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E. Suchyta

Publications and source records attributed to E. Suchyta.

At least 181 records · Page 10Linked to original sources

No Evidence for Orbital Clustering in the Extreme Trans-Neptunian Objects

The apparent clustering in longitude of perihelion $\varpi$ and ascending node $Ω$ of extreme trans-Neptunian objects (ETNOs) has been attributed to the gravitational effects of an unseen 5-10 Earth-mass planet in the outer solar system. To investigate how selection bias may contribute to this clustering, we consider 14 ETNOs discovered by the Dark Energy Survey, the Outer Solar System Origins Survey, and the survey of Sheppard and Trujillo. Using each survey's published pointing history, depth, and TNO tracking selections, we calculate the joint probability that these objects are consistent with an underlying parent population with uniform distributions in $\varpi$ and $Ω$. We find that the mean scaled longitude of perihelion and orbital poles of the detected ETNOs are consistent with a uniform population at a level between $17\%$ and $94\%$, and thus conclude that this sample provides no evidence for angular clustering.

astro-ph.EP↗

Dark Energy Survey Year 3 Results: Optimizing the Lens Sample in Combined Galaxy Clustering and Galaxy-Galaxy Lensing Analysis

We investigate potential gains in cosmological constraints from the combination of galaxy clustering and galaxy-galaxy lensing by optimizing the lens galaxy sample selection using information from Dark Energy Survey (DES) Year 3 data and assuming the DES Year 1 Metacalibration sample for the sources. We explore easily reproducible selections based on magnitude cuts in $i$-band as a function of (photometric) redshift, $z_{\rm phot}$, and benchmark the potential gains against those using the well established redMaGiC sample. We focus on the balance between density and photometric redshift accuracy, while marginalizing over a realistic set of cosmological and systematic parameters. Our optimal selection, the MagLim sample, satisfies $i < 4 \, z_{\rm phot} + 18$ and has $\sim 30\%$ wider redshift distributions but $\sim 3.5$ times more galaxies than redMaGiC. Assuming a wCDM model and equivalent scale cuts to mitigate nonlinear effects, this leads to $40\%$ increase in the figure of merit for the pair combinations of $Ω_m$, $w$, and $σ_8$, and gains of $16\%$ in $σ_8$, $10\%$ in $Ω_m$, and $12\%$ in $w$. Similarly, in LCDM we find an improvement of $19\%$ and $27\%$ on $σ_8$ and $Ω_m$, respectively. We also explore flux-limited samples with a flat magnitude cut finding that the optimal selection, $i < 22.2$, has $\sim 7$ times more galaxies and $\sim 20\%$ wider redshift distributions compared to MagLim, but slightly worse constraints. We show that our results are robust with respect to the assumed galaxy bias and photometric redshift uncertainties with only moderate further gains from increased number of tomographic bins or the inclusion of bin cross-correlations, except in the case of the flux-limited sample, for which these gains are more significant.

astro-ph.CO↗

DES Y1 results: Splitting growth and geometry to test $Λ$CDM

We analyze Dark Energy Survey (DES) data to constrain a cosmological model where a subset of parameters -- focusing on $Ω_m$ -- are split into versions associated with structure growth (e.g. $Ω_m^{\rm grow}$) and expansion history (e.g. $Ω_m^{\rm geo}$). Once the parameters have been specified for the $Λ$CDM cosmological model, which includes general relativity as a theory of gravity, it uniquely predicts the evolution of both geometry (distances) and the growth of structure over cosmic time. Any inconsistency between measurements of geometry and growth could therefore indicate a breakdown of that model. Our growth-geometry split approach therefore serves as both a (largely) model-independent test for beyond-$Λ$CDM physics, and as a means to characterize how DES observables provide cosmological information. We analyze the same multi-probe DES data as arXiv:1811.02375 : DES Year 1 (Y1) galaxy clustering and weak lensing, which are sensitive to both growth and geometry, as well as Y1 BAO and Y3 supernovae, which probe geometry. We additionally include external geometric information from BOSS DR12 BAO and a compressed Planck 2015 likelihood, and external growth information from BOSS DR12 RSD. We find no significant disagreement with $Ω_m^{\rm grow}=Ω_m^{\rm geo}$. When DES and external data are analyzed separately, degeneracies with neutrino mass and intrinsic alignments limit our ability to measure $Ω_m^{\rm grow}$, but combining DES with external data allows us to constrain both growth and geometric quantities. We also consider a parameterization where we split both $Ω_m$ and $w$, but find that even our most constraining data combination is unable to separately constrain $Ω_m^{\rm grow}$ and $w^{\rm grow}$. Relative to $Λ$CDM, splitting growth and geometry weakens bounds on $σ_8$ but does not alter constraints on $h$.

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The Effect of Environment on Type Ia Supernovae in the Dark Energy Survey Three-Year Cosmological Sample

Analyses of type Ia supernovae (SNe Ia) have found puzzling correlations between their standardised luminosities and host galaxy properties: SNe Ia in high-mass, passive hosts appear brighter than those in lower-mass, star-forming hosts. We examine the host galaxies of SNe Ia in the Dark Energy Survey three-year spectroscopically-confirmed cosmological sample, obtaining photometry in a series of "local" apertures centred on the SN, and for the global host galaxy. We study the differences in these host galaxy properties, such as stellar mass and rest-frame $U-R$ colours, and their correlations with SN Ia parameters including Hubble residuals. We find all Hubble residual steps to be $>3σ$ in significance, both for splitting at the traditional environmental property sample median and for the step of maximum significance. For stellar mass, we find a maximal local step of $0.098\pm0.018$ mag; $\sim 0.03$ mag greater than the largest global stellar mass step in our sample ($0.070 \pm 0.017$ mag). When splitting at the sample median, differences between local and global $U-R$ steps are small, both $\sim 0.08$ mag, but are more significant than the global stellar mass step ($0.057\pm0.017$ mag). We split the data into sub-samples based on SN Ia light curve parameters: stretch ($x_1$) and colour ($c$), finding that redder objects ($c > 0$) have larger Hubble residual steps, for both stellar mass and $U-R$, for both local and global measurements, of $\sim0.14$ mag. Additionally, the bluer (star-forming) local environments host a more homogeneous SN Ia sample, with local $U-R$ r.m.s. scatter as low as $0.084 \pm 0.017$ mag for blue ($c < 0$) SNe Ia in locally blue $U-R$ environments.

astro-ph.CO↗

Is diffuse intracluster light a good tracer of the galaxy cluster matter distribution?

We explore the relation between diffuse intracluster light (central galaxy included) and the galaxy cluster (baryonic and dark) matter distribution using a sample of 528 clusters at $0.2\leq z \leq 0.35$ found in the Dark Energy Survey (DES) Year 1 data. The surface brightness of the diffuse light shows an increasing dependence on cluster total mass at larger radius, and appears to be self-similar with a universal radial dependence after scaling by cluster radius. We also compare the diffuse light radial profiles to the cluster (baryonic and dark) matter distribution measured through weak lensing and find them to be comparable. The IllustrisTNG galaxy formation simulation, TNG300, offers further insight into the connection between diffuse stellar mass and cluster matter distributions -- the simulation radial profile of the diffuse stellar component does not have a similar slope with the total cluster matter content, although that of the cluster satellite galaxies does. Regardless of the radial trends, the amount of diffuse stellar mass has a low-scatter scaling relation with cluster's total mass in the simulation, out-performing the total stellar mass of cluster satellite galaxies. We conclude that there is no consistent evidence yet on whether or not diffuse light is a faithful radial tracer of the cluster matter distribution. Nevertheless, both observational and simulation results reveal that diffuse light is an excellent indicator of the cluster's total mass.

astro-ph.GA↗

A statistical standard siren measurement of the Hubble constant from the LIGO/Virgo gravitational wave compact object merger GW190814 and Dark Energy Survey galaxies

We present a measurement of the Hubble constant $H_0$ using the gravitational wave (GW) event GW190814, which resulted from the coalescence of a 23 $M_\odot$ black hole with a 2.6 $M_\odot$ compact object, as a standard siren. No compelling electromagnetic counterpart has been identified for this event, thus our analysis accounts for thousands of potential host galaxies within a statistical framework. The redshift information is obtained from the photometric redshift (photo-$z$) catalog from the Dark Energy Survey. The luminosity distance is provided by the LIGO/Virgo gravitational wave sky map. Since this GW event has the second-smallest localization volume after GW170817, GW190814 is likely to provide the best constraint on cosmology from a single standard siren without identifying an electromagnetic counterpart. Our analysis uses photo-$z$ probability distribution functions and corrects for photo-$z$ biases. We also reanalyze the binary-black hole GW170814 within this updated framework. We explore how our findings impact the $H_0$ constraints from GW170817, the only GW merger associated with a unique host galaxy. From a combination of GW190814, GW170814 and GW170817, our analysis yields $H_0 = 72.0^{+ 12}_{- 8.2 }~{\rm km~s^{-1}~Mpc^{-1}}$ (68\% Highest Density Interval, HDI) for a prior in $H_0$ uniform between $[20,140]~{\rm km~s^{-1}~Mpc^{-1}}$. The addition of GW190814 and GW170814 to GW170817 improves the 68\% HDI from GW170817 alone by $\sim 18\%$, showing how well-localized mergers without counterparts can provide a significant contribution to standard siren measurements, provided that a complete galaxy catalog is available at the location of the event.

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Shadows in the Dark: Low-Surface-Brightness Galaxies Discovered in the Dark Energy Survey

We present a catalog of 23,790 extended low-surface-brightness galaxies (LSBGs) identified in $\sim 5000 °^2$ from the first three years of imaging data from the Dark Energy Survey (DES). Based on a single-component Sérsic model fit, we define extended LSBGs as galaxies with $g$-band effective radii $R_{eff}(g) > 2.5''$ and mean surface brightness $\barμ_{eff}(g) > 24.2 \,mag ȧrcsec^{-2}$. We find that the distribution of LSBGs is strongly bimodal in $(g-r)$ vs.\ $(g-i$) color space. We divide our sample into red ($g-i \geq 0.60$) and blue ($g-i<0.60$) galaxies and study the properties of the two populations. Redder LSBGs are more clustered than their blue counterparts and are correlated with the distribution of nearby ($z < 0.10$) bright galaxies. Red LSBGs constitute $\sim 33\%$ of our LSBG sample, and $\sim 30\%$ of these are located within 1 deg of low-redshift galaxy groups and clusters (compared to $\sim 8\%$ of the blue LSBGs). For nine of the most prominent galaxy groups and clusters, we calculate the physical properties of associated LSBGs assuming a redshift derived from the host system. In these systems, we identify 41 objects that can be classified as ultra-diffuse galaxies, defined as LSBGs with projected physical effective radii $R_{eff} > 1.5 \,kpc$ and central surface brighthness $μ_0(g) > 24.0\, mag \,arcsec^{-2}$. The wide-area sample of LSBGs in DES can be used to test the role of environment on models of LSBG formation and evolution.

astro-ph.GA↗

Dark Energy Survey Year 3 Results: Clustering Redshifts -- Calibration of the Weak Lensing Source Redshift Distributions with redMaGiC and BOSS/eBOSS

We present the calibration of the Dark Energy Survey Year 3 (DES Y3) weak lensing source galaxy redshift distributions $n(z)$ from clustering measurements. In particular, we cross-correlate the weak lensing (WL) source galaxies sample with redMaGiC galaxies (luminous red galaxies with secure photometric redshifts) and a spectroscopic sample from BOSS/eBOSS to estimate the redshift distribution of the DES sources sample. Two distinct methods for using the clustering statistics are described. The first uses the clustering information independently to estimate the mean redshift of the source galaxies within a redshift window, as done in the DES Y1 analysis. The second method establishes a likelihood of the clustering data as a function of $n(z)$, which can be incorporated into schemes for generating samples of $n(z)$ subject to combined clustering and photometric constraints. Both methods incorporate marginalisation over various astrophysical systematics, including magnification and redshift-dependent galaxy-matter bias. We characterise the uncertainties of the methods in simulations; the first method recovers the mean $z$ of tomographic bins to RMS (precision) of $\sim 0.014$. Use of the second method is shown to vastly improve the accuracy of the shape of $n(z)$ derived from photometric data. The two methods are then applied to the DES Y3 data.

astro-ph.CO↗

The Dark Energy Survey Supernova Program: Modelling selection efficiency and observed core collapse supernova contamination

The analysis of current and future cosmological surveys of type Ia supernovae (SNe Ia) at high-redshift depends on the accurate photometric classification of the SN events detected. Generating realistic simulations of photometric SN surveys constitutes an essential step for training and testing photometric classification algorithms, and for correcting biases introduced by selection effects and contamination arising from core collapse SNe in the photometric SN Ia samples. We use published SN time-series spectrophotometric templates, rates, luminosity functions and empirical relationships between SNe and their host galaxies to construct a framework for simulating photometric SN surveys. We present this framework in the context of the Dark Energy Survey (DES) 5-year photometric SN sample, comparing our simulations of DES with the observed DES transient populations. We demonstrate excellent agreement in many distributions, including Hubble residuals, between our simulations and data. We estimate the core collapse fraction expected in the DES SN sample after selection requirements are applied and before photometric classification. After testing different modelling choices and astrophysical assumptions underlying our simulation, we find that the predicted contamination varies from 5.8 to 9.3 per cent, with an average of 7.0 per cent and r.m.s. of 1.1 per cent. Our simulations are the first to reproduce the observed photometric SN and host galaxy properties in high-redshift surveys without fine-tuning the input parameters. The simulation methods presented here will be a critical component of the cosmology analysis of the DES photometric SN Ia sample: correcting for biases arising from contamination, and evaluating the associated systematic uncertainty.

astro-ph.CO↗

Machine Learning for Searching the Dark Energy Survey for Trans-Neptunian Objects

In this paper we investigate how implementing machine learning could improve the efficiency of the search for Trans-Neptunian Objects (TNOs) within Dark Energy Survey (DES) data when used alongside orbit fitting. The discovery of multiple TNOs that appear to show a similarity in their orbital parameters has led to the suggestion that one or more undetected planets, an as yet undiscovered "Planet 9", may be present in the outer Solar System. DES is well placed to detect such a planet and has already been used to discover many other TNOs. Here, we perform tests on eight different supervised machine learning algorithms, using a dataset consisting of simulated TNOs buried within real DES noise data. We found that the best performing classifier was the Random Forest which, when optimised, performed well at detecting the rare objects. We achieve an area under the receiver operating characteristic (ROC) curve, (AUC) $= 0.996 \pm 0.001$. After optimizing the decision threshold of the Random Forest, we achieve a recall of 0.96 while maintaining a precision of 0.80. Finally, by using the optimized classifier to pre-select objects, we are able to run the orbit-fitting stage of our detection pipeline five times faster.

astro-ph.EP↗

Increasing the census of L and T dwarfs in wide binary and multiple systems using Dark Energy Survey DR1 and Gaia DR2 data

We present the discovery of 255 binary and six multiple system candidates with wide > 5" separation composed by ultracool dwarfs companions to stars, plus nine double ultracool dwarf systems. These systems were selected based on common distance criteria. About 90% of the total sample has proper motions available and 73% of the systems also satisfy a common proper motion criterion. The sample of ultracool candidates was taken from the Dark Energy Survey (DES) and the candidate stellar primaries are from Gaia DR2 and DES data. We compute chance alignment probabilities in order to assess the physical nature of each pair. We find that 174 candidate pairs with Gaia DR2 primaries and 81 pairs with a DES star as a primary have chance alignment probabilities < 5%. Only nine candidate systems composed of two ultracool dwarfs were identified. The sample of candidate multiple systems is made up of five triple systems and one quadruple system. The majority of the ultracool dwarfs found in binaries and multiples are of early L type and the typical wide binary fraction over the L spectral types is 2-4%. Our sample of candidate wide binaries with ultracool dwarfs as secondaries constitutes a substantial increase over the known number of such systems, which are very useful to constrain the formation and evolution of ultracool dwarfs.

astro-ph.SR↗

Dark Energy Survey Year 1 Results: the lensing imprint of cosmic voids on the Cosmic Microwave Background

Cosmic voids gravitationally lens the cosmic microwave background (CMB) radiation, resulting in a distinct imprint on degree scales. We use the simulated CMB lensing convergence map from the MICE N-body simulation to calibrate our detection strategy for a given void definition and galaxy tracer density. We then identify cosmic voids in DES Year 1 data and stack the Planck 2015 lensing convergence map on their locations, probing the consistency of simulated and observed void lensing signals. When fixing the shape of the stacked convergence profile to that calibrated from simulations, we find imprints at the $3σ$ significance level for various analysis choices. The best measurement strategies based on the MICE calibration process yield $S/N \sim 4$ for DES Y1, and the best-fit amplitude recovered from the data is consistent with expectations from MICE ($A \sim 1$). Given these results as well as the agreement between them and N-body simulations, we conclude that the previously reported excess integrated Sachs-Wolfe (ISW) signal associated with cosmic voids in DES Y1 has no counterpart in the Planck CMB lensing map.

astro-ph.CO↗

Reducing ground-based astrometric errors with Gaia and Gaussian processes

Stochastic field distortions caused by atmospheric turbulence are a fundamental limitation to the astrometric accuracy of ground-based imaging. This distortion field is measurable at the locations of stars with accurate positions provided by the Gaia DR2 catalog; we develop the use of Gaussian process regression (GPR) to interpolate the distortion field to arbitrary locations in each exposure. We introduce an extension to standard GPR techniques that exploits the knowledge that the 2-dimensional distortion field is curl-free. Applied to several hundred 90-second exposures from the Dark Energy Survey as a testbed, we find that the GPR correction reduces the variance of the turbulent distortions $\approx12\times$, on average, with better performance in denser regions of the Gaia catalog. The RMS per-coordinate distortion in the $riz$ bands is typically $\approx7$ mas before any correction, and $\approx2$ mas after application of the GPR model. The GPR astrometric corrections are validated by the observation that their use reduces, from 10 to 5 mas RMS, the residuals to an orbit fit to $riz$-band observations over 5 years of the $r=18.5$ trans-Neptunian object Eris. We also propose a GPR method, not yet implemented, for simultaneously estimating the turbulence fields and the 5-dimensional stellar solutions in a stack of overlapping exposures, which should yield further turbulence reductions in future deep surveys.

astro-ph.IM↗

Optical follow-up of gravitational wave triggers with DECam during the first two LIGO/VIRGO observing runs

Gravitational wave (GW) events detectable by LIGO and Virgo have several possible progenitors, including black hole mergers, neutron star mergers, black hole--neutron star mergers, supernovae, and cosmic string cusps. A subset of GW events are expected to produce electromagnetic (EM) emission that, once detected, will provide complementary information about their astrophysical context. To that end, the LIGO--Virgo Collaboration (LVC) sends GW candidate alerts to the astronomical community so that searches for their EM counterparts can be pursued. The DESGW group, consisting of members of the Dark Energy Survey (DES), the LVC, and other members of the astronomical community, uses the Dark Energy Camera (DECam) to perform a search and discovery program for optical signatures of LVC GW events. DESGW aims to use a sample of GW events as standard sirens for cosmology. Due to the short decay timescale of the expected EM counterparts and the need to quickly eliminate survey areas with no counterpart candidates, it is critical to complete the initial analysis of each night's images as quickly as possible. We discuss our search area determination, imaging pipeline, and candidate selection processes. We review results from the DESGW program during the first two LIGO--Virgo observing campaigns and introduce other science applications that our pipeline enables.

astro-ph.IM↗

Is every strong lens model unhappy in its own way? Uniform modelling of a sample of 13 quadruply+ imaged quasars

Strong-gravitational lens systems with quadruply-imaged quasars (quads) are unique probes to address several fundamental problems in cosmology and astrophysics. Although they are intrinsically very rare, ongoing and planned wide-field deep-sky surveys are set to discover thousands of such systems in the next decade. It is thus paramount to devise a general framework to model strong-lens systems to cope with this large influx without being limited by expert investigator time. We propose such a general modelling framework (implemented with the publicly available software Lenstronomy) and apply it to uniformly model three-band Hubble Space Telescope Wide Field Camera 3 images of 13 quads. This is the largest uniformly modelled sample of quads to date and paves the way for a variety of studies. To illustrate the scientific content of the sample, we investigate the alignment between the mass and light distribution in the deflectors. The position angles of these distributions are well-aligned, except when there is strong external shear. However, we find no correlation between the ellipticity of the light and mass distributions. We also show that the observed flux-ratios between the images depart significantly from the predictions of simple smooth models. The departures are strongest in the bluest band, consistent with microlensing being the dominant cause in addition to millilensing. Future papers will exploit this rich dataset in combination with ground based spectroscopy and time delays to determine quantities such as the Hubble constant, the free streaming length of dark matter, and the normalization of the initial stellar mass function.

astro-ph.GA↗

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.

astro-ph.CO↗

The impact of spectroscopic incompleteness in direct calibration of redshift distributions for weak lensing surveys

Obtaining accurate distributions of galaxy redshifts is a critical aspect of weak lensing cosmology experiments. One of the methods used to estimate and validate redshift distributions is apply weights to a spectroscopic sample so that their weighted photometry distribution matches the target sample. In this work we estimate the \textit{selection bias} in redshift that is introduced in this procedure. We do so by simulating the process of assembling a spectroscopic sample (including observer-assigned confidence flags) and highlight the impacts of spectroscopic target selection and redshift failures. We use the first year (Y1) weak lensing analysis in DES as an example data set but the implications generalise to all similar weak lensing surveys. We find that using colour cuts that are not available to the weak lensing galaxies can introduce biases of $Δ~z\sim0.015$ in the weighted mean redshift of different redshift intervals. To assess the impact of incompleteness in spectroscopic samples, we select only objects with high observer-defined confidence flags and compare the weighted mean redshift with the true mean. We find that the mean redshift of the DES Y1 weak lensing sample is typically biased at the $Δ~z=0.005-0.05$ level after the weighting is applied. The bias we uncover can have either sign, depending on the samples and redshift interval considered. For the highest redshift bin, the bias is larger than the uncertainties in the other DES Y1 redshift calibration methods, justifying the decision of not using this method for the redshift estimations. We discuss several methods to mitigate this bias.

astro-ph.GA↗

Constraining Radio Mode Feedback in Galaxy Clusters with the Cluster Radio AGN Properties to z$\sim$1

We study the properties of the Sydney University Molonglo Sky Survey (SUMSS) 843~MHz radio AGN population in galaxy clusters from two large catalogs created using the Dark Energy Survey (DES): $\sim$11,800 optically selected RM-Y3 and $\sim$1,000 X-ray selected MARD-Y3 clusters. We show that cluster radio loud AGN are highly concentrated around cluster centers to $z\sim1$. We measure the halo occupation number for cluster radio AGN above a threshold luminosity, finding that the number of radio AGN per cluster increases with cluster halo mass as $N\propto M^{1.2\pm0.1}$ ($N\propto M^{0.68\pm0.34}$) for the RM-Y3 (MARD-Y3) sample. Together, these results indicate that radio mode feedback is favoured in more massive galaxy clusters. Using optical counterparts for these sources, we demonstrate weak redshift evolution in the host broad band colors and the radio luminosity at fixed host galaxy stellar mass. We use the redshift evolution in radio luminosity to break the degeneracy between density and luminosity evolution scenarios in the redshift trend of the radio AGN luminosity function (LF). The LF exhibits a redshift trend of the form $(1+z)^γ$ in density and luminosity, respectively, of $γ_{\rm D}=3.0\pm0.4$ and $γ_{\rm P}=0.21\pm0.15$ in the RM-Y3 sample, and $γ_{\rm D}=2.6\pm0.7$ and $γ_{\rm P}=0.31\pm0.15$ in MARD-Y3. We discuss the physical drivers of radio mode feedback in cluster AGN, and we use the cluster radio galaxy LF to estimate the average radio-mode feedback energy as a function of cluster mass and redshift and compare it to the core ($<0.1R_{500}$) X-ray radiative losses for clusters at $z<1$.

astro-ph.GA↗