hyp

Spectral hypothesis models.

Classes:

Flux()	Abstract base class for fluxes.
SplineFluxModel(norm, psp_table, ...)	Spline flux spectrum.
SeyfertCoreCoronaFlux(psp_table, ...[, ...])	Implements the Core-Corona Seyfert Galaxy neutrino flux model of A.
PowerLawFlux(gamma[, norm, energy_range, ...])	Power law spectrum.
BinnedFlux(bins_energy, flux[, ...])	Energy-binned spectrum.

class csky.hyp.Flux

Bases: object

Abstract base class for fluxes.

This class provides basic operations for flux functions of the form dN/dE=f(E), where E is in GeV and dN/dE is in units 1/GeV/cm2/s. The main value-added from this class is counts <–> flux calculations, which are performed in terms of total signal acceptance.

Todo

• Check and then document the exact units of “total signal acceptance”.

Methods:

__call__(E)	Get dN/dE given E.
to_model_norm(ns, acc_total)	Get the model normalization resulting in ns, given the total acceptance.
to_dNdE(ns, acc_total[, E0, unit])	Get dN/dE for particular reference energy and units.
to_E2dNdE(ns, acc_total[, E0, unit])	Get E0^2 * dN/dE for particular reference energy and units.
to_ns(flux, acc_total[, E0, unit, use_E2dNdE])	Get number of signal events corresponding to a particular flux.
__init__()

Attributes:

as_params	Convert to str->value fit parameter kwargs.
energy_range	Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

abstract __call__(E)

Get dN/dE given E.

Parameters:

E (float) – energy in GeV

Returns:

dN/dE in units 1/GeV/cm2/s

Return type:

float

abstract property as_params

Convert to str->value fit parameter kwargs.

abstract property energy_range

Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

to_model_norm(ns, acc_total)

Get the model normalization resulting in ns, given the total acceptance.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

Returns:

model normalization

Return type:

float

Todo

• Check units of acc_total

This is just a semantically meaningful way of expressing ns / acc_total.

to_dNdE(ns, acc_total, E0=1, unit=1)

Get dN/dE for particular reference energy and units.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

Returns:

dN/dE in units 1/(unit * GeV)/cm2/s

Return type:

float

For example, to get dN/dE at 100 TeV in units 1/TeV/cm2/s, use to_dNdE(ns, acc_total, E0=100, unit=1000).

Todo

• Check units of acc_total

to_E2dNdE(ns, acc_total, E0=1, unit=1)

Get E0^2 * dN/dE for particular reference energy and units.

Just like Flux.to_dNdE(), except multiplied by E0^2.

to_ns(flux, acc_total, E0=1, unit=1, use_E2dNdE=True)

Get number of signal events corresponding to a particular flux.

Parameters:

• flux (float) – dN/dE or E0^2 * dN/dE(see argument E2dNdE)

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

• E2dNdE (bool) – if true(default), flux gives E0^2 * dN/dE. otherwise, flux gives dN/dE.

Returns:

number of signal events

Return type:

float

Todo

• Check units of acc_total

__init__()

class csky.hyp.SplineFluxModel(norm, psp_table, crit_log_nu_energy_lower, crit_log_nu_energy_upper)

Bases: Flux

Spline flux spectrum.

Methods:

__init__(norm, psp_table, ...)
__call__(E)	Get dN/dE given E.
to_E2dNdE(ns, acc_total[, E0, unit])	Get E0^2 * dN/dE for particular reference energy and units.
to_dNdE(ns, acc_total[, E0, unit])	Get dN/dE for particular reference energy and units.
to_model_norm(ns, acc_total)	Get the model normalization resulting in ns, given the total acceptance.
to_ns(flux, acc_total[, E0, unit, use_E2dNdE])	Get number of signal events corresponding to a particular flux.

Attributes:

psp_table	The photospline.SplineTable object that describes the neutrino flux as function of neutrino energy via B-spline interpolation.
norm	The relative flux normalization.
crit_log_nu_energy_lower	The lower bound of the support of the spline interpolator
crit_log_nu_energy_upper	The upper bound of the support of the spline interpolator
as_params	Convert to str->value fit parameter kwargs.
energy_range	Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

__init__(norm, psp_table, crit_log_nu_energy_lower, crit_log_nu_energy_upper)

property psp_table

The photospline.SplineTable object that describes the neutrino flux as function of neutrino energy via B-spline interpolation.

property norm

The relative flux normalization. norm=1 corresponds to the nominal model flux.

property crit_log_nu_energy_lower

The lower bound of the support of the spline interpolator

property crit_log_nu_energy_upper

The upper bound of the support of the spline interpolator

abstract __call__(E)

Get dN/dE given E.

Parameters:

E (float) – energy in GeV

Returns:

dN/dE in units 1/GeV/cm2/s

Return type:

float

abstract property as_params

Convert to str->value fit parameter kwargs.

abstract property energy_range

Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

to_E2dNdE(ns, acc_total, E0=1, unit=1)

Get E0^2 * dN/dE for particular reference energy and units.

Just like Flux.to_dNdE(), except multiplied by E0^2.

to_dNdE(ns, acc_total, E0=1, unit=1)

Get dN/dE for particular reference energy and units.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

Returns:

dN/dE in units 1/(unit * GeV)/cm2/s

Return type:

float

For example, to get dN/dE at 100 TeV in units 1/TeV/cm2/s, use to_dNdE(ns, acc_total, E0=100, unit=1000).

Todo

• Check units of acc_total

to_model_norm(ns, acc_total)

Get the model normalization resulting in ns, given the total acceptance.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

Returns:

model normalization

Return type:

float

Todo

• Check units of acc_total

This is just a semantically meaningful way of expressing ns / acc_total.

to_ns(flux, acc_total, E0=1, unit=1, use_E2dNdE=True)

Get number of signal events corresponding to a particular flux.

Parameters:

• flux (float) – dN/dE or E0^2 * dN/dE(see argument E2dNdE)

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

• E2dNdE (bool) – if true(default), flux gives E0^2 * dN/dE. otherwise, flux gives dN/dE.

Returns:

number of signal events

Return type:

float

Todo

• Check units of acc_total

class csky.hyp.SeyfertCoreCoronaFlux(psp_table, log_xray_lumin, src_dist, norm, lumin_scale=1.0, crit_log_energy_flux=-50, crit_log_nu_energy_lower=2.0, crit_log_nu_energy_upper=7.0)

Bases: SplineFluxModel

Implements the Core-Corona Seyfert Galaxy neutrino flux model of A. Kheirandish et al., Astrophys.J. 922 (2021) 45 by means of B-spline interpolation.

Methods:

__init__(psp_table, log_xray_lumin, ...[, ...])
__call__(E)	The flux value dN/dE at energy E.
to_E2dNdE(ns, acc_total[, E0, unit])	Get E0^2 * dN/dE for particular reference energy and units.
to_dNdE(ns, acc_total[, E0, unit])	Get dN/dE for particular reference energy and units.
to_model_norm(ns, acc_total)	Get the model normalization resulting in ns, given the total acceptance.
to_ns(flux, acc_total[, E0, unit, use_E2dNdE])	Get number of signal events corresponding to a particular flux.

Attributes:

energy_range	Get the energy range containing nonzero flux, (Emin,Emax), in GeV.
log_xray_lumin	The log10 of the intrinsic source luminosity in 2-10keV x-ray band
lumin_scale	correct normalization of model flux by relative factor
src_dist	The distance to the source in units of Mpc
crit_log_energy_flux	defines when the flux is considered to be 0
math_function_str	We have used hash of this representation in skyllh.core.source_hypothesis.get_fluxmodel_to_source_map() to map fluxes with KDE PDFs.
as_params	Convert to str->value fit parameter kwargs.
crit_log_nu_energy_lower	The lower bound of the support of the spline interpolator
crit_log_nu_energy_upper	The upper bound of the support of the spline interpolator
norm	The relative flux normalization.
psp_table	The photospline.SplineTable object that describes the neutrino flux as function of neutrino energy via B-spline interpolation.

__init__(psp_table, log_xray_lumin, src_dist, norm, lumin_scale=1.0, crit_log_energy_flux=-50, crit_log_nu_energy_lower=2.0, crit_log_nu_energy_upper=7.0)

property energy_range

Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

property log_xray_lumin

The log10 of the intrinsic source luminosity in 2-10keV x-ray band

property lumin_scale

correct normalization of model flux by relative factor

property src_dist

The distance to the source in units of Mpc

property crit_log_energy_flux

defines when the flux is considered to be 0

property math_function_str

We have used hash of this representation in skyllh.core.source_hypothesis.get_fluxmodel_to_source_map() to map fluxes with KDE PDFs. So far KDEs only depend on log_xray_lumin value and not on src_dist.

__call__(E)

The flux value dN/dE at energy E. :param E: Evaluation energy [GeV] :type E: float | 1d numpy.ndarray of float

Returns:

flux – Flux at energy E in units of GeV^-1 cm^-2 s^-1.

Return type:

float | 1d ndarray of float

property as_params

Convert to str->value fit parameter kwargs.

property crit_log_nu_energy_lower

The lower bound of the support of the spline interpolator

property crit_log_nu_energy_upper

The upper bound of the support of the spline interpolator

property norm

The relative flux normalization. norm=1 corresponds to the nominal model flux.

property psp_table

The photospline.SplineTable object that describes the neutrino flux as function of neutrino energy via B-spline interpolation.

to_E2dNdE(ns, acc_total, E0=1, unit=1)

Get E0^2 * dN/dE for particular reference energy and units.

Just like Flux.to_dNdE(), except multiplied by E0^2.

to_dNdE(ns, acc_total, E0=1, unit=1)

Get dN/dE for particular reference energy and units.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

Returns:

dN/dE in units 1/(unit * GeV)/cm2/s

Return type:

float

For example, to get dN/dE at 100 TeV in units 1/TeV/cm2/s, use to_dNdE(ns, acc_total, E0=100, unit=1000).

Todo

• Check units of acc_total

to_model_norm(ns, acc_total)

Get the model normalization resulting in ns, given the total acceptance.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

Returns:

model normalization

Return type:

float

Todo

• Check units of acc_total

This is just a semantically meaningful way of expressing ns / acc_total.

to_ns(flux, acc_total, E0=1, unit=1, use_E2dNdE=True)

Get number of signal events corresponding to a particular flux.

Parameters:

• flux (float) – dN/dE or E0^2 * dN/dE(see argument E2dNdE)

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

• E2dNdE (bool) – if true(default), flux gives E0^2 * dN/dE. otherwise, flux gives dN/dE.

Returns:

number of signal events

Return type:

float

Todo

• Check units of acc_total

class csky.hyp.PowerLawFlux(gamma, norm=1, energy_range=(0, inf), energy_cutoff=inf)

Bases: Flux

Power law spectrum.

Methods:

__init__(gamma[, norm, energy_range, ...])
__call__(E)	Get dN/dE given E.
to_E2dNdE(ns, acc_total[, E0, unit])	Get E0^2 * dN/dE for particular reference energy and units.
to_dNdE(ns, acc_total[, E0, unit])	Get dN/dE for particular reference energy and units.
to_model_norm(ns, acc_total)	Get the model normalization resulting in ns, given the total acceptance.
to_ns(flux, acc_total[, E0, unit, use_E2dNdE])	Get number of signal events corresponding to a particular flux.

Attributes:

as_params	Convert to str->value fit parameter kwargs.
energy_range	Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

__init__(gamma, norm=1, energy_range=(0, inf), energy_cutoff=inf)

Parameters:

• gamma (float) – spectral index

• norm (float) – normalization factor(at 1 GeV)

• energy_range (tuple of (float, float)) – hard energy bounds(flux is zero elsewhere)

• energy_cutoff (float) – exponential cutoff energy(in GeV)

__call__(E)

Get dN/dE given E.

Parameters:

E (float) – energy in GeV

Returns:

dN/dE in units 1/GeV/cm2/s

Return type:

float

property as_params

Convert to str->value fit parameter kwargs.

property energy_range

Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

to_E2dNdE(ns, acc_total, E0=1, unit=1)

Get E0^2 * dN/dE for particular reference energy and units.

Just like Flux.to_dNdE(), except multiplied by E0^2.

to_dNdE(ns, acc_total, E0=1, unit=1)

Get dN/dE for particular reference energy and units.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

Returns:

dN/dE in units 1/(unit * GeV)/cm2/s

Return type:

float

For example, to get dN/dE at 100 TeV in units 1/TeV/cm2/s, use to_dNdE(ns, acc_total, E0=100, unit=1000).

Todo

• Check units of acc_total

to_model_norm(ns, acc_total)

Get the model normalization resulting in ns, given the total acceptance.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

Returns:

model normalization

Return type:

float

Todo

• Check units of acc_total

This is just a semantically meaningful way of expressing ns / acc_total.

to_ns(flux, acc_total, E0=1, unit=1, use_E2dNdE=True)

Get number of signal events corresponding to a particular flux.

Parameters:

• flux (float) – dN/dE or E0^2 * dN/dE(see argument E2dNdE)

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

• E2dNdE (bool) – if true(default), flux gives E0^2 * dN/dE. otherwise, flux gives dN/dE.

Returns:

number of signal events

Return type:

float

Todo

• Check units of acc_total

class csky.hyp.BinnedFlux(bins_energy, flux, max_energy_approx_gamma=1000000.0)

Bases: Flux

Energy-binned spectrum.

Methods:

__init__(bins_energy, flux[, ...])	Construct a BinnedFlux.
to_E2dNdE(ns, acc_total[, E0, unit])	Get E0^2 * dN/dE for particular reference energy and units.
to_dNdE(ns, acc_total[, E0, unit])	Get dN/dE for particular reference energy and units.
to_model_norm(ns, acc_total)	Get the model normalization resulting in ns, given the total acceptance.
to_ns(flux, acc_total[, E0, unit, use_E2dNdE])	Get number of signal events corresponding to a particular flux.
__call__(E)	Get dN/dE given E.

Attributes:

as_params	Convert to str->value fit parameter kwargs.
energy_range	Get the energy range containing nonzero flux, (Emin,Emax), in GeV.

__init__(bins_energy, flux, max_energy_approx_gamma=1000000.0)

Construct a BinnedFlux.

Parameters:

• bins_energy (ndarray of float) – energy bin edges(up to or including Emax of highest energy bin)

• flux (ndarray of float) – average dN/dE, in 1/GeV/cm2/s, for each energy bin

• max_energy_approx_gamma (float) – maximum energy(in GeV) to consider when computing approximate average spectral index(used by :meth:BinnedFlux.as_params)

to_E2dNdE(ns, acc_total, E0=1, unit=1)

Get E0^2 * dN/dE for particular reference energy and units.

Just like Flux.to_dNdE(), except multiplied by E0^2.

to_dNdE(ns, acc_total, E0=1, unit=1)

Get dN/dE for particular reference energy and units.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

Returns:

dN/dE in units 1/(unit * GeV)/cm2/s

Return type:

float

For example, to get dN/dE at 100 TeV in units 1/TeV/cm2/s, use to_dNdE(ns, acc_total, E0=100, unit=1000).

Todo

• Check units of acc_total

to_model_norm(ns, acc_total)

Get the model normalization resulting in ns, given the total acceptance.

Parameters:

• ns (float) – number of signal events

• acc_total (float) – total signal acceptance

Returns:

model normalization

Return type:

float

Todo

• Check units of acc_total

This is just a semantically meaningful way of expressing ns / acc_total.

to_ns(flux, acc_total, E0=1, unit=1, use_E2dNdE=True)

Get number of signal events corresponding to a particular flux.

Parameters:

• flux (float) – dN/dE or E0^2 * dN/dE(see argument E2dNdE)

• acc_total (float) – total signal acceptance

• E0 (float) – reference energy in units unit * GeV

• unit (float) – energy unit for E0 as well as in denominator of return value

• E2dNdE (bool) – if true(default), flux gives E0^2 * dN/dE. otherwise, flux gives dN/dE.

Returns:

number of signal events

Return type:

float

Todo

• Check units of acc_total

__call__(E)

Get dN/dE given E.

Parameters:

E (float) – energy in GeV

Returns:

dN/dE in units 1/GeV/cm2/s

Return type:

float

property as_params

Convert to str->value fit parameter kwargs.

property energy_range

Get the energy range containing nonzero flux, (Emin,Emax), in GeV.