Table 6. Open in new tab The...

Parameter	Definition	Unit	Posterior
⁵⁶Ni model
M_ej	Ejecta mass	M_⊙	[0.1, 50]
v₉	Ejecta velocity	10⁹ cm s⁻¹	[0.1, 5.0(10.0)]^a
M_Ni	⁵⁶Ni mass	M_⊙	[0.001, 2.0(20.0)]^a
κ_{γ, Ni}	Gamma-ray opacity of ⁵⁶Ni-cascade-decay photons	cm² g⁻¹	[0.027, 10⁴]^c
T_f	Temperature floor of the photosphere	10³ K	[1000, 10, 000]
\|$t_{\rm shift}^{\rm b}$\|	Explosion time relative to the first data	days	[ − 20, 0]
Cooling model with three additional parameters compared to the ⁵⁶Ni model.
M_e	Envelope mass	M_⊙	[0.01, 30]
R_{e, 12}	Envelope radius	10¹² cm	[10, 3000]
E_{e, 50}	Energy passed into the envelope from SN core	10⁵⁰ erg s⁻¹	[10⁻⁵, 10³]^c
Magnetar model with three different parameters compared to the ⁵⁶Ni model, but dropped M_Ni and κ_{γ, Ni}.
P₀	Initial period of the magnetar	ms	[0.8, 50]
B_{p, 14}	Magnetic field strength of the magnetar	10¹⁴ G	[0.1, 100]
κ_{γ, mag}	Gamma-ray opacity of magnetar photons	cm² g⁻¹	[0.01, 10⁴]^c

Parameter	Definition	Unit	Posterior
⁵⁶Ni model
M_ej	Ejecta mass	M_⊙	[0.1, 50]
v₉	Ejecta velocity	10⁹ cm s⁻¹	[0.1, 5.0(10.0)]^a
M_Ni	⁵⁶Ni mass	M_⊙	[0.001, 2.0(20.0)]^a
κ_{γ, Ni}	Gamma-ray opacity of ⁵⁶Ni-cascade-decay photons	cm² g⁻¹	[0.027, 10⁴]^c
T_f	Temperature floor of the photosphere	10³ K	[1000, 10, 000]
\|$t_{\rm shift}^{\rm b}$\|	Explosion time relative to the first data	days	[ − 20, 0]
Cooling model with three additional parameters compared to the ⁵⁶Ni model.
M_e	Envelope mass	M_⊙	[0.01, 30]
R_{e, 12}	Envelope radius	10¹² cm	[10, 3000]
E_{e, 50}	Energy passed into the envelope from SN core	10⁵⁰ erg s⁻¹	[10⁻⁵, 10³]^c
Magnetar model with three different parameters compared to the ⁵⁶Ni model, but dropped M_Ni and κ_{γ, Ni}.
P₀	Initial period of the magnetar	ms	[0.8, 50]
B_{p, 14}	Magnetic field strength of the magnetar	10¹⁴ G	[0.1, 100]
κ_{γ, mag}	Gamma-ray opacity of magnetar photons	cm² g⁻¹	[0.01, 10⁴]^c

Table 6.

The definitions, units, and prior ranges of the parameters of the fitting models.

Parameter	Definition	Unit	Posterior
⁵⁶Ni model
M_ej	Ejecta mass	M_⊙	[0.1, 50]
v₉	Ejecta velocity	10⁹ cm s⁻¹	[0.1, 5.0(10.0)]^a
M_Ni	⁵⁶Ni mass	M_⊙	[0.001, 2.0(20.0)]^a
κ_{γ, Ni}	Gamma-ray opacity of ⁵⁶Ni-cascade-decay photons	cm² g⁻¹	[0.027, 10⁴]^c
T_f	Temperature floor of the photosphere	10³ K	[1000, 10, 000]
\|$t_{\rm shift}^{\rm b}$\|	Explosion time relative to the first data	days	[ − 20, 0]
Cooling model with three additional parameters compared to the ⁵⁶Ni model.
M_e	Envelope mass	M_⊙	[0.01, 30]
R_{e, 12}	Envelope radius	10¹² cm	[10, 3000]
E_{e, 50}	Energy passed into the envelope from SN core	10⁵⁰ erg s⁻¹	[10⁻⁵, 10³]^c
Magnetar model with three different parameters compared to the ⁵⁶Ni model, but dropped M_Ni and κ_{γ, Ni}.
P₀	Initial period of the magnetar	ms	[0.8, 50]
B_{p, 14}	Magnetic field strength of the magnetar	10¹⁴ G	[0.1, 100]
κ_{γ, mag}	Gamma-ray opacity of magnetar photons	cm² g⁻¹	[0.01, 10⁴]^c

Parameter	Definition	Unit	Posterior
⁵⁶Ni model
M_ej	Ejecta mass	M_⊙	[0.1, 50]
v₉	Ejecta velocity	10⁹ cm s⁻¹	[0.1, 5.0(10.0)]^a
M_Ni	⁵⁶Ni mass	M_⊙	[0.001, 2.0(20.0)]^a
κ_{γ, Ni}	Gamma-ray opacity of ⁵⁶Ni-cascade-decay photons	cm² g⁻¹	[0.027, 10⁴]^c
T_f	Temperature floor of the photosphere	10³ K	[1000, 10, 000]
\|$t_{\rm shift}^{\rm b}$\|	Explosion time relative to the first data	days	[ − 20, 0]
Cooling model with three additional parameters compared to the ⁵⁶Ni model.
M_e	Envelope mass	M_⊙	[0.01, 30]
R_{e, 12}	Envelope radius	10¹² cm	[10, 3000]
E_{e, 50}	Energy passed into the envelope from SN core	10⁵⁰ erg s⁻¹	[10⁻⁵, 10³]^c
Magnetar model with three different parameters compared to the ⁵⁶Ni model, but dropped M_Ni and κ_{γ, Ni}.
P₀	Initial period of the magnetar	ms	[0.8, 50]
B_{p, 14}	Magnetic field strength of the magnetar	10¹⁴ G	[0.1, 100]
κ_{γ, mag}	Gamma-ray opacity of magnetar photons	cm² g⁻¹	[0.01, 10⁴]^c

^aFor four luminous or superluminous SNe (SNe 2008fz, 2010hy, 2012aa, and 2018cow; see Table S3 in the supplementary material), the upper limits of prior of v₉ and M_Ni are set to be 10 and 20.0, respectively.

^bFor the SNe whose explosion date (t₀) had been inferred (see Table 5), the t_shift parameter was set to be fixed.

^cParameter was distributed in log space.

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