Simulations of Early Kilonova Emission from Neutron Star Mergers

As the ionization is high in the early phase, electron scattering can conceivably play an important role in the opacity. The number density (n_e) of the electrons in the single-element ejecta can be estimated as

$$\begin{eqnarray}&&{n}_{{\rm{e}}}=\displaystyle \frac{\rho }{{{Am}}_{{\rm{p}}}}j,\end{eqnarray} \tag{ 1 }$$

where A is the mass number, m_p is the mass of the proton, and j is the ionization degree (j = 10 for 10th (XI) ionization) of an element. From this, the electron scattering opacity (κ^es) can be calculated via

$$\begin{eqnarray}&&{\kappa }^{\mathrm{es}}=\displaystyle \frac{{n}_{{\rm{e}}}{\sigma }_{\mathrm{Th}}}{\rho }=\displaystyle \frac{{\sigma }_{\mathrm{Th}}}{{{Am}}_{{\rm{p}}}}j,\end{eqnarray} \tag{ 2 }$$

where σ_Th is the Thomson scattering cross section. For the single-element ejecta with maximum ionization, i.e., j = 10, the electron scattering opacity is estimated as ${\kappa }^{\mathrm{es}}=(3\mbox{--}10)\,\times {10}^{-2}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ for elements Z = 20–56, with a greater opacity value for the lower-Z (and thus lower-A) elements. For iron (Fe, Z = 26), the value is $7\times {10}^{-2}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$.

Free–free transitions constitute another component of the total opacity (${\kappa }_{i,j}^{\mathrm{ff}}(\lambda )$). For a particular element i at an ionization state j, this opacity component can be calculated as in Rybicki & Lightman (1986):

$$\begin{eqnarray}\begin{array}{rcl}{\kappa }_{i,j}^{\mathrm{ff}}(\lambda ) & = & \displaystyle \frac{4{e}^{6}{\lambda }^{3}}{3{m}_{{\rm{e}}}{{hc}}^{4}\rho }{\left(\displaystyle \frac{2\pi }{3{{km}}_{{\rm{p}}}}\right)}^{\tfrac{1}{2}}{T}_{{\rm{e}}}^{-\tfrac{1}{2}}{\left(j-1\right)}^{2}{n}_{{\rm{e}}}{n}_{i,j}\\ & & \times \,(1-{e}^{-\tfrac{{hc}}{\lambda {{kT}}_{{\rm{e}}}}}){\bar{g}}_{\mathrm{ff}},\end{array}\end{eqnarray} \tag{ 3 }$$

where T_e is the electron temperature (for which we substitute the common temperature, T, under LTE), ${\overline{g}}_{\mathrm{ff}}$ is the velocity-averaged free–free Gaunt factor (which is fixed at unity, following the method of Tanaka & Hotokezaka 2013), and n_{i, j} is the ion density, estimated as

$$\begin{eqnarray}&&{n}_{i,j}=\displaystyle \frac{{f}_{i,j}{X}_{i}\rho }{{{Am}}_{{\rm{p}}}}.\end{eqnarray} \tag{ 4 }$$

Here X_i is the fraction of the ith element in the ejecta and ${f}_{i,j}$ is the fraction of the ith element at the jth ionization state. To obtain an analytic estimate of the free–free opacity component for single-element ejecta, the electron density is calculated from Equation (1), while the ion density is estimated by putting f_i,j = 1 and X_i = 1 in Equation (4). We find that a single-element ejecta, with temperature T = 10⁵ K and density $\rho ={10}^{-10}\,{\rm{g}}\,{\mathrm{cm}}^{-3}$, has a free–free opacity component of ${\kappa }_{i,j}^{\mathrm{ff}}=(2\mbox{--}3)\times {10}^{-4}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ at a wavelength λ = 1000 Å for Z = 20–56. This opacity component is greater for lower-Z elements. For Fe (Z = 26), ${\kappa }_{i,j}^{\mathrm{ff}}=2.6\times {10}^{-4}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$. Thus, even in the early phase, the free–free transition opacity component is relatively small.

Another process contributing to the opacity is photoionization or bound–free transition. The bound–free transition opacity is calculated by

$$\begin{eqnarray}&&{\kappa }_{i,j}^{\mathrm{bf}}(\lambda )=\displaystyle \frac{{n}_{i,j}{\sigma }_{i,j}^{\mathrm{bf}}}{\rho },\end{eqnarray} \tag{ 5 }$$

where ${\sigma }_{i,j}^{\mathrm{bf}}$ is the bound–free cross section for the ith element in the jth ionization state. The bound–free cross section is estimated from a fitting formula taken from Verner et al. (1996). For Fe (Z = 26) in the 10th (XI) ionization state for T = 10⁵ K, the cross section is ${\sigma }_{i,j}^{\mathrm{bf}}=0.45$ Mb at the ionization threshold.

The elements with atomic numbers Z = 20–56 have a 10th ionization potential energy ≥250 eV (Figure 1), corresponding to a wavelength of λ ≤ 50 Å. According to the blackbody function at a temperature of T = 10⁵ K, the fraction of photon energy present at such a short wavelength range is ∼10⁻⁶. Calculating the same for different ionization states of different elements in a temperature range of T = 10³–10⁵ K, we find that the fraction never reaches beyond 10⁻⁴. Therefore, although the photoionization cross section itself is high, the number of photons with energy greater than the ionization potential is negligible. Therefore, the bound–free opacity component does not significantly contribute to the total opacity.

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There is no available bound–free cross section data for the elements with Z > 26, i.e., Fe. Following the method adopted by Tanaka & Hotokezaka (2013), we use the cross sections of Fe for elements with a higher Z in the radiative transfer simulation (Section 4). This crude approximation does not alter the results since the bound–free transition opacity is not predominant, as discussed above.

We perform atomic structure calculations by using the Hebrew University Lawrence Livermore Atomic Code (HULLAC; Bar-Shalom et al. 2001). The calculation methods follow those adopted by Tanaka et al. (2020), where the calculation was limited from neutral atoms (I) to triply ionized ions (IV). We extend the calculations up to the 10th ionization state (XI) for elements with Z = 20–56.

Past atomic calculations of r-process elements for kilonova ejecta could only achieve typical energy level accuracies of a few tens of percent (Kasen et al. 2013; Tanaka et al. 2018). This is not particularly accurate compared to standard accuracy measurements in atomic physics. Complete and accurate calculations for r-process elements with several excited levels are still difficult to achieve (Gaigalas et al. 2019; Radžiūtė et al. 2020). The inaccuracy in the atomic calculations typically results in a systematic uncertainty in the bound–bound opacity by a factor of around ∼2 (Kasen et al. 2013; Gaigalas et al. 2019). As discussed below, evaluating the accuracy for highly ionized ions is not currently possible. Therefore, we assert that the factor of 2 uncertainty also exists in the opacities given in this paper.

The main differences in our calculations compared to Tanaka et al. (2020) are the configurations included in the atomic calculations. For the highly ionized ions considered in this paper, information on energy levels and electronic configurations is lacking. Therefore, when only a few configurations are listed in the National Institute of Science and Technology atomic spectra database (NIST ASD; Kramida et al. 2018), we implement the configurations of isoelectronic neutral atoms. A typical number of included configurations for each ion is 13. This assumption provides some convergence in the opacity, typically within an uncertainty of less than 10% (Tanaka et al. 2020), a small enough value compared to the expected systematic uncertainty.

Since the available data for energy levels in the NIST ASD are limited, we are unable to evaluate the accuracy of our calculations with well-evaluated data. Instead, we compare the calculated ionization potentials with those in the NIST ASD (Figure 1). The mean accuracy is found to be 1.6%, 1.1%, 1.0%, 0.8%, 0.8%, 0.6%, and 0.6% for ions V–XI, respectively. Highly ionized ions have fewer bound electrons, and thus the system becomes simpler. In addition, correlation converges more rapidly when ionization of elements increases. As a result, the accuracy for the highly ionized ions is much better than that obtained for lower ionization states (4%–14%; Tanaka et al. 2020).

Equipped with the atomic data for highly ionized ions, we calculate the bound–bound opacity for early-time ejecta. In supernovae and NS mergers, the matter is expanding at high velocity and with a high-velocity gradient. In such a system, the opacity can be enhanced (Karp et al. 1977). To calculate this opacity, we use the expansion opacity formalism (Eastman & Pinto 1993):

$$\begin{eqnarray}&&{\kappa }_{\exp }(\lambda )=\displaystyle \frac{1}{{ct}\rho }\displaystyle \sum _{l}\displaystyle \frac{{\lambda }_{l}}{{\rm{\Delta }}\lambda }(1-{e}^{-{\tau }_{l}}),\end{eqnarray} \tag{ 6 }$$

where λ_l is the transition wavelength in a wavelength interval Δλ and τ_l is the Sobolev optical depth at the transition wavelength, calculated as

$$\begin{eqnarray}&&{\tau }_{l}=\displaystyle \frac{\pi {e}^{2}}{{m}_{{\rm{e}}}c}{n}_{i,j}{\lambda }_{l}{f}_{l}t\displaystyle \frac{{g}_{l}}{{g}_{0}}{e}^{-\tfrac{{E}_{l}}{{kT}}}.\end{eqnarray} \tag{ 7 }$$

Here E_l, g_l, and f_l are the energy, statistical weight of the lower level of the transition, and strength of transition, respectively. The statistical weight of the ground state is expressed as g₀.

3.2.1. Opacity of Individual Element

We calculate the expansion opacity as a function of wavelength for the elements with Z = 20–56. The elements are categorized as either d-, p-, or s-shell elements according to the electron configurations of their neutral state (in Figure 2; d-, p-, and s-shell elements are shown in the top, middle, and bottom panels, respectively). The temperature and density are assumed to be T ∼ 10⁵ K and $\rho ={10}^{-10}\,{\rm{g}}\,{\mathrm{cm}}^{-3}$, typical conditions at t = 0.1 days. Depending on the element, the expansion opacity varies, with ${\kappa }_{\exp }=0.001\mbox{--}4\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$. The opacity is higher at UV wavelengths, similar to the behavior at later times.

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The temperature dependence of the expansion opacity can be understood by calculating the Planck mean opacity, κ_mean. Since the overall variation of the mean opacity is different for each element, we first discuss the trend for a few representative elements from different shells (Figure 3). There are two main factors that determine the trend of opacity for highly ionized ions: half-closed shells have the highest complexity measure, and the increment in Z in a shell raises the energy distribution upward (Tanaka et al. 2020). The Boltzmann statistics predicts that lower energy levels are more populated and the transitions from such levels contribute to the opacity the most. At moderate temperatures, the elements or ions with half-closed shells do not necessarily have the highest opacity because their energy levels are pushed toward higher energies. At higher temperatures, higher energy levels are more populated and the opacities of the ions with half-closed shell are greater than other elements within the same shell.

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As the ionization degree of d-shell element yttrium (Y, Z = 39) increases with temperature, the Planck mean opacity evolves as shown in top left panel of Figure 3. When Y is singly or doubly ionized (II–III) at T = 5000–10,000 K, it has a similar energy level distribution to the neutral s-shell elements strontium (Sr, Z = 38) and rubidium (Rb, Z = 37). These elements contain only a few strong transitions. When Y becomes triply ionized (IV), it has a closed p-shell and the opacity decreases. As Y is ionized further, up to V–VI, the shell configuration resembles neutral p-shell elements (Z = 35–34) with an energy level distribution at a higher energy. The opacity peaks when Y reaches the sixth ionization degree (VII) at T ∼ 50,000 K, at which it has a similar structure to neutral arsenic (As, Z = 33), with a half-closed shell structure. Beyond this ionization (VIII–XI), Y becomes similar to the neutral p (Z = 32 − 31) and d (Z = 30 − 29) shell elements. This leads to a decrease in the number of available energy levels, consequently reducing the opacity.

The behavior of the d-shell element cadmium (Cd, Z = 48) is more straightforward (top right panel of Figure 3). As the temperature increases, it loses d-shell electrons. When the d-shell has a half-closed structure, the element reaches peak opacity. Then, the opacity decreases as more d-shell electrons are lost at higher temperature.

The p-shell element iodine (I, Z = 53) has a complicated variation in opacity with the temperature but can be explained in a similar way (bottom left panel of Figure 3). The opacity is high when I resembles elements with half-closed shells. Namely, the opacity peaks at T ∼ 10⁴ K and at T ∼ 10⁵ K, when I has a similar structure to the neutral p-shell element antimony (Sb, Z = 51) and d-shell element technetium (Te, Z = 43), respectively, being doubly (III) and 10th (XI) ionized.

For the s-shell element barium (Ba, Z = 56, bottom right panel of Figure 3), the opacity reaches a peak at T ∼ 4000 K, when Ba is singly ionized (II) and has one neutral s electron, similar to caesium (Cs, Z = 55). The opacity drops to a negligible value at T ∼ 8000 K, when doubly ionized Ba (III) resembles the energy level distribution of neutral p-shell element xenon (Xe, Z = 54), which has a closed p-shell. Such ions have most of their energy levels distributed at higher energies, and thus fewer transitions take place, as the Boltzmann statistics predicts that most electrons exist in the lower-lying energy levels at this temperature range. The opacity rises to a higher value at T ∼ 30,000 K when the energy distribution is similar to the half-closed neutral p-shell element Sb (Z = 51). As the ionization degree increases, the opacity decreases again when Ba resembles the configuration of neutral d-shell elements with lower complexity.

The variation of the Planck mean opacity with temperature for all the elements of interest can be understood in the same manner (Figure 4). With the increasing temperature and ionization, the effective shell structure of the ions changes, the opacity varying accordingly. Highly ionized elements have the maximum bound–bound opacities when they have a half-closed shell structure.

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For d-shell elements, opacity as a function of temperature peaks when it has half-closed p-shell or half-closed d-shell structures. The peak opacity is higher when the element has a half-closed d-shell structure (${\kappa }_{\mathrm{mean}}\sim 1\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$) rather than a half-closed p-shell structure (${\kappa }_{\mathrm{mean}}\sim 0.1\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$). Most of the p-shell elements have d-shell electrons at high ionization, with the opacity peaking at ${\kappa }_{\mathrm{mean}}\sim 1\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$. This is the reason why at early times (higher temperature) p-shell elements have comparable opacity contributions to d-shell elements.

The s-shell elements have comparatively lower opacity ${\kappa }_{\mathrm{mean}}\sim 0.001\mbox{--}0.1\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$. This lower opacity can be explained by s-shell elements never resembling neutral half d-shell elements at higher ionization, although they can be similar to neutral half p-shell elements.

The behavior of opacity and temperature for different elements is summarized in Figure 5. At lower temperatures, the elements with the maximum number of low-lying energy levels have the maximum opacity. At high temperatures, ions lose their initial outermost electrons and effectively have different shell structures. Furthermore, the higher-level transitions become attainable at high temperatures since higher energy levels are populated. In this case, the maximum contribution to the opacity typically comes from ions that have half-closed shells, with the highest complexity measure.

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3.2.2. Opacity of Element Mixture

In this section, we consider the bound–bound opacities in the ejecta that consist of a mixture of different elements. Depending on the electron fraction Y_e, a different abundance pattern is realized in the ejecta. To estimate the bound–bound opacity for blue kilonovae, we calculate the opacity for the mixture of elements in an ejecta, assuming ${Y}_{{\rm{e}}}=0.30\mbox{--}0.40$. We take the abundance pattern using the results from Wanajo et al. (2014). We assume that the mass distribution in each Y_e bin is flat. At such high Y_e, the second and third peak r-process elements are not synthesized. The elements with a significant abundance are Z ∼ 35–45 (Figure 6).

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The left panel of Figure 7 shows the expansion opacity as a function of wavelength for the element mixture at t = 0.1 days and t = 1 day. To model the typical conditions at these times, we set ρ = 10⁻¹⁰ g cm⁻³, T = 10⁵ K for t = 0.1 days and $\rho ={10}^{-13}\,{\rm{g}}\,{\mathrm{cm}}^{-3}$, T = 10⁴ K for t = 1 day. At t = 1 day, the expansion opacity peaks at ${\kappa }_{\exp }\sim {10}^{2}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$, whereas the peak expansion opacity at t = 0.1 days only reaches ${\kappa }_{\exp }\sim 1\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$. The Planck mean opacity also shows an increase with time (right panel of Figure 7). The value of opacity is ${\kappa }_{\mathrm{mean}}\sim 0.5\mbox{--}1\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ for the typical conditions at t = 0.1 days; under the typical conditions at t = 1 day, ${\kappa }_{\mathrm{mean}}\sim 5\mbox{--}10\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$. These results can be understood using Equation (6). Since the expansion opacity is inversely proportional to ρt, the change in ρt from t ∼ 0.1 to 1 day increases the opacity by a factor of 100. Meanwhile, the Sobolev optical depth decreases with time, which reduces the contribution from the summation of $1-{e}^{-{\tau }_{l}}$. As a result, the opacity increases by a factor of about 10 as time increases from t = 0.1 to 1 day.

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The Planck mean opacity results for an element mixture as a function of temperature (right panel of Figure 7) can be understood by individual element properties. At relatively low temperatures (T < 20,000 K), the opacity increases with temperature. This is a property of d-shell elements that have the largest contribution to the opacity in this temperature range. The opacity displays some modulation by reflecting the behaviors of abundant individual elements. At high temperatures (T > 20,000 K), the opacity evolves more smoothly with temperature because the contributions from p- and d-shell elements with different peak positions in the Planck mean opacity are averaged out.

Hence, as evidenced by the results, the bound–bound opacity is orders of magnitude greater than the electron scattering, bound–free, and free–free opacities. At t = 0.1 days, the Planck mean of bound–bound opacity can reach up to a value of ${\kappa }_{\mathrm{mean}}\sim 2\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$, whereas other contributions to the total opacity, ${\kappa }^{\mathrm{es}}=(3\mbox{--}10)\times {10}^{-2}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ and ${\kappa }_{i,j}^{\mathrm{ff}}=(2\mbox{--}3)\,\times {10}^{-4}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$, are negligible at a wavelength λ = 1000 Å for Z = 20–56 (Section 2). The bound–free opacity is not significant at this time since the fraction of photons with energy beyond the photoionization threshold is small (Section 2). Therefore, we conclude that bound–bound opacity is the most significant component of the total opacity at an early time (t ∼ 0.1 days).

We use a simple ejecta model (Metzger et al. 2010) that considers a spherical ejecta expanding homologously. As our fiducial case, we use the power-law density structure ρ ∝ r⁻³ from a velocity v = 0.05c to 0.2c, a total ejecta mass of M_ej = 0.05 M_⊙, and an electron fraction range of Y_e = 0.30–0.40. Similarly to Section 3.2, we assume a flat distribution of mass for each value in the Y_e range, subsequently using the results from Wanajo et al. (2014) to calculate the abundance pattern. Throughout the ejecta, the same Y_e distribution, and hence homogeneous elemental abundance pattern, is assumed. The velocity scale and the range of Y_e in our fiducial model are typical for disk wind ejecta, particularly in the case of a relatively long-lived hypermassive NS (Metzger & Fernández 2014; Perego et al. 2014; Lippuner et al. 2017; Siegel & Metzger 2017; Fujibayashi et al. 2018; Fernández et al. 2019). In such conditions, the main nucleosynthesis products are light r-process elements (Figure 6).

In reality, the disk wind ejecta are enveloped inside a faster-moving dynamical ejecta (Hotokezaka et al. 2013). To study the effect of this dynamical ejecta, we further include models with a continuous thin outer layer at v > 0.2c with a fixed mass of M_out = 0.005 M_⊙. The layer has a steeper density structure ρ ∝ rⁿ, where n = −6, −8, and −10. According to the slope, the maximum outer velocity changes as v ∼ 0.24c, 0.25c, and 0.33c for n = −6, −8, and −10, respectively. We assume the same Y_e range for these outer ejecta components. These modeling conditions may be applicable for a shock-heated polar dynamical ejecta, where Y_e can rise by e⁺ capture and ν_e absorption (Goriely et al. 2015; Sekiguchi et al. 2015, 2016; Martin et al. 2018; Radice et al. 2018). Thus, even with relatively high Y_e, our model can provide a sound approximation for the emission viewed from the polar direction. We do not include lanthanide-rich ejecta, as the main focus of this work is to present the light curves of blue kilonovae.

As the ejecta expands, the temperature and the density of the ejecta decrease. The opacity also evolves with time accordingly. Therefore, it is useful to study the time evolution of the opacities at a fixed position in the ejecta. Figure 8 shows the temperature, density, and opacity evolution at the ejecta point $v=0.1c$ for our fiducial model. The dominant component is the bound–bound opacity, followed by the electron scattering, bound–free, and free–free opacity. The total opacity varies from 0.1 to 10 ${\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ with time.

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The contribution of electron scattering to the total opacity is higher at earlier times, reaching a majority contribution, >50%, at t ∼ 1 hr (Figure 8). This high electron scattering contribution occurs at an early time, as high temperatures (T > 10⁵ K) cause a high degree of ionization, which raises electron density. The electron scattering opacity decreases with time as the ejecta temperature decreases. Around t ∼ 6 days, the electron scattering contribution drops steeply because most of the elements recombine to neutral atoms.

The free–free component remains small throughout the evolution of the total opacity. At t ∼ 0.1 days, the opacity has a value of ${\kappa }_{\mathrm{mean}}^{\mathrm{ff}}\sim {10}^{-4}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ ; this value falls faster than the electron scattering opacity component as time increases(Figure 8). From Equations (3) and (4), we can see that the free–free opacity varies as ${\kappa }_{i,j}^{\mathrm{ff}}(\lambda )\propto \rho \,{T}^{-\tfrac{1}{2}}(1-{e}^{-\tfrac{{hc}}{\lambda {kT}}})$. Since the density decreases faster than temperature as time increases, the free–free opacity decreases with time.

The bound–free opacity varies with time but never becomes large enough to significantly contribute to the total opacity. As discussed in Section 2.3, although the photoionization cross section itself is high, the fraction of high-energy photons is small, and thus the Planck mean opacity is moderate. The bound–free opacity component shows an increasing trend, reaching its peak value of ${\kappa }_{\mathrm{mean}}^{\mathrm{bf}}\sim 0.04\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ a few days after the merger. This is due to the ionization degree decreasing with time; hence, more photons are present beyond the potential energy of ions. It should be noted that the value of the bound–free opacity before t = 0.2 days is not correctly followed in the radiative transfer code, since the wavelength range beyond the ionization threshold is not covered by our wavelength grid (down to 100 Å).

The bound–bound opacity component evolves from ${\kappa }_{\mathrm{mean}}^{\mathrm{bb}}\sim 0.5$ to 5 cm² g⁻¹ from t = 0.1 to 1 day. Excluding the time around 1 hr, this component alone is representative of the total opacity. It is to be noted that most of the previous works have considered a fixed opacity value of 1 ${\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ or less (Kasliwal et al. 2017; Villar et al. 2017; Piro & Kollmeier 2018; Gottlieb & Loeb 2020) to calculate blue kilonovae at t < 1 day. This assumption is not valid precisely, as the change in the opacity with time is quite large for even high-Y_e ejecta.

The bolometric luminosity for the fiducial model is shown in Figure 9. The luminosity deposited to the ejecta (or thermalized radioactive luminosity) is shown by the dashed line for comparison. At t < 1 day, the observable bolometric luminosity is an order of magnitude lower than the deposition luminosity because the ejecta are optically thick; hence, photons cannot escape from the ejecta. At t > 1 day, the previously stored radiation energy from t < 1 day starts to be released and the bolometric luminosity supersedes the deposition luminosity. Finally, the bolometric luminosity follows the thermalized radioactive emission at t > 10 days.

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The bolometric light curve of GW170817 (Waxman et al. 2018) is shown for comparison. Our fiducial model with M_ej = 0.05 M_⊙ gives a reasonable agreement with the observed data at early times. The required ejecta mass is consistent with the findings of previous works (Kasliwal et al. 2017; Waxman et al. 2018; Hotokezaka & Nakar 2020).

The presence of a thin outer layer affects the light curves at an early time (Figure 10). The steeper slope of the outer ejecta makes the luminosity fainter at t ≤ 1 day. In the early time, the ejecta are optically thick and the emission from the outermost layer determines the light curve. Adding a thin outer layer to the ejecta changes the mass located outside of the diffusion sphere in the early time. Our fiducial model has a higher density at the diffusion sphere, producing a high luminosity in the early time (Figure 10). For the models with thin layers, the density at the diffusion sphere becomes lower. Since the model with a steeper slope has a lower density of the optically thin layer for a fixed mass of the outer ejecta, the model displays a fainter luminosity. After around t > 1 day, the thin layer has almost no effect on the light curve because thin ejecta are already optically thin and so do not contribute to the luminosity anymore.

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The spectra at t = 0.1, 1, and 10 days after the merger and the multicolor light curves, both plotted in absolute magnitude, are shown for the fiducial model (left and right panels of Figure 11). The spectral shape shows a strong time evolution from shorter wavelengths (λ ≤ 10000 Å ) toward infrared wavelengths (λ ≥ 10000 Å) at later times. This trend is also displayed in the multicolor light curves. The peak times of the light curves gradually move from shorter to longer wavelengths: the UV light curves peak at t ∼ 4.3 hr, blue optical light curves peak at t ∼ 16.8 hr, and red optical and NIR light curves peak at t > 1 day. The early UV emission declines very quickly and becomes fainter than an absolute magnitude of −10 in t ≤ 2 days. A similar pattern for blue optical emission occurs over a somewhat longer timescale. The NIR brightness remains bright from 1 day to a week.

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We compare our model with the multicolor light curves of GW170817 (Villar et al. 2017). The data are corrected for Galactic extinction with E(B − V) = 0.1. This comparison provides insight on the emission mechanism of GW170817-like events. Similar to the bolometric luminosity (Figure 9), our fiducial model shows reasonable agreement with the data. Hence, our model shows that a one-component, purely radioactive, high-Y_e ejecta can explain early-time bright UV and blue emission. Previous studies that assumed a constant opacity also show good agreement for early UV and blue optical data (Cowperthwaite et al. 2017; Drout et al. 2017; Kasen et al. 2017; Villar et al. 2017). However, our calculations directly calculate atomic opacities, and thus the opacity is not a free parameter in our model.

The UV magnitudes become fainter and decline faster upon the inclusion of a thin layer outside the fiducial model ejecta (Figure 12), also pointed out by Kasen et al. (2017). The UV light curves are shown for the fiducial model and the case where n = −10. The UVW1 magnitude of the fiducial model without a thin layer peaks at an absolute magnitude of −16 mag at t ∼ 4.3 hr, whereas that of the model incorporating a thin layer with n = −10 is fainter at t > 0.1 days, reaching a peak of −15.7 mag at t ∼ 2.4 hr.

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It should be noted that our models assume that the outer ejecta are lanthanide-free, with Y_e = 0.30–0.40. If the outer ejecta have a lower Y_e, as expected for dynamical ejecta in the equatorial plane, the UV brightness can be suppressed further. Hence, the purely radioactive kilonova models may not be able to explain the observed early light curve, depending on the structure and composition of the outer ejecta. In this case, a heating source other than radioactive decays of r-process nuclei may be necessary, for example, heating by shock or cocoon (Kasliwal et al. 2017; Piro & Kollmeier 2018), β decay luminosity from free neutrons (Metzger et al. 2015; Gottlieb & Loeb 2020), or some other central power source (Metzger et al. 2008; Yu et al. 2013; Metzger & Fernández 2014; Li et al. 2018; Matsumoto et al. 2018; Metzger et al. 2018; Wollaeger et al. 2019). Although it is difficult to draw firm conclusions owing to a lack of atomic data on highly ionized lanthanides, our new atomic opacities provide the foundation for a discussion on the detailed properties of blue kilonova models at an early phase.

Finally, we discuss the prospect of observing an early kilonova emission. Our simulations give the first synthetic light curves of kilonovae at a timescale of hours after the merger, based on the detailed atomic opacities. As discussed in Section 5.1, the early UV emission is sensitive to the structure of the ejecta. Furthermore, contributions from other heating sources may play important roles in determining the early luminosity. Therefore, the early-time observations provide clues to distinguish these models.

Although the first UVOIR data of GW170817 were obtained at 11 hr, the early data suggest that UV and blue optical emissions peak before this time. In our fiducial model, UVW1 and optical g-band magnitudes peak at t ∼ 4.3 and 16.8 hr, respectively (Figure 11). When the ejecta is enveloped by a thin outer layer, with a density slope n = −10, the UVW1 magnitude peaks earlier, reaching a value of −15.7 mag at t ∼ 2.4 hr (Figure 12). Figure 13 shows the expected observed magnitudes in UV and optical g band at 200 Mpc. The UVW1 and g-band magnitudes at 200 Mpc reach apparent magnitudes of ∼20.5 and 19.8 mag, respectively, at the peak time.

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The early UV signals are bright enough to be detected by existing facilities like Swift (Roming et al. 2005), which has a limiting magnitude of 22 mag for an exposure time of 1000 s (Brown et al. 2014), if a counterpart is discovered early enough to start UV observations promptly. A more promising detection method is via wide-field survey observations in the UV wavelengths, as UV emissions peak earlier than optical emissions. Upcoming wide-field surveys, such as those carried out by the Ultraviolet Transient Astronomy Satellite (ULTRASAT; Sagiv et al. 2014), which can detect down to the AB magnitude of about 22.4 mag in 900 s, are able to detect the expected signal from our fiducial model even at 500 Mpc distance.