Source code for gammapy.astro.source.pulsar

# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Pulsar source models."""
import numpy as np
from astropy.units import Quantity

__all__ = ["Pulsar", "SimplePulsar"]

DEFAULT_I = Quantity(1e45, "g cm2")
"""Pulsar default moment of inertia"""

DEFAULT_R = Quantity(1e6, "cm")
"""Pulsar default radius of the neutron star"""

B_CONST = Quantity(3.2e19, "gauss s^(-1/2)")
"""Pulsar default magnetic field constant"""


[docs]class SimplePulsar: """Magnetic dipole spin-down model for a pulsar. Reference: http://www.cv.nrao.edu/course/astr534/Pulsars.html Parameters ---------- P : `~astropy.units.Quantity` Rotation period (sec) P_dot : `~astropy.units.Quantity` Rotation period derivative (sec sec^-1) I : `~astropy.units.Quantity` Moment of inertia (g cm^2) R : `~astropy.units.Quantity` Radius of the pulsar (cm) """ def __init__(self, P, P_dot, I=DEFAULT_I, R=DEFAULT_R): self.P = Quantity(P, "s") self.P_dot = P_dot self.I = I self.R = R @property def luminosity_spindown(self): r"""Spin-down luminosity (`~astropy.units.Quantity`). .. math:: \dot{L} = 4\pi^2 I \frac{\dot{P}}{P^{3}} """ return 4 * np.pi ** 2 * self.I * self.P_dot / self.P ** 3 @property def tau(self): r"""Characteristic age (`~astropy.units.Quantity`). .. math:: \tau = \frac{P}{2\dot{P}} """ return (self.P / (2 * self.P_dot)).to("yr") @property def magnetic_field(self): r"""Magnetic field strength at the polar cap (`~astropy.units.Quantity`). .. math:: B = 3.2 \cdot 10^{19} (P\dot{P})^{1/2} \text{ Gauss} """ return B_CONST * np.sqrt(self.P * self.P_dot)
[docs]class Pulsar(SimplePulsar): """Magnetic dipole spin-down pulsar model. Reference: http://www.cv.nrao.edu/course/astr534/Pulsars.html Parameters ---------- P_0 : float Period at birth B : `~astropy.units.Quantity` Magnetic field strength at the poles (Gauss) n : float Spin-down braking index I : float Moment of inertia R : float Radius """ def __init__( self, P_0="0.1 s", B="1e10 G", n=3, I=DEFAULT_I, R=DEFAULT_R, age=None, L_0=None ): P_0 = Quantity(P_0, "s") B = Quantity(B, "G") self.I = I self.R = R self.P_0 = P_0 self.B = B self.P_dot_0 = (B / B_CONST) ** 2 / P_0 self.tau_0 = P_0 / (2 * self.P_dot_0) self.n = float(n) self.beta = -(n + 1.0) / (n - 1.0) if age is not None: self.age = Quantity(age, "yr") if L_0 is None: self.L_0 = 4 * np.pi ** 2 * self.I * self.P_dot_0 / self.P_0 ** 3
[docs] def luminosity_spindown(self, t): r"""Spin down luminosity. .. math:: \dot{L}(t) = \dot{L}_0 \left(1 + \frac{t}{\tau_0}\right)^{-\frac{n + 1}{n - 1}} Parameters ---------- t : `~astropy.units.Quantity` Time after birth of the pulsar """ t = Quantity(t, "yr") return self.L_0 * (1 + (t / self.tau_0)) ** self.beta
[docs] def energy_integrated(self, t): r"""Total energy released by a given time. Time-integrated spin-down luminosity since birth. .. math:: E(t) = \dot{L}_0 \tau_0 \frac{t}{t + \tau_0} Parameters ---------- t : `~astropy.units.Quantity` Time after birth of the pulsar. """ t = Quantity(t, "yr") return self.L_0 * self.tau_0 * (t / (t + self.tau_0))
[docs] def period(self, t): r"""Rotation period. .. math:: P(t) = P_0 \left(1 + \frac{t}{\tau_0}\right)^{\frac{1}{n - 1}} Parameters ---------- t : `~astropy.units.Quantity` Time after birth of the pulsar """ t = Quantity(t, "yr") return self.P_0 * (1 + (t / self.tau_0)) ** (1.0 / (self.n - 1))
[docs] def period_dot(self, t): r"""Period derivative at age t. P_dot for a given period and magnetic field B, assuming a dipole spin-down. .. math:: \dot{P}(t) = \frac{B^2}{3.2 \cdot 10^{19} P(t)} Parameters ---------- t : `~astropy.units.Quantity` Time after birth of the pulsar. """ t = Quantity(t, "yr") return self.B ** 2 / (self.period(t) * B_CONST ** 2)
[docs] def tau(self, t): r"""Characteristic age at real age t. .. math:: \tau = \frac{P}{2\dot{P}} Parameters ---------- t : `~astropy.units.Quantity` Time after birth of the pulsar. """ t = Quantity(t, "yr") return self.period(t) / 2 * self.period_dot(t)
[docs] def magnetic_field(self, t): r"""Magnetic field at polar cap (assumed constant). .. math:: B = 3.2 \cdot 10^{19} (P\dot{P})^{1/2} \text{ Gauss} Parameters ---------- t : `~astropy.units.Quantity` Time after birth of the pulsar. """ t = Quantity(t, "yr") return B_CONST * np.sqrt(self.period(t) * self.period_dot(t))