A COSMIC VARIANCE COOKBOOK

By B. Moster, R. Somerville, J. Newman, Hans-Walter Rix. 2010

176 citations recorded by the source corpus.

Deep pencil beam surveys (<1 deg2) are of fundamental importance for studying the high-redshift universe. However, inferences about galaxy population properties (e.g., the abundance of objects) are in practice limited by “cosmic variance.” This is the uncertainty in observational estimates of the number density of galaxies arising from the underlying large-scale density fluctuations. This source of uncertainty can be significant, especially for surveys which cover only small areas and for massive high-redshift galaxies. Cosmic variance for a given galaxy population can be determined using predictions from cold dark matter theory and the galaxy bias. In this paper, we provide tools for experiment design and interpretation. For a given survey geometry, we present the cosmic variance of dark matter as a function of mean redshift and redshift bin size Δz. Using a halo occupation model to predict galaxy clustering, we derive the galaxy bias as a function of mean redshift for galaxy samples of a given stellar mass range. In the linear regime, the cosmic variance of these galaxy samples is the product of the galaxy bias and the dark matter cosmic variance. We present a simple recipe using a fitting function to compute cosmic variance as a function of the angular dimensions of the field, , Δz, and stellar mass m*. We also provide tabulated values and a software tool. The accuracy of the resulting cosmic variance estimates (δσv/σv) is shown to be better than 20%. We find that for GOODS at and with Δz = 0.5, the relative cosmic variance of galaxies with m*>1011 M☉ is ∼38%, while it is ∼27% for GEMS and ∼12% for COSMOS. For galaxies of m* ∼ 1010 M☉, the relative cosmic variance is ∼19% for GOODS, ∼13% for GEMS, and ∼6% for COSMOS. This implies that cosmic variance is a significant source of uncertainty at for small fields and massive galaxies, while for larger fields and intermediate mass galaxies, cosmic variance is less serious.

Subfields: Astronomy and Astrophysics, Electrical and Electronic Engineering, Instrumentation

View Paper: https://www.semanticscholar.org/paper/a29cf3205e854c2bcbe4b2922838d58d51c78360

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Citations in the corpus

A SUBSTANTIAL POPULATION OF MASSIVE QUIESCENT GALAXIES AT z ∼ 4 FROM ZFOURGE (2013, background): “Uncertainties are the quadratic sum of the Poisson uncertainty and variations due to large scale structure (Moster et al. 2011).”
The VIMOS Ultra-Deep Survey: ~10 000 galaxies with spectroscopic redshifts to study galaxy assembly at early epochs 2 < z ≃ 6 (2014, background): “As discussed in Moster et al. (2011), the fluctuations in number density of objects observed in deep surveys result from the cosmic variance in the distribution of galaxies in large scale structures.”
SUBMILLIMETER GALAXIES AS PROGENITORS OF COMPACT QUIESCENT GALAXIES (2014, background): “The error includes a contribution of cosmic variance of 12% (Moster et al. 2011).”
Mass assembly in quiescent and star-forming galaxies since z ≃ 4 from UltraVISTA (2013, methodology): “Moster et al. (2011) provide an estimate of the bias as a function of redshift and stellar mass.”
GOODS-ALMA: 1.1 mm galaxy survey (2018, background): “Based on Moster et al. (2011), the cosmic variance for our sources is ∼15 %, which does not significantly affect the calculation of the errors on our number counts.”
PRIMUS: CONSTRAINTS ON STAR FORMATION QUENCHING AND GALAXY MERGING, AND THE EVOLUTION OF THE STELLAR MASS FUNCTION FROM z = 0–1 (2013, background): “…the shape of the SMF over a large dynamic range of stellar mass, while simultaneously minimizing the effects of sample variance.13 For example, Moster et al. (2011) estimate a ∼ 25% uncertainty in the number density of ∼ 1011 M⊙ galaxies in a ∆z = 0.1 wide redshift bin at z = 0.5 due to…”
The mass evolution of the first galaxies: stellar mass functions and star formation rates at 4 < z < 7 in the CANDELS GOODS-South field (2014, methodology): “We also show using the error bars at the top of each panel the cosmic variance expected for galaxies of stellar mass ≈109.5 M , as predicted by the method outlined in Moster et al. (2011).”
Extragalactic science, cosmology, and Galactic archaeology with the Subaru Prime Focus Spectrograph (2012, background): “At 〈z〉 = 2.5 the cosmic variance uncertainty in the stellar mass function will be 0.02 dex, while at 〈z〉 = 3.5 it will be 0.02 dex and 0.08 dex for log M∗ = 10.25/ M⊙ and logM∗ = 11.25/ M⊙, respectively, according to Moster et al. (2011).”
THE EVOLUTION OF THE GALAXY REST-FRAME ULTRAVIOLET LUMINOSITY FUNCTION OVER THE FIRST TWO BILLION YEARS (2014, methodology): “…two techniques: a semi-empirical technique, combining the QUICKCV calculator provided by Newman & Davis (2002; using the updated version provided by Moster et al. 2011) with the recent clustering-based bias measurements from Barone-Nugent et al. (2014); and a semi-analytic technique, based on the…”
THE EVOLUTION OF THE GALAXY STELLAR MASS FUNCTION AT z = 4–8: A STEEPENING LOW-MASS-END SLOPE WITH INCREASING REDSHIFT (2015, methodology): “Figure 15 also shows calculations of cosmic variance using the recipe of Moster et al. (2011) with the tool getcv and the method of Newman & Davis (2002) with quickcv.”
Near infrared spectroscopy and star-formation histories of 3 ≤ z ≤ 4 quiescent galaxies (2018, background): “Following Moster et al. (2011), we estimate the amplitude of cosmic variance on these numbers to be 22%.”
Galactic star formation and accretion histories from matching galaxies to dark matter haloes (2012, background): “This fiducial value is motivated by high-resolution simulations of binary galaxy mergers (e.g. Nipoti et al. 2003; Naab & Burkert 2003; Moster et al. 2011).”
GALAXY STELLAR MASS FUNCTIONS FROM ZFOURGE/CANDELS: AN EXCESS OF LOW-MASS GALAXIES SINCE z = 2 AND THE RAPID BUILDUP OF QUIESCENT GALAXIES (2013, methodology): “We calculate cosmic variance as a function of redshift and mass using the getcv routine described in Moster et al. (2011).”
The COSMOS2015 galaxy stellar mass function . Thirteen billion years of stellar mass assembly in ten snapshots (2017, methodology): “Cosmic variance is estimated by means of a modified version of the “cosmic variance calculator” by Moster et al. (2011), for the geometry of our survey and the cosmology we assumed.”