diffsph package

Subpackages

Submodules

diffsph.limits module

diffsph.limits.decay_rate_gausslim(nu, a_fit, sigma_fit, beam_size, galaxy, rad_temp, D0=3e+28, delta='kol', B=2, mchi=50, channel='mumu', manual=False, **kwargs)

Maximum dark matter decay rate allowed by the exclusion of a Gaussian-shaped signal

\[a_\text{fit}\exp\left(-\frac{\theta^2}{2\sigma_\text{fit}^2}\right)\]
Parameters:

  • nu – frequency in GHz

  • a_fit – fitted gaussian amplitude in \(\mu\) Jy / beam

  • sigma_fit – width parameter of the Gaussian template in arcmin

  • beam_size – beam size in arcseconds

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – dark matter halo model ('NFW', 'Einasto', etc.)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

upper limit on the DM decay rate in 1/s

Return type:

float

diffsph.limits.decay_rate_limest(nu, rms_noise, beam_size, galaxy, rad_temp, ratio=1, D0=3e+28, delta='kol', B=2, mchi=50, channel='mumu', manual=False, high_res=False, accuracy=1, **kwargs)

(Estimated) maximum dark matter decay rate given the rms noise level of an observation

Parameters:

  • nu – frequency in GHz

  • rms_noise – RMS noise level of the observation in \(\mu\) Jy / beam

  • beam_size – beam size in arcseconds

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – dark matter halo model ('NFW', 'Einasto', etc.)

  • ratio – ratio between the diffusion halo and half-light radii

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\). (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Estimated upper limit on the DM decay rate in 1/s

Return type:

float

diffsph.limits.generic_rate_gausslim(nu, a_fit, sigma_fit, beam_size, galaxy, rad_temp, D0=3e+28, delta='kol', B=2, Gamma=2, **kwargs)

Maximum CRE production rate (generic power-law hypothesis) allowed by the exclusion of a Gaussian-shaped signal

\[a_\text{fit}\exp\left(-\frac{\theta^2}{2\sigma_\text{fit}^2}\right)\]
Parameters:

  • nu – frequency in GHz

  • a_fit – fitted gaussian amplitude in \(\mu\) Jy / beam

  • sigma_fit – width parameter of the Gaussian template in arcmin

  • beam_size – beam size in arcseconds

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – dark matter halo model ('NFW', 'Einasto', etc.)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\), default value = 2)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

upper limit on the generic CRE production rate in 1/s

Return type:

float

diffsph.limits.generic_rate_limest(nu, rms_noise, beam_size, galaxy, rad_temp, ratio=1, D0=3e+28, delta='kol', B=2, Gamma=2, high_res=False, accuracy=1, **kwargs)

(Estimated) maximum CRE production rate (generic power-law hypothesis) given the rms noise level of an observation

Parameters:

  • nu – frequency in GHz

  • rms_noise – RMS noise level of the observation in \(\mu\) Jy / beam

  • beam_size – beam size in arcseconds

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – dark matter halo model ('NFW', 'Einasto', etc.)

  • ratio – ratio between the diffusion halo and half-light radii

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\), default value = 2)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\). (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Estimated upper limit on the generic CRE production rate in 1/s

Return type:

float

diffsph.limits.sigmav_gausslim(nu, a_fit, sigma_fit, beam_size, galaxy, rad_temp, D0=3e+28, delta='kol', B=2, mchi=50, channel='mumu', self_conjugate=True, manual=False, **kwargs)

Maximum WIMP self-annihilation cross-section allowed by the exclusion of a Gaussian-shaped signal

\[a_\text{fit}\exp\left(-\frac{\theta^2}{2\sigma_\text{fit}^2}\right)\]
Parameters:

  • nu – frequency in GHz

  • a_fit – fitted gaussian amplitude in \(\mu\) Jy / beam

  • sigma_fit – width parameter of the Gaussian template in arcmin

  • beam_size – beam size in arcseconds

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – dark matter halo model ('NFW', 'Einasto', etc.)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

upper limit for the WIMP self-annihilation cross-section in cm \({}^3\) /s

Return type:

float

diffsph.limits.sigmav_limest(nu, rms_noise, beam_size, galaxy, rad_temp, ratio=1, D0=3e+28, delta='kol', B=2, mchi=50, channel='mumu', self_conjugate=True, manual=False, high_res=False, accuracy=1, **kwargs)

(Estimated) maximum WIMP self-annihilation cross-section given the rms noise level of an observation

Parameters:

  • nu – frequency in GHz

  • rms_noise – RMS noise level of the observation in \(\mu\) Jy / beam

  • beam_size – beam size in arcseconds

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – dark matter halo model ('NFW', 'Einasto', etc.)

  • ratio – ratio between the diffusion halo and half-light radii

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\). (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Estimated upper limit on WIMP self-annihilation cross-section in cm \({}^3\) /s

Return type:

float

diffsph.pyflux module

diffsph.pyflux.Dec_rad(galaxy)
diffsph.pyflux.RA_rad(galaxy)
diffsph.pyflux.coeff(n, nu, galaxy, rad_temp, hyp, ratio, D0, delta, B, manual=False, **kwargs)

n-th coefficient participating in the Fourier-expanded Green’s function solution of the CRE transport equation

\[s_n = h_n\times X_n\]
Parameters:

  • n – order of the halo/bulge factor

  • theta – angular radius in arcmin

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

n-th coefficient in the which_N function

diffsph.pyflux.synch_TB(theta, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, manual=False, high_res=False, accuracy=1, **kwargs)

Model-specific brightness temperature from synchrotron radiation

Parameters:

  • theta – angular radius in arcmin

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\). (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Brightness temperature in mK

diffsph.pyflux.synch_TB_approx(theta, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, regime='B', manual=False, **kwargs)

Model-specific brightness temperature in the Regime “A”, “B” or “C” approximations

Parameters:

  • theta – angular radius in arcmin

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • regime – regime of the approximation. Must be either upper or lower case a, b, c or I/II/III.

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Brightness temperature in mK

diffsph.pyflux.synch_brightness(theta, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, manual=False, high_res=False, accuracy=1, **kwargs)

Model-specific brightness from synchrotron radiation

Parameters:

  • theta – angular radius in arcmin

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\). (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Brightness in Jy/sr

Return type:

float

diffsph.pyflux.synch_brightness_approx(theta, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, regime='B', manual=False, **kwargs)

Model-specific brightness from synchrotron radiation in the Regime “A”, “B” or “C” approximations

Parameters:

  • theta – angular radius in arcmin

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • regime – regime of the approximation. Must be either upper or lower case a, b, c or I/II/III.

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Brightness in Jy/sr

diffsph.pyflux.synch_emissivity(r, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, manual=False, high_res=False, accuracy=1, **kwargs)

Model-specific emissivity from synchrotron radiation

Parameters:

  • r – galactocentric distance in kpc

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\) (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Emissivity in erg/cm \({}^3\) /Hz/s/sr

Return type:

float

diffsph.pyflux.synch_emissivity_approx(r, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, regime='B', manual=False, **kwargs)

Model-specific emissivity from synchrotron radiation in the Regime “A”, “B” or “C” approximations

Parameters:

  • r – galactocentric distance in kpc

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • regime – regime of the approximation. Must be either upper or lower case a, b, c or I/II/III.

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Emissivity in erg/cm \({}^3\) /Hz/s/sr

diffsph.pyflux.synch_flux_density(theta, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, manual=False, high_res=False, accuracy=1, **kwargs)

Model-specific flux density from synchrotron radiation

Parameters:

  • theta – angular radius in arcmin

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\). (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Flux density in µJy

diffsph.pyflux.synch_flux_density_approx(theta, nu, galaxy, rad_temp, hyp='wimp', ratio=1, D0=3e+28, delta='kol', B=2, regime='B', manual=False, **kwargs)

Model-specific flux density from synchrotron radiation in the Regime “A”, “B” or “C” approximations

Parameters:

  • theta – angular radius in arcmin

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • regime – regime of the approximation. Must be either upper or lower case a, b, c or I/II/III.

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

Flux density in µJy

class diffsph.pyflux.transport(rh=None, B=None, D0=None, tau0=None, delta=None)

Bases: object

property D0
Dcoeff(E)

Diffusion coefficient in cm \({}^2\) /s

Parameters:

  • E – cosmic-ray energy in GeV

  • delta – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

Returns:

Diffusion coefficient for CRE with energy \(E\) (GeV) in cm \({}^2\) /s

Elosses(E)

Total energy loss function in GeV/s

Parameters:

  • E – cosmic-ray energy in GeV

  • B – magnitude of the magnetic field’s smooth component in \(\mu\)G

Returns:

energy-loss rate in GeV/s

Syrovatskii_var(E)

Syrovatskii variable in kpc2

Parameters:

  • E – cosmic-ray energy in GeV

  • B – magnitude of the magnetic field’s smooth component in \(\mu\)G

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm2/s

  • delta – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3)

Returns:

Syrovatskii variable in kpc2

eta_var(E)

\(\eta\) variable as a function of the CRE’s energy, magnetic field, tau and delta parameters

Parameters:

  • E – CRE energy in GeV

  • B – magnetic field strength in µG

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm2/s

  • delta – power-law exponent of the diffusion coefficient as a function of the CRE’s energy

Returns:

\(\eta\) variable

hatXne(E, E0)

CRE number-density function kernel in s/GeV \(\hat X_n\)

Parameters:

  • E – CRE energy in GeV

  • E0 – injected CRE’s energy in GeV

  • B – magnetic field strength in µG

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm2/s

  • delta – power-law exponent of the diffusion coefficient as a function of the CRE’s energy

Returns:

Electron number density kernel in s/GeV

property rh
property tau0
diffsph.pyflux.which_N(nu, galaxy, rad_temp, hyp, ratio, D0, delta, B, manual=False, high_res=False, accuracy=1, **kwargs)

Determines at which order should the Fourier-expanded Green’s function solution be truncated and stores the associated \(s_n = h_n\times X_n\) coefficients as an array in the /cache folder

Parameters:

  • nu – frequency in GHz

  • galaxy (str) – name of the galaxy

  • rad_temp (str) – radial template ('NFW', 'Einasto', etc.)

  • hyp (str) – hypothesis: 'wimp' (default), 'decay' or 'generic'

  • ratio – ratio between the diffusion halo/bulge and half-light radii (default value = 1)

  • D0 – magnitude of the diffusion coefficient for a 1 GeV CRE in cm \({}^2\)/s (default value = \(3\times 10^{28}\) cm \({}^2\) /s)

  • delta (float, str) – power-law exponent of the diffusion coefficient as a function of the CRE’s energy (default value = 1/3 or 'kol')

  • B – magnitude of the magnetic field’s smooth component in \(\mu\) G (default value \(= 2 \mu\) G)

  • manual (bool) – manual input of parameter values in rad_temp (default value = 'False')

  • high_res (bool) – spatial resolution. If 'True', synch_emissivity() computes as many terms as needed in order to converge at \(r=0\). (default value = 'False')

  • accuracy – theoretical accuracy in % (default value = 1%)

Keyword arguments

  • hyp = 'wimp' (default)

Parameters:

  • sv – annihilation rate (annihilation cross section times relative velocity) \(\sigma v\) in cm \({}^3\)/s (default value = \(3 \times 10^{-26}\) cm \({}^3\) /s)

  • self_conjugate – if set 'True' (default value) the DM particle is its own antiparticle

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – annihilation channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'decay'

Parameters:

  • width – decay width of the DM particle in 1/s

  • mchi – mass of the DM particle in GeV/c \({}^2\)

  • channel (str) – decay channel: \(b\bar b\) ('bb'), \(\mu^+ \mu^-\) ('mumu'), \(W^+ W^-\) ('WW'), etc.

  • hyp = 'generic'

Parameters:

  • Gamma – power-law exponent of the generic CRE source (\(1.1 < \Gamma < 3\))

  • rate – CRE production rate in 1/s

  • manual = 'False'

Parameters:

ref – reference used ('Martinez' or '1309.2641', 'Geringer-Sameth' or '1408.0002', etc.)

  • manual = 'True'

Parameters:
Returns:

series truncation order N

Module contents