On the central engine of the fastest-declining Type I supernova SN2019bkc

TL;DR

This paper presents an analytic model for SN2019bkc, a rapidly declining Type I supernova, attributing its light curve to magnetic dipole radiation from a non-explosive white dwarf merger remnant.

Contribution

It introduces a novel model linking the supernova's light curve to the viscous evolution of a white dwarf merger remnant's magnetic dipole radiation.

Findings

The model explains the rapid decline in brightness.

The viscous evolution timescale matches observed light curve features.

Magnetic dipole radiation from the remnant accounts for energy supply.

Abstract

An analytic model is presented for the fastest-declining Type I supernova SN2019bkc. The model of the central engine consists of the magnetic dipole radiation from a non-explosive remnant of a double white dwarf merger. We consider the viscous evolution of the rotating remnant, which may lead to the diminishing energy supply in an appropriate time scale for the light curve.

Equations

$$\dot{R}=\kappa {\alpha }^2\sqrt{\frac{GM}{R}}$$

$$R(t)=R(0){\left(1+{\alpha }^2\kappa \sqrt{\frac{GM}{R(0{)}^3}}t\right)}^{\frac{2}{3}}.$$

$$L(t)$$

Full text

On the central engine of the fastest-declining Type I supernova SN2019bkc

Shin’ichirou Yoshida

yoshida@ea.c.u-tokyol.ac.jp

Department of Earth Science and Astronomy, Graduate School of Arts and Sciences, The University of Tokyo

3-8-1 Komaba, Meguro-ku, Tokyo 153-18902, Japan

supernovae: individual (SN 2019bkc)

1

Chen et al. (2019) recently reported observations of a transient (SN 2019bkc/ATLAS19dqr) which has been identified as a type I supernova with the shortest declining time. Here I propose a simple model that explains the light curve of the transient whose central engine is a remnant of non-explosive merger of double white dwarfs. The light curve is modeled by the magnetic dipole radiation of the highly magnetized remnant.

Our model is based on the evolution scenario of a double dwarf merger described by Shen et al. (2019). If a merger of a white dwarf binary resulting from gravitational wave radiation is not directly followed by a violent merger explosion(Pakmor et al., 2012), a highly differentially rotating remnant may remain which evolves in viscous time scale $t=10^{4}-10^{8}$s after the merger, depending on the strength of the viscous mechanism. The viscosity induces exchanges of the angular momentum inside the star resulting in a slower and uniform rotation. Meanwhile it heats and puffs the star up. The merger may lead to the formation of a strong magnetic white dwarf (Garcia-Berro et al., 2012). We assume a strong magnetic field of order $10^{9}$G is established in the initial dynamical phase of the remnant. In the viscous evolution phase, the virial theorem holds and the kinetic energy dissipation $\delta T$ into heat $\delta Q$ is related to the increment of gravitational energy $\delta W$ and the internal energy $\delta U$ as $\delta W+\delta U=-2\delta T=2\delta Q$ , where we assumed adiabatic index $\gamma=4/3$. From the mass conservation, the radius of the star is then $GM^{2}/R^{2}\dot{R}=\dot{Q}$ where the overdots represent time-derivatives. We assume the viscosity is expressed by ”alpha” prescription(Shakura & Sunyaev, 1973) thus $\dot{Q}=4\pi\bar{c_{s}}/3\gamma\alpha^{2}\bar{p}R^{2}$. Here $\bar{c_{s}}$ and $\bar{p}$ are averaged sound speed and pressure. Thus we have $\dot{R}=\beta R^{4}/(GM^{2})\alpha^{2}\bar{c_{s}}\bar{p}$ where $\alpha$ is the ’alpha’ parameter of viscosity (Shakura & Sunyaev, 1973) and $\beta$ is the factor of order unity. By assuming hydrostatic equilibrium, we have $\bar{p}\sim GM\bar{\rho}\lambda/R$ and $\bar{c_{s}}\sim\sqrt{GM\lambda/R}$ where $\lambda$ is the ratio of average pressure to the maximum and $\bar{\rho}=3M/4\pi R^{3}$ . Finally we see how the radius changes as

[TABLE]

where $\kappa$ is a factor of the order of unity. The solution of Eq.(1) is

[TABLE]

Next we consider the central engine. The remnant conserves its total angular momentum in the viscous phase, thus $R(t)^{2}\Omega(t)=R(0)^{2}\Omega(0)$. On the other hand from the magnetic flux conservation we have $B(t)R(t)^{2}=B(0)R(0)^{2}$ where $B(t)$ is the surface magnetic field. Assuming the magnetic dipole radiation to be the central engine, we have the luminosity$L(t)$ from the magnetic dipole $\mu$ rotating at $\Omega$ as

[TABLE]

where we have used Eq.(2).

In Fig.1 we plot the light curve of Eq.(3) as well as the data points from Fig.4 of Chen et al. (2019). A model that reproduces the light curve well has a typical parameter of rapidly rotating (rotational frequency$\sim 0.5$Hz) and highly magnetized star ($B(0)\sim 10^{9}$G) with the viscosity’s $\alpha$ parameter to be ${\cal O}[10^{-3}]$ (since $\kappa$ is of order unity). Notice that the Kepler limit of spherical star is $f_{0}\sim 0.67$Hz for these parameter set. With the higher (lower) magnetic field a star has a higher (lower) luminosity. With the larger (smaller) $\alpha$ parameter the luminosity decreases more rapidly (slowly). The dependence of the curves on the stellar mass is weak. Finally, without the remnant’s evolution being taken into account, the magnetic dipole radiation has a too long decay time to explain the observed light curve. The decay time scale $\tau$ of the radiation from a rotating magnetic dipole with fixed strength is estimated as $\tau~{}(\rm{d})=\frac{3c^{3}I}{4m_{\perp}^{2}\Omega_{0}^{2}}\sim\frac{3c^{3}}{10}MR^{-4}B^{-2}\Omega_{0}^{2}\sim 3\times 10^{7}(\frac{M}{M_{\odot}})(\frac{R}{0.01R_{\odot}})^{-4}(\frac{B}{10^{9}G})^{-2}(\frac{f_{0}}{1Hz})^{-2}.$

The central engine of our model is a rotating magnetic dipole, which may be reminiscent of a recently proposed engine for an X-ray transient powered by a newly-born magnetar (Xue et al., 2019). There the spin-down luminosity is the energy source of a transient. In the current case, the decline of the luminosity cannot be explained solely by the spin-down of the fixed strength of dipole. In our model the rapid decline of luminosity results from the weakening of surface magnetic field and from the spinning down of the star. Both of the factors are outcomes of the thermal expansion of the star due to the viscous heating, whose energy source is the rapid differential rotation of the remnant.

This study is supported by JSPS Grant-in-Aid for Scientific Research(C) 18K03641.