Statistics of the fractional polarisation of extragalactic dusty sources in Planck HFI maps

We estimate the average fractional polarisation at 143, 217 and 353 GHz of a sample of 4697 extragalactic dusty sources by applying stacking technique. The sample is selected from the second version of the Planck Catalogue of Compact Sources at 857 GHz, avoiding the region inside the Planck Galactic mask (fsky ~ 60 per cent). We recover values for the mean fractional polarisation at 217 and 353 GHz of (3.10 \pm 0.75) per cent and (3.65 \pm 0.66) per cent, respectively, whereas at 143 GHz we give a tentative value of (3.52 \pm 2.48) per cent. We discuss the possible origin of the measured polarisation, comparing our new estimates with those previously obtained from a sample of radio sources. We test different distribution functions and we conclude that the fractional polarisation of dusty sources is well described by a log-normal distribution, as determined in the radio band studies. For this distribution we estimate {\mu}_{217GHz} = 0.3 \pm 0.5 (that would correspond to a median fractional polarisation of {\Pi}_{med} = (1.3 \pm 0.7) per cent) and {\mu}_{353GHz} = 0.7 \pm 0.4 ({\Pi}_{med} = (2.0 \pm 0.8) per cent), {\sigma}_{217GHz} = 1.3 \pm 0.2 and {\sigma}_{353GHz} = 1.1 \pm 0.2. With these values we estimate the source number counts in polarisation and the contribution given by these sources to the CMB B-mode angular power spectrum at 217, 353, 600 and 800 GHz. We conclude that extragalactic dusty sources might be an important contaminant for the primordial B-mode at frequencies > 217 GHz.Comment: arXiv admin note: text overlap with arXiv:1703.0995

A direct and robust method to observationally constrain the halo mass function via the submillimeter magnification bias: Proof of concept

Aims. The main purpose of this work is to provide a proof-of-concept method to derive tabulated observational constraints on the halo mass function (HMF) by studying the magnification bias effect on high-redshift submillimeter galaxies. Under the assumption of universality, we parametrize the HMF according to two traditional models, namely the Sheth and Tormen (ST) and Tinker fits, derive posterior distributions for their parameters, and assess their performance in explaining the measured data within the \u39b cold dark matter model. We also study the potential influence of the halo occupation distribution (HOD) parameters in this analysis and discuss two aspects regarding the HMF parametrization, namely its normalization and the possibility of allowing negative values for the parameters. Methods. We measure the cross-correlation function between a foreground sample of GAMA galaxies with spectroscopic redshifts in the range 0.2 < z < 0.8 and a background sample of H-ATLAS galaxies with photometric redshifts in the range 1.2 < z < 4.0 and carry out a Markov chain Monte Carlo algorithm in the context of Bayesian inference to check this observable against its mathematical prediction within the halo model formalism, which depends on both the HOD and HMF parameters. Results. Under the assumption that all HMF parameters are positive, the ST fit only seems to fully explain the measurements by forcing the mean number of satellite galaxies in a halo to increase substantially from its prior mean value. The Tinker fit, on the other hand, provides a robust description of the data without relevant changes in the HOD parameters, but with some dependence on the prior range of two of its parameters. When the normalization condition for the HMF is dropped and we allow negative values of the p1 parameter in the ST fit, all the involved parameters are better determined, unlike the previous models, thus deriving the most general HMF constraints. While all the aforementioned cases are in agreement with the traditional fits within the uncertainties, the last one hints at a slightly higher number of halos at intermediate and high masses, raising the important point of the allowed parameter range

Overdensity of SMGs in fields containing z ∼ 0.3 galaxies: magnification bias and the implications for studies of galaxy evolution

We report a remarkable overdensity of high-redshift submillimetre galaxies (SMG), 4–7 times the background, around a statistically complete sample of twelve 250 μm selected galaxies at z = 0.35, which were targeted by ALMA in a study of gas tracers. This overdensity is consistent with the effect of lensing by the haloes hosting the target z = 0.35 galaxies. The angular cross-correlation in this sample is consistent with statistical measures of this effect made using larger sub-mm samples. The magnitude of the overdensity as a function of radial separation is consistent with intermediate scale lensing by haloes of the order of 7×1013 M⊙ ⁠, which should host one or possibly two bright galaxies and several smaller satellites. This is supported by observational evidence of interaction with satellites in four out of the six fields with SMG, and membership of a spectroscopically defined group for a fifth. We also investigate the impact of these SMG on the reported Herschel fluxes of the z = 0.35 galaxies, as they produce significant contamination in the 350 and 500 μm Herschel bands. The higher than random incidence of these boosting events implies a significantly larger bias in the sub-mm colours of Herschel sources associated with z < 0.7 galaxies than has previously been assumed, with fboost = 1.13, 1.26, 1.44 at 250, 350, and 500 μm . This could have implications for studies of spectral energy distributions, source counts, and luminosity functions based on Herschel samples at z = 0.2–0.7

Methodological refinement of the submillimeter galaxy magnification bias. Paper I: cross-correlation function measurements

The measurement of the cross-correlation function is crucial to assess magnification bias in galaxy surveys. Previous works used mini-tile subsampling, but accurately determining the integral constraint (IC) correction for unbiased estimation is challenging due to various factors. We present a new methodology for estimating the cross-correlation function, utilizing full field area and reducing statistical uncertainty. Covariance matrices were estimated by dividing each field into at least five patches using a k-mean clustering algorithm. Robustness was assessed by comparing spectroscopic and photometric lens samples, yielding compatible results. Cross-correlation and auto-correlation analyses in the GAMA fields revealed a stronger signal in GAMA15, likely due to rare large-scale structure combinations. Our findings highlight the robustness of the new methodology and suggest sample-specific effects. Subsequent papers in this series will explore other aspects of magnification bias and address potential biases from the GAMA15 signal on cosmological parameter constraints.Comment: This work is the first one of a three-paper serie. 14 pages, 9 figures, submitted for publication by A&

Methodological refinement of the submillimeter galaxy magnification bias. Paper III: cosmological analysis with tomography

This paper is the third in a series on submillimeter galaxy magnification bias, focusing on the tomographic scenario. It refines the methodology used to constrain the halo occupation distribution model and cosmological parameters within a flat $\Lambda$CDM model, using updated data. The study aims to optimize CPU time, explore strategies for analyzing different redshift bins, and assess the impact of excluding the GAMA15 field. The tomographic approach involves dividing the redshift range into bins and analyzing cross-correlation measurements between submillimeter and foreground galaxies. The results show good agreement between the mean-redshift and full model cases, with an increase in the minimum mass of lenses at higher redshifts. The inferred cosmological parameters have narrower posterior distributions, indicating reduced measurement uncertainties compared to previous studies. Excluding the GAMA15 field reduces the cross-correlation signal, suggesting sample variance within the large-scale structure. Extending the redshift range improves robustness against sample variance and produces similar but tighter constraints. The study highlights the importance of sample variance and redshift binning in tomographic analyses, and suggests using additional wide-area fields and updated foreground catalogues for more effective implementation.Comment: This work is the third of a series of three. 17 pages and 19 figure. submitted to A&

Tomography-based observational measurements of the halo mass function via the submillimeter magnification bias

Aims: The main goal of this paper is to derive observational constraints on the halo mass fuction (HMF) by performing a tomographic analysis of the magnification bias signal on a sample of background submillimeter galaxies. The results can then be compared with those from a non-tomographic study. Methods: We measure the cross-correlation function between a sample of foreground GAMA galaxies with spectroscopic redshifts in the range 0.1 &lt; z &lt; 0.8 (and divided up into four bins) and a sample of background submillimeter galaxies from H-ATLAS with photometric redshifts in the range 1.2 &lt; z &lt; 4.0. We model the weak lensing signal within the halo model formalism and carry out a Markov chain Monte Carlo algorithm to obtain the posterior distribution of all HMF parameters, which we assume to follow the Sheth and Tormen (ST) three-parameter and two-parameter fits. Results: While the observational constraints on the HMF from the non-tomographic analysis are not stringent, there is a remarkable improvement in terms of uncertainty reduction when tomography is adopted. Moreover, with respect to the traditional ST triple of values from numerical simulations, the results from the three-parameter fit predict a higher number density of halos at masses below ∼1012 M⊙ h−1 at 95% credibility. The two-parameter fit yields even more restricting results, with a larger number density of halos below ∼1013 M⊙ h−1 and a lower one above ∼1014 M⊙ h−1, this time at more than 3σ credibility. Our results are therefore in disagreement with the standard N-body values for the ST fit at 2σ and 3σ, respectively

Galaxy cluster mass density profile derived using the submillimetre galaxies magnification bias

Context. The magnification bias is a gravitational lensing eect that produces an increase or decrease in the detection probability of background sources near the position of a lense. The special properties of the submillimetre galaxies (SMGs; steep source number counts, high redshift, and a very low cross-contamination with respect to the optical band) makes them the optimal background sample for magnification bias studies. Aims. We want to study the average mass density profile of tens to hundreds of clusters of galaxies acting as lenses that produce a magnification bias on the SMGs, and to estimate their associated masses and concentrations for dierent richness ranges. The cluster richness is defined as R = L200=L with L200 as the total r-band luminosity within the radius r200. Methods. The background sample is composed of SMGs observed by Herschel with 1:2 &lt; z &lt; 4:0 (mean redshift at 2:3) while the foreground sample is made up of galaxy clusters extracted from the Sloan Digital Sky Survey III with photometric redshifts of 0:05 &lt; z &lt; 0:8 (mean redshift at 0:38). Measurements are obtained by stacking the SMG–cluster pairs to estimate the crosscorrelation function using the Davis-Peebles estimator. This methodology allows us to derive the mass density profile for a wide range of angular scales, 2250 arcsec or 101300 kpc for z = 0:38, with a high radial resolution, and in particular to study the inner part of the dark matter halo (&lt;100 kpc). In addition, we also divide the cluster sample into five bins of richness and we analyse the estimated cross-correlation data using dierent combinations of the most common theoretical mass density profiles. Results. It is impossible to fit the data with a single mass density profile at all scales: in the inner part there is a clear excess in the mass density profile with respect to the outer part that we interpret as the galactic halo of the big central galaxy. As for the outer part, the estimated average masses increase with richness from M200c = 5:8 1013 M to M200c = 51:5 1013 M (M200c = 7:1 1013 M for the total sample). With respect to the concentration parameter, its average also increases with richness from C = 0:74 to C = 1:74 (C = 1:72 for the total sample). In the small-scale regions, the obtained average masses fluctuate around M200c = 34 1013 M with average concentration values of around C 4. Conclusions. The total average masses are in perfect agreement with the mass–richness relationship estimated from the cluster catalogue. In the bins of lowest richness, the central galactic halo constitutes 40% of the total mass of the cluster and its relevance decreases for higher richness values. While the estimated average concentration values of the central galactic halos are in agreement with traditional mass–concentration relationships, we find low concentrations for the outer part. Moreover, the concentrations decrease for lower richness values, probably indicating that the group of galaxies cannot be considered to be relaxed systems. Finally, we notice a systematic lack of signal at the transition between the dominance of the cluster halo and the central galactic halo (100 kpc). This feature is also present in previous studies using dierent catalogues and/or methodologies, but is never discussed

Cosmological constraints on the magnification bias on sub-millimetre galaxies after large-scale bias corrections

Context. The study of the magnification bias produced on high-redshift sub-millimetre galaxies by foreground galaxies through the analysis of the cross-correlation function was recently demonstrated as an interesting independent alternative to the weak-lensing shear as a cosmological probe. Aims. In the case of the proposed observable, most of the cosmological constraints mainly depend on the largest angular separation measurements. Therefore, we aim to study and correct the main large-scale biases that aect foreground and background galaxy samples to produce a robust estimation of the cross-correlation function. Then we analyse the corrected signal to derive updated cosmological constraints. Methods. We measured the large-scale, bias-corrected cross-correlation functions using a background sample of H-ATLAS galaxies with photometric redshifts &gt;1.2 and two dierent foreground samples (GAMA galaxies with spectroscopic redshifts or SDSS galaxies with photometric ones, both in the range 0.2 &lt; z &lt; 0.8). These measurements are modelled using the traditional halo model description that depends on both halo occupation distribution and cosmological parameters. We then estimated these parameters by performing a Markov chain Monte Carlo under multiple scenarios to study the performance of this observable and how to improve its results. Results. After the large-scale bias corrections, we obtain only minor improvements with respect to the previous magnification bias results, mainly confirming their conclusions: a lower bound on m &gt; 0:22 at 95% CL and an upper bound 8 &lt; 0:97 at 95% CL (results from the zspec sample). Neither the much higher surface density of the foreground photometric sample nor the assumption of Gaussian priors for the remaining unconstrained parameters significantly improve the derived constraints. However, by combining both foreground samples into a simplified tomographic analysis, we were able to obtain interesting constraints on the m8 plane as follows: m = 0:50+0:14 0:20 and 8 = 0:75+0:07 0:10 at 68% C

Cosmology with the submillimetre galaxies magnification bias: Tomographic analysis

Context. High-z submillimetre galaxies can be used as a background sample for gravitational lensing studies thanks to their magnification bias. In particular, the magnification bias can be exploited in order to constrain the free parameters of a halo occupation distribution (HOD) model and some of the main cosmological parameters. A pseudo-tomographic analysis shows that the tomographic approach should improve the parameter estimation. Aims. In this work the magnification bias has been evaluated as cosmological tool in a tomographic set-up. The cross-correlation function (CCF) data have been used to jointly constrain the astrophysical parameters Mmin, M1, and α in each of the selected redshift bins as well as the cosmological parameters ωM, σ8, and H0 for the lambda cold dark matter (ΛCDM) model. Moreover, we explore the possible time evolution of the dark energy density by also introducing the ω0, ωa parameters in the joint analysis (ω0CDM and ω0ωaCDM). Methods. The CCF was measured between a foreground spectroscopic sample of Galaxy And Mass Assembly galaxies and a background sample of Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) galaxies. The foreground sample was divided into four redshift bins (0.1-0.2, 0.2-0.3, 0.3-0.5, and 0.5-0.8) and the sample of H-ATLAS galaxies has photometric redshifts &gt; 1.2. The CCF was modelled using a halo model description that depends on HOD and cosmological parameters. Then a Markov chain Monte Carlo method was used to estimate the parameters for different cases. Results. For the ΛCDM model the analysis yields a maximum posterior value at 0.26 with [0.17, 0.41] 68% C.I. for ωM and at 0.87 with [0.75, 1] 68% C.I. for σ8. With our current results H0 is not yet constrained. With a more general ω0CDM model, the constraints on ωM and σ8 are similar, but we found a maximum posterior value for ω0 at -1 with [ - 1.56, -0.47] 68% C.I. In the ω0ωaCDM model, the results are -1.09 with [ - 1.72, -0.66] 68% C.I. for ω0 and -0.19 with [ - 1.88, 1.48] 68% C.I. for ωa. Conclusions. The results on Mmin show a trend towards higher values at higher redshift confirming recent findings. The tomographic analysis presented in this work improves the constraints in the σ8 - ωM plane with respect to previous findings exploiting the magnification bias and it confirms that magnification bias results do not show the degeneracy found with cosmic shear measurements. Moreover, related to dark energy, we found a trend of higher ω0 values for lower H0 values