The Deepest Radio Observations of Nearby SNe Ia: Constraining Progenitor Types and Optimizing Future Surveys

We observed SN 2013dy in the nearby (D = 13.7 Mpc) galaxy NGC 7250 with the electronic Multi-Element Radio Linked Interferometer Network (e-MERLIN; Pérez-Torres et al. 2013). SN 2013dy was discovered on 2013 July 10.45 UT (Casper et al. 2013; Zheng et al. 2013), and our radio observations were carried out during 2013 August 4–6, about 1 week after the SN had reached its B-band maximum. We observed SN 2013dy with e-MERLIN at a central frequency of 5.09 GHz and used a total bandwidth of 512 MHz, which resulted in a synthesized Gaussian beam of 013 × 011. We centered our observations at the position of the optical discovery and followed standard calibration and imaging procedures. We imaged a 20'' × 20'' region centered at this position, after having stacked all our data. We found no evidence of radio emission above a 3σ limit of 300 μJy beam⁻¹ in a circular region of 1'' in radius, centered at the SN position. This value corresponds to an upper limit of the monochromatic 5.0 GHz luminosity of $6.7\times {10}^{25}$ erg s⁻¹ Hz⁻¹ (3σ).

We observed SN 2016coj in the nearby (D = 20.1 Mpc) galaxy NGC 4125 with e-MERLIN on 2016 May 28.18 UT (MJD 57,536.18; Pérez-Torres et al. 2017) . Our observations were carried out on 2016 June 3–4, 1 week after the SN discovery and about 1 week before reaching its V-band maximum (Zheng et al. 2016, 2017). e-MERLIN observed at a central frequency of 1.51 GHz and used a total bandwidth of 512 MHz, which resulted in a synthesized Gaussian beam of 013 × 012. We centered our observations at the position of the optical discovery and imaged a 16'' × 16'' region centered at this position. We found no evidence of radio emission in the region of SN 2016coj down to a 3σ limit of 126 μJy beam⁻¹, which corresponds to an upper limit of the monochromatic 1.51 GHz luminosity of $6.1\times {10}^{25}$ erg s⁻¹ Hz⁻¹ (3σ).

In our analysis we also include data from AMI and the Jansky VLA (JVLA). In addition to what is reported in Mooley et al. (2016), further data are tabulated here.¹¹ These data cover epochs from 2016 June 3.86 to 13.81, estimated to correspond to 15–25 days after explosion (see Table 2).

Table 2.  Observations of Studied Supernovae

SN Name	Observation	Facility	Central	Time since	Flux	Luminosity	$\dot{M}/{v}_{w}$	n0	References
	Date		Freq.	Explosion	Density (1σ)	Upper Limit (3σ)	Upper Limit	Upper Limit
	(UT)		(GHz)	(Days)	(μJy)	(1025 erg s−1 Hz−1)	($\tfrac{{10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}}{100\,\mathrm{km}\,{{\rm{s}}}^{-1}}$)	(${\mathrm{cm}}^{-3}$)
SN 2013dy	2013 Aug 4–6	e-MERLIN	5.09	26	100	6.74	12	300	(1), (2)
SN 2016coj	2016 Jun 3.42	e-MERLIN	1.51	11	42	6.09	2.8	240	(1), (3)
	2016 Jun 3.86	AMI	15.0	11	101	14.6	18	2300	(4)
	2016 Jun 5.89	AMI	15.0	13	74	10.7	17	1600	(4)
	2016 Jun 9.76	AMI	15.0	17	52	7.54	18	1000	(4)
	2016 Jun 11.07	JVLA	2.7	18	20	2.95	3.3	120	(4)
		JVLA	4.5	18	20	2.90	4.5	180	(4)
		JVLA	7.4	18	16	2.32	5.4	220	(4)
		JVLA	8.5	18	17	2.42	6.1	260	(4)
		JVLA	10.9	18	18	2.56	7.4	330	(4)
		JVLA	13.5	18	13	1.93	7.1	310	(4)
		JVLA	16.5	18	16	2.36	9.3	420	(4)
	2016 Jun 11.81	AMI	15.0	19	65	9.47	23	1200	(4)
	2016 Jun 12.81	AMI	15.0	20	65	12.8	30	1400	(4)
	2016 Jun 13.81	AMI	15.0	21	65	10.4	27	1100	(4)
SN 2018gv	2018 Jan 18.6	ATCA	5.5	6	40	4.05	2.3	610	(1), (5)
		ATCA	9.0	6	10	1.01	1.3	300	(1), (5)
SN 2018pv	2018 Feb 9.23	e-MERLIN	5.1	14	19	1.18	2.1	120	(1), (6)
SN 2019np	2019 Jan 11.97	MeerKAT	1.28	7	19	3.30	(1.8)a	220	(7)
	2019 Jan 14.81	e-MERLIN	1.51	10	22	3.82	1.7	160	(1), (8)

Notes. The columns, from left to right, are as follows: SN name; starting observing time, UT; observational facility; central frequency in GHz; mean observing epoch (in days since explosion); 1σ flux density upper limits, in μJy; the corresponding 3σ spectral luminosity in units of 10²⁵ erg s⁻¹ Hz⁻¹; inferred 3σ upper limit to the mass-loss rate in units of ${10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, for an assumed wind velocity of $100\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (the values for $\dot{M}$ are for ${\epsilon }_{{\rm{B}}}={\epsilon }_{{\rm{e}}}=0.1$); inferred 3σ upper limit to the circumstellar density for a constant-density medium, in units of ${\mathrm{cm}}^{-3}$. References: (1) this paper; (2) Pérez-Torres et al. 2013; (3) Pérez-Torres et al. 2017; (4) Mooley et al. 2016, and data tabulated on the web as described in Section 2.2; (5) Ryder et al. 2018; (6) Pérez-Torres et al. 2018; (7) Heywood et al. 2019; (8) Pérez-Torres et al. 2019.

^aNo solution exists (see Figure 4).

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We used the ATCA at 5.5 and 9.0 GHz with 2 GHz bandwidths on 2018 January 18.6 UT to observe SN 2018gv (Ryder et al. 2018) situated in the galaxy NGC 2525. This SN was discovered on 2018 January 15.681 UT by Koichi Itagaki (TNS discovery report no. 16498) and identified as an SN Ia by Bufano et al. (2018) and Siebert et al. (2018). The observations and data reduction followed the same procedures as outlined for SN 2011hs by Bufano et al. (2014). No radio emission was detected down to 3σ upper limits of 120 μJy beam⁻¹ at 5.5 GHz and 30 μJy beam⁻¹ at 9.0 GHz. The total on-source time at each frequency was 6.8 hr. Adopting the host galaxy distance from Tully et al. (2013) of 16.8 Mpc, this implies an upper limit on the 9.0 GHz luminosity of $1.0\times {10}^{25}$ erg s⁻¹ Hz⁻¹ (3σ), and four times higher at 5.5 GHz.

We observed the SN Ia SN 2018pv with e-MERLIN at 5.1 GHz on 2018 February 3.63 UT (MJD 58,153.13) in the nearby (z = 0.0031) galaxy NGC 3941 (Tsuboi, TNS discovery report no. 16800). A spectrum on 2018 February 8.78 (MJD 58,158.78) confirmed the SN as a Type Ia event a few days before maximum (Yamanaka et al. 2018). Our observations (Pérez-Torres et al. 2018) were carried out on 2018 February 9–10 UT (MJD 58,159.08), 6 days after the SN discovery. We centered our observations at the position of the optical discovery (see Table 1). We found no evidence of radio emission in a circular region of 40 diameter surrounding SN 2018pv, down to a 3σ upper limit of 57.6 μJy beam⁻¹. For an assumed distance of 13.1 Mpc, the corresponding upper limit on the monochromatic 5.1 GHz luminosity is $1.2\times {10}^{25}$ erg s⁻¹ Hz⁻¹ (3σ).

We observed the SN Ia SN 2019np with e-MERLIN between 2019 January 14.81 and 15.46 UT (Pérez-Torres et al. 2019). SN 2019np was discovered on 2019 January 9.67 UT in the nearby (z = 0.00452) galaxy NGC 3254 (Itagaki, TNS discovery report no. 28550), and a spectrum on 2019 January 10.83 UT confirmed the SN as a Type Ia event 2 weeks before maximum (Burke, TNS classification report no. 3399). This is probably a lower limit since B-band maximum appears to have occurred around 2019 January 26 (S. Dong and N. Elias-Rosa 2020, private communication). Our observations were thus carried out 5 days after the SN discovery and t ≲ 10 days after the SN explosion. For a conservative estimate of t we have used 10 days. We observed at a central frequency of 1.51 GHz, with a bandwidth of 512 MHz, and centered our observations at the position of the optical discovery (see Table 1). We found no evidence of radio emission in a circular region of 100 diameter surrounding SN 2019np, down to a 3σ upper limit of 66 μJy beam⁻¹. For an assumed distance of 22 Mpc, the corresponding upper limit of the monochromatic 1.51 GHz luminosity is $3.82\times {10}^{25}$ erg s⁻¹ Hz⁻¹ (3σ). In our analysis we also include MeerKAT observations, commencing at 2019 January 11.97 UT (Heywood et al. 2019). The total integration lasted 3.25 hr in the frequency band 856–1690 MHz. The observation resulted in a 3σ upper limit of 57 μJy beam⁻¹ at 1280 MHz, corresponding to $3.30\times {10}^{25}$ erg s⁻¹ Hz⁻¹ (3σ). We have used t = 7 days, but this should be considered as an upper limit on t.

Radio emission from SNe Ia is attenuated by free–free absorption (FFA) in the external unshocked circumstellar medium and by SSA. In early analyses of SNe Ia (e.g., Panagia et al. 2006; Hancock et al. 2011), FFA was considered to dominate the absorption. However, more recent papers (Chomiuk et al. 2012, 2016; Horesh et al. 2012; Pérez-Torres et al. 2014; Kundu et al. 2017) conclude that FFA is insignificant. As discussed in Pérez-Torres et al. (2014), the free–free optical depth, τ_ff, for a fully ionized wind at 10⁴ K and moving at v_w = 100 $\mathrm{km}\,{{\rm{s}}}^{-1}$ is ${\tau }_{\mathrm{ff}}\sim {10}^{-4}{\lambda }^{2}{(\dot{M}/{10}^{-7}{M}_{\odot }{\mathrm{yr}}^{-1})}^{2}{({r}_{s}/{10}^{15}\mathrm{cm})}^{-3}$, where λ is in cm. From our calculations, using the N100 model, the shock radius is at ∼10¹⁵ cm already at ∼2 days for $\dot{M}={10}^{-7}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$ ${M}_{\odot }\,{\mathrm{yr}}^{-1}$, which means that ${\tau }_{\mathrm{ff}}\sim 3\times {10}^{-3}{(\dot{M}/{10}^{-7}{M}_{\odot }{\mathrm{yr}}^{-1})}^{2}$ at 5.5 GHz at that epoch. Considering that X-ray nondetections for SN 2011fe and SN 2014J (Margutti et al. 2012, 2014) have put limits on $\dot{M}/{v}_{w}$ of order ${10}^{-9}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ for ${v}_{w}=100\,\mathrm{km}\,{{\rm{s}}}^{-1}$ for these SNe Ia, it is not a bold assumption that FFA can be neglected for normal SNe Ia. Horesh et al. (2012) used a similar argument to dismiss FFA in their analysis of radio emission from SN 2011fe. In what follows, we only discuss frequencies higher than 1 GHz and concentrate on $\dot{M}\lesssim {10}^{-7}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$ ${M}_{\odot }\,{\mathrm{yr}}^{-1}$ and t ≳ 2 days, and therefore only consider SSA.

We have used the model in Section 3 to calculate the expected emission from a circumstellar medium created by a wind (the s = 2 case) and for a constant-density medium (the s = 0 case). Expressions for epochs when SSA is negligible are given by Equations (4) and (5). These expressions can be used to study the dependence between the various parameters and are in most cases sufficient in order to estimate $\dot{M}/{v}_{w}$ and n₀. However, SSA can be important at very early epochs and especially at low frequencies, so the expressions for optically thin synchrotron emission may underestimate $\dot{M}/{v}_{w}$ and n₀. As discussed in Section 3, our models do include SSA.

4.1.1. The Constant-density Case, s = 0

4.1.2. The Wind Case, s = 2

While limits on n₀ in the s = 0 for young SNe Ia case are of limited value, except for SN 2011fe and SN 2014J, early radio observations can be used to constrain $\dot{M}/{v}_{w}$ in the s = 2 case with some stringency. As shown in Table 2, deep limits on $\dot{M}/{v}_{w}$ are obtained for SN 2016coj, SN 2018gv, SN 2018pv, and SN 2019np. For ${\epsilon }_{{\rm{B}}}={\epsilon }_{{\rm{e}}}=0.1$, and using the N100 explosion model with n = 13, we find upper limits of $\dot{M}\lesssim 2.8\,(1.3,2.1,1.7)\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$ for these four SNe, respectively. The limit on $\dot{M}/{v}_{w}$ for SN 2013dy is about an order of magnitude larger.

We show modeled light curves for SN 2016coj in Figure 1, for SN 2018gv and SN 2018pv in Figure 2, and for SN 2019np in Figure 3. All models use ${\epsilon }_{{\rm{e}}}=0.1$, ${T}_{\mathrm{bright}}=5\times {10}^{10}\,{\rm{K}}$, and n = 13, and we show results for both _B = 0.01 and _B = 0.1. For SN 2016coj, the most constraining data are from the e-MERLIN 1.51 GHz observations on day 11 (see Table 2), but the JVLA data at 2.7 GHz also provide stringent constraints. In particular, for _B = 0.01, SSA is important at 1.51 GHz, while the optically thin 2.7 GHz emission not only serves as an independent check but also sets a more stringent limit on $\dot{M}/{v}_{w}$. The mass-loss rate limit for the ${\epsilon }_{{\rm{B}}}=0.01$ case is $\dot{M}\lesssim 1.7\,\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$, i.e., almost an order of magnitude higher than for _B = 0.1.

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In the models for SN 2018gv and SN 2018pv, SSA does not play a role for the 5–9 GHz light curves in Figure 2, not even for the models with _B = 0.01. Models with _B = 0.1 and _B = 0.01 line up on top of each other, just by changing $\dot{M}/{v}_{w}$ by a factor of 10^0.71 ≈ 5.1, as expected from Equation (5) for optically thin synchrotron radiation. The corresponding factor is larger (≈6.7) for the marginally optically thick situation at 1.51 GHz in Figure 1. The limits on $\dot{M}/({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$ for _B = 0.01 and _B = 0.1 for SN 2018gv and SN 2018pv are shown in Figure 2.

For SN 2019np, SSA is important at the low frequencies (1.28 and 1.51 GHz) used for observations of this SN (see Figure 3). For 1.28 GHz at t = 7 days, the peak luminosity for _B = 0.1 is $3.25\times {10}^{25}$ erg s⁻¹ Hz⁻¹ and occurs for $\dot{M}\approx 1.8\,\times {10}^{-8}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. This 1.28 GHz luminosity is lower than the 3σ limit listed in Table 2. To highlight this, we have put the upper limit on $\dot{M}/{v}_{w}$ for 1.28 GHz in Table 2 in parentheses. For 1.51 GHz, at t = 10 days, the modeled luminosity for _B = 0.1 is higher than the observed 3σ limit for $1.7\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ ≲ $\dot{M}{({v}_{w}/100\mathrm{km}{{\rm{s}}}^{-1})}^{-1}$ ≲ $2.4\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. The corresponding limits for _B = 0.01 are $9.5\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ ≲ $\dot{M}{({v}_{w}/100\mathrm{km}{{\rm{s}}}^{-1})}^{-1}$ ≲ $5.1\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. For $\dot{M}{({v}_{w}/100\mathrm{km}{{\rm{s}}}^{-1})}^{-1}$ ≳ $2.4\,(5.1)\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ and _B = 0.1 (0.01) SSA mutes the modeled 1.51 GHz luminosity so that it becomes lower than the observed 3σ luminosity limit. In Table 2 and in the following we have, however, treated $1.7\,\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$ as a true upper limit for _B = 0.1.

Figure 4 illustrates the relevance of SSA in probing $\dot{M}/{v}_{w}$ from SN Ia observations. We show, for a putative SN Ia at a distance of D = 15 Mpc, which minimum value of $\dot{M}/{v}_{w}$ can be probed, given the observing frequency, the time since explosion, and the flux limit. We have rescaled the flux density levels for the SNe marked in the figure to correspond to D = 15 Mpc. Solution curves for a given flux density level and vertical tick marks marking the time since explosion overlap for the $\dot{M}/{v}_{w}$ values tabulated in Tables 2 and 3. SSA attenuates the flux densities so that there is a minimum time since explosion when the SN can be detected for a given flux limit and observing frequency. For earlier times, SSA is so large that observations cannot constrain $\dot{M}/{v}_{w}$. In particular, there is no solution corresponding to the flux limit of the 1.28 GHz observations at t = 7 days for SN 2019np. This is also highlighted in Table 2, where $\dot{M}/{v}_{w}$ for the closest distance between the solution curve and the vertical line marking time since explosion in the panel has been put in parentheses. The situation is different for 1.51 GHz at 10 days (middle panel; see also Table 3). Figure 4 provides a useful tool for selecting radio telescope facility and observing frequency for a newly detected SN Ia. For very young SNe (i.e., a few days old), the very lowest frequencies (≲2 GHz) should be avoided, unless one can expect a 3σ flux limit that is $\lesssim 10\,{(D/15\mathrm{Mpc})}^{-2}$ μJy. For a 5-day old SN Ia, the corresponding flux limit is $\lesssim 30\,{(D/15\mathrm{Mpc})}^{-2}$μJy.

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Table 3.  SNe Ia with the Most Constraining Data for a Wind-like Circumstellar Scenario

SN Name	Host and	Distance	Central	Time since	Flux	Luminosity	$\dot{M}/{v}_{w}$	Reference
	Host Type		Freq.	Explosion	Density (1σ)	Upper Limit (3σ)	Upper Limit
		(Mpc)	(GHz)	(Days)	(μJy)	(1025 erg s−1 Hz−1)	$\left(\tfrac{{10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}}{100\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)$
SN 1989B	NGC 3627, SAB(s)b	10	4.8	13	30	1.08	1.8	(1), (2)
SN 1995al	NGC 3021, SA(rs)bc	27	1.4	17	80	6.98	4.0	(1), (2)
SN 2006X	NGC 4321. SAB(s)bc	17	8.4	5.9	18	1.87	1.8	(1)
SN 2010fz	NGC 2967, SA(s)c	31	6.0	8.9	9	3.11	3.0	(1)
SN 2011at	PGC 26905, SB(s)d	25	5.9	20.2	5	1.12	3.2	(1)
SN 2011by	NGC 3972, SA(s)bc	20	5.9	8.1	3	0.48	0.78	(1)
SN 2011dm	UGC 11861, SABdm	20	5.9	14.1	5	0.72	1.7	(1)
SN 2011ek	NGC 918, SAB(rs)c	18	5.9	7.4	5	0.58	0.81	(1)
SN 2011fe	M101, SAB(rs)cd	6.4	5.9	2.1	5.8	0.118	0.087	(1), (3)
SN 2011iv	NGC 1404, E1	19	6.8	6.2	18	3.11	2.3	(1)
SN 2012Z	NGC 1309, SA(s)bc	29	5.9	7.0	7	1.81	1.6	(1)
SN 2012cg	NGC 4424, SB(s)a	15	4.1	5	5	0.40	0.35	(1)
SN 2012cu	NGC 4772, SA(s)a	29	5.9	15.2	5	1.61	3.1	(1)
SN 2012ei	NGC 5611, S0	25	5.9	16.0	6	1.35	2.9	(1)
SN 2012fr	NGC 1365, SB(s)b	18	5.9	3.9	7	1.12	0.69	(1)
SN 2012ht	NGC 3447, Pec	20	5.9	4.6	5	0.91	0.70	(1)
SN 2014J	M 82, Irr	3.4	5.5	8.2	4	0.0167	0.081	(1), (3)
SN 2016coj	NGC 4125, E pec	20.1	1.51	11	42	6.09	2.8	(4), (5)
SN 2018gv	NGC 2525, SB(s)c	16.8	9.0	6	10	1.01	1.3	(4), (6)
SN 2018pv	NGC 3941, SB(s)	13.1	5.1	14	19	1.18	2.1	(4), (7)
SN 2019np	NGC 3254, SA(s)bc	22	1.51	10	22	3.82	1.7	(4), (8)

Note. The columns, from left to right, are as follows: SN name; host galaxy and galaxy type; distance in Mpc; central frequency in GHz; mean observing epoch (in days since explosion); 1σ flux density upper limits, in μJy; the corresponding 3σ spectral luminosity in units of 10²⁵ erg s⁻¹ Hz⁻¹; inferred 3σ upper limit to the mass-loss rate in units of ${10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, for an assumed wind velocity of $100\,\mathrm{km}\,{{\rm{s}}}^{-1}$. (The values for $\dot{M}$ are for ${\epsilon }_{{\rm{B}}}={\epsilon }_{{\rm{e}}}=0.1$.) References: (1) Chomiuk et al. 2016; (2) Panagia et al. 2006; (3) Pérez-Torres et al. 2014; (4) this paper; (5) Pérez-Torres et al. 2017; (6) Ryder et al. 2018; (7) Pérez-Torres et al. 2018; (8) Pérez-Torres et al. 2019.

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As discussed in Section 4.1.1, early radio data are often not useful to probe the s = 0 scenario, and in the following we will mainly concentrate on the s = 2 scenario. To put things in perspective, we have in Table 3 compiled all SNe Ia with the most constraining radio data for that scenario. Our four best cases, SN 2016coj, SN 2018gv, SN 2018pv, and SN 2019np, are the four most recent in this sample of 21 SNe Ia. To form this sample, we have added to our SNe the ones with the lowest limits on $\dot{M}/{v}_{w}$ in the compilation of Chomiuk et al. (2016). In Table 3 we list upper limits on $\dot{M}/{v}_{w}$ using the same model as in Section 4.1.2 with _B = 0.1. According to such an estimate, no SN in the sample has $\dot{M}\gtrsim 4.0\times {10}^{-8}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. Seven SNe have $\dot{M}\lesssim 1.0\times {10}^{-8}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, and they are SN 2011by, SN 2011ek, SN 2011fe, SN 2012cg, SN 2012fr, SN 2012 hr, and SN 2014J. SN 2011fe and SN 2014J have limits as low as $\dot{M}\lesssim 9\times {10}^{-10}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$.

The limits on $\dot{M}/{v}_{w}$ in Table 3 (and used throughout this paper) were derived using the same distances to the SNe as in Section 2 and Chomiuk et al. (2016).

There are several possible SD scenarios, and all (except the so-called spun-up/spun-down super-Chandrasekhar mass scenario; see below) are characterized by a mass-loss rate and wind speed of the circumstellar gas expelled from the progenitor system. The expected mass-loss rate from the progenitor system, in decreasing order, includes symbiotic systems, WDs with steady nuclear burning, and recurrent novae. We have marked areas in Figure 5 (showing $\dot{M}$ vs. v_w) where possible SD progenitor systems reside. We have also marked (dashed lines) 3σ limits on $\dot{M}/{v}_{w}$ from Table 3 for seven of the tabulated SNe, assuming _B = _e = 0.1, n = 13, s = 2, ${T}_{\mathrm{bright}}=5\times {10}^{10}$ K, and the N100 explosion model. Areas in Figure 5 for the possible SD progenitor systems, lying below and to the right of the 3σ limit dashed lines, are ruled out.

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In symbiotic systems (red region in Figure 5), the WD accretes mass from a giant star (Hachisu et al. 1999), but the WD loses some of this matter at rates of $\dot{M}\gtrsim {10}^{-8}$ ${M}_{\odot }\,{\mathrm{yr}}^{-1}$ and velocity v_w ≈ 30 $\mathrm{km}\,{{\rm{s}}}^{-1}$. From Figure 5 it is clear that this scenario is ruled out for all SNe in Table 3 with $\dot{M}\leqslant 1.7\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}({v}_{w}/(100\,\mathrm{km}\,{{\rm{s}}}^{-1}))$, including our observed cases SN 2018gv and SN 2019np. This conclusion, however, rests on ${\epsilon }_{{\rm{B}}}={\epsilon }_{{\rm{e}}}=0.1$, which is uncertain (see Section 5.3).

Circumstellar medium can also be created during Roche lobe overflow from a main-sequence, subgiant, helium, or giant star onto the WD. The expected rate is $3.1\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}\lesssim {\dot{M}}_{\mathrm{acc}}\lesssim 6.7\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ (Nomoto et al. 2007). At those accretion rates, the WD experiences steady nuclear burning (Shen & Bildsten 2007). Assuming an efficiency of 99%, the mass-loss rate from the system is $3.1\times {10}^{-9}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}\lesssim \dot{M}\lesssim 6.7\times {10}^{-9}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. Typical speeds of the gas in the CSM are 100 $\mathrm{km}\,{{\rm{s}}}^{-1}$ ≲ v_w ≲ 3000 $\mathrm{km}\,{{\rm{s}}}^{-1}$. The lower part of the range is for steady nuclear burning. The highest speeds are relevant for systems with the highest accretion rates. Of particular interest is the speed for those systems with the lowest mass-loss rates, and they lose mass through the outer Lagrangian points at speeds up to ∼600 $\mathrm{km}\,{{\rm{s}}}^{-1}$. We have marked this region in purple ("Outer Lagrangian losses") in Figure 5. With _B = _e = 0.1, systems of this sort are ruled out for SN 2011fe and SN 2014J, and partly for SN 2012cg, but not for the other SNe.

If the accretion rate is higher, i.e., ${\dot{M}}_{\mathrm{acc}}\sim 6\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, winds around the WD are likely optically thick, limiting the accretion. Any further potential mass transfer will be lost from the system at an expected wind speed of order 10³ $\mathrm{km}\,{{\rm{s}}}^{-1}$ (Hachisu et al. 1999, 2008). This is marked by the cyan-colored box in Figure 5. Assuming _B = _rel = 0.1, SN 2011fe, SN 2012cg, and SN 2014J do not stem from such a type of progenitor system, while other SNe marked in the figure could.

Systems giving rise to recurrent novae are other possible SN Ia progenitors. These systems have a low accretion rate, ${\dot{M}}_{\mathrm{acc}}\approx (1\mbox{--}3)\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. At nova outbursts, they eject shells at speeds of a few × 1000 $\mathrm{km}\,{{\rm{s}}}^{-1}$, with a time between shell ejections of a few or several years. From Table 3, the radio observations probe observing times between 2 and 20 days. For a model with N100, s = 2, and $\dot{M}=1.0\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$, the shock in our models reaches ≃1.2 × 10¹⁶ cm. This constrains the presence of shells with recurrence times of ≲1.9 (v_shell/2000 $\mathrm{km}\,{{\rm{s}}}^{-1}$)⁻¹ yr. Since the nova ejection is a transient event, the nova shell will be rather confined, and the likelihood for an SN shock being caught while interacting with a nova shell for the first ∼20 days is small (about 30%, according to Chomiuk et al. 2012). To estimate $\dot{M}$ during such a phase, we make use of the fact that models of recurrent novae predict that ≲15% of the accreted material between nova bursts is ejected (Yaron et al. 2005; Shen & Bildsten 2009). We follow Chomiuk et al. (2012) and highlight the estimated range for $\dot{M}$ and v_w with the yellow box in Figure 5. Using ${\epsilon }_{{\rm{B}}}={\epsilon }_{{\rm{e}}}=0.1$, we cannot rule out nova shells completely for SN 2011fe and SN 2014J, and not at all for the other SNe.

The final box in Figure 5 is marked in green and is for novae during the quiescent phase between nova shell ejections. This is most likely for novae with long recurrence periods, and thus for those with the lowest accretion rates (i.e., ${\dot{M}}_{\mathrm{acc}}\sim 1\times {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$). The mass loss from the system is in this case $\dot{M}\sim 1\times {10}^{-9}\ ({\epsilon }_{\mathrm{loss}}/0.01)\,({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$. If _B = _e = 0.1, the models rule out almost completely the scenario with WD accretion during the quiescent phase of the star for SN 2011fe and SN 2014J, whereas systems with the highest winds and lowest mass-loss rates are viable possibilities for the other SNe in Table 3.

For Figure 5 in general, the parameters in the upper left corner, i.e., low $\dot{M}$ and high v_w, the radio emission is too weak to be detected for any hitherto-observed SN Ia. The opposite is true for the lower right part of the figure, for which all the SNe Ia in Table 3 would have been detected if _B = _e = 0.1, and if they would have belonged to any of the highlighted progenitor scenarios in Figure 5. In particular, for SN 2011fe and SN 2014J, only a small part of parameter space for possible SD progenitors is allowed.

Progenitor constraints on the SNe in Table 3 were discussed in Section 5.2 under the assumption of ${\epsilon }_{{\rm{B}}}={\epsilon }_{{\rm{e}}}=0.1$. This assumption has been used in most previous studies (e.g., Chomiuk et al. 2012, 2016; Pérez-Torres et al. 2014; Kundu et al. 2017), although cases with _B = 0.01 have also been considered. A more general assumption is that _B and _e (and thus _rel) can take any reasonable value, and this may differ from _e = 0.1, in combination with 0.01 ≤ _B ≤ 0.1.

As no SN Ia has yet been detected in the radio, observational constraints on _B and _rel can only be obtained from core-collapse SNe, preferably from stripped-envelope SNe, as they have compact progenitors and fast SN ejecta. Assuming that all nonrelativistic electrons go into a power-law distribution with γ_min ≥ 1, Chevalier & Fransson (2006) argued for ${\epsilon }_{\mathrm{rel}}\geqslant 0.16\,{({v}_{s}/5\times {10}^{4}\mathrm{km}{{\rm{s}}}^{-1})}^{-2}$ and used _B ∼ 0.1. The question is whether the assumptions going into this are general. An example is the early-phase radio and X-ray emission of SN 2011dh. Soderberg et al. (2012; see also Krauss et al. 2012; Horesh et al. 2013) modeled this emission under the assumption of 0.1 ≲ _rel ≲ 0.3 and 0.01 ≲ _B ≲ 0.1 and arrived at a wind density characterized by $\dot{M}\approx 6\times {10}^{-5}\,{M}_{\odot }$ yr⁻¹ (for an assumed wind velocity of v_w = 1000 $\mathrm{km}\,{{\rm{s}}}^{-1}$). This is a considerably less dense environment than estimated using models for the thermal X-ray emission from the SN, at the somewhat later epoch of ∼500 days, for which Maeda et al. (2014) and Kundu et al. (2019) estimate $\dot{M}\sim (2\mbox{--}4)\times {10}^{-6}\,{M}_{\odot }$ yr⁻¹ (for v_w = 10 $\mathrm{km}\,{{\rm{s}}}^{-1}$), i.e., ∼5 times denser than that in the analysis of Soderberg et al. (2012). This could signal a decreased wind density toward the end of the life of the progenitor, but it may also be explained by too high values used by Soderberg et al. (2012) for _B and _rel. Kundu et al. (2019) found good solutions to radio light curves at late epochs of the SNe IIb SN 1993J and SN 2011dh using ${\epsilon }_{{\rm{B}}}={\epsilon }_{{\rm{e}}}=0.03$ and _B = 0.03 and _e = 0.04, respectively.

One can also gain information about microphysics parameters from the youngest SN Ia remnant detected in radio and X-rays, namely, G1.9+0.3 in the Milky Way (Condon et al. 1998; Reynolds et al. 2008). Models for its radio emission, assuming a constant-density medium around it, suggest the use of _rel = 10⁻⁴ and _B ∼ 0.01 (Sarbadhicary et al. 2019; see also below).

In Figure 6, we show solutions for several of the SNe in Table 3. The figure shows solutions for _B and _rel for an assumed wind described by $\dot{M}=1.7\times {10}^{-8}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})$, which corresponds to the upper left corner of the "Symbiotics" box in Figure 5. For combinations of _B and _rel lying below and to the left of the solution curves, a symbiotic progenitor system cannot be excluded, based on the radio data in Table 3 alone. For our standard set of model parameters (i.e., n = 13, s = 2, ${T}_{\mathrm{bright}}=5\times {10}^{10}$ K, and the N100 explosion model) _rel = _e in Figure 6 when _B ≳ 0.1, whereas for lower values of _B, _rel < _e (see Section 3). The vertical axis of the figure can also be used for _e if one makes extrapolations toward smaller values of _B, like those extrapolations shown by dashed black lines for SN 2011fe and SN 2014J.

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The horizontal blue dashed line highlights 0.01 ≤ _B ≤ 0.1 for _rel = 0.1 In most analyses, only this small stretch in the _B–_rel plane is explored (e.g., Chomiuk et al. 2012, 2016; Pérez-Torres et al. 2014; Kundu et al. 2017), and, except in a few cases (e.g., Kundu et al. 2017), _rel is allowed to deviate from _e. Only solutions for SN 2011fe, SN 2012cg, and SN 2014J lie (in the case of SN 2012cg, marginally) below this blue region, which would mean that they cannot stem from symbiotic systems if _rel = 0.1 and _B > 0.01. However, for _B = _rel (i.e., relativistic particles and magnetic field strength being in equipartition), and both being ≲0.01, symbiotic systems cannot be fully excluded, even for SN 2011fe and 2014J.

In Figure 7 we show a similar diagram for n = 13, s = 0, ${T}_{\mathrm{bright}}=5\times {10}^{10}$ K, and the merger explosion model. For SN 2011fe and SN 2014J we have used the 3 GHz 3σ upper limit at 1468 days and the 1.66 GHz 3σ upper limit at 410 days, respectively (Kundu et al. 2017). For G1.9+0.3, the 1.4 GHz luminosity, at the estimated age of 125 yr, was used. This is $(6.4\pm 0.3)\times {10}^{22}$ ergs s⁻¹ Hz⁻¹ (Sarbadhicary et al. 2019). An interesting note is that a remnant elsewhere with such a luminosity could be detected with present-day instrumentation at distances ≲2.3 Mpc, assuming a 3σ upper limit of 10 μJy.

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For our s = 0 models of SN 2011fe, SN 2014J, and G1.9+0.3 we have assumed densities of the circumstellar/interstellar medium to be 0.1–1.0 ${\mathrm{cm}}^{-3}$, and we show the influence on the derived solutions for _B and _rel for this range in n₀ in Figure 7 for SN 2011fe. From this it can be seen that a density as low as $0.1\,{\mathrm{cm}}^{-3}$ would require high efficiency of magnetic field amplification and creation of relativistic particle energy density, so that both _B and _rel would have to be in excess of 0.1 (if in equipartition) to correspond to the observed radio upper limit. However, as discussed in Kundu et al. (2017), both SN 2011fe and SN 2014J are likely to have exploded in an interstellar region with a density of $\sim 1\,{\mathrm{cm}}^{-3}$. The solution for SN 2014J in Figure 7 is for that density. If any of those SNe would stem from a DD scenario, they would therefore indicate that the values for _B and _rel could be smaller than the standard range marked by the blue region in Figure 7.

A caveat with the model run for SN 2011fe exploding into a $\sim 1\,{\mathrm{cm}}^{-3}$ environment is that our assumption of n = 13 only holds for maximum ejecta velocities of $\gtrsim 2.5\times {10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$. At lower velocities, the ejecta slope gets flatter (Kundu et al. 2017). A careful check shows that the maximum ejecta velocity is $\approx 3.05\times {10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$ at 1468 days for n = 13 and ${n}_{0}=1\,{\mathrm{cm}}^{-3}$, so the solution for SN 2011fe in Figure 7 is not outside model bounds. However, for G1.9+0.3, with ${n}_{0}=0.1\,{\mathrm{cm}}^{-3}$ (as in Figure 7), ${v}_{s}\sim 1.45\times {10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$ (and the maximum ejecta velocity is $\approx 1.65\times {10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$) at 125 yr, which is at the base of the steep outer ejecta (see Figure 1 of Kundu et al. 2017). The observed velocities of the expanding radio structures are actually $\lesssim {10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$ (Sarbadhicary et al. 2019), which means that the reverse shock has advanced deeper into the ejecta than in our model. Moreover, ${T}_{\mathrm{bright}}$ is unlikely to remain constant over such a long period. Our model for G1.9+0.3 should therefore only serve as rough estimates for _B and _rel. With this in mind, for _B = 0.02 in Figure 7 we obtain _rel ∼ 0.003. In their models, more tuned to the remnant stage, Sarbadhicary et al. (2019) use _rel = 10⁻⁴ and p = 2.2 to obtain a best fit for ${n}_{0}=0.18\,{\mathrm{cm}}^{-3}$. Although there is some controversy regarding the density around G1.9+0.3, probably in the range 0.02–0.3 ${\mathrm{cm}}^{-3}$ (Sarbadhicary et al. 2019, and references therein), densities much less than ${n}_{0}\sim 0.1\,{\mathrm{cm}}^{-3}$ may confront the apparent slow propagation of radio structures. It therefore seems reasonable to assume that _B and _rel are low for G1.9+0.3, as they also appear to be for slightly older remnants (e.g., Marcowith et al. 2016; Sarbadhicary et al. 2019).

In summary, both ${\epsilon }_{{\rm{B}}}$ and _rel are at present probably too uncertain to exclude most SD scenarios in Figure 5. If we use SN 2011dh as an example to constrain microphysics parameters for SNe Ia, we note that Soderberg et al. (2012) argue for _B = 0.01 and _e/_B ≈ 30 for that SN. Kundu et al. (2019) estimate a factor of ∼6.7 higher circumstellar density than Soderberg et al. (2012) and therefore have to invoke less efficient radio production. If we assume _e/_B ≈ 30, as did Soderberg et al. (2012), Equation (5) and the study of Kundu et al. (2019) suggest _e ≈ 0.11 and _B ≈ 0.0036 for SN 2011dh, rather than _e = 0.30 and _B = 0.01 argued for by Soderberg et al. (2012). If we further compensate for T_bright = 5 × 10¹⁰ K used in the analysis here and ${T}_{\mathrm{bright}}=4\times {10}^{10}$ K used by Kundu et al. (2019) for SN 2011dh, _e ≈ 0.1 and _B ≈ 0.0033 may provide possible parameter values for SNe Ia. If we use those numbers in a model based on N100 and n = 13, the upper limits on mass loss for SN 2011fe (SN 2014J) are $\dot{M}\approx 9.8\,(9.1)\times {10}^{-9}\,{M}_{\odot }$ yr⁻¹ (for ${v}_{w}=100\,\mathrm{km}\,{{\rm{s}}}^{-1}$), and for SN 2012cg it is $\dot{M}\approx 3.9\times {10}^{-8}\,{M}_{\odot }$ yr⁻¹. This means that such a combination of _rel and _B would fully rule out symbiotics for SN 2011fe and SN 2014J, but not for any of the other SNe in Table 3.

The uncertainty in especially _B is not surprising from a theoretical point of view. Our current understanding of shock formation suggests the creation of intense turbulence with _B ∼ 0.01 immediately behind the shock (Marcowith et al. 2016), but how this high level of turbulence can be maintained throughout the post-shock region is a conundrum. It may in fact be that the generation of magnetic field energy density is mainly driven by large-scale instabilities in connection with the contact discontinuity. If so, _B would depend less on the conditions at the blast wave than on, e.g., the structure of the SN ejecta being overrun by the reverse shock (Björnsson & Keshavarzi 2017). Spatially resolved studies, and modeling thereof, of young SNe like SN 1993J and young SNRs are essential to constrain this alternative.

In addition to radio emission, there are other clues to the origin of SNe Ia. Many of them involve circumstellar matter. We now discuss this, with emphasis on the SNe in Table 3.

5.4.1. Circumstellar Absorption-line Features

5.4.2. Circumstellar Emission and Interaction

5.4.3. X-Ray Observations of SN 2011fe, SN 2012cg, and SN 2014J

5.4.4. Dust Extinction of SN 1989B, SN 2006X, SN 2012cg, SN 2012cu, and SN 2014J

5.4.5. Interaction with a Binary Companion

5.4.6. Nebular Emission

5.4.7. SN 2013dy, SN 2016coj, SN 2018gv, SN 2018pv, and SN 2019np

The deepest radio limits on circumstellar gas are for SN 2011fe and SN 2014J. A leap in sensitivity will occur when the Square Kilometre Array (SKA) comes online. In the SKA1-mid phase, a 1σ sensitivity of ∼1.0 μJy beam⁻¹ can be reached in a 1 hr integration at 1.4 GHz. The same limit is also expected at higher frequencies (e.g., 8.5 and 15 GHz). In Figure 8 we show a plot similar to that in Figure 4, but tuned to detection limits more relevant for SKA.

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Judging from Figure 8, such a limit at 1.4 GHz will probe $\dot{M}/{v}_{w}$ down to $\sim 3.7\times {10}^{-10}\,({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ for an SN at 15 Mpc, observed 3 days after explosion, assuming the same model parameters used in Table 3. (The choice of 3 days after explosion in the estimate above rests on the currently planned cadence of the Large Synoptic Survey Telescope [LSST], which, like SKA, will be a southern hemisphere facility.) This is ≳2.2–2.4 times lower in $\dot{M}/{v}_{w}$ compared to the limits for SN 2011fe and SN 2014J in Table 3, despite those SNe Ia being much closer than 15 Mpc. For an SN at a distance of 20 Mpc, the limit on $\dot{M}/{v}_{w}$ would be $\sim 5.5\times {10}^{-10}\,({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. Judging from the VLA campaign by Chomiuk et al. (2016), mainly during 2011 and 2012 (see Table 3), we can expect approximately three to four SNe Ia per year within that distance, so a sample like that in Table 3 could be built in just a couple of years using SKA, and with limits on $\dot{M}/{v}_{w}$ that are almost a factor of two better than our current limits for SN 2011fe and SN 2014J, and ∼6 times better than for SN 2012cg.

Alternatively, we will be able to constrain ${\epsilon }_{{\rm{B}}}$ and ${\epsilon }_{\mathrm{rel}}$ to unprecedented levels. Figure 8 shows solutions not only for for _B = 0.1 but also for _B = 0.0033 and _B = 0.01 (see Section 5.3). For an SN at 15 Mpc, observed at 1.4 GHz 3 days after explosion, one would probe mass-loss rates down to $\dot{M}\sim 4.2\times {10}^{-9}\,({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, even if ${\epsilon }_{{\rm{B}}}=0.0033$. This would roughly correspond to the blue dashed line for SN 2012cg in Figure 5, but for ${\epsilon }_{{\rm{B}}}=0.0033$ instead of ${\epsilon }_{{\rm{B}}}=0.1$. For a distance of 5 Mpc and ${\epsilon }_{{\rm{B}}}=0.0033$, one would probe down to $\dot{M}\sim 9.6\times {10}^{-10}\,({v}_{w}/100\,\mathrm{km}\,{{\rm{s}}}^{-1})\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, and one would essentially be bound to detect an SN Ia, if of SD origin. For SNRs, a remnant like G1.9+0.3 would be detected with SKA1-mid at 3σ out to ∼4 Mpc.

A difference between Figures 4 and 8 is that $\dot{M}$ cannot be constrained in Figure 4 for short times since explosion and moderate flux limits, in particular for low frequencies. For deep flux limits like that in Figure 8 this is not a problem, as SSA is unimportant at the low mass-loss rates to be probed by SKA.