4 X-ray emission from an SN fragment in a low density medium

Many of the isolated SN fragments are propagating through a low-density hot environment. That concerns both relatively low velocity fragments moving inside the forward shock radius of SN and fast velocity fragments of an SN exploding in a low-density environment of number density $n \approx 0.1 \rm ~cm^{-3}$, gas temperature T $\approx 2 \times 10^4$ K and magnetic field value $\sim$3 $\rm\mu G$. We first considered the same SN fragment as that in the dense medium, but in a wider velocity range $1000 < v_{\rm k} < 7000 \rm ~km~s^{-1}$ because even very high velocity fragments are long-lived in a low density environment. The diffusion coefficient normalization at 1 keV was fixed to be $k_0 \approx 3\times 10^{19} \rm ~cm^2~s^{-1}$. We summarize the simulated X-ray line luminosities (measured in 10³⁶ photon s^-1) in Table 2. One can see that the X-ray line luminosities $L_{\rm x} <$ 10 $^{29}~ \rm ~erg~s^{-1}$ (per 10 $^{-4}~\mbox{$M_{\odot}$ }$ of Si, S, Ar, Ca, Fe) are predicted from an individual SN fragment of the scale 3$\times$10¹⁶ cm in a tenuous medium. In Table 2 we assumed that the gas micro-turbulence velocity w₆ = 1, and the ion temperature $T \la10^4$ K in the fragment body.

However, simulations of somewhat larger $\ga$10¹⁷ cm fragments show that the luminosity corrected for absorption increases to $L_{\rm x} \ga$ 10 $^{30}~ \rm ~erg~s^{-1}$ and even higher due to decreasing of the optical depth, and Coulomb losses. It is important that the large scale fragments are much thinner (and hotter), providing a substantial amount of ions in high ionization states. These faint transparent fragments would contribute substantially to the observed diffuse X-ray line emission of highly ionized matter. Note that the fragment deceleration time is $\propto$ $M n_{\rm a}^{-1} R^{-2}$. That implies that the fragments in the old remnants could only be observed if they spent most of the time in the tenuous medium.

4.1 A model of the shrapnel A in the Vela SNR

We simulated the line emission from a fragment of a scale $\sim$10¹⁸ cm to model the Vela shrapnel A discovered by Aschenbach et al. (1995) and recently studied with Chandra by Miyata et al. (2001). The oxygen-dominated fragment of mass $M \sim 10^{-2}~\mbox{$M_{\odot}$ }$ and velocity $v_{\rm k} \ga10^8 ~\rm ~cm~s^{-1}$ would have a deceleration time about 10 000 years in an ambient medium of $n \approx 0.1 \rm ~cm^{-3}$. We found that the temperature behind the fragment bow shock dominated by nonthermal particles is about 0.5 keV. The silicon line at 1.8 keV would have a luminosity $L_{\rm x} \sim$ 10 $^{30}~ \rm ~erg~s^{-1}$ if $\sim 10^{-3}~\mbox{$M_{\odot}$ }$ of Si is contained in the fragment and the oxygen line at 0.6 keV - $L_{\rm x} \ga$ 10 $^{31}~ \rm ~erg~s^{-1}$. The resonant absorption depth of the Si K-shell line is $\tau_{\rm max} \sim 0.5$ while that of oxygen is $\tau_{\rm max} \sim 30$ assuming the gas micro-turbulence velocity w₆ = 10, and the ion temperature $T \ga10^6$ K in the large diluted fragment. The mean escape probabilities $p_{\rm f}(\tau)$ are about 0.8 for Si and 0.07 for oxygen. The optical depth effect could account for the apparent Si overabundance observed by Miyata et al. (2001).

 

 

Table 2: K-shell line from the fragment interacting with low-density gas.

Linea	$v_{\rm k}(\rm ~km~s^{-1})$			$\tau_{\rm max}$
	1600	3200	6400
O (0.5-0.6 keV)	38.0	66.5	99.8	33 880
Si (1.7-1.8 keV)	2.6	4.5	6.7	592b
Ar (2.9-3.1 keV)	1.9	3.4	5.0	272b
Fe (6.4-6.9 keV)	0.8	1.4	2.1	78b
T(2) [107 K]	1.2	2.8	6.6

^a The luminosities are in 10³⁶ ph s^-1.
^b The absorption depths can be applied only for the ionization states Si VI, Ar X, Fe XVIII and higher.