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 2

Models and comparison of the properties of compression during reverberation.

Model	$t_{max}^{thin} / T_{ch}$ $Mathematical equation: $\[t_{\text {max}}^{\text {thin}} / T_{\text {ch}}\]$$	$R_{max}^{thin} / R_{c h}$ $Mathematical equation: $\[R_{\text {max}}^{\text {thin}} / R_{\mathrm{ch}}\]$$	$t_{max}^{thick} / T_{ch}$ $Mathematical equation: $\[t_{\text {max}}^{\text {thick}} / T_{\text {ch}}\]$$	$R_{max}^{thick} / R_{ch}$ $Mathematical equation: $\[R_{\text {max}}^{\text {thick}} / R_{\text {ch}}\]$$	$t_{min}^{thin} / T_{c h}$ $Mathematical equation: $\[t_{\text {min}}^{\text {thin}} / T_{\mathrm{ch}}\]$$	$R_{min}^{thin} / R_{ch}$ $Mathematical equation: $\[R_{\text {min}}^{\text {thin}} / R_{\text {ch}}\]$$	$t_{min}^{thick} / T_{ch}$ $Mathematical equation: $\[t_{\text {min}}^{\text {thick}} / T_{\text {ch}}\]$$	$R_{min}^{thick} / R_{ch}$ $Mathematical equation: $\[R_{\text {min}}^{\text {thick}} / R_{\text {ch}}\]$$	CF^thin	CF^thick
`C0`	1.250	0.719	1.452	0.745	3.405	0.219	5.111	0.258	3.278	2.885
`S1`	1.204	0.731	1.607	0.766	2.490	0.562	5.359	0.612	1.301	1.251
`S2`	1.219	0.726	1.483	0.754	6.025	0.387	6.506	0.444	1.875	1.697
`S3`	1.328	0.697	1.405	0.722	3.359	0.080	4.739	0.094	8.702	7.674
`S4`	1.436	0.663	1.343	0.695	3.142	0.022	4.243	0.024	30.48	29.02
`L1`	1.963	0.428	1.793	0.491	2.646	0.024	2.863	0.026	17.71	18.63
`L2`	1.576	0.613	1.297	0.646	2.987	0.129	3.576	0.144	4.759	4.477
`L3`	1.033	0.719	1.777	0.842	5.405	0.256	7.111	0.245	2.814	3.439
`L4`	1.560	0.828	1.839	0.873	6.537	0.210	7.886	0.213	3.943	4.100

Notes. Thin and thick refers to the standard thin-shell formalism and to the formalism presented here for a thick layer, respectively. Max and min refers to the conditions when the PWN reaches its maximum size and its first minimum after compression. The compression factors CF are defined as the ratio of the minimum to maximum radius.

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