models – astronomy-specific models for pymodelfit¶

This module makes use of the pymodelfit package to define a number of models inteded for data-fitting that are astronomy-specific. Note that pymodelfit was originally written as part of astropysics, and hence it is tightly integrated (including the Fit GUI, where relevant) to other parts of astropysics, often using the models in this module.

Note

Everything in the pymodelfit package is imported to this package. This is rather bad form, but is currently done because other parts of astropysics is written for when pymodelfit was part of astropysics. This may change in the future, though, so it is recommended that user code always use from pymodelfit import ... instead of from astropysics.models import ....

Classes and Inheritance Structure¶

Inheritance diagram of astropysics.models

Module API¶

class astropysics.models.BlackbodyModel(unit='wl')¶

Bases: pymodelfit.core.FunctionModel1DAuto, astropysics.spec.HasSpecUnits

A Planck blackbody radiation model.

Output/y-axis is taken to to be specific intensity.

A = 1¶

T = 5800¶

c = 29979245800.0¶

f(x, A=1, T=5800)¶

getFlux(x, radius=None, distance=None)¶

Returns the flux density at the requested wavelength for a blackbody of the given radius at a specified distance.

Parameters:	x (float) – x-value of the model radius (float) – radius of the blackbody in cm distance (float) – distance to the blackbody in cm
Returns:	flux/wl at the specified distance from the blackbody

getFluxDistance(radius)¶: Determines the distance to a spherical blackbody of the specified radius assuming the flux is given by the model at the given temperature.

getFluxRadius(distance)¶: Determines the radius of a spherical blackbody at the specified distance assuming the flux is given by the model at the given temperature.

h = 6.626068e-27¶

kb = 1.3807e-16¶

peak¶

rangehint¶

setFlux(radius, distance)¶

Sets A so that the output is the flux at the specified distance from a spherical blackbody with the specified radius.

Parameters:	radius (float) – Radius of the blackbody in cm distance (float) – distance to the blackbody in cm

setIntensity()¶: Sets A so that the output is specific intensity/surface brightness.

static stephanBoltzmannLaw(T, area=1)¶: assumes cgs units

wienDisplacementLaw(peakval)¶

Uses the Wien Displacement Law to calculate the temperature given a peak input location (wavelength, frequency, etc) or compute the peak location given the current temperature.

Parameters:	peakval (float or None) – The peak value of the model to use to compute the new temperature.
Returns:	The temperature for the provided peak location or the peak location for the current temperature if peakval is None.

xaxisname¶

yaxisname = 'I'¶

class astropysics.models.BurkertModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

Burkert (1996) profile defined as:

$\frac{\rho_0 r_0^3}{(r+r_0)(r^2+r_0^2)}$

where rho0 is the central density.

f(r, rho0=1, r0=1)¶

r0 = 1¶

rangehint¶

rho0 = 1¶

xaxisname = 'r'¶

yaxisname = 'rho'¶

class astropysics.models.DeVaucouleursModel¶

Bases: astropysics.models.SersicModel

Sersic model with n=4.

Ae = 1¶

f(r, Ae=1, re=1)¶

re = 1¶

xaxisname = 'r'¶

class astropysics.models.EinastoModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

Einasto profile given by

$\ln(\rho(r)/A) = (-2/\alpha)((r/r_s)^{\alpha} - 1) .$

A is the density where the log-slope is -2, and rs is the corresponding radius. The alpha parameter defaults to .17 as suggested by Navarro et al. 2010

Note

The Einasto profile is is mathematically identical to the Sersic profile (SersicModel), although the parameterization is different. By Convention, Sersic generally refers to a 2D surface brightness/surface density profile, while Einasto is usually treated as a 3D density profile.

A = 1¶

alpha = 0.17¶

f(r, A=1, rs=1, alpha=0.17)¶

rs = 1¶

xaxisname = 'r'¶

yaxisname = 'rho'¶

class astropysics.models.ExponentialDiskModel¶

Bases: pymodelfit.core.FunctionModel2DScalarAuto

A disk with an exponential profile along both vertical and horizontal axes. The first coordinate is the horizontal/in-disk coordinate (scaled by l) wile the second is z. i.e.

$A e^{-|s/l|} e^{-|z/h|}$

for pa = 0 ; non-0 pa rotates the profile counter-clockwise by pa radians.

A = 1¶

f(inarr, A=1, l=2, h=1, pa=0)¶

h = 1¶

l = 2¶

pa = 0¶

rangehint¶

class astropysics.models.ExponentialSechSqDiskModel¶

Bases: pymodelfit.core.FunctionModel2DScalarAuto

A disk that is exponential along the horizontal/in-disk (first) coordinate, and follows a ${\rm sech}^2(z)$ profile along the vertical (second) coordinate. i.e.

$A e^{-|s/l|} {\rm sech}^2 (z/h)$

for pa = 0 ; non-0 pa rotates the profile counter-clockwise by pa radians.

A = 1¶

f(inarr, A=1, l=2, h=1, pa=0)¶

h = 1¶

l = 2¶

pa = 0¶

rangehint¶

class astropysics.models.GaussHermiteModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

Model notation adapted from van der Marel et al 94

hj3 are h3,h4,h5,... (e.g. N=len(hj3)+2 )

A = 1¶

f(v, A=1, v0=0, sig=1, *hj3)¶

gaussHermiteMoment(l, f=None, lower=-inf, upper=inf)¶: compute the requested moment on the supplied function, or this object if f is None

paramnames = 'h'¶

paramoffsets = 3¶

rangehint¶

sig = 1¶

v0 = 0¶

class astropysics.models.HernquistModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

Hernquist (1990) profile defined as:

$\frac{A r_0}{2 \pi r (r+r_0)^3}$

where A is the total mass enclosed. Note that r0 does not enclose half the mass - the radius enclosing half the mass is $r_h = \frac{r_0}{\sqrt{2}-1}$ .

Note

This form is equivalent to an AlphaBetaGammaModel with $(\alpha,\beta,\gamma) = (1,4,1)$ , but with a slightly different overall normalization.

A = 1¶

f(r, A=1, r0=1)¶

r0 = 1¶

rangehint¶

xaxisname = 'r'¶

yaxisname = 'rho'¶

class astropysics.models.InclinedDiskModel(inc=0, pa=0, degrees=True, **kwargs)¶

Bases: pymodelfit.core.FunctionModel2DScalarDeformedRadial

Inclined Disk model – identical to FunctionModel2DScalarDeformedRadial but with inclination (inc and incdeg) and position angle (pa and padeg) in place of axis-ratios.

class astropysics.models.JaffeModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

Jaffe (1983) profile as defined in Binney & Tremaine as:

$\frac{A}{4 \pi} \frac{r_j}{r^2 (r+r_j)^2)}$

where A is the total mass enclosed. rj is the radius that encloses half the mass.

Note

This form is equivalent to an AlphaBetaGammaModel with $(\alpha,\beta,\gamma) = (1,4,2)$ , but with a slightly different overall normalization.

A = 1¶

f(r, A=1, rj=1)¶

rangehint¶

rj = 1¶

xaxisname = 'r'¶

yaxisname = 'rho'¶

class astropysics.models.King2DrModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

2D (projected/surface brightness) King model of the form:

$f(r) = A r_c^2 (\frac{1}{\sqrt{r^2+r_c^2}} - \frac{1}{\sqrt{r_t^2+r_c^2}})^2$

See also

King (1966) AJ Vol. 71, p. 64

A = 1¶

f(r, rc=1, rt=2, A=1)¶

rangehint¶

rc = 1¶

rt = 2¶

xaxisname = 'r'¶

class astropysics.models.King3DrModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

3D (deprojected) King model of the form:

$f(r) = A/(z^2 \pi r_c) ((1+(r_t/r_c)^2)^{-3/2}) \arccos(z)/(z-\sqrt{1-z^2})$

A = 1¶

f(r, rc=1, rt=2, A=1)¶

rangehint¶

rc = 1¶

rt = 2¶

xaxisname = 'r'¶

class astropysics.models.MoffatModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

Moffat function given by:

$A \frac{(\beta-1}{\pi \alpha^2} \left(1+\left(\frac{r}{\alpha}\right)^2\right)^{-\beta}$

A = 1¶

FWHM¶: Full Width at Half Maximum for this model - setting changes alpha for fixed beta

alpha = 1¶

beta = 4.765¶

f(r, A=1, alpha=1, beta=4.765)¶

rangehint¶

class astropysics.models.NFWModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

A Navarro, Frenk, and White 1996 profile – the canonical $\Lambda {\rm CDM}$ dark matter halo profile:

$\rho(r) = \frac{\rho_0}{r/r_c (1+r/r_c)^2} .$

Where unspecified, units are r in kpc and rho in Msun pc^-3, although units can always be arbitrarily scaled by rescaling rho0.

Note

This form is equivalent to an AlphaBetaGammaModel with $(\alpha,\beta,\gamma) = (1,3,1)$ , but with a slightly different overall normalization. This class also has a number of helper methods.

static Cvir_to_Mvir(Cvir, z=0)¶

from Maller & Bullock ‘04 M_sun

Warning

These scalings are approximations.

Parameters:	Cvir (float) – Concentration parameter rvir/rc z (float) – Redshift
Returns:	Virial mass in Msun

static Mvir_to_Cvir(Mvir, z=0)¶

from Maller & Bullock ‘04 M_sun

Warning

These scalings are approximations.

Parameters:	Mvir (float) – Virial Mass in Msun z (float) – Redshift
Returns:	Concentration parameter (rvir/rc)

static Mvir_to_Rvir(Mvir, z=0)¶

from Bullock ‘01 M_sun,kpc

Warning

These scalings are approximations.

Parameters:	Mvir (float) – Virial Mass in Msun z (float) – Redshift
Returns:	Virial radius in kpc

static Mvir_to_Vmax(Mvir, z=0)¶

Convert virial mass to vmax using the scalings here

Warning

These scalings are approximations.

Parameters:	Mvir (float) – Virial Mass in Msun z (float) – Redshift
Returns:	Maximum circular velocity in km/s

static Mvir_to_Vvir(Mvir, z=0)¶

from Bullock ‘01 km/s,M_sun

Warning

These scalings are approximations.

Parameters:	Mvir (float) – Virial Mass in Msun z (float) – Redshift
Returns:	Virial Velocity in km/s

static RvirMvir_to_Vvir(Rvir, Mvir)¶

Computes virial velocity from virial radius and virial mass.

Parameters:	Rvir (float) – Virial Radius in kpc Mvir (float) – Virial Mass in Msun
Returns:	Virial Velocity in km/s

static Rvir_to_Mvir(Rvir, z=0)¶

from Bullock ‘01 M_sun,kpc

Warning

These scalings are approximations.

Parameters:	Rvir (float) – Virial Radius in kpc z (float) – Redshift
Returns:	Virial mass in Msun

static Vmax_to_Mvir(Vmax, z=0)¶

Convert vmax to virial mass using the scalings here

Warning

These scalings are approximations.

Parameters:	Vmax (float) – Maximum circular velocity in km/s z (float) – Redshift
Returns:	Virial mass in Msun

static Vmax_to_Rvir(Vmax, z=0)¶

Convert vmax to virial radius using the scalings here.

Warning

These scalings are approximations.

Parameters:	Vmax (float) – Maximum circular velocity in km/s z (float) – Redshift
Returns:	Virial radius in kpc

static Vmax_to_Vvir(Vmax)¶

from Maller & Bullock ‘04 good from 80-1200 km/s in vvir

Warning

These scalings are approximations.

Parameters:	Vmax (float) – Maximum circular Velocity in km/s z (float) – Redshift
Returns:	Virial Velocity in km/s

static Vvir_to_Mvir(Vvir, z=0)¶

from Bullock ‘01 km/s,M_sun

Warning

These scalings are approximations.

Parameters:	Vvir (float) – Virial velocity in km/s z (float) – Redshift
Returns:	Virial mass in Msun

static Vvir_to_Tvir(Vvir, mu=0.59)¶

Compute the Virial temperature for a given virial radius.

From Barkana & Loeb 2001: $T_{\rm vir} = \frac{\mu m_p V_c^2}{2 k_B}$

$\mu$ is the mean molecular weight, which is 0.59 for fully ionized primordial gas, .61 for fully ionized hydrogen but singly ionized helium, and 1.22 neutral. $m_p$ is the proton mass, $k_B$ is the Boltzmann constant, and $V_c$ is the virial velocity.

Parameters:	Vvir (float) – Virial velocity in km/s mu (float) – Mean molecular weight
Returns:	Virial Temperatur in Kelvin

static Vvir_to_Vmax(Vvir)¶

from Bullock ‘01 good from 80-1200 km/s in vvir

Warning

These scalings are approximations.

Parameters:	Vvir (float) – Virial velocity in km/s
Returns:	Virial velocity in km/s

static create_Cvir(Cvir, z=0)¶

Generates a new NFWModel with the given Mvir using the Cvir_to_Mvir() function to get the scaling.

Warning

These scalings are approximations.

Parameters:	Cvir (float) – Concentration parameter (rvir/rc) z (float) – Redshift at which the model is valid
Returns:	A `NFWModel` object with the provided Cvir and normalization set by the approximate scalings here.

static create_Mvir(Mvir, z=0)¶

Generates a new NFWModel with the given Mvir using the Mvir_to_Cvir() function to get the scaling.

Warning

These scalings are approximations.

Parameters:	Mvir (float) – Virial Mass in Msun z (float) – Redshift at which model is valid
Returns:	A `NFWModel` object with the provided Mvir and concentration set by the approximate scalings here.

static create_Rvir(Rvir, z=0)¶

Generates a new NFWModel with the given Mvir using the Mvir_to_Cvir and Rvir_to_Mvir() functions to get the scaling.

Warning

These scalings are approximations.

Parameters:	Rvir (float) – Virial Radius in kpc z (float) – Redshift at which the model is valid
Returns:	A `NFWModel` object with the provided Rvir and concentration set by the approximate scalings here.

static create_VmaxRvmax(vmax, rvmax)¶

Generates a new NFWModel with the given Vmax and R_Vmax.

Parameters:	vmax (float) – maximum circular velocity in km/s. rvmax (float) – radius of maximum circular velocity in kpc.

See Bullock et al. 2001 for reflated reference.

Returns:	A `NFWModel` object matching the supplied vmax and rvmax

deltavir(z=0)¶

Returns the virial overdensity at a given redshift.

This method should be overridden if a particular definition of virial radius is desired. E.g. to use r200 instead of rvir, do:

nfwmodel.deltavir = lambda z:200

Parameters:	z (scalar) – redshift at which to compute virial overdensity
Returns:	virial overdensity

f(r, rho0=1, rc=1)¶

getC(z=0)¶: Returns the concentration of this profile(rvir/rc) for a given redshift.

Note

If setC() has been called with an explicitly provided Rvir and Mvir, the concentration will be saved and this will return the saved concentration instead of one computed for a given redshift. If this is not desired, delete the _c attribute after calling setC() .

getMv(z=0)¶: Gets the mass within the virial radius (for a particular redshift)

getRhoMean(r)¶

Computes the mean density within the requested radius, i.e.

$\rho_m = M(<r)/(4/3 pi r^3)$

density in units of Msun pc^-3 assuming r in kpc

getRv(z=0)¶

Get the virial radius at a given redshift, with deltavir choosing the type of virial radius - if ‘fromcosmology’ it will be computed from the cosmology, otherwise, it should be a multiple of the critical density

units in kpc for mass in Msun

getV(r, **kwargs)¶

Computes the circular velocity of the halo at a given radius. i.e. $v = \sqrt{\frac{G M(<r)}{r}}$ .

Parameters:	r – The radius (or radii) at which to compute the circular velocity, in kpc.

Additional keyword arguments are passed into integrateSpherical().

Returns:	The circular velocity at r (if r is a scalar, this will return a scalar, otherwise an array)

getVmax()¶

Computes the maximum circular velocity of this profile.

Returns:	(vmax,rvmax) where vmax is the maximum circular velocity in km/s and rvmax is the radius at which the circular velocity is maximized.

integrateSpherical(lower, upper, method=None, **kwargs)¶: NFW Has an analytic form for the spherical integral - if the lower is not 0 or or if method is not None, this function will fall back to the numerical version.

rangehint¶

rc = 1¶

rho0 = 1¶

setC(c, Rvir=None, Mvir=None, z=0)¶

Sets the model parameters to match a given concentration given virial radius and mass.

Parameters:

c (scalar) – concentration = rvir/rc
Rvir (scalar or None) – virial radius to assume in kpc - if None, will be inferred from Mvir, c and the virial overdensity (see deltavir).
Mvir (scalar or None) – virial mass to assume in Msun - if None, will be inferred from Rvir, c, and the virial overdensity (see deltavir), or if Rvir is None, from the current virial mass.
z (scalar) – redshift at which to compute virial overdensity if Rvir or Mvir are None. If both are given, this is ignored.

toAlphaBetaGamma()¶: returns a new AlphaBetaGammaModel based on this model’s parameters.

xaxisname = 'r'¶

yaxisname = 'rho'¶

class astropysics.models.NFWProjectedModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

f(R, rc=1, sig0=1)¶

integrateCircular(lower, upper, method=None, **kwargs)¶: NFW Has an analytic form for the spherical integral - if the lower is not 0 or or if the keyword ‘numerical’ is True, this function will fall back to FunctionModel1D.integrateCircular

rangehint¶

rc = 1¶

sig0 = 1¶

class astropysics.models.PlummerModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

Plummer model of the form

$\frac{3M}{4 \pi r_p^3} (1+(r/r_p)^2)^{-5/2}$

M = 1.0¶

f(r, rp=1.0, M=1.0)¶

rangehint¶

rp = 1.0¶

xaxisname = 'r'¶

class astropysics.models.RoundBulgeModel(Ae=1, re=1, n=4)¶

Bases: pymodelfit.core.FunctionModel2DScalarSeperable

A bulge modeled as a radially symmetric sersic profile (by default the sersic index is kept fixed - to remove this behavior, set the fixedpars attribute to None)

By default, the ‘n’ parameter does not vary when fitting.

fixedpars = ('n',)¶

class astropysics.models.SchechterLumModel¶

Bases: pymodelfit.core.FunctionModel1DAuto

The Schechter Function, commonly used to fit the luminosity function of galaxies, in luminosity form:

$\phi(L) = \frac{\phi^*}{L_*} \left(\frac{L}{L_*}\right)^\alpha e^{-L/L_*}$

models – astronomy-specific models for pymodelfit¶

Classes and Inheritance Structure¶

Module API¶

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Parameters:	val – If None, nothing will be set, otherwise, if True, the exact Bn computation will be used, or if False, the estimate will be used.
Returns:	True if the exact computation is being used, False if the estimate.

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models – astronomy-specific models for pymodelfit¶

Classes and Inheritance Structure¶

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