Magpies method list

Here we briefly describe most functions implemented in the Magpies python library.

magpies.xg(Rns, Mns)

Compute compactenss parameters of neutron star.

\(x_g = 2 G M / (R c^2)\)

Parameters:

  • Rns – neutron star radius [km]

  • Mns – neutron star mass [Solar mass]

Returns:

compactness parameter [uniteless]


magpies.g14(Rns, Mns)

Calculate the free fall acceleration at the surface of neutron star.

\(g_{14} = G M / (R^2 \sqrt{1 - x_g}) / 10^{14}\)

Parameters:

  • Rns – neutron star radius [km]

  • Mns – neutron star mass [Solar mass]

Returns:

free fall acceleration at the surface of neutron star [g/1e14 cm/s/s]


magpies.compute_L(Tmap, Rns)

Calculate the total thermal X-ray luminosity of neutron star.

\(L = \sigma_\mathrm{SB} R_\mathrm{NS}^2 \int_{4\pi} T_s^4 (\theta, \phi) \sin \theta d\theta d\phi\)

Parameters:

  • Tmap – member of Tmap class containing surface temperature map.

  • Rns – radius of neutron star [km]

The thermal map can be one dimensional (in the case of axisymmetric temperature distribution) or two-dimensional.

Returns:

total thermal luminosity [erg/s]


magpies.compute_L_param(param, Teff, Rns, Mns)

Calculate the total thermal X-ray luminosity produced by single/two or more parameter blackbody.

Parameters:

  • param – list of areas and relative temperatures

  • Teff – effective temperature

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

Returns:

total thermal luminosity [erg/s]

Example:

compute_L_param ([1, 1], 1e6, 12, 1.4) computes luminosity of neutron star with surface temperature 1 MK, radius 12 km and mass 1.4 solar mass


magpies.compute_Teff(Tmap, Rns)

Calculate the effective temperature of neutron star.

Parameters:

  • Tmap – member of Tmap class containing surface temperature map.

  • Rns – radius of neutron star [km]

The thermal map can be one dimensional (in the case of axisymmetric temperature distribution) or two-dimensional.

Returns:

Effective temperature [K]


magpies.D_factor(cospsi, Rns, Mns)

Calculate the lensing factor following the article Poutanen (2020) A&A 640, A24 (2020).

\(\mathcal D = 1 + \frac{3 u^2 y^2}{112} - \frac{e}{100} uy \left[ 2 \log \left( 1 - \frac{y}{2} \right) + y \frac{1-3y/4}{1-y/2}\right]\)

where \(u = \frac{Rg}{R_\mathrm{NS}}\) and \(y = 1 - \cos\psi\).

Parameters:

  • cospsi – cosine of propagation angle \(\cos\psi\)

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

Returns:

Dimensionless lensing factor \(\mathcal D\)


magpies.single_BB_photons(Teff, Rns, Mns, eph, nphot, integ=True)

Calculate thermal spectra [number of photons per energy bin] emitted by neutron star with fixed surface temperature.

Parameters:

  • Teff – effective temperature of neutron star [K]

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • eph – list of energies where spectra is to be calculated [keV]

  • nphot – total number of received photons

  • integ – if True it returns integer counts (0.3 means no counts in a bin), if False it returns fraction of counts as well.

Returns:

redshifted spectra [number of photons per energy bin]


magpies.two_BB_photons(param, Teff, Rns, Mns, eph, nphot, integ=True)

Calculate thermal spectra [number of photons per energy bin] composed of two blackbodies.

Parameters:

  • param – array of four parameters [sc, sh, pc, ph]

  • Teff – effective temperature of neutron star

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • eph – list of energies where spectra is to be calculated [keV]

  • nphot – total number of received photons

  • integ – integ = True correspond to integer result and integ = False corresponds to float result

Sc:

fraction of total surface area covered with first hot spot

Sh:

fraction of total surface area covered with second hot spot

Pc:

temperature of first hot spot as a fraction of Teff

Ph:

temperature of second hot spot as a fraction of Teff

Returns:

sp:

redshifted spectra [number of photons per energy bin]


magpies.examine_spectral_fit_1BB_photons(param, Teff, Rns, Mns, eph, nphot, L, integ=True)

Function to examine the quality of single blackbody fit [number of photons per energy bin] in comparison the neutron star spectra.

Parameters:

  • param –

    sc:

    relative area of hot region, :pc: relative temperature of hot region

  • Teff – effective temperature of neutron star [K]

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • eph – list of energies where spectra is to be calculated [keV]

  • nphot – total number of received photons

  • L – luminosity of neutron star

  • integ – if True it returns integer counts (0.3 means no counts in a bin), if False it returns fraction of counts as well.

Returns:

redshifted spectra [number of photons per energy bin]


magpies.examine_spectral_fit_2BB_photons(param, Teff, Rns, Mns, eph, nphot, L, integ=True)

Function to examine the quality of two blackbody fit [number of photons per energy bin] in comparison the neutron star spectra.

Parameters:

  • param –

    sc:

    relative area of hot region, :pc: relative temperature of hot region

  • Teff – effective temperature of neutron star [K]

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • eph – list of energies where spectra is to be calculated [keV]

  • nphot – total number of received photons

  • L – luminosity of neutron star

  • integ – if True it returns integer counts (0.3 means no counts in a bin), if False it returns fraction of counts as well.

Returns:

redshifted spectra [number of photons per energy bin]


magpies.Cstat_1BB(param, Teff, Rns, Mns, spec, eph, nphot, L)

Calculate C-statistics for synthetic spectra [counts per energy bin] composed of single blackbody.

Parameters:

  • sc – fraction of total surface area covered with hot spot

  • Teff – effective temperature of hot spot

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • eph – list of energies where spectra is to be calculated [keV]

  • nphot – total number of received photons

  • L – luminosity of neutron star which we try to model

Returns:

C-stat


magpies.Cstat_2BB(param, Teff, Rns, Mns, spec, eph, nphot, L)

Calculate C-statistics for synthetic spectra [number of photons per energy bin] composed of two blackbody.

Parameters:

  • param – array of two parameters [sc, sh, pc, ph]

  • Teff – effective temperature of neutron star

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • eph – list of energies where spectra is to be calculated [keV]

  • nphot – total number of received photons

  • L – luminosity of neutron star which we try to fit

Sc:

fraction of total surface area covered with first hot spot

Pc:

temperature of first hot spot as a fraction of Teff

Returns:

C-stat


magpies.fit_spectral_model_Cstat(Teff, Rns, Mns, spec, eph, nphot, L, significance=2.7)

Fit spectra [spec] with two models: (1) single blackbody model and (2) sum of two blackbody model and choose the best model using C-statistics

Parameters:

  • Teff – effective temperature of neutron star

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • spec – spectra which we try to fit

  • eph – list of energies where spectra was calculated [keV]

  • nphot – total number of received photons

  • L – luminosity of neutron star which we try to fit

  • significance – Critical value of \(\Delta C\) to make a choice between single and two-blackbody model

Returns:

list [s1, s2, p1, p2, Cstat BB1, Cstat BB2]


magpies.spectra_pole(Tmap, Rns, Mns, eph)

Calculate redshifted thermal spectra [erg s^-1 cm^-2 keV^-1] emitted by neutron star observed from its magnetic pole (top row of thermal map).

\(H_E^\infty = \frac{15 \sigma_{SB}}{\pi^5 k_B^4} \int_\mathrm{viz} \frac{E^3 \cos \alpha \; \mathcal{D} \sin \theta d\theta d\phi}{\exp(E/(k_B T_s^\infty)) - 1}\)

Parameters:

  • Tmap – member of Tmap class containing surface temperature map.

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • eph – list containing energy mesh \(E\) [keV]

Returns:

sp:

redshifted spectra [erg s^-1 cm^-2 keV^-1]

visible_map:

two-dimensional array which contains only the temperature distribution on visible hemisphere


magpies.spectra_any(Tmap, Rns, Mns, phase, chi, inc, eph)

Calculate redshifted thermal spectra [erg s^-1 cm^-2 keV^-1] emitted by neutron star observed from arbitrary orientation.

\(H_E^\infty = \frac{15 \sigma_{SB}}{\pi^5 k_B^4} \int_\mathrm{viz} \frac{E^3 \cos \alpha \; \mathcal{D} \sin \theta d\theta d\phi}{\exp(E/(k_B T_s^\infty)) - 1}\)

Parameters:

  • Tmap – member of Tmap class containing surface temperature map.

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • phase – rotational phase [radian]

  • chi – magnetic obliquity angle (angle between orientation of original dipolar magnetic field - top of the surface thermal map)

  • inc – inclination of the observer with respect to the rotational axis.

  • eph – list containing energy mesh \(E\) [keV]

Returns:

sp:

redshifted spectra [erg s^-1 cm^-2 keV^-1]

visible_map:

two-dimensional array which contains only the temperature distribution on visible hemisphere


magpies.lightcurve(Tmap, Rns, Mns, phases, chi, inc)

Calculate soft X-ray lightcurve

Parameters:

  • Tmap – member of Tmap class containing surface temperature map.

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • phases – list of phases [radian]

  • chi – magnetic obliquity angle (angle between orientation of original dipolar magnetic field - top of the surface thermal map)

  • inc – inclination of the observer with respect to the rotational axis.

Returns:

Soft X-ray lightcurve in units of intensity for each rotational phase [erg/s]


magpies.phase_resolved_spectroscopy(Tmap, Rns, Mns, phases, chi, inc, eph)

Calculate phase-resolved spectroscopy for neutron star.

Parameters:

  • Tmap – member of Tmap class containing surface temperature map.

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • phases – rotational phases [radian]

  • chi – magnetic obliquity angle (angle between orientation of original dipolar magnetic field - top of the surface thermal map)

  • inc – inclination of the observer with respect to the rotational axis.

  • eph – list energies where spectra should be computed [keV]

Returns:

sp:

number of photons per energy bin


magpies.precompute_Dcos_alpha(Rns, Mns, chi, inc, phase, phi1, theta1)

Calculate \(\mathcal D \cos\alpha\) factor for all points of the mesh at the neutron star surface.

Parameters:

  • Rns – radius of neutron star [km]

  • Mns – mass of neutron star [Solar mass]

  • chi – magnetic obliquity angle (angle between orientation of original dipolar magnetic field - top of the surface thermal map)

  • inc – inclination of the observer with respect to the rotational axis.

  • phase – rotational phase [radian]

  • phi1 – list of magnetic longuitudets [radians] where Tmap is provided

  • theta1 – list magnetic latitude [radians] where Tmap is provided

Returns:

array of \(\mathcal D \cos\alpha\) factors


magpies.flux_to_photons(flx, eph, nph)

Convert fluxes into number of photons

\(N_\mathrm{phot} = \frac{F}{E}\)

Parameters:

  • flx – spectral fluxes […]

  • eph – mesh of energies [keV]

  • nph – total number of photons received by X-ray telescope.

Returns:

number of photons per energy bin