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Research in China

I partly resolve the firewall issue by using VPN, but the connectivity is still poor.

I read Chapter 4,5 of Astrophysics in a nutshell and get some basic idea and questions about star formation, PN and PPN. It is interesting that the birth and death of stars in a molecular cloud is connected by turbulence, magnetic field and radiation.

I did not manage to see the Dean of Astronomy of Beijing Normal University because I felt uncomfortable in Beijing after staying for 5 days and went back to Wuhan.

Below is the research in stellar wind:

The next goal is to change the intensity of radiation force. Restate the governing equation first. To change the radiation force means to change the sonic radius and perhaps the temperature.

(\frac{v^2}{a^2}-1)-ln{\frac{v^2}{a^2}}=4ln{\frac{r}{r_c}}+4(\frac{r_c}{r}-1)

The first way is to solve this algebraic equation by Newton-Raphson method (This is one of the many methods). A given r will correspond to 2 v values as solutions. Then plug the r vs. v, r vs. \rho profile (from the wind base up to sonic point) back to outflow source and then change the wind.

Another way is to solve the hydrostatic equation:

\nabla P=-\frac{GM}{r^2}

M is constant mass because I assume the wind base is at moderate radius s.t. the inner mass dominate. Use isothermal assumption:

P=\frac{2\rho k T}{m_p}

The gas is assumed to be consisted of fully ionized hydrogen. m_p is the proton mass and \rho is the gas density.

The final solution of \rho is:

\rho=\rho_0 Exp(\frac{m_p G M}{2 k T}(\frac{1}{r}-\frac{1}{r_0}))

where \rho_0=\rho(r_0)

Hydrostatic solution is appropriate only when \nabla P \gg \rho u \cdot \nabla u i.e. in much inner region than the sonic radius.

The strategy is to specify the wind base v and \rho profile and let AstroBEAR build self consistent atmosphere and wind via Riemann solver.

Remark: People may think the first way is easier and more computationally economic, but the second way also has certain advantage: it is more self consistent, we can further specify the nonuniform magnetic field at the wind base. If we go deeper into the AGB star I think we will touch the regime of dynamo theory and polytrope.

astrobear

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Research in China

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