Astronomy and Astrophysics
Vol. 07  No. 03 ( 2019 ), Article ID: 30763 , 9 pages
10.12677/AAS.2019.73004

Study on Synchrotron Radiation Signal and Dark Matter Annihilation Signal in Small Magellanic Cloud

Zhanfang Chen

Department of Astronomy, Xiamen University, Xiamen Fujian

Received: May 23rd, 2019; accepted: June 7th, 2019; published: June 14th, 2019

ABSTRACT

High-energy positrons and electrons lose energy in the magnetic field to produce synchrotron radiation signals. In irregular dwarf galaxies, both dark matter self-annihilation and cosmic rays produce high-energy positrons and electrons. In this paper, we review the synchrotron radiation signals in the Small Magellanic Cloud, an irregular dwarf galaxy in the neighborhood, and compare the constraints on dark matter mass with and without cosmic ray contributions. We first assume that all the synchrotron radiation signals are generated by dark matter annihilation. Given the thermal relic annihilation cross section, the mass constraints on dark matter particles are limited by fitting observed data under the assumption of three different typical dark matter annihilation channels and we find ${\tau }^{+}{\tau }^{-}$ is the best annihilation channel to fit the spectrum shape. Furthermore, we calculate the synchrotron radiation signal generated by cosmic rays through radio-infrared correlation, subtracting the contribution of this part of the detected flux and using the remaining part as the upper limit from the self-annihilation of dark matter. Taking into account ${\tau }^{+}{\tau }^{-}$ annihilation channel, we give the corresponding dark matter mass under the two magnetic field assumptions by adjusting the dark matter mass to fit the data. When the contribution of cosmic rays is reasonably deducted, the upper mass of dark matter particles allowed is larger than that obtained without cosmic ray contribution subtracted at the same thermal annihilation cross-section.

Keywords:Small Magellanic Cloud, Dark Matter, Cosmic Ray

1. 引言

2. 小麦哲伦云的射电能谱

2.1. 小麦哲伦云射电数据拟合

${S}_{\nu }={S}_{0}{\left(\frac{\nu }{{\nu }_{0}}\right)}^{-{\alpha }_{0}}$ (1)

Table 1. Radio data from SMC at low frequencies

Figure 1. Spectral energy distribution of SMC at low frequencies

2.2. 宇宙线贡献的同步辐射

$\text{log}\frac{{L}_{\text{1}.\text{4},\text{GHz}}}{\text{W}\cdot {\text{Hz}}^{-\text{1}}}=1.032×log\frac{{L}_{24,obs}}{{L}_{\odot }}+11.642$ (2)

${S}_{CR}={S}_{1}{\left(\frac{\nu }{{\nu }_{1}}\right)}^{-{\alpha }_{1}}$ (3)

${\alpha }_{0}$ 在文献中也得到了广泛的探讨，我们假设它是0.8 [11] 。因此，我们可以得到宇宙线幂律分布为： ${S}_{CR}=\text{7}\text{.0}{\left(\nu /\text{1}.\text{4GHz}\right)}^{-0.8}$

3. 限制暗物质粒子属性

3.1. 源函数

 (3)

Figure 2. Electron spectrums $\text{d}{N}_{e}/\text{d}E$ for different annihilation channels

${\rho }_{DM}\left(r\right)$ 是暗物质粒子密度，我们采用是NFW模型：

${\rho }_{NFW}\left(r\right)=\frac{{\rho }_{s}}{\left(\frac{r}{{r}_{s}}\right){\left[1+\left(\frac{r}{{r}_{s}}\right)\right]}^{2}}$ (4)

3.2. 暗物质湮灭同步辐射信号

${S}_{syn}\approx \frac{1}{{D}_{A}^{2}}\int \text{d}r{r}^{2}{j}_{syn}\left(\nu ,r\right)$ (5)

${j}_{syn}\left(\nu ,r\right)\text{}=2{\int }_{{m}_{e}}^{{M}_{\chi }}\text{d}E\frac{\text{d}{n}_{e}}{E}\left(E,r\right){P}_{syn}\text{}\left(\nu ,E,r\right)\text{}$ (6)

${P}_{syn}\left(\nu ,E,r\right)={\int }_{0}^{\text{π}}\text{d}\theta \frac{\mathrm{sin}\theta }{2}2\text{π}\sqrt{3}{r}_{0}{m}_{e}c{\nu }_{0}\mathrm{sin}\theta F\left(\frac{x}{\mathrm{sin}\theta }\right)$ (7)

$x\equiv \frac{2\nu \left(1+z\right){m}_{e}^{2}}{3{\nu }_{0}{E}^{2}}$ (8)

$F\left(s\right)\equiv s{\int }_{s}^{\infty }\text{d}\zeta {K}_{5/3}\left(\zeta \right)\approx 1.25{s}^{1/3}{e}^{-s}{\left[648+{s}^{2}\right]}^{1/12}$ (9)

$\frac{\text{d}{n}_{e}}{\text{d}E}\left(E,\stackrel{\to }{r}\right)=\frac{〈\sigma v〉{\rho }_{DM}^{2}\left(r\right)}{2b\left(E,r\right){m}_{\chi }{}^{2}}\underset{E}{\overset{{m}_{\chi }{c}^{2}}{\int }}{q}_{e}\left({E}^{\prime },r\right)\text{d}{E}^{\prime }$ (10)

${b}_{sync}=0.025{\left(\frac{B\left(\stackrel{\to }{r}\right)}{1\text{μG}}\right)}^{2}{\left(\frac{E}{1\text{GeV}}\right)}^{2}$ (11)

3.3. 限制暗物质粒子质量

Figure 3. The flux varies with frequency for the $b\stackrel{¯}{b}$ annihilation channel

Figure 4. The flux varies with frequency for the  annihilation channel

Figure 5. The flux varies with frequency for the ${\tau }^{+}{\tau }^{-}$ annihilation channel

Figure 6. The flux varies with frequency for the ${\tau }^{+}{\tau }^{-}$ annihilation channel

Figure 7. The magnetic field is 1.7 mG and the observed data are fitted

Figure 8. After deducting cosmic rays, we fit the radio spectrum

4. 结论

Study on Synchrotron Radiation Signal and Dark Matter Annihilation Signal in Small Magellanic Cloud[J]. 天文与天体物理, 2019, 07(03): 31-39. https://doi.org/10.12677/AAS.2019.73004

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