Luminosity source in supernova ASASSN-15nx with long linear light curve

TL;DR

This paper proposes a novel luminosity mechanism for supernova ASASSN-15nx involving neutron star magnetosphere interaction, explaining its linear light curve and indicating an aspherical explosion with low ejecta mass.

Contribution

It introduces a new model for supernova luminosity based on neutron star magnetosphere interaction, differing from traditional radioactive decay or circumstellar interaction explanations.

Findings

Neutron star magnetosphere interaction can power the supernova luminosity.

The supernova has low ejecta mass (~1 solar mass).

The explosion was likely aspherical.

Abstract

The available spectra of the anomalous supernova ASASSN-15nx permit us to rule out the radioactivity and circumstellar interaction as the luminosity source. I propose an alternative mechanism for the ASASSN-15nx luminosity based on the interaction of the neutron star rotating magnetosphere with the gravitationally bound material of the envelope ejected by the shock wave. In the regime of the stationary accretion the rotational frequency decreases exponentially with time, which could account for the linearity of the light curve. The modelling of the light curve at the stage of the luminosity rise in combination with the expansion velocity implies the low mass of ejecta, ~ 1 M_{\odot}. The profile of the [O\,I] 6300, 6364\,\AA\ doublet indicates the asphericity of the oxygen distribution, which in turn suggests the aspherical explosion.

Tables

Model	$v_1$	$v_2$	$i$	${\mu }_0$	$\chi$	$A$
ER	1500	3200	70	0.6	6	1
PC1	1400	2800	20	0.6	2.8	0.38
PC2	1300	2900	19	0.5	2.8	0.7
PC3	1400	2800	19	0.5	2.8	0.6

Parameter	Units	Value
$R_{ns}$	km	12
$I$	${10}^{45}$ g cm2	1
$\mu$	${10}^{30}$ G cm3	51.8
$P_0$		0.011
$\dot{m}$	${10}^{23}$ g s-1	1.5

Equations

$$I\omega \dot{\omega }=-(1/2)\dot{m}(r_m\omega {)}^2.$$

$$dE/dt=-E/t-E/t_e+L_p.$$

Full text

The available spectra of the anomalous supernova ASASSN-15nx permit us to rule out the radioactivity and circumstellar interaction as the luminosity source. I propose an alternative mechanism for the ASASSN-15nx luminosity based on the interaction of the neutron star rotating magnetosphere with the gravitationally bound material of the envelope ejected by the shock wave. In the regime of stationary accretion the rotational frequency decreases exponentially with time, which could account for the linearity of the light curve. The modelling of the light curve at the stage of the luminosity rise in combination with the expansion velocity implies the low mass of ejecta, $\sim$1$M_{\odot}$. The profile of the [O I] 6300, 6364 Å doublet indicates the asphericity of the oxygen distribution, which in turn suggests the aspherical explosion.

*Institute of Astronomy of Russian Academy of Sciences, Moscow

Keywords: stars - evolution, supernovae, neutron stars

∗ email: $<$nchugai@inasan.ru$>$

1 Introduction

The anomalous type II supernova ASASSN-15nx (Bose et al. 2018) with the maximal magnitude $M_{V}\approx-20$ demonstrates unusual light curve that is characterized by a perfect, as authors emphasise, linear decline (2.5 mag per 100 d) during long period of 250 days. This peculiarity has no counterpart among SNe II, including SNe IIL. Such a light curve cannot be an outcome of the diffusion cooling of the explosion energy: the long-lasting source of energy is required. In the original paper authors propose two possibilities: (i) 1.6$M_{\odot}$ of the radioactive 56Ni in the 2$M_{\odot}$ ejecta; (ii) the energy released in the circumstellar (CS) interaction (Bose et al. 2018). Generally, both mechanisms can operate in SNe II and either could be a contender for the power source in ASASSN-15nx.

A conjecture on the nature of the energy source in ASASSN-15nx, however, requires verification. A top priority is the examination of possible spectral effects that accompany a certain mechanism. Note that the spectral verification was not a subject of the original paper. It is essential therefore to make up for the lack of this study, which is one of goals of this paper addressed in the next section. As will become clear, the spectra reveal serious difficulties both for radioactive mechanism and for the CS interaction. I will propose an alternative mechanism that, under minimum of assumptions, is able to account for the luminosity and the linear light curve of ASASSN-15nx.

Below I use the explosion moment and distance following Bose et al (2018).

2 Interpretation of ASASSN-15nx spectra

2.1 Lines identification

Spectra of ASASSN-15nx taken between days 53 and 262 after the explosion (Bose et al. 2018) look like a set of emission lines on the quasi-continuum composed by numerous metal lines (Fig. 1). The dominant emission line are H$\alpha$ (detail $b$), triplets of Ca II 8600 Å ($g$) and O I 7774 Å, ($e$), doublets of Na I 5892 Å ($a$), and [Ca II] 7300 Å ($d$). Late time spectra show doublet [O I] 6300, 6364 Å. All these lines lie in the red part of the spectrum that will be addressed below. Some unusual features of the spectra has been already noted by Bose et al. (2018), particularly, two-component structure of O I 7774 Å profile on day 53. Yet several interesting detailes, central to understanding of the energy source, remained beyond the scope.

Since the line identification is hampered by the non-local scattering in line blends as well as the Thomson scattering we rely on the synthetic spectrum that takes into account both effects. The model suggests spherical envelope with the homologous expansion, $v=r/t$. The line intrinsic emissivity is set in the parametric form $j=j_{0}/[1+(v/v_{0})^{k}]$. The line Sobolev optical depth is set by the similar distribution but with a different power index $k$. At the certain age parameters $v_{0}$ and $k$ are the same, except for oxygen lines. The continuum emissivity is distributed in the same way. The electron distribution is set assuming the recombination origin of H$\alpha$ as $n_{e}\propto\sqrt{j(\mbox{H}\alpha)}$.

The Thomson optical depth on day 53 is estimated from the H$\alpha$ with the spectrum fluxed on the bases of the photometric data (Bose et al. 2018). The inferred H$\alpha$ luminosity at this age is $L=7\times 10^{39}$ erg s*-1*. When combined with the H$\alpha$ profile this value results in the Thomson optical depth $\tau_{\sc T}=1.3$. The found electron distribution is used for the synthetic spectrum on day 53. The spectrun is computed by the Monte Carlo technique. Note that we does not compute quasi-continuum produced by the emission of numerous metal lines; instead we adopt smooth continuum. This proviso should be taken into account when comparing synthetic and observational spectra.

I start with the two-component profile of O I 7774 Å on day 53 that was highlighted by Bose et al. (2018). The importance of this issue is emphasised by a possible relation with the oxygen asymmetry addressed below in a separate section. In fact, the two-component structure of O I 7774 Å on day 53 has nothing to do with the asymmetry; instead the red component should be attributed to Mg II 7877, 7896 Å emission lines. The presence of these lines is apparent also on day 87 as well (emission $e$); the same spectrum shows Mg II 8214, 8235 Å (emission $f$). Besides, Mg II 9218, 7896 Å together with O I 9261, 9266 Å constitute the emission 9250 Å (band $h$). All the identified lines of Mg II and O I with high contrast were identified earlier in SN Ibn SN 2006jc (Chugai 2009).

The ASASSN-15nx spectra at all phases show He I 7065 Å line (Fig. 1). This suggests that the He I 5876 Å line contributes to the Na I 5892 Å emission with the relative intensity $I(5876)/I(7065)$ in the range of 1… 2 judging by spectra of SN 2006jc (Anupama et al. 2009). The He I 5876 Å is included in all the synthetic spectra shown in Fig. 1.

2.2 The absence of [Co III] 5890 Å line

The radiactive mechanism for the ASASSN-15nx luminosity suggests 1.6$M_{\odot}$ of 56Ni in the low mass envelope, 2$M_{\odot}$ (Bose et al. 2018). The direct implication of this model should be a strong emission line of [Co III] 5890 Å at 70-150 days likewise in spectra of SNe Ia (e.g., SN 2011fe, SN 2014J, Bikmaev et al. 2015). Spectra of ASASSN-15nx indeed show 5890 Å emission (Fig.1, emission ”a”) that might belong to Co III. The problem with the Co III attribution is that emission does not show the expected significant decline with respect to Fe II blend in the range of 5000-5500 Å in the spectrum on day 262 (Bose et al. 2018) due to the radioactive decay of 56Co, — the effect always being present in SNe Ia. This obvious inconsistency implies that the radioactive mechanism for the ASASSN-15nx should be rejected.

In fact, the 5890 Å emission belongs to the Na I doublet that scatter the continuum and He I 5876 Å radiation; the latter line is scattered by sodium doublet due to the reddening in the comoving frame. This effect is included in the shown synthetic spectrum (Fig. 1). The adopted ratio of emissivities $j(5876)/j(7065)$ is 1, 1, and 2 in spectra on days 53, 87, and 165 respectively.

2.3 Absence of circumstellar interaction

Spectra of ASASSN-15nx reveal the Ca II 3934, 3968 Å broad absorption. This line on day 53 is shown in Fig. 1 (panelinset) together with the model profile. The model is specified by the emissivity distribution, the Sobolev optical depth, and the resonant photon loss probability $\epsilon_{13}=A_{32}\beta_{23}/(A_{31}\beta_{13}+A_{32}\beta_{23})$, where $A_{ki}$ is the rate of the spontaneous emission, $\beta_{ik}$ is the local escape probability, and indices 1, 2, and 3 denote 2S, 2D, and 2P therms. The doublet 3950 Å corresponds to 1-3 transition while triplet 8600 Å corresponds to 2-3 transition. For optically thick lines the $\epsilon_{13}$ value depends on the excitation temperature; for $T=6000$ K (cf. Bose et al. 2018) $\epsilon_{13}=0.7$. This value provides a significant conversion of 3950 Å doublet emission into the 8600 Å triplet emission. The doublet emissivity therefore can be set comparable to the intensity of the Ca II infrared triplet. However on day 53 the spectrum in the range of 8600 Å is absent. We therefore make use of the spectrum on day 87 in which the fluxes of Ca Å triplet and H$\alpha$ are comparable. Basing on this fact the doublet emissivity on day 53 is also set equal to that of H$\alpha$.

The presence of the deep absorption of Ca II doublet suggests that the background quasi-continuum forms in the inner zone of the envelope. This in turn indicates that the source of the ASASSN-15nx luminosity resides in the envelope interiors and not the outer layers. It is the latter that is expected in the mechanism of the CS interaction. The internal location of the luminosity source thus rules out the luminosity mechanism based on the ejecta collision with the dense CS envelope.

2.4 Oxygen and helium abundance

The high intensity of the oxygen triplet O I 7774 Å relative to H$\alpha$ on day 53, $F(7774)/F(\mbox{H}\alpha)\approx 0.5$, indicates high oxygen abundance. Indeed, similar ionization potentials of hydrogen and oxygen secure their comparable ionization, so for the comparable intensity of their recombination lines the total number of atoms of these elements should be relatively close. Taking into account the effective recombination coefficient for these lines (Pequignot et al. 1991) at the electron temperature of 6000 K (Bose et al. 2018) and assuming that oxygen and hydrogen are not mixed we find the mass of ionized hydrogen and oxygen to be 0.03$M_{\odot}$ and 0.12$M_{\odot}$ respectively. The ionization fraction cannot be reliably estimated. However, the presence of neutral Na suggests that the ionization fraction is far from unity. For the ionization fraction of 0.5 the hydrogen and oxygen mass are 0.06$M_{\odot}$ and 0.24$M_{\odot}$ respectively. Despite these estimates are crude, they indicate that the hydrogen mass is low (\sim 0.1$$M_{\odot}) and the oxygen mass is relatively high, at least several tenths of solar mass.

The intensity of a single He I 7065 Å line with respect to H$\alpha$ is approximately equal to 0.1. This is twice as high compared to the case of normal He abundance and similar ionization fraction of the hydrogen and helium. In reality, the helium ionization fraction is likely lower than that of hydrogen, so the helium abundance relative to hydrogen is higher.

2.5 Asymmetry of oxygen distribution

The profile of the observed [O I] 6300, 6364 Å doublet on day 165 significantly differs from the synthetic one in the range of radial velocities $|v_{r}|<2000$ km s*-1*(Fig. 1): the observed profile shows flat top with two peaks. The similar profile with even more pronounced peaks is seen in the spectrum on day 262 (cf. Bose et al. 2018). This sort of the oxygen doublet profile is inconsistent with the spherical picture and obviously related to the asphericity of the oxygen distribution.

To get an idea of the oxygen distribution I consider a model in which on the background of the spherically symmetric distribution of emissivity $j_{s}\propto 1/[1+(v/v_{0})^{k}]$ there is an additional non-spherical component, either the equatorial ring or bipolar caps with constant contrast $\chi=j/j_{s}$ in the velocity range $v_{1}<v<v_{2}$. Angular size of these components is set by the cosine of the polar angle $\mu_{0}$: $|\mu|<\mu_{0}$ for the equatorial ring and $|\mu|>\mu_{0}$ for the polar caps. The orientation is set by the inclination angle $i$. The adopted doublet ratio is 1:3 that corresponds to optically thin lines. Note, the finite optical depth of these lines worsen any axial model.

The modelling shows that the equatorial ring cannot reproduce the profile. The optimal model of equatorial ring (ER) for the line on day 165 (Fig. 2) is characterized by parameters given in Table 1. The ring is assumed to be axisymmetric, which corresponds to $A=1$, where $A$ is the parameter of the azimuthal asymmetry, i.e., the ratio of emissivities in the near and rear hemisphere. In fact, the profile indicates the azimuthal asymmetry. However, to reproduce this by the ring model one needs to suppress ring emission not only in the far hemisphere, but also at the limb. This sort of a deviation from the axial symmetry is convenient to describe by asymmetric polar caps (PC). On day 165 the model PC1 (Fig. 2, Table 1) reproduces the profile with the asymmetry parameter $A=j(\mbox{red})/j(\mbox{blue})=0.38$. On day 262 we show two version: with the constant continuum and the inclined continuum (PC2 and PC3 respectively). Models are almost identical which emphasises the robustness of the conclusion on the asymmetry of the oxygen distribution.

The fact that the significant fraction of the oxygen shows conspicuous angular and central asymmetry at the velocities 1300-3000 km s*-1* evidences for the significant explosion asymmetry that essentially affects oxygen ejecta. This sort of phenomena was never observed in SNe II, although some asymmetry in oxygen doublet related to the 56Ni asymmetry was detected in SN 2004dj (Chugai et al. 2005).

3 Light curve

After discarding radioactivity and CS interaction, we consider alternative possibilities: (i) rotational energy of a young magnetar and (ii) supercritical accretion onto a black hole. Magnetar mechanism with the luminosity defined by the formula of magneto-dipole radiation was employed earlier (Kasen & Bildsten 2010) for the interpretation of superluminous supernovae (SLSN). A problem with the application of this mechanism to ASASSN-15nx is evident: the power law decay of the magnetar luminosity is inconsistent with the observed exponential luminosity decay. The supercritical accretion onto a black hole generally cannot be rulled out. This mechanism was employed for the supernova iPTF-14hls (Arcavi et al. 2017, Chugai 2018). The exponential luminosity decay is expected, if the accretion rate declines exponentially. It is, however, not clear what physics might provide the required evolution of the accretion rate.

Yet another mechanism is conceivable that could account for the exponential luminosity decay. Suppose that the explosion of ASASSN-15nx was accompanied by the formation of a rapidly rotating neutron star with a strong magnetic field but with a relatively low magnetar luminosity. The process that might provide powerful energy release is the accretion of the gravitationally bound gas onto the rotating magnetosphere of the neutron star with mass $M$ and the rotation frequency $\omega$. The interaction of the magnetosphere with the accreating gas in the regime of a supersonic propeller could power the ASASSN-15nx luminosity. This scenario requires that for the magnetosphere with the magnetic momentum $\mu$ and the accretion rate $\dot{m}$ the magnetosphere radius $r_{m}=(\mu^{4}/8\dot{m}^{2}GM)^{1/7}$ should be less than the radius of the light cylinder $r_{lc}=c/\omega$ and be larger than the corotation radius $r_{c}=(GM/\omega^{2})^{1/3}$ (Shakura 1975, Davis et al. 1979). The maximum rate of the rotational energy loss is $L_{p}=(1/2)\dot{m}(r_{m}\omega)^{2}$ (Davis et al. 1979). With this luminosity the braking of the neutron star with the inertia moment $I$ is described by the equation (Shakura 1975):

[TABLE]

This equation shows that the constant accretion rate $\dot{m}=const$ implies the exponential braking $\omega=\omega_{0}\exp{(-bt)}$, where $b=0.5\dot{m}r_{m}^{2}/I$. The rate of the rotational energy loss follows the exponential law $L\propto\omega^{2}\propto\exp{(-2bt)}$ which could account for the linear light curve of ASASSN-15nx. The steady state accretion rate is thus necessary condition for the exponential decay of the luminosity in the proposed mechanism. It is noteworthy that the study of the fall-back after the supernova explosion admits a possibility of the stationary accretion regime on the time scale of one year (Chevalier 1989).

The complicated transformation of the energy generated by the propeller mechanism is left beyond the proposed scenario. It is conceivable that inside the expanding SN envelope 3-dimensional picture emerges that includes accretion flow and ejected plasma. The latter forms hot bubble ($T\sim 5\times 10^{9}$ K). The energy is transferred in the supernova envelope by X/$\gamma$-rays emitted by the hot bubble, although relativistic particles can also contribute. In the light curve modelling we assume that all the power of the propeller mechanism is deposited in the supernova envelope. The Table 2 contains the optimal set of parameters of the light curve model: the radius of the neutron star, the inertia moment, the magnetic moment, the initial rotation period, and the accretion rate. The magnetic moment corresponds to the equatorial magnetic field at the neutron star surface of $3\times 10^{13}$ G. The total mass involved in the accretion during 250 days is 1.6\times 10^{-3}$$M_{\odot}111The mass of gravitationaly bound ejecta can attain \sim 0.1$$M_{\odot} (Chevalier 1989)..

The present model does not depend on the mass $M_{ej}$ and kinetic energy $E_{k}$ of the supernova envelope. To get an idea about their values we consider a model of homogeneous ejecta with the radiation diffusion that is aimed at the description of the rising part of the light curve. The optical bolometric luminosity is calculated via the thermal energy $E$ and the radiation escape time $t_{e}$ as $L_{bol}=E/t_{e}$. The time $t_{e}$ is taken to be equal the average escape time for the photon emitted in the center of the homogeneous envelope $t_{e}=\tau R/2c$ (Sunyaev & Titarchuk 1980), where $R$ is the enevelope radius, $\tau$ is optical depth, and $c$ is the speed of light. The evolution of the thermal energy is determined by the energy equation

[TABLE]

The first term is adiabatic losses, the second is the bolometric luminosity, and the third is the luminosity of the propeller mechanism. The opacity is assumed to be Thomson opacity with the number of free electrons per barion $y_{e}=0.2$. This value is supported by the following arguments. The envelope with the mass of 1$M_{\odot}$, the kinetic energy of $10^{51}$ erg, and mass fraction of H, He, O respectively beng equal $x_{1}=0.1$, $x_{2}=0.1$, and $x_{8}=0.8$ at the maximum (14 d) is characterized by the equilibrium ionization $y_{e}=0.16$ for the effective temperature 10400 K. For somewhat different composition $x_{1}=0.1$, $x_{2}=0.4$, and $x_{8}=0.5$ we get $y_{e}=0.18$. Allowing for deep layers, where the ionization is higher, the value $y_{e}=0.2$ seems to be quite reasonable.

Apart from data on the bolometric luminosity (Fig. 3) we plot also photometry in $V$-band (Bose et al. 2018) that are matched to the bolometric light curve at the maximum. These additional data permit us to get an idea of the rising part of the light curve. We show two models (Fig. 3) with the different ejecta mass: 3$M_{\odot}$ with the kinetic energy $E_{k}=1.7\times 10^{52}$ erg and 0.5$M_{\odot}$ with the energy $E_{k}=1.5\times 10^{50}$ erg. Both models well reproduce the light curve. Note, the model light curve model does not include the narrow initial peak related to the shock breakout.

The uncertainty of the choice of the ejecta mass is eliminated if we take into account the expansion velocity. The evolution of the photosphere radius at the early stage (Bose et al. 2018) suggests the velocity at the photosphere $\approx 10^{4}$ km s*-1*. This value coinsides with the maximum velocity in the H$\alpha$ wings on day 53. The models shown in Fig. 3 are characterised by the maximum velocity of 31000 km s*-1* in the case of M_{ej}=3$$M_{\odot}  and 7100 km s*-1* in the case of M_{ej}=0.5$$M_{\odot}. Both velocities differ from the observational value $\approx 10^{4}$ km s*-1* in either side. The acceptable mass therefore should lie in the range 0.5<M_{ej}<3$$M_{\odot}. The optimal model with the maximum velocity of 10300 km s*-1*is characterized by the ejecta mass M_{ej}=0.7$$M_{\odot} and the kinetic energy $E_{k}=4.5\times 10^{50}$ erg.

Despite adopted approximations, the model of the early light curve indicates that the ejecta mass is low, \sim 1$$M_{\odot} and the kinetic energy is $E_{k}=(0.5-1)\times 10^{51}$ erg. Note that the constraints for the magnetosphere radius $r_{c}<r_{m}<r_{lc}$ hold for the considered model.

4 Discussion and conclusions

The spectra of the unusual supernova ASASSN-15nx with long linear light curve permits us to rule out the radioactive mechanism of the luminosity and the mechanism of the shock interaction with the dense CS envelope. The alternative mechanism proposed here suggests that the neutron star with strong magnetic field and fast rotation lose its rotational energy due to the interaction of the magnetosphere with the gravitationally bound ejecta in the propeller regime. In the case of the stationary accretion rate, the rotation energy loss decreases exponentially thus explaining the linear light curve. Deviations from the steady state accretion regime should bring about deviations from the linearity of the light curve which could be observed in other supernovae of this category.

The modelling of the initial rising stage of the light curve along with the ejecta expansion velocity lead to the ejecta mass estimate which turns out low, about 1$M_{\odot}$. Remarkably, the low mass is also indicated by the behavior of $B-V$ color. Accoding to data (Bose et al. 2018) $B-V$ rises the same way as in the case of SNe IIP. However, if for SNe IIP the rise span is  $\approx 100$ days, in the case of ASASSN-15nx the rise takes only $\approx 50$ days. Since the $B-V$ behavior reflects the envelope cooling in the photospheric regime, this means that for ASASSN-15nx the duration of the photospheric phase is twice as short compared to SN IIP. Given comparable expansion velocities this indicates significantly lower mass of ASASSN-15nx compared to SNe IIP. Combining the neutron star and ejecta we come to the preSN mass in the range of \sim 2-2.5$$M_{\odot}. Noteworthy that the hydrogen mass in the preSN was likely less then 10%.

A difficult question arises concerning the origin of ASASSN-15nx. In a single progenitor scenario the preSN should be a helium core with the leftovers of the hydrogen envelope. For the He core mass of 2.5$M_{\odot}$ the preSN presumably is the outcome of the evolution of a star with ZAMS mass about 10$M_{\odot}$ (Nomoto 1984). This scenario, however, does not admit the significant amount of the oxygen over the collapsing core, which contradicts to the presence of at least several tenth of solar mass of synthesised oxygen in ASASSN-15nx.

An alterantive evolutionary scenario for ASASSN-15nx suggests close binary that consists of ONeMg white dwarf (primary) and low mass star with CO degenerate core at the AGB stage. The evolution of this system might result in the merging of CO-core and ONeMg white dwarf with the subsequent collapse of the ONeMg white dwarf initiated by $e$-capture. The advantage of this scenario is that it could account for the presence of a significant amount of oxygen in low mass ejecta. The oxygen in this scenario is the result of the disruption of the CO-core of the secondary component during the merger. The remains of the hydrogen envelope of the secondary could explain the presence of the low amount (\sim 0.1$$M_{\odot}) of hydrogen in ASASSN-15nx ejecta. The merging scenario and related fast rotation could be the reason for the explosion asphericity indicated by the oxygen doublet.

5 Acknowledgement

I thank Konstantin Postnov, Lev Yungelson, Victor Utrobin for discussions, and Subo Dong for sharing the spectra of ASASSN-15nx.