# Solar Radio Emissions and Ultralight Dark Matter
## 5 Detection
The sensitivity obtained in Figure 2 can be translated to the axion case via the relation in Equation (21), and the result is plotted in \[v_{\theta}=v_{0}\frac{b}{r},\ \ v_{r}=\sqrt{v_{0}^{2}-v_{\theta}^{2}+\frac{2 GM_{ \odot}}{r}},\ \ \ v^{2}=v_{r}^{2}+v_{\theta}^{2}. \tag{28}\]3 As shown in [88], the magnetic field strength is about 1-4 Gauss in the solar corona at 1.05-1.35 \(R_{\odot}\) from the Sun centre. To be conservative, we take the transverse magnetic field \(|\mathbf{B}_{T}|=1\) Gauss in Equation (21). As we can see from Figure 3, our projected sensitivities are better than the light-shining-through-a-wall experiments (LSW, including CROWS, ALPS, and OSQAR [89; 90; 91]). Furthermore, they are better than the constraint from the CAST experiment in part of the SKA1 frequency range. However, in most of the relevant frequency range, they cannot exceed the constraints from multiple astrophysical searches in various environments [57; 92; 93; 94; 95; 96; 97; 98] (shown as a combined constraint in Figure 3). The performance of sensitivity in the axion case is not as good as that in the dark photon case. This is because the solar magnetic field is relatively low which suppresses the axion-photon conversion rate as we can see from Equation (21). Figures 2 and 3 are based on the simplified scenario of the propagation process of the converted photons that took \(P_{\rm sur}\) in Equation (26) and assumed \(\beta=1\) in Equation (34). Instead, [PERSON]. [78] numerically simulated the radio photon propagation based on the Monte Carlo ray-tracing method. Furthermore, the Maxwellian velocity distribution has been considered in computing the emitted power (Equation (33)), although this effect does not make much difference. Furthermore, Ref. [78] analysed real data of LOFAR (three samples of 17 min observations at different dates). Finally, Ref. [78] obtained a constraint of \(\epsilon\)\(\sim\)\(10^{-13}\) about one to two orders of magnitude better than the CMB constraint [8; 86] in the frequency range 30-80 MHz. This constraint is weaker than the projections in Figure 2, mainly because the angular distribution in Equation (34) of converted photons is based on the numerical simulation. A similar constraint on the axion-photon coupling strength \(g_{\alpha\gamma\gamma}\)\(\sim\)\(10^{-9}\) GeV\({}^{-1}\) has been obtained in the same frequency range [78], which is about one to two orders of magnitude better than the existing constraints from the LSW experiments [89; 90; 91], but does not exceed the constraints from the CAST experiment [99] and multiple astrophysical bounds [57; 92; 93; 94; 95; 96; 97; 98]. \[v_{\theta}=v_{0}\frac{b}{r},\ \ v_{r}=\sqrt{v_{0}^{2}-v_{\theta}^{2}+\frac{2 GM_{ \odot}}{r}},\ \ \ v^{2}=v_{r}^{2}+v_{\theta}^{2}. \tag{28}\]4 The projected sensitivity of the parameter space of the axion photon dark matter based on the radio telescopes SKA phase 1 and LOFAR, with the observation time assumed to be 1 and 100 h, respectively. The results are translated from Figure 2 via the relation in Equation (21) with \(|\mathbf{B}_{T}|\) taken as 1 Gauss [88]. Together we show the existing constraints, which can be classified into four categories: the astrophysical searches for axions in various environments, including white dwarfs, neutron stars and pulsars, quasars and blazars, the radio galaxy NGC 1275, globular clusters, etc. [92; 93; 94; 95; 96; 97; 98; 99; 90; 91; 92; 93; 94; 95; 97; 98; 99; 90; 92; 93; 95; 99; 96; 97; 98; 99; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 112; 113; 114; 115; 116; 117; 118; 119; 120; 121; 122; 123; 124; 125]; the helioscope, CAST, aiming to detect axions emitted by the Sun; and light-shining-through-a-wall (LSW) experiments including CEOWS, ALPS, and OSQAR [89; 90; 91]. The existing constraints are also nicely summarized in [126].