DeprojSersicModel
- class deprojected_sersic_models.DeprojSersicModel(total_mass=1.0, Reff=1.0, n=1.0, q=0.4, i=90.0, Upsilon=1.0)[source]
Bases:
_SersicDistBaseDeprojected Sersic mass distribution, with arbitrary flattening (or elongation).
- Parameters:
total_mass (float) – Total mass of the component [Msun]
Reff (float) – Effective radius of Sersic profile [kpc]
n (float) – Sersic index
q (float) – Intrinsic axis ratio of Sersic profile (c/a)
i (float) – Inclination of system [deg]
Upsilon (float, optional) – Mass-to-light ratio. Default: 1. (i.e., constant ratio)
invq (float, derived) – Flattening of Sersic profile; invq=1/q. (Derived)
Ie (float, derived) – Normalization of Sersic intensity profile at kap = Reff. (Derived)
Methods Summary
density(R)Density profile at \(m=R\) of the deprojected Sersic mass distribution.
dlnrho_dlnR(R)Slope of the log density profile, \(d\ln\rho/d\ln{}R\), in the midplane at radius \(m=R\) of the deprojected Sersic mass distribution.
drho_dR(R)Derivative of the density profile, \(d\rho/dR\), at distance \(m=R\) of the deprojected Sersic mass distribution.
enclosed_mass(R[, cumulative])Enclosed 3D mass within a sphere of radius r=R, assuming a constant M/L ratio Upsilon.
enclosed_mass_ellipsoid(R[, cumulative])Enclosed 3D mass within an ellpsoid of major axis radius r and intrinsic axis ratio q (e.g. the same as the Sersic profile isodensity contours), assuming a constant M/L ratio Upsilon.
profile_table(R[, cumulative, ...])Create a set of profiles as a dictionary, calculated over the specified radii.
Projected 2D mass enclosed within an ellipse (or elliptical shell), assuming a constant M/L ratio Upsilon.
Surface density distribution for a Sersic profile, assuming a M/L ratio Upsilon.
v_circ(R)Circular velocity in the midplane of the deprojected Sersic mass distribution.
virial_coeff_3D(R[, m3D, vc])The "3D" virial coefficient k3D, which satisfies
virial_coeff_tot(R[, vc])The "total" virial coefficient ktot, which satisfies
Methods Documentation
- density(R)[source]
Density profile at \(m=R\) of the deprojected Sersic mass distribution.
See Eq. 2 of Price et al. 2022 (also Eq. 9 of Noordermeer 2008)
- dlnrho_dlnR(R)[source]
Slope of the log density profile, \(d\ln\rho/d\ln{}R\), in the midplane at radius \(m=R\) of the deprojected Sersic mass distribution.
See Eq. 17 of Price et al. 2022
- drho_dR(R)[source]
Derivative of the density profile, \(d\rho/dR\), at distance \(m=R\) of the deprojected Sersic mass distribution.
See Eq. 17 of Price et al. 2022
- enclosed_mass(R, cumulative=False)[source]
Enclosed 3D mass within a sphere of radius r=R, assuming a constant M/L ratio Upsilon.
See Eq. 8 of Price et al. 2022
- Parameters:
- Returns:
Menc3D_sphere
- Return type:
float or array_like
- enclosed_mass_ellipsoid(R, cumulative=False)[source]
Enclosed 3D mass within an ellpsoid of major axis radius r and intrinsic axis ratio q (e.g. the same as the Sersic profile isodensity contours), assuming a constant M/L ratio Upsilon.
See Eq. 6, Price et al. 2022
- Parameters:
- Returns:
Menc3D_ellip
- Return type:
float or array_like
- profile_table(R, cumulative=None, add_reff_table_values=True)[source]
Create a set of profiles as a dictionary, calculated over the specified radii. Also includes constants for the specified Sersic profile parameters, and information about values at Reff or the 3D half mass radius.
- Parameters:
R (float or array_like) – Radius array, in kpc
cumulative (bool, optional) – Shortcut option to only calculate the next annulus, then add to the previous Menc(r-rdelt). Default: Uses cumulative if n >= 2.
add_reff_table_values (bool, optional) – Add select values at Reff to the table. Requires Reff to be in
RDefault: True
- Returns:
table – Dictionary containing the various profiles & values.
- Return type:
- projected_enclosed_mass(R)[source]
Projected 2D mass enclosed within an ellipse (or elliptical shell), assuming a constant M/L ratio Upsilon.
See Graham & Driver 2005.
- surface_density(R)[source]
Surface density distribution for a Sersic profile, assuming a M/L ratio Upsilon.
See Price et al. 2002, Eq 3; Noordermeer 2008, Eq 11; Graham & Driver 2005; etc.
- v_circ(R)[source]
Circular velocity in the midplane of the deprojected Sersic mass distribution.
See Eq. 5 of Price et al. 2022 (also Eq. 10 of Noordermeer 2008)
- virial_coeff_3D(R, m3D=None, vc=None)[source]
The “3D” virial coefficient k3D, which satisfies
\[M_{\mathrm{3D,sphere}}(R) = k_{\mathrm{3D}}(R) \frac{v_{\mathrm{circ}}(R)^2 R}{ G },\]to convert between the circular velocity at any given radius and the mass enclosed within a sphere of radius R.
See Eq. 9, Price et al. 2022
- Parameters:
R (float or array_like) – Major axis radius within which to determine total enclosed 2D projected mass [kpc]
m3D (float or array_like, optional) – Pre-calculated evaluation of Menc3D_sphere(R) (saves time to avoid recalculating Menc3D_sphere(R)) [Msun]
vc (float or array_like, optional) – Pre-calculated evaluation of vcirc(R) (saves time to avoid recalculating vcirc(R)) [km/s]
- Returns:
k3D – k3D = Menc3D_sphere(R) * G / (vcirc(R)^2 * R)
- Return type:
float or array_like
- virial_coeff_tot(R, vc=None)[source]
The “total” virial coefficient ktot, which satisfies
\[M_{\mathrm{tot}} = k_{\mathrm{tot}}(R) \frac{v_{\mathrm{circ}}(R)^2 r}{ G },\]to convert between the circular velocity at any given radius and the total system mass.
See Eq. 10, Price et al. 2022
- Parameters:
- Returns:
ktot – ktot = Mtot * G / (vcirc(R)^2 * r)
- Return type:
float or array_like