# 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')