Cosmic Variance and Luminosity Function Fitting

1. Cosmic Variance and Luminosity Function Fitting Michele Trenti August 8, 2007 In collaboration with Massimo Stiavelli and the UDF05 team

2. Outline • Large scale structure and galaxy number counts • Cosmic variance and luminosity function fitting: • Number countsuncertainty • M* and a dependence on environment • Quantifying luminosity function evolution STScI Summer PostDoc Talks Michele Trenti

3. Context • Ultimate goal is to get a reliable measure of the galaxy luminosity function (LF) and to quantify its error • A measure has little meaning without proper error bars, both random and systematic • LF fundamental measure for: • Global star formation history • Galaxy assembly process • At z6: Reionization history of the Universe STScI Summer PostDoc Talks Michele Trenti

4. High z galaxies • Hundreds of galaxies have been detected in recent years at z>4: • HDF • GOODS • UDF, UDF05 • Subaru deep fields • …. STScI Summer PostDoc Talks Michele Trenti

5. Field to field variations • Cosmic volume probed by these high z surveys is however limited • typically tens to hundreds of arcmin2 • tiny fraction of the sky! • How does the result depend on the pointing chosen, that is what is the distribution of the expected number counts of galaxies? STScI Summer PostDoc Talks Michele Trenti

6. Field to field variations • Universe is not homogenous on small scales! • E.g.: UDF V or i dropouts volume is 104 (Mpc/h)3 • This volume contains only  1015 M/h • Large Scale Structure is important • Significant uncertainty in the number counts due to galaxy clustering SDSS Cosmic Web STScI Summer PostDoc Talks Michele Trenti

7. Cosmic variance Simulated number counts distribution for i-dropouts in the UDF • Number counts distribution in Galaxy surveys does not follow Poisson • We define cosmic variance the excess relative variance over Poisson noise: Trenti & Stiavelli (2007) STScI Summer PostDoc Talks Michele Trenti

8. Cosmic variance and the total error budget • The total 1s fractional error (vr) in the number counts is given by combining: • Cosmic variance (intrinsic property of galaxy population) • Poisson noise associated to the observed counts (includes observational incompletness): STScI Summer PostDoc Talks Michele Trenti

9. Estimating cosmic variance: Analytical approach • The cosmic variance is related to the two point correlation function x(r) of the sample (e.g. Somerville et al. 2004): • Depends on clustering properties (x(r)) and on the geometry of the survey (volume integral) STScI Summer PostDoc Talks Michele Trenti

10. Cosmic variance and survey geometry Relative 1s uncertainty in number counts • Spherical volumes have the largest variations in number counts: • The volume may easily sit on top of overdensities/ underdensities • Pencil beam surveys for LBG galaxies probe a variety of environments: • Dz=1  320 Mpc/h at z=6.1 • Uncertainty is reduced ~Cubic volume Pencil beam Trenti & Stiavelli (2007) STScI Summer PostDoc Talks Michele Trenti

11. Estimating cosmic variance: Cosmologic simulations • Analytical approach inexpensive but limited to the variance of the counts distribution • Counts may have strong skew and non gaussian tails • Cosmological simulations computationally expensive but provide synthetic catalogs • Full probability distribution of counts • In addition: allow us to explore fitting of the LF from the mock catalogs STScI Summer PostDoc Talks Michele Trenti

12. Mock Catalogs from Cosmological Simulations • Cosmological simulation with 300 million particles, 128Mpc/h box • ≈1010 M/h halos resolved • Dark matter halos populated using HOD models • Luminosity-Mass relation based on Cooray (2005) • Pencil beam traced through the box • Redshift evolution taken into account (snapshots spaced by Dz=0.125) STScI Summer PostDoc Talks Michele Trenti

13. Mock Catalogs from Cosmological Simulations V dropouts counts in two combined UDF05 fields • For Lyman Break galaxies selection Dz≈1 • pencil beam is 300Mpc/h  it wraps around the box, spaced by >15Mpc/h • negligible correlation (rlin<0.01) introduced in the counts • Different HOD models give similar p(N) at fixed <N> • minor changes in average bias of galaxies even changing detection probability by factor 2 Adapted from Oesch et al. (2007) STScI Summer PostDoc Talks Michele Trenti

14. Total fractional error for V and i-dropouts, ACS field of view Trenti & Stiavelli (2007) Typical deep field has >25% uncertainty in number counts, 2.5-3 times larger than Poisson STScI Summer PostDoc Talks Michele Trenti

15. Total fractional counts error for i-dropouts in GOODS • GOODS N+S fields have ~30 times UDF area, but not as deep • Detected objects are more luminous  more massive • more clustered, higher bias • Cosmic variance still high despite larger area! GOODS N+S fields, ~ 320 arcmin2 ~18% uncertainty! Trenti & Stiavelli (2007) STScI Summer PostDoc Talks Michele Trenti

16. Total fractional error for z and J-dropouts • Significant total fractional error • vr> 50% • Independent fields beat cosmic variance: • 6 independent deep NICMOS fields (already existing) better than one deep WFC3 field, despite smaller area! Trenti & Stiavelli (2007) STScI Summer PostDoc Talks Michele Trenti

17. Luminosity function and environment • Does the luminosity function depend on the environment? • First order dependence in normalization: • f* proportional to the galaxy number counts • Does the shape of the LF (that is a and M*) also depend on number counts? • Fundamental question to properly address claims of evolution of the LF shape over redshift f Faint end: power law, slope a Bright end: exponential L* (Typical luminosity) L STScI Summer PostDoc Talks Michele Trenti

18. Shape of the luminosity function and LSS from our mock catalogs LF from synthetic V-drop catalogs, 1 ACS field, UDF depth from Trenti & Stiavelli (2007) M* is fainter in underdense fields (consistent with the local universe, see SDSS LF in voids – Hoyle et al. 2005) a independent of environment STScI Summer PostDoc Talks Michele Trenti

19. LF fitting: M*-a degeneracy and binning • LFfrom synthetic V-drop catalogs, 1 ACS field, UDF depth • Well known degeneracy between a and M* is present • Smaller uncertainty when Maximum Likelihood is used: binning leads to information loss BINNED UNBINNED STScI Summer PostDoc Talks Michele Trenti

20. Combining fields: luminosity function fitting • Combining independent fields helps beating cosmic variance • Fields at different depths provide optimal use of telescope time: • large area to constraint bright end of LF • ultradeep field to constraint faint end of FL • for example: combination of GOODS+UDF • But… • Is the resulting LF sensitive to fitting method used? • Is there an optimal method to derive the LF and to “correct for” cosmic variance (e.g. see Bouwens et al. 2006)? STScI Summer PostDoc Talks Michele Trenti

21. An attempt to correct for LSS • Bouwens et al. (2006) assume that Large Scale Structure can be measured from bright detections • Correction on normalization of deep fields for i-dropouts based on GOODS counts: • Degradation of deeper fields to GOODS depth • Re-Normalization of the faint end of the LF based on the ratio of degraded counts over expected counts from GOODS. • Is this justified? • We need to investigate the faint-bright counts relation! • Note however, that as of July (Bouwens et al. 2007), they no longer consider this method the preferred choice for LF fitting. STScI Summer PostDoc Talks Michele Trenti

22. Bright-Faint counts relation Faint (UDF) – Bright (GOODS) i-drop counts, uncorrelated Poisson World • Assume a linear faint-bright counts relation: • <Nft> = h +k <Nbr> • In a uncorrelated world: • k=1, h0 • When <Nft> >> <Nbr> field to field variations in faint counts cannot be corrected • no information from Nbr k=1 Trenti & Stiavelli (2007) STScI Summer PostDoc Talks Michele Trenti

23. Bright-Faint counts relation Faint (UDF) – Bright (GOODS) i-drop counts, LSS Mock Catalog • LSS correlates bright and faint counts, but not completely • h 0, k > 1 • Bouwens et al. 2006 assume total correlation, that is h= 0 • Artificial steepening of the faint end in underdense fields! LSS h=0 STScI Summer PostDoc Talks Michele Trenti

24. LF fitting using LSS renormalization • Significant artificial steepening introduced in presence of a deficit of brigh objects in the deep field STScI Summer PostDoc Talks Michele Trenti

25. LF fitting using Maximum Likelihood • Normalization is left free between fields at different depths • Unbiased measure of the LF slope • M* has residual dependence on counts (but physical origin) STScI Summer PostDoc Talks Michele Trenti

26. Conclusions I • Cosmic variance introduces significant uncertainty in galaxy number counts in deep field surveys • Dominant over Poisson noise for typical deep surveys: • UDF and GOODS have similar cosmic variance at their respective depths • GOODS area larger but UDF deeper, so bias is smaller • Sparse coverage beats cosmic variance • but contiguous fields are useful beyond LF determination (e.g. weak lensing) STScI Summer PostDoc Talks Michele Trenti

27. Conclusions II • Cosmic variance introduces uncertainty in the shape of the luminosity function • M* measured in underdense LBG fields is fainter (like in local voids) • Degeneracy between M* and a • Systematic errors are important: hard to assess changes in LF of Da < 0.15 (68% cl) • Naïve “renormalization” for large scale structure may introduce significant bias • Unbinned data analysis with free f* optimal for recovering information STScI Summer PostDoc Talks Michele Trenti