The Dust Obscuration bias in Damped Ly a systems

1. The Dust Obscuration bias in Damped Ly a systems Giovanni Vladilo Osservatorio Astronomico di Trieste Istituto Nazionale di Astrofisica Vladilo & Péroux 2005 (astro-ph/0502137) IAU Coll. 199 - Shanghai 2005

2. Motivation • Understanding the origin of the empirical thresholdlog N(ZnII) ≤ 13.15 (Boissé et al. 1998) • Recent DLA surveysconfirm the existence of the threshold • The threshold is NOT due to any observational limitation • Is the threshold due to dust extinction as proposed by Boissé et al. ? IAU Coll. 199 - Shanghai 2005

3. Extinction vs. N(ZnII)theoretical relation Derived comparing the column densities of a volatile and a refractory element in the interstellar medium Zn & Fe If right term ~ constant, the relation is linear A linear relation is equivalent to Al 10 log N(Zn) IAU Coll. 199 - Shanghai 2005

4. Extinction vs. N(ZnII)empirical relation • HST and IUE interstellar data • Agree with theoretical prediction • Zinc indeed excellent tracer of extinction • The existence of a barrier of extinction vs log N(ZnII) is proven in the ISM • By defining the turning point as • we obtain log N(ZnII) ≤ 13.18 • Remarkably close to the Boissé threshold IAU Coll. 199 - Shanghai 2005

5. From the ISM to DLAs sources of variation of the relation • Dust grain properties: yes • But ISM sample includes lines of sight with different grain properties • And we can at least recalibrate the relation in the SMC • Dust depletions: yes • But we know the behaviour of dust depletions in DLAs • Relative abundances: no • Redshift variation of the extinction in the observer's frame • We can model the extinction curve IAU Coll. 199 - Shanghai 2005

6. The extinction in DLAs from MW and SMC data from abundance studies of DLAs IAU Coll. 199 - Shanghai 2005

7. fFe vs. metallicity in DLAs • Vladilo (2004, A&A 421, 479) IAU Coll. 199 - Shanghai 2005

8. Original features of the relation • Analytical expression for iron depletion • "Kills" the extinction at very low metallicities • We do not need to know the dust grain parameters at the very early stages of galactic evolution • We only need to know the grain parameters for metallicities not much below solar • Allows the extinction to be expressed as a function of N H and Z • Given a distribution of N H and Z in a given redshift interval • the distribution of extinctions is specified  the obscuration bias is specified • Dust grain parameters could be taken from grain models (not done yet) IAU Coll. 199 - Shanghai 2005

9. Mathematical formulationbased on the extinction relation • Aims • Find the relations between true and biased distributions of N (HI) and Z • Provide a method for deriving the true distributions given the empirical distributions • Assumptions • Multiple DLAs absorptions in a given line of sight ignored • Distributions of N (HI) and Z statistically independent • Both assumptions are conservative • Slightly underestimate the magnitude of the obscuration effect IAU Coll. 199 - Shanghai 2005

10. Core equations Bias function Fraction of DLA-quasar pairs that can be detected in the differential element dNH dZ dz in a survey with limiting magnitude ml IAU Coll. 199 - Shanghai 2005

11. Core equations Bias function Relation between true and biased distributions Aim of the procedure: to invert these equations IAU Coll. 199 - Shanghai 2005

12. Test of the equations • Perfect agreement with Fall & Pei (1993) predictions • for the specific case considered in that work Constant dust-to-gas ratio Power law distribution of quasar luminosities IAU Coll. 199 - Shanghai 2005

13. The quasar magnitude distribution IAU Coll. 199 - Shanghai 2005

14. The distribution is modestly affected by the bias • Example of determination of • quasar magnitude distribution n(m) IAU Coll. 199 - Shanghai 2005

15. The procedure True distributions modelled using analytical expressions with free input parameters IAU Coll. 199 - Shanghai 2005

16. Implementation of the procedure • Empirical distributions • Built from N(HI) & N(ZnII) data in 1.8 ≤ z ≤ 3.0 • ~60 DLAs with N(HI) ; limiting magnitude ~19.5 • ~40 DLAs with N(ZnII) ; limiting magnitude ~19 • Quasar apparent magnitude distribution from SDSS • Functional form of the true distributions • N(HI) distribution • Power law f [N(HI)] = C x N(HI)-b • Metallicity distribution • Schechter function f (Z ) = C' x (Z/Z*)a e-Z/Z* • Extinction parameters • MW & SMC type dust • Extinction calculated in g' and r' bands of SDSS • 4800 and 6200 Å respectively IAU Coll. 199 - Shanghai 2005

17. Results Normalization factors of the distributions irrelevant for the determination of the bias effect IAU Coll. 199 - Shanghai 2005

18. Obscuration function f[N(Zn)] • Fraction of obscured DLAs as a function of N (ZnII) • Important output of the method • Natural explanation of the threshold proposed by Boissé et al. • Without any tuning of the dust parameters ! • Supports the existence of the obscuration bias IAU Coll. 199 - Shanghai 2005

19. Distribution of DLAs extinctionsat z ~ 2.3 Median extinction: 0.14 mag Median reddening ~ 0.05 mag IAU Coll. 199 - Shanghai 2005

20. Total obscuration fraction ~ 20 ~ 20% to 40% • At limiting magnitude ~ 19 the fraction of DLAs lost is ~ 30% to 50% IAU Coll. 199 - Shanghai 2005

21. Obscuration functions f[N(H)] and f(Z) • Obscuration function of N (HI) • might explain the lack of DLAs with N (HI) > 1022 cm-2 • Obscuration function of Z • number of DLAs with near-solar metallicity severely underestimated • Combined effect of the obscuration bias and of the DLA N (HI) definition threshold ! IAU Coll. 199 - Shanghai 2005

22. The f [N (HI)] distribution • A power law works well in the range sampled by observations • At higher N (HI) a much faster decline may well be present • Power law index similar to that measured in QSO absorbers of lower column density ±0.12 IAU Coll. 199 - Shanghai 2005

23. The metallicity distribution • Metallicity distribution significantly affected by the bias • Mean metallicity higher than canonical value -1.1 dex • Unbiased distribution may overlap that of Milky-Way disk stellar populations • Error bar still large to draw final conclusions • No discrepancy with CORALS data IAU Coll. 199 - Shanghai 2005

24. Distribution of DLAs extinctionsat z ~ 2.3 Median reddening: 0.05 mag Median extinction might decrease at high z since metallicity decreases with redshift and fFe may drop fastly at z ~ 3 IAU Coll. 199 - Shanghai 2005

25. Conclusions • Extinction relation for DLAs • Original expression for depletion as a function of metallicity • No need to know dust grain properties at very low metallicities • Method for recovering the unbiased distributions • f [N (HI)] and f (Z) from the observed ones • Application of the method to DLAs at z 2.3 • Observational surveys of N (HI) and Z in 1.8 ≤ z ≤ 3.0 • Results • Bias naturally explains the well-known N (ZnII) threshold • At limiting magnitude ≈ 19 fraction of missed DLAs ≈ 30/50% • Mean metallicity of DLAs might be as high as -0.4/-0.3 • But error bar still large (≈ ±0.25) • No serious discrepancies with CORALS results at the same z • Median reddening of DLAs ~ 0.05 mag • But may drop at z ~ 3 IAU Coll. 199 - Shanghai 2005

26. DLA contribution to the barionic density • We need to introduce an upper cutoff Cutoff at 1022 good agreement with Ellison et al. (2001)  = 2.6 (±1.2) x 10-3 IAU Coll. 199 - Shanghai 2005

27. Number density vs. magnitude relation • Ellison et al. (2001) find n(z) ~ 0.31±0.09 at z ~ 2.3 • From the plateau at faint magnitudes • By adopting a value of n(z) we can predict the number density vs. magnitude relation • Adopting n(z) ~ 0.4 at z ~ 2.3, still consistent with Ellison et al., our predictions are consistent with the CORALS data IAU Coll. 199 - Shanghai 2005