| 其他摘要 | Dark matter is one of the most concerned issues in astronomy and physics today. Since Zwicky proposed that dark matter may exist in galaxy clusters in the 1930s, more and more observational evidences have shown the existence of dark matter, such as the rotation curves of galaxies, the mass to light ratio of elliptical galaxies and the large-scale structure of the universe. Therefore, a cold dark matter model has been proposed to explain the observational evidence. However, in recent years, more and more small scale observations contradict the cold dark matter model, which makes the distribution of dark matter near galactic cores and massive black holes more interesting. In this work, we mainly study the following problems: Firstly, based on the power law profile of dark matter near the black hole, we use the datas of LSB galaxies to limit the Rastall gravity theory; Secondly, the enhancement effect of the eccentricity of a IMRI system is used to limit the distribution of dark matter spike;Thirdly, based on the perfect fluid dark matter model, the density profile containing both black hole and dark matter distribution is studied, and the datas of LSB galaxies are used to test it. Our main results are as follows:(1) Based on the power-law form of the dark matter profile near the black hole, the Rastall gravity model is constrained by the rotation curves of the LSB galaxies, so as to study the conservation law of energy momentum tensor in the strong gravitational field. We find that the values of Rastall parameters are diverse in different LSB galaxies, which indicates that the Rastall parameters are not universal constants of gravity. According to previous discussions, such a result can only be interpreted as a material distribution parameter. Therefore, Rastall gravity theory is equivalent to general relativity, and the conservation law of energy momentum tensor can be tested under strong gravitational field.(2) We generalized the work of Yue et al., studied the influence of the more general distribution of dark matter spike on the eccentricity enhancement effect in the IMRI system, calculated the influence of different masses of the central black holes on the eccentricity, and compared the dark matter spike and dark matter halo. We find that the influence of the more general spike distribution of dark matter on the eccentricity enhancement effect is very little different from the results of Yue et al., which is difficult to be showed in the gravitational wave measurements of the IMRI system. The change of the mass of the central black hole has a larger impact on the eccentricity. When the mass of the central black hole is about $10^{3}M_{\odot}$, the enhancement effect of dark matter on the eccentricity is significant. When the mass of the black hole is about $10^{5} M_{\odot}$, the effect of dark matter on the eccentricity becomes very small. Compared to the dark matter spike, the influence of dark matter halo on the enhancement effect of the eccentricity needs to be seen at a much larger distance, which makes observation more difficult.(3) The dark matter is approximated to the perfect fluid dark matter, and the profile of dark matter is obtained by selecting the appropriate equation of state. It is observed that the density of dark matter in galactic cores is close to a constant, which contradicts the results of the cold dark matter model. Therefore, it is interesting to find the distribution of dark matter with a constant core. In this model, by selecting the state equation of perfect fluid dark matter, we find that the perfect fluid dark matter can contain both the constant core of dark matter in the center of the galaxy and the power law profile of dark matter in the outer of galaxy, and we can also get the PI profile. These profiles can better fit the rotation curves of LSB galaxies.In conclusion, we have studied the dark matter profiles near the black hole, and our research contributes to the understanding of the dark matter model. |
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