def test_dens_in_criticaldens():
#Test the scaling, as a 2nd derivative of the potential / G, should scale as velocity^2/position^2
vofid, rofid = 200., 8.
assert numpy.fabs(
4. * bovy_conversion.dens_in_criticaldens(vofid, rofid) /
bovy_conversion.dens_in_criticaldens(2. * vofid, rofid) -
1.) < 10.**-10., 'dens_in_criticaldens did not work as expected'
assert numpy.fabs(
.25 * bovy_conversion.dens_in_criticaldens(vofid, rofid) /
bovy_conversion.dens_in_criticaldens(vofid, 2 * rofid) -
1.) < 10.**-10., 'dens_in_critical did not work as expected'
return None
def rvir(self,
H=70.,
Om=0.3,
t=0.,
overdens=200.,
wrtcrit=False,
ro=None,
vo=None,
use_physical=False
): # use_physical necessary bc of pop=False, does nothing inside
"""
NAME:
rvir
PURPOSE:
calculate the virial radius for this density distribution
INPUT:
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
ro= distance scale in kpc or as Quantity (default: object-wide, which if not set is 8 kpc))
vo= velocity scale in km/s or as Quantity (default: object-wide, which if not set is 220 km/s))
OUTPUT:
virial radius
HISTORY:
2014-01-29 - Written - Bovy (IAS)
"""
if ro is None: ro = self._ro
if vo is None: vo = self._vo
if wrtcrit:
od = overdens / bovy_conversion.dens_in_criticaldens(vo, ro, H=H)
else:
od = overdens / bovy_conversion.dens_in_meanmatterdens(
vo, ro, H=H, Om=Om)
dc = 12. * self.dens(self.a, 0., t=t, use_physical=False) / od
x = optimize.brentq(
lambda y: (numpy.log(1. + y) - y / (1. + y)) / y**3. - 1. / dc,
0.01, 100.)
return x * self.a
def rvir(self,H=70.,Om=0.3,overdens=200.,wrtcrit=False,ro=None,vo=None,
use_physical=False): # use_physical necessary bc of pop=False, does nothing inside
"""
NAME:
rvir
PURPOSE:
calculate the virial radius for this density distribution
INPUT:
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
ro= distance scale in kpc or as Quantity (default: object-wide, which if not set is 8 kpc))
vo= velocity scale in km/s or as Quantity (default: object-wide, which if not set is 220 km/s))
OUTPUT:
virial radius
HISTORY:
2014-01-29 - Written - Bovy (IAS)
"""
if ro is None: ro= self._ro
if vo is None: vo= self._vo
if wrtcrit:
od= overdens/bovy_conversion.dens_in_criticaldens(vo,ro,H=H)
else:
od= overdens/bovy_conversion.dens_in_meanmatterdens(vo,ro,
H=H,Om=Om)
dc= 12.*self.dens(self.a,0.,use_physical=False)/od
x= optimize.brentq(lambda y: (numpy.log(1.+y)-y/(1.+y))/y**3.-1./dc,
0.01,100.)
return x*self.a
def rvir(self, vo, ro, H=70., Om=0.3, overdens=200., wrtcrit=False):
"""
NAME:
rvir
PURPOSE:
calculate the virial radius for this density distribution
INPUT:
vo - velocity unit in km/s
ro - length unit in kpc
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
OUTPUT:
virial radius in natural units
HISTORY:
2014-01-29 - Written - Bovy (IAS)
"""
if wrtcrit:
od = overdens / bovy_conversion.dens_in_criticaldens(vo, ro, H=H)
else:
od = overdens / bovy_conversion.dens_in_meanmatterdens(
vo, ro, H=H, Om=Om)
dc = 12. * self.dens(self.a, 0.) / od
x = optimize.brentq(
lambda y: (numpy.log(1. + y) - y / (1. + y)) / y**3. - 1. / dc,
0.01, 100.)
return x * self.a
def _rvir(self,vo,ro,H=70.,Om=0.3,overdens=200.,wrtcrit=False):
"""
NAME:
_rvir
PURPOSE:
calculate the virial radius for this density distribution
INPUT:
vo - velocity unit in km/s
ro - length unit in kpc
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
OUTPUT:
virial radius in natural units
HISTORY:
2014-01-29 - Written - Bovy (IAS)
"""
if wrtcrit:
od= overdens/bovy_conversion.dens_in_criticaldens(vo,ro,H=H)
else:
od= overdens/bovy_conversion.dens_in_meanmatterdens(vo,ro,H=H,Om=Om)
dc= 12.*self.dens(self.a,0.)/od
x= optimize.brentq(lambda y: (numpy.log(1.+y)-y/(1.+y))/y**3.-1./dc,
0.01,100.)
return x*self.a
def __init__(self,amp=1.,a=1.,normalize=False,
conc=None,mvir=None,
vo=None,ro=None,
H=70.,Om=0.3,overdens=200.,wrtcrit=False):
"""
NAME:
__init__
PURPOSE:
Initialize a NFW potential
INPUT:
amp - amplitude to be applied to the potential (default: 1); can be a Quantity with units of mass or Gxmass
a - scale radius (can be Quantity)
normalize - if True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.
Alternatively, NFW potentials can be initialized using
conc= concentration
mvir= virial mass in 10^12 Msolar
in which case you also need to supply the following keywords
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
ro=, vo= distance and velocity scales for translation into internal units (default from configuration file)
OUTPUT:
(none)
HISTORY:
2010-07-09 - Written - Bovy (NYU)
2014-04-03 - Initialization w/ concentration and mass - Bovy (IAS)
"""
Potential.__init__(self,amp=amp,ro=ro,vo=vo,amp_units='mass')
if _APY_LOADED and isinstance(a,units.Quantity):
a= a.to(units.kpc).value/self._ro
if conc is None:
self.a= a
self.alpha= 1
self.beta= 3
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
self.normalize(normalize)
else:
if wrtcrit:
od= overdens/bovy_conversion.dens_in_criticaldens(self._vo,
self._ro,H=H)
else:
od= overdens/bovy_conversion.dens_in_meanmatterdens(self._vo,
self._ro,
H=H,Om=Om)
mvirNatural= mvir*100./bovy_conversion.mass_in_1010msol(self._vo,
self._ro)
rvir= (3.*mvirNatural/od/4./numpy.pi)**(1./3.)
self.a= rvir/conc
self._amp= mvirNatural/(numpy.log(1.+conc)-conc/(1.+conc))
self._scale= self.a
self.hasC= True
self.hasC_dxdv= True
self._nemo_accname= 'NFW'
return None
def __init__(self,amp=1.,a=1.,normalize=False,
conc=None,mvir=None,
vo=220.,ro=8.,
H=70.,Om=0.3,overdens=200.,wrtcrit=False):
"""
NAME:
__init__
PURPOSE:
Initialize a NFW potential
INPUT:
amp - amplitude to be applied to the potential
a - "scale" (in terms of Ro)
normalize - if True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.
Alternatively, NFW potentials can be initialized using
conc= concentration
mvir= virial mass in 10^12 Msolar
in which case you also need to supply the following keywords
vo= (220.) velocity unit in km/s
ro= (8.) length unit in kpc
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
OUTPUT:
(none)
HISTORY:
2010-07-09 - Written - Bovy (NYU)
2014-04-03 - Initialization w/ concentration and mass - Bovy (IAS)
"""
Potential.__init__(self,amp=amp)
if conc is None:
self.a= a
self.alpha= 1
self.beta= 3
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
self.normalize(normalize)
else:
if wrtcrit:
od= overdens/bovy_conversion.dens_in_criticaldens(vo,ro,H=H)
else:
od= overdens/bovy_conversion.dens_in_meanmatterdens(vo,ro,H=H,Om=Om)
mvirNatural= mvir*100./bovy_conversion.mass_in_1010msol(vo,ro)
rvir= (3.*mvirNatural/od/4./numpy.pi)**(1./3.)
self.a= rvir/conc
self._amp= mvirNatural/(numpy.log(1.+conc)-conc/(1.+conc))
self._scale= self.a
self.hasC= True
return None
def __init__(self,
amp=1.,
a=1.,
normalize=False,
conc=None,
mvir=None,
vo=None,
ro=None,
H=70.,
Om=0.3,
overdens=200.,
wrtcrit=False):
"""
NAME:
__init__
PURPOSE:
Initialize a NFW potential
INPUT:
amp - amplitude to be applied to the potential (default: 1); can be a Quantity with units of mass or Gxmass
a - scale radius (can be Quantity)
normalize - if True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.
Alternatively, NFW potentials can be initialized using
conc= concentration
mvir= virial mass in 10^12 Msolar
in which case you also need to supply the following keywords
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
ro=, vo= distance and velocity scales for translation into internal units (default from configuration file)
OUTPUT:
(none)
HISTORY:
2010-07-09 - Written - Bovy (NYU)
2014-04-03 - Initialization w/ concentration and mass - Bovy (IAS)
"""
Potential.__init__(self, amp=amp, ro=ro, vo=vo, amp_units='mass')
if _APY_LOADED and isinstance(a, units.Quantity):
a = a.to(units.kpc).value / self._ro
if conc is None:
self.a = a
self.alpha = 1
self.beta = 3
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
self.normalize(normalize)
else:
if wrtcrit:
od = overdens / bovy_conversion.dens_in_criticaldens(
self._vo, self._ro, H=H)
else:
od = overdens / bovy_conversion.dens_in_meanmatterdens(
self._vo, self._ro, H=H, Om=Om)
mvirNatural = mvir * 100. / bovy_conversion.mass_in_1010msol(
self._vo, self._ro)
rvir = (3. * mvirNatural / od / 4. / numpy.pi)**(1. / 3.)
self.a = rvir / conc
self._amp = mvirNatural / (numpy.log(1. + conc) - conc /
(1. + conc))
self._scale = self.a
self.hasC = True
self.hasC_dxdv = True
self._nemo_accname = 'NFW'
return None
def __init__(self,
amp=1.,
a=1.,
normalize=False,
conc=None,
mvir=None,
vo=220.,
ro=8.,
H=70.,
Om=0.3,
overdens=200.,
wrtcrit=False):
"""
NAME:
__init__
PURPOSE:
Initialize a NFW potential
INPUT:
amp - amplitude to be applied to the potential
a - "scale" (in terms of Ro)
normalize - if True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.
Alternatively, NFW potentials can be initialized using
conc= concentration
mvir= virial mass in 10^12 Msolar
in which case you also need to supply the following keywords
vo= (220.) velocity unit in km/s
ro= (8.) length unit in kpc
H= (default: 70) Hubble constant in km/s/Mpc
Om= (default: 0.3) Omega matter
overdens= (200) overdensity which defines the virial radius
wrtcrit= (False) if True, the overdensity is wrt the critical density rather than the mean matter density
OUTPUT:
(none)
HISTORY:
2010-07-09 - Written - Bovy (NYU)
2014-04-03 - Initialization w/ concentration and mass - Bovy (IAS)
"""
Potential.__init__(self, amp=amp)
if conc is None:
self.a = a
self.alpha = 1
self.beta = 3
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
self.normalize(normalize)
else:
if wrtcrit:
od = overdens / bovy_conversion.dens_in_criticaldens(
vo, ro, H=H)
else:
od = overdens / bovy_conversion.dens_in_meanmatterdens(
vo, ro, H=H, Om=Om)
mvirNatural = mvir * 100. / bovy_conversion.mass_in_1010msol(
vo, ro)
rvir = (3. * mvirNatural / od / 4. / numpy.pi)**(1. / 3.)
self.a = rvir / conc
self._amp = mvirNatural / (numpy.log(1. + conc) - conc /
(1. + conc))
self._scale = self.a
self.hasC = True
self.hasC_dxdv = True
self._nemo_accname = 'NFW'
return None
def test_dens_in_criticaldens():
#Test the scaling, as a 2nd derivative of the potential / G, should scale as velocity^2/position^2
vofid, rofid= 200., 8.
assert numpy.fabs(4.*bovy_conversion.dens_in_criticaldens(vofid,rofid)/bovy_conversion.dens_in_criticaldens(2.*vofid,rofid)-1.) < 10.**-10., 'dens_in_criticaldens did not work as expected'
assert numpy.fabs(.25*bovy_conversion.dens_in_criticaldens(vofid,rofid)/bovy_conversion.dens_in_criticaldens(vofid,2*rofid)-1.) < 10.**-10., 'dens_in_critical did not work as expected'
return None