paper, as well as all of the previously known Milky Way
dwarfs. So, with the ultra-faint dwarfs included we now see a rising circular velocity
function and a satellite underabundance of a factor of 4 for halos with masses
between v = 10 and 20 km/s. At v = 6 km/s the discrepancy increases again toward
an order of magnitude, but if the current observational census is still incomplete at
the faint end, this is the mass range where that would manifest itself. The ultra-faint
dwarfs significantly fill in the gap for satellites in the two lowest mass bins, but have
masses that are too small to affect the satellite deficit at higher circular velocities.
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Since just adding the new ultra-faint dwarf galaxies isn’t enough to solve the missing satellites
problem, there are a few other possible solutions.
The observed dwarf galaxies could inhabit the most massive subhalos at the present day or
the subhalos that were the most massive at the time they were accreted by the Milky Way,
and not in anything smaller. We show the results of these tests in these figures. To compare
the observed dwarfs to the most massive subhalos, we identified the 51 halos (to match the
number of Milky Way satellites projected to be found once the remainder of the sky has
been surveyed) located within the virial radius that have the largest total masses at the
present day in the VL simulation. The circular velocity function of these subhalos is plotted as
the solid cyan curve. Another possibility is to compare the observed circular velocity function
with the circular velocity function of the subhalos that were most massive when they were
accreted (dashed purple curve).We selected the largest before accretion subhalos from the
VL simulation as the halos located within the virial radius of the main halo at z = 0 that had
the largest circular velocities at any point in the past. If the observed dwarf galaxies inhabit
only the most massive dark matter subhalos around the Milky Way, the shape of the mass
function of the most massive subhalos fails to match the shape of the observed mass
function. Using the subhalos that were most massive at the time they were accreted instead
of the ones most massive today (i.e., allowing for mass lost by tidal stripping) brings the
subhalo mass function slightly closer to the observed one, but there are still a factor of 3 too
few dwarfs in the v = 10-30 km/s range. Note that because they chose the total number of
subhalos to match the total number of Milky Way dwarfs, the agreement between the
observed distribution and both the curves in the lowest mass bin is trivial.
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The final astrophysical solution we consider is that only halos that collapsed prior to
reionization were able to form significant numbers of stars. Among the VL subhalos
that are located within the virial radius at z = 0, we select the objects with the 51
largest values of circular velocity at various high redshifts. The solid red, dashed cyan,
and dotted blue curves represent the subhalos that would be selected if z(reion) =
13.6, 11.9, and 9.6, respectively. If reionization occurred around redshift 9-14, and
dwarf galaxy formation was strongly suppressed thereafter, the circular velocity
function of Milky Way satellite galaxies approximately matches that of CDM subhalos.
If reionization occurred at z < 8, we again find an underabundance of Milky Way
dwarfs with v = 15-30 km/s compared to theoretical models. Therefore suggest that
the observed mass function of Milky Way satellite galaxies constrains reionization to
have taken place before z = 8, in agreement with the 3 yr WMAP results from
measurements of the cosmic microwave background (z(reion) = 10.9 +-2.7 Page et al.
2007).
While this model gives a good fit for the pattern of observed dwarf galaxies, we
cannot forget that this fit it pinned at the first point, so the fit at that point could be
wildly offbase.
So, while the discovery of the ultra-faint dwarfs has lessened the Missing Satellite
problem and new theories are coming closer to explaining the discrepancy, no
complete solution yet exists.
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Refers to the shape of the dark matter profile of galactic halos as the radius goes to
zero
Theory states there should be a cusp at the galactic centre
Observations show no such cusp. Kinematic studies of low surface brightness galaxies
have shown that the mass profiles of these objects are less centrally dense than
expected. They are more compatible with flatter, cored halo functions, rather than
the cuspier profiles seen in simulations
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A paper by Collins et al in 2014 uses the Hernquist profile
From the Hernquist profile
Where γ > 0 gives a generally “cuspy” profile
While γ = 0 gives a “cored” profile
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NFW: If you set Gamma =1 in the previous equation, you get the NFW profile, where
Vmax is the maximum circular velocity of the halo, RS is the scale radius of the halo
and η = 2.16
Cored: with η = 4.42, α = 1, and γ = 0
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Half-light radius vs. velocity dispersion for MW (red triangles) and M31 dSphs (blue circles).
Overlaid are best fitting NFW and core mass profiles to these data. Open symbols represent
MW dSphs that are too faint to be observed in M31, and hence are excluded from the fits.
The authors of this paper were testing a previous claim by Walker et al. (2009) that the dwarf
galaxies in the Local Group followed a universal mass profile. However, better observational
data has changed this assumption. It is very clear that neither the NFW or cored radius
profiles are good fits to the data, This is statistically demonstrated by the fact that ∼50% of
all observations are inconsistent with these fits, with 24 of the 39 points being characterized
as outliers by the reduced Chi-Squared Test. The authors came to the conclusion that dSphs
are embedded in halos do NOT follow a universal density profile. They also found that when
comparing fits for solely MW dSphs to solely M31 dSphs, the latter prefer significantly lower
masses for a given size than the former. One could therefore argue that the outliers seen in
this study, such as Hercules, And XIX, XXI, and XXV, may have fallen in to their host galaxies
earlier, and onto more radial orbits where they interact tidally more significantly with their
host, leading to a more pronounced mass loss
Many have argued that the observed core profile is a result of bursty, energetic star
formation and supernova (SN) within these faint galaxies. These processes drive mass out
from the center of the halo, flattening the high density cusp into a lower density core, leading
to a lower central mass than predicted by pure dark matter simulations. Could the lower than
expected central masses of the Local Group dSphs also be caused by feedback? To match the
current observed central masses in MW dSph galaxies, one would need to deposit 100% of
the energy resulting from 40,000 SN directly to the dark matter halos, which is greater than
the expected total number of SN to have ever occurred in the majority of these systems. So
feedback from Supernovae is probably not the answer and the Cusp-Core debate remains
unsolved.
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Related to the cusp-core problem is the “too big to fail” (TBTF) problem, which was
originally identified by Read et al. (2006). From measurements of their central
velocity dispersion, σv, one can get a good grasp of the central masses, i.e., the mass
within the two-dimensional (2D) half-light radius, rhalf, of these systems and compare
these with those of simulated subhalos. Using the Aquarius set of simulations
(Springel et al. 2008), and they found that each MW-like Aquarius halo they studied
had of the order of 10 subhalos with central masses that were significantly higher
than those of the MW dSphs. This means either that the most massive subhalos
within MW systems do not necessarily form stars or that we are missing some crucial
physics from these models (either baryonic, or with respect to the properties of dark
matter itself) that can explain this discrepancy.
This problem with this problem is that the discrepancy most likely arises due to the
fact that those simulations were dark-matter only, not taking into account baryonic
matter. When later models were developed that took baryons into account, it was
found that the best-fit profiles to the MW, M31, and total Local Group dSph they have
derived are not hugely at odds with predictions from simulations (especially when
observational error is taken into account.), so this problem is likely solved.
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Missing satellite problem on its way to being resolved
Core-cusp problem still unsolved
TBTF problem was likely a failing in simulations
Better instrumentation has led finding ultra-faint dwarf galaxies, and improving
instrumentation and better analysis of current surveys is sure to reveal more ultrafaint dwarfs
These ultra faint dSph are dark matter dominated
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