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Transcript
23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/
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Sterrenstelsels en Cosmologie
Dates of the courses
Docent: M. Franx, kamer 425
on Monday, 11:15-13:00
Jan 26 - June 1, room 414, (exceptions April 8 and
June 1)
College assistenten: Margot Brouwer, kamer 541,
Marijke Segers, kamer 436
Two books are relevant for this course. None are obligatory:
Binney and Tremaine: ‘Galactic Dynamics’ (B&T)
(2nd edition) (69 euro bol.com)
Introduction into theory of galaxy dynamics,
i.e. potential theory, orbits, distribution functions, equilibria, disks, mergers, etc.
QUESTION HOURS:
generally 13:45, Thursday BEFORE next course (except May 13).
room 207 (except May 6, 14 room 106)
Extragalactic Astronomy and Cosmology
Peter Schneider, edition 2
76 euro bij bol
These books are not obligatory. Their level is very high
(advanced Master course), but this means they remain
useful throughout your career.
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 voor
de huiswerk opgaves is nodig om deel te kunnen
1 other book is also sometimes used: Binney and Merrifield: Galactic Astronomy (indicated with “BM”)
De huiswerk opgaven moeten voor het begin van
het volgende college worden gemaild naar:
[email protected]trw.leidenuniv.nl (scannen kan bij de
kopieerapparaten). Te laat inleveren betekent het cijfer
0.
De vragen uurtjes geven specifiek de mogelijkheid om
hulp te krijgen bij het maken van het huiswerk.
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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
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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
Content Handout 1:
i) What is a galaxy?
•Optical
•Radio
•X-Ray
•Dark Matter (halo)
ii) Why do we study galaxies ?
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i) What is a galaxy ?
Galaxies emit in many wavelengths
[See the multiwavelength color show
http://www.strw.leidenuniv.nl/˜ franx/
college/sterrenstelsels15/galaxies.pdf ]
Radio:
•Continuum emission follows spiral arms
•Compact emission regions - supernova remnants
•Active nuclei produce jets, radio lobes...
•Line emission: HI 21 cm, CO,
molecular lines
iii) Optical Photometry
iv) Surveys and Selection Effects
Infrared:
•Continuum emission by dust
•Star forming regions, active nuclei
v) Luminosity Function
Near Infrared:
•Red super giants, some extinction
Study material from B&M:
4.1,
4.2,
4.3,
4.4,
4.6,
(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
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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
23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/
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)
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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/f̃ranx/
college/sterrenstelsels15/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:
4) Why are galaxy classifications problematic ?
5) Describe in your own words 3 criteria which are used
to classify spirals into Sa, Sb to Sd.
6) What is the type of the Milky Way ? Motivate your
answer
7) Why don’t we classify the Magellanic Clouds as ellipticals ? They don’t have spiral arms.
8) What is the type of the galaxy on the cover of BM
? Give the reasons for your classification
9) 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 TV 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 !
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 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 based on optical surveys
Consider galaxy with 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 (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 galaxy too small: misclassified as star
if galaxy 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
10) 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)
11) How can we attempt to classify galaxies automatically (i.e., by computer) ?
12) What is the luminosity function?
13) 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.
14) 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.
15) 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 ?)
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16) 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.