[Paper Review] The VIMOS VLT Deep Survey: Evolution of the non-linear galaxy bias up to z=1.5

C. Marinoni, O. Le Fèvre+45 more|ArXiv.org|Jun 23, 2005

Galaxies: Formation, Evolution, Phenomena110 references58 citations

TL;DR

This paper presents the first measurement of the probability distribution function (PDF) of galaxy density fluctuations in the VIMOS VLT Deep Survey (VVDS), revealing that galaxy bias evolves with redshift up to z=1.5. It finds that bias increases with redshift beyond z≈0.8, is stronger for brighter and redder galaxies, and exhibits non-linear effects of 3–10% on scales >5 h⁻¹ Mpc, with the rms fluctuation σ₈ ≈ 0.94 ± 0.07 in the redshift range 0.7 < z < 1.5.

ABSTRACT

We present the first measurements of the Probability Distribution Function (PDF) of galaxy fluctuations in the VIMOS-VLT Deep Survey (VVDS) cone, covering 0.4x0.4 deg between 0.40.8; ii) the formation of bright galaxies is inhibited below a characteristic mass-overdensity threshold whose amplitude increases with redshift and luminosity; iii) the biasing function is non linear in all the redshift bins investigated with non-linear effects of the order of a few to 10% on scales &gt;5Mpc.

Motivation & Objective

• To measure the probability distribution function (PDF) of galaxy density fluctuations in the VIMOS VLT Deep Survey (VVDS) over a redshift range 0.4 < z < 1.5.
• To investigate how galaxy bias—defined as the relation between galaxy and matter overdensities—evolves with redshift, scale, luminosity, and color.
• To assess the validity of the linear bias model by quantifying non-linear and scale-dependent effects in the galaxy-mass clustering relation.
• To correct for survey geometry and selection effects using a Wiener filter to reconstruct the true underlying density field from flux-limited data.
• To compare observed galaxy PDFs with theoretical predictions to infer the redshift-, density-, and scale-dependent bias function b(z, δ, R) up to z=1.5.

Proposed method

• Reconstructing the 3D galaxy density field on a regular grid (0.5 h⁻¹ Mpc spacing) using a smoothing kernel defined in equation (5), applied to the VVDS first-epoch data.
• Applying a Wiener filter to correct for the survey's pencil-beam geometry and low signal-to-noise in sparse, high-redshift regions, using the filter response derived from the survey window function and power spectrum.
• Computing the Fourier transform of the survey window function using cylindrical geometry, with the window function expressed via spherical Bessel functions (eq. 53), to model the survey's spatial response.
• Evaluating the theoretical variance of the density field in redshift space by correcting for redshift-space distortions induced by peculiar velocities, as detailed in section 5.
• Using the GALICS semi-analytical simulation to test the effectiveness of the Wiener filter, comparing uncorrected and corrected PDFs of galaxy overdensities.
• Measuring the second and third moments of the PDF (variance σ₈ and skewness) to quantify non-linear bias effects and their evolution with cosmic time.

Experimental results

Research questions

• RQ1 How does the probability distribution function (PDF) of galaxy density contrasts evolve with redshift in the VVDS survey up to z=1.5?
• RQ2 To what extent is the galaxy bias non-linear, and how does it depend on scale, redshift, luminosity, and color?
• RQ3 Is the linear bias model sufficient to describe galaxy clustering, or are non-linear and scale-dependent corrections required?
• RQ4 How does the relative bias between red and blue galaxies evolve with cosmic time, and does it match local observations?
• RQ5 To what extent do survey geometry and flux-limited selection effects distort the true PDF of galaxy overdensities, and can they be corrected?

Key findings

• The PDF of galaxy density contrasts in the VVDS is an unbiased tracer of the underlying mass distribution up to z=1.5 on scales R=8 and 10 h⁻¹ Mpc.
• The rms fluctuation of the galaxy density field, σ₈, is constant at 0.94 ± 0.07 in redshift space for galaxies brighter than MB^c = -20 + 5 log h over 0.7 < z < 1.5.
• The skewness of the PDF increases with cosmic time, indicating a greater probability of underdense regions at z ≈ 0.7 compared to z ≈ 1.5.
• Galaxy bias increases with redshift, with marginal evolution up to z ≈ 0.8 and stronger evolution for z > 0.8, indicating non-linear evolution of clustering.
• Brighter galaxies are more strongly biased than fainter ones at all redshifts, and the luminosity dependence at z ≈ 0.8 is consistent with local observations.
• Red galaxies are systematically more biased than blue galaxies, with a relative bias b^rel ≈ 1.4 that remains constant in the redshift range 0.7 < z < 1.5, matching the local value.