Source code for galpy.df.jeans

# jeans.py: utilities related to the Jeans equations
import numpy
from scipy import integrate
from ..potential.Potential import evaluateDensities, \
    evaluaterforces, evaluateSurfaceDensities
from ..potential.Potential import flatten as flatten_pot
from ..util.bovy_conversion import physical_conversion, \
    potential_physical_input
_INVSQRTTWO= 1./numpy.sqrt(2.)
[docs]@potential_physical_input @physical_conversion('velocity',pop=True) def sigmar(Pot,r,dens=None,beta=0.): """ NAME: sigmar PURPOSE: Compute the radial velocity dispersion using the spherical Jeans equation INPUT: Pot - potential or list of potentials (evaluated at R=r/sqrt(2),z=r/sqrt(2), sphericity not checked) r - Galactocentric radius (can be Quantity) dens= (None) tracer density profile (function of r); if None, the density is assumed to be that corresponding to the potential beta= (0.) anisotropy; can be a constant or a function of r OUTPUT: sigma_r(r) HISTORY: 2018-07-05 - Written - Bovy (UofT) """ Pot= flatten_pot(Pot) if dens is None: dens= lambda r: evaluateDensities(Pot,r*_INVSQRTTWO,r*_INVSQRTTWO, phi=numpy.pi/4., use_physical=False) if callable(beta): intFactor= lambda x: numpy.exp(2.*integrate.quad(lambda y: beta(y)/y, 1.,x)[0]) else: # assume to be number intFactor= lambda x: x**(2.*beta) return numpy.sqrt(integrate.quad(lambda x: -intFactor(x)*dens(x) *evaluaterforces(Pot, x*_INVSQRTTWO, x*_INVSQRTTWO, phi=numpy.pi/4., use_physical=False), r,numpy.inf)[0]/ dens(r)/intFactor(r))
[docs]@potential_physical_input @physical_conversion('velocity',pop=True) def sigmalos(Pot,R,dens=None,surfdens=None,beta=0.,sigma_r=None): """ NAME: sigmalos PURPOSE: Compute the line-of-sight velocity dispersion using the spherical Jeans equation INPUT: Pot - potential or list of potentials (evaluated at R=r/sqrt(2),z=r/sqrt(2), sphericity not checked) R - Galactocentric projected radius (can be Quantity) dens= (None) tracer density profile (function of r); if None, the density is assumed to be that corresponding to the potential surfdens= (None) tracer surface density profile (value at R or function of R); if None, the surface density is assumed to be that corresponding to the density beta= (0.) anisotropy; can be a constant or a function of r sigma_r= (None) if given, the solution of the spherical Jeans equation sigma_r(r) (used instead of solving the Jeans equation as part of this routine) OUTPUT: sigma_los(R) HISTORY: 2018-08-27 - Written - Bovy (UofT) """ Pot= flatten_pot(Pot) if dens is None: densPot= True dens= lambda r: evaluateDensities(Pot,r*_INVSQRTTWO,r*_INVSQRTTWO, use_physical=False) else: densPot= False if callable(surfdens): called_surfdens= surfdens(R) elif surfdens is None: if densPot: called_surfdens= evaluateSurfaceDensities(Pot,R,numpy.inf, use_physical=False) if not densPot or numpy.isnan(called_surfdens): called_surfdens=\ 2.*integrate.quad(lambda x: dens(numpy.sqrt(R**2.+x**2.)), 0.,numpy.inf)[0] else: called_surfdens= surfdens if callable(beta): call_beta= beta else: call_beta= lambda x: beta if sigma_r is None: call_sigma_r= lambda r: sigmar(Pot,r,dens=dens,beta=beta) elif not callable(sigma_r): call_sigma_r= lambda x: sigma_r else: call_sigma_r= sigma_r return numpy.sqrt(2.*integrate.quad(\ lambda x: (1.-call_beta(x)*R**2./x**2.)*x*dens(x)\ *call_sigma_r(x)**2./numpy.sqrt(x**2.-R**2.),R,numpy.inf)[0]\ /called_surfdens)