arXiv subjects

Dillon Brout

Publications and source records attributed to Dillon Brout.

At least 37 records · Page 2Linked to original sources

arXiv2023

The Impact of Dust on Cepheid and Type Ia Supernova Distances

Milky-Way and intergalactic dust extinction and reddening must be accounted for in measurements of distances throughout the universe. This work provides a comprehensive review of the various impacts of cosmic dust focusing specifically on its effects on two key distance indicators used in the distance ladder: Cepheid variable stars and Type Ia supernovae. We review the formalism used for computing and accounting for dust extinction and reddening as a function of wavelength. We also detail the current state of the art knowledge of dust properties in the Milky Way and in host galaxies. We discuss how dust has been accounted for in both the Cepheid and SN distance measurements. Finally, we show how current uncertainties on dust modeling impact the inferred luminosities and distances, but that measurements of the Hubble constant remain robust to these uncertainties.

astro-ph.CO↗

arXiv2023

Amalgame: Cosmological Constraints from the First Combined Photometric Supernova Sample

Future constraints of cosmological parameters from Type Ia supernovae (SNe Ia) will depend on the use of photometric samples, those samples without spectroscopic measurements of the SNe Ia. There is a growing number of analyses that show that photometric samples can be utilised for precision cosmological studies with minimal systematic uncertainties. To investigate this claim, we perform the first analysis that combines two separate photometric samples, SDSS and Pan-STARRS, without including a low-redshift anchor. We evaluate the consistency of the cosmological parameters from these two samples and find they are consistent with each other to under $1σ$. From the combined sample, named Amalgame, we measure $Ω_M = 0.328 \pm 0.024$ with SN alone in a flat $Λ$CDM model, and $Ω_M = 0.330 \pm 0.018$ and $w = -1.016^{+0.055}_{-0.058}$ when combining with a Planck data prior and a flat $w$CDM model. These results are consistent with constraints from the Pantheon+ analysis of only spectroscopically confirmed SNe Ia, and show that there are no significant impediments to analyses of purely photometric samples of SNe Ia.

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arXiv2023

Roman CCS White Paper: Measuring Type Ia Supernovae Discovered in the Roman High Latitude Time Domain Survey

We motivate the cosmological science case of measuring Type Ia supernovae with the Nancy Grace Roman Space Telescope as part of the High Latitude Time Domain Survey. We discuss previously stated requirements for the science, and a baseline survey strategy. We discuss the various areas that must still be optimized and point to the other white papers that consider these topics in detail. Overall, the baseline case should enable an exquisite measurement of dark energy using SNe Ia from z=0.1 to z>2, and further optimization should only strengthen this once-in-a-generation experiment.

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arXiv2023

Connecting Infrared Surface Brightness Fluctuation Distances to Type Ia Supernova Hosts: Testing the Top Rung of the Distance Ladder

We compare infrared surface brightness fluctuation (IR SBF) distances measured in galaxies that have hosted type Ia supernovae (SNIa) to distances estimated from SNIa light curve fits. We show that the properties of SNIa found in IR SBF hosts are very different from those exploding in Cepheid calibrators, therefore, this is a direct test of systematic uncertainties on estimation of the Hubble constant (Ho) using supernovae. The IR SBF results from Jensen et al. (2021; arXiv:2105.08299) provide a large and uniformly measured sample of IR SBF distances which we directly compare with distances to 25 SNIa host galaxies. We divide the Hubble flow SNIa into sub-samples that best match the divergent supernova properties seen in the IR SBF hosts and Cepheid hosts. We further divide the SNIa into a sample with light curve widths and host masses that are congruent to those found in the SBF-calibrated hosts. We refit the light curve stretch and color correlations with luminosity, and use these revised parameters to calibrate the Hubble flow supernovae with IR SBF calibrators. Relative to the Hubble flow, the average calibrator distance moduli vary by 0.03mag depending on the SNIa subsamples examined and this adds a 1.8% systematic uncertainty to our Hubble constant estimate. Based on the IR SBF calibrators, Ho=74.6$\pm$0.9(stat)$\pm$ 2.7(syst) km/s/Mpc, which is consistent with the Hubble constant derived from supernovae calibrated from Cepheid variables. We conclude that IR SBF provides reliable calibration of SNIa with a precision comparable to Cepheid calibrators, and with a significant saving in telescope time.

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arXiv2023

NANCY: Next-generation All-sky Near-infrared Community surveY

The Nancy Grace Roman Space Telescope is capable of delivering an unprecedented all-sky, high-spatial resolution, multi-epoch infrared map to the astronomical community. This opportunity arises in the midst of numerous ground- and space-based surveys that will provide extensive spectroscopy and imaging together covering the entire sky (such as Rubin/LSST, Euclid, UNIONS, SPHEREx, DESI, SDSS-V, GALAH, 4MOST, WEAVE, MOONS, PFS, UVEX, NEO Surveyor, etc.). Roman can uniquely provide uniform high-spatial-resolution (~0.1 arcsec) imaging over the entire sky, vastly expanding the science reach and precision of all of these near-term and future surveys. This imaging will not only enhance other surveys, but also facilitate completely new science. By imaging the full sky over two epochs, Roman can measure the proper motions for stars across the entire Milky Way, probing 100 times fainter than Gaia out to the very edge of the Galaxy. Here, we propose NANCY: a completely public, all-sky survey that will create a high-value legacy dataset benefiting innumerable ongoing and forthcoming studies of the universe. NANCY is a pure expression of Roman's potential: it images the entire sky, at high spatial resolution, in a broad infrared bandpass that collects as many photons as possible. The majority of all ongoing astronomical surveys would benefit from incorporating observations of NANCY into their analyses, whether these surveys focus on nearby stars, the Milky Way, near-field cosmology, or the broader universe.

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arXiv2023

Leveraging SN Ia spectroscopic similarity to improve the measurement of $H_0$

Recent studies suggest spectroscopic differences explain a fraction of the variation in Type Ia supernova (SN Ia) luminosities after light-curve/color standardization. In this work, (i) we empirically characterize the variations of standardized SN Ia luminosities, and (ii) we use a spectroscopically inferred parameter, SIP, to improve the precision of SNe Ia along the distance ladder and the determination of the Hubble constant ($H_0$). First, we show that the \texttt{Pantheon+} covariance model modestly overestimates the uncertainty of standardized magnitudes by $\sim 7$%, in the parameter space used by the $\texttt{SH0ES}$ Team to measure $H_0$; accounting for this alone yields $H_0 = 73.01 \pm 0.92$ km s$^{-1}$ Mpc$^{-1}$. Furthermore, accounting for spectroscopic similarity between SNe~Ia on the distance ladder reduces their relative scatter to $\sim0.12$ mag per object (compared to $\sim 0.14$ mag previously). Combining these two findings in the model of SN covariance, we find an overall 14% reduction (to $\pm 0.85$km s$^{-1}$ Mpc$^{-1}$) of the uncertainty in the Hubble constant and a modest increase in its value. Including a budget for systematic uncertainties itemized by Riess et al. (2022a), we report an updated local Hubble constant with $\sim1.2$% uncertainty, $H_0 = 73.29 \pm 0.90$km s$^{-1}$ Mpc$^{-1}$. We conclude that spectroscopic differences among photometrically standardized SNe Ia do not explain the ``Hubble tension." Rather, accounting for such differences increases its significance, as the discrepancy against $Λ$CDM calibrated by the ${\it Planck}$ 2018 measurement rises to 5.7$σ$.

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arXiv2022

Cosmicflows-4

With Cosmicflows-4, distances are compiled for 55,877 galaxies gathered into 38,065 groups. Eight methodologies are employed, with the largest numbers coming from the correlations between the photometric and kinematic properties of spiral galaxies (TF) and elliptical galaxies (FP). Supernovae that arise from degenerate progenitors (type Ia Sne) are an important overlapping component. Smaller contributions come from distance estimates from the surface brightness fluctuations of elliptical galaxies and the luminosities and expansion rates of core collapse supernovae (SNII). Cepheid period-luminosity relation and tip of the red giant branch observations founded on local stellar parallax measurements along with the geometric maser distance to NGC 4258 provide the absolute scaling of distances. The assembly of galaxies into groups is an important feature of the study in facilitating overlaps between methodologies. Merging between multiple contributions within a methodology and between methodologies is carried out with Bayesian Markov chain Monte Carlo procedures. The final assembly of distances is compatible with a value of the Hubble constant of $H_0=74.6$ km s$^{-1}$ Mpc$^{-1}$ with the small statistical error of $\pm 0.8$ km s$^{-1}$ Mpc$^{-1}$ but a large potential systematic error of ~3 km s$^{-1}$ Mpc$^{-1}$. Peculiar velocities can be inferred from the measured distances. The interpretation of the field of peculiar velocities is complex because of large errors on individual components and invites analyses beyond the scope of this study.

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arXiv2022

The Pantheon+ Analysis: Forward-Modeling the Dust and Intrinsic Colour Distributions of Type Ia Supernovae, and Quantifying their Impact on Cosmological Inferences

Recent studies have shown that the observed colour distributions of Type Ia SNe (SNIa) are well-described by a combination of distributions from dust and intrinsic colour. Here we present a new forward-modeling fitting method (Dust2Dust) to measure the parent dust and colour distributions, including their dependence on host-galaxy mass. At each fit step, the SNIa selection efficiency is determined from a large simulated sample that is re-weighted to reflect the proposed distributions. We use five separate metrics to constrain the Dust2Dust parameters: distribution of fitted light-curve colour $c$, cosmological residual trends with $c$, cosmological residual scatter with $c$, fitted colour-luminosity relationship $β_{\rm SALT2}$, and intrinsic scatter $σ_{\rm int}$. Using the Pantheon+ data sample, we present results for a Dust2Dust fit that includes 4 parameters describing intrinsic colour variations and 8 parameters describing dust. Furthermore, we propagate the Dust2Dust parameter uncertainties and covariance to the dark energy equation-of-state $w$ and Hubble constant H$_0$: we find $σ_w = 0.005$ and $σ_{\textrm{H}_0} = 0.145~$km/s/Mpc. The Dust2Dust code is publically available.

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arXiv2022

Deep Drilling in the Time Domain with DECam: Survey Characterization

This paper presents a new optical imaging survey of four deep drilling fields (DDFs), two Galactic and two extragalactic, with the Dark Energy Camera (DECam) on the 4 meter Blanco telescope at the Cerro Tololo Inter-American Observatory (CTIO). During the first year of observations in 2021, $>$4000 images covering 21 square degrees (7 DECam pointings), with $\sim$40 epochs (nights) per field and 5 to 6 images per night per filter in $g$, $r$, $i$, and/or $z$, have become publicly available (the proprietary period for this program is waived). We describe the real-time difference-image pipeline and how alerts are distributed to brokers via the same distribution system as the Zwicky Transient Facility (ZTF). In this paper, we focus on the two extragalactic deep fields (COSMOS and ELAIS-S1), characterizing the detected sources and demonstrating that the survey design is effective for probing the discovery space of faint and fast variable and transient sources. We describe and make publicly available 4413 calibrated light curves based on difference-image detection photometry of transients and variables in the extragalactic fields. We also present preliminary scientific analysis regarding Solar System small bodies, stellar flares and variables, Galactic anomaly detection, fast-rising transients and variables, supernovae, and active galactic nuclei.

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arXiv2022

The Pantheon+ Analysis: SuperCal-Fragilistic Cross Calibration, Retrained SALT2 Light Curve Model, and Calibration Systematic Uncertainty

We present here a re-calibration of the photometric systems used in the Pantheon+ sample of Type Ia supernovae (SNe Ia) including those used for the SH0ES distance-ladder measurement of H$_0$. We utilize the large and uniform sky coverage of the public Pan-STARRS stellar photometry catalog to cross-calibrate against tertiary standards released by individual SN Ia surveys. The most significant updates over the `SuperCal' cross-calibration used for the previous Pantheon and SH0ES analyses are: 1) expansion of the number of photometric systems (now 25) and filters (now 105), 2) solving for all filter offsets in all systems simultaneously in order to produce a calibration uncertainty covariance matrix that can be used in cosmological-model constraints, and 3) accounting for the change in the fundamental flux calibration of the HST CALSPEC standards from previous versions on the order of $1.5\%$ over a $Δλ$ of 4000~Å. The re-calibration of samples used for light-curve fitting has historically been decoupled from the retraining of the light-curve model. Here, we are able to retrain the SALT2 model using this new calibration and find the change in the model coupled with the change to the calibration of the light-curves themselves causes a net distance modulus change ($dμ/dz$) of 0.04 mag over the redshift range $0<z<1$. We introduce a new formalism to determine the systematic impact on cosmological inference by propagating the covariance in fitted calibration offsets through retraining simultaneously with light-curve fitting and find a total calibration uncertainty impact of $σ_w=0.013$, which is roughly half the size of the sample statistical uncertainty. Similarly, we find a systematic SN calibration contribution to the SH0ES H$_0$ uncertainty is less than 0.2~km/s/Mpc, suggesting that SN Ia calibration cannot resolve the current level of the `Hubble Tension'.

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arXiv2022

The Pantheon+ Analysis: Cosmological Constraints

We present constraints on cosmological parameters from the Pantheon+ analysis of 1701 light curves of 1550 distinct Type Ia supernovae (SNe Ia) ranging in redshift from $z=0.001$ to 2.26. This work features an increased sample size, increased redshift span, and improved treatment of systematic uncertainties in comparison to the original Pantheon analysis and results in a factor of two improvement in cosmological constraining power. For a Flat$Λ$CDM model, we find $Ω_M=0.334\pm0.018$ from SNe Ia alone. For a Flat$w_0$CDM model, we measure $w_0=-0.90\pm0.14$ from SNe Ia alone, H$_0=73.5\pm1.1$ km s$^{-1}$ Mpc$^{-1}$ when including the Cepheid host distances and covariance (SH0ES), and $w_0=-0.978^{+0.024}_{-0.031}$ when combining the SN likelihood with constraints from the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO); both $w_0$ values are consistent with a cosmological constant. We also present the most precise measurements to date on the evolution of dark energy in a Flat$w_0w_a$CDM universe, and measure $w_a=-0.1^{+0.9}_{-2.0}$ from Pantheon+ alone, H$_0=73.3\pm1.1$ km s$^{-1}$ Mpc$^{-1}$ when including SH0ES, and $w_a=-0.65^{+0.28}_{-0.32}$ when combining Pantheon+ with CMB and BAO data. Finally, we find that systematic uncertainties in the use of SNe Ia along the distance ladder comprise less than one third of the total uncertainty in the measurement of H$_0$ and cannot explain the present "Hubble tension" between local measurements and early-Universe predictions from the cosmological model.

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arXiv2022

The Pantheon+ Analysis: Improving the Redshifts and Peculiar Velocities of Type Ia Supernovae Used in Cosmological Analyses

We examine the redshifts of a comprehensive set of published Type Ia supernovae, and provide a combined, improved catalogue with updated redshifts. We improve on the original catalogues by using the most up-to-date heliocentric redshift data available; ensuring all redshifts have uncertainty estimates; using the exact formulae to convert heliocentric redshifts into the Cosmic Microwave Background (CMB) frame; and utilising an improved peculiar velocity model that calculates local motions in redshift-space and more realistically accounts for the external bulk flow at high-redshifts. In total we reviewed 2821 supernova redshifts; 534 are comprised of repeat-observations of the same supernovae and 1764 pass the cosmology sample quality cuts. We found 5 cases of missing or incorrect heliocentric corrections, 44 incorrect or missing supernova coordinates, 230 missing heliocentric or CMB frame redshifts, and 1200 missing redshift uncertainties. Of the 2287 unique Type Ia supernovae in our sample (1594 of which satisfy cosmology-sample cuts) we updated 990 heliocentric redshifts. The absolute corrections range between $10^{-8} \leq Δz \leq 0.038$, and RMS$(Δz) \sim 3\times 10^{-3}$. The sign of the correction was essentially random, so the mean and median corrections are small: $4\times 10^{-4}$ and $4\times 10^{-6}$ respectively. We examine the impact of these improvements for $H_0$ and the dark energy equation of state $w$ and find that the cosmological results change by $ΔH_0 = -0.11$ km s$^{-1}$ Mpc$^{-1}$ and $Δw = -0.001$, both significantly smaller than previously reported uncertainties for $H_0$ of 1.4 km s$^{-1}$ Mpc$^{-1}$ and $w$ of 0.04 respectively.

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arXiv2022

Constraining R$_V$ Variation Using Highly Reddened Type Ia Supernovae from the Pantheon+ Sample

Type Ia supernovae (SNe Ia) are powerful tools for measuring the expansion history of the universe, but the impact of dust around SNe Ia remains unknown and is a critical systematic uncertainty. One way to improve our empirical description of dust is to analyse highly reddened SNe Ia ($E(B-V)>0.4$, roughly equivalent to the fitted SALT2 light-curve parameter $c>0.3$). With the recently released Pantheon+ sample, there are 57 SNe Ia that were removed because of their high colour alone (with colours up to $c=1.61$), which can provide enormous leverage on understanding line-of-sight $R_V$. Previous studies have claimed that $R_V$ decreases with redder colour, though it is unclear if this is due to limited statistics, selection effects, or an alternative explanation. To test this claim, we fit two separate colour-luminosity relationships, one for the main cosmological sample ($c<0.3$) and one for highly reddened ($c>0.3$) SNe Ia. We find the change in the colour-luminosity coefficient to be consistent with zero. Additionally, we compare the data to simulations with different colour models, and find that the data prefers a model with a flat dependence of $R_V$ on colour over a declining dependence. Finally, our results strongly support that line-of-sight $R_V$ to SNe Ia is not a single value, but forms a distribution.

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arXiv2022

A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team

We report observations from HST of Cepheids in the hosts of 42 SNe Ia used to calibrate the Hubble constant (H0). These include all suitable SNe Ia in the last 40 years at z<0.01, measured with >1000 orbits, more than doubling the sample whose size limits the precision of H0. The Cepheids are calibrated geometrically from Gaia EDR3 parallaxes, masers in N4258 (here tripling that Cepheid sample), and DEBs in the LMC. The Cepheids were measured with the same WFC3 instrument and filters (F555W, F814W, F160W) to negate zeropoint errors. We present multiple verifications of Cepheid photometry and tests of background determinations that show measurements are accurate in the presence of crowding. The SNe calibrate the mag-z relation from the new Pantheon+ compilation, accounting here for covariance between all SN data, with host properties and SN surveys matched to negate differences. We decrease the uncertainty in H0 to 1 km/s/Mpc with systematics. We present a comprehensive set of ~70 analysis variants to explore the sensitivity of H0 to selections of anchors, SN surveys, z range, variations in the analysis of dust, metallicity, form of the P-L relation, SN color, flows, sample bifurcations, and simultaneous measurement of H(z). Our baseline result from the Cepheid-SN sample is H0=73.04+-1.04 km/s/Mpc, which includes systematics and lies near the median of all analysis variants. We demonstrate consistency with measures from HST of the TRGB between SN hosts and NGC 4258 with Cepheids and together these yield 72.53+-0.99. Including high-z SN Ia we find H0=73.30+-1.04 with q0=-0.51+-0.024. We find a 5-sigma difference with H0 predicted by Planck+LCDM, with no indication this arises from measurement errors or analysis variations considered to date. The source of this now long-standing discrepancy between direct and cosmological routes to determining the Hubble constant remains unknown.

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arXiv2022

The Dark Energy Survey Supernova Program results: Type Ia Supernova brightness correlates with host galaxy dust

Cosmological analyses with type Ia supernovae (SNe Ia) often assume a single empirical relation between color and luminosity ($β$) and do not account for varying host-galaxy dust properties. However, from studies of dust in large samples of galaxies, it is known that dust attenuation can vary significantly. Here we take advantage of state-of-the-art modeling of galaxy properties to characterize dust parameters (dust attenuation $A_V$, and a parameter describing the dust law slope $R_V$) for the Dark Energy Survey (DES) SN Ia host galaxies using the publicly available \texttt{BAGPIPES} code. Utilizing optical and infrared data of the hosts alone, we find three key aspects of host dust that impact SN Ia cosmology: 1) there exists a large range ($\sim1-6$) of host $R_V$ 2) high stellar mass hosts have $R_V$ on average $\sim0.7$ lower than that of low-mass hosts 3) there is a significant ($>3σ$) correlation between the Hubble diagram residuals of red SNe Ia that when corrected for reduces scatter by $\sim13\%$ and the significance of the ``mass step'' to $\sim1σ$. These represent independent confirmations of recent predictions based on dust that attempted to explain the puzzling ``mass step'' and intrinsic scatter ($σ_{\rm int}$) in SN Ia analyses. We also find that red-sequence galaxies have both lower and more peaked dust law slope distributions on average in comparison to non red-sequence galaxies. We find that the SN Ia $β$ and $σ_{\rm int}$ both differ by $>3σ$ when determined separately for red-sequence galaxy and all other galaxy hosts. The agreement between fitted host-$R_V$ and SN Ia $β$ \& $σ_{\rm int}$ suggests that host dust properties play a major role in SN Ia color-luminosity standardization and supports the claim that SN Ia intrinsic scatter is driven by $R_V$ variation.

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arXiv2022

SOAR/Goodman Spectroscopic Assessment of Candidate Counterparts of the LIGO-Virgo Event GW190814

On 2019 August 14 at 21:10:39 UTC, the LIGO/Virgo Collaboration (LVC) detected a possible neutron star-black hole merger (NSBH), the first ever identified. An extensive search for an optical counterpart of this event, designated GW190814, was undertaken using the Dark Energy Camera (DECam) on the 4m Victor M. Blanco Telescope at the Cerro Tololo Inter-American Observatory. Target of Opportunity interrupts were issued on 8 separate nights to observe 11 candidates using the 4.1m Southern Astrophysical Research (SOAR) telescope's Goodman High Throughput Spectrograph in order to assess whether any of these transients was likely to be an optical counterpart of the possible NSBH merger. Here, we describe the process of observing with SOAR, the analysis of our spectra, our spectroscopic typing methodology, and our resultant conclusion that none of the candidates corresponded to the gravitational wave merger event but were all instead other transients. Finally, we describe the lessons learned from this effort. Application of these lessons will be critical for a successful community spectroscopic follow-up program for LVC observing run 4 (O4) and beyond.

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arXiv2022

Measurements of the Hubble Constant with a Two Rung Distance Ladder: Two Out of Three Ain't Bad

The three rung distance ladder, which calibrates Type Ia supernovae through stellar distances linked to geometric measurements, provides the highest precision direct measurement of the Hubble constant. In light of the Hubble tension, it is important to test the individual components of the distance ladder. For this purpose, we report a measurement of the Hubble constant from 35 extragalactic Cepheid hosts measured by the SH0ES team, using their distances and redshifts at cz < 3300 km /s , instead of any, more distant Type Ia supernovae, to measure the Hubble flow. The Cepheid distances are calibrated geometrically in the Milky Way, NGC 4258, and the Large Magellanic Cloud. Peculiar velocities are a significant source of systematic uncertainty at z $\sim$ 0.01, and we present a formalism for both mitigating and quantifying their effects, making use of external reconstructions of the density and velocity fields in the nearby universe. We identify a significant source of uncertainty originating from different assumptions about the selection criteria of this sample, whether distance or redshift limited, as it was assembled over three decades. Modeling these assumptions yields central values ranging from H0 = 71.8 to 77.0 km/s/Mpc. Combining the four best fitting selection models yields H0 = 73.1 (+2.6/-2.3) km/s/Mpc as a fiducial result, at $2.6σ$ tension with Planck. While Type Ia supernovae are essential for a precise measurement of H0, unknown systematics in these supernovae are unlikely to be the source of the Hubble tension

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arXiv2022

The Pantheon+ Analysis: The Full Dataset and Light-Curve Release

Here we present 1701 light curves of 1550 spectroscopically confirmed Type Ia supernovae (SNe Ia) that will be used to infer cosmological parameters as part of the Pantheon+ SN analysis and the SH0ES (Supernovae and H0 for the Equation of State of dark energy) distance-ladder analysis. This effort is one part of a series of works that perform an extensive review of redshifts, peculiar velocities, photometric calibration, and intrinsic-scatter models of SNe Ia. The total number of light curves, which are compiled across 18 different surveys, is a significant increase from the first Pantheon analysis (1048 SNe), particularly at low redshift ($z$). Furthermore, unlike in the Pantheon analysis, we include light curves for SNe with $z<0.01$ such that SN systematic covariance can be included in a joint measurement of the Hubble constant (H$_0$) and the dark energy equation-of-state parameter ($w$). We use the large sample to compare properties of 151 SNe Ia observed by multiple surveys and 12 pairs/triplets of "SN siblings" - SNe found in the same host galaxy. Distance measurements, application of bias corrections, and inference of cosmological parameters are discussed in the companion paper by Brout et al. (2022b), and the determination of H$_0$ is discussed by Riess et al. (2022). These analyses will measure w with $\sim3\%$ precision and H$_0$ with 1 km/s/Mpc precision.

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