nugridpy.astronomy¶
Constants and methods for astronomy & astrophysics
Functions
Gamma1_gasrad(beta) |
Gamma1 for a mix of ideal gas and radiation | ||
Nasv(macs, T) |
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Pgas(rho, T, mu) |
P = R/mu * rho * T | ||
Prad(T, mu) |
P = a/3 * T**4 | ||
Trho_iddeg(rho, mu, mu_e) |
T(rho) that separates ideal gas and degenerate pressure dominated regions. | ||
Trho_idrad(rho, mu) |
T(rho) that separates P_rad from P_gas dominated regions. | ||
am_orb(m1, m2, a, e) |
orbital angular momentum. | ||
core_mass_L(MH) |
Core-mass luminosity relationship from Bloecker (1993). | ||
energ_orb(m1, m2, r) |
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escape_velocity(M, R) |
escape velocity. | ||
imf(m) |
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int_imf_dm(m1, m2, m, imf[, bywhat, integral]) |
Integrate IMF between m1 and m2. | ||
macs(nasv, T) |
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mass_loss_loon05(L, Teff) |
mass loss rate van Loon etal (2005). | ||
mimf_ferrario(mi) |
Curvature MiMf from Ferrario etal. | ||
mu(X, Z, A) |
mean molecular weight assuming full ionisation. | ||
mu_e(X) |
mean molecular weight per free electron, assuming full ionisation, and | ||
period(A, M1, M2) |
calculate binary period from separation. | ||
visc_mol_sol(T, rho, X) |
Molecular plasma viscosity (Spitzer 1962) | ||
visc_rad_kap_sc(T, rho, X) |
Radiative viscosity (Thomas, 1930) for e- scattering opacity |
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nugridpy.astronomy.Gamma1_gasrad(beta)¶ Gamma1 for a mix of ideal gas and radiation
Hansen & Kawaler, page 177, Eqn. 3.110
Parameters: beta (float) – Gas pressure fraction Pgas/(Pgas+Prad)
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nugridpy.astronomy.Nasv(macs, T)¶ Returns: for MACS [mb] at T [K]. Return type: Na*<sigma v>
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nugridpy.astronomy.Pgas(rho, T, mu)¶ P = R/mu * rho * T
Parameters: - mu (float) – Mean molecular weight
- rho (float) – Density [cgs]
- T (float) – Temperature [K]
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nugridpy.astronomy.Prad(T, mu)¶ P = a/3 * T**4
Parameters: - a (float) – Radiation constant [erg cm^-3 K^-4].
- T (float) – Temperature [K].
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nugridpy.astronomy.Trho_iddeg(rho, mu, mu_e)¶ T(rho) that separates ideal gas and degenerate pressure dominated regions.
Kippenhahn & Weigert, Eq. 16.6
Parameters: - rho (float) – Density array [cgs].
- mu (float) – Mean molecular weight.
- mu_e (float) – Mean molecular weight per free electron.
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nugridpy.astronomy.Trho_idrad(rho, mu)¶ T(rho) that separates P_rad from P_gas dominated regions.
Kippenhahn & Weigert, Eq. 16.10
Parameters: - rho (float) – Density array [cgs].
- mu (float) – Mean molecular weight.
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nugridpy.astronomy.am_orb(m1, m2, a, e)¶ orbital angular momentum.
e.g Ge etal2010
Parameters: - m2 (m1,) – Masses of both stars in Msun.
- A (float) – Separation in Rsun.
- e (float) – Eccentricity
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nugridpy.astronomy.core_mass_L(MH)¶ Core-mass luminosity relationship from Bloecker (1993).
Parameters: MH (float) – Core mass in Msun. Returns: Luminosity in Lsun Return type: L
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nugridpy.astronomy.energ_orb(m1, m2, r)¶ Parameters: - m2 (m1,) – M in Msun.
- r (float) – Distance in Rsun.
Returns: Epot in erg.
Return type: Epot
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nugridpy.astronomy.escape_velocity(M, R)¶ escape velocity.
Parameters: - M (float) – Mass in solar masses.
- R (float) – Radius in solar radiu.
Returns: in km/s.
Return type: v_escape
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nugridpy.astronomy.imf(m)¶ Returns: for given mass according to Kroupa IMF, vectorization available via vimf() Return type: N(M)dM
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nugridpy.astronomy.int_imf_dm(m1, m2, m, imf, bywhat='bymass', integral='normal')¶ Integrate IMF between m1 and m2.
Parameters: - m1 (float) – Min mass
- m2 (float) – Max mass
- m (float) – Mass array
- imf (float) – IMF array
- bywhat (string, optional) – ‘bymass’ integrates the mass that goes into stars of that mass interval; or ‘bynumber’ which integrates the number of stars in that mass interval. The default is ‘bymass’.
- integrate (string, optional) – ‘normal’ uses sc.integrate.trapz; ‘cum’ returns cumulative trapezoidal integral. The default is ‘normal’.
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nugridpy.astronomy.macs(nasv, T)¶ Returns: [mb] at T [K] from Na*<sigma v>. Return type: MACS
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nugridpy.astronomy.mass_loss_loon05(L, Teff)¶ mass loss rate van Loon etal (2005).
Parameters: - L (float) – L in L_sun.
- Teff (float) – Teff in K.
Returns: Mdot in Msun/yr
Return type: Mdot
Notes
ref: van Loon etal 2005, A&A 438, 273
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nugridpy.astronomy.mimf_ferrario(mi)¶ Curvature MiMf from Ferrario etal. 2005MNRAS.361.1131.
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nugridpy.astronomy.mu(X, Z, A)¶ mean molecular weight assuming full ionisation.
(Kippenhahn & Weigert, Ch 13.1, Eq. 13.6)
Parameters: - X (float) – Mass fraction vector.
- Z (float) – Charge number vector.
- A (float) – Mass number vector.
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nugridpy.astronomy.mu_e(X)¶ mean molecular weight per free electron, assuming full ionisation, and approximating mu_i/Z_i ~ 2 for all elements heavier then Helium.
(Kippenhahn & Weigert, Ch 13.1, Eq. 13.8)
Parameters: X (float) – Mass fraction of H.
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nugridpy.astronomy.period(A, M1, M2)¶ calculate binary period from separation.
Parameters: - A (float) – separation A Rsun.
- M2 (M1,) – M in Msun.
Returns: period in days.
Return type: p
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nugridpy.astronomy.visc_mol_sol(T, rho, X)¶ Molecular plasma viscosity (Spitzer 1962)
Parameters: - X (float) – H mass fraction
- T (float) – temperature in K
- rho (float) – density in cgs
Returns: nu – molecular diffusivity in [cm**2/s]
Return type: float
Notes
According to Eq 22 in Schatzman (1977). Assume log Lambda = 15. (see Table 5.1), a H/He mix (for different mix use Eq. 5.54 in Spitzer text book)
Examples
see astronomy.visc_rad_kap_sc
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nugridpy.astronomy.visc_rad_kap_sc(T, rho, X)¶ Radiative viscosity (Thomas, 1930) for e- scattering opacity
Parameters: - X (float) – H mass fraction
- T (float) – temperature in K
- rho (float) – density in cgs
Returns: nu – radiative diffusivity in [cm**2/s]
Return type: float
Examples
>>> In [1]: import astronomy as ast >>> In [2]: l = 100*1.e5 # 100km >>> In [3]: v = 1.e5 # typical velocity >>> In [4]: T = 90.e6 # temperature >>> In [5]: X = 0.001 # H mass fraction >>> In [6]: rho = 100. # density >>> In [7]: nu = ast.visc_rad_kap_sc(T,rho,X) >>> In [8]: Re=v*l/nu >>> In [9]: print "Re_rad = "+str('%g'%Re) >>> Re_rad = 4.43512e+08
Notes
Eqn. 14’ in Schatzman, 1977, assume electron scattering opacity kappa_sc = 0.2*(1+X), Kippenhahn (2nd edn, Eqn 17.2)
