Polarization Signature of Companion-Fed Supernovae Arising from BH-NS/BH Progenitor Systems

Since the groundbreaking detection of the first gravitational wave (GW) event, GW150914 (Abbott, 2016), emanating from the merger of a binary-black-hole (BH-BH) system, the LIGO and Virgo scientific collaborations, which are now complemented by KAGRA (Akutsu, 2021), have confirmed the occurrence of a total of 90 compact binary-system mergers during the initial three observing runs (Abbott, 2021a, b), among which are two binary-neutron-star (NS-NS) mergers (namely, GW170817 (Abbott, 2017a, b) and GW190425 (Abbott, 2020)), various possible black hole-neutron star (BH-NS) mergers (Abbott, 2021a), as well as a large number of BH-BH mergers. With the onset of the fourth observing run (O4), the LIGO-Virgo-KAGRA collaboration (LVKC) has entered a phase of regular gravitational wave observations.

At present, the formation channel of the BH-NS/BH system is still under debated. There are mainly two scenarios for the formation of BH-NS/BH systems, one of which is the isolated binary evolution in the galaxy fields (Tutukov & Yungelson, 1973; Lipunov et al., 1997; Belczynski et al., 2016), and the other is the dynamical interaction in dense environments (Sigurdsson & Hernquist, 1993; Portegies Zwart & McMillan, 2000; Rodriguez et al., 2015). In the binary evolution scenario, the faster evolving star is first to produce a BH through core collapse, and forms a BH - massive star binary. The second core collapse event after a certain time delay will then result in the formation of the BH-NS/BH system.

Gao et al. (2020) proposed that the formation of a BH-NS/BH system through isolated binary evolution might be accompanied by a special supernova due to the accretion process of the first-formed companion BH (henceforth companion-fed SN). In this scenario, the companion BH injects additional energy into the supernova ejecta through the Blandford-Payne (BP) mechanism (Blandford & Payne, 1982), resulting in a sharp peak in the lightcurve with luminosity even up to the level of superluminous supernovae (SLSNe), or a plateau feature compared to the regular luminosity of core collapse SNe. The non-spherical injection of energy from the BP mechanism imparts a heterogeneous luminosity distribution on the photosphere surface of the supernova ejecta, with the highest concentration of energy observed in the equatorial direction. This phenomenon has the potential to induce polarization signals, and the origin of these polarization signals differs from the classical cause of polarization, which arise from a non-spherical photosphere (Shapiro & Sutherland, 1982; Höflich, 1991; Höflich et al., 1996; Dessart & Hillier, 2011; Bulla et al., 2015), the blocking effect of absorbing material above the photosphere (Kasen, 2003; Hole, 2010; Tanaka et al., 2017), and the existence of an off-center radiation source (Höflich et al., 1995).

In this work, we develop a 3-dimensional (3D) Monte Carlo polarization simulation code (MCPSC) to calculate the continuum polarization properties of the companion-fed SNe. The primary objective is to advance the identification of such kind of distinctive SNe through polarization observations in the future, leading to a better comprehension of the generation channel of the BH-NS/BH systems.

We performed radiative transfer simulations using MCPSC code and collected photons along the line of sight (LOS) direction to obtain the spectral and polarizing features of the SNe. Figure 4 shows the emergent spectra for Case A and Case B at a distance of 10 pc from the source, when the SN is observed with the viewing angle $\theta_{\rm los}$ $=90^{\circ}$. In Case A, the flux density only slightly increases with a greater $\theta_{\rm BP}$ in the optical band, while in Case B, the increasing of flux density with a greater $\theta_{\rm BP}$ is obvious at $t\sim 50-80$ days (plateau phase). The emergent spectra observed along different LOS directions for a given $\theta_{\rm BP}$ at different observing time are shown in Figure 5. Overall, under the same $\theta_{\rm BP}$ and with same observing angle $\theta_{\rm los}$, the spectrum of the SN in Case B, due to its relatively lower effective temperature, would be redder than that in Case A.

Then, we discuss the continuum polarization property for the SNe in Case A and Case B separately. The radioactive-decay process uniformly heats the ejecta in regions I and II, which itself might power an isotropic thermal radiation from the photosphere. The BP mechanism could provide additional internal energy to region I , making thermal radiation from region I significantly brighter than that from region II, breaking the isotropy. Considering that a photon packet experiences one or several times of scattering, and is finally collected by the observer, its polarization property might have changed. Since the SN envelope is assumed to be spherically symmetric, for an observer with arbitrary viewing angle, there would always be two directions, from which the two photon packets should have opposite polarization properties and finally can be cancelled out by each other. However, because more photons will be released from the photosphere in region I than region II, usually the polarization cannot be totally cancelled out.

In case A, near the peak of the SN, the contribution to the total luminosity from region I, is much higher than that from region II. Their significant difference in luminosity serves as the main reason for the emergence of continuum polarization, which highly depends on the the viewing angle ($\theta_{\rm los}$) and the opening angle of region I ($\theta_{\rm BP}$). Denote the polarization degree as $P=Q/I$, where the Stokes vector $U$ is 0 due to symmetry. We calculate the continuum polarization properties produced at 39 days after the SN explosion, as shown in Figure 6. Here we choose $\theta_{\rm BP}=(15^{\circ},30^{\circ},45^{\circ},60^{\circ},75^{\circ})$ and a series of $\theta_{\rm los}$ from $0^{\circ}$ to $180^{\circ}$. This case allows to produce a significantly polarized signal in some conditions, with a maximum continuous polarization degree ($P_{\rm max}$) as about $\sim 2\%$ when $\theta_{\rm BP}=15^{\circ}$ and $\theta_{\rm los}=90^{\circ}$. $P$ decreases as $\theta_{\rm BP}$ increases and approaches a maximum when the luminosity is mainly distributed near the equator like $\theta_{\rm BP}=15^{\circ}$. The continuum polarization tends to be approximately zero at $\theta_{\rm BP}\geq 75^{\circ}$ where the luminosity becomes quasi-isotropic. On the other hand, with a fixed $\theta_{\rm BP}$, the polarization degree peaks at $\theta_{\rm los}=90^{\circ}$ (near the equator). This is because the projection area of region I in the LOS direction is the largest at around $\theta=90^{\circ}$, where the contribution from the high luminosity part with significant polarization to the finally observed SN signal reaches the maximum. As the LOS gets closer to the polar direction, the polarization degree gradually decreases and eventually falls to $0\%$.

The evolution of the polarization degree with time is shown in Figure 7. As the BP mechanism gradually dominates the SN emission, $P$ also increases with time and reaches a maximum value at the light curve’s peak, after which the $P$ decreases with time since the BP power decays faster than the radioactive power. We calculate the polarization degrees at 25, 39, 50, 60, 80 and 100 days after the SN explosion. For comparison purposes, we also consider the conditions with $\theta_{\rm BP}=(15^{\circ},30^{\circ},45^{\circ},60^{\circ},75^{\circ})$. Here we fix the viewing angle as $\theta_{\rm los}=90^{\circ}$ to make the polarization as recognizable as possible. Even so, for large $\theta_{\rm BP}$ (i.e. $\theta_{\rm BP}\geq 80^{\circ}$), we find it is difficult to identify the evolution of polarization degree with time, because $P$ is too close to $0\%$ after the peak of the SN light curve. The cases with different $\theta_{\rm BP}$ have the similar evolving trend.

In Case B, the BP effect only becomes dominant at at a later time when the radioactive power has significantly decayed. Therefore, the polarization degree of the SN signal should also be higher in the plateau phase in Figure 2, when the non-isotropy of the luminosity arises. Again, we firstly study the continuum polarization property for the signal at a certain time with different $\theta_{\rm BP}$ and $\theta_{\rm los}$. Then, study the evolution of the polarization degree with time. Figure 8 shows the $P$ value’s dependence on $\theta_{\rm BP}$ and $\theta_{\rm los}$, at $39$ days after the SN explosion. Similar to that in Case A, we calculated the $P$ values under different $\theta_{\rm BP}$ and $\theta_{\rm los}$ values. Generally, $P$ values tend to be smaller than that in Case A, because the luminosity in the two regions have the same order of magnitude. For a given LOS direction, in the absence of very significant brightness differences between the two regions on the photosphere, the polarization level depends mainly on the geometric distribution of the polarization vector in the projection plane, which is determined by $\theta_{\rm BP}$. At $\theta_{\rm BP}=15^{\circ}$, $P_{\rm max}$ can reach about $0.7\%$, which is smaller than the $P_{\rm max}\sim 2\%$ in Case A, but still may be identified in observation. The dependency of $P$ on factors $\theta_{\rm los}$ and $\theta_{\rm BP}$ is evident, with higher $P$ values predominantly observed for lower values of $\theta_{\rm BP}$ and at observation angles near the equator (approximately $\theta_{\rm los}\pm 90$). Figure 9 reveals the time evolution of P, showing how it behaves as a time-delayed feature after the supernova explosion. At the beginning of the explosion, $P$ remains at a low level because the BP mechanism had not yet produced a significant feedback effect. As the light curve enters the plateau phase, polarization starts to be generated and reaches its peak with the enhancement of the BP feedback and the weakening of the radioactive decay heating. After the peak, both of the powers decline and $P$ starts to decrease as a result.

Further, we test the impact of non-spherical ejecta structures on observed polarization levels. In principle, a non-spherically symmetric ejecta could generate an additional polarization signal due to geometric effects. In some cases, the ejecta along the polar direction may experience faster expansion due to the strong jet-energy injection (Soker, 2022). There is another possibility that, when the BP mechanism is the main contributor to the energy in region near equator, the ejecta in this region may expand faster than that along the polar direction. Therefore, the envelope could either have a prolate ellipsoidal or oblate ellipsoidal shape, whose geometry can be generally described as

where the prolate elliptic and oblate elliptic geometries can be defined respectively in cylindrical coordinates as

We adopt the axis ratio as $A_{1}=A_{2}=0.8$ and calculate the continuum polarization at 39 days after the supernova explosion under the conditions of Case A and Case B, respectively. Figure 10 illustrates the results of $P$ for the oblate ellipsoid case at different viewing angles $\theta_{\rm los}$ with $\theta_{\rm BP}=45^{\circ}$. To facilitate a comprehensive comparison, we evaluate the polarization signal solely generated by the distorted geometry for the ejecta, under the energy input from radioactive element decay (red line in Figure 10), and the polarization signal fully resulting from the BP mechanism in the region I (green line in Figure 10). The polarization signal from the BP mechanism appears as a double-humped profile over the viewing angle due to the effect of the ejecta geometry distortion (reaching a maximum value of $P$ at around $90^{\circ}\pm 30^{\circ}$). In Case A, the observed polarization is dominated by the BP mechanism, despite the fact that non-spherical ejecta could produce highly polarized signals with opposite signs. However, in Case B, the polarization signal mainly comes from the geometric effect because the luminosity from the BP mechanism is smaller than that from the decay of radioactive elements. The presence of the BP mechanism could further weaken the polarization level from the geometry distortion. The polarization from the prolate ellipsoid is significantly different from that from the oblate ellipsoid (as shown in Figure 11). The prolate ellipsoidal ejecta geometry could have the same sign as the polarization signal generated by the BP mechanism, which implies that these two effects can be mutually reinforcing (Case B in Figure 11). In Case A, the polarization is completely dominated by the BP mechanism. In general, the observed polarization levels depend mainly on the total contribution of the two polarization-generating channels, the ejecta’s geometric distortion and the BP mechanism. Although the polarization could be generated only by the ejecta’s geometric distortion, BP mechanism would bring more variability.

In this study, we propose that a SN that is fed by a companion compact star would exhibit non-uniform distribution of luminosity on its photosphere. This can be attributed to the BP mechanism, which serves as a crucial mechanism for accretion feedback, leading to heating of the SN ejecta along the equatorial direction within a confined opening angle ($\theta_{\rm BP}$). We find that the non-uniform distribution of luminosity may serve as a promising novel source of polarization. This is a distinct phenomenon from the well-established factors, such as variations from spherically symmetric photospheres (Shapiro & Sutherland, 1982; Höflich, 1991; Höflich et al., 1996; Dessart & Hillier, 2011; Bulla et al., 2015), the presence of obstructing materials at the photosphere (Kasen, 2003; Hole, 2010; Tanaka et al., 2017), and the existence of off-center radiation sources within the ejecta(Höflich et al., 1995).

The characteristics of the polarization signal for a engine-fed SN depends mainly on the properties of the binary system, the half-opening angle of the radiative region, and the viewing angle. Firstly, the distance between the binary orbits actively influences the polarization degree level and time-evolving characteristic by impacting both the accretion rate and the accretion start time of the companion BH. When the binary is close, the heating power produced by the BP mechanism is much higher than that from the radioactive decay. Consequently, observers in the equatorial direction could witness a significant continuum polarization level in the early days of the supernova explosion. However, as the distance between the binary stars increases, the polarization level gradually diminishes, and the peak polarization occurs at later times. Moreover, for a given line of sight, smaller radiation cone opening angles, which represent the region where accretion feedback acts upon the ejecta, are more likely to generate higher levels of polarization. This is because the energy from the accretion feedback is more concentrated into the projectile, resulting in more significant differences in the photospheric surface luminosity. Lastly, the viewing angle adds another layer of complexity in determining the level of polarization. Distinct polarization features are observed from various LOS directions, with the maximum polarization occurring at $\theta_{\rm los}=90^{\circ}$ and the minimum polarization occurring at $\theta_{\rm los}=0^{\circ}$. While parameter degeneracy is more likely to occur at low $P$ values, systems with larger $P$ values will exhibit a more prominent angular dependence, indicating the polarimetry as a potential tool to probe angle-dependent information (Bulla, 2022).

In addition, we also consider that the engine-fed SN ejecta may also be susceptible to distortion, resulting in a non-spherical shape. In this scenario, the extent of observed polarization is reliant on the interplay between the two channels responsible for generating polarization, as each channel vies for dominance in determining the overall polarization. Specifically, in the context of an oblate ellipsoidal geometry, the polarization direction caused by geometric distortion is antipodal to that produced by non-uniform luminosity. As a result, the net polarization degree is subject to cancellation between these two channels. On the other hand, polarization generated by geometric distortion in the prolate ellipsoidal geometry aligns with that generated by non-uniform luminosity, amplifying the overall polarization degree.

We need to point out that there are still some uncertainties in the results of this work, which would require future complex numerical simulations to fully address. For instance, although there may be cases where a mild transition between two radiation zones will not have a clear demarcation line, it remains valid to consider these cases by assigning specific $\theta_{\rm BP}$ values and $L_{\mathrm{heat},\mathrm{I}}$/$L_{\mathrm{heat},\mathrm{II}}$. On the other hand, the distribution of ⁵⁶Ni within the ejecta may not be uniform in practical situations. This non-uniform distribution can have a direct impact on both the magnitude and spatial distribution of luminosity, consequently affecting the observed polarization. Finally, if there is an intermittent black hole accretion process, or a slower rate of accretion as the black hole passes through the innermost ejecta, the lightcurve would be more complex (Gao et al., 2020). The polarization, which is dependent on luminosity variations, would then oscillate over time or have a shallower feature of magnitude at peaks or plateaus.

At present, significant progress has been made in the observation of supernova polarization (Brown et al., 2016; Inserra et al., 2016; Cikota et al, 2018; Lee, 2019, 2020; Leloudas et al, 2015, 2017; Maundet et al, 2019; Maund et al, 2020, 2021; Saito et al, 2020). In future surveys, companion-fed SNe could be effectively searched for through the combination of their unique photometric behavior and special polarization properties. Comparing the event rate density of these special SN signals with the event rate density of LIGO-Virgo detected BH–NS/BH systems could help to distinguish the BH–NS/BH formation channel.