text:
\section{Introduction} \label{sec:Introduction}
\par
Mergers of binary neutron star (BNS) and neutron star--black hole (NSBH) systems have long been hypothesised to be an ideal location for the synthesis of the rapid neutron capture (\mbox{$r$-process}) elements \citep[see discussion by][]{Metzger2017}. Theoretical modelling has shown that the large neutron fraction in expelled material from these mergers is sufficient to generate these heavy elements \citep{Lattimer1974, Eichler1989, Freiburghaus1999, Rosswog1999, Goriely2011, Goriely2013, Goriely2015, Perego2014, Just2015, Sekiguchi2016}. However, spectrophotometric observations are needed to confirm the validity of the models. The first kilonova (KN; the optical counterpart of a BNS merger) was detected in 2017 \citep[AT2017gfo,][]{LigoVirgo2017,Andreoni2017,Arcavi2017,Chornock2017,Coulter2017,Cowperthwaite2017,Drout2017,Evans2017,Kasliwal2017,Lipunov2017,Nicholl2017,Pian2017,Smartt2017,Tanvir2017,Troja2017,Utsumi2017,Valenti2017}. Early theoretical models \citep{Kasen2017} predicted the overall shape of the spectra, and showed that it can be readily explained by the presence of \mbox{$r$-process}\ material, as the associated high opacities lead to a red, long-lived component.

\par
Radiative transfer simulations for the spectra of AT2017gfo have taken two approaches. The first is to attempt direct identification of species contributing to apparent absorption features in the early spectra. \cite{Smartt2017} suggested attribution of spectral features to Te\,{\sc i}\ and Cs\,{\sc i}, elements from the second \mbox{$r$-process}\ peak. Further work by \cite{Watson2019} attributed the same absorption features to lighter \mbox{$r$-process}\ elements, specifically Sr\,{\sc ii}. Both works, however, rely on incomplete atomic data. Specifically, both use data from \cite{Kurucz2017} for their models. This atomic line list provides data for the lowest few ionisation stages for all elements up to the first \mbox{$r$-process}\ peak. However, due to the difficulties involved with generating this information for heavier elements, the line lists are mostly incomplete beyond this first peak. This makes any modelling, and subsequent conclusions difficult, as the elements without complete atomic data will be excluded from consideration.

\par
The second approach is to calculate new atomic data for heavy elements, and to model the temporal evolution of the spectra in a broad sense. The models of \cite{Kasen2017} and \cite{Tanaka2018,Tanaka2020} calculate broad-band spectral energy distributions (SEDs) for low $Y_{\rm e}$ material, which can reproduce the rising near-infrared (NIR) flux observed in AT2017gfo. The main reason why these works have focussed on modelling the broad spectral shapes is due to the accuracy of the atomic data used. \cite{Kasen2017} have used elements with complete and well-calibrated\footnote{Calibrated data means that the energy levels from theoretical calculations have been effectively `shifted' to match those obtained experimentally.} atomic data to represent their less well-sampled homologues (e.g. the atomic data for the elements with $Z=21-28$ have been used as `surrogate' data for the open $d$-shell \mbox{$r$-process}\ elements with $Z=39-48$ and $Z=72-80$). This allows them to approximate the general behaviour of these heavier open $d$-shell elements, but restricts them from predicting individual features. They also use new atomic data for the elements with $Z=58-70$, but these data have not been calibrated (with the exception of Nd). Therefore they cannot be used to accurately predict the locations of individual transitions, as these will be systematically offset from the true wavelengths. Similarly, the atomic data used by \cite{Tanaka2018, Tanaka2020} have not been calibrated, and so these results also cannot be used to accurately predict the locations of individual transitions either. \cite{Even2020} used tabulated wavelength-dependent opacities to produce SEDs, but this method does not allow identification of specific transitions.

\par
We are focussed on the first of these two methods, but our progress thus 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 the relevant important heavy elements, with a focus on reliably calibrating to any experimental data that exist. This will enable us to base our models on accurate atomic data, and allow us to make strong predictions about individual transitions of interest. To that end, the work presented here is a pilot study, focussing specifically on platinum and gold, to demonstrate the validity and usefulness of such a study.

\par
Two of the most interesting heavy elements to search for signatures of are platinum (Pt) and gold (Au). Their cosmic origin is currently unknown and \cite{Kobayashi2020} argue two sites of production may be needed, with a rapid injection of the elements to explain abundance patterns in metal-poor stars. The BNS channel may have a natural time delay that cannot account for the early excess in Pt and Au observed. Collapsar accretion disks have been suggested as potential production sites of these elements, and could be the dominant source of heavy elements in the early Universe, as they do not suffer from as long a time delay \citep{Siegel2019}. However, no distinct spectroscopic signature has yet been identified to corroborate this.

\par
No signature of any ion of Pt or Au has been identified in the spectra of AT2017gfo, and hence our motivation for this work is to employ recently calculated, high quality atomic data to predict possible spectral features in kilonova-type expanding ejecta.

\par
We note that there have been previous reports of observations of Pt and Au lines in astrophysical objects. \cite{Ross1972} report observations of the Au\,{\sc i}\ 3122.8\,\AA\ line in the solar photospheric spectrum. \cite{Jaschek1970} report detections of Pt and Au lines in the spectrum of the A-type star 73 Draconis; they observe seven Pt\,{\sc ii}\ lines, the strongest of which is the Pt\,{\sc ii}\ 4645\,\AA\ transition, and four lines belonging to Au\,{\sc i}. There have been other observing efforts since, which have observed more Pt and Au lines in various different stars \citep[see e.g.][]{Fuhrmann1989,Adelman1994}. Also, \cite{Castelli2004} identify two Pt lines in the spectrum of HD\,175640, a narrow lined, chemically peculiar star. They identify the Pt\,{\sc ii}\ 4061.6, 4514.1\,\AA\ transitions. They also identify two Au lines in the spectra; specifically, they detected the Au\,{\sc ii}\ 4016.7, 4052.8\,\AA\ transitions.

\par
These line detections have all been made in the photospheric spectra of the different stars under investigation. These all have surface temperatures on the order $\sim 4000 - 10000$\,K, which is comparable to the temperature of KN ejecta at early times \citep[see][where, at $0.5 - 1.5$\,d post-merger, the characteristic black-body temperature drops from $\sim 10000$ to $\sim 5000$\,K]{Shappee2017,Smartt2017}. It is therefore expected that the strongest Pt and Au lines that have been observed in these stellar spectra could feasibly also appear in the spectra of KNe, at least while the KN exhibits similar temperatures.

\par
All these observed Pt and Au features correspond to strong permitted transitions. To date, there have been no observations of forbidden Pt or Au transitions in astrophysical sources. Forbidden lines for other elements are routinely observed in the late-time spectra of SNe \citep{Jerkstrand2017-HB}. However, the lines observed correspond to elements that are abundant in the ejecta of these transients. Since typical SNe \citep[with the exception of collapsars;][]{Siegel2019} are not predicted to synthesise large masses of \mbox{$r$-process}\ material, the only \mbox{$r$-process}\ material in the ejecta will be present from the initial formation of the star. This results in abundances much lower than that required to produce any spectral features of Pt or Au, hence the lack of observations. However, the late-phase spectra of KNe may have promise for the detection of these elements, and other \mbox{$r$-process}\ elements, since the explosions are hypothesised to synthesise significant masses of \mbox{$r$-process}\ material. This will result in late-phase spectra dominated by emission features from \mbox{$r$-process}\ material, and, if Pt and Au are produced in significant quantities, then their spectral signatures could be identified.

\par
Our work consists of two parts. First, we determine which strong features of Pt or Au are most likely to be prominent in the early, photospheric spectra of KNe. Second, we determine whether any forbidden transitions of Pt or Au could provide emission lines in the late time, nebular spectra of KNe. In both cases, we present predictions and compare to the spectra of AT2017gfo. In Section \ref{sec:Spectra}, we detail the sources of the AT2017gfo spectra we compare our models to. In Section \ref{sec:Atomic_data}, we summarise how the atomic data we use in this work was generated. Section \ref{sec:Motivation_of_parameters} contains some motivation for the values we chose for ejecta mass in our work. In Section \ref{sec:Photospheric_phase}, we outline the steps taken to produce our photospheric phase spectral models, and we highlight our main results. Section \ref{sec:Nebular_phase} details how we generated our synthetic nebular phase spectra, and also contains our results. Finally, we summarise our work in Section \ref{sec:Conclusions}.

\section{Spectra} \label{sec:Spectra}
\par
As well as providing model spectra and predictions for the features of Pt and Au, we compare our models with the one known kilonova with a spectroscopic sequence, AT2017gfo. The data we primarily use is the set of 10 X-shooter spectra originally published by \cite{Pian2017} and \cite{Smartt2017}. As part of the ENGRAVE project, all the X-shooter spectra were flux-calibrated to a compiled set of photometric measurements taken from the published values of \cite{Andreoni2017,Arcavi2017,Chornock2017,Cowperthwaite2017,Drout2017,Evans2017,Kasliwal2017,Pian2017,Smartt2017,Tanvir2017,Troja2017,Utsumi2017,Valenti2017}. This data set is publicly available, and can be accessed through the ENGRAVE webpage\footnote{\url{www.engrave-eso.org}}, along with release notes describing the calibration, extinction correction, rest-frame velocity correction, and smoothing.

\par
We supplemented this set of spectra with data from two other sources, to extend its temporal coverage to earlier times, and to improve the spectral quality (where possible). \cite{Shappee2017} present early spectra for AT2017gfo. The spectrum taken at +0.5\,d \citep[obtained 0.9\,d before the earliest X-shooter spectrum presented by][]{Pian2017, Smartt2017} is useful for demonstrating the blue, featureless shape characteristic of early KN spectra, and so we use it here to compare with our early models. We flux-calibrated this spectrum \citep[using the \textsc{sms} code; see][]{Inserra2018} to the same compiled set of photometric points as detailed above; we also corrected for extinction, and rest-frame velocity. \cite{Tanvir2017} present \textit{HST} spectra of AT2017gfo, obtained at four separate epochs. The +9.4\,d spectrum is particularly interesting as it contains a broad, emission-like feature at 13750\,\AA, which lies in the telluric region, and so it is not observable in our X-shooter spectrum at the same epoch. We merged this \textit{HST} spectrum with the X-shooter spectrum at this epoch, replacing the pixels of X-shooter with the flux-calibrated \textit{HST} pixels, within the telluric region.

\section{Atomic Data} \label{sec:Atomic_data}
\par
For KN observations at times, $t \gtrsim 1$\,d, and ejecta temperatures, $T \lesssim 20000$\,K, the typical ionisation stages of heavy elements are neutral up to triply ionised \citep[\,{\sc i}--\,{\sc iv};][]{Tanaka2020}. For AT2017gfo, after $\sim 0.5$\,d, the ejecta temperature dropped to $\sim 10000$\,K, and so we expect that typical ionisation stages of heavy elements in AT2017gfo are neutral up to doubly ionised (\,{\sc i}--\,{\sc iii}). Hence, for this work we focussed on these ionisation stages of Pt and Au.

\par
The atomic structure for these first three ion stages of platinum and gold were calculated within a Dirac-Coulomb framework, employing the General Relativistic Atomic Structure Package ($\textsc{grasp}^{0}$), \citep{Dyall1989}. The orbitals were variationally determined using a multi-configurational Dirac-Fock approach for each of the six ion stages under consideration. Our goal was to accurately determine the lowest $25 - 40$ levels of each ion stage, from a much larger configuration set. Although the National Institute of Standards and Technology Atomic Spectra Database \citep[NIST ASD;][]{NIST2020} provides a more comprehensive list of energy levels for the neutral ion stages of platinum and gold, the higher ion stages have sparse, incomplete energy state listings. Furthermore, we appreciate that the Einstein $A$-coefficients for the lowest levels of each ion stage involve non-dipole transitions that scale $\propto E^{5}$, and therefore we have utilised the option with $\textsc{grasp}^{0}$\ to adopt spectroscopically accurate energy separations before the calculation of transition matrix elements, where available. This obviously impacts the accuracy of the \mbox{$A$-values}\ and any subsequent modelling.

\par
For Pt\,{\sc i}, the first 32 energy levels were calibrated to the energies given in the NIST ASD \citep[][]{NIST2020}. For Pt\,{\sc ii}, the first 40 levels were calibrated. For Au\,{\sc i}, the first 37 levels were calibrated, excluding levels 21, 28, 31 and 34, which did not have identifiable counterparts. The first 21 levels of Au\,{\sc ii}\ were calibrated. The NIST ASD has no atomic data for either Pt\,{\sc iii}\ or Au\,{\sc iii}, aside from the ground level. Therefore, all energy levels in these structures are taken as calculated in $\textsc{grasp}^{0}$. The configurations that contain calibrated energy levels in neutral and singly ionised platinum and gold are shown in Table \ref{tab:Configuations}. $\textsc{grasp}^{0}$\ has also been further modified to interface with the $\textsc{tardis}$\ code to provide easier future integration of new atomic data sets.

\setlength{\tabcolsep}{2pt}
\begin{table}
\centering
\begin{tabular}{c|l}
Pt\,{\sc i}   &5d$^{10}$, 5d$^{9}$6s, 5d$^{8}$6s$^{2}$, 5d$^{9}$6p, 5d$^{8}$6s6p    \\
Pt\,{\sc ii}  &5d$^{9}$, 5d$^{8}$6s, 5d$^{7}$6s$^{2}$, 5d$^{8}$6p \\
Au\,{\sc i}   &5d$^{10}$6s, 5d$^{9}$6s$^{2}$, 5d$^{10}$6p, 5d$^{9}$6s6p, 5d$^{10}$7s, 5d$^{10}$7p, 5d$^{10}$6d, 5d$^{9}$6s7s \\
Au\,{\sc ii}   &5d$^{10}$, 5d$^{9}$6s, 5d$^{8}$6s$^{2}$, 5d$^{9}$6p    \\
\end{tabular}
\caption{
Configurations that contained calibrated energies, for neutral and singly ionised platinum and gold. Doubly ionised platinum and gold had no calibrated levels.
}
\label{tab:Configuations}
\end{table}
\setlength{\tabcolsep}{6pt}

\par
Although these atomic structure calculations provide the foundation of any plasma modelling under LTE conditions, a companion paper (McCann et al. in prep) will provide greater detail on the atomic structure calculations, as well as the electron-impact excitation of neutral gold. This excitation calculation shall be bench-marked against the spectra of ongoing gold experiments \citep{Bromley2020} and provide insight into populating mechanisms, when the observed spectra drop out of LTE into the collisional radiative regime. This will also address the incompleteness of data for the more highly charged systems, where observed and synthetic spectra may be compared to determine the identification of higher excited states. It will also provide the mechanisms by which excited states are populated, and hopefully provide temperature and density line ratios. For an in-depth discussion of the atomic data generation, see McCann et al. (in prep). Finally, we note that all wavelengths presented throughout this paper are quoted as in vacuum.

\begin{table*}
\centering
\caption{
Input parameters used to generate the various $\textsc{tardis}$\ models presented in this work.
}
\begin{threeparttable}
\centering
\begin{tabular}{>{\centering}p{0.12\textwidth}*{3}{>{\centering}p{0.06\textwidth}}>{\centering}p{0.001\textwidth}*{2}{>{\centering}p{0.06\textwidth}}>{\centering\arraybackslash}p{0.06\textwidth}}
\hline
\hline
    &\multicolumn{3}{c}{Pt}     &     &\multicolumn{3}{c}{Au}       \\
\cline{2-4}
\cline{6-8}
 &Model 0     &Model 1      &Model 2   &     &Model 0   &Model 1       &Model 2     \\
\hline
$t_{\rm exp}$\,(days)                   &0.5    &1.4     &2.4     &   &0.5    &1.4    &2.4    \\
$T$\,(K)                                &10000  &5000    &3700    &   &10000  &5000   &3700   \\
$v_{\rm min}$\,($c$)                    &0.30   &0.25    &0.20    &   &0.30   &0.25   &0.20   \\
$v_{\rm max}$\,($c$)                    &0.35   &0.35    &0.35    &   &0.35   &0.35   &0.35   \\
$\rho_{0}$\,($10^{-11}$ g\,cm$^{-3}$)   &0.1    &0.5     &1       &   &0.1    &1      &0.5    \\
$v_{0}$\,(\mbox{\,$\rm{km}\,s^{-1}$})                         &14000  &14000   &14000   &   &14000  &14000  &14000  \\
$t_{0}$\,(days)                         &2      &2       &2       &   &2      &2      &2      \\
$\Gamma$                                &3      &3       &3       &   &3      &3      &3      \\
$M_{\rm ej}$ ($\mbox{M$_{\odot}$}$)\tnote{*}         &0.014  &0.15   &0.50   &   &0.014  &0.30  &0.25  \\
\hline
\end{tabular}
\begin{tablenotes}
      \small
      \item[*] $M_{\rm ej}$ is a derived property of our models, but is included here for reference. It represents the mass bound by the $\textsc{tardis}$\ computational domain, and so is a lower limit for a model's ejecta mass.
\end{tablenotes}
\end{threeparttable}
\label{tab:TARDIS_model_parameters}
\end{table*}

\section{Motivation of Parameters} \label{sec:Motivation_of_parameters}
\par
To determine what ejecta mass to use in our calculations, we considered both observational and theoretical estimates. We also performed our own calculation, to estimate Pt and Au production in KNe.

\par
Observationally, the ejecta mass can be estimated from the lightcurve modelling of AT2017gfo. The bolometric lightcurve and filter band lightcurves have been fit with ejecta masses between $0.01 - 0.05$\,\mbox{M$_{\odot}$}\ \citep{Cowperthwaite2017,Smartt2017,Tanvir2017,Coughlin2018,Waxman2018}.

\par
The expected mass of dynamical ejecta in BNS merger simulations is in the region $10^{-4} < M_{\rm dyn} < 10^{-2}$\,\mbox{M$_{\odot}$}\ \citep{Bauswein2013,Hotokezaka2013,Sekiguchi2016,Ciolfi2017,Radice2018}, with a large fraction of neutron-rich material ($Y_{\rm e} < 0.2$), which would favour Pt and Au production. However, disk wind ejecta can potentially be more massive ($10^{-2} < M_{\rm dw} < 10^{-1}$\,\mbox{M$_{\odot}$}), slower moving \citep[$v\simeq0.1$c,][]{Wu2016,Siegel2017}, and may be composed of either low or high $Y_{\rm e}$ material. Nuclear trajectories for low $Y_{\rm e}$ regimes \citep[][]{Bauswein2013, Goriely2013, Goriely2015} indicate that Pt and Au compositions could be as high as $5 - 15$\,per cent, by mass, which would potentially mean ejecta masses of either element of $\sim 5 \times 10^{-4} - 1.5 \times 10^{-2}$\,\mbox{M$_{\odot}$}, in low $Y_{\rm e}$ ejecta.

\par
A simple calculation to determine Pt and Au production in KNe, assuming they are the sole source of these elements in the Milky Way, also provides approximate Pt and Au masses per event. The currently accepted LIGO--Virgo rate for binary neutron star mergers in our local Universe is $R_{\textsc{bns}} = 320^{+490}_{-240}$\,Gpc$^{-3}$\,yr$^{-1}$ \citep[][]{Abbott2020_LIGO_KN_Rates}. From \cite{Abadie2010_MW_density}, the density of Milky Way equivalent galaxies (MWEG) is $\sim 1.16 \times 10^{-2}$\,Mpc$^{-3}$. From these values, we calculated a rate of BNS mergers of $2.8^{+4.2}_{-2.1} \times 10^{-5}$\,MWEG$^{-1}$\,yr$^{-1}$, which we take as the rate of mergers in the Milky Way. \cite{Asplund2009} provide estimates for the abundance of elements in the Solar System. They quote number densities for Pt and Au of $3.8 \times 10^{-11}$ and $7.7 \times 10^{-12}$, respectively. Given a MW baryonic mass of $\sim 6.4 \times 10^{10}$\,\mbox{M$_{\odot}$}\ \citep[][]{McMillan2011}, and assuming that the abundances of Pt and Au throughout the Milky Way are consistent with their Solar System abundances, we estimate that there is 378\,\mbox{M$_{\odot}$}\ of Pt, and 77\,\mbox{M$_{\odot}$}\ of Au in the galaxy. Given a MW age of $\sim 10^{10}$ years, and assuming a constant rate of BNS mergers since galaxy formation, we estimate there have been $2.8^{+4.2}_{-2.1} \times 10^{5}$\,KNe to date in the Milky Way. If we assume the sole 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 Au masses of $M_{\rm Pt} = 0.5-5.4 \times 10^{-3}$\,\mbox{M$_{\odot}$}\ and $M_{\rm Au} = 0.1-1.1 \times 10^{-3}$\,\mbox{M$_{\odot}$}.

\par
From our simple calculation, we predict that $\sim 5$ times more Pt will be synthesised than Au, per event. Similarly, from the nuclear trajectories of \cite{Bauswein2013, Goriely2013, Goriely2015}, we expect Pt/Au ratios of $\sim$\,a few. Since the uncertainties for predicted Pt and Au masses per event are large, we do not make calculations that explore the relative masses of these elements in detail, but we do note that if either element is present, the other should also have been produced and that the abundance of Pt is expected to be higher than Au by a moderate factor.

\par
Given all of the above, we conclude that Pt and Au masses on the order of $\sim 10^{-3}$\,\mbox{M$_{\odot}$}\ are reasonable, and so we adopt this characteristic mass for all our modelling, unless otherwise stated.

\section{Photospheric phase} \label{sec:Photospheric_phase}
\par
The spectra of AT2017gfo have been interpreted in different ways, with many authors invoking two components. A low opacity, blue component and a red contribution from high opacity ejecta are physically motivated from numerical simulations of neutron star mergers. In particular, the models of \cite{Kasen2017} have been widely used to argue for two components to explain the SED of the spectra \citep[see also e.g.][]{Chornock2017,Coughlin2018}. However, the existence of two components is by no means settled, with some work arguing that the evolution of the SED and the bolometric luminosity is dominated by one component with low to moderate opacity \citep{Smartt2017,Waxman2018}. In this paper, we model the spectra of AT2017gfo using a one-component model, to evaluate the presence of Pt and Au signatures.

\subsection{Method} \label{sec:Photospheric_phase-method}
\par
To determine if any photospheric phase spectral features could be produced by Pt or Au, we generated synthetic spectra using $\textsc{tardis}$\ \citep{tardis, tardis2}, a one-dimensional Monte Carlo radiative transfer code capable of rapidly generating synthetic spectra for explosive transients. $\textsc{tardis}$\ has been used previously to produce KN spectra \citep{Smartt2017, Watson2019, Perego2020}. We note that these previous works did not make use of the full relativistic treatment recently implemented for $\textsc{tardis}$\ \citep[as outlined by][]{Vogl2019}, whereas we have incorporated this feature into our modelling here.

\par
First, we used the new data to generate an atomic data set capable of being read by $\textsc{tardis}$. For this, we used the $\textsc{carsus}$\ package, which extracted the level energies and statistical weights, and also the Einstein \mbox{$A$-values}\ for all transitions from the $\textsc{grasp}^{0}$\ output. This was then parsed into an atomic data file for use in our $\textsc{tardis}$\ models\footnote{The atomic data set we produced for our modelling efforts is publicly available - see Data Availability.}. 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 order multipole transitions are not likely to contribute substantial opacity (or emissivity) in the diffusion phase and therefore are not expected to feature in the emergent early-phase spectra.

\par
Input parameters for the $\textsc{tardis}$\ models are given in Table \ref{tab:TARDIS_model_parameters}. We initially used similar parameters to the models presented by \cite{Smartt2017} and \cite{Watson2019}, which broadly reproduced the early SED of AT2017gfo. We used a power law density profile for all of our models, which had the general form:
\begin{equation}
    \rho(v,t_{\rm exp}) = \rho_{\rm 0}\left(\frac{t_{\rm 0}}{t_{\rm exp}}\right)^{3}\left(\frac{v}{v_{\rm 0}}\right)^{-\Gamma}
    \label{eqn:Density_profile_eqn}
\end{equation}
for ${v_{\rm min}} < v < {v_{\rm max}}$, where $\rho_{\rm 0}$, $t_{\rm 0}$, $v_{\rm 0}$, $\Gamma$ and ${v_{\rm max}}$ are constants. The values for these constants were chosen empirically to reproduce the general shape of the early SED of AT2017gfo, assuming it is dominated by a single black-body component. Table \ref{tab:TARDIS_model_parameters} lists these values. The choice of photospheric ejecta velocity ($v_{\rm min}$) is in line with previous works that model the early spectra of AT2017gfo \citep[$\sim 0.2 \, c$,][]{Smartt2017, Watson2019}. The time since explosion ($t_{\rm exp}$) is well constrained based on the GW detection \citep{MMApaper2017}. A value of $\Gamma = 3$ was chosen as it typically agrees with hydrodynamical calculations \citep{Hotokezaka2013, Tanaka2013}, and has been adopted by other modelling efforts for AT2017gfo \citep[][]{Watson2019}. The values for $\rho_{0}$ were chosen so that the emergent spectrum had pronounced and observable features. The photospheric temperatures ($T_{\rm ph}$) chosen for the models closely resemble the black-body temperatures of the early spectra of AT2017gfo, but we allowed some variation to improve the match to the observed spectra. The photospheric luminosity ($L_{\rm ph}$) for the models is then derived using:
\begin{equation}
    L_{\rm ph} = 4 \pi \left(v_{\rm min} \, t_{\rm exp}\right)^{2} \sigma \, T_{\rm ph}^{4}
    \label{eqn:Luminosity_eqn}
\end{equation}
where $\sigma$ is the Stefan-Boltzmann constant.

\par
The focus of this photospheric phase modelling was not to fully reproduce, or `fit' the observed spectra of AT2017gfo; rather, it was to place constraints on what features the ions of Pt and Au would produce if such elements were present in the ejecta. Therefore, we calculated model compositions that were composed entirely of either Pt or Au. We acknowledge that these compositions are extreme and unphysical, but they demonstrate if features are potentially detectable. This approach can be justified when we consider the issue of atomic data availability.

\par
In the KN explosions with significant heavy \mbox{$r$-process}\ material synthesised (focussed on the third \mbox{$r$-process}\ peak), as well as seeing large amounts of Pt and Au, we also expect to see significant amounts of Os and Pb \citep[][]{Bauswein2013, Goriely2013, Goriely2015}. The existing data for the first few ionisation states of both of these elements is sparse. For example, the NIST ASD has only 135, 97, and 41 lines for Pb\,\,{\sc i}, \,{\sc ii}, and \,{\sc iii}, respectively. For Os\,\,{\sc i}--\,{\sc iii}, there are 534, 38, and 1061 lines respectively, although all lines for Os\,\,{\sc iii}\ lie in the UV, with wavelengths $< 2100$\,\AA. The lack of a complete atomic data set, spanning the optical and NIR, prevents us from making any predictions for observable features for either of these elements. Therefore, if we wish to model KN ejecta rich in heavy \mbox{$r$-process}\ material, we have to generate new atomic data, as we have done here for the first three ionisation stages of Pt and Au. For the purpose of this study (to demonstrate the usefulness of complete atomic data for modelling the neutron-rich ejecta of kilonovae), we argue that the pure Pt and Au models we have generated are reasonable, and useful. They predict specific Pt and Au features that should be prominent in the spectra of KN ejecta containing significant amounts of either of these elements, and demonstrate what one can do with good atomic data. Ultimately, a fully consistent analysis for realistic compositions will depend on further extension of the atomic data sets for other elements.

\par
We present two sets of photospheric calculations in this paper, which differ primarily in ejecta mass. Our first set of $\textsc{tardis}$\ model spectra are presented in Figure \ref{fig:TARDIS_model_spectra}. The mass enclosed in these $\textsc{tardis}$\ models ($M_{\rm ej}$) are listed in Table \ref{tab:TARDIS_model_parameters}. Table \ref{tab:TARDIS_models_strongest_lines} contains the properties of a subset of the strongest permitted lines that appear in our spectra for Pt\,{\sc i}, \,{\sc ii}, \,{\sc iii}, and Au\,{\sc i}, \,{\sc ii}, \,{\sc iii}, that we have selected from our atomic data. Also included in Table \ref{tab:TARDIS_models_strongest_lines} are the \mbox{$A$-values}\ of the transitions as quoted in the NIST ASD, where available. Some lines are completely absent from the database, and some of those that are present do not have known \mbox{$A$-values}, hence the sparse data. From the few values that are available, there is reasonable agreement between the values predicted by $\textsc{grasp}^{0}$, and those in the NIST ASD (mostly agree within a factor $\lesssim 2$, with the only exception being the Pt\,{\sc i}\ 7115.7\,\AA\ transition, which varies by a factor $\lesssim 5$). While Table \ref{tab:TARDIS_models_strongest_lines} contains only the transitions that are highlighted in Figure \ref{fig:TARDIS_model_spectra}, in the supplementary materials, we provide complete lists of all permitted transitions in our models with a Sobolev optical depth (calculated by $\textsc{tardis}$), $\tau_{\mathrm{\textsc{s}}}$\;$ > 0.01$, and $\lambda_{\rm vac} > 3000$\,\AA. The full atomic data information for the lower levels of the transitions (electronic configuration, term, J, parity and energy) are provided in Tables \ref{tab:PtI_config}--\ref{tab:AuIII_config}.

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{Figures/TARDIS_Pt+Au_synthetic_spectra_vs_17gfo.pdf}
\caption{
Comparison of our high ejecta mass $\textsc{tardis}$\ models for pure Pt and Au compositions to early spectra of AT2017gfo. \textit{Left panels}: Model spectra for our pure Pt KN models compared to observed spectra of AT2017gfo at the corresponding epochs (+0.5, +1.4 and +2.4\,d, for the top, middle and bottom panels, respectively). \textit{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 of interaction with one (or many) strong transitions, are shaded and labelled. The shaded regions labelled with `Blend' signify that the feature is produced as a result of many different transitions, all with comparable strength. The regions where the feature was produced predominantly by a few strong transitions are labelled in descending order of contribution.
} \label{fig:TARDIS_model_spectra}
\end{figure*}

\begin{table*}
\centering
\caption{
Subset of the strongest lines in our $\textsc{tardis}$\ models. The lines are ranked by their Sobolev optical depth ($\tau_{\mathrm{\textsc{s}}}$) in the models. Only lines that are highlighted in Figure \ref{fig:TARDIS_model_spectra} are included here. All lines with $\tau_{\mathrm{\textsc{s}}} > 0.01$ and $\lambda_{\rm vac} > 3000$\,\AA\ are included in the supplementary materials. The electronic configurations and terms for each of the lower level indices indicated here can be found in Tables \ref{tab:PtI_config}--\ref{tab:AuIII_config}.
}
\begin{threeparttable}
\centering
\begin{tabular}{cccccccccc}
\hline
\hline
Species     &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ lower \\ level index \end{tabular}}    &{\begin{tabular}[c]{@{}c@{}}  $\textsc{grasp}^{0}$\ upper \\ level index \end{tabular}}    &{\begin{tabular}[c]{@{}c@{}} Sobolev optical \\ depth, $\tau_{\mathrm{\textsc{s}}}$ \end{tabular}}      &{\begin{tabular}[c]{@{}c@{}} Transition \\ wavelength, $\lambda_{\rm vac}$ (\AA) \end{tabular}}      &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ \\ $A$-value ($\mathrm{s^{-1}}$) \end{tabular}}     &{\begin{tabular}[c]{@{}c@{}} NIST ASD \\ $A$-value ($\mathrm{s^{-1}}$) \end{tabular}}       \\
\hline
\multicolumn{7}{c}{Pt model 0}      \\
\hline
Pt\,{\sc iii}  &45\tnote{*}	  &64\tnote{*}	&0.72	&6228.1	  &3.85$\times 10^{5}$      &N/A    \\
\hline
\multicolumn{7}{c}{Au model 0}      \\
\hline
Au\,{\sc iii}	 &13\tnote{*}  &19\tnote{*}	&3.81	&3849.9	  &2.42$\times 10^{5}$      &N/A   \\
\hline
\multicolumn{7}{c}{Pt model 1}      \\
\hline
Pt\,{\sc ii}     &16	  &22	&12.8	 &4515.4	&5.63$\times 10^{5}$        &5.0$\times 10^{5}$	    \\
Pt\,{\sc ii}     &19	  &22	&3.61	 &5966.2	&3.24$\times 10^{5}$        &N/A	    \\
Pt\,{\sc ii}     &19	  &26	&2.71	 &5200.7	&2.93$\times 10^{5}$        &N/A	    \\
Pt\,{\sc ii}     &23	  &22	&0.85	 &10026	    &1.15$\times 10^{5}$        &N/A	    \\
Pt\,{\sc ii}     &25	  &26	&0.32	 &9863.8	&7.16$\times 10^{4}$        &N/A	    \\
\hline
\multicolumn{7}{c}{Au model 1}      \\
\hline
Au\,{\sc i}      &3	  &4	&2.76	 &6279.9	&1.70$\times 10^{6}$        &3.4$\times 10^{6}$	    \\
Au\,{\sc ii}     &7	  &16	&1.44	 &4053.9	&2.08$\times 10^{6}$        &N/A       \\
Au\,{\sc ii}     &7	  &17	&1.26	 &3805.1	&1.57$\times 10^{6}$        &N/A	    \\
Au\,{\sc ii}     &7	  &14	&0.94	 &4017.2	&2.31$\times 10^{6}$        &N/A	    \\
Au\,{\sc ii}     &8	  &10	&0.51	 &7796.0	&2.15$\times 10^{5}$        &N/A	    \\
Au\,{\sc i}      &5	  &10	&0.33	 &7512.8	&8.29$\times 10^{7}$        &4.24$\times 10^{7}$	    \\
\hline
\multicolumn{7}{c}{Pt model 2}      \\
\hline
Pt\,{\sc i}      &9	  &15	&32.1	&5841.7	  &4.13$\times 10^{5}$      &8.0$\times 10^{5}$	    \\
Pt\,{\sc i}      &11	  &15	&8.66	&7115.7	  &2.03$\times 10^{5}$      &9.4$\times 10^{5}$	    \\
Pt\,{\sc i}      &12	  &24	&3.22	&6328.3	  &2.87$\times 10^{5}$      &N/A	    \\
Pt\,{\sc i}      &12	  &18	&2.95	&8227.0	  &1.20$\times 10^{5}$      &N/A	    \\
Pt\,{\sc i}      &13	  &18	&0.26	&13363	  &1.52$\times 10^{4}$      &N/A	    \\
\hline
\multicolumn{7}{c}{Au model 2}      \\
\hline
Au\,{\sc i}    	&3  &4	&27.7	  &6279.9	&1.70$\times 10^{6}$        &3.4$\times 10^{6}$	   \\
Au\,{\sc i}    	&3  &5	&5.62	  &5066.0   &3.27$\times 10^{5}$        &5.2$\times 10^{5}$	   \\
Au\,{\sc i}    	&5  &10	&0.43	  &7512.8	&8.29$\times 10^{7}$        &4.24$\times 10^{7}$	   \\
\hline
\end{tabular}
\begin{tablenotes}
      \small
      \item[*] These levels were not scaled to any experimental data. All others levels were scaled to experimentally calculated levels \citep[][]{NIST2020}.
\end{tablenotes}
\end{threeparttable}
\label{tab:TARDIS_models_strongest_lines}
\end{table*}

\par
The masses invoked in some of our $\textsc{tardis}$\ models presented in Figure \ref{fig:TARDIS_model_spectra} are unreasonably high compared to expectations for KN ejecta. The total ejecta mass for a BNS merger is likely to lie in the region $10^{-3} \lesssim M_{\rm ej} \lesssim 10^{-1}$\,\mbox{M$_{\odot}$}, which will be a mixture of \mbox{$r$-process}\ elements (see Section \ref{sec:Motivation_of_parameters}). Our models have been constructed to determine the spectral regions showing the strongest features of Pt and Au ions that could exist in early phase KN spectra, and we find that such high mass models are necessary to illustrate these features. For comparison, we produced a second set of $\textsc{tardis}$\ models, with ejecta masses more consistent with what is expected for the Pt and Au composition in KNe. As discussed in Section \ref{sec:Motivation_of_parameters}, we chose $M_{\rm ej} = 10^{-3}$\,\mbox{M$_{\odot}$}, and these models are presented in Figure \ref{fig:varying_T_TARDIS_model_spectra}. The models cover a range of temperature, which correlates strongly with $t_{\rm exp}$. They illustrate the effect that a modest amount of Pt and Au can have on the evolution of early KN spectra.

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{Figures/varying_T_TARDIS_models.pdf}
\caption{
$\textsc{tardis}$\ models for pure Pt and Au KNe, with varying temperatures, and $M_{\rm ej} = 10^{-3}$\,\mbox{M$_{\odot}$}. The spectra have been scaled and offset for clarity. Redward of $\sim 8000$\,\AA, there are no observable spectral features. The contribution the ejecta material has to the spectral shape is highlighted by the shaded regions. These shaded regions illustrate the deviation our model spectra have from a model with no interactions. \textit{Left panel:} Sequence of spectra for our pure Pt KN models. \textit{Right panel:} Sequence of spectra for our pure Au KN models.
} \label{fig:varying_T_TARDIS_model_spectra}
\end{figure*}

\subsection{Model results} \label{sec:Photospheric_phase-Model_results}
\par
Figure \ref{fig:TARDIS_model_spectra} shows the model spectra generated with $\textsc{tardis}$, compared with three of the earliest spectra of AT2017gfo, when the photospheric regime is most likely to be applicable. The overall SED of the models approximately match the observed spectra of AT2017gfo at the same epochs, indicating that the temperatures and photospheric radii of the models are appropriate.

\subsubsection{Pt models} \label{sec:Photospheric_phase-Model_results-Pt_models}
\par
In the pure Pt model at +0.5\,d post-merger (Pt model 0, with parameters as in Table \ref{tab:TARDIS_model_parameters}), there is a shallow absorption feature, centred at 4500\,\AA. This is produced by a blend of Pt\,{\sc iii}\ lines, with the most prominent being the $6228.1$\,\AA\ transition. There are two absorption features spanning the $2800 - 3500$\,\AA\ wavelength range, which are produced by a blend of many Pt\,{\sc iii}\ lines, all of comparable strength. At wavelengths $< 2500$\,\AA, there is strong Pt\,{\sc ii}\ and Pt\,{\sc iii}\ absorption. These strong UV features are not attributable to individual transitions; they are effectively blanket absorption due to many transitions at these wavelengths.

\par
In the second spectrum (Pt Model 1, at +1.4\,d post-merger), there is a strong absorption feature visible, with a trough at 7900\,\AA, which is due to the blue-shifted blend of the Pt\,{\sc ii}\ 9863.8, 10026\,\AA\ transitions. There are two other distinctive broad features between $3000 - 5000$\,\AA, which are the result of Pt\,{\sc ii}\ absorption, dominated by the 4515.4, 5200.7, 5966.2\,\AA\ lines.

\par
The third spectrum, Pt Model 2, calculated +2.4\,d after merger, displays a photosphere that has cooled sufficiently such that the Pt\,{\sc ii}\ lines present in the previous model have disappeared, and all observed features are now produced by Pt\,{\sc i}. The NIR transition at 13363\,\AA\ is visible as a shallow absorption at 11000\,\AA. There are two additional absorption features, centred at 5500 and 6700\,\AA, and these are produced by the Pt\,{\sc i}\  5841.7, 6328.3, 7115.7 and 8227.0\,\AA\ transitions. Table \ref{tab:TARDIS_models_strongest_lines} contains the details of these strong optical and NIR lines that produce the distinct features in the $\textsc{tardis}$\ models.

\subsubsection{Au models} \label{sec:Photospheric_phase-Model_results-Au_models}
\par
In the pure Au model at +0.5\,d post-merger (Au model 0), there is strong absorption and emission due to Au\,{\sc ii}\ and Au\,{\sc iii}, blueward of 3200\,\AA. The features are a result of a myriad of Au\,{\sc ii}\ and Au\,{\sc iii}\ transitions, all with comparable strength. The transition with the strongest contribution in this region is the Au\,{\sc iii}\  3849.9\AA\ transition. No distinct transitions redward of 3000\,\AA\ are clearly visible at this temperature.

\par
The second pure Au model (Au model 1), at +1.4\,d, has a shallow absorption feature centred at 6100\,\AA, which is produced by a blend of the Au\,{\sc i}\ 7512.8\,\AA\ line, and the Au\,{\sc ii}\ 7796.0\,\AA\ line. Centred at 5000\,\AA, there is another, much more pronounced absorption feature, which is dominated by the Au\,{\sc i}\ 6279.9\,\AA\ line. There is also another feature at $\sim 3000$\,\AA, which is produced by the Au\,{\sc ii}\ 3805.1, 4017.2, 4053.9\,\AA\ lines.

\par
The third pure Au model (Au model 2, at +2.4\,d post-merger) has cooled significantly from the previous epoch and all spectral features are now produced by Au\,{\sc i}. The absorption at $\sim 3900$\,\AA\ is dominated by the Au\,{\sc i}\ 5066.0\,\AA\ transition. The feature at 5000\,\AA, which was present at the previous epoch, is again produced here, predominantly by the Au\,{\sc i}\ 6279.9\,\AA\ transition. The absorption feature in the earlier Au model centred at $\sim 6100$\,\AA\ has become shallower, and the contribution from Au\,{\sc ii}\ has disappeared. Now it is dominated by the Au\,{\sc i}\ 7512.8\,\AA\ transition.

\subsubsection{Interpretation} \label{sec:Photospheric_phase-Model_results-interpretation}
\par
The overall SED of the models approximately reproduce the observed spectra of AT2017gfo, as expected, since the velocities and temperatures in our $\textsc{tardis}$\ models were chosen to produce a match to the luminosity of the transient. Although the models are simply pure Pt or Au, they do serve a purpose for determining if any absorption-like features in the photospheric spectra of AT2017gfo could be identified as Pt or Au, and for making predictions for future events.

\par
We find no plausible transition of any of the three ionisation states of Pt or Au can be uniquely matched with the features in AT2017gfo. There is strong absorption between $\sim 7000 - 10000$\,\AA\ in the observed spectra at +1.4 and +2.4\,d, which is not replicated well by contributions from Pt or Au models. Additionally, the model spectra exhibit strong absorption in regions where the observed spectra do not (e.g. Au model 1 at $\sim 5000$\,\AA). From these model spectra, it is clear that the early phase spectra of AT2017gfo are not dominated by Pt or Au features. This is not to say that there is none of these elements present in the ejecta of AT2017gfo, but it does mean that, if present, their contribution to the spectra are not prominent. It is possible that the Pt\,{\sc ii}\ blend of the 9863.8, 10026\,\AA\ transitions contribute to the broad absorption observed at 8000\,\AA, at +1.4\,d. However, this feature has been attributed to Sr\,{\sc ii}\ by \cite{Watson2019}, and only a very large mass of Pt would produce a significant contribution.

\par
The effect of reducing the mass of Pt and Au in the line-forming region to a more realistic $10^{-3}$\,\mbox{M$_{\odot}$}\ is illustrated in the $\textsc{tardis}$\ models presented in Figure \ref{fig:varying_T_TARDIS_model_spectra}. At wavelengths redward of $\sim 8000$\,\AA, where we might hope to be able to detect features due to particular transitions, we find no strong, observable spectral features. For Pt, there is strong, line blended, UV absorption ($500 - 4000$\,\AA) at each temperature (with the absorption extending into the optical for the 6000\,K model). This absorption is almost exclusively Pt\,{\sc iii}\ absorption for the 10000\,K and hotter models, a blend of Pt\,{\sc ii}\ and Pt\,{\sc iii}\ absorption at 8000\,K, almost exclusively Pt\,{\sc ii}\ absorption for the 6000\,K model, and almost exclusively Pt\,{\sc i}\ for the 4000\,K model. The 16000\,K model exhibits little absorption, but this is a result of our atomic data only containing transitions up to doubly ionised Pt. At this temperature, most of the Pt present in the ejecta is at least triply ionised, as Pt\,{\sc iv}. The feature at $\sim 7500$\,\AA\ in the 6000\,K model is the same feature as in the +1.4\,d high ejecta mass Pt model, presented in Figure \ref{fig:TARDIS_model_spectra}. This feature is produced by the 9863.8, 10026\,\AA\ Pt\,{\sc ii}\ transitions. Although there is visible absorption here, we require a significantly higher mass of Pt to produce a feature comparable in strength to the observed absorption feature.

\par
The Au models exhibit similar behaviour to the Pt ones. The UV absorption is almost exclusively Au\,{\sc iii}\ absorption for the 10000\,K and hotter models, a blend of Au\,{\sc ii}\ and Au\,{\sc iii}\ absorption at 8000\,K, almost exclusively Au\,{\sc ii}\ absorption for the 6000\,K model, and almost exclusively Au\,{\sc i}\ for the 4000\,K model. Similarly, the 16000\,K model exhibits little absorption, for the same reason as discussed for the Pt case. The feature at $\sim 5800$\,\AA\ in the 6000\,K model is a result of the Au\,{\sc ii}\ 7796.0\,\AA\ transition (same feature as in the +1.4\,d high ejecta mass Au model in Figure \ref{fig:TARDIS_model_spectra}). The feature at $\sim 4500$\,\AA\ in the 4000\,K model is the same feature as in the +2.4\,d high ejecta mass Au model in Figure \ref{fig:TARDIS_model_spectra}, produced predominantly by the Au\,{\sc i}\ 6279.9\,\AA\ transition.

\par
The strong UV line blanketing exhibited in these models illustrates the effect Pt and Au have on the opacity of the ejecta material, and the continuum in the UV. However, this UV absorption is not likely to be uniquely attributed to either Pt or Au in a KN spectrum, as UV line blanketing will be produced by many other heavy elements, either with $d$- or $f$-shell valence electrons. In addition, observing this region would require time-resolved spectra from a space-based telescope within the first 24\,hrs, which could only be facilitated by a rapid response of the \textit{Hubble Space Telescope}. We conclude that a mass $\sim 10^{-3}$\,\mbox{M$_{\odot}$}\ of either Pt or Au is unlikely to produce a detectable, uniquely identifiable feature in the photospheric phase spectra of a kilonova, with the exception of the few shallow features in the optical, as discussed. These features are not well pronounced, and would require more Pt or Au mass for them to be prominent enough to be detected.

\section{Nebular phase} \label{sec:Nebular_phase}
\par
The spectra of AT2017gfo exhibit rapid evolution, the rate of which is unprecedented, compared to other optical and NIR extragalactic transients. By $\sim 1$ week after explosion, broad features appear in the spectra that could be interpreted as being emission lines arising in a quasi-nebular plasma. Here, we make some physically motivated estimates for the different properties of a KN (temperature, density, ejecta velocity), and then make predictions for which lines we 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 emission spectra, under the assumption of LTE level populations. While such calculations are not as physically realistic as those in radiative transfer codes such as \textsc{cmfgen} \citep{Hillier-CMFGEN-1998,Dessart-CMFGEN-2005}, \textsc{artis} \citep{ARTIS-OG2009,ARTIS-neb2020}, \textsc{sumo} \citep{Jerkstrand-SUMO-2011} and \textsc{jekyll} \citep{Ergon-JEKYLL-2018}, they serve the purpose of identifying the strongest predicted transitions of these two elements.

\par
We then provide a qualitative comparison with the observed spectra of AT2017gfo, in the phases where the continuum weakens and  line features become prominent. For AT2017gfo, the high ejecta velocity and low mass \citep[$v_{\rm ej} \simeq 0.2 \, c$ and $M_{\rm ej} \simeq 0.03 \, \mbox{M$_{\odot}$}$,][]{Smartt2017} imply the electron density drops to $n_{\rm e} \sim 10^{9}$\,cm$^{-3}$ within $2-3$ days, depending on the electron fraction and filling factor, and assuming a uniform expanding sphere \citep{Jerkstrand2017-HB}. To favour radiative de-excitation, we require transitions with Einstein \mbox{$A$-values}\;$<< 100$\,s$^{-1}$ \citep{Jerkstrand2017-HB}. Such transitions would potentially give rise to nebular emission lines in the spectra of AT2017gfo, taken after $\sim 4$\,days.

\par
The spectra taken from +7.4 to +10.4\,d show broad, emission-like features at 0.79, 1.08, 1.23, 1.40, 1.58 and 2.07\,$\mu$m. In a companion paper (Gillanders et al. in prep), we propose that these are consistent with being emission features of width $36000 \pm 6000$\,\mbox{\,$\rm{km}\,s^{-1}$}, and could be arising from optically thin, nebular-phase emission. We use this hypothesis to compare the forbidden (electric quadrupole and magnetic dipole) transitions of Pt and Au to the positions of these features. Further discussion on the nature of these late-time spectra will be provided by Gillanders et al. (in prep).

\subsection{Method} \label{sec:Nebular_phase-method}
\par
To identify candidate transitions that may appear in emission in the late-time KN spectra, we first exclude any that originate from an upper level with energy greater than the ionisation energy of the species under consideration \citep[acquired from the NIST ASD,][]{NIST2020}. Such levels would be expected to have very small populations, and therefore the corresponding transitions would have negligible contributions to our synthetic spectra.

\par
We further excluded all transitions that originate from an upper level that was not metastable, on the grounds that the upper levels of such transitions can be expected to be strongly depopulated (relative to LTE) under nebular conditions. We calculated the radiative lifetimes of all levels using:
\begin{equation} \label{eqn:radiative_lifetime}
    \tau_{\rm rad} = \left(\sum_{\textsc{L < U}} A_{\textsc{ul}} \right)^{-1}
\end{equation}
where $\tau_{\rm rad}$ is the mean radiative lifetime of the level, and $A_{\textsc{ul}}$ is the Einstein $A$-coefficient for spontaneous decay, from upper state $U$ to lower state $L$. In this work, we consider any levels with a mean radiative lifetime, $\tau_{\rm rad} \geq 10^{-2}$\,s, to be metastable (based on the discussion above). Therefore, all transitions originating from non-metastable levels (i.e. $\tau_{\rm rad} < 10^{-2}$\,s) were discarded, as the rate of emission in these transitions at late times is likely to be much lower than in LTE (which we adopt to estimate the level populations -- see below). For more on nebular phase spectra, see \cite{Jerkstrand2017-HB}. Although this leaves a large number of plausible lines (96, 593 and 1510 for Pt\,{\sc i}, \,{\sc ii}\ and \,{\sc iii}\ respectively, and 10, 87 and 339 for the same three ionisation stages of Au), the vast majority of these transitions come from relatively highly excited levels, which will be heavily disfavoured in our subsequent analysis, as discussed below.

\par
To determine the approximate strengths of emission lines arising from our selected transitions, we assume LTE excitation, and estimate the population of atoms and ions in different excited states, using the Boltzmann equation:
\begin{equation} \label{eqn:no_ions_upper_lvl}
    N_{\textrm{\textsc{u}}} = N_{\textrm{\textsc{t}}} \left(\frac{g_{\textrm{\textsc{u}}}}{Z}\right) e^{-\frac{E_{\textrm{\textsc{u}}}}{k_{\textrm{\textsc{b}}} T}}
\end{equation}
where $N_{\textrm{\textsc{u}}}$ is the number of atoms or ions in the excited state, $N_{\textrm{\textsc{t}}}$ is the total number of atoms or ions, $g_{\textrm{\textsc{u}}}$ is the statistical weight of the upper level, $Z$ is the LTE partition function, $E_{\textrm{\textsc{u}}}$ is the energy of the upper level, $k_{\textrm{\textsc{b}}}$ is the Boltzmann constant, and $T$ is the temperature.

\par
We calculate $g_{\textrm{\textsc{u}}}$ from the J values in the atomic data. With the estimates for $N_{\textrm{\textsc{u}}}$, and the Einstein \mbox{$A$-values}\ from the atomic data, we are able to calculate the total line luminosity arising from each transition,
for temperatures $T \in [2000, 3500, 5000]$\,K, assuming optically thin emission:
\begin{equation} \label{eqn:Luminosity_of_gaussians}
    L_{\rm em} = A_{\textsc{ul}} \, N_{\textrm{\textsc{u}}} \left(\frac{h c}{\lambda_{\rm vac}}\right)
\end{equation}

\par
The strongest transitions of  Pt\,{\sc i}, \,{\sc ii}, \,{\sc iii}\ and  Au\,{\sc i}, \,{\sc ii}, \,{\sc iii}\ in the framework of the simple LTE approximation (at a temperature of 3500\,K) are listed in Tables \ref{tab:Pt_nebular_transitions} and \ref{tab:Au_nebular_transitions}. These tables only contain the strongest transitions from our analysis; i.e. only transitions that have $L_{\rm em} > 1$\,per cent of the strongest line luminosity in our analysis are included. As expected, electric dipole transitions do not appear in either table, as these have been deselected due to the radiative lifetime cut, leaving only forbidden lines. As in Table \ref{tab:TARDIS_models_strongest_lines}, the corresponding \mbox{$A$-values}\ for the transitions from the NIST ASD are included, where available. Again, there is good agreement between these values, and the theoretically obtained values from $\textsc{grasp}^{0}$, with values agreeing to within a factor $\lesssim 2$. The full atomic data information for the lower and upper levels of the transitions (electronic configuration, term, J, parity and energy) are provided in Tables \ref{tab:PtI_config}--\ref{tab:AuIII_config}. We note that $\tau_{\rm sob} << 1$ for all our calculated transitions, indicating that we are in an optically thin regime, as expected.

\begin{table*}
\centering
\caption{
Strongest [Pt\,{\sc i}], [Pt\,{\sc ii}]\ and [Pt\,{\sc iii}]\ transitions, at a temperature of 3500\,K. The electronic configurations and terms for each of the level indices indicated here can be found in Tables \ref{tab:PtI_config}--\ref{tab:PtIII_config}.
}
\begin{threeparttable}
\centering
\begin{tabular}{ccccccccc}
\hline
\hline
Species   &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ lower \\ level index \end{tabular}} &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ upper \\ level index \end{tabular}} &{\begin{tabular}[c]{@{}c@{}} Transition \\ wavelength, $\lambda_{\rm vac}$ (\AA) \end{tabular}} &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ \\ $A$-value ($\mathrm{s^{-1}}$) \end{tabular}}     &{\begin{tabular}[c]{@{}c@{}} NIST ASD \\ $A$-value ($\mathrm{s^{-1}}$) \end{tabular}}  &Transition type         &Relative intensity \\
\hline
Pt\,{\sc i}    &2	    &6	    &10761	    &20.1	 &24.0    &M1    &1.0      \\
Pt\,{\sc i}    &1	    &5	    &15227	    &4.21	 &2.6     &M1    &0.45     \\
Pt\,{\sc i}    &3	    &7	    &10688	    &9.28	 &13.3    &M1    &0.20     \\
Pt\,{\sc i}    &1	    &8	    &7409.5	    &7.68	 &15.6    &M1    &0.10     \\
Pt\,{\sc i}    &3	    &6	    &10706	    &0.97	 &N/A     &M1    &0.049    \\
Pt\,{\sc i}    &3	    &9	    &6790.7	    &7.33	 &N/A     &M1    &0.045    \\
Pt\,{\sc i}    &5	    &9	    &11193	    &3.97	 &N/A     &M1    &0.015    \\
Pt\,{\sc i}    &2	    &12	    &4729.6	    &10.8	 &N/A     &M1    &0.012    \\
Pt\,{\sc i}    &3	    &8	    &7861.4	    &0.905	 &N/A     &M1    &0.011    \\
Pt\,{\sc i}    &3	    &5	    &17266	    &0.111	 &N/A     &M1    &0.011    \\
\hline
Pt\,{\sc ii}    &1     &3        &11877    &9.05     &8.75   &M1    &1.0          \\
Pt\,{\sc ii}    &2     &4        &21883    &2.54     &1.38   &M1    &0.21         \\
Pt\,{\sc ii}    &2     &8        &7512.5   &15.2     &21.1   &M1    &0.10         \\
Pt\,{\sc ii}    &1     &6        &6332.6   &3.61     &N/A    &M1    &0.036        \\
Pt\,{\sc ii}    &4     &7        &13397    &6.46     &13.3   &M1    &0.030        \\
Pt\,{\sc ii}    &4     &5        &25170    &1.96     &N/A    &M1    &0.020        \\
Pt\,{\sc ii}    &1     &4        &10688    &0.0970   &N/A    &M1    &0.016        \\
Pt\,{\sc ii}    &1     &8        &5525.5   &1.42     &N/A    &E2    &0.013        \\
\hline
Pt\,{\sc iii}    &1	        &3\tnote{*}	&10917	&19.3   &N/A   &M1	  &1.0     \\
Pt\,{\sc iii}    &2\tnote{*}	&4\tnote{*}	&12465	&8.19   &N/A   &M1    &0.026   \\
\hline
\end{tabular}
\begin{tablenotes}
      \small
      \item[*] These levels were not scaled to any experimental data. All others levels were scaled to experimentally calculated levels \citep[sourced from][]{NIST2020}.
    \end{tablenotes}
\end{threeparttable}
\label{tab:Pt_nebular_transitions}
\end{table*}

\begin{table*}
\centering
\caption{
Strongest [Au\,{\sc i}], [Au\,{\sc ii}]\ and [Au\,{\sc iii}]\ transitions, at a temperature of 3500\,K. The electronic configurations and terms for each of the level indices indicated here can be found in Tables \ref{tab:AuI_config}--\ref{tab:AuIII_config}. Note the [Au\,{\sc ii}]\ 38446\,\AA\ transition, which does not appear in Figure \ref{fig:nebular_synthetic_emission_spectra}. We predict this to be one of the strongest [Au\,{\sc ii}]\ features in our nebular phase model spectra.
}
\begin{threeparttable}
\centering
\begin{tabular}{cccccccc}
\hline
\hline
Species   &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ lower \\ level index \end{tabular}} &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ upper \\ level index \end{tabular}} &{\begin{tabular}[c]{@{}c@{}} Transition \\ wavelength, $\lambda_{\rm vac}$ (\AA) \end{tabular}} &{\begin{tabular}[c]{@{}c@{}} $\textsc{grasp}^{0}$\ \\ $A$-value ($\mathrm{s^{-1}}$) \end{tabular}}     &{\begin{tabular}[c]{@{}c@{}} NIST ASD \\ $A$-value ($\mathrm{s^{-1}}$) \end{tabular}}  &Transition type     &Relative intensity \\
\hline
Au\,{\sc i}    &2	    &3	    &8147.3	    &29.8	  &N/A    &M1       &1.0     \\
Au\,{\sc i}    &1	    &2	    &10916	    &0.0229	  &N/A    &E2       &0.13    \\
Au\,{\sc i}    &1	    &3	    &4665.2	    &1.20	  &N/A    &E2       &0.071   \\
\hline
Au\,{\sc ii}    &1   &3   &5668.7    &0.405      &N/A    &E2      &1.0     \\
Au\,{\sc ii}    &2   &5   &6857.9    &27.1       &N/A    &M1      &0.40    \\
Au\,{\sc ii}    &3   &4   &9876.4    &27.2       &N/A    &M1      &0.36    \\
Au\,{\sc ii}    &1   &5   &3376.0    &8.27       &N/A    &E2      &0.25    \\
Au\,{\sc ii}    &2   &3   &38446     &0.287      &N/A    &M1      &0.10    \\
Au\,{\sc ii}    &3   &5   &8346.8    &1.74       &N/A    &M1      &0.021   \\
\hline
Au\,{\sc iii}   &1   &2\tnote{*}   &8382.3    &27.4    &N/A     &M1     &1.0        \\
\hline
\end{tabular}
\begin{tablenotes}
      \small
      \item[*] These levels were not scaled to any experimental data. All others levels were scaled to experimentally calculated levels \citep[sourced from][]{NIST2020}.
\end{tablenotes}
\end{threeparttable}
\label{tab:Au_nebular_transitions}
\end{table*}

\par
To produce a simple visualisation of how nebular emission lines may appear, we generated Gaussian emission features for all transitions. These were centred on the rest-wavelength of the transition, with a full-width, half-maximum (FWHM) velocity of 0.1\,$c$, and a peak value ($P_{\textsc{g}}$) determined from the total luminosity calculated for the transition. These peak values were determined by integrating to get the area under the Gaussian, which corresponds to the luminosity of the feature, or $L_{\rm em}$, and rearranging. This gives the expression:
\begin{equation} \label{eqn:Gaussian_height_eqn}
    P_{\textsc{g}} = 2 \sqrt{ \frac{\ln(2)}{\pi}} \frac{L_{\rm em}}{\rm FWHM}
\end{equation}

\par
With $P_{\textsc{g}}$, we were able to compute Gaussian emission features for all transitions. Then, these Gaussians were all co-added to form one composite emission spectrum. This spectrum illustrates the relative strengths of all the transitions that we predict should be prominent in an observed nebular spectrum, which contains the species under consideration. These composite spectra are plotted in Figure \ref{fig:nebular_synthetic_emission_spectra}.

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{Figures/nebular_phase_synthetic_spectra.pdf}
\caption{
Synthetic emission spectra for Pt\,{\sc i}, \,{\sc ii}, \,{\sc iii}, and Au\,{\sc i}, \,{\sc ii}, \,{\sc iii}, for a range of temperatures (2000, 3500 and 5000\,K). The emission spectra for the different transition types (E1, M1 and E2) have been plotted separately to make it clear what family the strongest emission features belong to. The spectra are offset, and scaling factors were applied, for clarity. The dominant features are labelled with their rest wavelengths, as in vacuum.
} \label{fig:nebular_synthetic_emission_spectra}
\end{figure*}

\subsection{Model results} \label{sec:Nebular_phase_model-results}
\par
Before we analyse the individual features in our models, it is worth noting that, for the Einstein \mbox{$A$-values}\ of the strongest Pt lines, at a temperature, $T = 3500$\,K, with total ion masses, $M_{\rm ion} = 10^{-3} $\,\mbox{M$_{\odot}$}\ (which is comfortably within the range of expected Pt and Au masses discussed in Section \ref{sec:Motivation_of_parameters}), we calculate line luminosities on the order $L_{\rm Pt} \sim 10^{38}$\,erg\,s$^{\mathrm{-1}}$. These luminosities are similar in strength to the observed features in the late-time spectra of AT2017gfo, if indeed these features are a result of emission. This motivates the study of individual features of Pt, and by extension, Au, and other third \mbox{$r$-process}\ peak elements that are expected to be produced by KNe, as we have determined that they may be capable of producing features similar in strength to those observed in AT2017gfo.

\par
In Figure \ref{fig:nebular_synthetic_emission_spectra}, we present the LTE synthetic emission spectra for Pt\,{\sc i}, \,{\sc ii}, \,{\sc iii}, and Au\,{\sc i}, \,{\sc ii}, \,{\sc iii}, at three example temperatures (2000, 3500 and 5000\,K). In each case, the ion masses are $M_{\rm ion} = 10^{-3}$\,\mbox{M$_{\odot}$}, motivated by the discussion in Section \ref{sec:Motivation_of_parameters}. The intensity of the lines scales linearly with mass, or $N_{\textrm{\textsc{t}}}$, as shown in Equations \ref{eqn:no_ions_upper_lvl} and \ref{eqn:Luminosity_of_gaussians}. We predict these lines to be the strongest features, when the ejecta has reached the optically thin regime. As discussed in Section \ref{sec:Nebular_phase-method}, low mass and high velocity ejecta can reach this regime in a few days. While high velocities and a multitude of heavy elements will likely make line blending common place in the spectra of KNe \citep{Kasen2017,Tanaka2020}, the optical and NIR wavelength range covered in Figure \ref{fig:nebular_synthetic_emission_spectra} appears to be the optimal place to observe signatures of these two elements. Tables \ref{tab:Pt_nebular_transitions} and \ref{tab:Au_nebular_transitions} indicate that these lines are all at wavelengths observable from the ground ($0.33 - 2.52 \, \mu$m), apart from the [Au\,{\sc ii}]\ line at 3.8446\,$\mu$m.

\par
We compare the line positions and approximate intensities to the  late-time spectra of AT2017gfo in Figure \ref{fig:comparison_of_nebular_emission_spectra_vs_17gfo}. The strongest features that could be emission lines have peaks at 0.79, 1.08, 1.23, 1.40, 1.58 and 2.07\,$\mu$m (Gillanders et al. in prep.). The strong 1.08\,$\mu$m feature weakens significantly between +7.4 and 8.4\,d. It is possible that this is the evolution of the emission component of the P-Cygni line of Sr\,{\sc ii}, identified by \cite{Watson2019}, causing the 8000\,\AA\ absorption dip in the +1.4\,d spectrum, but it could also be unrelated emission developing, coincidentally, at the same wavelength.

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{Figures/Pt+Au_M1+E2_synthetic_spectra_vs_17gfo.pdf}
\caption{
Comparison of the 3500\,K synthetic emission spectra for the M1 Pt\,{\sc i}, \,{\sc ii}, \,{\sc iii}, and Au\,{\sc i}, \,{\sc ii}, \,{\sc iii}\ transitions, and the late-time spectra of AT2017gfo. The spectra have been offset for clarity.
} \label{fig:comparison_of_nebular_emission_spectra_vs_17gfo}
\end{figure*}

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{Figures/Pt-7.4d+Au-8.4d_emission_spectra_vs_17gfo.pdf}
\caption{
Comparison of the synthetic emission spectra for [Pt] and [Au] transitions, with the +7.4 and +8.4\,d AT2017gfo spectra. \textit{Upper panel:} Pt\,{\sc i}, \,{\sc ii}\ and \,{\sc iii}\ M1 and E2 synthetic emission spectra plotted with the +7.4\,d AT2017gfo spectrum. We have scaled the relative ion masses arbitrarily to qualitatively match the emission features in the observed spectrum of AT2017gfo. The ion masses used for Pt\,{\sc i}, \,{\sc ii}, \,{\sc iii}\ are $M_{\rm ion} = 10^{-3}, \; 10^{-3} \; \rm{and} \; 5 \times 10^{-4}$\,\mbox{M$_{\odot}$}, respectively. \textit{Lower panel:} Au\,{\sc i}, \,{\sc ii}\ and \,{\sc iii}\ M1 and E2 synthetic emission spectra plotted with the +8.4\,d AT2017gfo spectrum. Similar to the Pt synthetic emission spectra above, we have arbitrarily scaled the ion masses: $M_{\rm ion} = 5 \times 10^{-3}, \; 5 \times 10^{-3} \; \rm{and} \; 5 \times 10^{-4}$\,\mbox{M$_{\odot}$}\ for the Au\,{\sc i}, \,{\sc ii}, \,{\sc iii}\ spectra, respectively. The synthetic emission spectra are shifted to qualitatively match the continua of the observed spectra, for clarity.
} \label{fig:Pt+Au-synthetic_spectra_vs_7.4d+8.4d_gfo_spectra}
\end{figure*}

\subsubsection{Pt Models} \label{sec:Nebular_phase_model-results-Pt_models}
\par
There is an interesting coincidence between this observed emission feature, and our predicted strongest [Pt\,{\sc i}]\ 10761\,\AA\ and [Pt\,{\sc iii}]\ 10917\,\AA\ lines. If there was a significant contribution of [Pt\,{\sc i}]\ 10761\,\AA\ to this feature, then the next strongest transitions of [Pt\,{\sc i}]\ would be at 7409.5\,\AA\ and 15227\,\AA. These do not align with the peaks of the 7900\,\AA\ and  15800\,\AA\ observed features, but both of those features show asymmetric profiles, with a significant excess in the blue wing. Hence, it is possible that the five strongest [Pt\,{\sc i}]\ transitions in our models are contributing emission in the +7.4\,d spectrum of AT2017gfo. Figure \ref{fig:Pt+Au-synthetic_spectra_vs_7.4d+8.4d_gfo_spectra} illustrates how different ion masses of Pt\,{\sc i}, \,{\sc ii}\ and \,{\sc iii}\ may combine to result in a composite Pt emission spectrum which is capable of reproducing some of the emission features in the +7.4\,d spectrum of AT2017gfo.

\par
There is only one strong line of [Pt\,{\sc iii}], at 10917\,\AA, which lies at a similar wavelength to the strong [Pt\,{\sc i}]\ line, at 10761\,\AA, and no further statement can be made as to the presence of this ion. The three strongest [Pt\,{\sc ii}]\ lines at 7512.5, 11877 and 21883\,\AA\ do not correspond to any of the most pronounced peaks in  the +7.4 to +10.4\,d spectra of AT2017gfo, but the 7512.5 and 11877\,\AA\ lines do lie on the asymmetric wings of observed features. We predict a [Pt\,{\sc ii}]\ line at 21883\,\AA, but this is much redder than the observed peak of the feature at 20700\,\AA. As the AT2017gfo spectra evolve from +7.4 to +10.4\,d, the emission peaks between $0.8 - 1.6 \, \mu$m weaken, and no other strong features emerge. Therefore, no further conclusive evidence for the presence of neutral or low ion stages of Pt emerge. The possible coincidences we highlight are interesting but not conclusive, and even if some Pt\,{\sc i}\ or Pt\,{\sc ii}\ is contributing at a low or moderate level, the spectrum is dominated by other species.

\subsubsection{Au Models} \label{sec:Nebular_phase_model-results-Au_models}
\par
In the case of Au, the two strongest transitions are close in wavelength and would be blended if they co-existed: [Au\,{\sc i}]\ 8147.3\,\AA, and [Au\,{\sc iii}]\ 8382.3\,\AA. One may dominate over the other depending on temperature and ionisation.  There is no obvious signature of an emission line or excess flux in any of the spectra of AT2017gfo at $\sim 8250$\,\AA, and any other lines of these ions would likely be weaker. The strongest [Au\,{\sc ii}]\ lines are at 5668.7\,\AA\ and 6857.9\,\AA, but again, no obvious feature is distinguishable above the noise in the AT2017gfo spectra, although this is a region where many lines may blend together in a pseudo-continuum (Gillanders et al. in prep). Figure \ref{fig:Pt+Au-synthetic_spectra_vs_7.4d+8.4d_gfo_spectra} illustrates how different ion masses for Au\,{\sc i}, \,{\sc ii}\ and \,{\sc iii}\ may combine to result in a composite Au emission spectrum which has features of comparable strength to those observed in the +8.4\,d spectrum of AT2017gfo. Unlike the Pt analysis, we find that the Au composite spectrum does not reproduce any of the strong observed emission features.

\par
We further note that one of the strongest [Au\,{\sc ii}]\ transitions lies beyond the observed range of the X-shooter data for AT2017gfo. The 3.8446\,$\mu$m transition would be of particular interest in the future, as the mid-infrared regime opens up with the capability of the \textit{James Webb Space Telescope} (\textit{JWST}), and the expectation that the $3 - 4 \, \mu$m region may suffer from less line-blending effects. In summary, we find no obvious coincidence with the predictions for the strongest [Au] lines and features in the spectra of AT2017gfo, at any epoch.

\section{Conclusions} \label{sec:Conclusions}
\par
The main aim of this work was to highlight the usefulness of good quality atomic data for the exploration of \mbox{$r$-process}\ element synthesis. Here we have presented our new atomic data for neutral, singly- and doubly-ionised Pt and Au, and we have also presented some models we generated with this data. We specifically investigated the mergers of binary neutron star systems as a source of \mbox{$r$-process}\ material in this work, and performed some spectral analysis of the kilonova AT2017gfo.

\par
First, we used $\textsc{tardis}$\ to produce model spectra with properties similar to those expected for KNe at early times, while still in the photospheric phase (see Figures \ref{fig:TARDIS_model_spectra} and \ref{fig:varying_T_TARDIS_model_spectra}). We found that we required unrealistically large amounts of material (up to 0.5\,\mbox{M$_{\odot}$}\ in cases, see Table \ref{tab:TARDIS_model_parameters}) to produce observable individual features of any ion of Pt or Au. We were able to demonstrate that, for realistic masses of Pt and Au, we see broad line-blended absorption in the UV. This property is not unique to Pt and Au, and is expected for many heavy elements.

\par
We then generated simple emission spectra for the individual species under investigation here (Pt\,{\sc i}, \,{\sc ii}, \,{\sc iii}\ and Au\,{\sc i}, \,{\sc ii}, \,{\sc iii}), using a simple LTE excitation approximation. These models are presented in Figures \ref{fig:nebular_synthetic_emission_spectra}, \ref{fig:comparison_of_nebular_emission_spectra_vs_17gfo} and \ref{fig:Pt+Au-synthetic_spectra_vs_7.4d+8.4d_gfo_spectra}. With these models, we make strong predictions for forbidden emission lines that could be detectable in the late-time, nebular-phase spectra of a KN, which has ejecta rich in these species. Many of our features lie at wavelengths $> 8000$\,\AA, demonstrating that the best method of identifying these species is through obtaining NIR spectra of future objects. X-shooter is capable of observing $\lesssim 2.5 \, \mu$m, which would capture all but one of our strongest predicted lines; the [Au\,{\sc ii}]\ 3.8446\,$\mu$m transition would only be detectable through \textit{JWST} observations.

\par
We then compared our model photospheric and nebular-phase spectra to the observed spectra of AT2017gfo. The $\textsc{tardis}$\ model spectra were computed at the epochs of the early spectral observations of AT2017gfo (+0.5, +1.4 and +2.4\,d). We find that the strong observed feature at $\sim 7000 - 10000$\,\AA\ in the +1.4\,d spectrum may be reproducible by Pt, but the model requires a very large amount of material to do so. We identify no evidence of Au features in the early observations. We conclude that it is unlikely there are prominent Pt or Au features in the early spectra of AT2017gfo.

\par
Comparisons of our late-time model spectra with those of AT2017gfo were presented in Section \ref{sec:Nebular_phase}. At the beginning of this section, we demonstrated that, for the temperatures and masses that we have estimated for our models, the strongest forbidden transitions in our analysis have line luminosities on the order $\sim 10^{38}$\,erg\,s$^{\mathrm{-1}}$. This demonstrates that we can expect features from these elements to be bright enough to be observed.

\par
We identify some coincidence with the [Pt\,{\sc i}]\ 10761\,\AA\ and the [Pt\,{\sc iii}]\ 10917\,\AA\ transitions, and a strong emission-like feature in the +7.4\,d spectrum of AT2017gfo. If there is Pt\,{\sc i}\ present in the ejecta, then other strong features from Pt\,{\sc i}\ should be detectable at wavelengths of 7409.5\,\AA, and 15227\,\AA. There are features near these wavelengths ($\sim 7900$\,\AA\ and $\sim 15800$\,\AA), with asymmetric profiles, displaying excess blue-wing flux. This flux could be a result of these [Pt\,{\sc i}]\ features, and so we conclude it is plausible that there is [Pt\,{\sc i}]\ emission in the observed late-time spectra of AT2017gfo. A definitive statement, however, will depend on future work with atomic data for many more elements, as needed to synthesise a full spectrum.

\par
It is harder to motivate the presence of Pt\,{\sc iii}\ in the ejecta, as we only predict one prominent strong [Pt\,{\sc iii}]\ line (at 10917\,\AA), preventing us from drawing further conclusions on its presence. We predict three strong [Pt\,{\sc ii}]\ features, none of which correspond exactly to the observed emission features, but they do lie on asymmetric wings. We conclude that it is possible that there is some contribution from Pt in the late-time spectra of AT2017gfo, but it is likely that the spectra are dominated by other species.

\par
Similar comparisons with the late-time AT2017gfo spectra and our model Au spectra do not yield such informative results. We predict a handful of strong [Au\,{\sc i}], [Au\,{\sc ii}], and [Au\,{\sc iii}]\ lines, none of which correspond to observed emission features. We conclude that there is no evidence for the presence of Au in the late-time spectra of AT2017gfo.

\par
Pt and Au are expected to be co-produced in KN ejecta. Therefore, if we observe spectral signatures for one, it is reasonable to expect to see signatures of the other. However, in Section \ref{sec:Motivation_of_parameters}, we highlighted the ratio of Pt and Au production; specifically, Pt is expected to be $\sim$\,a few times more abundant than Au. Hence, it is reasonable for us to speculate that Pt may be contributing towards features in the spectra of AT2017gfo, without also detecting any Au features.

\par
Despite the fact we cannot definitively prove the presence of Pt or Au in the spectra of AT2017gfo, we have demonstrated the usefulness of having access to complete atomic data, and have also demonstrated the study that can be performed with such data. This work supports the idea that having complete atomic data for the heavy elements is useful, and we hope that these data become available in the near future. A complete set of atomic data could then be used for quantitative modelling works, where many elements are included, and more physical KN ejecta compositions are explored in detail.

\section*{Acknowledgements} \label{sec:Acknowledgements}
\par
We thank Andreas Bauswein and Stephane Goriely for useful insights and discussion.
We thank Ryan Gallagher for assisting with data visualisation.
SAS, SJS, CB acknowledge funding from STFC Grants ST/P000312/1 and ST/T000198/1.
This research made use of $\textsc{tardis}$, a community-developed software package for spectral synthesis in supernovae.
The development of $\textsc{tardis}$\ received support from the Google Summer of Code initiative and from ESA's Summer of Code in Space program. $\textsc{tardis}$\ makes extensive use of Astropy and PyNE.
We are grateful for use of the computing resources from the Northern Ireland High Performance Computing (NI-HPC) service funded by EPSRC (EP/T022175).
Based on observations collected at the European Southern Observatory under ESO programmes 1102.D-0353, 0102.D-0348, 0102.D-0350, we made use of the flux-calibrated versions of the X-shooter spectra publicly available through ENGRAVE.

\section*{Data Availability} \label{sec:Data_availability}
\par
All models presented in this paper, the atomic data file used for the $\textsc{tardis}$\ modelling, and extended versions of the tables presented are available, and can be accessed from \textcolor{blue}{<insert-PURE-link-here>}.

\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


Danmon Systems Group announces the completion of a major project for Greenland's state television and radio broadcaster, Kalaallit Nunaata Radioa (KNR) in Nuuk. This involved moving the entire existing facility into new premises. In 2012-13 it was decided that KNR should be relocated due to an accumulation of unhealthy mould and fungus in the structure of the building which was originally built for the Air Greenland heliport.
"The central element of this project was the relocation of all KNR's existing radio and television broadcast studios, postproduction and playout infrastructure to two new buildings," comments Danmon Systems Group Project Director Peter Thomsen. "It was essential that the move, rewiring and post-installation tests be performed without interrupting the normal daily schedule of live broadcasts. In close partnership with KNR, we were able to agree a work schedule which ensured that the network was able to maintain full-time on-air status. This required precise organisation. A closely monitored build schedule was achieved over nine weeks in two phases.


text:
Iain MacInnes: Sealbh
A rich inheritance
That Iain MacInnes is a consummate musician would have been reason enough to encourage him to produce this CD of bagpipe and whistle music. But with this he combines a sensitive appreciation of how to accompany his preferred instruments with others to produce beautiful music. He also has an intimate knowledge of the nation's traditional music collections and a deep understanding of Scottish culture in general. As if that were not enough Iain has an uncommon talent when it comes to composing new music. In Sealbh, we have the happy result of Iain's abundant talents being brought to bear. Sealbh is inspired, full of novelty, and simply beautiful.
Currently producer of BBC Radio Scotland's Pipeline programme, Iain's musical pedigree is impressive, being a former member of the famous combines, the Tannahill Weavers, Smalltalk and Ossian. His CD, Tryst, published in 1999 received critical acclaim and was hugely popular (I recently spoke to a Canadian piper whose copy of Tryst he claimed was worn through, having being played so often).
The Gaelic word Sealbh (pronounced shall-av) incorporates the idea of inheritance and good fortune, an appropriate sentiment in a CD that draws from the well of musical tradition; a rich inheritance, indeed.
The cover photograph depicts a hut in Airidh a' Bhruaich on the Isle of Lewis (the hut, by the way, is not part of Iain's sealbh) which is just a few miles across the hill from Iain's parents' home village of Gravir.
As a musician and broadcaster Iain has been involved in the revival of bellows-blown bagpipes in Scotland since the early 1980s. He also plays Highland pipes and whistles, and, together, these instruments are at the heart of his new recording project Sealbh. In this he is joined by David McGuinness playing keyboards (including harpsichord and harmonium), Mairi Cambell and John Martin on fiddles, Ross Kennedy and Iain MacLeod on strings and Simon Thoumire on concertina. The repertoire is drawn mainly from traditional sources, both Highland and Lowland, with a few contemporary tunes thrown in for good measure.
Iain learnt his piping from Pipe Major Jimmy MacGregor, a former Queen's piper on the Balmoral estate who was a huge source of musical knowledge and inspiration. In the mid-'80s he joined the Tannahill Weavers, following in the footsteps of the band's original piper, Alan MacLeod, and in the early-'90s he teamed up with Billy Ross and Stuart Morison to form the acclaimed trio Smalltalk. His first solo album Tryst (produced by Billy Jackson) was released in 1999.
Iain also has an interest in piping history. In 1988 he completed a thesis exploring the development of the Highland bagpipe from the 1740s to 1840s, a period of cultural transition within Scotland, and he has written widely on the subject of Scotland's 'alternative' piping culture, that of the bellows-blown or 'cauld wind' bagpipe (including a piece in Josh Dickson's recent publication The Highland Bagpipe, published by Ashgate). As a music producer at BBC Scotland he has helped nurture emerging talent for almost 20 years, as well as finding time to perform and lecture.
Spark's Rant[5:07]
Go To Berwick[4:55]
Karuna[5:22]
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Quicksteps[4:23]
Nighean na Cailliche[4:17]
MacDonald of the Isles[5:05]
Rusty Gully[3:56]
Castle Stalker[3:17]
Loudon[3:35]
Loch Bee[5:27]
Spark's Rant £0.79
Go To Berwick £0.79
Karuna £0.79
Cow Hill £0.79
Quicksteps £0.79
Nighean na Cailliche £0.79
MacDonald of the Isles £0.79
Rusty Gully £0.79
Castle Stalker £0.79
Loudon £0.79
Loch Bee £0.79

redpajama_set_name: RedPajamaCommonCrawl


An informal walk around the reserve specifically aimed at beginners or novice birders.
Your friendly guide will outline the principles of avian ID so that you will be able to identify birds not only on the reserve but wherever you bird watch.
Birding for beginners - An informal walk around the reserve specifically aimed at beginners or novice birders.


When you understand the true character—the personality, if you will—of a product, using it takes on new meaning. It becomes more meditation than application; the birth of a new relationship, with not only the product, but with yourself. Facilitating this unique sense is our purpose as we delve into our beloved Bois de Rose body balm in the second installment of our new series, Transport Yourself Through Scent.
The result is a scent that is complex and alive, yet comforting and corrective—with a teeny bit of badass thrown in.
The scent of a rose is often associated with feelings of softness, gentleness, and nurturing; she is a harmonizing agent. But rose possesses a sensual duality, as evidenced by her soft petals and sharp thorns. The flower of the goddess Venus, rose is also symbolic of the blood of Aphrodite. Roses are presented throughout the bible as icons of virginity and fertility, purity and passion. In matters of floriography, the language of flowers which became popular in the Victorian Era, roses represented a range of emotions: flirtation, friendship, embarrassment, and disdain.
Bois de Rose perpetuates this acute contrast. An In Fiore signature, the balm presents Rosa damascena (Bulgarian rose) as its central and predominant note, supported by geranium and vetiver, which lift and deepen the sensorial experience. The result is a scent that is complex and alive, yet comforting and corrective—with a teeny bit of badass thrown in. Its Mother energy is alive and well (rose is associated with the heart chakra and is nothing if not supportive and agreeable) but the effect of Bois de Rose is more in the vein of tough love. It's as if we handed this quiet, delicate flower a leather jacket and a shot of whiskey and set her loose on the town.
On a physical level, rose oil is less dichotomous and more diversified. Its applications are vast—a characteristic which undoubtedly contributes to its widespread appeal. Treatments include issues related to both the respiratory and digestive systems and the liver, specifically. Its mental benefits are equally extensive, and encompass the treatment of depression, mental fatigue and exhaustion, anxiety, and insomnia; all of which make it a classically appealing yet genuinely interesting—and ever effective—journey for you to join us on.


text:
Bucak (also known as nahiye) is the Turkish word for subdistrict, literally meaning "corner." In principle, all Turkish provinces () are divided into districts (), and the districts were then divided into bucaks. Thus, bucak was the third-level administrative unit in Turkey. Despite this designation, about half the districts had no bucaks. For example, in Konya Province (the province with the highest number of settlements), among the 31 districts, only 15 districts had bucaks, and the total number of bucaks was 23. However, there was only one bucak in Yalova Province. The total number of bucaks in Turkey was 634. Villages () are parts of the districts or bucaks.

Bucaks were important part of the Turkish administrative system prior to 1970, but since transportation facilities to villages were improved, the importance of bucaks declined.

Until 2014, bucaks were almost defunct, but their legal entity continued. According to 2012 law 6360, bucaks as well as villages in 30 provinces were abolished, but the legal entity of bucak in other (51) provinces continued to exist. (See Metropolitan municipalities in Turkey) With changes approved on 11 September 2014, all bucaks were abolished.

References

Subdivisions of Turkey
Subdivisions of the Ottoman Empire

redpajama_set_name: RedPajamaWikipedia


A while back, I was perusing the supermarket looking for potential ingredients that could be used in creams, lotions & potions (forget putting food in ones belly, there are far more interesting things to be doing in the kitchen).
Anyway, I came upon the herbs and spices and, when one is in the mindset that I was that day, you don't see flavours. You see colours, textures, aromas, functionality, brief glimpses of finished products and the effects that could be achieved from them.
What really caught my eye this day was the ground cardomon. So fine, so delicate, soooo aromatic and certainly not a spice that I keep in my cupboard (I'm not an adventurous or creative cook). I bought it and took it home.
Cardomon is not the cheapest of essential oils but the aroma is just lovely and few people dislike it. The ground spice is equally as lovely, being warm, spicy-sweet & balsamic and, like the essential oil, its aroma strength is very good and certainly a much cheaper alternative.
The powder of the ground cardomon is super-fine and got me thinking about its potential for gentle exfoliation and facial skin refinement. I tried it in a cleansing cream wash that I made previously, adding about a heaped teaspoon to roughly 50g of cream and worked this into my face for about a minute (using gentle pressure and working in small circles) and the result was truly outstanding. My skin felt fresh, clean and so very, very smooth. No stinging, no irritation. What's more, the aroma was wonderful and seemed to last an age - just lovely. Now, I just use it a couple of times a week, mixing a small amount into my usual measure of cleanser.
I've not tried it in soap (yet) although I did use ground cinnamon, clove and sugar M&P soap. Here, I used the cinnamon and a dash of tumeric for colour (which was just lovely) and it gave the soap a multi-grade exfoliant texture - a good compliment to to the courser grade of the sugar. The aroma of the cinnamon was fairly good although I did boost it with some essential oil.
We have had a number of discussion on the Melting Pot Cafe Forum at Fresholi about herbs/spices in products. I would love to hear your experiences in soaps, products and infusions.
That sounds like a highly successful spicy experiment! I bet the cleanser smells amazing with the Cardomon!
Ooh Sue... It smells just lovely, ahh... But the exfoliant properties is truly excellent and leaves the skin so silky smooth.


I forgotten more music than can remember but here goes.
When the 90's hit, all bets were off with alternative and grunge. Couldn't get enough of Pearl Jam, Alice in Chains, Soundgarden, STP, Nirvana, Jane's Addiction, Red Hot Chili Peppers, Sloan, REM, etc.
As far as Country goes, it was never the same once Garth Brooks came on the scene. He did to country what Poison did to Rock.
My only other secret indulgence is a woman and a piano, i.e. Tori Amos, Sarah Mclachlan, Sara Bareilles, Missy Higgins, etc.
It's Friday night boys and girls. Let's start it off with some Olivia Newton John.
And I thought for sure she was singing this song to me.
And she's clearly searching for me here.
She was my first heartthrob !!
Dude, you know she was singing those songs for me!
Here's another most have long forgotten.
People forget all the movies she was in.
I wonder if Zina remembers this? This was on the radio in 84' when I lived in Belgium.
So funny to look back and see this.
Last edited by MR Snakes; 01-12-2019 at 07:40 PM.


Vijaya Bank is inviting online applications to fill the posts of Chief Managers in SMG Scale-IV in General Banking Stream.
Age: Candidates age must be in between 30 to 40 years as on 01-08-2018.
Educational Qualification: Candidates must complete Graduation/PG in any discipline or MBA (Finance)/CA/CFA/M.Sc (Statistics) from a recognized University & CAIIB, Diploma in Treasury and Risk Management and 7 years of Banking experience.
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Readers ask: How Does South Dakota Make Money From Tourism?
1 What is the main source of income for South Dakota?
2 What drives the economy of South Dakota?
3 How does South Dakota generate revenue?
4 What did tourism increase in South Dakota?
5 What food is South Dakota known for?
6 What is South Dakota best known for?
7 What is the No 1 industry in South Dakota?
8 What is the most important industry in South Dakota?
9 What industries are big in South Dakota?
10 Is South Dakota in debt?
11 Is South Dakota tax friendly for retirees?
12 Do you pay taxes in South Dakota?
What is the main source of income for South Dakota?
The major sources of income for the state government are a sales tax, revenue from licenses and other user fees, and profits from state-owned tourist facilities. There is no personal or corporate income tax in South Dakota.
What drives the economy of South Dakota?
South Dakota's economy is driven by agriculture, tourism, financial services and manufacturing, along with growing opportunities in professional, biotech and technical services. The state's economic snapshot shows why more businesses and people are choosing South Dakota as their next stepping stone for success.
How does South Dakota generate revenue?
South Dakota generates the bulk of its tax revenue by levying a general sales tax and select sales taxes (otherwise known as excise taxes). The rest comes from non-tax sources, such as intergovernmental aid (e.g., federal funds), lottery revenues and fees.
What did tourism increase in South Dakota?
Did you know Mount Rushmore was built to increase tourism to South Dakota?
You might be interested: Why Do People Move Temporarily To Give Birth Birth Tourism?
What food is South Dakota known for?
The top 18 South Dakota foods
Bison.
Chili and Cinnamon/Caramel Rolls.
Chislic.
Cookies 'n Cream Ice Cream.
Gabubu Bread.
Indian Tacos.
Kolache.
Kuchen.
What is South Dakota best known for?
Entered the Union: November 2, 1889 (40)
Capital: Pierre
State Gem Stone: Fairburn Agate State Insect: Honey Bee
State Song: "Hail! South Dakota " State Sport: Rodeo
Famous For: Mt. Rushmore • Black Hills Gold
What is the No 1 industry in South Dakota?
Agriculture is the life-blood of South Dakota and the state's No. 1 industry.
What is the most important industry in South Dakota?
The state has a strong agricultural base. It is the largest industry in the state. South Dakota routinely ranks among the top 10 states for the production of hay, sunflowers, rye, honey, soybeans, corn, wheat and cattle. Tourism is also a significant contributor, bringing in about $2 billion, annually.
What industries are big in South Dakota?
What Are The Biggest Industries In South Dakota?
Agriculture, Fishing and Forestry. South Dakota is a large -scale producer of corn, alfalfa, soybeans, rye, flaxseed, and wheat.
Mining and Power. The mining industry in South Dakota produces gold, cement, gravel, and sand.
Manufacturing.
Services and Labour.
Is South Dakota in debt?
[hide]Total fiscal year 2015 state debt, U.S. Census Bureau
Total state debt
State debt ranking
South Dakota $3,286,231,000 46
Minnesota $16,755,784,000 21
Nebraska $1,809,126,000 49
Is South Dakota tax friendly for retirees?
South Dakota is very tax – friendly toward retirees. Social Security income is not taxed. Withdrawals from retirement accounts are not taxed. Public and private pension income are not taxed.
You might be interested: FAQ: What Is The Hospitality And Tourism Industry?
Do you pay taxes in South Dakota?
Overview of South Dakota Taxes On a statewide basis, South Dakota does not levy a personal income tax. The state's sales tax is also among the lowest in the country. However, the average effective property tax rate in South Dakota is above the national average.
FAQ: What Is A Tourism Bureau?
Often asked: How Does Paris Manage Tourism Demands?
Quick Answer: Why Social Media Is Promoting Tourism?


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General>
New legislation>
In detail>
Direct taxes>
Income tax for individuals
Limit plant and equipment depreciation deductions to outlays actually incurred by investors
Legislation and supporting material
Income tax deductions for the decline in value of previously used plant and equipment in rental premises used for residential accommodation are no longer allowed. The changes are now law.
The changes apply from 1 July 2017 to:
previously used plant and equipment acquired at or after 7.30 pm on 9 May 2017 unless it was acquired under a contract entered into before this time
plant and equipment acquired before 1 July 2017 but not used to earn income in either the current or previous year.
Investors who purchase new plant and equipment will continue to be able to claim a deduction over the effective life of the asset.
The changes do not affect deductions that arise in the course of carrying on a business, or for:
corporate tax entities
superannuation plans other than self-managed superannuation funds
public unit trusts
managed investment trusts
unit trusts or partnerships whose members are the above listed entities.
The Treasury Laws Amendment (Housing Tax Integrity) Act 2017External Link received royal assent on 30 November 2017.
Media release No. 86External Link issued on 7 September 2017 by the Treasurer and the Assistant Minister to the Treasurer
Media release No. 46External Link issued on 9 May 2017 by the Treasurer and the Assistant Minister to the Treasurer
In the 2017–18 Budget, the Government announced that it will limit plant and equipment depreciation deductions to outlays actually incurred by real estate property investors.
Last modified: 05 Dec 2017QC 51990