arXiv subjects

R. P. Kirshner

Publications and source records attributed to R. P. Kirshner.

At least 37 records · Page 2Linked to original sources

arXiv2019

First Cosmology Results using Type Ia Supernovae from the Dark Energy Survey: Constraints on Cosmological Parameters

We present the first cosmological parameter constraints using measurements of type Ia supernovae (SNe Ia) from the Dark Energy Survey Supernova Program (DES-SN). The analysis uses a subsample of 207 spectroscopically confirmed SNe Ia from the first three years of DES-SN, combined with a low-redshift sample of 122 SNe from the literature. Our "DES-SN3YR" result from these 329 SNe Ia is based on a series of companion analyses and improvements covering SN Ia discovery, spectroscopic selection, photometry, calibration, distance bias corrections, and evaluation of systematic uncertainties. For a flat LCDM model we find a matter density Omega_m = 0.331 +_ 0.038. For a flat wCDM model, and combining our SN Ia constraints with those from the cosmic microwave background (CMB), we find a dark energy equation of state w = -0.978 +_ 0.059, and Omega_m = 0.321 +_ 0.018. For a flat w0waCDM model, and combining probes from SN Ia, CMB and baryon acoustic oscillations, we find w0 = -0.885 +_ 0.114 and wa = -0.387 +_ 0.430. These results are in agreement with a cosmological constant and with previous constraints using SNe Ia (Pantheon, JLA).

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arXiv2019

A Physical Basis for the H-band Blue-edge Velocity and Light-Curve Shape Correlation in Context of Type Ia Supernova Explosion Physics

Our recent work demonstrates a correlation between the high-velocity blue edge, $v_{edge}$, of the iron-peak Fe/Co/Ni $H$-band emission feature and the optical light curve shape of normal, transitional and sub-luminous type Ia Supernovae (SNe Ia). We explain this correlation in terms of SN Ia physics. $v_{edge}$ corresponds to the sharp transition between the complete and incomplete silicon burning regions in the ejecta. It measures the point in velocity space where the outer $^{56}$Ni mass fraction, $X_{\rm{Ni}}$, falls to the order of 0.03-0.10. For a given $^{56}$Ni mass, $M(^{56}Ni)$, $v_{edge}$ is sensitive to the specific kinetic energy $E_{\rm kin}$($M(^{56}Ni)/M_{WD}$) of the corresponding region. Combining $v_{edge}$ with light curve parameters (i.e., s$_{BV}$, $Δm_{15,s}$ in $B$ and $V$) allows us to distinguish between explosion scenarios. The correlation between $v_{edge}$ and light-curve shape is consistent with explosion models near the Chandrasekhar limit. However, the available sub-$M_{Ch}$ WD explosion model based on SN 1999by exhibits velocities which are too large to explain the observations. Finally, the sub-luminous SN 2015bo exhibits signatures of a dynamical merger of two WDs demonstrating diversity among explosion scenarios at the faint end of the SNe Ia population.

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arXiv2019

Cosmological Constraints from Multiple Probes in the Dark Energy Survey

The combination of multiple observational probes has long been advocated as a powerful technique to constrain cosmological parameters, in particular dark energy. The Dark Energy Survey has measured 207 spectroscopically--confirmed Type Ia supernova lightcurves; the baryon acoustic oscillation feature; weak gravitational lensing; and galaxy clustering. Here we present combined results from these probes, deriving constraints on the equation of state, $w$, of dark energy and its energy density in the Universe. Independently of other experiments, such as those that measure the cosmic microwave background, the probes from this single photometric survey rule out a Universe with no dark energy, finding $w=-0.80^{+0.09}_{-0.11}$. The geometry is shown to be consistent with a spatially flat Universe, and we obtain a constraint on the baryon density of $Ω_b=0.069^{+0.009}_{-0.012}$ that is independent of early Universe measurements. These results demonstrate the potential power of large multi-probe photometric surveys and pave the way for order of magnitude advances in our constraints on properties of dark energy and cosmology over the next decade.

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arXiv2019

Carnegie Supernova Project-II: Using Near-Infrared Spectroscopy to determine the location of the outer $^{56}$Ni in Type Ia Supernovae

We present the $H$-band wavelength region of thirty post-maximum light near-infrared (NIR) spectra of fourteen transitional and sub-luminous type Ia supernovae (SNe Ia), extending from $+$5d to +20d relative to the epoch of $B$-band maximum. We introduce a new observable, the blue-edge velocity, $v_{edge}$, of the prominent Fe/Co/Ni-peak $H$-band emission feature which is quantitatively measured. The $v_{edge}$ parameter is found to slowly decrease over sub-type ranging from around $-$13,000km/s for transitional SNe~Ia, down to $-$5,000km/s for the sub-luminous SNe Ia. Furthermore, inspection of the +10$\pm$3d spectra indicates that $v_{edge}$ is correlated with the color-stretch parameter, s$_{BV}$, and hence with peak luminosity. These results follow the previous findings that brighter SNe Ia tend to have $^{56}$Ni located at higher velocities as compared to sub-luminous objects. As $v_{edge}$ is a model-independent parameter, we propose it can be used in combination with traditional observational diagnostics to provide a new avenue to robustly distinguish between leading SNe Ia explosion models.

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arXiv2019

Gravity and Light: Combining Gravitational Wave and Electromagnetic Observations in the 2020s

As of today, we have directly detected exactly one source in both gravitational waves (GWs) and electromagnetic (EM) radiation, the binary neutron star merger GW170817, its associated gamma-ray burst GRB170817A, and the subsequent kilonova SSS17a/AT 2017gfo. Within ten years, we will detect hundreds of events, including new classes of events such as neutron-star-black-hole mergers, core-collapse supernovae, and almost certainly something completely unexpected. As we build this sample, we will explore exotic astrophysical topics ranging from nucleosynthesis, stellar evolution, general relativity, high-energy astrophysics, nuclear matter, to cosmology. The discovery potential is extraordinary, and investments in this area will yield major scientific breakthroughs. Here we outline some of the most exciting scientific questions that can be answered by combining GW and EM observations.

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arXiv2018

Carnegie Supernova Project-II: The Near-infrared Spectroscopy Program

Shifting the focus of Type Ia supernova (SN Ia) cosmology to the near-infrared (NIR) is a promising way to significantly reduce the systematic errors, as the strategy minimizes our reliance on the empirical width-luminosity relation and uncertain dust laws. Observations in the NIR are also crucial for our understanding of the origins and evolution of these events, further improving their cosmological utility. Any future experiments in the rest-frame NIR will require knowledge of the SN Ia NIR spectroscopic diversity, which is currently based on a small sample of observed spectra. Along with the accompanying paper, Phillips et al. (2018), we introduce the Carnegie Supernova Project-II (CSP-II), to follow up nearby SNe Ia in both the optical and the NIR. In particular, this paper focuses on the CSP-II NIR spectroscopy program, describing the survey strategy, instrumental setups, data reduction, sample characteristics, and future analyses on the data set. In collaboration with the Harvard-Smithsonian Center for Astrophysics (CfA) Supernova Group, we obtained 661 NIR spectra of 157 SNe Ia. Within this sample, 451 NIR spectra of 90 SNe Ia have corresponding CSP-II follow-up light curves. Such a sample will allow detailed studies of the NIR spectroscopic properties of SNe Ia, providing a different perspective on the properties of the unburned material, radioactive and stable nickel produced, progenitor magnetic fields, and searches for possible signatures of companion stars.

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arXiv2018

First Cosmology Results Using Type Ia Supernovae From the Dark Energy Survey: Survey Overview and Supernova Spectroscopy

We present spectroscopy from the first three seasons of the Dark Energy Survey Supernova Program (DES-SN). We describe the supernova spectroscopic program in full: strategy, observations, data reduction, and classification. We have spectroscopically confirmed 307 supernovae, including 251 type Ia supernovae (SNe Ia) over a redshift range of $0.017 < z < 0.85$. We determine the effective spectroscopic selection function for our sample, and use it to investigate the redshift-dependent bias on the distance moduli of SNe Ia we have classified. We also provide a full overview of the strategy, observations, and data products of DES-SN, which has discovered 12,015 likely supernovae during these first three seasons. The data presented here are used for the first cosmology analysis by DES-SN ('DES-SN3YR'), the results of which are given in DES Collaboration (2018a).

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arXiv2018

Extending Supernova Spectral Templates for Next-Generation Space Telescope Observations

Empirical models of supernova (SN) spectral energy distributions (SEDs) are widely used for SN survey simulations and photometric classifications. The existing library of SED models has excellent optical templates but limited, poorly constrained coverage of ultraviolet (UV) and infrared (IR) wavelengths. However, both regimes are critical for the design and operation of future SN surveys, particularly at IR wavelengths that will be accessible with the James Webb Space Telescope (JWST) and the Wide-Field Infrared Survey Telescope (WFIRST). We create a public repository of improved empirical SED templates using a sampling of Type Ia and core-collapse (CC) photometric light curves to extend the Type Ia parameterized SALT2 model and a set of SN Ib, SN Ic, and SN II SED templates into the UV and near-IR. We apply this new repository of extrapolated SN SED models to examine how future surveys can discriminate between CC and Type Ia SNe at UV and IR wavelengths, and present an open-source software package written in Python, SNSEDextend, that enables a user to generate their own extrapolated SEDs.

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arXiv2018

Should Type Ia Supernova Distances be Corrected for their Local Environments?

Recent analyses suggest that distance residuals measured from Type Ia supernovae (SNe Ia) are correlated with local host galaxy properties within a few kpc of the SN explosion. However, the well-established correlation with global host galaxy properties is nearly as significant, with a shift of 0.06 mag across a low to high mass boundary (the mass step). Here, with 273 SNe Ia at $z<0.1$, we investigate whether stellar masses and rest-frame $u-g$ colors of regions within 1.5 kpc of the SN Ia explosion site are significantly better correlated with SN distance measurements than global properties or properties measured at random locations in SN hosts. At $\lesssim2σ$ significance, local properties tend to correlate with distance residuals better than properties at random locations, though despite using the largest low-$z$ sample to date we cannot definitively prove that a local correlation is more significant than a random correlation. Our data hint that SNe observed by surveys that do not target a pre-selected set of galaxies may have a larger local mass step than SNe from surveys that do, an increase of $0.071\pm0.036$ mag (2.0$σ$). We find a $3σ$ local mass step after global mass correction, evidence that SNe Ia should be corrected for their local mass, but we note that this effect is insignificant in the targeted low-$z$ sample. Only the local mass step remains significant at $>2σ$ after global mass correction, and we conservatively estimate a systematic shift in H$_0$ measurements of -0.14 $\textrm{km}\,\textrm{s}^{-1}\textrm{Mpc}^{-1}$ with an additional uncertainty of 0.14 $\textrm{km}\,\textrm{s}^{-1}\textrm{Mpc}^{-1}$, $\sim$10\% of the present uncertainty.

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arXiv2018

The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample

We present optical light curves, redshifts, and classifications for 365 spectroscopically confirmed Type Ia supernovae (SNe Ia) discovered by the Pan-STARRS1 (PS1) Medium Deep Survey. We detail improvements to the PS1 SN photometry, astrometry and calibration that reduce the systematic uncertainties in the PS1 SN Ia distances. We combine the subset of 279 PS1 SN Ia ($0.03 < z < 0.68$) with useful distance estimates of SN Ia from SDSS, SNLS, various low-z and HST samples to form the largest combined sample of SN Ia consisting of a total of 1048 SN Ia ranging from $0.01 < z < 2.3$, which we call the `Pantheon Sample'. When combining Planck 2015 CMB measurements with the Pantheon SN sample, we find $Ω_m=0.307\pm0.012$ and $w = -1.026\pm0.041$ for the wCDM model. When the SN and CMB constraints are combined with constraints from BAO and local H0 measurements, the analysis yields the most precise measurement of dark energy to date: $w0 = -1.007\pm 0.089$ and $wa = -0.222 \pm0.407$ for the w0waCDM model. Tension with a cosmological constant previously seen in an analysis of PS1 and low-z SNe has diminished after an increase of $2\times$ in the statistics of the PS1 sample, improved calibration and photometry, and stricter light-curve quality cuts. We find the systematic uncertainties in our measurements of dark energy are almost as large as the statistical uncertainties, primarily due to limitations of modeling the low-redshift sample. This must be addressed for future progress in using SN Ia to measure dark energy.

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arXiv2018

Measuring Dark Energy Properties with Photometrically Classified Pan-STARRS Supernovae. II. Cosmological Parameters

We use 1169 Pan-STARRS supernovae (SNe) and 195 low-$z$ ($z < 0.1$) SNe Ia to measure cosmological parameters. Though most Pan-STARRS SNe lack spectroscopic classifications, in a previous paper (I) we demonstrated that photometrically classified SNe can be used to infer unbiased cosmological parameters by using a Bayesian methodology that marginalizes over core-collapse (CC) SN contamination. Our sample contains nearly twice as many SNe as the largest previous SN Ia compilation. Combining SNe with Cosmic Microwave Background (CMB) constraints from Planck, we measure the dark energy equation of state parameter $w$ to be -0.989$\pm$0.057 (stat$+$sys). If $w$ evolves with redshift as $w(a) = w_0 + w_a(1-a)$, we find $w_0 = -0.912 \pm 0.149$ and $w_a =$ -0.513$\pm$0.826. These results are consistent with cosmological parameters from the Joint Lightcurve Analysis and the Pantheon sample. We try four different photometric classification priors for Pan-STARRS SNe and two alternate ways of modeling CC SN contamination, finding that no variant gives a $w$ differing by more than 2% from the baseline measurement. The systematic uncertainty on $w$ due to marginalizing over CC SN contamination, $σ_w^{\textrm{CC}} = 0.012$, is the third-smallest source of systematic uncertainty in this work. We find limited (1.6$σ$) evidence for evolution of the SN color-luminosity relation with redshift, a possible systematic that could constitute a significant uncertainty in future high-$z$ analyses. Our data provide one of the best current constraints on $w$, demonstrating that samples with $\sim$5% CC SN contamination can give competitive cosmological constraints when the contaminating distribution is marginalized over in a Bayesian framework.

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arXiv2018

Hydrogen-Poor Superluminous Supernovae from the Pan-STARRS1 Medium Deep Survey

We present light curves and classification spectra of 17 hydrogen-poor superluminous supernovae (SLSNe) from the Pan-STARRS1 Medium Deep Survey (PS1 MDS). Our sample contains all objects from the PS1 MDS sample with spectroscopic classification that are similar to either of the prototypes SN2005ap or SN2007bi, without an explicit limit on luminosity. With a redshift range $0.3 < z < 1.6$, PS1MDS is the first SLSN sample primarily probing the high-redshift population; our multi-filter PS1 light curves probe the rest-frame UV emission, and hence the peak of the spectral energy distribution. We measure the temperature evolution and construct bolometric light curves, and find peak luminosities of $(0.5-5) \times 10^{44}$ erg s$^{-1}$ and lower limits on the total radiated energies of $(0.3-2) \times 10^{51}$ erg. The light curve shapes are diverse, with both rise- and decline times spanning a factor of $\sim 5$, and several examples of double-peaked light curves. When correcting for the flux-limited nature of our survey, we find a median peak luminosity at 4000 Å of $M_{\rm 4000} = -21.1$ mag, and a spread of $σ= 0.7$ mag.

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arXiv2017

The Foundation Supernova Survey: Motivation, Design, Implementation, and First Data Release

The Foundation Supernova Survey aims to provide a large, high-fidelity, homogeneous, and precisely-calibrated low-redshift Type Ia supernova (SN Ia) sample for cosmology. The calibration of the current low-redshift SN sample is the largest component of systematic uncertainties for SN cosmology, and new data are necessary to make progress. We present the motivation, survey design, observation strategy, implementation, and first results for the Foundation Supernova Survey. We are using the Pan-STARRS telescope to obtain photometry for up to 800 SNe Ia at z < 0.1. This strategy has several unique advantages: (1) the Pan-STARRS system is a superbly calibrated telescopic system, (2) Pan-STARRS has observed 3/4 of the sky in grizy making future template observations unnecessary, (3) we have a well-tested data-reduction pipeline, and (4) we have observed ~3000 high-redshift SNe Ia on this system. Here we present our initial sample of 225 SN Ia griz light curves, of which 180 pass all criteria for inclusion in a cosmological sample. The Foundation Supernova Survey already contains more cosmologically useful SNe Ia than all other published low-redshift SN Ia samples combined. We expect that the systematic uncertainties for the Foundation Supernova Sample will be 2-3 times smaller than other low-redshift samples. We find that our cosmologically useful sample has an intrinsic scatter of 0.111 mag, smaller than other low-redshift samples. We perform detailed simulations showing that simply replacing the current low-redshift SN Ia sample with an equally sized Foundation sample will improve the precision on the dark energy equation-of-state parameter by 35%, and the dark energy figure-of-merit by 72%.

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arXiv2017

A Second Case of Variable Na I D Lines in a Highly-Reddened Type Ia Supernova (with Erratum)

(Original) Recent high-resolution spectra of the Type Ia SN 2006X have revealed the presence of time-variable and blueshifted Na I D features, interpreted by Patat et al. as originating in circumstellar material within the progenitor system. The variation seen in SN 2006X induces relatively large changes in the total Na I D equivalent width ($Δ\rm{EW}\approx 0.5 \unicode{x212B}$ in just over two weeks), that would be detectable at lower resolutions. We have used a large data set comprising 2400 low-resolution spectra of 450 Type Ia supernovae (SNe Ia) obtained by the CfA Supernova Program to search for variable Na I D features. Out of the 31 SNe Ia (including SN 2006X) in which we could have detected similar EW variations, only one other (SN 1999cl) shows variable Na I D features, with an even larger change over a similar ~10-day timescale ($Δ\rm{EW} = 1.66 \pm 0.21 \unicode{x212B}$). Interestingly, both SN 1999cl and SN 2006X are the two most highly-reddened objects in our sample, raising the possibility that the variability is connected to dusty environments. (Erratum) The large variation in the Na I D equivalent width observed in SN 1999cl results in fact from a measurement error. Our new measurements show that the EW variation is significantly lower, at $0.43 \pm 0.14 \unicode{x212B}$. While the EW variation remains statistically significant (3.1$σ$ different from zero), it is now below the detection threshold of 0.5 $\unicode{x212B}$ derived from the Monte Carlo simulations published in the original paper. As a result, SN 1999cl should no longer be considered as an object displaying variable Na I D lines in our study. The fraction of SNe Ia in our sample displaying Na I D lines thus goes from $\sim$6% (2/31) in the original study to $\sim$3% (1/31) in the revised analysis, SN 2006X being the only SN Ia in our sample with variable Na I D lines.

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arXiv2017

Measuring the Properties of Dark Energy with Photometrically Classified Pan-STARRS Supernovae. I. Systematic Uncertainty from Core-Collapse Supernova Contamination

The Pan-STARRS (PS1) Medium Deep Survey discovered over 5,000 likely supernovae (SNe) but obtained spectral classifications for just 10% of its SN candidates. We measured spectroscopic host galaxy redshifts for 3,147 of these likely SNe and estimate that $\sim$1,000 are Type Ia SNe (SNe Ia) with light-curve quality sufficient for a cosmological analysis. We use these data with simulations to determine the impact of core-collapse SN (CC SN) contamination on measurements of the dark energy equation of state parameter, $w$. Using the method of Bayesian Estimation Applied to Multiple Species (BEAMS), distances to SNe Ia and the contaminating CC SN distribution are simultaneously determined. We test light-curve based SN classification priors for BEAMS as well as a new classification method that relies upon host galaxy spectra and the association of SN type with host type. By testing several SN classification methods and CC SN parameterizations on large SN simulations, we estimate that CC SN contamination gives a systematic error on $w$ ($σ_w^{CC}$) of 0.014, 29% of the statistical uncertainty. Our best method gives $σ_w^{CC} = 0.004$, just 8% of the statistical uncertainty, but could be affected by incomplete knowledge of the CC SN distribution. This method determines the SALT2 color and shape coefficients, $α$ and $β$, with $\sim$3% bias. However, we find that some variants require $α$ and $β$ to be fixed to known values for BEAMS to yield accurate measurements of $w$. Finally, the inferred abundance of bright CC SNe in our sample is greater than expected based on measured CC SN rates and luminosity functions.

astro-ph.CO↗

arXiv2016

Slowly fading super-luminous supernovae that are not pair-instability explosions

Super-luminous supernovae that radiate more than 10^44 ergs per second at their peak luminosity have recently been discovered in faint galaxies at redshifts of 0.1-4. Some evolve slowly, resembling models of 'pair-instability' supernovae. Such models involve stars with original masses 140-260 times that of the Sun that now have carbon-oxygen cores of 65-30 solar masses. In these stars, the photons that prevent gravitational collapse are converted to electron-positron pairs, causing rapid contraction and thermonuclear explosions. Many solar masses of 56Ni are synthesized; this isotope decays to 56Fe via 56Co, powering bright light curves. Such massive progenitors are expected to have formed from metal-poor gas in the early Universe. Recently, supernova 2007bi in a galaxy at redshift 0.127 (about 12 billion years after the Big Bang) with a metallicity one-third that of the Sun was observed to look like a fading pair-instability supernova. Here we report observations of two slow-to-fade super-luminous supernovae that show relatively fast rise times and blue colours, which are incompatible with pair-instability models. Their late-time light-curve and spectral similarities to supernova 2007bi call the nature of that event into question. Our early spectra closely resemble typical fast-declining super-luminous supernovae, which are not powered by radioactivity. Modelling our observations with 10-16 solar masses of magnetar-energized ejecta demonstrates the possibility of a common explosion mechanism. The lack of unambiguous nearby pair-instability events suggests that their local rate of occurrence is less than 6x10^-6 times that of the core-collapse rate.

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arXiv2016

PS1-14bj: A Hydrogen-Poor Superluminous Supernova With a Long Rise and Slow Decay

We present photometry and spectroscopy of PS1-14bj, a hydrogen-poor superluminous supernova (SLSN) at redshift $z=0.5215$ discovered in the last months of the Pan-STARRS1 Medium Deep Survey. PS1-14bj stands out by its extremely slow evolution, with an observed rise of $\gtrsim 125$ rest-frame days, and exponential decline out to $\sim 250$ days past peak at a measured rate of $0.01~{\rm mag~day}^{-1}$, consistent with fully-trapped $^{56}$Co decay. This is the longest rise time measured in a SLSN to date, and the first SLSN to show a rise time consistent with pair-instability supernova (PISN) models. Compared to other slowly-evolving SLSNe, it is spectroscopically similar to the prototype SN2007bi at maximum light, though lower in luminosity ($L_{\rm peak} \simeq 4.6 \times 10^{43} {\rm erg s}^{-1}$) and with a flatter peak than previous events. PS1-14bj shows a number of peculiar properties, including a near-constant color temperature for $>200$ days past peak, and strong emission lines from [O III] $λ$5007 and [O III] $λ$4363 with a velocity width of $\sim$3400 km/s, in its late-time spectra. These both suggest there is a sustained source of heating over very long timescales, and are incompatible with a simple $^{56}$Ni-powered/PISN interpretation. A modified magnetar model including emission leakage at late times can reproduce the light curve, in which case the blue continuum and [O III] features are interpreted as material heated and ionized by the inner pulsar wind nebula becoming visible at late times. Alternatively, the late-time heating could be due to interaction with a shell of H-poor circumstellar material.

astro-ph.HE↗

arXiv2016

The GALEX Time Domain Survey. II. Wavelength-Dependent Variability of Active Galactic Nuclei in the Pan-STARRS1 Medium Deep Survey

We analyze the wavelength-dependent variability of a sample of spectroscopically confirmed active galactic nuclei (AGN) selected from near-UV ($NUV$) variable sources in the GALEX Time Domain Survey that have a large amplitude of optical variability (difference-flux S/N $>$ 3) in the Pan-STARRS1 Medium Deep Survey (PS1 MDS). By matching GALEX and PS1 epochs in 5 bands ($NUV$, $g_{P1}$, $r_{P1}$, $i_{P1}$, $z_{P1}$) in time, and taking their flux difference, we create co-temporal difference-flux spectral energy distributions ($Δf$SEDs) using two chosen epochs for each of the 23 objects in our sample on timescales of about a year. We confirm the "bluer-when-brighter" trend reported in previous studies, and measure a median spectral index of the $Δf$SEDs of $α_λ$ = 2.1 that is consistent with an accretion disk spectrum. We further fit the $Δf$SEDs of each source with a standard accretion disk model in which the accretion rate changes from one epoch to the other. In our sample, 17 out of 23 ($\sim$74 %) sources are well described by this variable accretion-rate disk model, with a median average characteristic disk temperature $\bar{T}^*$ of $1.2\times 10^5$~K that is consistent with the temperatures expected given the distribution of accretion rates and black hole masses inferred for the sample. Our analysis also shows that the variable accretion rate model is a better fit to the $Δf$SEDs than a simple power law.

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