Constraints on dark matter annihilation in the Large Magellanic Cloud from multiple low-frequency radio observations

Low-frequency radio emission from the Large Magellanic Cloud~(LMC) is assumed to be dominated by nonthermal synchrotron radiation from energy loss of energetic $e^+/e^-$ in magnetic field. Two different kinds of sources of $e^+/e^-$, dark matter~(DM) annihilation and cosmic rays~(CR) related to massive stars, are taken into account in this paper. We fit the multiple low-frequency radio observations, from 19.7 MHz to 1.4 GHz, with a double power-law model $S_{nth} =S_{DM}(\frac {\nu}{\nu_{\star}})^{-\alpha_{DM}}+S_{CR}( \frac {\nu}{\nu_{\star}})^{-\alpha_{CR}}$. $\nu_{\star}$ is set to be $1.4$ GHz and $S_{CR}$ could be determined from the 24 $\mu m$ luminosity based on the global radio-infrared correlation. Our best fit with a fixed $\alpha_{CR}$ changing from $0.80$ to $0.55$ yields $\alpha_{DM}$ ranging from $0.21$ to $0.66$. Given a fixed value of $\alpha_{CR}$, we derive the upper limits of synchrotron emission induced by dark matter annihilation at different radio frequencies. Larger value of $\alpha_{CR}$ represents for a harder $e^+/e^-$ spectrum from cosmic rays, which leads to a smaller value of $\alpha_{DM}$ and allow less synchrotron emission resulted from dark matter annihilation in lower frequency. Under the same assumption on the magnetic field, we find that the lower the frequency, the stronger the restriction on DM parameter space. Meanwhile, as the peak frequency of synchrotron radiation decrease with the energy of $e^+/e^-$, constraints on DM properties obtained from lower frequency are more severe in the case of DM with lower mass. Future low-frequency radio survey should be considered a promising and powerful way to constrain DM.