Thermal emission at radio frequencies from supernova remnants and a modified theoretical Σ-D relation

In this paper, we discuss known discrepancies between theoretically derived and empirically measured relations between the radio surface brightness Σ and the diameter D of supernova remnants (SNRs): these relations are commonly known as the Σ-D relations. We argue that these discrepancies may be at least partially explained by taking into account thermal emission at radio frequencies from SNRs at particular evolutionary stages and located in particular environments. The major contributions of this paper may be summarized as follows: (i) we consider thermal emission at radio frequencies from SNRs in the following scenarios: a relatively young SNR evolving in a dense molecular cloud environment (n ∼ 100-1000 cm−3) and an extremely evolved SNR expanding in a dense warm medium (n ∼ 1-10 cm−3). Both of these SNRs are assumed to be in the adiabatic phase of evolution. We develop models of the radio emission from both of these types of SNRs and each of these models demonstrate that through the thermal bremsstrahlung process significant thermal emission at radio frequencies is expected from both types of SNR. Based on a literature search, we claim that thermal absorption or emission at radio frequencies has been detected for one evolved Galactic SNR and four young Galactic SNRs with similar properties to our modelled evolved and young SNRs. (ii) We construct artificial radio spectra for both of these two types of SNRs: in particular, we discuss our simulated spectrum for the evolved Galactic SNR OA 184. By including thermal emission in our simulated spectra, we obtain different slopes in Σ-D relations: these new slopes are in closer agreement to empirically obtained relations than the theoretically derived relations which do not take thermal emission into account. (iii) Lastly, we present an additional modification to the theoretical Σ-D relation for SNRs in the adiabatic expansion phase. This modification is based on the convolution of the synchrotron emissivity with the emissivity derived in this paper for thermal bremsstrahlung emission from an ionized gas cloud (that is, a theoretical construct of an SNR).