Old pulsar wind nebulae and the role of the thermal filaments

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Volume 712 (August 2026)

A&A, 712 (2026) A56

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Table 1

Models.

Model	Log₁₀(τ_sd/T_ch)	Log₁₀(L₀τ_sd/E_sn)	$t_{beg,rev}^{thin} / T_{ch}$ $Mathematical equation: $\[t_{\text {beg,rev}}^{\text {thin}} / T_{\text {ch}}\]$$	$R_{beg,rev}^{thin} / R_{c h}$ $Mathematical equation: $\[R_{\text {beg,rev}}^{\text {thin}} / R_{\mathrm{ch}}\]$$	$t_{beg,rev}^{thick} / T_{c h}$ $Mathematical equation: $\[t_{\text {beg,rev}}^{\text {thick}} / T_{\mathrm{ch}}\]$$	$R_{beg,rev}^{thick} / R_{ch}$ $Mathematical equation: $\[R_{\text {beg,rev}}^{\text {thick}} / R_{\text {ch}}\]$$
`C0`	−0.60	−2.00	1.033	0.671	0.785	0.650
`S1`	0.28	−1.20	0.940	0.667	0.739	0.640
`S2`	−0.12	−1.60	0.987	0.670	0.770	0.647
`S3`	−1.00	−2.45	1.157	0.660	0.878	0.663
`S4`	−1.40	−2.90	1.312	0.636	1.002	0.670
`L1`	1.20	−3.20	1.870	0.409	1.793	0.491
`L2`	0.30	−2.60	1.498	0.596	1.281	0.640
`L3`	−1.45	−1.40	0.661	0.625	0.398	0.495
`L4`	−2.30	−0.80	0.351	0.456	0.134	0.233

Notes. Models and comparison of the parameters at the beginning of the reverberation. Thin and thick refer to the standard thin-shell formalism and the formalism presented here for a thick layer, respectively.

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