Sterrenstelsels en Cosmologie - Leiden Observatoryhome.strw.leidenuniv.nl/~franx/college/sterrenstelsels15/handout1.pdf · Sterrenstelsels en Cosmologie Docent: M. Franx, kamer 425

23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-1

Sterrenstelsels en Cosmologie

Docent: M. Franx, kamer 425

College assistenten: Margot Brouwer, kamer 541,Marijke Segers, kamer 436

Two books are relevant for this course. None are oblig-atory:

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, equi-libria, disks, mergers, etc.

Extragalactic Astronomy and CosmologyPeter Schneider, edition 2

76 euro bij bol

These books are not obligatory. Their level is very high(advanced Master course), but this means they remainuseful throughout your career.

1 other book is also sometimes used: Binney and Mer-rifield: Galactic Astronomy (indicated with “BM”)


Dates of the courses

on Monday, 11:15-13:00Jan 26 - June 1, room 414, (exceptions April 8 andJune 1)

QUESTION HOURS:

generally 13:45, Thursday BEFORE next course (ex-cept May 13).room 207 (except May 6, 14 room 106)

Het cijfer voor het college wordt voor 66% bepaalddoor het tentamen, en voor 33% door de ingeleverdehuiswerk opgaven. Een minimum cijfer van een 6 voorde huiswerk opgaves is nodig om deel te kunnen

De huiswerk opgaven moeten voor het begin vanhet volgende college worden gemaild naar:[email protected] (scannen kan bij dekopieerapparaten). Te laat inleveren betekent het cijfer0.

De vragen uurtjes geven specifiek de mogelijkheid omhulp te krijgen bij het maken van het huiswerk.


Brief content of the course1) Introduction

What is a galaxy ?ClassificationsPhotometry, exponentials, r1/4 profiles, luminosityfunction

2) Keeping a galaxy together: GravityPotentials

3) Galactic DynamicsEquilibriumcollisions, Virial Theorem

4) Galactic Dynamics continuedTimescalesOrbits

5) Collisionless Boltzmann Equationequilibrium, phase mixingderivation of distribution function

6) Velocity MomentsJeans equationscomparison to observations

7) Mass distribution and dark matterEvidence for dark matter from rotation curvesSolar neighborhood, Oort limitElliptical galaxies and hot gasClusters of galaxies, the universeCandidate dark matter particles

8) Galaxy formation


Universe expansionGrowth of galaxies by gravityGalaxy scaling relations

9) Galaxy formation - forming the starsGas cooling and star formationformation of disksdynamical friction and mergerstidal tails in mergers

10) Observing galaxy formationHigh redshift galaxies from HSTFair samples of galaxies at high redshift


1. General Introduction

Content Handout 1:

i) What is a galaxy?•Optical•Radio•X-Ray•Dark Matter (halo)

ii) Why do we study galaxies ?

iii) Optical Photometry

iv) Surveys and Selection Effects

v) Luminosity Function

Study material from B&M:

4.1, (4.1.2), 4.1.3 to page 165, (4.1.4)4.2, (4.2.2), not 4.2.34.3, to page 1874.4, (not 4.4.2), 4.4.3 to page 2174.6, to page 244 (4.6.2)

subsection in brackets means for reading only


i) What is a galaxy ?Galaxies emit in many wavelengths

[See the multiwavelength color showhttp://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

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


Active Nuclei

•produce emission at all wavelengths

•at all lengthscales:from very close to the nucleus (≤ pc)to the largest scale (> 10 kpc)


Conclusion

a Galaxy consists of several components:

-bulge red, old (?)r1/4 law

stars:blue or red

-disk spiral arms, rings, barsexponential profile

H I gas-disk H2 gas

gas: dust

-extended Hot Gas

active nucleus: center black hole

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 ?


Homework Questions:

1) Why is the name “sterrenstelsel” “bad” ? In whatcomponent is most of the mass ?

2) What telescope would you use to measure the emis-sion of Andromeda at a frequency of (i) 1.415 109 hz,(ii) 5.9 1014 hz, (iii) 1017 hz. First calculate the wave-lengths of this emission.

3) Give an estimate from literature of the total massof the Milky Way, and the total stellar mass. Give therelevant source (i.e., mention where you got these esti-mates from)


Optical images of galaxies and classification

See the pdf file on the web for nice pictureshttp://www.strw.leidenuniv.nl/̃franx/college/sterrenstelsels15/galaxies.pdf

All classification systems are idealizations.Independent of true size of the galaxy and Luminosity!

Often used systems:

1. Hubble-Sandageor

2. de Vaucouleurs

Numerical types T (based on de Vaucouleurs) wereoften 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 (Re-vised Shapley Ames Catalogue, Sandage)


23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-13 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-14

“Normal” Spirals are classified from Sa to Sd. Alongthis sequence the following properties change:1) degree of central concentration (or Bulge-to-diskratio). (decreasing from Sa to Sd)2) angle of the spiral arm (increasing from Sa to Sd)3 degree of resolution of spiral arms into individualclumps (from smooth to clumpy from Sa to Sd).


Bars occur at all types. Their strength can be used asanother dimension in the classification.


These galaxies have rings


These are peculiar galaxies (Arp et al, 1987). Thesegalaxies are generally mergers (collisions between galax-ies).


De Vaucouleurs introduced a classification schemewhich was slightly different, classifying into “ring” and“s-shaped”, and bars. He also introduced a numericaltype t running from -5 to 10.


van den Bergh introduced yet another scheme:


Currently, these classifications have become less im-portant. We now have distances to most galaxies, andmulti-wavelength information. We characterize galaxiesby their stellar mass, age, star formation rate, metallic-ity, and halo mass (or environment).

Homework Questions:

4) Why are galaxy classifications problematic ?5) Describe in your own words 3 criteria which are usedto classify spirals into Sa, Sb to Sd.

6) What is the type of the Milky Way ? Motivate youranswer

7) Why don’t we classify the Magellanic Clouds as el-lipticals ? 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 ?


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 theirbrightness distribution

•Big technical problem: galaxies are really large, andhave low surface brightness wings. See the beautifulimage of M31


As can be seen, the galaxy does not really stop !How to measure average surface brightness

profile ?

Measure the intensity on ellipses of (nearly) constantsurface brightnessIn practice, our images “stop” when there might stillbe very faint galaxy light. This would not be a prob-lem, but we also have the much brighter light from thenight sky. We have to estimate this, and we make sys-tematic errors in the profiles if we estimate it too lowor too high


Resulting profiles:

•Ellipticals:King profilede Vaucouleurs law (r1/4)

•Spirals:Disks: exponential profileBulges: 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 emit-ted inside Re. Because of uncertainties in the back-ground subtraction, we never know the exact half lightradius. The parameter Ie is the surface brightness atR = Re.No galaxy follows the r1/4 law exactly !

On the next page, some examples are shown.


The profiles can change systematically from brightgalaxies to faint elliptical galaxies.


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 shownabove show a straight profile - hence have an exponen-tial profile. The inside shows an upturn, and that ismodeled as a separate component. This is the bulge.Many galaxies are modelled well by fitting an r1/4 lawto the bulge and an exponential model to the disk.



Surveys and Catalogs of galaxies

most catalogs based on optical surveys

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 ofgalaxies, 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 CatalogSandage and Tammann

Third Reference Catalogue of Bright Galaxiesde Vaucouleurs et al

e.g.:

Very important were Palomar Sky Survey Plates, thesehave been used for systematische surveys

UGC: northern galaxiesESO catalog: southern galaxiesLauberts, Lauberts en Valentijn


Selection effects in optical catalogs

Consider galaxy with certain luminosity

If galaxy too small: misclassified as star

if galaxy too big: surface brightess is too low − > notdetected !


Luminosity Function

SDSS Luminosity function from Blanton 2005

Determine for each galaxy the intrinsic luminosity fromapparent luminosity and distance.

Correct for bandpass, internal absorbtion and absorb-tion by the Milky Way.

The luminosity function is defined byΦ dM = number density of galaxies in magnituderange (M ,M + dM)

The distribution of luminosities is given by a Schechterfunction


Φ(L) = (Φ∗

0/L∗) (L/L∗)α exp(−L/L∗)

Typical values:Φ∗ = (1.6± 0.3)× 10−2h3Mpc−3

M∗

B = −19.7± 0.1 + 5 log hα = −1.07± 0.07L∗

B = (1.2± 0.1)× h−2 1010LSun

where H0 = h100km/sThe number of galaxies with a luminosity larger than Lis given byN(> L) =

∫∞

LΦ(L′)dL′ = N0Γ(1 + α,L/L∗)

Here we used the following definition for the incom-plete gamma functionΓ(α, x) =

∫∞

xt(α−1)e−tdt

Total amount of light produced

ltot =∫∞

0Φ(L′)L′dL′ = Φ∗L∗Γ(2 + α)

= Φ∗L∗ for α = −1

Hence, huge numbers of low luminosity galaxies ex-pected, but finite luminosity.

Most of the luminosity comes from galaxies with L =L∗. A simple approximation is that the universe isfilled with L∗ galaxies with a density Φ∗


Homework questions

10) Given a galaxy with an exponential profile I(R) =I0exp(−R/Rd)a) what is the total emount of light emitted ? (Ex-press in terms of I0 and Rd.) (Hint: integrate the lightemitted as a function of radius, where radius runs from0 to infinity)b) what is the half light radius ? (i.e., the radius inwhich half the light is emitted) (Hint: use the integralfrom 10a, now to Re instead of infinity)

11) How can we attempt to classify galaxies automati-cally (i.e., by computer) ?

12) What is the luminosity function?

13) Given a Schechter Luminosity function, what is theluminosity at which half of the total luminosity densityis emitted by galaxies brighter than that luminosity ?Assume α = −1.

14) What is the luminosity of a typical galaxy in termsof solar luminosities? Motivate your answer, and give afull reference if you take a value from a source.

15) The Schechter function implies that the total num-ber of galaxies per volume element is infinite if theSchechter luminosity function extends to luminosity0. Derive that this is the case for a simple Schechterluminosity 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 ?)


16) Find the website of a catalogue with more than100.000 galaxies (and NOT the Sloan Digital Sky Sur-vey or GAMA ). Give the full reference.

Documents

Sterrenstelsels en Cosmologie - Leiden Observatoryhome.strw.leidenuniv.nl/~franx/college/sterrenstelsels15/handout1.pdf · Sterrenstelsels en Cosmologie Docent: M. Franx, kamer 425