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Lecture 2, Galaxy Number Counts and Luminosity Functions

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Lecture 2, Galaxy Number Counts and Luminosity Functions Galaxies 626 Lecture 2: Galaxy number counts and luminosity functions How much of the extragalactic background light can we identify, and how much is unidentified (unresolved)? The next step is to count all the galaxies we can find and see how much light they contain So we now want to form the galaxy number counts at all wavelengths B, R, z/ 15/ x 15/ B (1.7hrs) R (5.2hrs) z’ (3.9hrs) B (27) R (26.4) z’ (25.4) Optical Image Capak et al. 2003 Measuring Galaxy Luminosities Galaxies, unlike stars, are not point sources The Hubble Space Telescope can resolve (i.e. detect the extended nature of) essentially all galaxies Even from the ground, most galaxies can easily be distinguished from stars morphologically and on the basis of their colors Measuring Galaxy Luminosities Define the surface brightness of a galaxy I as the amount of light from the galaxy per square arcsecond on the sky Consider a small square patch, of side D, in a galaxy at distance d: d D Angle patch subtends on sky α = D/d Finding Galaxies in an Image Finding galaxies in an image and constructing the number counts is the subject of the first student project Essentially we look for all objects above a limiting surface brightness and covering more than a specified area SExtractor is a commonly used package 20 cm Radio Image from the VLA Number Counts We then need to measure the fluxes of all the objects that we find The number counts are simply the number of objects we find in a given flux or magnitude bin per unit area of the sky Measuring Galaxy Luminosities Consider again the small square patch, of side D, in a galaxy at distance d d D Angle patch subtends on sky α = D/d If the luminosity of all the stars within the patch is L, then the total flux is L F = 4"d 2 Define surface brightness as: L /4"d 2 L ! I = = D2 /d 2 4"D2 Units of I are mag arcsec-2; i.e., if a galaxy has a surface -2 brightness! of 20 mag arcsec , then we receive as many photons from one square arcsecond of the galaxy’s image as from a star of 20th magnitude -2 Centers of galaxies have IB ~ 18 mag arcsec To measure the total amount of light coming from a galaxy, need to integrate the surface brightness across the galaxy image. This leads to a related problem: galaxies do not have sharp well-defined edges Typically integrate out to some limiting isophote; e.g., sum up all the light coming from regions with surface -2 brightness IB < 25 mag arcsec . Alternatively, we can measure to a surface brightness level relative to the central surface brightness (say 1 percent) This measure of the total galaxy brightness is called an isophotal magnitude---numerous variations are possible An alternative and commonly used procedure is to measure the magnitudes in an aperture that contains most of the galaxy light and to apply an average correction for the light outside the aperture These are usually called corrected aperture magnitudes The UBL – Unidentified (Unresolved) Background Light Key Issues: • We need to know the EBL to high accuracy (removal of spurious foregrounds, calibration issues) • We need to determine the extragalactic galaxy counts to very faint levels and properly measure their total fluxes (calibration and getting the fainter surface brightness parts of the galaxies) -2 -1 -1 -1 N(m) deg 0.5mag iν cgs Hz sr γ=0.4 Counts from U through K extend well into γ<0.4 regime Madau & Pozzetti (2000) MNRAS 312, L9 The UBL (above & beyond known counts) # UBL= EBL - I" = $ i" (m)dm -# 0.4(m+const) where # i" (m) =10 N(m) ! Multiplying flux of the sources by N(m), the! d ifferential counts per unit magnitude per unit area Units 1 Jansky = 10-26 W m-2 Hz-1 1 nW m-2 sr-1 = 3000/λ(µm) MJy sr-1 Contributions to the Optical EBL Capak et al. 2004 Pozzetti et al. 2000 Ground-based data Ground + HST data Contributions from integrated counts nW m-2 sr-1 • Extrapolated counts enable contribution to integrated light from known populations to be evaluated as function of wavelength -2 -1 • Find EBL = ∫ ν Iν dν = 55 nW m sr ; largest contribution in NIR 4 • Observational issues: isophotal losses and (1+z) redshift dimming CCDDF-FN-N 503 sources 12 MMss RED: 0.5-2 keV GREEN: 2-4 keV BLUE: 4-8 keV 3D70. sAoulercxesander 460 sq arcmin CDF-N + HAWAII COMBINED CDF-S COMBINED CDF-N CDF-S SSA13 Moretti et al. 2003 Measurements of the 2-8 keV background How much unidentified light do we have? Resolved background Hickox & Markevitch 2006 Moretti et al. 2003 Measured backgrounds Contribution from counts The Galaxy Luminosity Function The luminosities of galaxies span a very wide range---most luminous ellipticals are 107 more luminous than the faintest dwarfs Luminosity function, Φ(L), describes the relative number of galaxies of different luminosities Definition: If we count galaxies in a representative volume of the Universe, Φ(L)dL is the number of galaxies with luminosities between L and L + dL Identical to the definition of the stellar luminosity function Luminosity functions are easiest to measure in clusters of galaxies, where all the galaxies have the same distance Coma Cluster The Schecter Luminosity Function A convenient approximation to the luminosity function was suggested by Paul Schecter in 1976: * $ L ' $ L ' dL "(L)dL = n#& ) exp& + ) % L# ( % L # ( L# In this expression: • n* is a normalization factor which defines the overall ! density of galaxies (number per cubic Mpc) • L* is a characteristic galaxy luminosity. An L* galaxy is a bright galaxy, roughly comparable in luminosity to the Milky Way. A galaxy with L < 0.1 L* is a dwarf. • α defines the `faint-end slope’ of the luminosity function. α is typically negative, implying large numbers of galaxies with low luminosities. The Schecter Luminosity Function The Schecter function is: • a fitting formula that does not distinguish between galaxy types • as with the stellar mass function, parameters must be determined observationally: Illustrative -3 -3 n* = 8 x 10 Mpc - related to mean galaxy numbers density 10 L* = 1.4 x 10 Lsun - luminosity of galaxies that dominate light output α = −0.7 - lots of faint galaxies 33 -1 …where Lsun = 3.9 x 10 erg s is the Solar luminosity The Schecter function plotted for different faint-end slopes, α = -0.5 (red), α = -0.75 (green), α = -1 (blue): Properties of the Schecter Luminosity Function The total number of galaxies per unit volume with luminosity greater than L is: # n = (L)dL This integral is not expressible in $ " terms of elementary functions L If α < -1, n diverges as L tends toward zero. Obviously unphysical, so Schecter law must fail for very low luminosity! galaxies (or have a larger alpha). The luminosity density (units Solar luminosities per cubic Megaparsec) is given by: # $ "(L)LdL L Dominated by galaxies with L ~ L* for typical value of α. ! Significance of the Schecter Function Does the Schecter form of the luminosity function have any deeper significance, or is it just a good fitting function? • Luminous galaxies become exponentially rarer at high enough luminosities. Similar to a general result in cosmology (confusingly, Press-Schecter theory) - the number density of massive objects (e.g. clusters) drops off exponentially at high masses. • But remember that Schecter function is a composite which includes all types of galaxies. Luminosity function of any individual class of galaxies looks very different - irregular galaxies typically have much lower luminosities than ellipticals for example. Mass Function of Galaxies For stars, measurements of the luminosity function can be used to derive the Initial Mass Function (IMF). For galaxies, this is more difficult: • Mass to light ratio (M/L) of the stellar population depends upon the star formation history of the galaxy. • Image of the galaxy tells us nothing about the amount and distribution of the dark matter. More difficult measurements are needed to try and get at the mass function of galaxies. Local Inventory of Stars Relevant papers: Fukugita et al. 1998, ApJ, 503, 518 Fukugita & Peebles 2004, ApJ, 616, 643 Survey data: Cole et al. 2001, MNRAS, 326, 255 (2dF+2MASS) Kauffmann et al. 2003, MNRAS, 341, 33 (SDSS) Stellar density: measure local infrared LF, Φ (LK), and scale by a mean mass/light ratio (M/LK), which depends on the initial mass function (IMF) Most of the mass is in lower-mass stars, and most of the light is from solar mass stars. One empirically tries to determine the M/LK ratio, but the only information below 1 solar mass is from the disk of the Milky Way One calculates all of the galaxy properties one would expect for a particular IMF to see if it gives a self-consistent description Some Initial Mass Functions where the contributions are coming from Salpeter > 1 M reproduces colors and Hα properties of spirals IMF < 1 M makes minor contribution to light but is very important for mass inventory (Salpeter diverges at low- Mass (M) mass end) Stellar Mass Function at z=0 17,000 K-band selected galaxies with K<13.0 2dFGRS redshifts & 2MASS photometry Stellar K mass Stellar Mass Density at Present-Day Cole et al find Ωstars h = 0.0014 ± 0.00013; M/LK = 0.73 (Miller-Scalo) Ωstars h = 0.0027 ± 0.00027; M/LK = 1.32 (Salpeter) Fukugita & Peebles: Ωstars h = 0.0027 ± 0.0005 (5% in brown dwarfs) Ωgas = 0.00078 ± 0.00016 (H I, He I, H2) NB: a comparison with WMAP result for the baryon density, only 6% of baryons are in stars! Baryon density is dominated by gas (WHIM), not stars Would expect the integral of the past activity to agree with the locally-determined stellar density (Fukugita & Peebles 2004) If both the local value and the cumulative star formation are calibrated
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