1. Constraints on a Universal IMF1 from the Entire Stellar Population2,3
Ivan Baldry
Johns Hopkins University
working with Karl Glazebrook
1Assuming a universal IMF and constraining the upper-mass IMF slope (M >~ 1 solar mass).
Footnote 1: Really constraining 1 to 100 solar mass exponent of IMF.
Footnote 2: Surveys at many wavelengths. Low redshift and high redshift. Consensus of light in the Universe is good except for the lowest surface brightness regions e.g. intra-cluster stars.
2UV to IR galaxy luminosity densities (e.g. SDSS, FOCA, 2MASS, 2dFGRS and IRAS data) - “the Cosmic Spectrum”.
3Based on Baldry & Glazebrook, 2003, in ApJ, Vol. 593

2. Integrated Stellar Populations
Extragalactic astronomers fit population synthesis models to colors or spectra of galaxies to gain insights into star formation history, dust content, etc.
Usually a stellar initial mass function (IMF) is assumed because of the age-IMF degeneracy.
This age-IMF degeneracy can be broken for the Universe as a whole (assuming the Copernican principle):
Age = 13.70.2 Gyr (Spergel et al. 2003);
Meas. of cosmic star formation history (Madau et al. 1996, `98);
Meas. of the local “cosmic spectrum” (Baldry et al. 2002).

3. Overview of Fitting Stellar initial mass function (IMF)
Cosmic star formation history (SFR tracers 0 < z < ~5)
Chemical evolution
Dust attenuation
Population synthesis models
DATA – luminosity densities (0 < z < 0.2):
FOCA (balloon), 0.2 microns (Sullivan et al. 2000);
SDSS ugriz, microns (Blanton et al. 2003);
2MASS, 2 microns, with z (Cole et al., Kochanek et al. 2001);
H-alpha, attenuation-corrected (Gallego et al and others);
IRAS FIR (Saunders et al. 1990) converted to total dust emission.

4. Stellar IMF Parameterization
Note unusual y-axis scaling: mass fraction
m– for 0.1 < m < 0.5
m–G for 0.5 < m < 120
nlog m 
G=1.35 is Salpeter slope

5. Cosmic Star Formation History
REDSHIFT
“Madau plot” versus time
Various measurements, e.g, Lilly et al. 1996, Madau et al. 1996/98, Cowie et al. 1999, Steidel et al. 1999, Lanzetta et al. 2002, + more.
SFR  (1+z)b for z<1 (0.5 < b < 4.0 allowed) and,
SFR  (1+z)a for 1<z<5 (SFR = 0 for z>5; meet at z=1).

6. Cosmic Chemical Evolution
The cosmic stellar-mass weighted metallicity is approx. solar (cf. our neighborhood in the Milky Way).
Compare ‘closed box’ with ‘constant metallicity’ approximations. Allow average Z from about 0.5 Zsolar to 2 Zsolar.

7. Cosmic Dust Attenuation Law
Inclination-averaged attenuations.
Compilation from Calzetti (2001).
Estimated dust attenuation allowing for different contributions from late- and early-type galaxies as a function of wavelength. About 90% of the luminosity density is derived from late type galaxies at 0.2 microns and about 50% at visible to near-IR wavelengths.
Power-law with exponent ~ –0.8

8. Population Synthesis PEGASE.2 (Fioc & Rocca-Volmerange 1997, 1999):
Covers UV to IR;
Includes stellar and nebular (continuum and line emission);
Can specify arbitrary power law IMFs and SFH.
Evolutionary tracks from Padova group.
Theoretical spectra from Clegg & Middlemass (1987) and Lejeune et al. (1997) (derived from Kurucz models, NextGen and Fluks catalogues).
From the output spectra, determine:
Colors through FOCA, SDSS and 2MASS filters;
Total dust emission for various dust power laws;
H-alpha luminosity (reprocessed Lyman continuum emission).

9. Data Summary
Local Luminosity Density Measurements from Various Surveys (0<z<0.2)
Band
l / mm
FWHM
quantity
log(q / h W Mpc-3)
References, notes
FOCA 2000
0.20
0.02
nfn
34.35  0.12
Sullivan et al. 2000
SDSS 0.1u
0.32
0.05
34.25  0.08
Blanton et al. 2003
SDSS 0.1g
0.42
0.11
34.56  0.04
SDSS 0.1r
0.56
0.10
34.73  0.04
SDSS 0.1i
0.68
34.78  0.04
SDSS 0.1z
0.81
0.09
34.83  0.04
2MASS Ks
2.16
0.28
34.53  0.12
Average: Cole et al., Kochanek et al. Ha
0.6563
(line)
(bolo.)
32.63  0.20
Attenuation-corrected, average
TIR
3–1100
(broad)
34.70  0.15
Scaled from FIR of Saunders et al.

10. Effect of Various Parameters
Normalized at 0.56 microns.
DATA
FOCA, Sullivan et al. 2000
SDSS, Blanton et al. 2003
2MASS, Cole et al. 2001, Kochanek et al.
Hawaii, Huang et al. 2003
AB Magnitudes (a log fn)
Wavelength ( microns)

11. Results
Assuming: constant SFR from z = 1 to 5, average metallicity = solar.
Fitting to 0.20, 0.32, 0.42, 0.56, 0.68, 0.81, Ha + dust emission.
Red contours for constant Z
Blue contours for closed box approx.
redshift < 1 star formation power law
(Salpeter = 1.35)
Dc2=(1, 2.3, 6.2, 11.2)

12. Results continued
Assuming: high z>1 SFR a (1+z)2, average metallicity = solar.
Fitting to , Ha + total dust emission.
Red contours for constant Z
Blue contours for closed box approx.
redshift < 1 star formation power law
(Salpeter = 1.35)
Dc2=(1, 2.3, 6.2, 11.8)

13. Results continued
G=1.1±0.2 marginalized over dust, SFH, 0.5<Z/Zsolar<2.
Scalo IMF is inconsistent with data and models (cf. Madau, Pozzetti & Dickinson 1998 and Kennicutt, Tamblyn & Congdon 1994 [incl. Ha EWs]).
Stellar mass density of the Universe is in the range 0.15% to 0.28% (0.12% to 0.35% with low-mass IMF uncertainty, or 3% to 8% of baryon density).
Stellar bolometric emission is ( ) x 1035 W Mpc-3 and dust emission is ( ) x 1035, which implies a modest effective average attenuation in the ultraviolet of A2000 < ~60% (< ~1 mag).
CAVEAT – results rely on accuracy of population synthesis…

14. Local Luminosity Densities
bolometric luminosity per log l bin
Data and best-fit model spectrum: the stellar and the HII region gas emission (Fioc & Rocca-Volmerange) and; the dust emission (Dale & Helou). AGN contribution not shown.

15. Future and Current Surveys
Local imaging surveys (z~0.1):
(SDSS has set the bench mark, >105 galaxies with redshifts and ugriz photometry, >103 deg2) – optical;
GALEX all-sky survey – ultraviolet;
VISTA – near-infrared (also 2MASS with 6dFGS redshifts);
ASTRO-F – mid- to far-infrared.
Deeper imaging surveys:
GALEX deep surveys – ultraviolet;
HST – ACS, NICMOS – optical, near-IR;
SIRTF – mid- to far-infrared.

16. …
Extra slides follow.

17. Cosmic Star Formation History
Meas. of comoving star-formation rate density (MO/yr/Mpc3) as a function of redshift (or time).
CSFH analysis removes uncertainties associated with dynamical history, i.e. consider the Universe to be a single average galaxy.
Determine SFR per comoving volume:
(modulo dust, SB, etc… corrections)
Luv, LFIR, L700Mhz
LHa, LHb, L[OII]
Number of massive stars formed / unit time

18. Madau, Pozetti & Dickinson 1998
Fig 3: Salpeter IMF; SMC-type dust in a foreground screen; E(B–V)=0.1.
2.2 mm
1.0 mm
.44 mm
.28 mm
.15 mm

19. Madau, Pozetti & Dickinson 1998
2.2 mm
1.0 mm
.44 mm
.28 mm
.15 mm
Salpeter IMF, E(B–V) = 0.011(1+z)2.2
Scalo IMF, no dust

20. Table of IMF Comparisons