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

2. IAU Coll. 199 - Shanghai 2005 Motivation Understanding the origin of the empirical threshold log N(ZnII) ≤ 13.15 (Boissé et al. 1998) Recent DLA surveys confirm 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. ?

3. IAU Coll. 199 - Shanghai 2005 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 A  10 log N(Zn)

4. IAU Coll. 199 - Shanghai 2005 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

5. IAU Coll. 199 - Shanghai 2005 From the ISM to DLAs sources of variation of the relation 1.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 2.Dust depletions: yes But we know the behaviour of dust depletions in DLAs 3.Relative abundances: no 4.Redshift variation of the extinction in the observer's frame We can model the extinction curve

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

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

8. IAU Coll. 199 - Shanghai 2005 Original features of the relation 1.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 2.Dust grain parameters could be taken from grain models (not done yet)

9. IAU Coll. 199 - Shanghai 2005 Mathematical formulation based 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

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

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

12. IAU Coll. 199 - Shanghai 2005 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

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

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

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

16. IAU Coll. 199 - Shanghai 2005 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)  –Metallicity distribution Schechter function f (Z ) = C' x (Z/Z * )  e  Z/Z * Extinction parameters –MW & SMC type dust –Extinction calculated in g' and r' bands of SDSS 4800 and 6200 Å respectively

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

18. IAU Coll. 199 - Shanghai 2005 Obscuration function  [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

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

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

21. IAU Coll. 199 - Shanghai 2005 Obscuration function of N (HI) –might explain the lack of DLAs with N (HI) > 10 22 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 ! Obscuration functions  [N(H)] and  (Z)

22. IAU Coll. 199 - Shanghai 2005 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

23. IAU Coll. 199 - Shanghai 2005 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

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

25. IAU Coll. 199 - Shanghai 2005 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

26. IAU Coll. 199 - Shanghai 2005 DLA contribution to the barionic density We need to introduce an upper cutoff Cutoff at 10 22  good agreement with Ellison et al. (2001)  = 2.6 (±1.2) x 10 -3

27. IAU Coll. 199 - Shanghai 2005 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