Sterrenstelsels en Cosmologie Docent: M. Franx, kamer 425

Transcription

22-1-2016see http://www.strw.leidenuniv.nl/˜ franx/college/
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Sterrenstelsels en Cosmologie
Dates of the courses
Docent: M. Franx, kamer 425
on Tuesdays, 11:15-13:00, with exceptions (today,
and mid-may)
room 414
College assistenten: Margot Brouwer, kamer 541,
Marijke Segers, kamer 436, Leindert Boogaard 101
Three books are relevant for this course. None are
obligatory:
Binney and Tremaine: ‘Galactic Dynamics’
(B&T) (2nd edition)
Introduction into theory of galaxy dynamics,
i.e. potential theory, orbits, distribution functions,
equilibria, disks, mergers, etc.
Extragalactic Astronomy and Cosmology
Peter Schneider, edition 2
Introduction to Cosmology
Barbara Ryden. Zeer aantrekkelijk boek, ook gebruikt
in de Masters.
These books are not obligatory. Their level is very
high (advanced Master course), but this means they
remain useful throughout your career.
1 other book is also sometimes used: Binney and
Merrifield: Galactic Astronomy (indicated with “BM”)
QUESTION HOURS:
generally 13:45, Thursday BEFORE next course (except May) room 204
Het cijfer voor het college wordt voor 66% bepaald
door het tentamen, en voor 33% door de ingeleverde
huiswerk opgaven. Een minimum cijfer van een 6.0
voor de huiswerk opgaves is nodig om deel te kunnen
nemen aan het tentamen en hertentamen.
De huiswerk opgaven moeten voor het begin van
het volgende college worden gemaild naar:
[email protected] (scannen kan bij de
kopieerapparaten op de 4de en 5de verdiepingen Oort
gebouw). Te laat inleveren betekent het cijfer 0.
De vragen uurtjes geven specifiek de mogelijkheid om
hulp te krijgen bij het maken van het huiswerk. De
ervaring leert dat diegenen die gebruik maken van
het vragenuurtje het huiswerk in de regel met een
voldoende afsluiten.
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Brief content of the course
1) Introduction
What is a galaxy ?
Classifications
Photometry, exponentials, r1/4 profiles, luminosity function
2) Keeping a galaxy together: Gravity
Potentials
3) Galactic Dynamics
Equilibrium
collisions, Virial Theorem
4) Galactic Dynamics continued
Timescales
Orbits
5) Collisionless Boltzmann Equation
equilibrium, phase mixing
derivation of distribution function
6) Velocity Moments
Jeans equations
comparison to observations
7) Mass distribution and dark matter
Evidence for dark matter from rotation curves
Solar neighborhood, Oort limit
Elliptical galaxies and hot gas
Clusters of galaxies, the universe
Candidate dark matter particles
8) Galaxy formation
Universe expansion
Growth of galaxies by gravity
Galaxy scaling relations
9) Galaxy formation - forming the stars
Gas cooling and star formation
formation of disks
dynamical friction and mergers
tidal tails in mergers
10) Observing galaxy formation
High redshift galaxies from HST
Fair samples of galaxies at high redshift
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1. General Introduction
[See the multiwavelength color show
http://www.strw.leidenuniv.nl/˜ franx/
college/sterrenstelsels16/galaxies.pdf ]
•Optical
ii) Why do we study galaxies ?
iii) Optical Photometry
iv) Surveys and Selection Effects
Radio:
•Continuum emission follows spiral arms
caused by synchrotron emission, electrons accelerated by shocks/SN
•Compact emission regions - supernova remnants
same mechanism
•Active nuclei produce jets, radio lobes...
same mechanism
•Line emission: HI 21 cm, CO,
molecular lines
v) Luminosity Function
Study material from B&M:
4.1,
4.2,
4.3,
4.4,
4.6,
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i) What is a galaxy ?
Galaxies emit in many wavelengths
Content Handout 1:
i) What is a galaxy?
Observe in different ways:
•Radio
•X-Ray
•Dark Matter (halo)
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(4.1.2), 4.1.3 to page 165, (4.1.4)
(4.2.2), not 4.2.3
to page 187
(not 4.4.2), 4.4.3 to page 217
to page 244 (4.6.2)
subsection in brackets means for reading only
Infrared:
•Continuum emission by dust
•Star forming regions, active nuclei
Near Infrared:
•Red super giants, some extinction
Optical-UV:
•Visible stars, dust absorbtion
•Emission lines
•Blue active nuclei
X-Ray:
•(Double) stars, neutron stars,
star forming regions
•Very hot gas
•active nuclei
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Active Nuclei
•produce emission at all wavelengths
Conclusion
a Galaxy consists of several components:
-bulge
•at all lengthscales:
from very close to the nucleus (≤ pc)
to the largest scale (> 10 kpc)
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red, old (?)
r1/4 law
stars:
-disk
blue or red
spiral arms, rings, bars
exponential profile
-disk
H I gas
H2 gas
dust
-extended
Hot Gas
center
black hole
gas:
active nucleus:
Dark Halo:
large, dominant unknown particles
Why study galaxies ?
What are the main questions ?
What is the structure of galaxies ?
What is their equilibrium ?
What are they made off ?
What is their mass distribution ?
How do they evolve in time ?
How have they formed ?
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Homework Questions:
1) Why is the name “sterrenstelsel” “bad” ? In what
component is most of the mass ?
2) What telescope would you use to measure the
emission of Andromeda at a frequency of (i) 1.415
109 hz, (ii) 5.9 1014 hz, (iii) 1017 hz. First calculate
the wavelengths of this emission.
3) Give an estimate from literature of the total mass
of the Milky Way, and the total stellar mass. Give
the relevant source (i.e., mention where you got these
estimates from)
4) Starforming galaxies like the Milky Way emit XRays. What objects within the Milky Way dominate
this emission ? What part of these objects actually
produce the major part ? Is the emission mechanism
thermal or synchrotron radiation ?
5) a) How is the continuum radio emission in star
forming galaxies produced ? What is the emission
mechanism ?
b) What produces the emission at 100µm in star
forming galaxies ?
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Optical images of galaxies and classification
See the pdf file on the web for nice pictures
http://www.strw.leidenuniv.nl/˜franx/
college/sterrenstelsels16/galaxies.pdf
All classification systems are idealizations.
Independent of true size of the galaxy and Luminosity!
Often used systems:
1. Hubble-Sandage
or
2. de Vaucouleurs
Numerical types T (based on de Vaucouleurs) were
often used
Disadvantages of ALL classifications
•Only based on optical image −>
independent of true size!
•Galaxies vary in more than one dimension
•Many galaxies are peculiar,
i.e. inclassifiable
We first highlight the classifications from the RSA
(Revised Shapley Ames Catalogue, Sandage)
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“Normal” Spirals are classified from Sa to Sd. Along
this sequence the following properties change:
1) degree of central concentration (or Bulge-to-disk
ratio). (decreasing from Sa to Sd)
2) angle of the spiral arm (increasing from Sa to Sd)
3) degree of resolution of spiral arms into individual
clumps (from smooth to clumpy from Sa to Sd).
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Bars occur at all types. Their strength can be used
as another dimension in the classification.
These galaxies have rings
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De Vaucouleurs introduced a classification scheme
which was slightly different, classifying into “ring”
and “s-shaped”, and bars. He also introduced a numerical type t running from -5 to 10.
These are peculiar galaxies (Arp et al, 1987). These
galaxies are generally mergers (collisions between
galaxies).
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van den Bergh introduced yet another scheme:
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Currently, these classifications have become less important. We now have distances to most galaxies,
and multi-wavelength information. We characterize galaxies by their stellar mass, age, star formation
rate, metallicity, and halo mass (or environment).
Homework Questions:
6) Why are galaxy classifications problematic ?
7) Describe in your own words 3 criteria which are
used to classify spirals into Sa, Sb to Sd. How do
these change from Sa to Sd ?
8) What is the type of the Milky Way ? Motivate
your answer
9) Why don’t we classify the Magellanic Clouds as
ellipticals ? They don’t have spiral arms.
10) What is the type of the galaxy on the cover of
BM ? Give the reasons for your classification
11) How do you recognize mergers ?
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Quantitative photometry of galaxies
In the past: photographic plates:
•Limited dynamic range
Now: CCDs (= very sensitive digital photo camera’s)
•Sizes ≥ 2048x2048 pixels
•Quantum efficiency ≥ 90 %
•Very good dynamic range
Photometry −> Imaging galaxies and measuring their
brightness distribution
•Big technical problem: galaxies are really large, and
have low surface brightness wings. See the beautiful
image of M31
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As can be seen, the galaxy does not really stop !
As the objects are extended, we like to describe the
distribution of light on the sky, and not just the total
magnitude (which would be appropriate for a star).
Hence we measure the amount of light per area on
the sky. This is called the surface brightness. It is
often expressed as magnitude per square arcsec.
How to measure average surface brightness profile ?
Measure the intensity on ellipses of (nearly) constant
surface brightness
In practice, our images “stop” when there might
still be very faint galaxy light. This would not be a
problem, but we also have the much brighter light
from the night sky. We have to estimate this, and we
make systematic errors in the profiles if we estimate it
too low or too high
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Resulting profiles:
•Ellipticals:
King profile
de Vaucouleurs law (r1/4 )
•Spirals:
Disks: exponential profile
Bulges: r1/4
For elliptical galaxies we often find the r1/4 law:
I(R) = Ie exp(−7.67[(R/Re )1/4 − 1])
where Re is the half light radius: half the light is
emitted inside Re . Because of uncertainties in the
background subtraction, we never know the exact half
light radius. The parameter Ie is the surface brightness at R = Re .
No galaxy follows the r1/4 law exactly !
On the next page, some examples of surface brightness profiles are shown.
The profiles can change systematically from bright
galaxies to faint elliptical galaxies.
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An exponential disk has
I(R) = I0 exp(−R/Rd )
where Rd is the disk scalelength.
You can see that the outer parts of the galaxies shown
above show a straight profile - hence have an exponential profile. The inside shows an upturn, and
that is modeled as a separate component. This is the
bulge.
Many galaxies are modelled well by fitting an r1/4 law
to the bulge and an exponential model to the disk.
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Surveys and Catalogs of galaxies
Selection effects in optical catalogs
most catalogs are based on optical surveys
Consider a galaxy with a certain luminosity
Currently used:
Sloan Digital Sky Survey:
Data Release 7 covers 11.000 sq degrees
> 300 million objects (galaxies, stars, ...)
spectra over 9380 sq degrees: 1.6 million spectra
of galaxies, quasars, stars!
Many optical surveys over smaller areas to higher
redshifts (GAMA, BOSS, )
Near-IR: 2MASS (imaging, all sky)
Mid-IR: Wise (all sky)
X-Ray: ROSAT All-Sky Survey
OLDER
Revised Shapley-Ames Catalog
Sandage and Tammann
Third Reference Catalogue of Bright Galaxies
de Vaucouleurs et al
e.g.:
Very important were Palomar Sky Survey Plates,
these have been used for systematische surveys
UGC: northern galaxies
ESO catalog: southern galaxies
Lauberts, Lauberts en Valentijn
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If the galaxy is too small: misclassified as star
if the galaxy is too big: surface brightess is too low
− > not detected !
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Luminosity Function
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Φ(L) = (Φ∗0 /L∗ ) (L/L∗ )α exp(−L/L∗ )
Typical values:
Φ∗ = (1.6 ± 0.3) × 10−2 h3 M pc−3
MB∗ = −19.7 ± 0.1 + 5 log h
α = −1.07 ± 0.07
L∗B = (1.2 ± 0.1) × h−2 1010 LSun
where H0 = h100km/s
The number of galaxies with a luminosity larger than
L is given by
R∞
N (> L) = L Φ(L′ )dL′ = N0 Γ(1 + α, L/L∗ )
Here we used the following definition for the incomplete gamma
R ∞function
Γ(α, x) = x t(α−1) e−t dt
Total amount of light produced
SDSS Luminosity function from Blanton 2005
R∞
ltot = 0 Φ(L′ )L′ dL′ = Φ∗ L∗ Γ(2 + α)
= Φ∗ L∗ for α = −1
Determine for each galaxy the intrinsic luminosity
from apparent luminosity and distance.
Hence, huge numbers of low luminosity galaxies expected, but finite luminosity.
Correct for bandpass, internal absorbtion and absorbtion by the Milky Way.
Most of the luminosity comes from galaxies with L =
L∗ . A simple approximation is that the universe is
filled with L∗ galaxies with a density Φ∗
The luminosity function is defined by
Φ dM = number density of galaxies in magnitude
range (M ,M + dM )
The distribution of luminosities is given by a Schechter
function
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Homework questions
12) Given a galaxy with an exponential profile I(R) =
I0 exp(−R/Rd )
a) what is the total emount of light emitted ? (Express in terms of I0 and Rd .) (Hint: integrate the
light emitted as a function of radius, where radius
runs from 0 to infinity)
b) what is the half light radius ? (i.e., the radius in
which half the light is emitted) (Hint: use the integral from 10a, now to Re instead of infinity)
13) How can we attempt to classify galaxies automatically (i.e., by computer) ?
14) What is the luminosity function?
15) Given a Schechter Luminosity function, what is
the luminosity at which half of the total luminosity
density is emitted by galaxies brighter than that luminosity ? Assume α = −1.
16) What is the luminosity of a typical galaxy in
terms of solar luminosities? Motivate your answer,
and give a full reference if you take a value from a
source.
17) The Schechter function implies that the total
number of galaxies per volume element is infinite
if the Schechter luminosity function extends to luminosity 0. Derive that this is the case for a simple
Schechter luminosity function with α = −1.
How can it be that the total amount of light is finite,
despite the fact that the number of galaxies is infinite
? (per volume element ?)
18) Find the website of a catalogue with more than
100.000 galaxies (and NOT the Sloan Digital Sky
Survey or GAMA ). Give the full reference.

Sterrenstelsels en Cosmologie Docent: M. Franx, kamer 425

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