Galaxy Bias Parameter Research Articles

High-resolution tomography for galaxy spectroscopic surveys with angular redshift fluctuations

In the context of next-generation spectroscopic galaxy surveys, new statistics of the distribution of matter are currently being developed. Among these, we investigated the angular redshift fluctuations (ARF), which probe the information contained in the projected redshift distribution of galaxies. Relying on the Fisher formalism, we show how ARF will provide complementary cosmological information compared to traditional angular galaxy clustering. We tested both the standard ΛCDM model and the wCDM extension. We find that the cosmological and galaxy bias parameters express different degeneracies when inferred from ARF or from angular galaxy clustering. As such, combining both observables breaks these degeneracies and greatly decreases the marginalised uncertainties by a factor of at least two on most parameters for the ΛCDM and wCDM models. We find that the ARF combined with angular galaxy clustering provide a great way to probe dark energy by increasing the figure of merit of the w0 − wa parameter set by a factor of more than ten compared to angular galaxy clustering alone. Finally, we compared ARF to the CMB lensing constraints on the galaxy bias parameters. We show that a joint analysis of ARF and angular galaxy clustering improves constraints by ∼40% on galaxy bias compared to a joint analysis of angular galaxy clustering and CMB lensing.

Perturbation theory for modeling galaxy bias: Validation with simulations of the Dark Energy Survey

We describe perturbation theory (PT) models of galaxy bias for applications to photometric galaxy surveys. We model the galaxy-galaxy and galaxy-matter correlation functions in configuration space and validate against measurements from mock catalogs designed for the Dark Energy Survey (DES). We find that an effective PT model with five galaxy bias parameters provides a good description of the 3D correlation functions above scales of 4 Mpc/$h$ and $z < 1$. Our tests show that at the projected precision of the DES-Year 3 analysis, two of the non-linear bias parameters can be fixed to their co-evolution values, and a third (the $k^2$ term for higher derivative bias) set to zero. The agreement is typically at the 2 percent level over scales of interest, which is the statistical uncertainty of our simulation measurements. To achieve this level of agreement, our {\it fiducial} model requires using the full non-linear matter power spectrum (rather than the 1-loop PT one). We also measure the relationship between the non-linear and linear bias parameters and compare them to their expected co-evolution values. We use these tests to motivate the galaxy bias model and scale cuts for the cosmological analysis of the Dark Energy Survey; our conclusions are generally applicable to all photometric surveys.

On the impact of galaxy bias uncertainties on primordial non-Gaussianity constraints

We study the impact that uncertainties on assumed relations between galaxy bias parameters have on constraints of the local PNG fNL parameter. We focus on the relation between the linear density galaxy bias b1 and local PNG bias bϕ in an idealized forecast setup with multitracer galaxy power spectrum and bispectrum data. We consider two parametrizations of galaxy bias: 1) one inspired by the universality relation where bϕ = 2δc(b1 − p) and p is a free parameter; and 2) another in which the product of bias parameters and fNL, like fNL bϕ, is directly fitted for. The constraints on the fNL−p plane are markedly bimodal, and both the central value and width of marginalized constraints on fNL depend sensitively on the priors on p. Assuming fixed p=1 in the constraints with a fiducial value of p=0.55 can bias the inferred fNL by 0.5σ to 1σ; priors Δ p ≈ 0.5 around this fiducial value are however sufficient in our setup to return unbiased constraints. In power spectrum analyses, parametrization 2, that makes no assumptions on bϕ, can distinguish fNL ≠ 0 with the same significance as parametrization 1 assuming perfect knowledge of bϕ (the value of fNL is however left unknown). A drawback of parametrization 2 is that the addition of the bispectrum information is not as beneficial as in parametrization 1. Our results motivate strongly the incorporation of mitigation strategies for bias uncertainties in PNG constraint analyses, as well as further theoretical studies on the relations between bias parameters to better inform those strategies.

Capturing non-Gaussianity of the large-scale structure with weighted skew-spectra

The forthcoming generation of wide-field galaxy surveys will probe larger volumes and galaxy densities, thus allowing for a much larger signal-to-noise ratio for higher-order clustering statistics, in particular the galaxy bispectrum. Extracting this information, however, is more challenging than using the power spectrum due to more complex theoretical modeling, as well as significant computational cost of evaluating the bispectrum signal and the error budget. To overcome these challenges, several proxy statistics have been proposed in the literature, which partially or fully capture the information in the bispectrum, while being computationally less expensive than the bispectrum. One such statistics are weighted skew-spectra, which are cross-spectra of the density field and appropriately weighted quadratic fields. Using Fisher forecasts, we show that the information in these skew-spectra is equivalent to that in the bispectrum for parameters that appear as amplitudes in the bispectrum model, such as galaxy bias parameters or the amplitude of primordial non-Gaussianity. We consider three shapes of the primordial bispectrum: local, equilateral and that due to massive particles with spin two during inflation. To obtain constraints that match those from a measurement of the full bispectrum, we find that it is crucial to account for the full covariance matrix of the skew-spectra.

Effects of redshift uncertainty on cross-correlations of CMB lensing and galaxy surveys

We explore the effects of incorporating redshift uncertainty into measurements of galaxy clustering and cross-correlations of galaxy positions and cosmic microwave background (CMB) lensing maps. We use a simple Gaussian model for a redshift distribution in a redshift bin with two parameters: the mean, $z_0$, and the width, $\sigma_z$. We vary these parameters, as well as a galaxy bias parameter, $b_{\text{g}}$, and a matter fluctuations parameter, $\sigma_8$, for each redshift bin, as well as the parameter $\Omega_{\text{m}}$, in a Fisher analysis across 12 redshift bins from $z=0-7$. We find that incorporating redshift uncertainties degrades constraints on $\sigma_8(z)$ in the Large Synoptic Survey Telescope (LSST)/CMB-S4 era by about a factor of 10 compared to the case of perfect redshift knowledge. In our fiducial analysis of LSST/CMB-S4 including redshift uncertainties, we project constraints on $\sigma_8(z)$ for $z<3$ of less than $5 \%$. Galaxy imaging surveys are expected to have priors on redshift parameters from photometric redshift algorithms and other methods. When adding priors with the expected precision for LSST redshift algorithms, the constraints on $\sigma_8(z)$ can be improved by a factor of 2-3 compared to the case of no prior information. We also find that `self-calibrated' constraints on the redshift parameters from just the autocorrelation and cross-correlation measurements (with no prior information) are competitive with photometric redshift techniques. In the LSST/CMB-S4 era, we find uncertainty on the redshift parameters ($z_0,\sigma_z$) to be below 0.004(1+z) at $z<1$. For all parameters, constraints improve significantly if smaller scales can be used. We also project constraints for nearer term survey combinations, Dark Energy Survey (DES)/SPT-SZ, DES/SPT-3G, and LSST/SPT-3G, and analyze how our constraints depend on a variety of parameter and model choices.

Baryon-CDM isocurvature galaxy bias with IllustrisTNG

We study the impact that baryon-CDM relative density perturbations δbc have on galaxy formation using cosmological simulations with the IllustrisTNG model. These isocurvature (non-adiabatic) perturbations can be induced primordially, if multiple fields are present during inflation, and are generated before baryon-photon decoupling when baryons did not comove with CDM. The presence of long-wavelength δbc perturbations in our simulations is mimicked by modifying the ratios of the cosmic densities of baryons Ωb and CDM Ωc, at fixed total matter density Ωm. We measure the corresponding galaxy bias parameter bδbc as the response of galaxy abundances to δbc. When selecting by total host halo mass, bδbc is negative and it decreases with mass and redshift. Stellar-mass selected simulated galaxies show a weaker or even the opposite trend because of the competing effects of δbc on the halo mass function and stellar-to-halo-mass relations. We show that simple modeling of the latter two effects describes bδbc for stellar-mass-selected objects well. We find bδbc =0.6 for M* = 1011 M⊙/h and z=0.5, which is representative of BOSS DR12 galaxies. For δbc modes generated by baryon-photon interactions, we estimate the impact on the DR12 power spectrum to be below 1%, and shifts on inferred distance and growth rate parameters should not exceed 0.1%.

Bias loop corrections to the galaxy bispectrum

Combination of the power spectrum and bispectrum is a powerful way of breaking degeneracies between galaxy bias and cosmological parameters, enabling us to maximize the constraining power from galaxy surveys. Recent cosmological constraints treat the power spectrum and bispectrum on an uneven footing: they include one-loop bias corrections for the power spectrum but not the bispectrum. To bridge this gap, we develop the galaxy bias description up to fourth order in perturbation theory, conveniently expressed through a basis of Galilean invariants that clearly split contributions that are local and nonlocal in the second derivatives of the linear gravitational potential. In addition, we consider relevant contributions from short-range nonlocality (higher-derivative terms), stress-tensor corrections and stochasticity. To sidestep the usual renormalization of bias parameters that complicates predictions beyond leading order, we recast the bias expansion in terms of multipoint propagators, which take a simple form in our split-basis with loop corrections depending only on bias parameters corresponding to nonlocal operators. We show how to take advantage of Galilean invariance to compute the time evolution of bias and present results for the fourth-order parameters for the first time. We also discuss the possibilities of reducing the bias parameter space by using the evolution of bias and exploiting degeneracies between various bias contributions in the large-scale limit. Our baseline model allows to verify these simplifications for any application to large-scale structure data sets.

Neutrino mass and dark energy constraints from redshift-space distortions

Cosmology in the near future promises a measurement of the sum of neutrino masses ∑ mν, a fundamental Standard Model parameter, as well as substantially-improved constraints on the dark energy. We use the shape of the BOSS redshift-space galaxy power spectrum, in combination with CMB and supernova data, to constrain the neutrino masses and the dark energy. Essential to this calculation are several recent advances in non-linear cosmological perturbation theory, including fast Fourier transform methods, redshift space distortions, and scale-dependent growth. Our 95% confidence upper bound ∑ mν < 180 meV degrades substantially to ∑ mν < 540 meV when the dark energy equation of state and its first derivative are also allowed to vary, representing a significant challenge to current constraints. We also study the impact of additional galaxy bias parameters, finding that a greater allowed range of scale-dependent bias only slightly shifts the preferred ∑ mν, weakens its upper bound by ≈ 20%, and has a negligible effect on the other cosmological parameters.

The Aemulus Project. III. Emulation of the Galaxy Correlation Function

Abstract Using the N-body simulations of the Aemulus Project, we construct an emulator for the nonlinear clustering of galaxies in real and redshift space. We construct our model of galaxy bias using the halo occupation framework, accounting for possible velocity bias. The model includes 15 parameters, including both cosmological and galaxy bias parameters. We demonstrate that our emulator achieves ∼1% precision at the scales of interest, 0.1 h −1 Mpc &lt; r &lt; 10 h −1 Mpc, and recovers the true cosmology when tested against independent simulations. Our primary parameters of interest are related to the growth rate of structure, f, and its degenerate combination, fσ 8. Using this emulator, we show that the constraining power on these parameters monotonically increases as smaller scales are included in the analysis, all the way down to 0.1 h −1 Mpc. For a BOSS-like survey, the constraints on fσ 8 from r &lt; 30 h −1 Mpc scales alone are nearly a factor of two tighter than those from the fiducial BOSS analysis of redshift-space clustering using perturbation theory at larger scales. The combination of real- and redshift-space clustering allows us to break the degeneracy between f and σ 8, yielding an 11% constraint on f alone for a BOSS-like analysis. The current Aemulus simulations limit this model to surveys of massive galaxies. Future simulations will allow this framework to be extended to all galaxy target types, including emission-line galaxies.

Robustness of the covariance matrix for galaxy clustering measurements

We present a study on the robustness of the covariance matrix estimation for galaxy clustering measurements depending on the cosmological parameters and galaxy bias. To this end, we have produced 9000 galaxy mock catalogues relying on the effective Zel'dovich approximation implemented in the EZmocks computer code, using different input cosmological models and bias parameters. The reference catalogue has also been produced with this code making our study insensitive to the approximation at least on a relative-qualitative level. Our findings indicate that the covariance matrix is insensitive to the input power spectrum (including $\sigma_8$), as long as the 2- and 3-point galaxy clustering measurements agree with the given data. In fact, the covariance matrix shows a bias at small scales ($r\lesssim40 h^{-1}$Mpc) when the chosen galaxy bias parameters yield a 3-point statistics, which is not compatible with the reference one within the error bars, even though the 2-point statistics agree within 1%. Nevertheless, the error becomes negligible at large scales making the covariance matrix still reliable for data analysis using only measurements in that regime (e.g., measuring baryon acoustic oscillations). High precision in cosmological parameter estimation is expected for covariance matrices extracted from mock galaxy catalogues which take accurately into account both the 2- and the 3- point statistics. This is independent of whether this is achieved by using the right cosmology and galaxy bias (which are not a priori known) or just any combination of both fitting the net observed galaxy clustering.

TOWARD A TOMOGRAPHIC ANALYSIS OF THE CROSS-CORRELATION BETWEEN PLANCK CMB LENSING AND H-ATLAS GALAXIES

ABSTRACT We present an improved and extended analysis of the cross-correlation between the map of the cosmic microwave background (CMB) lensing potential derived from the Planck mission data and the high-redshift galaxies detected by the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) in the photometric redshift range . We compare the results based on the 2013 and 2015 Planck datasets, and investigate the impact of different selections of the H-ATLAS galaxy samples. Significant improvements over our previous analysis have been achieved thanks to the higher signal-to-noise ratio of the new CMB lensing map recently released by the Planck collaboration. The effective galaxy bias parameter, b, for the full galaxy sample, derived from a joint analysis of the cross-power spectrum and of the galaxy auto-power spectrum is found to be . Furthermore, a first tomographic analysis of the cross-correlation signal is implemented by splitting the galaxy sample into two redshift intervals: and . A statistically significant signal was found for both bins, indicating a substantial increase with redshift of the bias parameter: for the lower and for the higher redshift bin. Consistent with our previous analysis, we find that the amplitude of the cross-correlation signal is a factor of higher than expected from the standard ΛCDM model for the assumed redshift distribution. The robustness of our results against possible systematic effects has been extensively discussed, although the tension is mitigated by passing from 4 to 3σ.

The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions atz∼ 1.4

AbstractWe measure the redshift-space correlation function from a spectroscopic sample of 2783 emission line galaxies from the FastSound survey. The survey, which uses the Subaru Telescope and covers a redshift range of 1.19 &amp;lt; z &amp;lt; 1.55, is the first cosmological study at such high redshifts. We detect clear anisotropy due to redshift-space distortions (RSD) both in the correlation function as a function of separations parallel and perpendicular to the line of sight and its quadrupole moment. RSD has been extensively used to test general relativity on cosmological scales at z &amp;lt; 1. Adopting a ΛCDM cosmology with the fixed expansion history and no velocity dispersion (σv = 0), and using the RSD measurements on scales above 8 h−1 Mpc, we obtain the first constraint on the growth rate at the redshift, f (z)σ8(z) = 0.482 ± 0.116 at z ∼ 1.4 after marginalizing over the galaxy bias parameter b(z)σ8(z). This corresponds to 4.2 σ detection of RSD. Our constraint is consistent with the prediction of general relativity fσ8 ∼ 0.392 within the 1 σ confidence level. When we allow σv to vary and marginalize over it, the growth rate constraint becomes $f\sigma _8=0.494^{+0.126}_{-0.120}$. We also demonstrate that by combining with the low-z constraints on fσ8, high-z galaxy surveys like the FastSound can be useful to distinguish modified gravity models without relying on CMB anisotropy experiments.

Joint constraints on galaxy bias and σ8 through the N-pdf of the galaxy number density

We present a full description of the N-probability density function of the galaxy number density fluctuations. This N-pdf is given in terms, on the one hand, of the cold dark matter correlations and, on the other hand, of the galaxy bias parameter. The method relies on the assumption commonly adopted that the dark matter density fluctuations follow a local non-linear transformation of the initial energy density perturbations. The N-pdf of the galaxy number density fluctuations allows for an optimal estimation of the bias parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if there exists any a priori information on the bias parameter), and of those parameters defining the dark matter correlations, in particular its amplitude (σ8). It also provides the proper framework to perform model selection between two competitive hypotheses. The parameters estimation capabilities of the N-pdf are proved by SDSS-like simulations (both, ideal log-normal simulations and mocks obtained from Las Damas simulations), showing that our estimator is unbiased. We apply our formalism to the 7th release of the SDSS main sample (for a volume-limited subset with absolute magnitudes Mr ⩽ −20). We obtain b̂ = 1.193 ± 0.074 and σ̂8 = 0.862 ± 0.080, for galaxy number density fluctuations in cells of the size of 30h−1Mpc. Different model selection criteria show that galaxy biasing is clearly favoured.

The VIMOS Public Extragalactic Redshift Survey

Aims. Using the VIMOS Public Extragalactic Redshift Survey (VIPERS) we aim to jointly estimate the key parameters that describe the galaxy density field and its spatial correlations in redshift space. Methods. We use the Bayesian formalism to jointly reconstruct the redshift-space galaxy density field, power spectrum, galaxy bias and galaxy luminosity function given the observations and survey selection function. The high-dimensional posterior distribution is explored using the Wiener filter within a Gibbs sampler. We validate the analysis using simulated catalogues and apply it to VIPERS data taking into consideration the inhomogeneous selection function. Results. We present joint constraints on the anisotropic power spectrum as well as the bias and number density of red and blue galaxy classes in luminosity and redshift bins as well as the measurement covariances of these quantities. We find that the inferred galaxy bias and number density parameters are strongly correlated although these are only weakly correlated with the galaxy power spectrum. The power spectrum and redshift-space distortion parameters are in agreement with previous VIPERS results with the value of the growth rate $f\sigma_8 = 0.38$ with 18% uncertainty at redshift 0.7.

Position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 10 CMASS sample

We report on the first measurement of the three-point function with the position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 CMASS sample. This new observable measures the correlation between two-point functions of galaxy pairs within different subvolumes, ξ̂(ř,řL), where řL is the location of a subvolume, and the corresponding mean overdensities, δ̄(řL). This correlation, which we call the “integrated three-point function”, iζ(r)≡⟨ξ̂(ř,řL)δ̄(řL)⟩, measures a three-point function of two short- and one long-wavelength modes, and is generated by nonlinear gravitational evolution and possibly also by the physics of inflation. The iζ(r) measured from the BOSS data lies within the scatter of those from the mock galaxy catalogs in redshift space, yielding a ten-percent-level determination of the amplitude of iζ(r). The tree-level perturbation theory in redshift space predicts how this amplitude depends on the linear and quadratic nonlinear galaxy bias parameters (b1 and b2), as well as on the amplitude and linear growth rate of matter fluctuations (σ8 and f). Combining iζ(r) with the constraints on b1σ8 and fσ8 from the global two-point correlation function and that on σ8 from the weak lensing signal of BOSS galaxies, we measure b2=0.41±0.41 (68% C.L.) assuming standard perturbation theory at the tree level and the local bias model.

CROSS-CORRELATION BETWEEN THE CMB LENSING POTENTIAL MEASURED BYPLANCKAND HIGH-zSUBMILLIMETER GALAXIES DETECTED BY THEHERSCHEL-ATLAS SURVEY

We present the first measurement of the correlation between the map of the cosmic microwave background (CMB) lensing potential derived from the \emph{Planck} nominal mission data and $z\gtrsim 1.5$ galaxies detected by the \emph{Herschel}-ATLAS (H-ATLAS) survey covering about $600\,\hbox{deg}^2$, i.e. about 1.4\% of the sky. We reject the hypothesis that there is no correlation between CMB lensing and galaxy detection at a $20\,\sigma$ significance, checking the result by performing a number of null tests. The significance of the detection of the theoretically expected cross-correlation signal is found to be $10\,\sigma$. The galaxy bias parameter, $b$, derived from a joint analysis of the cross-power spectrum and of the auto-power spectrum of the galaxy density contrast is found to be $b=2.80^{+0.12}_{-0.11}$, consistent with earlier estimates for H-ATLAS galaxies at similar redshifts. On the other hand, the amplitude of the cross-correlation is found to be a factor $1.62 \pm 0.16$ higher than expected from the standard model and also found by cross-correlation analyses with other tracers of the large-scale structure. The enhancement due to lensing magnification can account for only a fraction of the excess cross-correlation signal. We suggest that part of it may be due to an incomplete removal of the contamination of the CIB, that includes the H-ATLAS sources we are cross-correlating with. In any case, the highly significant detection reported here using a catalog covering only 1.4\% of the sky demonstrates the potential of CMB lensing correlations with submillimeter surveys.

The cosmological impact of intrinsic alignment model choice for cosmic shear

We consider the effect of galaxy intrinsic alignments (IAs) on dark energy constraints from weak gravitational lensing. We summarise the latest version of the linear alignment model of IAs, following the brief note of Hirata & Seljak (2010) and further interpretation in Laszlo et al. (2011). We show the cosmological bias on the dark energy equation of state parameters w0 and wa that would occur if IAs were ignored. We find that w0 and wa are both catastrophically biased, by an absolute value of just greater than unity under the Fisher matrix approximation. This contrasts with a bias several times larger for the earlier IA implementation. Therefore there is no doubt that IAs must be taken into account for future Stage III experiments and beyond. We use a flexible grid of IA and galaxy bias parameters as used in previous work, and investigate what would happen if the universe used the latest IA model, but we assumed the earlier version. We find that despite the large difference between the two IA models, the grid flexibility is sufficient to remove cosmological bias and recover the correct dark energy equation of state. In an appendix, we compare observed shear power spectra to those from a popular previous implementation and explain the differences.

The 6dF Galaxy Survey: z≈ 0 measurements of the growth rate and σ8

We present a detailed analysis of redshift-space distortions in the two-point correlation function of the 6dF Galaxy Survey (6dFGS). The K-band selected sub-sample which we employ in this study contains 81971 galaxies distributed over 17000deg^2 with an effective redshift z = 0.067. By modelling the 2D galaxy correlation function, xi(r_p,pi), we measure the parameter combination f(z)sigma_8(z) = 0.423 +/- 0.055. Alternatively, by assuming standard gravity we can break the degeneracy between sigma_8 and the galaxy bias parameter, b. Combining our data with the Hubble constant prior from Riess et al (2011), we measure sigma_8 = 0.76 +/- 0.11 and Omega_m = 0.250 +/- 0.022, consistent with constraints from other galaxy surveys and the Cosmic Microwave Background data from WMAP7. Combining our measurement of fsigma_8 with WMAP7 allows us to test the relationship between matter and gravity on cosmic scales by constraining the growth index of density fluctuations, gamma. Using only 6dFGS and WMAP7 data we find gamma = 0.547 +/- 0.088, consistent with the prediction of General Relativity. We note that because of the low effective redshift of 6dFGS our measurement of the growth rate is independent of the fiducial cosmological model (Alcock-Paczynski effect). We also show that our conclusions are not sensitive to the model adopted for non-linear redshift-space distortions. Using a Fisher matrix analysis we report predictions for constraints on fsigma_8 for the WALLABY survey and the proposed TAIPAN survey. The WALLABY survey will be able to measure fsigma_8 with a precision of 4-10%, depending on the modelling of non-linear structure formation. This is comparable to the predicted precision for the best redshift bins of the Baryon Oscillation Spectroscopic Survey (BOSS), demonstrating that low-redshift surveys have a significant role to play in future tests of dark energy and modified gravity.

Tidal alignments as a contaminant of the galaxy bispectrum

If the orientations of galaxies are correlated with large-scale structure, then anisotropic selection effects such as preferential selection of face-on disc galaxies can contaminate large scale structure observables. Here we consider the effect on the galaxy bispectrum, which has attracted interest as a way to break the degeneracy between galaxy bias and the amplitude of matter fluctuations sigma_8. We consider two models of intrinsic galaxy alignments: one where the probability distribution for the galaxy's orientation contains a term linear in the local tidal field, appropriate for elliptical galaxies; and one with a term quadratic in the local tidal field, which may be applicable to disc galaxies. We compute the correction to the redshift-space bispectrum in the quasilinear regime, and then focus on its effects on parameter constraints from the transverse bispectrum, i.e. using triangles in the plane of the sky. We show that in the linear alignment model, intrinsic alignments result in an error in the galaxy bias parameters, but do not affect the inferred value of sigma_8. In contrast, the quadratic alignment model results in a systematic error in both the bias parameters and sigma_8. However, the quadratic alignment effect has a unique configuration dependence that should enable it to be removed in upcoming surveys.

Statistical analysis of galaxy surveys — II. The three-point galaxy correlation function measured from the 2dFGRS

We present new results for the 3-point correlation function, �, measured as a function of scale, luminosity and colour from the final version of the two-degree field galaxy redshift survey (2dFGRS). The reduced three point correlation function, Q3 � �/� 2 , is estimated for different triangle shapes and sizes, employing a full covariance analysis. The form of Q3 is consistent with the expectations for the �-cold dark matter model, confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on Gaussian primordial fluctuations. However, we find a clear offset in amplitude between Q3 for galaxies and the predictions for the dark matter. We are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9-� level. On weakly non-linear scales, we can interpret our results in terms of galaxy bias parameters. We find a linear bias term that is consistent with unity, b1 = 0.93 +0.10 0.08 and a quadratic bias c2 = b2/b1 = 0.34 +0.11 0.08 . This is the first significant detection of a non-zero quadratic bias, indicating a small but important non-gravitational contribution to the three point function. Our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations, so we can combine this with the measurement of the power spectrum of 2dFGRS galaxies to constrain the amplitude of matter fluctuations. We find that the rms linear theory variance in spheres of radius 8h 1 Mpc is �8 = 0.88 +0.12 0.10, providing an independent confirmation of values derived from other techniques. On non-linear scales, where � > 1, we find that Q3 has a strong dependence on scale, colour and luminosity.