Cosmic Variance and Its Effect on the Luminosity Function Determination in Deep High-z Surveys

By M. Trenti, M. Stiavelli. 2007

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We study cosmic variance in deep high-redshift surveys and its influence on the determination of the luminosity function for high-redshift galaxies. For several survey geometries relevant for Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) instruments, we characterize the distribution of the galaxy number counts. This is obtained by means of analytic estimates via the two-point correlation function in extended Press-Schechter theory, as well as by using synthetic catalogs extracted from N-body cosmological simulations of structure formation. We adopt a simple luminosity-dark halo mass relation to investigate the effects of environment on the fitting of the luminosity function. We show that in addition to variations of the normalization of the luminosity function, a steepening of its slope is also expected in underdense fields, similar to what is observed within voids in the local universe. Therefore, to avoid introducing artificial biases, caution must be taken when attempting to correct for field underdensity, such as in the case of the HST UDF i-dropout sample, which exhibits a deficit of bright counts with respect to the average counts in GOODS. A public version of the cosmic variance calculator based on the two-point correlation function integration is available on the Web at STScI.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/58bd08a06c0c25ffcd7bb7ca01144d016e8bbc67

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Citations in the corpus

The galaxy stellar mass function at 3.5 ≤z ≤ 7.5 in the CANDELS/UDS, GOODS-South, and HUDF fields (2015, methodology): “For the cosmic variance effect we do not rely on the rms computed only on A96, page 10 of 25 two fields, but we used the “cosmic variance” tool2 provided by Trenti & Stiavelli (2008) using as input parameters the number of galaxies observed in our two fields.”
The Dearth of z ∼ 10 Galaxies in All HST Legacy Fields—The Rapid Evolution of the Galaxy Population in the First 500 Myr (2017, methodology): “We include the effect of cosmic variance by adding a fractional uncertainty on the expected number counts per field which ranges from 35% in the CANDELS-Wide fields up to 65% in the HFF cluster fields (e.g. Trenti & Stiavelli 2008; Robertson et al. 2014).”
THE GRISM LENS-AMPLIFIED SURVEY FROM SPACE (GLASS). I. SURVEY OVERVIEW AND FIRST DATA RELEASE (2015, background): “Observing multiple clusters also minimizes cosmic variance (for >z 6 galaxies 10% for 10 clusters, compared to 30% for a single WFC3 field, Trenti & Stiavelli 2008).”
The bright end of the galaxy luminosity function at z≃7: before the onset of mass quenching? (2013, background): “026 (Trenti & Stiavelli 2008), assuming a Sheth-Tormen halo mass function, σ8 = 0.9 and a halo filling factor of 1.0.”
The 0.4 < z < 1.3 star formation history of the Universe as viewed in the far-infrared (2009, result): “This observed estimate of the cosmic variance is totally consistent with theoretical estimates of∼ 0.07 dex based on the area of our fields (see Trenti & Stiavelli 2008).”
NEWLY QUENCHED GALAXIES AS THE CAUSE FOR THE APPARENT EVOLUTION IN AVERAGE SIZE OF THE POPULATION (2013, result): “…consequently ∼84% (85,513/102,007), contributing a level of uncertainty to the absolute normalization of the size- and surface mass density ΣMASS-functions at each epoch computed herein comparable to that induced by cosmic variance (Trenti & Stiavelli 2008) in the COSMOS field (Oesch et al. 2010).”
The z ∼ 6 Luminosity Function Fainter than −15 mag from the Hubble Frontier Fields: The Impact of Magnification Uncertainties (2016, background): “…the field and HFF cluster results, as a result of large-scale structure variations (“cosmic variance”: Robertson et al. 2014; see also Somerville et al. 2004 and Trenti & Stiavelli 2008) and also small systematic errors in the estimates of the volume densities of galaxies in each of our probes.”
THE AVERAGE STAR FORMATION HISTORIES OF GALAXIES IN DARK MATTER HALOS FROM z = 0–8 (2012, background): “G1), and even at redshift 6, the Poisson and sample variance errors combined are on the order of 1% (Trenti & Stiavelli 2008) forΦ(1011.5M⊙).”
Early Results from GLASS-JWST. III. Galaxy Candidates at z ∼9–15 (2022, unknown): “See Trenti & Stiavelli (2008).”
The z = 9-10 galaxy population in the Hubble Frontier Fields and CLASH surveys: the z = 9 luminosity function and further evidence for a smooth decline in ultraviolet luminosity density at z≥ 8 (2016, background): “Notwithstanding the aforementioned concerns about uncertain lensing magnifications, an attraction of incorporating the CLASH imaging is that it provides a large number of widely separated pointings on the sky, potentially reducing the impact of cosmic variance (see Trenti & Stiavelli 2008).”
A COSMIC VARIANCE COOKBOOK (2010, background): “Trenti & Stiavelli (2008) presented estimates of cosmic variance for pencil beam geometries, again using the number density of the population to estimate the host halo mass and hence the bias.”
Quantifying cosmic variance (2010, methodology): “…with numerical simulations which encompass larger volumes such as the Millennium Simulation (e.g., Newman & Davis 2002; Somerville et al. 2004; Trenti & Stiavelli 2008; Moster et al. 2010); analytically using measurements of the 2 or 3-pt correlation functions (e.g., Driver et al. 2003);…”
THE BRIGHTEST OF REIONIZING GALAXIES SURVEY: CONSTRAINTS ON THE BRIGHT END OF THE z ∼ 8 LUMINOSITY FUNCTION (2012, methodology): “Additionally, given the random pointing nature of our pure-parallel HST program, the BoRG data set is distinct in that it is minimally affected by cosmic variance (Trenti & Stiavelli 2008).”
The dependence of star formation activity on environment and stellar mass at z∼ 1 from the HiZELS-Hα survey (2010, result): “…the faint-end slope of the Hα luminosity function, with the results showing that under-dense regions have Hα LFs with very steep faint-end slopes, while the highest densities have a shallow faint-end slope – this confirms analytic predictions such as those presented by Trenti & Stiavelli (2008).”
LOWER-LUMINOSITY GALAXIES COULD REIONIZE THE UNIVERSE: VERY STEEP FAINT-END SLOPES TO THE UV LUMINOSITY FUNCTIONS AT z ⩾ 5–8 FROM THE HUDF09 WFC3/IR OBSERVATIONS (2011, background): “The quoted uncertainties include the large-scale structure variance (20% at z ∼ 5-6: Trenti & Stiavelli 2008; Robertson 2010a).”
The Star Formation Rate Density and Dust Attenuation Evolution over 12 Gyr with the VVDS Surveys (2011, methodology): “We computed CV errors also with the recipe in Trenti & Stiavelli (2008), and we found lower estimates atz 1.2, going from∼ 20% atz = 0.1 down to∼ 12% at z = 1.1.”
The contribution of high-redshift galaxies to cosmic reionization: New results from deep WFC3 imaging of the Hubble Ultra Deep Field (2009, background): “The volume we probe is relatively small (∼ 104 Mpc3 comoving), and given the observed source counts, we estimate a cosmic variance of 35% assuming a pencil beam survey geometry with area 4.18 arcmin2 and a mean redshift of 7.0 with ∆z = 1.0 (Trenti & Stiavelli 2008).”
UV LUMINOSITY FUNCTIONS AT REDSHIFTS z ∼ 4 TO z ∼ 10: 10,000 GALAXIES FROM HST LEGACY FIELDS (2014, methodology): “Even in the case of perfect corrections, Trenti & Stiavelli (2008) showed through extensive simulations that the procedure Bouwens et al. (2006) used to cope with large-scale structure result in minor biases in the measured φ∗, 43 M∗, and α parameters (with M∗ too faint and α too steep).”
Galactic star formation and accretion histories from matching galaxies to dark matter haloes (2012, background): “The large volume of the sample leads to very low uncertainties due to cosmic variance (Trenti & Stiavelli 2008; Moster et al. 2011).”
CLASH: THREE STRONGLY LENSED IMAGES OF A CANDIDATE z ≈ 11 GALAXY (2012, background): “Subdominant uncertainties include cosmic variance in 17 independent fields (e.g., Trenti & Stiavelli 2008); uncertainties in the lens models (e.g., Bradač et al. 2009); and incompleteness in our ability to detect ∼26th magnitude galaxies (25.4 < F160W < 26.4) after masking out areas corresponding…”