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J. Colin Hill

Publications and source records attributed to J. Colin Hill.

At least 37 records · Page 2Linked to original sources

Minimizing Contaminant Leakage in Internal Linear Combination Maps Using a Data-Driven Approach

The thermal Sunyaev-Zel'dovich (tSZ) effect, the inverse-Compton scattering of cosmic microwave background (CMB) photons off high-energy electrons, is a powerful probe of hot, ionized gas in the Universe. It is often measured via cross-correlations of CMB data with large-scale structure (LSS) tracers to constrain gas physics and improve cosmological constraints. The largest source of bias to these measurements is the leakage of poorly understood thermal dust emission from star-forming galaxies -- the cosmic infrared background (CIB) -- into the tSZ maps. This CIB contamination is difficult to clean via multifrequency component separation methods, such as internal linear combination (ILC), due to uncertainty in its spectral energy distribution (SED), which exhibits spatial and line-of-sight variation and decorrelation. Thus, improved ILC-based techniques have been developed to null ("deproject") both the CIB and its first moment with respect to the emissivity index $β$ in order to robustly remove the CIB despite the lack of first-principles knowledge of its SED. While decreasing the bias, such procedures can significantly increase the noise in the resulting ILC maps. In this paper, we develop a data-driven algorithm for determining the optimal CIB SED to deproject when measuring a tSZ-LSS cross-correlation, obviating the need to deproject the first moment in the ILC map used for such a measurement. Our method gives an unbiased cross-correlation with increased signal-to-noise. We demonstrate its efficacy on simulations, finding a 60% improvement in the signal-to-noise ratio for an example tSZ cross-correlation with a halo sample at redshifts $0.8 < z < 1.8$, as compared to moment deprojection approaches. Though used here for CIB removal in tSZ cross-correlations, our method is broadly applicable to minimizing contaminant leakage in ILC maps. Our code is available in CIB-deproj.

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A new constraint on the $y$-distortion with FIRAS: robustness of component separation methods

The sky-averaged Compton-$y$ distortion in the cosmic microwave background (CMB) energy spectrum, $\langle y \rangle$, provides information about energy injection in the Universe occurring at $z \lesssim 5\times10^{4}$. It is primarily sourced by the thermal Sunyaev-Zeldovich effect -- the up-scattering of CMB photons on free electrons in collapsed dark matter halos. In this work and our companion paper, Ref. [1], we perform a re-analysis of the archival COBE/FIRAS data to constrain $\langle y \rangle$. We utilize two analysis approaches: (i) fitting the sky-averaged intensity spectrum (frequency monopole) and (ii) fitting the sky spectrum in each pixel (pixel-by-pixel). We obtain the baseline upper limits $\langle y \rangle < 31\times 10^{-6}$ and $\langle y \rangle < 8.3\times 10^{-6}$ (both at $95\%$ C.L.) for these two approaches, respectively. We present the first detailed comparison of these analysis methods on both mock skies and real data. Our findings suggest that accounting for the spatial variability of foregrounds via pixel-by-pixel fitting allows for tighter constraints on $\langle y \rangle$ by a factor of $\approx 3-5$ as compared to the frequency monopole method. We show that our frequency monopole results agree well with predictions from Fisher forecast techniques based on the sky-averaged signal, which have been used for forecasting future spectral distortion experiments. Our results thus suggest that the scientific reach of future spectral distortion experiments can potentially be enhanced by a factor of a few via more optimal component separation methods, and we identify the pixel-by-pixel method as one such robust way to achieve this. We discuss the implications of our improved constraints on $\langle y \rangle$ from the pixel-by-pixel method in Ref. [1].

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CLASS_SZ II: Notes and Examples of Fast and Accurate Calculations of Halo Model, Large Scale Structure and Cosmic Microwave Background Observables

These notes are very much work-in-progress and simply intended to showcase, in various degrees of details (and rigour), some of the cosmology calculations that class_sz can do. We describe the class_sz code in C, Python and Jax. Based on the Boltzmann code class, it can compute a wide range of observables relevant to current and forthcoming CMB and Large Scale Structure surveys. This includes galaxy shear and clustering, CMB lensing, thermal and kinetic Sunyaev and Zeldovich observables, Cosmic Infrared Background, cross-correlations and three-point statistics. Calculations can be done either within the halo model or the linear bias model. For standard $Λ$CDM cosmology and extensions, class_sz uses high-accuracy cosmopower emulators of the CMB and matter power spectrum to accelerate calculations. With this, along with efficient numerical integration routines, most class_sz output can be obtained in less than 500 ms (CMB $C_\ell$'s or matter $P(k)$ take $\mathcal{O}(1\mathrm{ms})$), allowing for fast or ultra-fast parameter inference analyses. Parts of the calculations are "jaxified", so the software can be integrated into differentiable pipelines.

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A Novel Bispectrum Estimator of the Kinematic Sunyaev-Zel'dovich Effect using Projected Fields

With the advent of current and future high-resolution CMB experiments, the kinematic Sunyaev-Zel'dovich (kSZ) effect has become a unique observational probe of the distribution of baryons and velocities in the Universe. In this work, we propose a novel binned bispectrum of the form temperature-temperature-density to extract the late-time kSZ effect from cleaned CMB maps. Unlike 'kSZ tomography' methods, this estimator can use any tracer of the large-scale structure density field projected along the line-of-sight and does not require individual redshifts. With our method, we forecast signal-to-noise ratios (SNR) of $\sim$100-200 for the upcoming Simons Observatory (SO) and CMB-S4 correlated with a galaxy sample from WISE that is restricted to the linear regime. We also extend galaxy modes into the non-linear regime and explore this harmonic space to show that the SNR peaks for squeezed triangles that have a short (linear) density mode and long temperature modes in harmonic space. The existing kSZ$^{2}-$density projected-fields estimator compresses the rich information contained in this bispectrum across various scales and triangle shapes. Moreover, we find that the lensing correction to this estimator's signal is relatively small for high-SNR squeezed triangle configurations. We study the dependence of this kSZ signal on $Λ$CDM parameters for SO and CMB-S4 and forecast initial constraints on the sum of neutrino masses while restricting to the linear galaxy bias regime. Our work illustrates the potential of the projected-fields kSZ bispectrum as a novel probe of baryonic abundance and beyond-$Λ$CDM cosmology with upcoming precision measurements.

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The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $Λ$CDM Parameters

We present power spectra of the cosmic microwave background (CMB) anisotropy in temperature and polarization, measured from the Data Release 6 maps made from Atacama Cosmology Telescope (ACT) data. These cover 19,000 deg$^2$ of sky in bands centered at 98, 150 and 220 GHz, with white noise levels three times lower than Planck in polarization. We find that the ACT angular power spectra estimated over 10,000 deg$^2$, and measured to arcminute scales in TT, TE and EE, are well fit by the sum of CMB and foregrounds, where the CMB spectra are described by the $Λ$CDM model. Combining ACT with larger-scale Planck data, the joint P-ACT dataset provides tight limits on the ingredients, expansion rate, and initial conditions of the universe. We find similar constraining power, and consistent results, from either the Planck power spectra or from ACT combined with WMAP data, as well as from either temperature or polarization in the joint P-ACT dataset. When combined with CMB lensing from ACT and Planck, and baryon acoustic oscillation data from DESI DR1, we measure a baryon density of $Ω_b h^2=0.0226\pm0.0001$, a cold dark matter density of $Ω_c h^2=0.118\pm0.001$, a Hubble constant of $H_0=68.22\pm0.36$ km/s/Mpc, a spectral index of $n_s=0.974\pm0.003$, and an amplitude of density fluctuations of $σ_8=0.813\pm0.005$. Including the DESI DR2 data tightens the Hubble constant to $H_0=68.43\pm0.27$ km/s/Mpc; $Λ$CDM parameters agree between the P-ACT and DESI DR2 data at the $1.6σ$ level. We find no evidence for excess lensing in the power spectrum, and no departure from spatial flatness. The contribution from Sunyaev-Zel'dovich (SZ) anisotropy is detected at high significance; we find evidence for a tilt with suppressed small-scale power compared to our baseline SZ template spectrum, consistent with hydrodynamical simulations with feedback.

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The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

We use new cosmic microwave background (CMB) primary temperature and polarization anisotropy measurements from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) to test foundational assumptions of the standard cosmological model and set constraints on extensions to it. We derive constraints from the ACT DR6 power spectra alone, as well as in combination with legacy data from Planck. To break geometric degeneracies, we include ACT and Planck CMB lensing data and baryon acoustic oscillation data from DESI Year-1, and further add supernovae measurements from Pantheon+ for models that affect the late-time expansion history. We verify the near-scale-invariance (running of the spectral index $d n_s/d\ln k = 0.0062 \pm 0.0052$) and adiabaticity of the primordial perturbations. Neutrino properties are consistent with Standard Model predictions: we find no evidence for new light, relativistic species that are free-streaming ($N_{\rm eff} = 2.86 \pm 0.13$, which combined with external BBN data becomes $N_{\rm eff} = 2.89 \pm 0.11$), for non-zero neutrino masses ($\sum m_ν< 0.082$ eV at 95% CL), or for neutrino self-interactions. We also find no evidence for self-interacting dark radiation ($N_{\rm idr} < 0.134$), early-universe variation of fundamental constants, early dark energy, primordial magnetic fields, or modified recombination. Our data are consistent with standard BBN, the FIRAS-inferred CMB temperature, a dark matter component that is collisionless and with only a small fraction allowed as axion-like particles, a cosmological constant, and the late-time growth rate predicted by general relativity. We find no statistically significant preference for a departure from the baseline $Λ$CDM model. In general, models introduced to increase the Hubble constant or to decrease the amplitude of density fluctuations inferred from the primary CMB are not favored by our data.

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The Atacama Cosmology Telescope: A search for late-time anisotropic screening of the Cosmic Microwave Background

Since the formation of the first stars, most of the gas in the Universe has been ionized. Spatial variations in the density of this ionized gas generate cosmic microwave background anisotropies via Thomson scattering, a process known as the ``anisotropic screening'' effect. We propose and implement for the first time a new estimator to cross-correlate unWISE galaxies and anisotropic screening, as measured by the Atacama Cosmology Telescope and Planck satellite. We do not significantly detect the effect; the null hypothesis is consistent with the data at 1.7 $σ$ (resp. 0.016 $σ$) for the blue (resp. green) unWISE sample. We obtain an upper limit on the integrated optical depth within a 6 arcmin disk to be $\barτ< 0.033$ arcmin$^2$ at 95\% confidence for the blue sample and $\barτ< 0.057$ arcmin$^2$ for the green sample. Future measurements with Simons Observatory and CMB-S4 should detect this effect significantly. Complementary to the kinematic Sunyaev-Zel'dovich effect, this probe of the gas distribution around halos will inform models of feedback in galaxy formation and baryonic effects in galaxy lensing.

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Constraining cosmology with thermal Sunyaev-Zel'dovich maps: Minkowski functionals, peaks, minima, and moments

The thermal Sunyaev-Zel'dovich effect (tSZ) is a sensitive probe of cosmology, as it traces the abundance of galaxy clusters and groups in the late-time Universe. Upcoming cosmic microwave background experiments such as the Simons Observatory (SO) and CMB-S4 will provide low-noise and high-resolution component-separated tSZ maps covering a large sky fraction. The tSZ signal is highly non-Gaussian; therefore, higher-order statistics are needed to optimally extract information from these maps. In this work, we study the cosmological constraining power of several tSZ statistics -- Minkowski functionals (MFs), peaks, minima, and moments -- that have yielded promising results in capturing non-Gaussian information from other cosmological data. Using a large suite of halo-model-based tSZ simulations with varying $Ω_{c}$ and $σ_{8}$ (154 cosmologies and over $800, 000$ maps, each $10.5\times10.5$ deg$^{2}$), we show that by combining these observables, we can achieve $\approx 29\times$ tighter constraints compared to using the tSZ power spectrum alone in an idealized noiseless case, with the MFs dominating the constraints. We show that much of the MF constraining power arises from halos below the detection threshold of cluster surveys, suggesting promising synergies with cluster-count analyses. Finally, we demonstrate that these statistics have the potential to deliver tight constraints even in the presence of noise. For example, using post-component-separation tSZ noise expected for SO, we obtain $\approx1.6\times$ and $\approx1.8\times$ tighter constraints than the power spectrum with MFs and all statistics combined, respectively. We show that the constraints from MFs approach the noiseless case for white-noise levels $\lesssim 1 \,\, μ$K-arcmin.

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Impact of Galactic non-Gaussian foregrounds on CMB lensing measurements

Weak gravitational lensing of the CMB has been established as a robust and powerful observable for precision cosmology. However, the impact of Galactic foregrounds, which has been studied less extensively than many other potential systematics, could in principle pose a problem for CMB lensing measurements. These foregrounds are inherently non-Gaussian and hence might mimic the characteristic signal that lensing estimators are designed to measure. We present an analysis that quantifies the level of contamination from Galactic dust in lensing measurements, focusing particularly on measurements with the Atacama Cosmology Telescope and the Simons Observatory. We employ a whole suite of foreground models and study the contamination of lensing measurements with both individual frequency channels and multifrequency combinations. We test the sensitivity of different estimators to the level of foreground non-Gaussianity, and the dependence on sky fraction and multipole range used. We find that Galactic foregrounds do not present a problem for the Atacama Cosmology Telescope experiment (the bias in the inferred CMB lensing power spectrum amplitude remains below $0.3σ$). For Simons Observatory, not all foreground models remain below this threshold. Although our results are conservative upper limits, they suggest that further work on characterizing dust biases and determining the impact of mitigation methods is well motivated, especially for the largest sky fractions.

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The ISW-Lensing Bispectrum & Trispectrum

Due to the integrated Sachs-Wolfe (ISW) effect, cosmic microwave background (CMB) temperature and polarization fluctuations are correlated with the gravitational lensing potential. Famously, this induces a CMB three-point function, whose shape can be used to constrain dark energy and modifications to gravity. An analogous effect occurs at higher-order, producing an ISW-lensing trispectrum whose amplitude is hitherto unconstrained. We present a detailed discussion of this effect, and define minimum-variance estimators for the ISW-lensing three- and four-point functions. These are implemented within the PolySpec code, and bear strong similarities to the quadratic estimators used in lensing analyses. Applying these tools to Planck, we obtain strong detections of the bispectrum amplitude (consistent with previous works), but find only weak constraints on the trispectrum, due to a strong cancellation between the various ISW-induced contributions. We additionally forecast the constraints from future datasets, finding that (a) simple estimators for the ISW-lensing bispectrum will be severely limited by non-Gaussian modifications to the covariance, and (b) the ISW-lensing trispectrum will be very challenging to detect even with high-resolution future experiments. We finally consider the induced bias on primordial non-Gaussianity amplitudes (and lensing itself), which we show to be large for the bispectrum (as expected) but negligible for the trispectrum.

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Too Hot to Handle: Searching for Inflationary Particle Production in Planck Data

Non-adiabatic production of massive particles is a generic feature of many inflationary mechanisms. If sufficiently massive, these particles can leave features in the cosmic microwave background (CMB) that are not well-captured by traditional correlation function analyses. We consider a scenario in which particle production occurs only in a narrow time-interval during inflation, eventually leading to CMB hot- or coldspots with characteristic shapes and sizes. Searching for such features in CMB data is analogous to searching for late-Universe hot- or coldspots, such as those due to the thermal Sunyaev-Zel'dovich (tSZ) effect. Exploiting this data-analysis parallel, we perform a search for particle-production hotspots in the Planck PR4 temperature dataset, which we implement via a matched-filter analysis. Our pipeline is validated on synthetic observations and found to yield unbiased constraints on sufficiently large hotspots across $\approx 60\%$ of the sky. After removing point sources and tSZ clusters, we find no evidence for new physics and place novel bounds on the coupling between the inflaton and massive particles. These bounds are strongest for larger hotspots, produced early in inflation, whilst sensitivity to smaller hotspots is limited by noise and beam effects. Through such methods we can constrain particles with masses $\mathcal{O}(100)$ times larger than the inflationary Hubble scale, which represents possibly the highest energies ever directly probed with observational data.

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The Atacama Cosmology Telescope: DR6 Maps

We present Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) maps of the Cosmic Microwave Background temperature and polarization anisotropy at arcminute resolution over three frequency bands centered on 98, 150 and 220 GHz. The maps are based on data collected with the AdvancedACT camera over the period 2017--2022 and cover 19,000 square degrees with a median combined depth of 10 uK arcmin. We describe the instrument, mapmaking and map properties and illustrate them with a number of figures and tables. The ACT DR6 maps and derived products are available on LAMBDA at https://lambda.gsfc.nasa.gov/product/act/actadv_prod_table.html. We also provide an interactive web atlas at https://phy-act1.princeton.edu/public/snaess/actpol/dr6/atlas and HiPS data sets in Aladin (e.g. https://alasky.cds.unistra.fr/ACT/DR4DR6/color_CMB).

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Systematic error mitigation for the PIXIE Fourier transform spectrometer

The Primordial Inflation Explorer (PIXIE) is an Explorer-class mission concept to measure the spectrum and polarization of the cosmic microwave background. Cosmological signals are small compared to the instantaneous instrument noise, requiring strict control of instrumental signals. The instrument design provides multiple levels of null operation, signal modulation, and signal differences, with only few-percent systematic error suppression required at each level. Jackknife tests based on discrete instrument symmetries provide an independent means to identify, model, and remove remaining instrumental signals. We use detailed time-ordered simulations, including realistic performance and tolerance parameters, to evaluate the instrument response to broad classes of systematic errors for both spectral distortions and polarization. The largest systematic errors contribute additional white noise at the few-percent level compared to the dominant photon noise. Coherent instrumental effects which do not integrate down are smaller still, and remain several orders of magnitude below the targeted cosmological signals.

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The Atacama Cosmology Telescope: Multi-probe cosmology with unWISE galaxies and ACT DR6 CMB lensing

We present a joint analysis of the CMB lensing power spectra measured from the Data Release 6 of the Atacama Cosmology Telescope and Planck PR4, cross-correlations between the ACT and Planck lensing reconstruction and galaxy clustering from unWISE, and the unWISE clustering auto-spectrum. We obtain 1.5% constraints on the matter density fluctuations at late times parametrised by the best constrained parameter combination $S_8^{\rm 3x2pt}\equivσ_8 (Ω_m/0.3)^{0.4}=0.815\pm0.012$. The commonly used $S_8\equivσ_8 (Ω_m/0.3)^{0.5}$ parameter is constrained to $S_8=0.816\pm0.015$. In combination with baryon acoustic oscillation (BAO) measurements we find $σ_8=0.815\pm 0.012$. We also present sound-horizon-independent estimates of the present day Hubble rate of $H_0=66.4^{+3.2}_{-3.7} \,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ from our large scale structure data alone and $H_0=64.3^{+2.1}_{-2.4}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ in combination with uncalibrated supernovae from Pantheon+. Using parametric estimates of the evolution of matter density fluctuations, we place constraints on cosmic structure in a range of high redshifts typically inaccessible with cross-correlation analyses. Combining lensing cross- and auto-correlations, we derive a 3.3% constraint on the integrated matter density fluctuations above $z=2.4$, one of the tightest constraints in this redshift range and fully consistent with a $Λ$CDM model fit to the primary CMB from Planck. Combining with primary CMB observations and using the extended low redshift coverage of these combined data sets we derive constraints on a variety of extensions to the $Λ$CDM model including massive neutrinos, spatial curvature, and dark energy. We find in flat $Λ$CDM $\sum m_ν<0.12$ eV at 95% confidence using the LSS data, BAO measurements from SDSS and primary CMB observations.

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On the Impacts of Halo Model Implementations in Sunyaev-Zeldovich Cross-Correlation Analyses

Statistical studies of the circumgalactic medium (CGM) using Sunyaev-Zeldovich (SZ) observations offer a promising method of studying the gas properties of galaxies and the astrophysics that govern their evolution. Forward modeling profiles from theory and simulations allows them to be refined directly off of data, but there are currently significant differences between the thermal SZ (tSZ) observations of the CGM and the predicted tSZ signal. While these discrepancies could be inherent, they could also be the result of decisions in the forward modeling used to build statistical measures off of theory. In order to see effects of this, we compare an analysis utilizing halo occupancy distributions (HODs) implemented in halo models to simulate the galaxy distribution against a previous studies which weighted their results off of the CMASS galaxy sample, which contains nearly one million galaxies, mainly centrals of group sized halos, selected for relatively uniform stellar mass across redshifts between $0.4<z<0.7$. We review some of the implementation differences that can account for changes, such as miscentering, one-halo/two-halo cutoff radii, and mass ranges, all of which will need to be given the proper attention in future high-signal-to-noise studies. We find that our more thorough model predicts a signal $\sim 25\%$ stronger than the one from previous studies on the exact same sample, resulting in a $33\%$ improved fit for non-dust-contaminated angular scales. Additionally, we find that modifications that change the satellite fraction even by just a few percents, such as editing the halo mass range and certain HOD parameters, result in strong changes in the final signal. Although significant, this discrepancy from the modeling choices is not large enough to completely account for the existing disagreements between simulations and measurements.

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The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra

The Atacama Cosmology Telescope Data Release 6 (ACT DR6) power spectrum is expected to provide state-of-the-art cosmological constraints, with an associated need for precise error modeling. In this paper we design, and evaluate the performance of, an analytic covariance matrix prescription for the DR6 power spectrum that sufficiently accounts for the complicated ACT map properties. We use recent advances in the literature to handle sharp features in the signal and noise power spectra, and account for the effect of map-level anisotropies on the covariance matrix. In including inhomogeneous survey depth information, the resulting covariance matrix prescription is structurally similar to that used in the $\textit{Planck}$ Cosmic Microwave Background (CMB) analysis. We quantify the performance of our prescription using comparisons to Monte Carlo simulations, finding better than $3\%$ agreement. This represents an improvement from a simpler, pre-existing prescription, which differs from simulations by $\sim16\%$. We develop a new method to correct the analytic covariance matrix using simulations, after which both prescriptions achieve better than $1\%$ agreement. This correction method outperforms a commonly used alternative, where the analytic correlation matrix is assumed to be accurate when correcting the covariance. Beyond its use for ACT, this framework should be applicable for future high resolution CMB experiments including the Simons Observatory (SO).

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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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The Atacama Cosmology Telescope: Large-scale velocity reconstruction with the kinematic Sunyaev--Zel'dovich effect and DESI LRGs

The kinematic Sunyaev--Zel'dovich (kSZ) effect induces a non-zero density-density-temperature bispectrum, which we can use to reconstruct the large-scale velocity field from a combination of cosmic microwave background (CMB) and galaxy density measurements, in a procedure known as ``kSZ velocity reconstruction''. This method has been forecast to constrain large-scale modes with future galaxy and CMB surveys, improving their measurement beyond what is possible with the galaxy surveys alone. Such measurements will enable tighter constraints on large-scale signals such as primordial non-Gaussianity, deviations from homogeneity, and modified gravity. In this work, we demonstrate a statistically significant measurement of kSZ velocity reconstruction for the first time, by applying quadratic estimators to the combination of the ACT DR6 CMB+kSZ map and the DESI LRG galaxies (with photometric redshifts) in order to reconstruct the velocity field. We do so using a formalism appropriate for the 2-dimensional projected galaxy fields that we use, which naturally incorporates the curved-sky effects important on the largest scales. We find evidence for the signal by cross-correlating with an external estimate of the velocity field from the spectroscopic BOSS survey and rejecting the null (no-kSZ) hypothesis at $3.8σ$. Our work presents a first step towards the use of this observable for cosmological analyses.

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