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NGC3603 中的尘埃颗粒

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NGC3603 中的尘埃颗粒. 新模型. 内容. 拟和 : 检验 模型 方法 结果 : 温度 尘埃密度 Gas-to-dust ratio TODO. 拟和检验. 卡方检验 : 测量次数 >50, 样本 ? 个体 ?(BingJiang) Cash 检验 (cstat): 中心极限定理之一 , 大数近似 , 复合泊松 -> 高斯分布 . 测量次数不确定 (MSX,helpdesk) Ref: Ciao(Yangchen),xspec(Yangchen),cash et al Xspec manual 及附录 ,

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slide2
内容

拟和:

  • 检验
  • 模型
  • 方法

结果:

  • 温度
  • 尘埃密度
  • Gas-to-dust ratio

TODO

slide3
拟和检验
  • 卡方检验: 测量次数>50,样本?个体?(BingJiang)
  • Cash检验(cstat):
    • 中心极限定理之一,大数近似,复合泊松->高斯分布.
    • 测量次数不确定(MSX,helpdesk)
    • Ref:
      • Ciao(Yangchen),xspec(Yangchen),cash et al
      • Xspec manual及附录,
      • Xspec作者主页http://lheawww.gsfc.nasa.gov/~kaa/head_stats/title.html
  • Least-square. Goodness. – 没有好的goodness评价方案,拟和时舍弃sigma数据(errorbar).
slide4
拟和模型
  • 4PAH+blackbody
  • 考虑到21um附近没有PAH辐射,令c=0,得到3PAH+blackbody

结果都不好,怀疑mathematica的结果,局部最小?且有警告.

换其他软件拟和?编程找到合适的a,b,c值?

slide7
拟和软件
  • Mathematica: NonlinearFit – ?分段函数
  • Matlab: cftool, Optimization Toolbox - ? ..
  • GSL:http://www.gnu.org/software/gsl
  • 1stOpt : “世界上最好的拟和软件”

算法最多(UGO)!支持全局优化!不受初值影响!可设定参数范围!支持代码分段!

slide8
GSL代码
  • #include "t.c" int main(void) { size_t np = 3; double par[2] = {1.39, 0.8}; const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex; gsl_multimin_fminimizer *s = NULL; gsl_vector *ss, *x; gsl_multimin_function minex_func; size_t iter = 0, i; int status; double size; /* Initial vertex size vector */ ss = gsl_vector_alloc (np); /* Set all step sizes to 1 */ gsl_vector_set_all (ss, 1.0); /* Starting point */ x = gsl_vector_alloc (np); gsl_vector_set (x, 0, 1.0);/* U */ gsl_vector_set (x, 1, 100);/* v */ gsl_vector_set (x, 2, 20);/* t */ /* Initialize method and iterate */ minex_func.f = &my_f; minex_func.n = np; minex_func.params = (void *)&par; s = gsl_multimin_fminimizer_alloc (T, np); gsl_multimin_fminimizer_set (s, &minex_func, x, ss); do { iter++; status = gsl_multimin_fminimizer_iterate(s); if (status) break; size = gsl_multimin_fminimizer_size (s); status = gsl_multimin_test_size (size, 1e-10); if (status == GSL_SUCCESS) { printf ("converged to minimum at\n"); } printf ("%5d ", iter); for (i = 0; i < np; i++) { printf ("%G ", gsl_vector_get (s->x, i)); } printf ("f() = %G size = %G\n", s->fval, size); } while (status == GSL_CONTINUE && iter < 100); //while (status == GSL_CONTINUE ); gsl_vector_free(x); gsl_vector_free(ss); gsl_multimin_fminimizer_free (s); return status; }
slide9
GSL的结果
  • LM方法非线性拟和:T=11K,目标函数值偏大,明显不是全局最小!
  • 最小值方法: 直接退出 .

无法编程寻找a,b

于是决定用土方法: 1stOpt穷举a,b对.

1stopt nd a b
1stOpt: 限制nd,寻找合理的a,b对

a 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

-ring 0.8 0.746 0.699 0.660 0.631 0.605 0.584 0.566 0.552 0.539 0.529

-A 0.915 0.845 0.790 0.745 0.708 0.678 0.653 0.633 0.616 0.6 0.588

-B 0.746 0.692 0.649 0.615 0.587 0.563 0.544 0.528 0.515 0.504 0.495

-C 0.563 0.527 0.499 0.476 0.458 0.443 0.432 0.422 0.414 0.408 0.403

-D 0.725 0.671 0.627 0.592 0.564 0.541 0.521 0.505 0.492 0.480 0.471

可以看到各个区域的b值单调减小,在a[1,2]内,b永不相交!

slide12
新的参数方案
  • 理由: 所有区域使用一致的PAH比例是不可能的.
  • 做法: exp[500/30*0.6]=exp[10]>>1,考虑到黑体谱只对E波段有影响,所以对于ACD,PAH比例从数据直接估算.
slide13
估算方案
  • 对原始数据做除法,求出对应区域每个点的流量比再对区域平均. Bin->div->平均. Msx+ds9 Region文件的bin: ciao格式(BingJiang).
  • 直接对最终数据(Fnu)做除法.
slide14
结果分析
  • C区域nd偏大3个量级,T偏小(20K)
  • BD区域偏小.
  • A~10ring.

仍然无法得到一致的尘埃密度

只选A,ring区.

1stopt
1stOpt代码

Title "ring";

Parameter u = 1 [0.1,10],v=100000000[10000,100000000000] ,t = 30[20,300];

Constant h=479.92156638356494;

Constant a=4.86/3.72,b=3.20/4.86;

DataSet;

x,y,s=

3.62319 3.72061 0.771501

2.47321 4.85386 1.44736

2.04778 3.20737 0.763918

1.40581 6.71629 2.05759

EndDataSet;

ConstStr FA=u+v*(x1^4)/(exp(h/t*x1)-1);

ConstStr FC=a*u+v*(x2^4)/(exp(h/t*x2)-1);

ConstStr FD=b*a*u+v*(x3^4)/(exp(h/t*x3)-1);

ConstStr FE=v*(x4^4)/(exp(h/t*x4)-1);

MinFunction (FA-y1)^2+(FC-y2)^2+(FD-y3)^2+(FE-y4)^2;

slide20
尘埃密度和尘气比
  • Q取ss433文:1.45*10^-16nu,得到尘埃密度:10 ^-9
  • (model2使用draine 1993之SiC数据)

Vring=6.401E+08

Va=1.10011E+07

Lunit=0.000203622 Unit=8.44253E-12 (kpc)(kpc)(kpc)

region ring:

model1: nd=1.49419E-10 g/d=4427.27

model2: nd=3.46971E-10 g/d=1906.55

region A:

model1: nd=2.99752E-09 g/d=220.689

model2: nd=6.93232E-09 g/d=95.4254

q lambd 2
Q,Lambd-2
  • Draine 1993: :Q(SiC)~Q(ss433)~0.1Q(Si)
  • 选sic还是si?why?or 其他颗粒?
  • Q的选取.只照顾到E就ok?(>21,q~lambd-2,draine 1984)
slide22
TODO
  • Draine 1984 和 Takeuchi文比较,后者做作lambda-2 fit(Yangchen).
  • 寻找NGC3603温度依据30kk? (22kk now).
  • 1000颗恒星的依据
  • Q值.