PowerLaw#
- class ctao_cr_spectra.spectral.PowerLaw(normalization, index, e_ref=<Quantity 1. TeV>)#
Bases:
objectA power law with normalization, reference energy and index.
Index includes the sign:
\[\Phi(E, \Phi_0, \gamma, E_\text{ref}) = \Phi_0 \left(\frac{E}{E_\text{ref}}\right)^{\gamma}\]- Attributes:
- normalization: astropy.units.Quantity[flux]
\(\Phi_0\),
- index: float
\(\gamma\)
- e_ref: astropy.units.Quantity[energy]
\(E_\text{ref}\)
Attributes Summary
Returns True if the normalization has units of diffuse flux rather than point-like flux.
Methods Summary
__call__(energy)Evaluate the flux at a given energy.
compute_events_rate(inner, outer, area, ...)Integrate all the quantities from the spectrum (except time).
compute_number_events(inner, outer, ...)Integrate all the quantities from the spectrum and derive the total number of events.
integrate_area(area)Integrate this powerlaw over the given observatory area.
integrate_cone(inner, outer)Integrate this powerlaw over solid angle in the given cone.
integrate_energy(energy_min, energy_max)Integrate this powerlaw over the given energy range.
integrate_time(obs_time)Integrate this powerlaw over the given observation time.
Attributes Documentation
- is_diffuse#
Returns True if the normalization has units of diffuse flux rather than point-like flux.
Methods Documentation
- __call__(energy)#
Evaluate the flux at a given energy.
- Parameters:
- energyastropy.units.Quantity
The energy at which to evaluate the flux. Should be in units of energy.
- Returns:
- astropy.units.Quantity
The flux at the given energy.
- compute_events_rate(inner, outer, area, energy_min, energy_max)#
Integrate all the quantities from the spectrum (except time).
Derive the events rate expected for an integration in a region of space (inner, outer), over the area of the observatory (area) and over an energy range (energy).
- Parameters:
- innerastropy.units.Quantity[angle]
inner opening angle of cone
- outerastropy.units.Quantity[angle]
outer opening angle of cone
- area: astropy.units.Quantity[area]
Observation time to integrate the flux.
- energy_min: astropy.units.Quantity[energy]
Minimum energy in the integration.
- energy_max: astropy.units.Quantity[energy]
Maximum energy in the integration.
- Returns:
- float:
events rate integrated from the spectral distribution.
- compute_number_events(inner, outer, obs_time, area, energy_min, energy_max)#
Integrate all the quantities from the spectrum and derive the total number of events.
- Parameters:
- innerastropy.units.Quantity[angle]
inner opening angle of cone
- outerastropy.units.Quantity[angle]
outer opening angle of cone
- obs_time: astropy.units.Quantity[time]
Observation time to integrate the flux.
- area: astropy.units.Quantity[area]
Observation time to integrate the flux.
- energy_min: astropy.units.Quantity[energy]
Minimum energy in the integration.
- energy_max: astropy.units.Quantity[energy]
Maximum energy in the integration.
- Returns:
- float:
number of events integrated from the spectral distribution.
- integrate_area(area)#
Integrate this powerlaw over the given observatory area.
- Parameters:
- area: astropy.units.Quantity[area]
Observation time to integrate the flux.
- Returns:
- integratedPowerLaw
A new area integrated powerlaw instance.
- integrate_cone(inner, outer)#
Integrate this powerlaw over solid angle in the given cone.
- Parameters:
- innerastropy.units.Quantity[angle]
inner opening angle of cone
- outerastropy.units.Quantity[angle]
outer opening angle of cone
- Returns:
- integratedPowerLaw
A new powerlaw instance with new normalization with the integration result.
- Raises:
- ValueError:
if the normalization unit does not allow a cone integration. if the inner radius is larger than outer radius.
- integrate_energy(energy_min, energy_max)#
Integrate this powerlaw over the given energy range.
- Parameters:
- energy_min: astropy.units.Quantity[energy]
Minimum energy in the integration.
- energy_max: astropy.units.Quantity[energy]
Maximum energy in the integration.
- Returns:
- integratedPowerLaw
A new area integrated powerlaw instance.
- integrate_time(obs_time)#
Integrate this powerlaw over the given observation time.
- Parameters:
- obs_time: astropy.units.Quantity[time]
Observation time to integrate the flux.
- Returns:
- integratedPowerLaw
A new time integrated powerlaw instance.