Is FRB 191001 embedded in a supernova remnant?

Fast radio bursts (FRBs) are transient millisecond duration bright radio pulses of unknown origins (Lorimer et al., 2007; Petroff et al., 2019; Cordes & Chatterjee, 2019). The progenitors of these exotic events have been remained elusive since their discovery in the last decade. The millisecond duration of these bursts suggests that the emissions are likely originated from compact sources. This hypothesis is further strengthened by the discovery of galactic FRB 200428 in association with the magnetar SGR 1935+2154 (CHIME/FRB Collaboration et al., 2020; Bochenek et al., 2020; Mereghetti et al., 2020; Li et al., 2021; Ridnaia et al., 2021) that formed due to the collapse of a massive star (Gaensler, 2014).

The localisation of FRB sources and the identification of host galaxies are important in understanding their progenitors. Among the localised events, FRB 191001 is discovered at the spiral arm of a highly star-forming galaxy at a redshift of 0.234 (Bhandari et al., 2020). The observed dispersion measure (DM) of this FRB is 506.9  pc cm^-3 (Bhandari et al., 2020), which may have contributions from the i) host galaxy of the FRB (${\rm DM_{\rm host}}/(1+z)$, where $z$ is the redshift of the host), ii) intergalactic medium (${\rm DM_{\rm IGM}}$), and iii) our Milky Way Galaxy (${\rm DM_{\rm MW}}$). From the galactic models NE2001 (Cordes & Lazio, 2002) and YMW16 (Yao et al., 2017) the DM contribution from our Galaxy, toward the direction of this FRB, is ${\rm DM_{\rm MW}}=94$ and 81  pc cm^-3 (Bhandari et al., 2020), respectively. The contribution of the intergalactic medium (IGM) is ${\rm DM_{\rm IGM}}\simeq 203$  pc cm^-3 as estimated from Macquart et al. (2020). Likewise the DM redshift relation, which is ${\rm DM_{\rm IGM}}\approx 855z_{\rm max}$ (Zhang, 2018) with $z_{\rm max}$ being the maximum value of the redshift of an FRB, predicts a ${\rm DM_{\rm IGM}}\approx 210$  pc cm^-3 for the redshift of 0.234. This implies a contribution of the host galaxy ${\rm DM_{\rm host}}\approx 200\times(1+0.234)\approx 250$  pc cm^-3. The host DM will have contributions from the immediate surroundings of the burst and from other ionised media that are encountered by the pulse in the host galaxy. Since the source of this radio burst resides in the spiral arm of its parent galaxy, it is possible that a significant amount of this excess DM has been contributed by the former.

In the nuclear region of a starburst galaxy, the star formation rate (${\rm SFR}$) is related to the rate of the core-collapse (CC) supernova (SN) (symbolised as ${\rm R}_{\rm CCSN}$) in that galaxy. For a Salpeter initial mass function, with a presumption that stars with masses between 0.1 M_⊙ and 125 M_⊙ are formed in the galaxy, and those typically between 8 M_⊙ and 50 M_⊙ undergo CC explosions, it is easy to show that ${\rm R}_{\rm CCSN}={\rm SFR}($ ${\rm M_{\odot}\,yr^{-1}}$$)\times 7\times 10^{-3}~{}~{}yr^{-1}$ (Mattila & Meikle, 2001). In the case of FRB 191001, an ${\rm SFR}$ of 11.2  ${\rm M_{\odot}\,yr^{-1}}$ (Bhandari et al., 2020) implies that there are around 80 SN remnants in the host galaxy of FRB 191001 that are younger than 1000 yrs. The location of this burst in the spiral arm, the excess DM and the prevalence of SNe in its parent galaxy give us a unique opportunity to explore the origin of this FRB. In the following section, we compare the position of FRB 191001 with the distribution of SNe in the spiral arm of their host galaxies. In $ 3 the evolution of DM and rotation measure (RM) when a radio wave propagates through an SN remnant are reviewed. The paper is closed with a discussion given in $ 4.

Aramyan et al. (2016) has given a sample of 215 SNe of different types in the spiral arm of their host galaxies, which we consider for this study. The coordinates of the host galaxies and SNe, and their redshifts are obtained using the SkyCoord class method from Astropy (Astropy Collaboration et al., 2013, 2018), from the NASA Extragalactic Database (NED)¹¹1https://ned.ipac.caltech.edu and bright SN catalog²²2https://www.rochesterastronomy.org/snimages/snredshiftall.html. Among the 215 entries, redshift information for 12 objects is not available in the literature. Besides, due to the large positional uncertainty of an SN event in its host galaxy that object is removed from our study. For the rest of the 202 SNe, the normalised distribution of the projected distance from the centre of their respective host galaxies is shown in the left panel of Fig.1. Out of these 202 SNe, 139 are CC events while the rest is thermonuclear explosions (Type Ia). Among the 139 CC SNe, 116 are Type II and the rest belongs to Type Ib/c. The different types of SNe are shown with different colours in Fig.1. For the sub-classes, the histograms are plotted such that the sum of the area under CC (II+Ib/c) and Ia is one. The overall distribution is fitted with a log-normal function which is exhibited with a blue dashed curve. The functional form of this function is

where $\mu$ and $s^{2}$ are the expected value and the variance of the variable’s natural logarithm. As a result, the mean and the standard deviation of the distribution are calculated as Mean $={\rm exp}(\mu+s^{2}/2)$ and $\sigma=\sqrt{[{\rm exp}(s^{2})-1]{\rm exp}(2\mu+s^{2})}$. From the fitting, the Mean and $\sigma$ of the SN distribution are estimated to be 10.2 kpc and 11 kpc, respectively. The cumulative distributions of different types of SNe along with the log-normal model are shown in the right panel of Fig.1. In both panels of Fig 1 the black star represents the position of FRB 191001, which is at a projected distance of around 11 kpc from the centre of its host galaxy (Heintz et al., 2020). The cumulative distributions demonstrate that around 70% of SNe has offset $\!\!\!\phantom{\leq}\smash{\buildrel\over{\lower 2.67502pt\hbox{$\buildrel\lower 2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,11$ kpc. The analysis of this section illustrates that the position of FRB 191001 is consistent with the distribution of SNe in the spiral arm of their parent galaxies.

Motivated by the results of §2, in this section, we study whether the DM and RM contributions due to CC and Ia events are compatible with the excesses observed for FRB 191001. When a source of an FRB is embedded in an SN remnant, the following contributes to the total DM: firstly, the ionised unshocked ejecta; secondly, the shocked shell that contains the shocked ejecta and the shocked circumstellar medium (CSM); and finally, the unshocked ionised CSM. For an SN with a constant density profile ($\rho_{\rm ej}(r)$) for $r<r_{\rm brk}$, where $r_{\rm brk}$ represents the radius corresponding to the break velocity $v_{\rm brk}$, the DM of the ionised ejecta decreases as $t^{-2}$ for a homologous expansion. In the case of the outer part of the ejecta, $\rho_{\rm ej}(r)\propto r^{-n}$ , with $n\sim$ 10 (Matzner & McKee, 1999; Kundu et al., 2017) being the power-law index of the density profile for $r>r_{\rm brk}$. For the shocked shell, the DM is ${\rm DM}_{\rm sh}=\int_{r_{\rm rev}}^{r_{s}}n_{e}(r)dr=\int_{r_{\rm rev}}^{r_{c}}n_{e}^{\rm rev}(r)dr+\int_{r_{c}}^{r_{s}}n_{e}^{s}(r)dr$, where $n_{e}^{\rm rev}(r)$ and $n_{e}^{s}(r)$ represent the electron density of the shocked ejecta and the shocked CSM, respectively. $r_{s}$, $r_{\rm rev}$ and $r_{c}$ are the radii of forward shock, reverse shock and contact discontinuity, respectively. The total contribution due to the shocked shell in the free-expansion (FE) phase is

(for details see Kundu & Ferrario (2020)), where the SN interacts with a wind-like or a constant density ambient medium. The density of the CSM can be written as $\rho_{\rm csm}=Ar^{-s}$, with $s=$ 2 (0) and $A=\dot{M}[4\pi v_{w}]^{-1}$ $(\mu m_{p}n_{\rm{ISM}})$ for a wind-like (constant density) medium. Here, $\dot{M}$ and $v_{w}$ represent the mass-loss rate from the pre-SN star and wind speed at which matter was ejected from the system. $\mu$ and $n_{\rm{ISM}}$ are the mean atomic weight and particle density of the ambient medium, respectively. $m_{p}$ represents the mass of a proton. $D=\xi v_{\rm brk}^{n}/A$ with $\xi$ being a constant. For $\beta=r_{\rm rev}/r_{c}$ and $\alpha=r_{s}/r_{c}$, $\phi_{\rm csm}=(\alpha^{1-s}-1)$ and $\phi_{\rm ej}=~{}\frac{(n-3)(n-4)}{(3-s)(4-s)}~{}(1-\beta^{1-s})$. At the end of the FE, the SN evolves into the Sedov-Taylor (ST) phase. If $T_{\rm{FE}}$ represents the duration of the FE phase then the evolution of the DM in the ST phase is written as

As shocks amplify magnetic fields (Bykov et al., 2013; Caprioli & Spitkovsky, 2014), the RM due to the shell, in FE and ST phases are

and

respectively, (Kundu & Ferrario, 2020), where $\Omega=4\frac{e^{3}}{2\pi m_{e}^{2}c^{4}}\frac{({9\pi\epsilon_{\rm B}A^{3}})^{1/2}}{\mu m_{p}}(\psi_{\rm csm}+\psi_{\rm ej})D^{\frac{(4-3s)}{2(n-s)}}$, $\epsilon_{\rm B}$ represents the fraction of post shock energy that goes to magnetic fields, $\psi_{\rm csm}=[\alpha^{(1-3s/2)}-1]$ and $\psi_{\rm ej}=\frac{(n-3)(n-4)}{(3-s)(4-s)}~{}(1-\beta^{(1-3s/2)})$. $c$, $m_{e}$ and $e$ represent the velocity of light in vacuum, electron mass and charge, respectively.

After the explosion of a star, radiation that comes from the shock breakout, shocked shell, and hot ejecta ionises a fraction of the CSM. In the case of a CC scenario, the DM contribution from the ambient medium is

While for a constant density medium ($s=0$)

(Kundu & Ferrario, 2020), where $\Delta r=r_{max}-r_{s}$ with $r_{max}$ being the radius up to which the medium is ionised, and $\mu\simeq$ 1 for a medium that contains hydrogen and helium with solar abundances. Nonetheless, this media would have an almost null contribution to the total RM as the magnetic field in the CSM is not expected to be oriented along a given direction.

Besides the immediate surroundings of an FRB source, the host galaxy of the burst also contributes to ${\rm DM_{\rm host}}$. For non-repeating FRBs, Zhang et al. (2020) infer a host galaxy contribution of 30 - 70  pc cm^-3 in the redshift range 0.1 to 1.5. The position of the one-off FRB 191001 is at the spiral arm of its host galaxy. Hence, we assume that the DM contribution from its parent galaxy is around 50  pc cm^-3. This leads to an excess DM of about 200  pc cm^-3. The reason for this excess DM could be a much higher contribution from the immediate surroundings of the FRB, similar to that is inferred as the source of excess DM for FRB 190608 (Chittidi et al., 2020) and FRB 121102 (Tendulkar et al., 2017). It may also be possible that the FRB has traversed through an unusual dense path along its way to us or a combination of both are the source of this excess DM. In this letter, the first scenario is examined in detail. Studies of host galaxies of different types of SNe demonstrate that star-forming spiral galaxies host a large number of CC SNe (van den Bergh et al., 2005; Hakobyan et al., 2014). With an ${\rm SFR}\approx 11$  ${\rm M_{\odot}\,yr^{-1}}$, it is expected that the parent galaxy of FRB 191001 has a number of CC events. Interestingly, the position of FRB 191001 is found to be consistent with the SN distribution in the spiral arm of the host galaxies as demonstrated in Section 2, and Fig.1. Motivated by these facts, we study the possibility of FRB 191001 being the results of an SN event based on its excess DM, RM and other observed properties.

When a star explodes, initially, the ionised unshocked ejecta dominate the evolution of the DM (see Kundu & Ferrario (2020) for details). As the density of the ionised particles is high in the beginning, this medium remains opaque to a GHz signal at this phase due to the free-free absorption. The free-free absorption coefficient, at a frequency $\nu$, for a plasma with an electron density $n_{e}$ and temperature $T$ can be written as $\alpha_{\nu}^{\rm ff}=\frac{4e^{6}}{3cm_{e}k_{B}}\bigg{(}\frac{2\pi}{3k_{B}m_{e}}\bigg{)}^{1/2}T^{-3/2}Z^{2}n_{e}n_{i}\nu^{-2}\bar{g}_{\rm ff}$ (Rybicki & Lightman, 1979), where $\bar{g}_{\rm ff}$ represent the velocity average gaunt factor. $Z$ and $n_{i}$ are the atomic number and density of the ion in that medium, respectively. $k_{B}$ represents the Boltzmann constant. In the left panel of Fig.2, the black, blue, green and maroon shaded regions show the time until the medium remains optically thick to a 1 GHz signal when the ejecta is ionised by 3$\%$, 10$\%$, 30$\%$ and 50$\%$, respectively. For Ia events, in Fig. 3, the same shaded regions represent the cases when the ejecta is ionised by 10$\%$, 30$\%$, 50$\%$ and 100$\%$, respectively. In these figures, the red dotted horizontal line represents a DM value of 200  pc cm^-3, which is the excess DM of FRB 191001. Unlike CC events central remnants are not usually formed in the case of SNe Ia. Therefore, if an Ia generates radio bursts at the time of the explosion, it is expected that the radio waves would be detected by the latest when the SN becomes optically thin to the GHz signal. In the case of FRB 191001, the evolution of the DM for both SD and DD scenarios shows that the DM contribution is around 1000  pc cm^-3 when the free-free optical depth is $\sim$ 1 (see Fig. 3), for any value of ejecta ionisation. This is almost double the total observed DM of this FRB. It, therefore, seems unlikely that FRB 191001 was the result of a thermonuclear explosion. Besides, no SNe Ia, with ages in the range 0 to $\sim$ 1 yr, are reported around the location of FRB  191001 (RA 21h:33m:24.373s, Dec -54^∘:44$\arcmin$:51.86$\arcsec$) by the SN surveys effective in this part of the sky, e.g., the Gaia (Gaia Collaboration et al., 2016) and ASAS-SN (Shappee et al., 2014; Kochanek et al., 2017). However, it should be noted that, with a redshift of 0.234 there are fair chances that an Ia event is missed by these surveys as, for SNe, these surveys are typically sensitive to redshifts $<1.5$ (Belokurov & Evans, 2003).

For the CC scenario, the excess DM of $\sim 200$  pc cm^-3 could be contributed by an SN remnant around 50 yr after the explosion when $\dot{M}$ is $1\times 10^{-4}$  ${\rm M_{\odot}\,yr^{-1}}$(see left panel of Fig.2). This amount of DM is contributed by a comparatively young SN with an age of $\sim$ 2 yr to 10 yr when the density of the surrounding medium is characterised by $\dot{M}=1\times 10^{-5}$ and $1\times 10^{-6}$  ${\rm M_{\odot}\,yr^{-1}}$and the ionisation fraction of the ejecta varies in the range 3% to 50%. The RM of FRB 191001 is reported to be 55.5 rad m^-2 (Bhandari et al., 2020). Since the line of sight of this FRB does not pass through our Galactic plane it is assumed that around 20 rad m^-2 is contributed by our Milky Way Galaxy. Therefore, the remnant contributes around 35 rad m^-2 on the presumption that almost nothing is contributed by the IGM and the parent galaxy. The red dotted horizontal line in the right panel of Fig.2 represents the remnant’s contribution. With the constraints on the age of the SN from DM evolution, it is found that to have a contribution as small as 35 rad m^-2, the $\epsilon_{\rm B}$ of the shock should be in the range $10^{-8}$ to $10^{-11}$ when 50% of the ejecta is ionised. This is many orders of magnitude lower compared to those that are usually seen in SN radio shells. However, it should be noted that the measured RM may vary significantly from its absolute value, as the resultant RM depends on the projection of magnetic fields along the line of sight. Besides, for a line of sight that is almost perpendicular to the magnetic field of the shell, the $\epsilon_{\rm B}$ is expected to be small. As a result, the RM can not confirm the presence of an SN remnant around the FRB source. However, it does not rule out a CC scenario either. It is, therefore, possible that FRB 191001 has originated from a central engine that formed as a result of a CC explosion.

I thank R. Bhat, C. James, S. McSweeney, N. Swainston and K. Smith for useful discussions. I acknowledge the Australian Research Council (ARC) grant DP180100857.

The data underlying this article will be shared on reasonable request to the corresponding author.