ZhaoProfile#

class gammapy.astro.darkmatter.ZhaoProfile(r_s=None, alpha=None, beta=None, gamma=None, rho_s=<Quantity 1. GeV / cm3>)[source]#

Bases: DMProfile

Zhao Profile.

This is taken from equation 1 from Zhao (1996). It is a generalization of the NFW profile. The volume density is parametrized with a double power-law. Scale radii smaller than the scale radius are described with a slope of \(-\gamma\) and scale radii larger than the scale radius are described with a slope of \(-\beta\). \(\alpha\) is a measure for the width of the transition region.

\[\rho(r) = \rho_s \left(\frac{r_s}{r}\right)^\gamma \left(1 + \left(\frac{r}{r_s}\right)^\frac{1}{\alpha} \right)^{(\gamma - \beta) \alpha}\]

Parameters:

r_sQuantity: Scale radius, \(r_s\).
alphaQuantity: \(\alpha\).
beta: `~astropy.units.Quantity`: \(\beta\).
gammaQuantity: \(\gamma\).
rho_sQuantity: Characteristic density, \(\rho_s\).

References

Attributes Summary

`DEFAULT_ALPHA`
`DEFAULT_BETA`
`DEFAULT_GAMMA`	(alpha, beta, gamma) = (1,3,1) is NFW profile.
`DEFAULT_SCALE_RADIUS`
`DISTANCE_GC`	Distance to the Galactic Center as given in reference 2
`LOCAL_DENSITY`	Local dark matter density as given in reference 2

Methods Summary

`__call__`(radius)	Call evaluate method of derived classes.
`evaluate`(radius, r_s, alpha, beta, gamma, rho_s)	Evaluate the profile.
`integral`(rmin, rmax, separation, ndecade[, ...])	Integrate dark matter profile numerically.
`integrate_spectrum_separation`(func, xmin, ...)	Squared dark matter profile integral.
`scale_to_local_density`()	Scale to local density.

Attributes Documentation

DEFAULT_ALPHA = 1#

DEFAULT_BETA = 3#

DEFAULT_GAMMA = 1#: (alpha, beta, gamma) = (1,3,1) is NFW profile. Default scale radius as given in reference 2 (same as for NFW profile)

DEFAULT_SCALE_RADIUS = <Quantity 24.42 kpc>#

DISTANCE_GC = <Quantity 8.5 kpc>#: Distance to the Galactic Center as given in reference 2

LOCAL_DENSITY = <Quantity 0.39 GeV / cm3>#: Local dark matter density as given in reference 2

Methods Documentation

__call__(radius)#: Call evaluate method of derived classes.

static evaluate(radius, r_s, alpha, beta, gamma, rho_s)[source]#: Evaluate the profile.

integral(rmin, rmax, separation, ndecade, squared=True)#

Integrate dark matter profile numerically.

\[\begin{split}F(r_{min}, r_{max}) = \int_{r_{min}}^{r_{max}}\rho(r)^\gamma dr \\ \gamma = 2 \text{for annihilation} \\ \gamma = 1 \text{for decay}\end{split}\]

Parameters:

rmin, rmaxQuantity: Lower and upper bound of integration range.
separationndarray: Separation angle in radians.
ndecadeint, optional: Number of grid points per decade used for the integration. Default is 10000.
squaredbool, optional: Square the profile before integration. Default is True.

integrate_spectrum_separation(func, xmin, xmax, separation, ndecade, squared=True)#

Squared dark matter profile integral.

Parameters:

xmin, xmaxQuantity: Lower and upper bound of integration range.
separationndarray: Separation angle in radians.
ndecadeint: Number of grid points per decade used for the integration.
squaredbool: Square the profile before integration. Default is True.

scale_to_local_density()#: Scale to local density.