2020-12-24 干了啥

By | 2020-12-24

2020-12-24

  1. 找到了 arXiv:1708.03491v1 中使用的 $$M{bh}$$ 和 $$M{stellar}$$ 的关系。这个关系是让 $$M{bh}$$ 的和等于 $$M{bulge}$$. 然后用 这篇文章 中的 Figure3 caption 中的方程得到的。
  2. 该关系为:
    def Mbh2Mbulge(Mbulge):
 """
 M_BH-M_bulge. Bulge mass to black hole mass (note that M_bulge = Mstar; assume these are the same)
 McConnell and Ma (2013) relation below Figure 3
 Includes scatter in the relation, \epsilon = 0.34
 Answer in solar masses.
 """
 exponent = 8.46+1.05*log10(Mbulge/1e11)
 ans_w_scatter = np.random.normal(exponent,0.34)
 #print locals()
 return 10**ans_w_scatter
    这是一个单调单参数函数，所以可以预期（并已经证明）只使用这个函数并没有什么用。

  3. 发现这个函数可能是我们需要关注的:

    def i_prob_Illustris(Mstar, Mtot, q, min_freq):
 """
 Probability that this galaxy contains a binary in the PTA band
 """
 chirpMass = mchirp_q(q,Mtot)/s_mass #in solar mass units
 M1 = Mtot/(1+q)
 M2 = M1*q
 mu_min, mu_max = 0.25, 1.0
 gamma = 1.0 # for Hernquist profile, see Dehen 1993

 #Mstar = Mstar*MzMnow(mu, sigma) # scale M* according to Figure 7 of de Lucia and Blaizot 2007
 MstarZ = 0.7*Mstar
 hardening_t, r_inf_here = t_hard(MstarZ,q,gamma,Mtot)
 friction_t = tfric(MstarZ,M2)
 timescale = hardening_t + friction_t  # Gyrs 

 # if timescale > 12.25 Gyrs (z=4), no merging SMBHs
 # also limit of validity for Rodriguez-Gomez + (2015) fit in Table 1.
 if timescale > 12.25: 
     return 0, 'nan', timescale*1e9, 'nan', 'nan',  r_inf_here, friction_t, hardening_t
 else:
     z = z_at_value(Planck15.age, (13.79-timescale) * u.Gyr) # redshift of progenitor galaxies
     t2c = time_to_c_wMc(chirpMass, min_freq) # in years
     mergRate = cumulative_merg_ill(mu_min, mu_max, MstarZ, z) # rate per Gigayear
     Tz = timescale*1e9
     ans = t2c*mergRate/1e9
     return ans, z, Tz, mergRate, t2c, r_inf_here, friction_t, hardening_t

    主要是里面写了 z>4 的时候没有并合，这可能跟我们想要的结果一致。

  4. 把 cpt 的程序写了一下，发现跑不通，明天再搞。
    image.png