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Cristóbal Sifón

Publications and source records attributed to Cristóbal Sifón.

At least 55 records · Page 3Linked to original sources

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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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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The history and mass content of cluster galaxies in the EAGLE simulation

We explore the mass content of galaxies residing in galaxy clusters at z=0 in the EAGLE hydrodynamical simulation as well as the galaxies' mass build-up through cosmic time. We use a galaxy catalogue generated with the HBT+ algorithm, which identifies subhaloes consistently over time by tracking their dynamical evolution throughout the simulation. The satellite subhalo-to-stellar mass relation (SHSMR) is well described by a double power-law. At stellar masses $9<\log m_\star/\mathrm{M}_\odot<10$, satellites have 20-25% the subhalo mass of central galaxies at fixed stellar mass. At high stellar masses the satellite SHSMR is consistent with that of centrals. The satellite SHSMR decreases steeply for satellites closer to the cluster centre, even in projection, broadly consistent with recent weak lensing measurements. The scatter in the satellite SHSMR is larger than that of central galaxies at all cluster masses and cluster-centric distances $R<R_\mathrm{200m}$. The SHSMR scatter decreases with stellar mass by about 12% over an order of magnitude, but this dependence can be explained by the mixing of infall times. There is significant dark matter preprocessing; the most recent infallers into massive clusters had already lost up to 50% of their dark matter by the time of infall, particularly if they fell in indirectly as satellites of another host. On the contrary, on average satellite galaxies are still gaining stellar mass at the time of infall and they do so for another 2 Gyr afterwards, although we see evidence of a slowing growth for indirect infallers. Overall, pre- and post-processing each have similar impacts on the satellite SHSMR. Finally, we provide a simple prescription to infer the mean mass loss experienced by satellites as a function of cluster-centric distance based on a comparison to central galaxies, convenient for observational weak lensing measurements. [abridged]

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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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The Atacama Cosmology Telescope: Galactic Dust Structure and the Cosmic PAH Background in Cross-correlation with WISE

We present a cross-correlation analysis between $1'$ resolution total intensity and polarization observations from the Atacama Cosmology Telescope (ACT) at 150 and 220 GHz and 15$''$ mid-infrared photometry from the Wide-field Infrared Survey Explorer (WISE) over 107 12.5$^\circ\times$12.5$^\circ$ patches of sky. We detect a spatially isotropic signal in the WISE$\times$ACT $TT$ cross power spectrum at 30$σ$ significance that we interpret as the correlation between the cosmic infrared background at ACT frequencies and polycyclic aromatic hydrocarbon (PAH) emission from galaxies in WISE, i.e., the cosmic PAH background. Within the Milky Way, the Galactic dust $TT$ spectra are generally well-described by power laws in $\ell$ over the range 10$^3 < \ell < $10$^4$, but there is evidence both for variability in the power law index and for non-power law behavior in some regions. We measure a positive correlation between WISE total intensity and ACT $E$-mode polarization at 1000$ < \ell \lesssim $6000 at $>$3$σ$ in each of 35 distinct $\sim$100 deg$^2$ regions of the sky, suggesting alignment between Galactic density structures and the local magnetic field persists to sub-parsec physical scales in these regions. The distribution of $TE$ amplitudes in this $\ell$ range across all 107 regions is biased to positive values, while there is no evidence for such a bias in the $TB$ spectra. This work constitutes the highest-$\ell$ measurements of the Galactic dust $TE$ spectrum to date and indicates that cross-correlation with high-resolution mid-infrared measurements of dust emission is a promising tool for constraining the spatial statistics of dust emission at millimeter wavelengths.

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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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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.

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The Atacama Cosmology Telescope: Map-Based Noise Simulations for DR6

The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a $\sim 20\%$ excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code, $\mathtt{mnms}$, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO).

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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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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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Dynamical cluster masses from photometric surveys

The masses of galaxy clusters can be measured using data obtained exclusively from wide photometric surveys in one of two ways: directly from the amplitude of the weak lensing signal or, indirectly, through the use of scaling relations calibrated using binned lensing measurements. In this paper, we build on a recently proposed idea and implement an alternative method based on the radial profile of the satellite distribution. This technique relies on splashback, a feature associated with the apocenter of recently accreted galaxies that offers a clear window into the phase-space structure of clusters without the use of velocity information. We carry out this dynamical measurement using the stacked satellite distribution around a sample of luminous red galaxies in the fourth data release of the Kilo-Degree Survey and validate our results using abundance-matching and lensing masses. To illustrate the power of this measurement, we combine dynamical and lensing mass estimates to robustly constrain scalar-tensor theories of gravity at cluster scales. Our results exclude departures from General Relativity of order unity. We conclude the paper by discussing the implications for future data sets. Because splashback mass measurements scale only with the survey volume, stage-IV photometric surveys are well-positioned to use splashback to provide high-redshift cluster masses.

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The Atacama Cosmology Telescope: limits on dark matter-baryon interactions from DR4 power spectra

Diverse astrophysical observations suggest the existence of cold dark matter that interacts only gravitationally with radiation and ordinary baryonic matter. Any nonzero coupling between dark matter and baryons would provide a significant step towards understanding the particle nature of dark matter. Measurements of the cosmic microwave background (CMB) provide constraints on such a coupling that complement laboratory searches. In this work we place upper limits on a variety of models for dark matter elastic scattering with protons and electrons by combining large-scale CMB data from the Planck satellite with small-scale information from Atacama Cosmology Telescope (ACT) DR4 data. In the case of velocity-independent scattering, we obtain bounds on the interaction cross section for protons that are 40\% tighter than previous constraints from the CMB anisotropy. For some models with velocity-dependent scattering we find best-fitting cross sections with a 2$σ$ deviation from zero, but these scattering models are not statistically preferred over $Λ$CDM in terms of model selection.

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The Atacama Cosmology Telescope: Measurement and Analysis of 1D Beams for DR4

We describe the measurement and treatment of the telescope beams for the Atacama Cosmology Telescope's fourth data release, DR4. Observations of Uranus are used to measure the central portion (<12') of the beams to roughly -40 dB of the peak. Such planet maps in intensity are used to construct azimuthally averaged beam profiles, which are fit with a physically motivated model before being transformed into Fourier space. We investigate and quantify a number of percent-level corrections to the beams, all of which are important for precision cosmology. Uranus maps in polarization are used to measure the temperature-to-polarization leakage in the main part of the beams, which is <1% (2.5%) at 150 GHz (98 GHz). The beams also have polarized sidelobes, which are measured with observations of Saturn and deprojected from the ACT time-ordered data. Notable changes relative to past ACT beam analyses include an improved subtraction of the atmospheric effects from Uranus calibration maps, incorporation of a scattering term in the beam profile model, and refinements to the beam model uncertainties and the main temperature-to-polarization leakage terms in the ACT power spectrum analysis.

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A high-resolution view of the filament of gas between Abell 399 and Abell 401 from the Atacama Cosmology Telescope and MUSTANG-2

We report a significant detection of the hot intergalactic medium in the filamentary bridge connecting the galaxy clusters Abell 399 and Abell 401. This result is enabled by a low-noise, high-resolution map of the thermal Sunyaev-Zeldovich signal from the Atacama Cosmology Telescope (ACT) and Planck satellite. The ACT data provide the $1.65'$ resolution that allows us to clearly separate the profiles of the clusters, whose centres are separated by $37'$, from the gas associated with the filament. A model that fits for only the two clusters is ruled out compared to one that includes a bridge component at $>5σ$. Using a gas temperature determined from Suzaku X-ray data, we infer a total mass of $(3.3\pm0.7)\times10^{14}\,\mathrm{M}_{\odot}$ associated with the filament, comprising about $8\%$ of the entire Abell 399-Abell 401 system. We fit two phenomenological models to the filamentary structure; the favoured model has a width transverse to the axis joining the clusters of ${\sim}1.9\,\mathrm{Mpc}$. When combined with the Suzaku data, we find a gas density of $(0.88\pm0.24)\times10^{-4}\,\mathrm{cm}^{-3}$, considerably lower than previously reported. We show that this can be fully explained by a geometry in which the axis joining Abell 399 and Abell 401 has a large component along the line of sight, such that the distance between the clusters is significantly greater than the $3.2\,\mathrm{Mpc}$ projected separation on the plane of the sky. Finally, we present initial results from higher resolution ($12.7"$ effective) imaging of the bridge with the MUSTANG-2 receiver on the Green Bank Telescope.

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Observations of compact sources in galaxy clusters using MUSTANG2

Compact sources can cause scatter in the scaling relationships between the amplitude of the thermal Sunyaev-Zel'dovich Effect (tSZE) in galaxy clusters and cluster mass. Estimates of the importance of this scatter vary - largely due to limited data on sources in clusters at the frequencies at which tSZE cluster surveys operate. In this paper we present 90 GHz compact source measurements from a sample of 30 clusters observed using the MUSTANG2 instrument on the Green Bank Telescope. We present simulations of how a source's flux density, spectral index, and angular separation from the cluster's center affect the measured tSZE in clusters detected by the Atacama Cosmology Telescope (ACT). By comparing the MUSTANG2 measurements with these simulations we calibrate an empirical relationship between 1.4 GHz flux densities from radio surveys and source contamination in ACT tSZE measurements. We find 3 per cent of the ACT clusters have more than a 20 per cent decrease in Compton-y but another 3 per cent have a 10 per cent increase in the Compton-y due to the matched filters used to find clusters. As sources affect the measured tSZE signal and hence the likelihood that a cluster will be detected, testing the level of source contamination in the tSZE signal using a tSZE selected catalog is inherently biased. We confirm this by comparing the ACT tSZE catalog with optically and X-ray selected cluster catalogs. There is a strong case for a large, high resolution survey of clusters to better characterize their source population.

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The Atacama Cosmology Telescope: Microwave Intensity and Polarization Maps of the Galactic Center

We present arcminute-resolution intensity and polarization maps of the Galactic center made with the Atacama Cosmology Telescope (ACT). The maps cover a 32 deg$^2$ field at 98, 150, and 224 GHz with $\vert l\vert\le4^\circ$, $\vert b\vert\le2^\circ$. We combine these data with Planck observations at similar frequencies to create coadded maps with increased sensitivity at large angular scales. With the coadded maps, we are able to resolve many known features of the Central Molecular Zone (CMZ) in both total intensity and polarization. We map the orientation of the plane-of-sky component of the Galactic magnetic field inferred from the polarization angle in the CMZ, finding significant changes in morphology in the three frequency bands as the underlying dominant emission mechanism changes from synchrotron to dust emission. Selected Galactic center sources, including Sgr A*, the Brick molecular cloud (G0.253+0.016), the Mouse pulsar wind nebula (G359.23-0.82), and the Tornado supernova remnant candidate (G357.7-0.1), are examined in detail. These data illustrate the potential for leveraging ground-based Cosmic Microwave Background polarization experiments for Galactic science.

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Atacama Cosmology Telescope measurements of a large sample of candidates from the Massive and Distant Clusters of WISE Survey: Sunyaev-Zeldovich effect confirmation of MaDCoWS candidates using ACT

Galaxy clusters are an important tool for cosmology, and their detection and characterization are key goals for current and future surveys. Using data from the Wide-field Infrared Survey Explorer (WISE), the Massive and Distant Clusters of WISE Survey (MaDCoWS) located 2,839 significant galaxy overdensities at redshifts $0.7\lesssim z\lesssim 1.5$, which included extensive follow-up imaging from the Spitzer Space Telescope to determine cluster richnesses. Concurrently, the Atacama Cosmology Telescope (ACT) has produced large area mm-wave maps in three frequency bands along with a large catalog of Sunyaev-Zeldovich (SZ) selected clusters, as part of its Data Release 5 (DR5). Using the maps and cluster catalog from DR5, we explore the scaling between SZ mass and cluster richness. We use complementary radio survey data from the Very Large Array, submillimeter data from Herschel, and ACT 224~GHz data to assess the impact of contaminating sources on the SZ signals. We then use a hierarchical Bayesian model to fit the mass-richness scaling relation. We find that MaDCoWS clusters have submillimeter contamination which is consistent with a gray-body spectrum, while the ACT clusters are consistent with no submillimeter emission on average. We find the best fit ACT SZ mass vs. MaDCoWS richness scaling relation has a slope of $κ= 1.84^{+0.15}_{-0.14}$, where the slope is defined as $M\propto λ_{15}^κ$ where $λ_{15}$ is the richness. Additionally, we find that the approximate level of in-fill of the ACT and MaDCoWS cluster SZ signals to be at the percent level

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The Atacama Cosmology Telescope: A search for Planet 9

We use Atacama Cosmology Telescope (ACT) observations at 98 GHz (2015--2019), 150 GHz (2013--2019) and 229 GHz (2017--2019) to perform a blind shift-and-stack search for Planet 9. The search explores distances from 300 AU to 2000 AU and velocities up to 6.3 arcmin per year, depending on the distance. For a 5 Earth-mass Planet 9 the detection limit varies from 325 AU to 625 AU, depending on the sky location. For a 10 Earth-mass planet the corresponding range is 425 AU to 775 AU. The search covers the whole 18,000 square degrees of the ACT survey, though a slightly deeper search is performed for the parts of the sky consistent with Planet 9's expected orbital inclination. No significant detections are found, which is used to place limits on the mm-wave flux density of Planet 9 over much of its orbit. Overall we eliminate roughly 17% and 9% of the parameter space for a 5 and 10 Earth-mass Planet 9 respectively. We also provide a list of the 10 strongest candidates from the search for possible follow-up. More generally, we exclude (at 95% confidence) the presence of an unknown Solar system object within our survey area brighter than 4--12 mJy (depending on position) at 150 GHz with current distance $300 \text{ AU} < r < 600 \text{ AU}$ and heliocentric angular velocity $1.5'/\text{yr} < v \cdot \frac{500 \text{ AU}}{r} < 2.3'\text{yr}$, corresponding to low-to-moderate eccentricities. These limits worsen gradually beyond 600 AU, reaching 5--15 mJy by 1500 AU.

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