Constraints on the presence of platinum and gold in the spectra of the kilonova AT2017gfo
James H. Gillanders, Michael McCann, Stuart A. Sim. Stephen J. Smartt, Connor P. Ballance
MMNRAS , 1–18 (2020) Preprint 22 January 2021 Compiled using MNRAS L A TEX style file v3.0
Constraints on the presence of platinum and gold in the spectra of thekilonova AT2017gfo
J. H. Gillanders (cid:63) , M. McCann S. A. Sim , S. J. Smartt , C. P. Ballance Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, BT7 1NN, UK Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen’s University Belfast, BT7 1NN, UK
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Binary neutron star mergers are thought to be one of the dominant sites of production for rapid neutron capture elements, and thesource of platinum and gold in the Universe. Since the discovery of the binary neutron star merger GW170817, and its associatedkilonova AT2017gfo, numerous works have attempted to determine the composition of its outflowing material, but they havebeen hampered by the lack of complete atomic data. Here, we demonstrate how inclusion of new atomic data in synthetic spectracalculations can provide insights and constraints on the production of the heaviest elements. We employ theoretical atomic datafor neutral, singly- and doubly-ionised platinum and gold, to generate photospheric and simple nebular-phase model spectra forkilonova-like ejecta properties. We make predictions for the locations of strong transitions, which could feasibly appear in thespectra of kilonovae that are rich in these species. We use grasp to generate the underlying atomic structure, and tardis to modelthe di ff usion phase, showing that the strongest features lie in the ultra-violet region. We identify low-lying electric quadrupoleand magnetic dipole transitions that may give rise to forbidden lines when the ejecta becomes optically thin. The strongestlines lie beyond 8000 Å, motivating high quality near-infrared spectroscopic follow-up of kilonova candidates. We compare ourmodel spectra to the observed spectra of AT2017gfo, and conclude that no platinum or gold signatures are prominent in theejecta. This work demonstrates how new atomic data of heavy elements can be included in radiative transfer calculations, andmotivates future searches for elemental signatures. Key words: neutron star mergers – stars: neutron – supernovae: individual: AT2017gfo – radiative transfer – atomic data – line:identification
Mergers of binary neutron star (BNS) and neutron star–black hole(NSBH) systems have long been hypothesised to be an ideal loca-tion for the synthesis of the rapid neutron capture ( r -process) ele-ments (see discussion by Metzger 2017). Theoretical modelling hasshown that the large neutron fraction in expelled material from thesemergers is su ffi cient to generate these heavy elements (Lattimer &Schramm 1974; Eichler et al. 1989; Freiburghaus et al. 1999; Ross-wog et al. 1999; Goriely et al. 2011, 2013, 2015; Perego et al. 2014;Just et al. 2015; Sekiguchi et al. 2016). However, spectrophotometricobservations are needed to confirm the validity of the models. Thefirst kilonova (KN; the optical counterpart of a BNS merger) wasdetected in 2017 (AT2017gfo, Abbott et al. 2017a; Andreoni et al.2017; Arcavi et al. 2017; Chornock et al. 2017; Coulter et al. 2017;Cowperthwaite et al. 2017; Drout et al. 2017; Evans et al. 2017;Kasliwal et al. 2017; Lipunov et al. 2017; Nicholl et al. 2017; Pianet al. 2017; Smartt et al. 2017; Tanvir et al. 2017; Troja et al. 2017;Utsumi et al. 2017; Valenti et al. 2017). Early theoretical models(Kasen et al. 2017) predicted the overall shape of the spectra, andshowed that it can be readily explained by the presence of r -process (cid:63) E-mail: [email protected] material, as the associated high opacities lead to a red, long-livedcomponent.Radiative transfer simulations for the spectra of AT2017gfo havetaken two approaches. The first is to attempt direct identificationof species contributing to apparent absorption features in the earlyspectra. Smartt et al. (2017) suggested attribution of spectral featuresto Te i and Cs i , elements from the second r -process peak. Furtherwork by Watson et al. (2019) attributed the same absorption featuresto lighter r -process elements, specifically Sr ii . Both works, how-ever, rely on incomplete atomic data. Specifically, both use data fromKurucz (2017) for their models. This atomic line list provides datafor the lowest few ionisation stages for all elements up to the first r -process peak. However, due to the di ffi culties involved with gener-ating this information for heavier elements, the line lists are mostlyincomplete beyond this first peak. This makes any modelling, andsubsequent conclusions di ffi cult, as the elements without completeatomic data will be excluded from consideration.The second approach is to calculate new atomic data for heavy el-ements, and to model the temporal evolution of the spectra in a broadsense. The models of Kasen et al. (2017) and Tanaka et al. (2018,2020) calculate broad-band spectral energy distributions (SEDs) forlow Y e material, which can reproduce the rising near-infrared (NIR)flux observed in AT2017gfo. The main reason why these works have © a r X i v : . [ a s t r o - ph . H E ] J a n J. H. Gillanders et al. focussed on modelling the broad spectral shapes is due to the accu-racy of the atomic data used. Kasen et al. (2017) have used elementswith complete and well-calibrated atomic data to represent theirless well-sampled homologues (e.g. the atomic data for the elementswith Z = −
28 have been used as ‘surrogate’ data for the open d -shell r -process elements with Z = −
48 and Z = − d -shell elements, but restricts them from predicting individ-ual features. They also use new atomic data for the elements with Z = −
70, but these data have not been calibrated (with the ex-ception of Nd). Therefore they cannot be used to accurately predictthe locations of individual transitions, as these will be systemati-cally o ff set from the true wavelengths. Similarly, the atomic dataused by Tanaka et al. (2018, 2020) have not been calibrated, and sothese results also cannot be used to accurately predict the locationsof individual transitions either. Even et al. (2020) used tabulatedwavelength-dependent opacities to produce SEDs, but this methoddoes not allow identification of specific transitions.We are focussed on the first of these two methods, but our progressthus far has been hampered by the availability of accurate, complete,and reliably calibrated atomic data for the heavy elements. Hence,our focus, as outlined in this paper, is to generate atomic data for therelevant important heavy elements, with a focus on reliably calibrat-ing to any experimental data that exist. This will enable us to baseour models on accurate atomic data, and allow us to make strongpredictions about individual transitions of interest. To that end, thework presented here is a pilot study, focussing specifically on plat-inum and gold, to demonstrate the validity and usefulness of such astudy.Two of the most interesting heavy elements to search for signa-tures of are platinum (Pt) and gold (Au). Their cosmic origin iscurrently unknown and Kobayashi et al. (2020) argue two sites ofproduction may be needed, with a rapid injection of the elementsto explain abundance patterns in metal-poor stars. The BNS chan-nel may have a natural time delay that cannot account for the earlyexcess in Pt and Au observed. Collapsar accretion disks have beensuggested as potential production sites of these elements, and couldbe the dominant source of heavy elements in the early Universe, asthey do not su ff er from as long a time delay (Siegel et al. 2019).However, no distinct spectroscopic signature has yet been identifiedto corroborate this.No signature of any ion of Pt or Au has been identified in thespectra of AT2017gfo, and hence our motivation for this work isto employ recently calculated, high quality atomic data to predictpossible spectral features in kilonova-type expanding ejecta.We note that there have been previous reports of observations ofPt and Au lines in astrophysical objects. Ross & Aller (1972) re-port observations of the Au i ii lines, the strongest of which is the Pt ii i . There have been other observinge ff orts since, which have observed more Pt and Au lines in vari-ous di ff erent stars (see e.g. Fuhrmann 1989; Adelman 1994). Also,Castelli & Hubrig (2004) identify two Pt lines in the spectrum ofHD 175640, a narrow lined, chemically peculiar star. They identifythe Pt ii Calibrated data means that the energy levels from theoretical calculationshave been e ff ectively ‘shifted’ to match those obtained experimentally. in the spectra; specifically, they detected the Au ii ff erent stars under investigation. These all have surfacetemperatures on the order ∼ − . − . ∼ ∼ r -process material, theonly r -process material in the ejecta will be present from the initialformation of the star. This results in abundances much lower thanthat required to produce any spectral features of Pt or Au, hence thelack of observations. However, the late-phase spectra of KNe mayhave promise for the detection of these elements, and other r -processelements, since the explosions are hypothesised to synthesise signifi-cant masses of r -process material. This will result in late-phase spec-tra dominated by emission features from r -process material, and, ifPt and Au are produced in significant quantities, then their spectralsignatures could be identified.Our work consists of two parts. First, we determine which strongfeatures of Pt or Au are most likely to be prominent in the early, pho-tospheric spectra of KNe. Second, we determine whether any forbid-den transitions of Pt or Au could provide emission lines in the latetime, nebular spectra of KNe. In both cases, we present predictionsand compare to the spectra of AT2017gfo. In Section 2, we detailthe sources of the AT2017gfo spectra we compare our models to. InSection 3, we summarise how the atomic data we use in this workwas generated. Section 4 contains some motivation for the valueswe chose for ejecta mass in our work. In Section 5, we outline thesteps taken to produce our photospheric phase spectral models, andwe highlight our main results. Section 6 details how we generatedour synthetic nebular phase spectra, and also contains our results.Finally, we summarise our work in Section 7. As well as providing model spectra and predictions for the featuresof Pt and Au, we compare our models with the one known kilonovawith a spectroscopic sequence, AT2017gfo. The data we primarilyuse is the set of 10 X-shooter spectra originally published by Pianet al. (2017) and Smartt et al. (2017). As part of the ENGRAVEproject, all the X-shooter spectra were flux-calibrated to a compiledset of photometric measurements taken from the published values ofAndreoni et al. (2017); Arcavi et al. (2017); Chornock et al. (2017);Cowperthwaite et al. (2017); Drout et al. (2017); Evans et al. (2017);Kasliwal et al. (2017); Pian et al. (2017); Smartt et al. (2017); Tan-vir et al. (2017); Troja et al. (2017); Utsumi et al. (2017); Valentiet al. (2017). This data set is publicly available, and can be accessed
MNRAS000
MNRAS000 , 1–18 (2020) t and Au constraints on kilonova spectra through the ENGRAVE webpage , along with release notes describ-ing the calibration, extinction correction, rest-frame velocity correc-tion, and smoothing.We supplemented this set of spectra with data from two othersources, to extend its temporal coverage to earlier times, and to im-prove the spectral quality (where possible). Shappee et al. (2017)present early spectra for AT2017gfo. The spectrum taken at + sms code; see Inserra et al. 2018) to thesame compiled set of photometric points as detailed above; we alsocorrected for extinction, and rest-frame velocity. Tanvir et al. (2017)present HST spectra of AT2017gfo, obtained at four separate epochs.The + HST spectrum with the X-shooter spec-trum at this epoch, replacing the pixels of X-shooter with the flux-calibrated
HST pixels, within the telluric region.
For KN observations at times, t (cid:38) T (cid:46) i – iv ; Tanaka et al. 2020). For AT2017gfo, after ∼ . ∼ i – iii ). Hence, for this work wefocussed on these ionisation stages of Pt and Au.The atomic structure for these first three ion stages of platinumand gold were calculated within a Dirac-Coulomb framework, em-ploying the General Relativistic Atomic Structure Package ( grasp ),(Dyall et al. 1989). The orbitals were variationally determined us-ing a multi-configurational Dirac-Fock approach for each of the sixion stages under consideration. Our goal was to accurately deter-mine the lowest 25 −
40 levels of each ion stage, from a much largerconfiguration set. Although the National Institute of Standards andTechnology Atomic Spectra Database (NIST ASD; Kramida et al.2020) provides a more comprehensive list of energy levels for theneutral ion stages of platinum and gold, the higher ion stages havesparse, incomplete energy state listings. Furthermore, we appreci-ate that the Einstein A -coe ffi cients for the lowest levels of each ionstage involve non-dipole transitions that scale ∝ E , and thereforewe have utilised the option with grasp to adopt spectroscopicallyaccurate energy separations before the calculation of transition ma-trix elements, where available. This obviously impacts the accuracyof the A -values and any subsequent modelling.For Pt i , the first 32 energy levels were calibrated to the energiesgiven in the NIST ASD (Kramida et al. 2020). For Pt ii , the first 40levels were calibrated. For Au i , the first 37 levels were calibrated,excluding levels 21, 28, 31 and 34, which did not have identifi-able counterparts. The first 21 levels of Au ii were calibrated. TheNIST ASD has no atomic data for either Pt iii or Au iii , aside fromthe ground level. Therefore, all energy levels in these structures aretaken as calculated in grasp . The configurations that contain cali-brated energy levels in neutral and singly ionised platinum and gold Pt i , 5d , 5d ii , 5d , 5d i , 5d ii , 5d , 5d Table 1.
Configurations that contained calibrated energies, for neutral andsingly ionised platinum and gold. Doubly ionised platinum and gold had nocalibrated levels. are shown in Table 1. grasp has also been further modified to inter-face with the tardis code to provide easier future integration of newatomic data sets.Although these atomic structure calculations provide the founda-tion of any plasma modelling under LTE conditions, a companionpaper (McCann et al. in prep) will provide greater detail on theatomic structure calculations, as well as the electron-impact exci-tation of neutral gold. This excitation calculation shall be bench-marked against the spectra of ongoing gold experiments (Bromleyet al. 2020) and provide insight into populating mechanisms, whenthe observed spectra drop out of LTE into the collisional radiativeregime. This will also address the incompleteness of data for themore highly charged systems, where observed and synthetic spectramay be compared to determine the identification of higher excitedstates. It will also provide the mechanisms by which excited statesare populated, and hopefully provide temperature and density lineratios. For an in-depth discussion of the atomic data generation, seeMcCann et al. (in prep). Finally, we note that all wavelengths pre-sented throughout this paper are quoted as in vacuum. To determine what ejecta mass to use in our calculations, we consid-ered both observational and theoretical estimates. We also performedour own calculation, to estimate Pt and Au production in KNe.Observationally, the ejecta mass can be estimated from thelightcurve modelling of AT2017gfo. The bolometric lightcurve andfilter band lightcurves have been fit with ejecta masses between0 . − .
05 M (cid:12) (Cowperthwaite et al. 2017; Smartt et al. 2017; Tan-vir et al. 2017; Coughlin et al. 2018; Waxman et al. 2018).The expected mass of dynamical ejecta in BNS merger simula-tions is in the region 10 − < M dyn < − M (cid:12) (Bauswein et al. 2013;Hotokezaka et al. 2013; Sekiguchi et al. 2016; Ciolfi et al. 2017;Radice et al. 2018), with a large fraction of neutron-rich material( Y e < . − < M dw < − M (cid:12) ), slower moving ( v (cid:39) . Y e mate-rial. Nuclear trajectories for low Y e regimes (Bauswein et al. 2013;Goriely et al. 2013, 2015) indicate that Pt and Au compositionscould be as high as 5 −
15 per cent, by mass, which would potentiallymean ejecta masses of either element of ∼ × − − . × − M (cid:12) ,in low Y e ejecta.A simple calculation to determine Pt and Au production in KNe,assuming they are the sole source of these elements in the MilkyWay, also provides approximate Pt and Au masses per event. Thecurrently accepted LIGO–Virgo rate for binary neutron star merg-ers in our local Universe is R bns = + − Gpc − yr − (The LIGOScientific Collaboration et al. 2020). From Abadie et al. (2010),the density of Milky Way equivalent galaxies (MWEG) is ∼ . × − Mpc − . From these values, we calculated a rate of BNS merg-ers of 2 . + . − . × − MWEG − yr − , which we take as the rate of MNRAS , 1–18 (2020)
J. H. Gillanders et al.
Table 2.
Input parameters used to generate the various tardis models presented in this work.Pt AuModel 0 Model 1 Model 2 Model 0 Model 1 Model 2 t exp (days) 0.5 1.4 2.4 0.5 1.4 2.4 T (K) 10000 5000 3700 10000 5000 3700 v min ( c ) 0.30 0.25 0.20 0.30 0.25 0.20 v max ( c ) 0.35 0.35 0.35 0.35 0.35 0.35 ρ (10 − g cm − ) 0.1 0.5 1 0.1 1 0.5 v ( kms − ) 14000 14000 14000 14000 14000 14000 t (days) 2 2 2 2 2 2 Γ M ej (M (cid:12) ) * * M ej is a derived property of our models, but is included here for reference. It represents the mass boundby the tardis computational domain, and so is a lower limit for a model’s ejecta mass. mergers in the Milky Way. Asplund et al. (2009) provide estimatesfor the abundance of elements in the Solar System. They quote num-ber densities for Pt and Au of 3 . × − and 7 . × − , respec-tively. Given a MW baryonic mass of ∼ . × M (cid:12) (McMillan2011), and assuming that the abundances of Pt and Au throughoutthe Milky Way are consistent with their Solar System abundances,we estimate that there is 378 M (cid:12) of Pt, and 77 M (cid:12) of Au in thegalaxy. Given a MW age of ∼ years, and assuming a constantrate of BNS mergers since galaxy formation, we estimate there havebeen 2 . + . − . × KNe to date in the Milky Way. If we assume thesole source of Pt and Au in the galaxy comes from these mergers,then we determine that each event has to eject, on average, Pt and Aumasses of M Pt = . − . × − M (cid:12) and M Au = . − . × − M (cid:12) .From our simple calculation, we predict that ∼ / Au ratios of ∼ a few. Since the uncertainties for predictedPt and Au masses per event are large, we do not make calculationsthat explore the relative masses of these elements in detail, but wedo note that if either element is present, the other should also havebeen produced and that the abundance of Pt is expected to be higherthan Au by a moderate factor.Given all of the above, we conclude that Pt and Au masses on theorder of ∼ − M (cid:12) are reasonable, and so we adopt this character-istic mass for all our modelling, unless otherwise stated. The spectra of AT2017gfo have been interpreted in di ff erent ways,with many authors invoking two components. A low opacity, bluecomponent and a red contribution from high opacity ejecta are physi-cally motivated from numerical simulations of neutron star mergers.In particular, the models of Kasen et al. (2017) have been widelyused to argue for two components to explain the SED of the spectra(see also e.g. Chornock et al. 2017; Coughlin et al. 2018). However,the existence of two components is by no means settled, with somework arguing that the evolution of the SED and the bolometric lumi-nosity is dominated by one component with low to moderate opacity(Smartt et al. 2017; Waxman et al. 2018). In this paper, we model thespectra of AT2017gfo using a one-component model, to evaluate thepresence of Pt and Au signatures. To determine if any photospheric phase spectral features couldbe produced by Pt or Au, we generated synthetic spectra using tardis (Kerzendorf & Sim 2014; Kerzendorf et al. 2019), a one-dimensional Monte Carlo radiative transfer code capable of rapidlygenerating synthetic spectra for explosive transients. tardis has beenused previously to produce KN spectra (Smartt et al. 2017; Watsonet al. 2019; Perego et al. 2020). We note that these previous worksdid not make use of the full relativistic treatment recently imple-mented for tardis (as outlined by Vogl et al. 2019), whereas we haveincorporated this feature into our modelling here.First, we used the new data to generate an atomic data set capableof being read by tardis . For this, we used the carsus package, whichextracted the level energies and statistical weights, and also the Ein-stein A -values for all transitions from the grasp output. This wasthen parsed into an atomic data file for use in our tardis models .For the photospheric modelling, we only included permitted lines,which are electric dipole transitions (conventionally labelled E1).Electric quadrupole (E2), magnetic dipole (M1), and higher ordermultipole transitions are not likely to contribute substantial opacity(or emissivity) in the di ff usion phase and therefore are not expectedto feature in the emergent early-phase spectra.Input parameters for the tardis models are given in Table 2. Weinitially used similar parameters to the models presented by Smarttet al. (2017) and Watson et al. (2019), which broadly reproduced theearly SED of AT2017gfo. We used a power law density profile forall of our models, which had the general form: ρ ( v , t exp ) = ρ (cid:32) t t exp (cid:33) (cid:32) vv (cid:33) − Γ (1)for v min < v < v max , where ρ , t , v , Γ and v max are constants. Thevalues for these constants were chosen empirically to reproduce thegeneral shape of the early SED of AT2017gfo, assuming it is dom-inated by a single black-body component. Table 2 lists these val-ues. The choice of photospheric ejecta velocity ( v min ) is in line withprevious works that model the early spectra of AT2017gfo ( ∼ . c ,Smartt et al. 2017; Watson et al. 2019). The time since explosion( t exp ) is well constrained based on the GW detection (Abbott et al.2017b). A value of Γ = ff orts The atomic data set we produced for our modelling e ff orts is publicly avail-able - see Data Availability.MNRAS000
Input parameters used to generate the various tardis models presented in this work.Pt AuModel 0 Model 1 Model 2 Model 0 Model 1 Model 2 t exp (days) 0.5 1.4 2.4 0.5 1.4 2.4 T (K) 10000 5000 3700 10000 5000 3700 v min ( c ) 0.30 0.25 0.20 0.30 0.25 0.20 v max ( c ) 0.35 0.35 0.35 0.35 0.35 0.35 ρ (10 − g cm − ) 0.1 0.5 1 0.1 1 0.5 v ( kms − ) 14000 14000 14000 14000 14000 14000 t (days) 2 2 2 2 2 2 Γ M ej (M (cid:12) ) * * M ej is a derived property of our models, but is included here for reference. It represents the mass boundby the tardis computational domain, and so is a lower limit for a model’s ejecta mass. mergers in the Milky Way. Asplund et al. (2009) provide estimatesfor the abundance of elements in the Solar System. They quote num-ber densities for Pt and Au of 3 . × − and 7 . × − , respec-tively. Given a MW baryonic mass of ∼ . × M (cid:12) (McMillan2011), and assuming that the abundances of Pt and Au throughoutthe Milky Way are consistent with their Solar System abundances,we estimate that there is 378 M (cid:12) of Pt, and 77 M (cid:12) of Au in thegalaxy. Given a MW age of ∼ years, and assuming a constantrate of BNS mergers since galaxy formation, we estimate there havebeen 2 . + . − . × KNe to date in the Milky Way. If we assume thesole source of Pt and Au in the galaxy comes from these mergers,then we determine that each event has to eject, on average, Pt and Aumasses of M Pt = . − . × − M (cid:12) and M Au = . − . × − M (cid:12) .From our simple calculation, we predict that ∼ / Au ratios of ∼ a few. Since the uncertainties for predictedPt and Au masses per event are large, we do not make calculationsthat explore the relative masses of these elements in detail, but wedo note that if either element is present, the other should also havebeen produced and that the abundance of Pt is expected to be higherthan Au by a moderate factor.Given all of the above, we conclude that Pt and Au masses on theorder of ∼ − M (cid:12) are reasonable, and so we adopt this character-istic mass for all our modelling, unless otherwise stated. The spectra of AT2017gfo have been interpreted in di ff erent ways,with many authors invoking two components. A low opacity, bluecomponent and a red contribution from high opacity ejecta are physi-cally motivated from numerical simulations of neutron star mergers.In particular, the models of Kasen et al. (2017) have been widelyused to argue for two components to explain the SED of the spectra(see also e.g. Chornock et al. 2017; Coughlin et al. 2018). However,the existence of two components is by no means settled, with somework arguing that the evolution of the SED and the bolometric lumi-nosity is dominated by one component with low to moderate opacity(Smartt et al. 2017; Waxman et al. 2018). In this paper, we model thespectra of AT2017gfo using a one-component model, to evaluate thepresence of Pt and Au signatures. To determine if any photospheric phase spectral features couldbe produced by Pt or Au, we generated synthetic spectra using tardis (Kerzendorf & Sim 2014; Kerzendorf et al. 2019), a one-dimensional Monte Carlo radiative transfer code capable of rapidlygenerating synthetic spectra for explosive transients. tardis has beenused previously to produce KN spectra (Smartt et al. 2017; Watsonet al. 2019; Perego et al. 2020). We note that these previous worksdid not make use of the full relativistic treatment recently imple-mented for tardis (as outlined by Vogl et al. 2019), whereas we haveincorporated this feature into our modelling here.First, we used the new data to generate an atomic data set capableof being read by tardis . For this, we used the carsus package, whichextracted the level energies and statistical weights, and also the Ein-stein A -values for all transitions from the grasp output. This wasthen parsed into an atomic data file for use in our tardis models .For the photospheric modelling, we only included permitted lines,which are electric dipole transitions (conventionally labelled E1).Electric quadrupole (E2), magnetic dipole (M1), and higher ordermultipole transitions are not likely to contribute substantial opacity(or emissivity) in the di ff usion phase and therefore are not expectedto feature in the emergent early-phase spectra.Input parameters for the tardis models are given in Table 2. Weinitially used similar parameters to the models presented by Smarttet al. (2017) and Watson et al. (2019), which broadly reproduced theearly SED of AT2017gfo. We used a power law density profile forall of our models, which had the general form: ρ ( v , t exp ) = ρ (cid:32) t t exp (cid:33) (cid:32) vv (cid:33) − Γ (1)for v min < v < v max , where ρ , t , v , Γ and v max are constants. Thevalues for these constants were chosen empirically to reproduce thegeneral shape of the early SED of AT2017gfo, assuming it is dom-inated by a single black-body component. Table 2 lists these val-ues. The choice of photospheric ejecta velocity ( v min ) is in line withprevious works that model the early spectra of AT2017gfo ( ∼ . c ,Smartt et al. 2017; Watson et al. 2019). The time since explosion( t exp ) is well constrained based on the GW detection (Abbott et al.2017b). A value of Γ = ff orts The atomic data set we produced for our modelling e ff orts is publicly avail-able - see Data Availability.MNRAS000 , 1–18 (2020) t and Au constraints on kilonova spectra for AT2017gfo (Watson et al. 2019). The values for ρ were chosenso that the emergent spectrum had pronounced and observable fea-tures. The photospheric temperatures ( T ph ) chosen for the modelsclosely resemble the black-body temperatures of the early spectraof AT2017gfo, but we allowed some variation to improve the matchto the observed spectra. The photospheric luminosity ( L ph ) for themodels is then derived using: L ph = π (cid:16) v min t exp (cid:17) σ T (2)where σ is the Stefan-Boltzmann constant.The focus of this photospheric phase modelling was not to fullyreproduce, or ‘fit’ the observed spectra of AT2017gfo; rather, it wasto place constraints on what features the ions of Pt and Au wouldproduce if such elements were present in the ejecta. Therefore, wecalculated model compositions that were composed entirely of ei-ther Pt or Au. We acknowledge that these compositions are extremeand unphysical, but they demonstrate if features are potentially de-tectable. This approach can be justified when we consider the issueof atomic data availability.In the KN explosions with significant heavy r -process materialsynthesised (focussed on the third r -process peak), as well as see-ing large amounts of Pt and Au, we also expect to see significantamounts of Os and Pb (Bauswein et al. 2013; Goriely et al. 2013,2015). The existing data for the first few ionisation states of bothof these elements is sparse. For example, the NIST ASD has only135, 97, and 41 lines for Pb i , ii , and iii , respectively. For Os i – iii , there are 534, 38, and 1061 lines respectively, although all linesfor Os iii lie in the UV, with wavelengths < r -process material, we have to generate new atomic data, aswe have done here for the first three ionisation stages of Pt and Au.For the purpose of this study (to demonstrate the usefulness of com-plete atomic data for modelling the neutron-rich ejecta of kilonovae),we argue that the pure Pt and Au models we have generated are rea-sonable, and useful. They predict specific Pt and Au features thatshould be prominent in the spectra of KN ejecta containing signifi-cant amounts of either of these elements, and demonstrate what onecan do with good atomic data. Ultimately, a fully consistent analy-sis for realistic compositions will depend on further extension of theatomic data sets for other elements.We present two sets of photospheric calculations in this paper,which di ff er primarily in ejecta mass. Our first set of tardis modelspectra are presented in Figure 1. The mass enclosed in these tardis models ( M ej ) are listed in Table 2. Table 3 contains the propertiesof a subset of the strongest permitted lines that appear in our spec-tra for Pt i , ii , iii , and Au i , ii , iii , that we have selected from ouratomic data. Also included in Table 3 are the A -values of the tran-sitions as quoted in the NIST ASD, where available. Some lines arecompletely absent from the database, and some of those that arepresent do not have known A -values, hence the sparse data. Fromthe few values that are available, there is reasonable agreement be-tween the values predicted by grasp , and those in the NIST ASD(mostly agree within a factor (cid:46)
2, with the only exception being thePt i (cid:46) tardis ), τ s > .
01, and λ vac > tardis models presented inFigure 1 are unreasonably high compared to expectations for KNejecta. The total ejecta mass for a BNS merger is likely to lie in theregion 10 − (cid:46) M ej (cid:46) − M (cid:12) , which will be a mixture of r -processelements (see Section 4). Our models have been constructed to de-termine the spectral regions showing the strongest features of Pt andAu ions that could exist in early phase KN spectra, and we findthat such high mass models are necessary to illustrate these fea-tures. For comparison, we produced a second set of tardis models,with ejecta masses more consistent with what is expected for the Ptand Au composition in KNe. As discussed in Section 4, we chose M ej = − M (cid:12) , and these models are presented in Figure 2. Themodels cover a range of temperature, which correlates strongly with t exp . They illustrate the e ff ect that a modest amount of Pt and Au canhave on the evolution of early KN spectra. Figure 1 shows the model spectra generated with tardis , comparedwith three of the earliest spectra of AT2017gfo, when the photo-spheric regime is most likely to be applicable. The overall SED ofthe models approximately match the observed spectra of AT2017gfoat the same epochs, indicating that the temperatures and photo-spheric radii of the models are appropriate.
In the pure Pt model at + iii lines, with the mostprominent being the 6228 . − iii lines, all of comparable strength.At wavelengths < ii and Pt iii absorption.These strong UV features are not attributable to individual transi-tions; they are e ff ectively blanket absorption due to many transitionsat these wavelengths.In the second spectrum (Pt Model 1, at + ii − ii absorption, dominated bythe 4515.4, 5200.7, 5966.2 Å lines.The third spectrum, Pt Model 2, calculated + ffi ciently such that thePt ii lines present in the previous model have disappeared, and allobserved features are now produced by Pt i . The NIR transition at13363 Å is visible as a shallow absorption at 11000 Å. There aretwo additional absorption features, centred at 5500 and 6700 Å, andthese are produced by the Pt i tardis models. In the pure Au model at + ii and Au iii , bluewardof 3200 Å. The features are a result of a myriad of Au ii and Au iii transitions, all with comparable strength. The transition with thestrongest contribution in this region is the Au iii MNRAS , 1–18 (2020)
J. H. Gillanders et al. L u m i n o s i t y ( e r g s − ˚A − ) +0.5 d 3000 5000 7000 9000Rest Wavelength (˚A) +0.5 d5000 10000 15000 200000.02.04.06.0 L u m i n o s i t y ( e r g s − ˚A − ) +1.4 d 5000 10000 15000 20000 +1.4 d5000 10000 15000 20000Rest Wavelength (˚A)0 . . . . . . L u m i n o s i t y ( e r g s − ˚A − ) +2.4 d 5000 10000 15000 20000Rest Wavelength (˚A)Pt synthetic spectra Au synthetic spectra AT2017gfo spectra +2.4 d Figure 1.
Comparison of our high ejecta mass tardis models for pure Pt and Au compositions to early spectra of AT2017gfo.
Left panels : Model spectra forour pure Pt KN models compared to observed spectra of AT2017gfo at the corresponding epochs ( + + + Right panels : As left, but for pure Au KN models. The regions of the spectra that deviate strongly from a black-body continuum, as a result ofinteraction with one (or many) strong transitions, are shaded and labelled. The shaded regions labelled with ‘Blend’ signify that the feature is produced as aresult of many di ff erent transitions, all with comparable strength. The regions where the feature was produced predominantly by a few strong transitions arelabelled in descending order of contribution. No distinct transitions redward of 3000 Å are clearly visible at thistemperature.The second pure Au model (Au model 1), at + i ii i ∼ ii + i . The absorption at ∼ i MNRAS000
Left panels : Model spectra forour pure Pt KN models compared to observed spectra of AT2017gfo at the corresponding epochs ( + + + Right panels : As left, but for pure Au KN models. The regions of the spectra that deviate strongly from a black-body continuum, as a result ofinteraction with one (or many) strong transitions, are shaded and labelled. The shaded regions labelled with ‘Blend’ signify that the feature is produced as aresult of many di ff erent transitions, all with comparable strength. The regions where the feature was produced predominantly by a few strong transitions arelabelled in descending order of contribution. No distinct transitions redward of 3000 Å are clearly visible at thistemperature.The second pure Au model (Au model 1), at + i ii i ∼ ii + i . The absorption at ∼ i MNRAS000 , 1–18 (2020) t and Au constraints on kilonova spectra Table 3.
Subset of the strongest lines in our tardis models. The lines are ranked by their Sobolev optical depth ( τ s ) in the models. Only lines that are highlightedin Figure 1 are included here. All lines with τ s > .
01 and λ vac > grasp lowerlevel index grasp upperlevel index Sobolev opticaldepth, τ s Transitionwavelength, λ vac (Å) grasp A -value (s − ) NIST ASD A -value (s − )Pt model 0Pt iii * * × N / AAu model 0Au iii * * × N / APt model 1Pt ii
16 22 12.8 4515.4 5.63 × × Pt ii
19 22 3.61 5966.2 3.24 × N / APt ii
19 26 2.71 5200.7 2.93 × N / APt ii
23 22 0.85 10026 1.15 × N / APt ii
25 26 0.32 9863.8 7.16 × N / AAu model 1Au i × × Au ii × N / AAu ii × N / AAu ii × N / AAu ii × N / AAu i × × Pt model 2Pt i × × Pt i
11 15 8.66 7115.7 2.03 × × Pt i
12 24 3.22 6328.3 2.87 × N / APt i
12 18 2.95 8227.0 1.20 × N / APt i
13 18 0.26 13363 1.52 × N / AAu model 2Au i × × Au i × × Au i × × These levels were not scaled to any experimental data. All others levels were scaled to experimentally calculated levels(Kramida et al. 2020). by the Au i ∼ ii has disappeared. Now it is dominated by the Au i The overall SED of the models approximately reproduce the ob-served spectra of AT2017gfo, as expected, since the velocities andtemperatures in our tardis models were chosen to produce a matchto the luminosity of the transient. Although the models are sim-ply pure Pt or Au, they do serve a purpose for determining if anyabsorption-like features in the photospheric spectra of AT2017gfocould be identified as Pt or Au, and for making predictions for fu-ture events.We find no plausible transition of any of the three ionisation statesof Pt or Au can be uniquely matched with the features in AT2017gfo.There is strong absorption between ∼ − + + ∼ ii blend of the 9863.8, 10026 Å transitions contributeto the broad absorption observed at 8000 Å, at + ii by Watson et al. (2019), and onlya very large mass of Pt would produce a significant contribution.The e ff ect of reducing the mass of Pt and Au in the line-formingregion to a more realistic 10 − M (cid:12) is illustrated in the tardis mod-els presented in Figure 2. At wavelengths redward of ∼ − iii ab-sorption for the 10000 K and hotter models, a blend of Pt ii andPt iii absorption at 8000 K, almost exclusively Pt ii absorption for the6000 K model, and almost exclusively Pt i for the 4000 K model. The16000 K model exhibits little absorption, but this is a result of ouratomic data only containing transitions up to doubly ionised Pt. Atthis temperature, most of the Pt present in the ejecta is at least triplyionised, as Pt iv . The feature at ∼ + ii transitions. Although there is visible absorption here, we require asignificantly higher mass of Pt to produce a feature comparable instrength to the observed absorption feature. MNRAS , 1–18 (2020)
J. H. Gillanders et al. S c a l e d L u m i n o s i t y Pt Au Figure 2. tardis models for pure Pt and Au KNe, with varying temperatures, and M ej = − M (cid:12) . The spectra have been scaled and o ff set for clarity. Redwardof ∼ Left panel:
Sequence of spectra for our pure Pt KN models.
Right panel:
Sequence of spectra for our pure Au KN models.
The Au models exhibit similar behaviour to the Pt ones. The UVabsorption is almost exclusively Au iii absorption for the 10000 Kand hotter models, a blend of Au ii and Au iii absorption at 8000 K,almost exclusively Au ii absorption for the 6000 K model, and al-most exclusively Au i for the 4000 K model. Similarly, the 16000 Kmodel exhibits little absorption, for the same reason as discussed forthe Pt case. The feature at ∼ ii + ∼ + i ff ect Pt and Au have on the opacity of the ejecta material,and the continuum in the UV. However, this UV absorption is notlikely to be uniquely attributed to either Pt or Au in a KN spec-trum, as UV line blanketing will be produced by many other heavyelements, either with d - or f -shell valence electrons. In addition,observing this region would require time-resolved spectra from aspace-based telescope within the first 24 hrs, which could only be fa-cilitated by a rapid response of the Hubble Space Telescope . We con-clude that a mass ∼ − M (cid:12) of either Pt or Au is unlikely to producea detectable, uniquely identifiable feature in the photospheric phasespectra of a kilonova, with the exception of the few shallow featuresin the optical, as discussed. These features are not well pronounced, and would require more Pt or Au mass for them to be prominentenough to be detected. The spectra of AT2017gfo exhibit rapid evolution, the rate of whichis unprecedented, compared to other optical and NIR extragalactictransients. By ∼ ff erent properties of a KN (temperature,density, ejecta velocity), and then make predictions for which lineswe would expect to dominate the nebular phases of these transients,assuming there is some component of the ejecta made up of Pt or Au.This information is then used to generate simple, synthetic emissionspectra, under the assumption of LTE level populations. While suchcalculations are not as physically realistic as those in radiative trans-fer codes such as cmfgen (Hillier & Miller 1998; Dessart & Hillier2005), artis (Kromer & Sim 2009; Shingles et al. 2020), sumo (Jerk-strand et al. 2011) and jekyll (Ergon et al. 2018), they serve the pur-pose of identifying the strongest predicted transitions of these twoelements.We then provide a qualitative comparison with the observed spec-tra of AT2017gfo, in the phases where the continuum weakens and MNRAS000
The Au models exhibit similar behaviour to the Pt ones. The UVabsorption is almost exclusively Au iii absorption for the 10000 Kand hotter models, a blend of Au ii and Au iii absorption at 8000 K,almost exclusively Au ii absorption for the 6000 K model, and al-most exclusively Au i for the 4000 K model. Similarly, the 16000 Kmodel exhibits little absorption, for the same reason as discussed forthe Pt case. The feature at ∼ ii + ∼ + i ff ect Pt and Au have on the opacity of the ejecta material,and the continuum in the UV. However, this UV absorption is notlikely to be uniquely attributed to either Pt or Au in a KN spec-trum, as UV line blanketing will be produced by many other heavyelements, either with d - or f -shell valence electrons. In addition,observing this region would require time-resolved spectra from aspace-based telescope within the first 24 hrs, which could only be fa-cilitated by a rapid response of the Hubble Space Telescope . We con-clude that a mass ∼ − M (cid:12) of either Pt or Au is unlikely to producea detectable, uniquely identifiable feature in the photospheric phasespectra of a kilonova, with the exception of the few shallow featuresin the optical, as discussed. These features are not well pronounced, and would require more Pt or Au mass for them to be prominentenough to be detected. The spectra of AT2017gfo exhibit rapid evolution, the rate of whichis unprecedented, compared to other optical and NIR extragalactictransients. By ∼ ff erent properties of a KN (temperature,density, ejecta velocity), and then make predictions for which lineswe would expect to dominate the nebular phases of these transients,assuming there is some component of the ejecta made up of Pt or Au.This information is then used to generate simple, synthetic emissionspectra, under the assumption of LTE level populations. While suchcalculations are not as physically realistic as those in radiative trans-fer codes such as cmfgen (Hillier & Miller 1998; Dessart & Hillier2005), artis (Kromer & Sim 2009; Shingles et al. 2020), sumo (Jerk-strand et al. 2011) and jekyll (Ergon et al. 2018), they serve the pur-pose of identifying the strongest predicted transitions of these twoelements.We then provide a qualitative comparison with the observed spec-tra of AT2017gfo, in the phases where the continuum weakens and MNRAS000 , 1–18 (2020) t and Au constraints on kilonova spectra line features become prominent. For AT2017gfo, the high ejecta ve-locity and low mass ( v ej (cid:39) . c and M ej (cid:39) . (cid:12) , Smartt et al.2017) imply the electron density drops to n e ∼ cm − within2 − A -values <<
100 s − (Jerkstrand 2017). Such transitions wouldpotentially give rise to nebular emission lines in the spectra ofAT2017gfo, taken after ∼ + + µ m. In a companionpaper (Gillanders et al. in prep), we propose that these are consis-tent with being emission features of width 36000 ± − , andcould be arising from optically thin, nebular-phase emission. We usethis hypothesis to compare the forbidden (electric quadrupole andmagnetic dipole) transitions of Pt and Au to the positions of thesefeatures. Further discussion on the nature of these late-time spectrawill be provided by Gillanders et al. (in prep). To identify candidate transitions that may appear in emission in thelate-time KN spectra, we first exclude any that originate from an up-per level with energy greater than the ionisation energy of the speciesunder consideration (acquired from the NIST ASD, Kramida et al.2020). Such levels would be expected to have very small popula-tions, and therefore the corresponding transitions would have negli-gible contributions to our synthetic spectra.We further excluded all transitions that originate from an upperlevel that was not metastable, on the grounds that the upper levelsof such transitions can be expected to be strongly depopulated (rel-ative to LTE) under nebular conditions. We calculated the radiativelifetimes of all levels using: τ rad = (cid:88) L < U A ul − (3)where τ rad is the mean radiative lifetime of the level, and A ul is theEinstein A -coe ffi cient for spontaneous decay, from upper state U tolower state L . In this work, we consider any levels with a mean radia-tive lifetime, τ rad ≥ − s, to be metastable (based on the discussionabove). Therefore, all transitions originating from non-metastablelevels (i.e. τ rad < − s) were discarded, as the rate of emission inthese transitions at late times is likely to be much lower than in LTE(which we adopt to estimate the level populations – see below). Formore on nebular phase spectra, see Jerkstrand (2017). Although thisleaves a large number of plausible lines (96, 593 and 1510 for Pt i , ii and iii respectively, and 10, 87 and 339 for the same three ionisa-tion stages of Au), the vast majority of these transitions come fromrelatively highly excited levels, which will be heavily disfavoured inour subsequent analysis, as discussed below.To determine the approximate strengths of emission lines arisingfrom our selected transitions, we assume LTE excitation, and esti-mate the population of atoms and ions in di ff erent excited states,using the Boltzmann equation: N u = N t (cid:18) g u Z (cid:19) e − E u k b T (4)where N u is the number of atoms or ions in the excited state, N t isthe total number of atoms or ions, g u is the statistical weight of theupper level, Z is the LTE partition function, E u is the energy of theupper level, k b is the Boltzmann constant, and T is the temperature. We calculate g u from the J values in the atomic data. With theestimates for N u , and the Einstein A -values from the atomic data,we are able to calculate the total line luminosity arising from eachtransition, for temperatures T ∈ [2000 , , L em = A ul N u (cid:32) hc λ vac (cid:33) (5)The strongest transitions of Pt i , ii , iii and Au i , ii , iii in theframework of the simple LTE approximation (at a temperature of3500 K) are listed in Tables 4 and 5. These tables only contain thestrongest transitions from our analysis; i.e. only transitions that have L em > A -values for the transitions from the NIST ASD are included, whereavailable. Again, there is good agreement between these values, andthe theoretically obtained values from grasp , with values agreeingto within a factor (cid:46)
2. The full atomic data information for the lowerand upper levels of the transitions (electronic configuration, term,J, parity and energy) are provided in Tables A1–A6. We note that τ sob << c , and apeak value ( P g ) determined from the total luminosity calculated forthe transition. These peak values were determined by integrating toget the area under the Gaussian, which corresponds to the luminosityof the feature, or L em , and rearranging. This gives the expression: P g = (cid:114) ln(2) π L em FWHM (6)With P g , we were able to compute Gaussian emission features forall transitions. Then, these Gaussians were all co-added to form onecomposite emission spectrum. This spectrum illustrates the relativestrengths of all the transitions that we predict should be prominentin an observed nebular spectrum, which contains the species underconsideration. These composite spectra are plotted in Figure 3. Before we analyse the individual features in our models, it is worthnoting that, for the Einstein A -values of the strongest Pt lines, at atemperature, T = M ion = − M (cid:12) (which is comfortably within the range of expected Pt and Aumasses discussed in Section 4), we calculate line luminosities on theorder L Pt ∼ erg s − . These luminosities are similar in strengthto the observed features in the late-time spectra of AT2017gfo, if in-deed these features are a result of emission. This motivates the studyof individual features of Pt, and by extension, Au, and other third r -process peak elements that are expected to be produced by KNe,as we have determined that they may be capable of producing fea-tures similar in strength to those observed in AT2017gfo.In Figure 3, we present the LTE synthetic emission spectra for Pt i , ii , iii , and Au i , ii , iii , at three example temperatures (2000, 3500 and5000 K). In each case, the ion masses are M ion = − M (cid:12) , motivatedby the discussion in Section 4. The intensity of the lines scales lin-early with mass, or N t , as shown in Equations 4 and 5. We predictthese lines to be the strongest features, when the ejecta has reached MNRAS , 1–18 (2020) J. H. Gillanders et al.
Table 4.
Strongest [Pt i ], [Pt ii ] and [Pt iii ] transitions, at a temperature of 3500 K. The electronic configurations and terms for each of the level indices indicatedhere can be found in Tables A1–A3.Species grasp lowerlevel index grasp upperlevel index Transitionwavelength, λ vac (Å) grasp A -value (s − ) NIST ASD A -value (s − ) Transition type Relative intensityPt i i i i i / A M1 0.049Pt i / A M1 0.045Pt i / A M1 0.015Pt i / A M1 0.012Pt i / A M1 0.011Pt i / A M1 0.011Pt ii ii ii ii / A M1 0.036Pt ii ii / A M1 0.020Pt ii / A M1 0.016Pt ii / A E2 0.013Pt iii * / A M1 1.0Pt iii * * / A M1 0.026 * These levels were not scaled to any experimental data. All others levels were scaled to experimentally calculated levels (sourced fromKramida et al. 2020).
Table 5.
Strongest [Au i ], [Au ii ] and [Au iii ] transitions, at a temperature of 3500 K. The electronic configurations and terms for each of the level indicesindicated here can be found in Tables A4–A6. Note the [Au ii ] 38446 Å transition, which does not appear in Figure 3. We predict this to be one of the strongest[Au ii ] features in our nebular phase model spectra.Species grasp lowerlevel index grasp upperlevel index Transitionwavelength, λ vac (Å) grasp A -value (s − ) NIST ASD A -value (s − ) Transition type Relative intensityAu i / A M1 1.0Au i / A E2 0.13Au i / A E2 0.071Au ii / A E2 1.0Au ii / A M1 0.40Au ii / A M1 0.36Au ii / A E2 0.25Au ii / A M1 0.10Au ii / A M1 0.021Au iii * / A M1 1.0 * These levels were not scaled to any experimental data. All others levels were scaled to experimentally calculated levels (sourced fromKramida et al. 2020). the optically thin regime. As discussed in Section 6.1, low mass andhigh velocity ejecta can reach this regime in a few days. While highvelocities and a multitude of heavy elements will likely make lineblending common place in the spectra of KNe (Kasen et al. 2017;Tanaka et al. 2020), the optical and NIR wavelength range coveredin Figure 3 appears to be the optimal place to observe signatures ofthese two elements. Tables 4 and 5 indicate that these lines are allat wavelengths observable from the ground (0 . − . µ m), apartfrom the [Au ii ] line at 3.8446 µ m.We compare the line positions and approximate intensities to thelate-time spectra of AT2017gfo in Figure 4. The strongest featuresthat could be emission lines have peaks at 0.79, 1.08, 1.23, 1.40,1.58 and 2.07 µ m (Gillanders et al. in prep.). The strong 1.08 µ mfeature weakens significantly between + ii , identified by Watson et al. (2019), causing the 8000 Åabsorption dip in the + There is an interesting coincidence between this observed emis-sion feature, and our predicted strongest [Pt i ] 10761 Å and [Pt iii ]10917 Å lines. If there was a significant contribution of [Pt i ]10761 Å to this feature, then the next strongest transitions of [Pt i ]would be at 7409.5 Å and 15227 Å. These do not align with the peaksof the 7900 Å and 15800 Å observed features, but both of those fea-tures show asymmetric profiles, with a significant excess in the blue MNRAS000
Strongest [Au i ], [Au ii ] and [Au iii ] transitions, at a temperature of 3500 K. The electronic configurations and terms for each of the level indicesindicated here can be found in Tables A4–A6. Note the [Au ii ] 38446 Å transition, which does not appear in Figure 3. We predict this to be one of the strongest[Au ii ] features in our nebular phase model spectra.Species grasp lowerlevel index grasp upperlevel index Transitionwavelength, λ vac (Å) grasp A -value (s − ) NIST ASD A -value (s − ) Transition type Relative intensityAu i / A M1 1.0Au i / A E2 0.13Au i / A E2 0.071Au ii / A E2 1.0Au ii / A M1 0.40Au ii / A M1 0.36Au ii / A E2 0.25Au ii / A M1 0.10Au ii / A M1 0.021Au iii * / A M1 1.0 * These levels were not scaled to any experimental data. All others levels were scaled to experimentally calculated levels (sourced fromKramida et al. 2020). the optically thin regime. As discussed in Section 6.1, low mass andhigh velocity ejecta can reach this regime in a few days. While highvelocities and a multitude of heavy elements will likely make lineblending common place in the spectra of KNe (Kasen et al. 2017;Tanaka et al. 2020), the optical and NIR wavelength range coveredin Figure 3 appears to be the optimal place to observe signatures ofthese two elements. Tables 4 and 5 indicate that these lines are allat wavelengths observable from the ground (0 . − . µ m), apartfrom the [Au ii ] line at 3.8446 µ m.We compare the line positions and approximate intensities to thelate-time spectra of AT2017gfo in Figure 4. The strongest featuresthat could be emission lines have peaks at 0.79, 1.08, 1.23, 1.40,1.58 and 2.07 µ m (Gillanders et al. in prep.). The strong 1.08 µ mfeature weakens significantly between + ii , identified by Watson et al. (2019), causing the 8000 Åabsorption dip in the + There is an interesting coincidence between this observed emis-sion feature, and our predicted strongest [Pt i ] 10761 Å and [Pt iii ]10917 Å lines. If there was a significant contribution of [Pt i ]10761 Å to this feature, then the next strongest transitions of [Pt i ]would be at 7409.5 Å and 15227 Å. These do not align with the peaksof the 7900 Å and 15800 Å observed features, but both of those fea-tures show asymmetric profiles, with a significant excess in the blue MNRAS000 , 1–18 (2020) t and Au constraints on kilonova spectra . . . . . . . . L u m i n o s i t y + C o n s t a n t ( e r g s − ˚A − ) Pt i Pt i Pt i . . . . . i Au i Au i . . . . . L u m i n o s i t y + C o n s t a n t ( e r g s − ˚A − ) Pt ii Pt ii Pt ii . . . . . . ii Au ii Au ii . . . . . . L u m i n o s i t y + C o n s t a n t ( e r g s − ˚A − ) Pt iii Pt iii Pt iii . . . . . . . iii Au iii Au iii Figure 3.
Synthetic emission spectra for Pt i , ii , iii , and Au i , ii , iii , for a range of temperatures (2000, 3500 and 5000 K). The emission spectra for the di ff erenttransition types (E1, M1 and E2) have been plotted separately to make it clear what family the strongest emission features belong to. The spectra are o ff set, andscaling factors were applied, for clarity. The dominant features are labelled with their rest wavelengths, as in vacuum. wing. Hence, it is possible that the five strongest [Pt i ] transitionsin our models are contributing emission in the + ff erent ion masses of Pt i , ii and iii may combine to result in a composite Pt emission spectrumwhich is capable of reproducing some of the emission features in the + iii ], at 10917 Å, which lies ata similar wavelength to the strong [Pt i ] line, at 10761 Å, and no fur-ther statement can be made as to the presence of this ion. The threestrongest [Pt ii ] lines at 7512.5, 11877 and 21883 Å do not corre- spond to any of the most pronounced peaks in the + + ii ] lineat 21883 Å, but this is much redder than the observed peak of thefeature at 20700 Å. As the AT2017gfo spectra evolve from + + . − . µ m weaken, and noother strong features emerge. Therefore, no further conclusive ev-idence for the presence of neutral or low ion stages of Pt emerge.The possible coincidences we highlight are interesting but not con- MNRAS , 1–18 (2020) J. H. Gillanders et al. L u m i n o s i t y + C o n s t a n t( e r g s − ˚A − ) AT2017gfo 0 +1 +2 Pt Au+7.4 d+8.4 d+9.4 d+10.4 d
Figure 4.
Comparison of the 3500 K synthetic emission spectra for the M1 Pt i , ii , iii , and Au i , ii , iii transitions, and the late-time spectra of AT2017gfo. Thespectra have been o ff set for clarity. clusive, and even if some Pt i or Pt ii is contributing at a low or mod-erate level, the spectrum is dominated by other species. In the case of Au, the two strongest transitions are close in wave-length and would be blended if they co-existed: [Au i ] 8147.3 Å,and [Au iii ] 8382.3 Å. One may dominate over the other depend-ing on temperature and ionisation. There is no obvious signature ofan emission line or excess flux in any of the spectra of AT2017gfoat ∼ ii ] lines are at 5668.7 Å and 6857.9 Å, butagain, no obvious feature is distinguishable above the noise in theAT2017gfo spectra, although this is a region where many lines mayblend together in a pseudo-continuum (Gillanders et al. in prep). Fig-ure 5 illustrates how di ff erent ion masses for Au i , ii and iii maycombine to result in a composite Au emission spectrum which hasfeatures of comparable strength to those observed in the + ii ] transitions lies be-yond the observed range of the X-shooter data for AT2017gfo. The3.8446 µ m transition would be of particular interest in the future, asthe mid-infrared regime opens up with the capability of the James Webb Space Telescope ( JWST ), and the expectation that the 3 − µ mregion may su ff er from less line-blending e ff ects. In summary, wefind no obvious coincidence with the predictions for the strongest[Au] lines and features in the spectra of AT2017gfo, at any epoch. The main aim of this work was to highlight the usefulness of goodquality atomic data for the exploration of r -process element synthe-sis. Here we have presented our new atomic data for neutral, singly-and doubly-ionised Pt and Au, and we have also presented somemodels we generated with this data. We specifically investigated themergers of binary neutron star systems as a source of r -process ma-terial in this work, and performed some spectral analysis of the kilo-nova AT2017gfo.First, we used tardis to produce model spectra with propertiessimilar to those expected for KNe at early times, while still in thephotospheric phase (see Figures 1 and 2). We found that we requiredunrealistically large amounts of material (up to 0.5 M (cid:12) in cases, seeTable 2) to produce observable individual features of any ion of Pt orAu. We were able to demonstrate that, for realistic masses of Pt andAu, we see broad line-blended absorption in the UV. This property isnot unique to Pt and Au, and is expected for many heavy elements.We then generated simple emission spectra for the individual MNRAS000
Comparison of the 3500 K synthetic emission spectra for the M1 Pt i , ii , iii , and Au i , ii , iii transitions, and the late-time spectra of AT2017gfo. Thespectra have been o ff set for clarity. clusive, and even if some Pt i or Pt ii is contributing at a low or mod-erate level, the spectrum is dominated by other species. In the case of Au, the two strongest transitions are close in wave-length and would be blended if they co-existed: [Au i ] 8147.3 Å,and [Au iii ] 8382.3 Å. One may dominate over the other depend-ing on temperature and ionisation. There is no obvious signature ofan emission line or excess flux in any of the spectra of AT2017gfoat ∼ ii ] lines are at 5668.7 Å and 6857.9 Å, butagain, no obvious feature is distinguishable above the noise in theAT2017gfo spectra, although this is a region where many lines mayblend together in a pseudo-continuum (Gillanders et al. in prep). Fig-ure 5 illustrates how di ff erent ion masses for Au i , ii and iii maycombine to result in a composite Au emission spectrum which hasfeatures of comparable strength to those observed in the + ii ] transitions lies be-yond the observed range of the X-shooter data for AT2017gfo. The3.8446 µ m transition would be of particular interest in the future, asthe mid-infrared regime opens up with the capability of the James Webb Space Telescope ( JWST ), and the expectation that the 3 − µ mregion may su ff er from less line-blending e ff ects. In summary, wefind no obvious coincidence with the predictions for the strongest[Au] lines and features in the spectra of AT2017gfo, at any epoch. The main aim of this work was to highlight the usefulness of goodquality atomic data for the exploration of r -process element synthe-sis. Here we have presented our new atomic data for neutral, singly-and doubly-ionised Pt and Au, and we have also presented somemodels we generated with this data. We specifically investigated themergers of binary neutron star systems as a source of r -process ma-terial in this work, and performed some spectral analysis of the kilo-nova AT2017gfo.First, we used tardis to produce model spectra with propertiessimilar to those expected for KNe at early times, while still in thephotospheric phase (see Figures 1 and 2). We found that we requiredunrealistically large amounts of material (up to 0.5 M (cid:12) in cases, seeTable 2) to produce observable individual features of any ion of Pt orAu. We were able to demonstrate that, for realistic masses of Pt andAu, we see broad line-blended absorption in the UV. This property isnot unique to Pt and Au, and is expected for many heavy elements.We then generated simple emission spectra for the individual MNRAS000 , 1–18 (2020) t and Au constraints on kilonova spectra L u m i n o s i t y ( e r g s − ˚A − ) +7.4 d Pt7500 10000 12500 15000 17500 20000 22500Rest Wavelength (˚A)0 . . . . . . L u m i n o s i t y ( e r g s − ˚A − ) AT2017gfo 0 +1 +2 M1 E2 +8.4 d Au
Figure 5.
Comparison of the synthetic emission spectra for [Pt] and [Au] transitions, with the + + Upper panel: Pt i , ii and iii M1 and E2 synthetic emission spectra plotted with the + i , ii , iii are M ion = − , − and 5 × − M (cid:12) , respectively. Lowerpanel: Au i , ii and iii M1 and E2 synthetic emission spectra plotted with the + M ion = × − , × − and 5 × − M (cid:12) for the Au i , ii , iii spectra, respectively. The synthetic emission spectra areshifted to qualitatively match the continua of the observed spectra, for clarity. species under investigation here (Pt i , ii , iii and Au i , ii , iii ), usinga simple LTE excitation approximation. These models are presentedin Figures 3, 4 and 5. With these models, we make strong predic-tions for forbidden emission lines that could be detectable in thelate-time, nebular-phase spectra of a KN, which has ejecta rich inthese species. Many of our features lie at wavelengths > (cid:46) . µ m, which would capture all but one of ourstrongest predicted lines; the [Au ii ] 3.8446 µ m transition would onlybe detectable through JWST observations.We then compared our model photospheric and nebular-phasespectra to the observed spectra of AT2017gfo. The tardis modelspectra were computed at the epochs of the early spectral observa-tions of AT2017gfo ( + + + ∼ − + ∼ erg s − . Thisdemonstrates that we can expect features from these elements to bebright enough to be observed.We identify some coincidence with the [Pt i ] 10761 Å and the[Pt iii ] 10917 Å transitions, and a strong emission-like feature in the + i present in the ejecta,then other strong features from Pt i should be detectable at wave-lengths of 7409.5 Å, and 15227 Å. There are features near thesewavelengths ( ∼ ∼ i ] features, and so we conclude it is plausible that there is [Pt i ]emission in the observed late-time spectra of AT2017gfo. A defini-tive statement, however, will depend on future work with atomic datafor many more elements, as needed to synthesise a full spectrum.It is harder to motivate the presence of Pt iii in the ejecta, as weonly predict one prominent strong [Pt iii ] line (at 10917 Å), prevent-ing us from drawing further conclusions on its presence. We predictthree strong [Pt ii ] features, none of which correspond exactly to theobserved emission features, but they do lie on asymmetric wings. Weconclude that it is possible that there is some contribution from Pt inthe late-time spectra of AT2017gfo, but it is likely that the spectraare dominated by other species. MNRAS , 1–18 (2020) J. H. Gillanders et al.
Similar comparisons with the late-time AT2017gfo spectra andour model Au spectra do not yield such informative results. We pre-dict a handful of strong [Au i ], [Au ii ], and [Au iii ] lines, none ofwhich correspond to observed emission features. We conclude thatthere is no evidence for the presence of Au in the late-time spectraof AT2017gfo.Pt and Au are expected to be co-produced in KN ejecta. Therefore,if we observe spectral signatures for one, it is reasonable to expectto see signatures of the other. However, in Section 4, we highlightedthe ratio of Pt and Au production; specifically, Pt is expected to be ∼ a few times more abundant than Au. Hence, it is reasonable forus to speculate that Pt may be contributing towards features in thespectra of AT2017gfo, without also detecting any Au features.Despite the fact we cannot definitively prove the presence of Pt orAu in the spectra of AT2017gfo, we have demonstrated the useful-ness of having access to complete atomic data, and have also demon-strated the study that can be performed with such data. This worksupports the idea that having complete atomic data for the heavy el-ements is useful, and we hope that these data become available inthe near future. A complete set of atomic data could then be used forquantitative modelling works, where many elements are included,and more physical KN ejecta compositions are explored in detail. ACKNOWLEDGEMENTS
We thank Andreas Bauswein and Stephane Goriely for useful in-sights and discussion. We thank Ryan Gallagher for assisting withdata visualisation. SAS, SJS, CB acknowledge funding from STFCGrants ST / P000312 / / T000198 /
1. This research made useof tardis , a community-developed software package for spectralsynthesis in supernovae. The development of tardis received sup-port from the Google Summer of Code initiative and from ESA’sSummer of Code in Space program. tardis makes extensive use ofAstropy and PyNE. We are grateful for use of the computing re-sources from the Northern Ireland High Performance Computing(NI-HPC) service funded by EPSRC (EP / T022175). Based on obser-vations collected at the European Southern Observatory under ESOprogrammes 1102.D-0353, 0102.D-0348, 0102.D-0350, we madeuse of the flux-calibrated versions of the X-shooter spectra publiclyavailable through ENGRAVE.
DATA AVAILABILITY
All models presented in this paper, the atomic data file used for the tardis modelling, and extended versions of the tables presented areavailable, and can be accessed from < insert-PURE-link-here > . REFERENCES
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APPENDIX A: LEVEL CONFIGURATION TABLES
Here we present tables containing information for the relevant levelsthat are of interest in our work, for Pt i , ii , iii , and Au i , ii , iii . Thetables include the level configuration and term, as well as J, parity,and energy. We have flagged any levels that were not calibrated toexperimental measurements. While these tables only contain levelinformation for the most important transitions highlighted in ourwork, we have included extended versions (in the supplementarymaterials), which contain all levels related to transitions presentedanywhere in this work. Additionally, we have included energy leveldiagrams, to visualise the strongest forbidden emission transitions. This paper has been typeset from a TEX / L A TEX file prepared by the author.
Table A1. Pt i energy levels. Only levels that are relevant to the transitionsdiscussed in the main text have been included. grasp level index Configuration Term J Parity Energy (cm − )1 5d D 3 even 0.002 5d F 4 even 823.663 5d D 2 even 775.884 5d
10 1
S 0 even 6140.175 5d D 2 even 6567.456 5d F 3 even 10116.727 5d D 1 even 10131.878 5d D 2 even 13496.269 5d F 2 even 15501.8310 5d P 0 even 16983.4411 5d P 1 even 18566.5412 5d G 4 even 21967.1013 5d D 2 even 26638.58 . . . . . . . . Figure A1. Pt i energy level diagram. Only transitions that are specified inTable 4 are shown. MNRAS , 1–18 (2020) J. H. Gillanders et al.
Table A2.
Same as Table A1 but for Pt ii energy levels. grasp level index Configuration Term J Parity Energy (cm − )1 5d D ⁄ even 0.002 5d F ⁄ even 4786.653 5d D ⁄ even 8419.844 5d F ⁄ even 9356.325 5d P ⁄ even 13329.286 5d D ⁄ even 15791.317 5d F ⁄ even 16820.938 5d F ⁄ even 18097.7616 5d G ⁄ even 29262.0119 5d F ⁄ even 34647.2723 5d P ⁄ even 41434.1225 5d G ⁄ even 43737.43 . . . . . . Figure A2. Pt ii energy level diagram. Only transitions that are specified inTable 4 are shown. Table A3.
Same as Table A1 but for Pt iii energy levels. grasp level index Configuration Term J Parity Energy (cm − )1 5d F 4 even 0.002 * D 2 even 6776.393 * F 3 even 9159.884 * F 2 even 14798.7845 * D 4 even 79582.08 * These levels were not scaled to any experimental data. All others levelswere scaled to experimentally calculated levels (sourced from Kramidaet al. 2020).
Figure A3. Pt iii energy level diagram. Only transitions that are specified inTable 4 are shown.MNRAS000
Figure A3. Pt iii energy level diagram. Only transitions that are specified inTable 4 are shown.MNRAS000 , 1–18 (2020) t and Au constraints on kilonova spectra Table A4.
Same as Table A1 but for Au i energy levels. grasp level index Configuration Term J Parity Energy (cm − )1 5d S / even 0.002 5d D / even 9161.183 5d D / even 21435.194 5d P / odd 37358.995 5d P / odd 41174.61 . . . . Figure A4. Au i energy level diagram. Only transitions that are specified inTable 5 are shown. Table A5.
Same as Table A1 but for Au ii energy levels. grasp level index Configuration Term J Parity Energy (cm − )1 5d
10 1
S 0 even 0.002 5d D 3 even 15039.573 5d D 2 even 17640.624 5d D 1 even 27765.765 5d D 2 even 29621.256 5d F 4 even 40478.757 5d D 2 even 48510.898 5d F 3 even 52176.51 . . . . . . . . . . Figure A5. Au ii energy level diagram. Only transitions that are specified inTable 5 are shown. MNRAS , 1–18 (2020) J. H. Gillanders et al.
Table A6.
Same as Table A1 but for Au iii energy levels. grasp level index Configuration Term J Parity Energy (cm − )1 5d D / even 0.002 * D / even 11929.8413 * G / even 59286.41 * These levels were not scaled to any experimental data. All others levelswere scaled to experimentally calculated levels (sourced from Kramidaet al. 2020). . . Figure A6. Au iii energy level diagram. Only transitions that are specified inTable 5 are shown.MNRAS000