PhaseCurveTableModel

class gammapy.time.models.PhaseCurveTableModel(table, time_0, phase_0, f0, f1, f2)

Bases: gammapy.utils.fitting.Model

Temporal phase curve model.

Phase for a given time is computed as:

\[\phi(t) = \phi_0 + f_0(t-t_0) + (1/2)f_1(t-t_0)^2 + (1/6)f_2(t-t_0)^3\]

Strictly periodic sources such as gamma-ray binaries have f1=0 and f2=0. Sources like some pulsars where the period spins up or down have f1!=0 and / or f2 !=0. For a binary, f0 should be calculated as 1/T, where T is the period of the binary in unit of seconds.

The “phase curve”, i.e. multiplicative flux factor for a given phase is given by a Table of nodes (phase, norm), using linear interpolation and circular behaviour, where norm(phase=0) == norm(phase=1).

Parameters:

table : Table

A table of ‘PHASE’ vs ‘NORM’ should be given

time_0 : float

The MJD value where phase is considered as 0.

phase_0 : float

Phase at the reference MJD

f0, f1, f2 : float

Derivatives of the function phi with time of order 1, 2, 3 in units of s^-1, s^-2 & s^-3, respectively.

Examples

Create an example phase curve object:

from astropy.table import Table
from gammapy.utils.scripts import make_path
from gammapy.time.models import PhaseCurveTableModel
filename = make_path('$GAMMAPY_DATA/tests/phasecurve_LSI_DC.fits')
table = Table.read(str(filename))
phase_curve = PhaseCurveTableModel(table, time_0=43366.275, phase_0=0.0, f0=4.367575e-7, f1=0.0, f2=0.0)

Use it to compute a phase and evaluate the phase curve model for a given time:

>>> phase_curve.phase(time=46300.0)
0.7066006737999402
>>> phase_curve.evaluate_norm_at_time(46300)
0.49059393580053845

Attributes Summary

f0
f1
f2
parameters	Parameters (Parameters)
phase_0
table
time_0

Methods Summary

copy()	A deep copy.
evaluate_norm_at_phase(phase)
evaluate_norm_at_time(time)	Evaluate for a given time.
phase(time)	Evaluate phase for a given time.

Attributes Documentation

f0

f1

f2

parameters

Parameters (Parameters)

phase_0

table

time_0

Methods Documentation

copy()

A deep copy.

evaluate_norm_at_phase(phase)

evaluate_norm_at_time(time)

Evaluate for a given time.

Parameters:

time : array_like

Time since the reference time.

Returns:

norm : array_like

phase(time)

Evaluate phase for a given time.

Parameters:

time : array_like

Returns:

phase : array_like