Distances to Two Galactic Supernova Remnants: G32.8-0.1 and G346.6-0.2

Distances to SNRs can be estimated by observations of extinction, X-ray, SN magnitude, background object, SNR kinematics and HI absorption, etc. (Strom 1988). In some literatures, the relation between the radio surface brightness (Σ) and the linear diameter (D) is also used to determine the distance when the SNR flux is available (Poveda & Woltjer 1968;Clark & Caswell 1976;Lozinskaya 1981;Huang & Thaddeus 1985;Duric & Seaquist 1986;Guseinov et al. 2003). However, for the remnants inside the circle of the Galaxy plane with its radius (R) less than 8.5 kpc yet not too near to the Galactic center, that is the the galactic longitude (l) should be 0 o < l < 90 o or 270 o < l < 360 o , then the rotation curve of the Galaxy can be used to derive the SNR distance after measuring and obtaining its LSR velocity (Fig. 1). But usually this method may lead to two distance values of a near one OA and another farther one OB. For two examples here, Koralesky et al. (1998) derived the kinematic distance to a shell-type remnant SNR G32.8-0.1 either a near distance of 5.5 kpc or a far distance of 8.8 kpc, and to another shell-type remnant SNR G346.6-0.2 yields a near value of 5.5 kpc and a far value of 11 kpc.

Through a group of equations for the shelltype SNRs separately at the adiabatic-phase or the radiative-phase, we can determine their distances when the SN initial explosion energy (E 0 ), the radio flux at 1 GHz and the observational angle (θ) have been detected. The relation between the surface brightness (Σ) and the remnant diameter (D) can also be used to confirm its distance. But this method is not adopted here because of its somewhat large deviation.

On the paper, we do numerical calculations of the group of equations at both stages individually in Sect. 2, and make some discussion in Sect. 3. At last we summarize our conclusion.

Let us list the following group of equations for shell-type remnants at the second stage (Wang & Seward 1984;Koyama & Meguro 1987;Bignami & Caraveo 1988;Xu et al. 2005), (2)

Here, D pc is the SNR diameter in units of pc, t yr is the remnant age in year, n is the ISM electron density in cm -3 , S 1GHz is the detected fluxes of an SNR in Jy at 1 GHz, θ arcmin is the viewing angle in arcmin, υ = dD dt is the velocity of shock waves in km s -1 . And we know tan θarcmin and 10 52 ergs), then a series of the diameters D pc (and distance d pc ) of both SNRs are obtained by solving the equations group above (table 1). Furthermore, when the assumed initial explosion energy (E 0 ) changes from 10 48 ergs to 10 53 ergs, then the kinematic distance of SNR G32.8-0.1 and G346.6-0.2 also increases (Fig. 2). We can obtain a certain distance value for both remnants corresponding to the typical well-known explosion energy of the SNRs E 0 = 10 51 ergs. The group of equations are not strictly correct as not to be figured out mathematically, but they are correct enough for us to determine the distance to both SNRs.

From Fig. 2 and table 1 we can see that the most likely kinematic distance to SNR G32.8-0.1 is about 7 kpc relevant typically to E 0 = 10 51 ergs. Since the remnant diameter evolving at the Sedovphase is typically less than 36 pc (Clark & Caswell 1976;Allakhverdiyev et al. 1983Allakhverdiyev et al. , 1985)), one can reasonably exclude the two cases of E 0 = 10 52 ergs, and E 0 = 5×10 51 ergs for their too large diameters 50 pc and 45 pc. For the smaller initial energy is E 0 = 10 50 ergs and E 0 = 5 × 10 49 ergs, both their outcomes are somewhat unlikely. Moreover, the typical SNe initial explosion energy is ∼ 10 51 ergs as the black numbers show (table 1). Therefore we subsequently conclude that the distance to SNR G32.8-0.1 is near 7 kpc, that is a little larger or less than 7 kpc. We can see from next subsection that it is lager than 7 kpc. The farther distance 8.8 kpc to the remnant is confirmed as we know later in our work at Sect. 2.2.

Similarly the far distance 11 kpc to SNR G346.6-0.2 is determined which is also consistency with the results done in the next subsection. we suppose here both the remnants evolving at snow-plough phase. When a series of the initial energies E 0 = 5 × 10 49 , 10 50 , 5 × 10 50 , 10 51 , 5 × 10 51 and 10 52 ergs are assumed, the remnant diameters D pc (and distance d pc ) can be derived by solving the equations group above (table 2). The same as in Sect. 2.1 when the assumed initial energy (E 0 ) enhances from 10 48 ergs to 10 53 ergs, the SNR G32.8-0.1 and G346.6-0.2 distance values also increase (Fig. 3). Corresponding to the SNRs typical explosion energy E 0 = 10 51 ergs one can obtain a certain distance value for both remnants.

One can see the equations ( 4) and ( 6) are rather different from equations ( 1) and ( 3). But formulae ( 5) and ( 2) are completely the same.

From Fig. 3 and table 2 we can see that the most likely distance to SNR G32.8-0.1 is about 9.4 kpc relevant to E 0 = 10 51 ergs. Therefore the farther distance 8.8 kpc to the remnant i

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