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# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import numpy as np
import astropy.units as u
from astropy.time import Time
__all__ = ['PeriodicEvent', 'EclipsingSystem']
class PeriodicEvent(object):
"""
A periodic event defined by an epoch and period.
"""
@u.quantity_input(period=u.day, duration=u.day)
def __init__(self, epoch, period, duration=None, name=None):
"""
Parameters
----------
epoch : `~astropy.time.Time`
Time of event
period : `~astropy.units.Quantity`
Period of event
duration : `~astropy.units.Quantity` (optional)
Duration of event
name : str (optional)
Name of target/event
"""
self.epoch = epoch
self.period = period
self.name = name
self.duration = duration
def phase(self, time):
"""
Phase of periodic event, on interval [0, 1). For example, the phase
could be an orbital phase for an eclipsing binary system.
Parameters
----------
time : `~astropy.time.Time`
Evaluate the phase at this time or times
Returns
-------
phase_array : `~numpy.ndarray`
Phase at each ``time``, on range [0, 1)
"""
return ((time - self.epoch).to(u.day).value %
self.period.to(u.day).value) / self.period.to(u.day).value
class EclipsingSystem(PeriodicEvent):
"""
Define parameters for an eclipsing system; useful for an eclipsing binary or
transiting exoplanet.
.. warning::
There are currently two major caveats in the implementation of
``EclipsingSystem``. The secondary eclipse time approximation is
only accurate when the orbital eccentricity is small, and the eclipse
times are computed without any barycentric corrections. The current
implementation should only be used forapproximate mid-eclipse times for
low eccentricity orbits, with event durations longer than the
barycentric correction error (<=16 minutes).
"""
@u.quantity_input(period=u.day, duration=u.day)
def __init__(self, primary_eclipse_time, orbital_period, duration=None,
name=None, eccentricity=None, argument_of_periapsis=None):
"""
Parameters
----------
primary_eclipse_time : `~astropy.time.Time`
Time of primary eclipse
orbital_period : `~astropy.units.Quantity`
Orbital period of eclipsing system
duration : `~astropy.units.Quantity` (optional)
Duration of eclipse
name : str (optional)
Name of target/event
eccentricity : float (optional)
Orbital eccentricity. Default is `None`, which assumes circular
orbit (e=0).
argument_of_periapsis : float (optional)
Argument of periapsis for the eclipsing system, in radians.
Default is `None`, which assumes pi/2.
"""
self.epoch = primary_eclipse_time
self.period = orbital_period
self.name = name
self.duration = duration
if eccentricity is None:
eccentricity = 0
self.eccentricity = eccentricity
if argument_of_periapsis is None:
argument_of_periapsis = np.pi/2
self.argument_of_periapsis = argument_of_periapsis
def in_primary_eclipse(self, time):
"""
Returns `True` when ``time`` is during a primary eclipse.
.. warning::
Barycentric offsets are ignored in the current implementation.
Parameters
----------
time : `~astropy.time.Time`
Time to evaluate
Returns
-------
in_eclipse : `~numpy.ndarray` or bool
`True` if ``time`` is during primary eclipse
"""
phases = self.phase(time)
return ((phases < float(self.duration/self.period)/2) |
(phases > 1 - float(self.duration/self.period)/2))
def in_secondary_eclipse(self, time):
r"""
Returns `True` when ``time`` is during a secondary eclipse
If the eccentricity of the eclipsing system is non-zero, then we compute
the secondary eclipse time approximated to first order in eccentricity,
as described in Winn (2010) Equation 33 [1]_:
The time between the primary eclipse and secondary eclipse :math:`\delta t_c`
is given by :math:`\delta t_c \approx 0.5 \left (\frac{4}{\pi} e \cos{\omega \right)`,
where :math:`e` is the orbital eccentricity and :math:`\omega` is the
angle of periapsis.
.. warning::
This approximation for the secondary eclipse time is only accurate
when the orbital eccentricity is small; and barycentric offsets
are ignored in the current implementation.
Parameters
----------
time : `~astropy.time.Time`
Time to evaluate
Returns
-------
in_eclipse : `~numpy.ndarray` or bool
`True` if ``time`` is during secondary eclipse
References
----------
.. [1] Winn (2010) https://arxiv.org/abs/1001.2010
"""
if self.eccentricity < 1e-5:
secondary_eclipse_phase = 0.5
else:
secondary_eclipse_phase = 0.5 * (1 + 4/np.pi * self.eccentricity *
np.cos(self.argument_of_periapsis))
phases = self.phase(time)
return ((phases < secondary_eclipse_phase + float(self.duration/self.period)/2) &
(phases > secondary_eclipse_phase - float(self.duration/self.period)/2))
def out_of_eclipse(self, time):
"""
Returns `True` when ``time`` is not during primary or secondary eclipse.
.. warning::
Barycentric offsets are ignored in the current implementation.
Parameters
----------
time : `~astropy.time.Time`
Time to evaluate
Returns
-------
in_eclipse : `~numpy.ndarray` or bool
`True` if ``time`` is not during primary or secondary eclipse
"""
return np.logical_not(np.logical_or(self.in_primary_eclipse(time),
self.in_secondary_eclipse(time)))
def next_primary_eclipse_time(self, time, n_eclipses=1):
"""
Time of the next primary eclipse after ``time``.
.. warning::
Barycentric offsets are ignored in the current implementation.
Parameters
----------
time : `~astropy.time.Time`
Find the next primary eclipse after ``time``
n_eclipses : int (optional)
Return the times of eclipse for the next ``n_eclipses`` after
``time``. Default is 1.
Returns
-------
primary_eclipses : `~astropy.time.Time`
Times of the next ``n_eclipses`` primary eclipses after ``time``
"""
eclipse_times = ((1-self.phase(time)) * self.period + time +
np.arange(n_eclipses) * self.period)
return eclipse_times
def next_secondary_eclipse_time(self, time, n_eclipses=1):
"""
Time of the next secondary eclipse after ``time``.
.. warning::
Barycentric offsets are ignored in the current implementation.
Parameters
----------
time : `~astropy.time.Time`
Find the next secondary eclipse after ``time``
n_eclipses : int (optional)
Return the times of eclipse for the next ``n_eclipses`` after
``time``. Default is 1.
Returns
-------
secondary_eclipses : `~astropy.time.Time`
Times of the next ``n_eclipses`` secondary eclipses after ``time``
"""
phase = self.phase(time)
if phase >= 0.5:
next_eclipse_phase = 1.5
else:
next_eclipse_phase = 0.5
eclipse_times = ((next_eclipse_phase - phase) * self.period + time +
np.arange(n_eclipses) * self.period)
return eclipse_times
def next_primary_ingress_egress_time(self, time, n_eclipses=1):
"""
Calculate the times of ingress and egress for the next ``n_eclipses``
primary eclipses after ``time``
.. warning::
Barycentric offsets are ignored in the current implementation.
Parameters
----------
time : `~astropy.time.Time`
Find the next primary ingress and egress after ``time``
n_eclipses : int (optional)
Return the times of eclipse for the next ``n_eclipses`` after
``time``. Default is 1.
Returns
-------
primary_eclipses : `~astropy.time.Time` of shape (``n_eclipses``, 2)
Times of ingress and egress for the next ``n_eclipses`` primary
eclipses after ``time``
"""
next_mid_eclipses = self.next_primary_eclipse_time(time, n_eclipses=n_eclipses)
next_ingresses = next_mid_eclipses - self.duration/2
next_egresses = next_mid_eclipses + self.duration/2
ing_egr = np.vstack([next_ingresses.utc.jd, next_egresses.utc.jd]).T
return Time(ing_egr, format='jd', scale='utc')
def next_secondary_ingress_egress_time(self, time, n_eclipses=1):
"""
Calculate the times of ingress and egress for the next ``n_eclipses``
secondary eclipses after ``time``
.. warning::
Barycentric offsets are ignored in the current implementation.
Parameters
----------
time : `~astropy.time.Time`
Find the next secondary ingress and egress after ``time``
n_eclipses : int (optional)
Return the times of eclipse for the next ``n_eclipses`` after
``time``. Default is 1.
Returns
-------
secondary_eclipses : `~astropy.time.Time` of shape (``n_eclipses``, 2)
Times of ingress and egress for the next ``n_eclipses`` secondary
eclipses after ``time``.
"""
next_mid_eclipses = self.next_secondary_eclipse_time(time, n_eclipses=n_eclipses)
next_ingresses = next_mid_eclipses - self.duration/2
next_egresses = next_mid_eclipses + self.duration/2
ing_egr = np.vstack([next_ingresses.utc.jd, next_egresses.utc.jd]).T
return Time(ing_egr, format='jd', scale='utc')
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