Light Curves of the Neutron Star Merger GW170817/SSS17a: Implications for R-Process Nucleosynthesis

References and Notes

Acknowledgements

We thank John Mulchaey (Carnegie Observatories director), Leopoldo Infante (Las Campanas Observatory director), and the entire Las Campanas staff for their dedication, professionalism, and excitement, which were all critical in obtaining the observations used in this study. We also thank Ian Thompson and the Carnegie Observatory Time Allocation Committee for approving the Swope Supernova Survey and scheduling our program. We thank the University of Copenhagen, DARK Cosmology Centre, and the Niels Bohr International Academy for hosting D.A.C., R.J.F., A.M.B., E.R., and M.R.S. during this work. R.J.F., A.M.B., and E.R. were participating in the Kavli Summer Program in Astrophysics, “Astrophysics with gravitational wave detections.” This program was supported by the the Kavli Foundation, Danish National Research Foundation, the Niels Bohr International Academy, and the DARK Cosmology Centre.

M.R.D., B.J.S., K.A.A., and A.P.J. were supported by NASA through Hubble Fellowships awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. M.R.D. is a Hubble and Carnegie-Dunlap Fellow. M.R.D. acknowledges support from the Dunlap Institue at the University of Toronto, and thanks M.W.B. Wilson, L.Z. Kelly, C. McCully, and R. Margutti for helpful discussions.

The UCSC group is supported in part by NSF grant AST–1518052, the Gordon & Betty Moore Foundation, the Heising-Simons Foundation, generous donations from many individuals through a UCSC Giving Day grant, and from fellowships from the Alfred P. Sloan Foundation (R.J.F), the David and Lucile Packard Foundation (R.J.F. and E.R.) and the Niels Bohr Professorship from the DNRF (E.R.). D.K. is supported in part by a Department of Energy (DOE) Early Career award DE-SC0008067, a DOE Office of Nuclear Physics award DE-SC0017616, and a DOE SciDAC award DE-SC0018297, and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Divisions of Nuclear Physics, of the U.S. Department of Energy under Contract No.DE-AC02-05CH11231.

Support for J.L.P. is in part provided by FONDECYT through the grant 1151445 and by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. C.M.B. was supported by FONDECYT through regular project 1150060. G.M. acknowledges support from CONICYT, Programa de Astronomía/PCI, FONDO ALMA 2014, Proyecto No 31140024. A.M.B. acknowledges support from a UCMEXUS-CONACYT Doctoral Fellowship. CA was supported by Caltech through a Summer Undergraduate Research Fellowship (SURF) with funding from the Associates SURF Endowment. T.C.B., K.C.R., and D.D.W. acknowledge partial support for this work from grant PHY 14-30152; Physics Frontier Center/JINA Center for the Evolution of the Elements (JINA-CEE), awarded by the US National Science Foundation, and from the Luksic Foundation.

This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. This work is based in part on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile as part of PESSTO (the Public ESO Spectroscopic Survey for Transient Objects Survey) through ESO program 199.D-0143. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

The data presented in this work and code used to perform the analysis is available at ftp://ftp.obs.carnegiescience.edu/pub/SSS17a. ESO and Swift-UVOT data analyzed in this work are available at http://archive.eso.org/eso/eso_archive_main.html (program ID 199.D-0143) and https://archive.stsci.edu/swiftuvot/search.php (target IDs 12167, 12978, and 12979), respectively. Reduced photometry is presented in Table S1 and is also avaliable at WISeREP (https://wiserep.weizmann.ac.il/) and on the Open Supernova Catalog (sne.space).

Supplemetary Materials: www.sciencemag.org Materials and Methods Figures S1, S2, S3 Tables S1, S2 References ($54$–$89$)

Supplementary Materials for Light Curves of the Neutron Star Merger GW170817/SSS17a: Implications for R-Process Nucleosynthesis

M. R. Drout,1∗ A. L. Piro,1 B. J. Shappee,1,2 C. D. Kilpatrick,3

J. D. Simon,1 C. Contreras,4 D. A. Coulter,3 R. J. Foley,3 M. R. Siebert,3

N. Morrell,4 K. Boutsia,4 F. Di Mille,4 T. W.-S. Holoien,1 D. Kasen,5,6

J. A. Kollmeier,1 B. F. Madore,1 A. J. Monson,1,7 A. Murguia-Berthier,3

Y.-C. Pan,3 J. X. Prochaska,3 E. Ramirez-Ruiz,3,8 A. Rest,9,10 C. Adams,11

K. Alatalo,1,9 E. Bañados,1 J. Baughman,12,13 T. C. Beers,14,15 R. A. Bernstein,1

T. Bitsakis,16 A. Campillay,17 T. T. Hansen,1 C. R. Higgs,18,19 A. P. Ji,1

G. Maravelias,20 J. L. Marshall,21 C. Moni Bidin,22 J. L. Prieto,13,23

K. C. Rasmussen,14,15 C. Rojas-Bravo,3 A. L. Strom,1 N. Ulloa,17

J. Vargas-González,4 Z. Wan,24 D. D. Whitten14,15

Correspondence to: mdrout@carnegiescience.edu.

This PDF file includes: Materials and Methods Figures S1, S2, S3 Tables S1, S2 References ($54$–$89$)

S1 Data Acquisition & Reductions

Swope Supernovae Survey 17a (SSS17a) was discovered in an $i$-band image obtained with the 1-m Swope telescope at Las Campanas Observatory at UT 2017 August 17 23:33, 10.9 hours after the LIGO Scientific Collaboration and Virgo Collaboration (referred to jointly as LVC) gravitational wave trigger . Immediately after discovery, we initiated a follow-up campaign of optical and near-IR photometric observations of SSS17a spanning from $\sim$11 hours to 18.5 days after the LVC trigger. In the sections below, we describe the data acquisition, reduction, and calibration. All photometry is presented in Table S1 on the AB magnitude scale.

Following the discovery of SSS17a, we obtained observations with the Swope telescope in the BVgri bands on five additional nights spanning 2017 August 18 to 2017 August 24. Details of the observations and data reduction are described in a companion paper We performed all reductions of our Swope imaging using photpipe as described in . Panoramic Survey Telescope and Rapid Response System (PanSTARRS) magnitudes of stars in the field of SSS17a were transformed into the Swope natural system using Supercal transformations .

S1.2 Magellan/LDSS-3 and Magellan/IMACS Optical Imaging

Photometric observations of SSS17a post-discovery included a series of three, 30 s $g$-band images obtained with the LDSS-3 imaging spectrograph on the 6.5-m Magellan/Clay telescope . Observations were obtained between UT 00:08 and 00:20 on 2017 August 18. These images served both as confirmation of the transient and acquisition images for the spectra of SSS17a .

On subsequent nights, we continued to observe SSS17a with LDSS-3 in the Bgriz bands. Observations were obtained on six additional nights spanning 2017 August 18 to 2017 August 25 and included $z$-band spectroscopic acquisition images and 2–5, 60 s exposures in the $B$- and $g$-bands, obtained once the transient had faded below the level accessible to the Swope telescope. In addition we observed SSS17a in the $r$-band on 2017 August 19 and the $z$-band on 2017 August 29 with the Inamori-Magellan Areal Camera and Spectrograph (IMACS; ) on the Magellan/Baade telescope.

Bias and flat field corrections were made to all LDSS-3 and IMACS images using standard routines in IRAF . For observations obtained within 3.5 days of the LVC trigger, all exposures were reduced independently. After that date, nightly stacks were produced in each band.

In order to account for host-galaxy light when performing photometry, we make use of the symmetry of the host galaxy. The galaxy light was subtracted after a 180 degree rotation around its center, thus flattening the target’s background. Tests on several images using Pan-STARRS1 3$\pi$ images of the field as templates yield consistent photometry, but worse residuals near the galaxy core. After galaxy subtraction, point-spread function (PSF) photometry was performed on each image using IRAF daophot tasks. Absolute calibration was performed using magnitudes of field stars. For observations in Bgri, we use field star magnitudes calibrated by the Swope telescope. For $z$-band observations, our magnitudes are tied directly to Pan-STARRS1 magnitudes. All magnitudes are listed in Table S1.

S1.3 Magellan/FourStar and du Pont/RetroCam near-IR Photometry

We observed SSS17a using the FourStar near-IR camera mounted on the 6.5-m Magellan/Baade telescope and the RetroCam near-IR camera mounted on the 2.5-m du Pont telescope at Las Campanas Observatory. FourStar observations were obtained on 11 nights beginning 11.5 hours after the LVC trigger as part of a joint Swope-Magellan search . The observations span 2017 August 17 to 2017 September 7 (0.5 to 18.5 days post-LVC trigger) and were obtained in the $J1$ (approximately $Y$), $J$, $H$, and $K_{\rm{s}}$ filters. RetroCam observations were carried out over 6 nights between 2017 August 21 and 2017 August 27 (4.5 to 10.5 days post-LVC trigger) in $Y$, $J$ and $H$. Initial FourStar and Retrocam data reduction was performed following normal procedures of dark subtraction and flat fielding. In addition, a linearity correction was applied to FourStar data and a fringing mask was subtracted from RetroCam images. Dithered pointing sequences were then co-added into final image combinations, masking bad pixels.

SSS17a remained bright in the near-IR for over three weeks after the LVC trigger, during which the target was only visible close to twilight. It was therefore not possible to obtain high-quality near-IR template images for image subtraction. In order to account for host galaxy light from NGC 4993 when measuring photometry of SSS17a, we again make use of the host galaxy symmetry, subtracting a 180 degree rotated image, as described above.

The instrumental PSF photometry was measured in most images using IRAF’s daophot package . For some images with a low signal-to-noise ratio, an empirical PSF was measured on a bright star and fit via a Markov Chain Monte Carlo (MCMC) to the target and other stars in the field. In this case, a bright star in the image is selected, sky subtracted, subsampled, and then stored in a 2-dimensional array. This array is used as a model of the PSF, which is then fitted to the target and stars individually, using an MCMC procedure where the fitted variables are the amplitude and the center of the star.

The final photometry of the target is measured relative to the calibrated stars in the field. The absolute calibration of field stars was made on one photometric night (2017 August 21) on du Pont/RetroCam for the $Y$, $J$ and $H$ bands. $K_{\rm{s}}$-band calibration of field stars was tied to the Two Micron All Sky Survey (2MASS) catalog . Calibrations from 2MASS or du Pont/Retrocam are fully consistent for the $J$ and $H$ bands. Final photometry is presented in Table S1 on the AB magnitude system. Instrumental magnitudes were converted to the AB scale using offsets from for $K_{\rm{s}}$ and for $Y$, $J$, and $H$.

The FourStar imaging of SSS17a obtained on the night of discovery used integration times long enough that the sky emission was saturated by the end of the exposure. However, the data saved by the detector electronics consist of the difference between the voltage of each pixel at the end of the exposure and the voltage after the 1.456 s it takes for an initial read of each pixel at the beginning of the exposure. A saturated image therefore contains a negative image of the field with an exposure time of 1.456 s. We reduced these data by subtracting a template of the saturation pattern and then taking the difference between consecutive dithered frames to remove any remaining sky emission or dark current. We combined the available dithered frames to construct a final image. We then made photometric measurements as described above.

S1.4 Swift Ultraviolet and Optical Photometry

We performed photometry on 9 epochs of publicly available Swift Ultraviolet/Optical Telescope (UVOT) observations of SSS17a taken between 2017 August 18 and 2017 August 21 . The UVOT observations were obtained in 6 filters: $v$ (effective wavelength 5402 Å), $b$ (4328 Å), $u$ (3494 Å), $uvw1$ (2589 Å), $uvm2$ (2228 Å), and $uvw2$ (2030 Å) . See S2.3 for discussion of the influence of the Swift-UVOT transmission functions on the analysis presented.

We extracted source counts from a 3.0′′ radius region around the transient using the software task Uvotsource. In order to account for host galaxy light, we extracted background counts from several 3.0′′ radius regions at a similar distance from the host galaxy core. Count rates were converted into magnitudes and fluxes using the most recent UVOT calibrations .

Our results produce UV and $u$-band magnitudes that are $\sim$0.1$-$0.2 mag fainter than the values reported in and . The deviation is larger in redder bands, where the host galaxy is brighter, and we attribute this difference to our method of background subtraction. If we instead choose a background region that is well separated from NGC 4993, we recover magnitudes consistent with those previously reported in the Gamma-ray Coordinates Network (GCN) circulars . Applying the same methods described above to the Swift $b$ and $v$ band images shows evidence for continued galaxy contamination, in the form of a flat light curve with large uncertainties over a $\sim$2 day timespan, which conflicts with evolution seen in higher resolution ground-based (e.g LDSS-3) imaging at similar wavelengths. In this manuscript, we report only values from Swift $u$, $uvw1$, $uvm2$ and $uvw2$ bands. All measured values are reported in Table S1 on the AB scale.

S1.5 PESSTO EFOSC and SOFI Imaging

The Public ESO Spectroscopic Survey of Transient Objects (PESSTO) obtained optical imaging of SSS17a with the ESO Faint Object Spectrograph and Camera v.2 (EFOSC2) and near-IR imaging with Son OF ISAAC (SOFI) on the New Technology Telescope (NTT) beginning on 2017 August 18 . We downloaded the raw PESSTO observations from the ESO archive and reduced them using the Pyraf pipeline described by . The PESSTO optical imaging consists of three 300 s exposures in $U$ and several $10-60$ s exposures in $V$ per night on the nights of 2017 August 18-19, 2017 August 19-20, and 2017 August 20-21. The PESSTO near-IR imaging consists of a sequence of $48-67$ dithered 90 s or 120 s exposures in a single band ($J$, $H$, or $K_{\rm s}$) per night.

We performed PSF photometry on the $U$- and $V$-band images using the IRAF task daophot and calibrated the instrumental magnitudes using stars in the Swope $V$- and Swift $U$-band images. Photometry on the SOFI $J$, $H$, and $K_{\rm s}$ images was carried out as described above for Magellan/FourStar.

S1.6 Keck Imaging

We imaged SSS17a with the Low Resolution Imaging Spectrometer (LRIS) on the Keck-I 10 m telescope on 24 August 2017 from UT 05:35 to 06:24. LRIS was configured in imaging mode with $g$ and $I$ filters on the blue and red sides, respectively, and the D560 dichroic. We observed SSS17a in $11$ blue-side frames and $27$ red-side frames starting during twilight, and our exposure times varied from $14$–$124$ s on the blue side and $25$–$120$ s on the red side. In order to minimize readout time on the red side, we binned the image $2\times 2$ and read out only the central $4\mbox{~arcmin}\times 4\mbox{~arcmin}$ region. Conditions were near photometric at the start of observations with $\sim$0.8′′ seeing, although the seeing degraded significantly in exposures at higher airmasses. We obtained bias frames and sky flats in the same instrumental configuration and the Landolt standard star field SA95 275 was observed at a similar airmass.

We reduced all Keck/LRIS images using the semi-automatic IDL/python software LPipe . Individual frames were bias corrected, flattened, and then registered using stars in the 2MASS Point Source Catalog . We aligned and co-added the registered images, weighting by the inverse variance of the emission-free regions. We performed PSF photometry using daophot and calibrated our photometry using APASS and Landolt standard stars from our standard star field.

S1.7 Synthetic Photometry from Flux-Calibrated Spectra

In addition, we supplement the photometry measured from broad-band imaging described above with synthetic photometry performed on flux calibrated spectra of SSS17a. Full details of the spectroscopic observations, reductions, calibration and synthetic photometry are described in . Briefly, the final flux calibrated spectra were corrected for instrumental response, atmospheric dispersion, differential flux losses, and telluric absorption, and were then scaled to the broad-band photometry described above.

The full set of synthetic photometry measured from the spectral sequence of SSS17a between 0.5 and 4.5 days can be found in . In this manuscript, we supplement our existing light curves and SEDs with measurements from synthetic photometry under the following conditions: (1) they add to a band in which we had existing observations, (2) they were obtained from a high S/N spectrum, (3) the entire filter response function falls within the observed spectrum, and (4) the relevant band lies interior or adjacent to the broad-band photometric points used to scale the spectrum. This results in the addition of V, r, and z-band measurements from the first night of observations and individual V and z-band points on later epochs. Synthetic photometry used in this analysis is presented in Table S1.

S2 Photometric Analysis

SSS17a exploded in NGC 4993 at a distance of $\sim$40 Mpc. Throughout this manuscript we adopt the Tully-Fisher distance of 39.5 Mpc from .

We adopt a value of $E(B-V)$ = 0.106 for the color excess due to Milky Way reddening in the direction of SSS17a based on the dust maps of . $E(B-V)\equiv A_{B}-A_{V}$ where $A_{B}$ and $A_{V}$ are the total extinction in the $B$ and $V$ band, respectively. This value is consistent with estimates based on Milky Way Na D absorption lines observed in high resolution spectra of SSS17a. Photometry is corrected for this reddening using a Milky Way extinction curve from with the parameter $R\equiv$ $A_{{V}}$/$E(B-V)$ $=$ 3.1. We use the SED of the source to iteratively calculate the extinction in each filter, Aλ, at each epoch as described below. Throughout this manuscript, we do not correct for reddening due to dust within the host galaxy. The lack of observed Na D features at the redshift of NGC4993 favors a low intrinsic absorption .

S2.2 Basic Photometric Properties from the UV to near-IR

The full light curve of SSS17a from the UV through near-IR is shown in Figure 1. In Table S2 we provide several basic parameters derived from the photometry in each band.

The quoted peak apparent and absolute magnitudes are observed values. For bands blueward of z-band, which rise in less than 12 hours, these are lower limits to the true peak. SSS17a peaks between $-$15.5 and $-$16.0 mag (AB) from the optical to near-IR, similar to the faintest core-collapse supernovae. In Figure S1 we plot the V, i, and H-band absolute magnitude light curves of SSS17a—accounting for the distance to NGC4993 and Milky Way reddening. Also shown are the F160W (roughly rest-frame H-band) measurement and F6060W (roughly rest-frame V-band) upper limit for the tentative kilonova associated with short GRB 130603B . At $+$7 days from the burst, GRB130603B has a slightly higher near-IR luminosity than observed for SSS17a.

In Table S2 we also report several measurements of the rise and decline timescales of SSS17a. We determine the time over which a band declines by half of its peak luminosity (t1/2) and number of magnitudes the light curve decline in the first 5 days after maximum ($\Delta$M5) by linearly interpolating the observed light curves. A linear decline rate was also obtained by fitting the data between maximum light and +5.5 days. SSS17a declines at a rate ranging from 2.6 mag day-1 ($u$-band) to 0.1 mag day-1 ($H$-band). The observed optical light curves are generally consistent with a single slope post-maximum. However, our final $B$-band points indicate a shallowing of the decay rate between 5 and 10 days post-merger.

SSS17a peaks earlier and declines faster in bluer bands. As a result, its colors transition quickly to the red. Between +0.5 and +4.5 days the $V-H$ color of SSS17a evolves from $-$1.2 mag to 3.6 mag (top panel, Figure S1). By comparison, the late time emission from GRB130603B was attributed to a kilonova in part because of its red color ($V-H$ $>$ 1.9 mag).

The characteristic timescale of SSS17a is faster than other known transients. For example, t1/2 $\sim$ 1.1 days in r-band is nearly a factor of 5 smaller than the fastest rapidly-evolving and luminous transient discussed in . A detailed comparison of the properties of SSS17a to other transients is made in .

S2.3 SED and Bolometric Light Curve Construction

We construct SEDs for SSS17a from our observed photometry at 10 epochs using the iterative, forward-modeling approach described in . This approach aims to mitigate systematic errors that occur when constructing an SED from photometry by applying standard offsets to obtain fluxes at filter’s pivot or effective wavelength. The translation from an observed broad-band magnitude to a flux at a given wavelength is fundamentally a function of the source’s spectrum, and systematic errors can be particularly large when applying standard conversion factors to Swift-UVOT $uvw1$ and $uvw2$ observations of red sources .

We begin by interpolating our observed light curves to a set of common epochs. Our observations predominately come from Las Campanas Observatory and other telescopes in Chile, where SSS17a was only visible for the first $\sim$1 hour of the night. As a result our SEDs are constructed predominately on daily, evenly-spaced epochs between 0.5 and 8.5 days after the LVC trigger. In addition, we also compute compute SEDs at the 0.67 and 1.0 days. These correspond to the first two epochs of Swift UVOT data, when the transient was rapidly evolving.

With our photometry integrated to common epochs, we then construct a simple SED with “pivot” points at the effective wavelength of each observed band and the outer edge of the filter functions for the exterior bands. The flux level at each pivot point is then adjusted until synthetic photometry performed on this simple SED is consistent with the observed measurements. Extinction correction factors, Aλ, and flux conversion factors for each band are then computed from this best-fitting SED and applied to the original data.

The time evolution of the resulting SEDs is shown in Figure 3. In Figure S2 we plot each epoch individually for clarity. As in Figure 3, the shaded bands represent best-fit blackbody temperatures for each epoch. For epochs 0.67 and 1.0 days, data redward of the Swift-u band data is derived from interpolating our ground based optical data on days 0.5 and 1.5. We find very similar best-fit blackbody temperatures if only the Swift-UVOT data are modeled.

SSS17a undergoes dramatic cooling over the first day post-merger. Between our first observations at 0.5 days, and the first epoch of Swift-UVOT measurements $\sim$ 4 hours later, we infer a total cooling of $\sim$2400K, or 600 K hr-1. Evidence for this rapid cooling is also seen in the evolution of the continuum between spectra taken $\sim$ 1 hour apart on the first night of observations .

While the SEDs are generally consistent with a thermal distribution, there are a few exceptions. Between days 1.5 and 4.5 the Y-band measurements consistently lead to fluxes in excess of the best-fit blackbody distribution. This is consistent with the emergence of a feature in in the optical spectra around $\sim$ 1$\mu$m at similar epochs. In addition, an apparent excess is visible in the $g$-band ($\sim$4800 Å ) at similar epochs. These features are indicated by dotted lines in Figure S2. At late epochs ($>$ 5.5 days) the slope between the bluest observed bands are steeper than a thermal distribution, possibly indicative of line-blanketing.

Pseudo-bolometric luminosities at each epoch were constructed by integrating these best-fit SEDs after applying a Milky Way extinction curve, and corrected for missing flux as described in the main text. At 0.5 days post-merger SSS17a has a bolometric flux of $\sim$1042 erg s-1.

S3 R-Process Heating and Ejecta Property Estimates

Models of r-process powered transients have become increasingly sophisticated over the last decade. Early models first showed that radioactive ejecta from a neutron star merger can power an electromagnetic transient, but assumed that the energy was provided by some fraction of the rest mass energy rather than using an actual model for the radioactive decay . The idea of a macronova or kilonova was then re-popularized by newer models that invoked the decay of radioactive species, without making the connection to r-process nucleosynthesis . The first true r-process powered transient calculation soon followed , and since that time the theoretical studies have quickly matured with more detailed nuclear networks, hydrodynamics in multi-dimensional numerical simulations, and detailed treatments of the radiative transfer. Here we summarize some of the basic aspects of r-process transients for use in comparing with our data. A more detailed comparison with specific models is provided in a companion paper .

One of the most robust predictions of r-process heating is the $t^{-1.3}$ dependence of the energy generation rate, $\dot{q}_{r}$ . We fit the heating rate from these works to find

where $t_{\rm day}$ is the time since explosion in units of days. There can be a $\approx$30% correction to this heating rate depending on $Y_{e}$. The thermalization depends on the ability to absorb the energy with energy losses from weak processes. To account for thermalization efficiency, $\epsilon_{\rm th}$, we use the fitting function

where $a$, $b$, and $d$ are fitting parameters whose values depend on the mass of of r-process elements, $M_{\rm{r}}$ and the average (lowest) velocity in the ejecta, $v_{0}$. $a=0.56$, $b=0.17$, and $d=0.74$ are appropriate for $M_{\rm{r}}=0.1\,M_{\odot}$ and $v_{0}=0.1c$ . Combining the above expressions the total r-process luminosity is

The rise time to peak ($t_{p}$) for an optically thick transient is roughly set by when the diffusion time is equal to the expansion time for the ejecta . For ejecta with a velocity gradient $v=v_{0}(M_{v}/M_{r})^{-1/\beta}$, where $M_{v}$ is the total mass with velocity greater than $v$, this timescale can be approximated as

where $\kappa$ is the specific opacity . A characteristic value for $\beta$ motivated by numerical simulations is about 3 , although in general the ejecta structure can be more complicated than in such simulations . Solving this equation for $\kappa$ and requiring that $t_{p}\lesssim 0.5\,{\rm days}$, we find an upper limit to the opacity during the peak of the kilonova of $\kappa\approx 0.08\,{\rm cm^{2}\,g^{-1}}$.

Similarly, the optical depth of a given depth moving at velocity $v$ is

is roughly the density of the material moving at $v$. Performing this integral and evaluating it at $v=v_{0}$, we find that the total optical depth is

Solving for the time when $\tau\approx 1$

thus up to a factor of order unity $t_{\tau=1}\approx(c/v_{0})^{1/2}t_{p}$. Setting $t_{\tau=1}\approx 20\,{\rm days}$ (motivated by the observed duration of the SSS17a emission), we derive a lower limit on the opacity of the red/cool component of $\kappa\gtrsim 5\,{\rm cm^{2}\,g^{-1}}$.

S4 Constraints on Radioactive Nickel Heating

Most hydrogen-deficient supernovae are powered by the radioactive decay of 56Ni, but radioactive nickel heating cannot reproduce the entire photometric evolution of SSS17a. The heating from the decay of 56Ni and subsequently 56Co, $\dot{q}_{56}$, scales as

where $\dot{q}_{\rm Ni}=3.9\times 10^{10}\,{\rm erg\,g^{-1}\,s^{-1}}$, $\dot{q}_{\rm Co}=6.8\times 10^{9}\,{\rm erg\,g^{-1}\,s^{-1}}$, $\tau_{\rm{Ni}}=8.8\,{\rm days}$, and $\tau_{\rm Co}=111.3\,{\rm days}$, are the heating rates and decay timescales for 56Ni and 56Co. The total amount of heating depends on how efficiently gamma-rays are thermalized. Gamma-ray thermalization efficiency, $\epsilon_{56}$, can be simply modeled with the following function

where the characteristic gamma-ray diffusion timescale is

where $\kappa_{\gamma}=0.03\,{\rm cm^{2}\,g^{-1}}$ is the fiducial gamma-ray opacity, $M_{\rm ej}$ is the total ejecta mass, and $C\sim 0.05$ is a structural factor that depends on the density distribution. A larger $T_{0}$ means that the gamma-rays take longer to diffuse and thus are more efficiently thermalized. The total luminosity is

In Figure S3, we compare the bolometric light curve of SSS17a to nickel curves with $M_{56}=0.014\,M_{\odot}$, the nickel mass required to match the first night’s luminosity. Since the total ejecta mass can be different from the nickel mass, we consider a range of $T_{0}=1-10\,{\rm days}$ (and in addition the least shallow curve is for $T_{0}=\infty$, or complete thermalization of gamma-rays), corresponding to a range of ejecta masses from $M_{\rm ej}=0.002-0.2\,M_{\odot}$. The lowest value is unphysical since it is smaller than $M_{\rm 56}$, but we include it just to demonstrate that no nickel-decay model can reproduce both the peak luminosity and subsequent evolution of SSS17a. In Figure S3 we also plot a nickel curve with $M_{56}=0.002\,M_{\odot}$ and $T_{0}=10\,{\rm days}$, corresponding to an ejecta mass of $\sim$0.2 M⊙ for $v=0.1c$. This curve reproduces the bolometric evolution of SSS17a between 7.5 and 18.5 days post-merger, but requires that another emission source dominates at early times. In addition, a transient powered by the radioactive decay of nickel does not naturally explain the color evolution observed in SSS17a.