Appendix A: X-ray flux until 4000 days after outburst

Measurement of the X-ray flux from the SN 1987A until $\sim$3000 days after outburst with the X-ray satellite ROSAT (Hasinger et al. 1996) showed a monotonic increase of the luminosity, where the variation in time could be linear or also steeper with $\propto t^{1.67\pm 0.35}$. A linear trend would be consistent with a constant external density (Hasinger et al. 1996). Later measurements with CHANDRA $\sim$13 years after outburst gave fluxes clearly above a linear trend (Burrows et al. 2000). To see how the X-ray flux evolved until the ISOCAM observations we derived the X-ray fluxes from a large number of available measurements that where made with the HRI and the PSPC instrument of ROSAT until $\sim$4000 days after outburst. For a direct comparison with the data published by Hasinger et al. we also included measurements which were made before $\sim$3000 days after outburst. The data were automatically calibrated with SASS. In calculating the counts of X-ray photons we used the same apertures to determine the source and the background counts used by Hasinger et al. (1996) and scaled the photon fluxes derived from the HRI-data with a factor 2.65 to allow comparison with the PSPC-data. To estimate the uncertainties we assumed poisson statistics for the source counts and gaussian statistics for the background noise.

   

Table A.1: Derived rates of X-ray photons towards SN 1987A.

obs. time	day	instr.a	$t_{\rm int}/{\rm s}$	N/1000 s
12.02.91-13.02.91	1448	HRI (1)	23107	0.17 $\pm$ 0.90
06.10.91-07.10.91	1685	PSPCB	16398	2.72 $\pm$ 0.63
30.04.92-14.05.92	1898	PSPCB	9340	2.05 $\pm$ 0.76
04.12.92-06.12.92	2110	PSPCB	2552	5.12 $\pm$ 1.80
07.04.93-10.04.93	2235	PSPCB	11259	2.63 $\pm$ 0.73
20.06.93-05.07.93	2315	PSPCB	10391	3.13 $\pm$ 0.76
28.09.93-30.09.93	2409	PSPCB	9131	3.79 $\pm$ 0.85
20.06.94-20.09.94	2718	HRI (4)	12223	5.01 $\pm$ 1.62
03.10.94-02.01.95	2823	HRI (2)	18756	3.54 $\pm$ 0.91
01.04.95-11.07.95	3008	HRI (3)	28833	4.61 $\pm$ 0.97
10.10.95-10.01.96	3196	HRI (2)	26034	7.29 $\pm$ 1.15
16.04.96-31.07.96	3392	HRI (2)	46907	7.54 $\pm$ 0.89
22.10.96-12.01.97	3568	HRI (2)	45192	7.22 $\pm$ 0.87
21.02.97-02.03.97	3654	PSPCB	15440	8.31 $\pm$ 0.86
04.03.97-03.06.97	3706	HRI (2)	52601	8.31 $\pm$ 0.86
16.12.97-17.12.97	3948	HRI (1)	21738	12.6 $\pm$ 1.5
19.02.98-22.02.98	4014	PSPCB	19382	9.19 $\pm$ 0.78

^a Number in brackets give the number of observations used.

The derived final counting rates of the observations are summarised in Table A.1 and shown in Fig. A.1 as open symbols. Until 3000 days after outburst they are consistent with the counting rates published by Hasinger et al. which are shown as black solid symbols. At later times the fluxes lay slightly above the linear trend. Fitting a potential to the counting rates derived here gives with a $\chi^2_{\rm min}=1.29$ a monotonic increase of:

$$N(t) \propto t^{2.06\pm 0.20}.$$ (A.1)

This may be because the shock is reaching denser material in time. On the other hand, numerical calculations for a HII-region with homogeneous density do not give a linear trend of the X-ray luminosity for the first several years (Borkowski et al. 1997).

To derive the volume V of the X-ray emitting gas at the time of the ISOCAM observations $\sim$4000 days after outburst we assumed that the X-ray luminosity was proportional to the emission measure $EM=n_{\rm e}n_{\rm i}V$, where $n_{\rm e}$ and $n_{\rm i}$ are the number density of the electrons and the ions. Taking the emission measure after $\sim$2500 days to be $(1.4\pm 0.4)\times 10^{57}~{\rm cm^{-3}}$ (Hasinger et al. 1996; Borkowski et al. 1997) and the abundances as given in Sect. 2.1, this volume was approximately $2.2\times 10^{52}~{\rm cm^3}$.

Figure A.1: Time evolution of the X-ray emission of SN 1987A, measured with the ROSAT satellite. The photon fluxes derived from observations with the HRI and the PSPC instrument are shown as triangles and squares. Published data (filled symbols) until 3000 days after outburst (Hasinger et al. 1996) are shown for comparison. These data can be described through a linear increase (dotted line) since 900 days and a potential (broken line) with $\propto t^{1.67}$ (Hasinger et al. 1996). The photon fluxes derived here (open symbols) give an increase with $\propto t^{2.06\pm 0.20}$ (solid line).