arXiv subjects

Matt Hilton

Publications and source records attributed to Matt Hilton.

At least 37 records · Page 2Linked to original sources

arXiv2024

The Atacama Cosmology Telescope: A measurement of galaxy cluster temperatures through relativistic corrections to the thermal Sunyaev-Zeldovich effect

The high electron temperature in galaxy clusters ($>1\,$keV or $>10^7\,$K) leads to corrections at the level of a few percent in their thermal Sunyaev-Zeldovich effect signatures. Both the size and frequency dependence of these corrections, which are known as relativistic temperature corrections, depend upon the temperature of the objects. In this work we exploit this effect to measure the average temperature of a stack of Compton-$y$ selected clusters. Specifically, we apply the "spectroscopic method" and search for the temperature that best fits the clusters' signal measured at frequencies from 30 to 545 GHz by the Atacama Cosmology Telescope and Planck satellite. We measure the average temperature of clusters detected in the ACT maps to be $8.5\pm 2.4\,$keV, with an additional systematic error of comparable amplitude dominated by passband uncertainty. Upcoming surveys, such as the Simons Observatory and CMB-S4, have the potential to dramatically improve upon these measurements and thereby enable precision studies of cluster temperatures with millimeter observations. The key challenge for future observations will be mitigating instrumental systematic effects, which already limit this analysis.

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arXiv2024

Masses of Sunyaev-Zel'dovich Galaxy Clusters Detected by The Atacama Cosmology Telescope: Stacked Lensing Measurements with Subaru HSC Year 3 data

We present a stacked lensing analysis of 96 galaxy clusters selected by the thermal Sunyaev-Zel'dovich (SZ) effect in maps of the cosmic microwave background (CMB). We select foreground galaxy clusters with a $5σ$-level SZ threshold in CMB observations from the Atacama Cosmology Telescope, while we define background source galaxies for the lensing analysis with secure photometric redshift cuts in Year 3 data of the Subaru Hyper Suprime Cam survey. We detect the stacked lensing signal in the range of $0.1 < R\, [h^{-1}\mathrm{Mpc}] < 100$ in each of three cluster redshift bins, $0.092<z\le0.445$, $0.445<z\le0.695$, and $0.695<z\le1.180$, with 32 galaxy clusters in each bin. The cumulative signal-to-noise ratios of the lensing signal are $14.6$, $12.0$, and $6.6$, respectively. Using a halo-based forward model, we then constrain statistical relationships between the mass inferred from the SZ observation (i.e. SZ mass) and the total mass derived from our stacked lensing measurements. At the average SZ mass in the cluster sample ($2.1-2.4\times10^{14}\, h^{-1}M_\odot$), our likelihood analysis shows that the average total mass differs from the SZ counterpart by a factor of $1.3 \pm 0.2$, $1.6 \pm 0.2$, and $1.6 \pm 0.3$ ($68\%$) in the aforementioned redshift ranges, respectively. Our limits are consistent with previous lensing measurements, and we find that the cluster modeling choices can introduce a $1σ$-level difference in our parameter inferences.

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arXiv2024

CARRSSPipeline: Flux Calibration and Non-linear Reprojection for SALT-RSS Multi-Object Spectroscopy over 3500-9500 Å

The Robert Stobie Spectrograph (RSS) on the Southern African Large Telescope (SALT) offers multi-object spectroscopy over an 8' field-of-view at resolutions up to 3000. Reduction is typically conducted using RSSMOSPipeline, which performs basic data calibrations, sky subtraction, and wavelength calibration. However, flux calibration of SALT-RSS using spectrophotometric standard star observations is difficult due to variable primary mirror illumination. We describe a novel approach where stars with Sloan Digital Sky Survey spectra are included as alignment stars on RSS slitmasks and then used to perform flux calibration of the resulting data. RSS offers multiple settings that can be pieced together to cover the entire optical range, utilizing grating angle dithers to fill chip gaps. We introduce a non-linear reprojection routine that defines an exponential wavelength array spanning 3500-9500 Angstroms with gradually decreasing resolution and then reprojects several individual settings into a single 2D spectrum for each object. Our flux calibration and non-linear reprojection routines are released as part of the Calibration And Reprojection for RSS Pipeline (CARRSSPipeline; https://github.com/GeorgeTheGeorgian/CARRSSPipeline.git ), that enables the extraction of full-optical-coverage, flux-calibrated, medium-resolution one-dimensional spectra.

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arXiv2024

Sensitive 3mm Imaging of Discrete Sources in the Fields of tSZ-Selected Galaxy Clusters

In this paper we present the results of a blind survey for compact sources in 243 Galaxy clusters that were identified using the thermal Sunyaev-Zeldovich effect (tSZ). The survey was carried out at 90 GHz using MUSTANG2 on the Green Bank telescope and achieved a $5σ$ detection limit of 1 mJy in the center of each cluster. We detected 24 discrete sources. The majority (18) of these correspond to known radio sources, and of these, 5 show signs of significant variability, either with time or in spectral index. The remaining sources have no clear counterparts at other wavelengths. Searches for galaxy clusters via the tSZ effect strongly rely on observations at 90 GHz, and the sources found have the potential to bias mass estimates of clusters. We compare our results to the simulation Websky that can be used to estimate the source contamination in galaxy cluster catalogs. While the simulation showed a good match to our observations at the clusters' centers, it does not match our source distribution further out. Sources over 104" from a cluster's center bias the tSZ signal high, for some of our sources, by over 50%. When averaged over the whole cluster population the effect is smaller but still at a level of 1 to 2%. We also discovered that unlike previous measurements and simulations we see an enhancement of source counts in the outer regions of the clusters and fewer sources than expected in the centers of this tSZ selected sample.

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arXiv2024

The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters

We present cosmological constraints from a gravitational lensing mass map covering 9400 sq. deg. reconstructed from CMB measurements made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with BAO measurements (from SDSS and 6dF), we obtain the amplitude of matter fluctuations $σ_8 = 0.819 \pm 0.015$ at 1.8% precision, $S_8\equivσ_8({Ω_{\rm m}}/0.3)^{0.5}=0.840\pm0.028$ and the Hubble constant $H_0= (68.3 \pm 1.1)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ at 1.6% precision. A joint constraint with CMB lensing measured by the Planck satellite yields even more precise values: $σ_8 = 0.812 \pm 0.013$, $S_8\equivσ_8({Ω_{\rm m}}/0.3)^{0.5}=0.831\pm0.023$ and $H_0= (68.1 \pm 1.0)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$. These measurements agree well with $Λ$CDM-model extrapolations from the CMB anisotropies measured by Planck. To compare these constraints to those from the KiDS, DES, and HSC galaxy surveys, we revisit those data sets with a uniform set of assumptions, and find $S_8$ from all three surveys are lower than that from ACT+Planck lensing by varying levels ranging from 1.7-2.1$σ$. These results motivate further measurements and comparison, not just between the CMB anisotropies and galaxy lensing, but also between CMB lensing probing $z\sim 0.5-5$ on mostly-linear scales and galaxy lensing at $z\sim 0.5$ on smaller scales. We combine our CMB lensing measurements with CMB anisotropies to constrain extensions of $Λ$CDM, limiting the sum of the neutrino masses to $\sum m_ν < 0.13$ eV (95% c.l.), for example. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the $Λ$CDM model, while paving a promising path for neutrino physics with gravitational lensing from upcoming ground-based CMB surveys.

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arXiv2024

The Atacama Cosmology Telescope: Extragalactic Point Sources in the Southern Surveys at 150, 220 and 280 GHz observed between 2008-2010

We present a multi-frequency, multi-epoch catalog of extragalactic sources. The catalog is based on 150, 220, and 280 GHz observations carried out in 2008, 2009, and 2010 using the Millimeter Bolometric Array Camera on the Atacama Cosmology Telescope. We also present and release 280 GHz maps from 2008 and 2010. The catalog contains 483 sources found in a sky area of ${\sim}600$ square degrees. It was obtained by cross-matching sources found in 11 sub-catalogs, one for each season and frequency band. We also include co-added data from ${\sim}150$ and ${\sim}160$ square degrees using two and three years of overlapping observations. We divide the sources into two populations, synchrotron and dusty emitters, based on their spectral behavior in the 150-280 GHz frequency range. We find 284 synchrotron sources and 183 dusty source candidates. Our cross-matching with catalogs from radio to X-ray results in 251 synchrotron sources (88%) and 92 dusty sources (51%) with counterparts and suggests that 91 dusty candidates are not in existing catalogs. We study the variability and number counts of each population. In the case of synchrotron sources, we find year-to-year variability, with a mean value around 35%. As expected, we find no evidence of dusty source variability. Our number counts generally agree with previous measurements and models, except for dusty sources at 280 GHz, where some models overestimate our results.

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arXiv2024

The Atacama Cosmology Telescope: Cosmology from cross-correlations of unWISE galaxies and ACT DR6 CMB lensing

We present tomographic measurements of structure growth using cross-correlations of Atacama Cosmology Telescope (ACT) DR6 and Planck CMB lensing maps with the unWISE Blue and Green galaxy samples, which span the redshift ranges $0.2 \lesssim z \lesssim 1.1$ and $0.3 \lesssim z \lesssim 1.8$, respectively. We improve on prior unWISE cross-correlations not just by making use of the new, high-precision ACT DR6 lensing maps, but also by including additional spectroscopic data for redshift calibration and by analysing our measurements with a more flexible theoretical model. An extensive suite of systematic and null tests within a blind analysis framework ensures that our results are robust. We determine the amplitude of matter fluctuations at low redshifts ($z\simeq 0.2-1.6$), finding $S_8 \equiv σ_8 (Ω_m / 0.3)^{0.5} = 0.813 \pm 0.021$ using the ACT cross-correlation alone and $S_8 = 0.810 \pm 0.015$ with a combination of Planck and ACT cross-correlations; these measurements are fully consistent with the predictions from primary CMB measurements assuming standard structure growth. The addition of Baryon Acoustic Oscillation data breaks the degeneracy between $σ_8$ and $Ω_m$, allowing us to measure $σ_8 = 0.813 \pm 0.020$ from the cross-correlation of unWISE with ACT and $σ_8 = 0.813\pm 0.015$ from the combination of cross-correlations with ACT and Planck. These results also agree with the expectations from primary CMB extrapolations in $Λ$CDM cosmology; the consistency of $σ_8$ derived from our two redshift samples at $z \sim 0.6$ and $1.1$ provides a further check of our cosmological model. Our results suggest that structure formation on linear scales is well described by $Λ$CDM even down to low redshifts $z\lesssim 1$.

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arXiv2024

X-ray observations of the Zwicky 3146 galaxy cluster reveal a 3.5 keV excess

In this note, we present spectral fits of the well-documented sloshing cool-core cluster Zwicky 3146 ($z=0.291$), to test the existence of the highly speculated 3.5 keV line. We report excesses at $>3σ$ significance at $E=3.575$ keV, yielding a flux $F = 8.73_{-2.22}^{+2.17}$ $\times 10^{-6}$ photons cm$^{-2}$ s$^{-1}$, in \textit{XMM-Newton}, and $E=3.55$ keV, with a flux $F = 10.0_{-2.96}^{+3.05}$ $\times 10^{-6}$ photons cm$^{-2}$ s$^{-1}$ in \textit{Chandra}. We explore the possibility that the 3.5 keV excess is correlated to the presence of cold gas within the cluster, based on optical and sub-mm literature analyses. Following the launch of the X-ray Imaging and Spectroscopy Mission (XRISM), high resolution spectroscopy ($\leq 7$ eV) will reveal in unprecedented detail, the origin of this unidentified feature, for which Zwicky 3146 should be considered a viable target, due to the strength of the feature in two independent X-ray telescopes, opening a new window into plasma or charge exchange studies in galaxy clusters.

astro-ph.HE↗

arXiv2024

The Atacama Cosmology Telescope: Reionization kSZ trispectrum methodology and limits

Patchy reionization generates kinematic Sunyaev-Zeldovich (kSZ) anisotropies in the cosmic microwave background (CMB). Large-scale velocity perturbations along the line of sight modulate the small-scale kSZ power spectrum, leading to a trispectrum (or four-point function) in the CMB that depends on the physics of reionization. We investigate the challenges in detecting this trispectrum and use tools developed for CMB lensing, such as realization-dependent bias subtraction and cross-correlation based estimators, to counter uncertainties in the instrumental noise and assumed CMB power spectrum. We also find that both lensing and extragalactic foregrounds can impart larger trispectrum contributions than the reionization kSZ signal. We present a range of mitigation methods for both of these sources of contamination, validated on microwave-sky simulations. We use ACT DR6 and Planck data to calculate an upper limit on the reionization kSZ trispectrum from a measurement dominated by foregrounds. The upper limit is about 50 times the signal predicted from recent simulations.

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arXiv2024

A full reconstruction of two galaxy clusters intra-cluster medium with strong gravitational lensing

Whilst X-rays and Sunyaev-Zel'dovich observations allow to study the properties of the intra-cluster medium (ICM) of galaxy clusters, their gravitational potential may be constrained using strong gravitational lensing. Although being physically related, these two components are often described with different physical models. Here, we present a unified technique to derive the ICM properties from strong lensing for clusters in hydrostatic equilibrium. In order to derive this model, we present a new universal and self-similar polytropic temperature profile, which we fit using the X-COP sample of clusters. We subsequently derive an analytical model for the electron density, which we apply to strong lensing clusters MACS J0242.5-2132 and MACS J0949.8+1708. We confront the inferred ICM reconstructions to XMM-Newton and ACT observations. We contrast our analytical electron density reconstructions with the best canonical $β$-model. The ICM reconstructions obtained prove to be compatible with observations. However they appear to be very sensitive to various dark matter halo parameters constrained through strong lensing (such as the core radius), and to the halo scale radius (fixed in the lensing optimisations). With respect to the important baryonic effects, we make the sensitivity on the scale radius of the reconstruction an asset, and use the inferred potential to constrain the dark matter density profile using ICM observations. The technique here developed should allow to take a new, and more holistic path to constrain the content of galaxy clusters.

astro-ph.CO↗

arXiv2024

The Atacama Cosmology Telescope: Flux Upper Limits from a Targeted Search for Extragalactic Transients

We have performed targeted searches of known extragalactic transient events at millimetre wavelengths using nine seasons (2013--2021) of 98, 150, and 229\,GHz Atacama Cosmology Telescope (ACT) observations that mapped ${\sim}40$ per cent of the sky for most of the data volume. Our data cover 88 gamma-ray bursts (GRBs), 12 tidal disruption events (TDEs) and 203 other transients, including supernovae (SNe). We stack our ACT observations to increase the signal-to-noise ratio of the maps. In all cases but one, we do not detect these transients in the ACT data. The single candidate detection (event AT2019ppm), seen at ${\sim}5σ$ significance in our data, appears to be due to active galactic nuclei (AGN) activity in the host galaxy coincident with a transient alert. For each source in our search we provide flux upper limits. For example, the medians for the 95 per cent confidence upper limits at 98\,GHz are $15$, $18$, and $16$\,mJy for GRBs, SNe, and TDEs respectively, in the first month after discovery. The projected sensitivity of future wide-area cosmic microwave background (CMB) surveys should be sufficient to detect many of these events using the methods described in this paper.

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arXiv2024

The Atacama Cosmology Telescope: Millimeter Observations of a Population of Asteroids or: ACTeroids

We present fluxes and light curves for a population of asteroids at millimeter (mm) wavelengths, detected by the Atacama Cosmology Telescope (ACT) over 18, 000 deg2 of the sky using data from 2017 to 2021. We utilize high cadence maps, which can be used in searching for moving objects such as asteroids and trans-Neptunian Objects (TNOs), as well as for studying transients. We detect 160 asteroids with a signal-to-noise of at least 5 in at least one of the ACT observing bands, which are centered near 90, 150, and 220 GHz. For each asteroid, we compare the ACT measured flux to predicted fluxes from the Near Earth Asteroid Thermal Model (NEATM) fit to WISE data. We confirm previous results that detected a deficit of flux at millimeter wavelengths. Moreover, we report a spectral characteristic to this deficit, such that the flux is relatively lower at 150 and 220 GHz than at 90 GHz. Additionally, we find that the deficit in flux is greater for S-type asteroids than for C-type.

astro-ph.EP↗

arXiv2023

The Atacama Cosmology Telescope: High-resolution component-separated maps across one-third of the sky

Observations of the millimeter sky contain valuable information on a number of signals, including the blackbody cosmic microwave background (CMB), Galactic emissions, and the Compton-$y$ distortion due to the thermal Sunyaev-Zel'dovich (tSZ) effect. Extracting new insight into cosmological and astrophysical questions often requires combining multi-wavelength observations to spectrally isolate one component. In this work, we present a new arcminute-resolution Compton-$y$ map, which traces out the line-of-sight-integrated electron pressure, as well as maps of the CMB in intensity and E-mode polarization, across a third of the sky (around 13,000 sq.~deg.). We produce these through a joint analysis of data from the Atacama Cosmology Telescope (ACT) Data Release 4 and 6 at frequencies of roughly 93, 148, and 225 GHz, together with data from the \textit{Planck} satellite at frequencies between 30 GHz and 545 GHz. We present detailed verification of an internal linear combination pipeline implemented in a needlet frame that allows us to efficiently suppress Galactic contamination and account for spatial variations in the ACT instrument noise. These maps provide a significant advance, in noise levels and resolution, over the existing \textit{Planck} component-separated maps and will enable a host of science goals including studies of cluster and galaxy astrophysics, inferences of the cosmic velocity field, primordial non-Gaussianity searches, and gravitational lensing reconstruction of the CMB.

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arXiv2023

ACT-DR5 Sunyaev-Zel'dovich Clusters: weak lensing mass calibration with KiDS

We present weak gravitational lensing measurements of a sample of 157 clusters within the Kilo Degree Survey (KiDS), detected with a $>5σ$ thermal Sunyaev-Zel'dovich (SZ) signal by the Atacama Cosmology Telescope (ACT). Using a halo-model approach we constrain the average total cluster mass, $M_{\rm WL}$, accounting for the ACT cluster selection function of the full sample. We find that the SZ cluster mass estimate $M_{\rm SZ}$, which was calibrated using X-ray observations, is biased with $M_{\rm SZ}/M_{\rm WL} = (1-b_{\rm SZ}) = 0.65\pm 0.05$. Separating the sample into six mass bins, we find no evidence of a strong mass-dependency for the mass bias, $(1-b_{\rm SZ})$. Adopting this ACT-KiDS SZ mass-calibration would bring the Planck SZ cluster count into agreement with the counts expected from the {\it Planck} cosmic microwave background $Λ$CDM cosmological model, although it should be noted that the cluster sample considered in this work has a lower average mass $M_{\rm SZ, uncor} = 3.64 \times 10^{14} M_{\odot}$ compared to the Planck cluster sample which has an average mass in the range $M_{\rm SZ, uncor} = (5.5-8.5) \times 10^{14} M_{\odot}$, depending on the sub-sample used.

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arXiv2023

The Atacama Cosmology Telescope: Mitigating the impact of extragalactic foregrounds for the DR6 CMB lensing analysis

We investigate the impact and mitigation of extragalactic foregrounds for the CMB lensing power spectrum analysis of Atacama Cosmology Telescope (ACT) data release 6 (DR6) data. Two independent microwave sky simulations are used to test a range of mitigation strategies. We demonstrate that finding and then subtracting point sources, finding and then subtracting models of clusters, and using a profile bias-hardened lensing estimator, together reduce the fractional biases to well below statistical uncertainties, with the inferred lensing amplitude, $A_{\mathrm{lens}}$, biased by less than $0.2σ$. We also show that another method where a model for the cosmic infrared background (CIB) contribution is deprojected and high frequency data from Planck is included has similar performance. Other frequency-cleaned options do not perform as well, incurring either a large noise cost, or resulting in biased recovery of the lensing spectrum. In addition to these simulation-based tests, we also present null tests performed on the ACT DR6 data which test for sensitivity of our lensing spectrum estimation to differences in foreground levels between the two ACT frequencies used, while nulling the CMB lensing signal. These tests pass whether the nulling is performed at the map or bandpower level. The CIB-deprojected measurement performed on the DR6 data is consistent with our baseline measurement, implying contamination from the CIB is unlikely to significantly bias the DR6 lensing spectrum. This collection of tests gives confidence that the ACT DR6 lensing measurements and cosmological constraints presented in companion papers to this work are robust to extragalactic foregrounds.

astro-ph.CO↗

arXiv2023

The Atacama Cosmology Telescope: Modeling the Gas Thermodynamics in BOSS CMASS galaxies from Kinematic and Thermal Sunyaev-Zel'dovich Measurements

The thermal and kinematic Sunyaev-Zel'dovich effects (tSZ, kSZ) probe the thermodynamic properties of the circumgalactic and intracluster medium (CGM and ICM) of galaxies, groups, and clusters, since they are proportional, respectively, to the integrated electron pressure and momentum along the line-of-sight. We present constraints on the gas thermodynamics of CMASS galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS) using new measurements of the kSZ and tSZ signals obtained in a companion paper. Combining kSZ and tSZ measurements, we measure within our model the amplitude of energy injection $εM_\star c^2$, where $M_\star$ is the stellar mass, to be $ε=(40\pm9)\times10^{-6}$, and the amplitude of the non-thermal pressure profile to be $α_{\rm Nth}<0.2$ (2$σ$), indicating that less than 20% of the total pressure within the virial radius is due to a non-thermal component. We estimate the effects of including baryons in the modeling of weak-lensing galaxy cross-correlation measurements using the best-fit density profile from the kSZ measurement. Our estimate reduces the difference between the original theoretical model and the weak-lensing galaxy cross-correlation measurements in arXiv:1611.08606 by half but does not fully reconcile it. Comparing the tSZ measurements to cosmological simulations, we find that simulations underestimate the CGM pressure at large radii while they fare better in comparison with the kSZ measurements. This suggests that the energy injected via feedback models in the simulations that we compared against does not sufficiently heat the gas at these radii. We do not find significant disagreement at smaller radii. These measurements provide novel tests of current and future simulations. This work demonstrates the power of joint, high signal-to-noise kSZ and tSZ observations, upon which future cross-correlation studies will improve.

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arXiv2022

The MeerKAT Galaxy Clusters Legacy Survey: star formation in massive clusters at 0.15 < z < 0.35

We investigate dust-unbiased star formation rates (SFR) as a function of the environment in 20 massive clusters ($M_{200}>4\times10^{14} {\rm M}_{\odot}$) between $0.15<z<0.35$ using radio luminosities ($L_{\rm 1.4GHz}$) from the recently released MeerKAT Galaxy Cluster Legacy Survey catalogue. We use optical data from the Dark Energy Camera Legacy Survey to estimate photo-$z$s and assign cluster membership. We observe a steady decline in the fraction ($f_{\rm SF}$) of star-forming galaxies from $2R_{200}$ to the cluster centres in our full cluster sample, but notice a significant difference in $f_{\rm SF}$ gradients between clusters hosting large-scale extended radio emission in the form of haloes and relics (associated with ongoing merger activity) and non-radio-halo/relic hosting clusters. For star-forming galaxies within $R_{200}$, the $f_{\rm SF}$ in clusters hosting radio haloes and relics ($0.148\pm0.016$) is $\approx23\%$ higher than in non-radio-halo/relic hosting clusters ($0.120\pm0.011$). We observe a $3σ$ difference between the total SFR normalised by cluster mass for non-radio-halo/relic hosting clusters ($21.5\pm1.9$ M$_{\odot}$yr$^{-1}$/$10^{14}$M$_{\odot}$) and for clusters with radio haloes and relics ($26.1\pm1.4$ M$_{\odot}$yr$^{-1}$/$10^{14}$M$_{\odot}$). There is a $\approx4\times$ decline in the mass normalised total SFR of clusters for galaxies with SFR above the luminous infrared galaxies (LIRGs) SFR limit at our redshift slice, corresponding to 2 Gyr in look-back time. This is consistent with the rapid decline in SF activity with decreasing redshift amongst cluster LIRGs seen by previous studies using infrared-derived SFR.

astro-ph.GA↗

arXiv2022

The thermal and non-thermal components within and between galaxy clusters Abell 399 and Abell 401

We measure the local correlation between radio emission and Compton-$y$ signal across two galaxy clusters, Abell~399 and Abell~401, using maps from the Low-Frequency Array (LOFAR) and the Atacama Cosmology Telescope (ACT) + \Planck. These datasets allow us to make the first measurement of this kind at $\sim$arcminute resolution. We find that the radio brightness scales as $F_{\mathrm{radio}} \propto y^{1.5}$ for Abell~401 and $F_{\mathrm{radio}} \propto y^{2.8}$ for Abell~399. Furthermore, using \XMM data, we derive a sublinear correlation between radio and X-ray brightness for both the clusters ($F_{\mathrm{radio}} \propto F_{\rm X}^{0.7}$). Finally, we correlate the Compton-$y$ and X-ray data, finding that an isothermal model is consistent with the cluster profiles, $y \propto F_{\rm X}^{0.5}$. By adopting an isothermal--$β$ model, we are able, for the first time, to jointly use radio, X-ray, and Compton-$y$ data to estimate the scaling index for the magnetic field profile, $B(r) \propto n_{\mathrm{e}}(r)^η$ in the injection and re-acceleration scenarios. Applying this model, we find that the combined radio and Compton-$y$ signal exhibits a significantly tighter correlation with the X-ray across the clusters than when the datasets are independently correlated. We find $η\sim 0.6{-}0.8$. These results are consistent with the upper limit we derive for the scaling index of the magnetic field using rotation measure values for two radio galaxies in Abell~401. We also measure the radio, Compton-$y$, and X-ray correlations in the filament between the clusters but conclude that deeper data are required for a convincing determination of the correlations in the filament.

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