# Research

### Mass-Radius Relation of Neutron Stars

• I got the relation between the central energy density and central mass density. In the polytropic n = 1 ($\gamma = 2$) case,

$P = K \rho^{\gamma} \ \text{ and } \ E_{\text{internal}} = \frac{P}{\gamma - 1}$

$\text{Since } \ \epsilon = \rho c^2 + E_{\text{internal}},$

$\epsilon = \rho c^2 + K \rho^2$

$\text{Therefore, } \ \rho = \frac{-c^2 + \sqrt{c^4 + 4K\epsilon}}{2K}$

• Using this relation, I put the central mass density into my TOV solver and compare with RNS result.
• The results are slightly different. Now I have to find why they are different.

# Study

### Astronomy & Astrophysics

• I have read no Astrophysical articles today. Today’s topics were not interesting for me.

### English

• I have studied 28 words using Anki.

### General Science

• I have read the Nature Briefing article. I found this article was very interesting. It says that two gut bacteria are linked to our quality of life, even we could experience some kind of depression when we lack them.

### Math

• I have solved 10 GRE Quantitative problems.