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A DIGEST OF A SERIES OF PAPERS ON DARK MATTER SUBSTRUCTURE: MASS FUNCTION, MASS-LOSS RATE, AND MASS FRACTION

Version 2012-01-18

This is like a working manual or tutorial on getting to know the field of subhalo mass function and dark matter substructures.

That’s my guess, i.e., the FP should be different.

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I Just Do Not Believe 1D Sersic fitting … It is susceptible by both the inner-most part of the surface brightness profile and the outskirt of the profile … How can we astronomers trust the effective radius given by such a ridiculous fitting procedure …

It took me some time to realize that basic conceptual thing. Hope you won’t make the following kind of stupid mistake:

(- i\hbar\nabla-q\vec{A})^2=-\hbar^2\nabla^2+i\hbar q(\vec{A}\cdot\nabla+\nabla\cdot\vec{A})+q^2\vec{A}^2

Instead, it should be:

(-i\hbar\nabla-q\vec{A})^2=-\hbar^2\nabla^2+i\hbar q(\vec{A}\cdot\nabla+2\nabla\cdot\vec{A})+q^2\vec{A}^2

The point is that we should always treat \nabla as an operator rather than a vector, i.e., when we are deriving a formula involving \nabla, we should always keep a function f at the end of each step !!!

This galaxy is well-known, so I will release the details later. It is very similar to its high-z counterpart in terms of its compactness, embeded disk, high velocity dispersion, stellar age and possibly its extended X-ray profile, except that it is an order of magnitude less massive, which will embarrass calling it an analogue, but won’t make it reside with ultra-compact dwarfs anyway.

There is a bunch of papers which have included it in samples for a variety of purposes, but this is the first time it is put into the context of galaxy growth and the origin of compactness. Hopefully it will provide us some clues about the detailed internal structure and environment of not only itself but also its high-z counterparts.

This is my report for the Numerical Project 1 of Prof. Sarbani Basu’s ASTR550 course on stellar structure and evolution at Yale University. In this report, I made 2 nice plots showing the anti-correlation between the reaction rate of CNO cycle and the critical mass above which a star develops a convective core.

yrec.proj.fangzhou.jiang

I realized classic 4th order Runge-Kutta method in C  and higer order Runge-Kutta-Fehlberg methods with adaptive step size (RKF5(4) and RKF7(8)) as well. This is my practice in ASTR520 course at Yale.

runge.kutta.methods.with.codes.in.c

(我用C语言实现了四阶龙格库塔方法(RK4)和更高阶的科学级的变步长龙格库塔方法(RKF5(4), RKF7(8)),这也是我在耶鲁大学天文系ASTR520课程的练习。)

bs.degree.thesis.fangzhou.jiang

Whimsy helped me a lot for this one, my first SCI paper, which can also be found at ArXiv.org:

http://arxiv.org/abs/1009.2562

I used YREC to evolve a 2 solar mass star with Z=0.02, Y=0.27 to the end of its main sequence. First I put overshoot off and then turned it on. It is obvious that convective overshoot increases effective temperature and thus luminosity, which fastens the evolution to make the star leave main-sequence earlier. And the increase in the abundance of Helium increased the the luminosity without increasing the temperature noticeably. This may be realized by a decreased radius, for $L=4*pi*r^2\sigma*T_{eff}$.


MATLAB codes for plotting:

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hold off

subplot(1,2,1)

luminosity1=track1(:,7)

t_eff1=track1(:,10)

plot(t_eff1,luminosity1,’LineWidth’,2)

ylabel(‘Log(L/L_{sun})’)

xlabel(‘Log(T_{eff})’)

axis([3.65 4 1.1 1.7])

set(gca,’xdir’,’reverse’)

title(‘H-R Diagram for 2M_{sun} Star Z=0.02, Y=0.27′)

hold on;

luminosity2=track2(:,7)

t_eff2=track2(:,10)

plot(t_eff2,luminosity2,’r’,’LineWidth’,2)

legend(‘without overshoot’,’with overshoot’)

subplot(1,2,2)

luminosity3=track3(:,7)

t_eff3=track3(:,10)

plot(t_eff3,luminosity3,’LineWidth’,2)

ylabel(‘Log(L/L_{sun})’)

xlabel(‘Log(T_{eff})’)

axis([3.65 4 1.1 1.7])

set(gca,’xdir’,’reverse’)

title(‘H-R Diagram for 2M_{sun} Star Z=0.02, Y=0.32’)

legend(‘without overshoot’)

hold off

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%