Galaxies Astro 530 Prof. Jeff Kenney. CLASS 23 April 18, 2018 Luminosity FuncDons in Galaxies

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1 Galaxies Astro 530 Prof. Jeff Kenney CLASS 23 April 18, 2018 Luminosity FuncDons in Galaxies 1

2 IntroducDon to LFs Galaxies have huge range of luminosity & mass : ~10 6 (M B - 7 to - 23) The Luminosity FuncDon specifies the reladve number of galaxies at each luminosity The Luminosity funcdon contains informadon about : primordial density fluctuadons processes that destroy/create galaxies processes that transform baryonic mass into light (e.g., gas cooling, star formadon, feedback from SF & AGN) processes that change one type of galaxy into another (e.g., mergers, stripping) Successful theory of galaxy formation & evolution must reproduce LF Also, must understand LF to properly interpret results from surveys

3 there are 2 very different kinds of reasons why the LF is important: constraints on galaxy formadon & evoludon (sciendfic) understanding which objects are in a flux- limited sample (observadonal selecdon effects)

4 luminosity funcdon φ(l) or φ(m) what is the reladve number of galaxies with different luminosides? defined by δn = φ(l) δl δv δn - - number of galaxies located in volume δv with luminosides between L and L+δL φ(l) has units of # galaxies (luminosity interval) (volume) density of galaxies n = φ(l)dl = φ(m)dm (# galaxies volume -1 ) 0 0 luminosity magnitudes

5 how do we learn the reladve numbers of galaxies at each L? how do we determine the luminosity funcdon?

6 Flux- limited samples It s very difficult to detect all galaxies in a given volume of space It s much easier to detect all galaxies brighter than some flux (or apparent magnitude) cutoff

7 observe all sources brighter than some minimum flux: number of sources observed vs L in flux- limited survey number observed in flux-limited survey

8 number observed in flux-limited survey faint sources can only be seen if nearby (typically high density) luminous sources can be seen to larger d (typically low density)

9 While observing you detect all sources brighter than a flux of f min. How far away can you detect a galaxy with luminosity L? or to rephrase: At what maximum distance D max will a galaxy with luminosity L be detected if the minimum flux detectable is f min?

10 while observing you detect all sources brighter than a flux of f min. how far away can you detect a star with luminosity L? or to rephrase, at what maximum distance D max will a star with luminosity L be detected if the minimum flux detectable is f min? L = 4πD 2 f D = (L/4πf) 1/2 D max = (L/4πf min ) 1/2 inverse square law. this relation is true for a a source with any flux. so it is also true for the minimum flux, and the mimimum flux corresponds to the maximum distance that you can detect a source.

11 while observing you detect all sources brighter than a flux of f min. how far away can you detect a star with luminosity L? or to rephrase, at what maximum distance D max will a star with luminosity L be detected if the minimum flux detectable is f min? L = 4πD 2 f D = (L/4πf) 1/2 D max = (L/4πf min ) 1/2 inverse square law. this relation is true for a a source with any flux. so it is also true for the minimum flux, and the mimimum flux corresponds to the maximum distance that you can detect a source. what volume of space does this maximum distance correspond to? 4π V max (L) = D 3 4π L max = ( ) 3 3 4πf 3/2 min photo of Gunner Malmquist, a Swedish astronomer volume surveyed is larger for luminous objects by L 3/2 this is the Malmquist bias (1925)! a certain kind of selection bias

12 we observe N(L) then need to divide by V max to get φ(l) φ(l) = N(L)/V max (L) number observed in fluxlimited survey

13 Schechter luminosity funcdon φ(l) Schechter (1976) found that LF seemed to be described by: φ(l) δl = n * (L/L*) α exp(- L/L*) δl/l* power law at low L exponential at high L α -1 ± 0.5 n * 5 x 10-3 galaxies Mpc -3 L* 2x10 10 L sun L MW M B * -20

14 Knee of luminosity funcdon knee Existence of knee where LF changes slope at L=L* 2x10 10 L sun L MW important informadon about galaxy formadon Important observadonal consequence for galaxy surveys

15 LF expressed in luminosity and magnitudes Slope is flaoer when expressed in magnitudes # galaxies per magnitude interval is nearly constant for L<L*

16 Remarks about Schechter LF SLF is for all galaxies regardless of type; galaxies of any 1 type do not follow SLF MW and M31 each have L~L* Galaxies with L>3L* are reladvely rare cd galaxies with L~10L* that exist in centers of many rich clusters are underpredicted by SLF SLF overpredicts galaxies at low L LF evolves in Dme

17 what is the overall galaxy number density? density of galaxies whose luminosides exceed L: n (>L) = φ(l ) dl = n * x α e - x dx L =L x=l/l* = n * Γ (1+α, L/L*) incomplete gamma function

18 what is the overall galaxy number density? density of galaxies whose luminosides exceed L: n (>L) = φ(l ) dl = n * x α e - x dx L =L x=l/l* = n * Γ (1+α, L/L*) incomplete gamma function for α - 1 and Lè 0, n(>l) è!! so SLF (with α - 1) predicts infinite number density of galaxies - > SLF must fail at low L for ANY α, SLF must fail at low L, since galaxies don t exist below some mass limit (there are no galaxies with L=1 L sun or M=1 M sun )

19 what is the overall galaxy number density? density of galaxies whose luminosides exceed L: n (>L) = φ(l ) dl = n * x α e - x dx L =L x=l/l* = n * Γ (1+α, L/L*) incomplete gamma function for case α=- 1 and L>L*, n(>l*) = n * Γ (0,1) 0.22 n * = 1.1 x 10-3 galaxies Mpc -3 i.e. 1 galaxy L* or brighter every ~1000 Mpc - 3 average separadon ~10 Mpc (this is average over clusters and voids )

20 what is the overall luminosity density of galaxies? luminosity density of galaxies (muldply number density by luminosity): ρ L = (l tot ) = φ(l )L dl = n * L* x α+1 e - x dx SG (BM) recall Γ(j+1) = j! when j=integer L =0 x=0 = n * L* Γ (2+α) gamma function = 1.0 n * L* for α= x10 8 L sun Mpc - 3 luminosity density is finite even though number density is infinite

21 does most of light in universe come from big or small galaxies? Solid line: Φ(M) number of galaxies per volume per magnitude interval (α=- 1) Do*ed line: LΦ(M) light from galaxies per volume per magnitude interval (α=- 1) for α>- 1.5, most stars are in bright galaxies (near L*)

22 Dark maoer galaxy mass funcdon predicted from cosmological simuladons

23 Dark maoer galaxy mass funcdon predicted from cosmological simuladons

24 Knee of luminosity funcdon knee Existence of knee where LF changes slope at L=L* 2x10 10 L sun L MW important informadon about galaxy formadon Important observadonal consequence for galaxy surveys

25 observed galaxies nearly match cosmological simuladons at knee of LF, but are underabundant at higher and lower luminosides à something suppresses star formadon at high and low galaxy masses

26 Behroozi+2013 rado of stellar mass to halo mass peaks at M halo ~5x10 11 M sun and M star ~2x10 10 M sun (Knee of LF) but M star /M halo is lower at higher and lower masses à something suppresses star forma:on at high and low galaxy masses

27 Possible ideas for suppression of star formadon at high and low galaxy masses

28 it is easier to measure LF in cluster than in general need to sample all galaxies within certain volume of space hard to detect faint galaxies at large distances so volume must be small need to know distances to galaxies accurately, so that you know which galaxies are in specified volume most previously- known galaxies cannot be used for LF studies, since most of them are intrinsically luminous galaxies at distances which lie outside the volume in which faint galaxies can be detected much easier to survey contents of cluster of galaxies, as it is a bunch of galaxies all at appx the same distance

29 LF vs. galaxy type in Virgo cluster LF for each sub- type NOT well fit by Schechter funcdon E, S0, Sp exist only over ~7 mags = factor of ~600 in L - > no true dwarf E, S0, Sp

30 LF vs. type varies with environment M halo 2x10 15 M sun M halo 2x10 14 M sun M halo 2x10 13 M sun Early types (E, S0, de) more common at high galaxy densides and in most massive halos

31 LF vs. type varies with environment Overall shape of total LF similar in different environments RaDo of blue star- forming to red, less star- forming galaxies varies strongly with environment

32 suppose you observe a flux- limited sample what galaxies do you have in your sample? how many galaxies do have at each luminosity? is your sample mostly high- luminosity galaxies or mostly low luminosity galaxies? if you know the LF you can answer these questions

33 Flux- limited samples What is the number of galaxies dn in a flux- limited sample with luminosi:es between L and L+dL? integrate over volume in which galaxies with luminosity L can be detected: δn = δn = φ(l) δl dv = V(L) φ(l) δl V V NOTE: can do integral in this simple way only if φ(l) φ(l,v) or φ(l,ρ) over what volume of space V(L)=V max (L) can a galaxy of luminosity L be detected in a sample selected to include galaxies brighter than some flux threshold f min?

34 at what maximum distance D max will a galaxy with luminosity L be detected if the minimum flux detectable is f min? L = 4πD 2 f L D max = ( ) 1/2 4πf min what volume of space does this maximum distance correspond to? 4π V max (L) = D 3 4π L max = ( ) 3/2 4π L* = ( ) 3/2 L ( ) 3 3 4πf 3/2 min 3 4πf min L* volume surveyed is larger for luminous galaxies by L 3/2 this is the Malmquist bias (1925)! a certain kind of selection bias

35 plug V(L)=V max into expression for δn δn = V(L) φ(l) δl L _ L _ δl L* L* L* δn = N c ( ) α+3/2 exp(- ) 4π L* 3 4πf min where N c = ( ) 3/2 n * L L δl L* L* L* for α = - 1.0, δn = N c ( ) 1/2 exp(- )

36 plug V(L)=V max into expression for δn δn = V(L) φ(l) δl L _ L _ δl L* L* L* δn = N c ( ) α+3/2 exp(- ) 4π L* 3 4πf min where N c = ( ) 3/2 n * L L δl L* L* L* for α = - 1.0, δn = N c ( ) 1/2 exp(- ) one can easily show for α=- 1 that: half of galaxies in a flux- limited sample have L > 1.2L* only ~5% of galaxies in a flux- limited sample have L > 3.9L* only ~5% of galaxies in a flux- limited sample have L < 0.2L* flux- limited samples are dominated by galaxies with L~L*

37 Flux- limited samples It s very difficult to detect all galaxies in a given volume of space It s much easier to detect all galaxies brighter than some flux (or apparent magnitude) cutoff This leads to Malmquist bias, the preferendal detecdon of intrinsically luminous objects Need to correct for Malmquist bias in order to derive LF, and to properly interpret results from flux- limited surveys In flux- limited sample, the surveyed volume, V max (L), is small for low luminosity objects, and large for high luminosity objects so correcdons are huge for low luminosity objects Flux- limited samples are dominated by galaxies with L~L*, even though lower L galaxies are more common

ASTRO 310: Galactic & Extragalactic Astronomy Prof. Jeff Kenney. Class 2 August 29, 2018 The Milky Way Galaxy: Stars in the Solar Neighborhood

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