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23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-1 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-2 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. 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-3 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 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ 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 mf-sts-2015-c01-4 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ 1. General Introduction Content Handout 1: i) What is a galaxy? •Optical •Radio •X-Ray •Dark Matter (halo) ii) Why do we study galaxies ? mf-sts-2015-c01-5 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ 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 mf-sts-2015-c01-6 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 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-7 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ 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) mf-sts-2015-c01-8 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 ? mf-sts-2015-c01-9 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-10 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) 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-11 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) 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-12 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. 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). 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-15 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ Bars occur at all types. Their strength can be used as another dimension in the classification. These galaxies have rings mf-sts-2015-c01-16 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-17 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-18 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). 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-19 van den Bergh introduced yet another scheme: 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-20 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 ? 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-21 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 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-22 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 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-23 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-24 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. 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-25 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. 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-26 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-27 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ 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 mf-sts-2015-c01-28 If galaxy too small: misclassified as star if galaxy too big: surface brightess is too low − > not detected ! 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-29 Luminosity Function 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-30 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 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-31 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 ?) 23-1-2015see http://www.strw.leidenuniv.nl/˜ franx/college/ mf-sts-2015-c01-32 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.