DMAnnihilation

class gammapy.astro.darkmatter.DMAnnihilation(mass, channel, scale=1, jfactor=1, z=0, k=2)[source]

Bases: gammapy.spectrum.models.SpectralModel

Spectral model for dark matter annihilation.

The gamma-ray flux is computed as follows:

\[\frac{\mathrm d \phi}{\mathrm d E} = \frac{\langle \sigma\nu \rangle}{4\pi k m^2_{\mathrm{DM}}} \frac{\mathrm d N}{\mathrm dE} \times J(\Delta\Omega)\]
Parameters:
mass : Quantity

Dark matter mass

channel : str

Annihilation channel for PrimaryFlux

scale : float

Scale parameter for model fitting

jfact : Quantity

Integrated J-Factor needed when SkyPointSource spatial model is used

z: float

Redshift value

k: int

Type of dark matter particle (k:2 Majorana, k:4 Dirac)

References

Examples

This is how to instantiate a DMAnnihilation model:

from astropy import units as u
from gammapy.astro.darkmatter import DMAnnihilation

channel = "b"
massDM = 5000*u.Unit("GeV")
jfactor = 3.41e19 * u.Unit("GeV2 cm-5")
modelDM = DMAnnihilation(mass=massDM, channel=channel, jfactor=jfactor)

Attributes Summary

THERMAL_RELIC_CROSS_SECTION Thermally averaged annihilation cross-section
channel
jfactor
k
mass
parameters Parameters (Parameters)
primary_flux
scale
z

Methods Summary

__call__(self, energy) Call evaluate method of derived classes
copy(self) A deep copy.
energy_flux(self, emin, emax, \*\*kwargs) Compute energy flux in given energy range.
energy_flux_error(self, emin, emax, \*\*kwargs) Compute energy flux in given energy range with error propagation.
evaluate(self, energy, scale) Evaluate dark matter annihilation model.
evaluate_error(self, energy) Evaluate spectral model with error propagation.
from_dict(val) Create from dict.
integral(self, emin, emax, \*\*kwargs) Integrate spectral model numerically.
integral_error(self, emin, emax, \*\*kwargs) Integrate spectral model numerically with error propagation.
inverse(self, value[, emin, emax]) Return energy for a given function value of the spectral model.
plot(self, energy_range[, ax, energy_unit, …]) Plot spectral model curve.
plot_error(self, energy_range[, ax, …]) Plot spectral model error band.
spectral_index(self, energy[, epsilon]) Compute spectral index at given energy.
to_dict(self) Convert to dict.

Attributes Documentation

THERMAL_RELIC_CROSS_SECTION = <Quantity 3.e-26 cm3 / s>

Thermally averaged annihilation cross-section

channel
jfactor
k
mass
parameters

Parameters (Parameters)

primary_flux
scale
z

Methods Documentation

__call__(self, energy)

Call evaluate method of derived classes

copy(self)

A deep copy.

energy_flux(self, emin, emax, **kwargs)

Compute energy flux in given energy range.

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE\]
Parameters:
emin, emax : Quantity

Lower and upper bound of integration range.

**kwargs : dict

Keyword arguments passed to func:integrate_spectrum
energy_flux_error(self, emin, emax, **kwargs)

Compute energy flux in given energy range with error propagation.

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE\]
Parameters:
emin, emax : Quantity

Lower bound of integration range.

**kwargs : dict

Keyword arguments passed to integrate_spectrum()
Returns:
energy_flux, energy_flux_error : tuple of Quantity

Tuple of energy flux and energy flux error.
evaluate(self, energy, scale)[source]

Evaluate dark matter annihilation model.

evaluate_error(self, energy)

Evaluate spectral model with error propagation.

Parameters:
energy : Quantity

Energy at which to evaluate
Returns:
flux, flux_error : tuple of Quantity

Tuple of flux and flux error.
classmethod from_dict(val)

Create from dict.

integral(self, emin, emax, **kwargs)

Integrate spectral model numerically.

\[F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} \phi(E) dE\]

If array input for emin and emax is given you have to set intervals=True if you want the integral in each energy bin.

Parameters:
emin, emax : Quantity

Lower and upper bound of integration range.

**kwargs : dict

Keyword arguments passed to integrate_spectrum()
integral_error(self, emin, emax, **kwargs)

Integrate spectral model numerically with error propagation.

Parameters:
emin, emax : Quantity

Lower adn upper bound of integration range.

**kwargs : dict

Keyword arguments passed to func:integrate_spectrum
Returns:
integral, integral_error : tuple of Quantity

Tuple of integral flux and integral flux error.
inverse(self, value, emin=<Quantity 0.1 TeV>, emax=<Quantity 100. TeV>)

Return energy for a given function value of the spectral model.

Calls the scipy.optimize.brentq numerical root finding method.

Parameters:
value : Quantity

Function value of the spectral model.

emin : Quantity

Lower bracket value in case solution is not unique.

emax : Quantity

Upper bracket value in case solution is not unique.
Returns:
energy : Quantity

Energies at which the model has the given value.
plot(self, energy_range, ax=None, energy_unit='TeV', flux_unit='cm-2 s-1 TeV-1', energy_power=0, n_points=100, **kwargs)

Plot spectral model curve.

kwargs are forwarded to matplotlib.pyplot.plot

By default a log-log scaling of the axes is used, if you want to change the y axis scaling to linear you can use:

from gammapy.spectrum.models import ExponentialCutoffPowerLaw
from astropy import units as u

pwl = ExponentialCutoffPowerLaw()
ax = pwl.plot(energy_range=(0.1, 100) * u.TeV)
ax.set_yscale('linear')
Parameters:
ax : Axes, optional

Axis

energy_range : Quantity

Plot range

energy_unit : str, Unit, optional

Unit of the energy axis

flux_unit : str, Unit, optional

Unit of the flux axis

energy_power : int, optional

Power of energy to multiply flux axis with

n_points : int, optional

Number of evaluation nodes
Returns:
ax : Axes, optional

Axis
plot_error(self, energy_range, ax=None, energy_unit='TeV', flux_unit='cm-2 s-1 TeV-1', energy_power=0, n_points=100, **kwargs)

Plot spectral model error band.

Note

This method calls ax.set_yscale("log", nonposy='clip') and ax.set_xscale("log", nonposx='clip') to create a log-log representation. The additional argument nonposx='clip' avoids artefacts in the plot, when the error band extends to negative values (see also https://github.com/matplotlib/matplotlib/issues/8623).

When you call plt.loglog() or plt.semilogy() explicitely in your plotting code and the error band extends to negative values, it is not shown correctly. To circumvent this issue also use plt.loglog(nonposx='clip', nonposy='clip') or plt.semilogy(nonposy='clip').

Parameters:
ax : Axes, optional

Axis

energy_range : Quantity

Plot range

energy_unit : str, Unit, optional

Unit of the energy axis

flux_unit : str, Unit, optional

Unit of the flux axis

energy_power : int, optional

Power of energy to multiply flux axis with

n_points : int, optional

Number of evaluation nodes

**kwargs : dict

Keyword arguments forwarded to matplotlib.pyplot.fill_between
Returns:
ax : Axes, optional

Axis
spectral_index(self, energy, epsilon=1e-05)

Compute spectral index at given energy.

Parameters:
energy : Quantity

Energy at which to estimate the index

epsilon : float

Fractional energy increment to use for determining the spectral index.
Returns:
index : float

Estimated spectral index.
to_dict(self)

Convert to dict.