Phase coverage

Given a certain period, portrait can be used to compute how much of an orbit is covered by certain observations.

Simulating some data

We start by simulating some observed times, but of course you can use your own observation times.

import numpy as np

length = 4 / 24  # the length (in hours) of a single observation
days = 20  # the number of observations
exposure = 20 / 60 / 24  # exposure of an observation

# we observe `length` hours every day for `days` days
times = np.hstack([np.arange(0, length, exposure) + i for i in np.arange(days)])

Computing the phase coverage

We would then like to compute the coverage for a range of periods

from portrait import coverage

periods = np.linspace(0.1, 10, 2000)  # in days
covered = coverage(times)(periods)

let’s plot the results

import matplotlib.pyplot as plt

plt.subplot(111, xlabel="periods", ylabel="coverage")
plt.plot(periods, covered, c="0.5")

Matplotlib is building the font cache; this may take a moment.

[<matplotlib.lines.Line2D at 0x7fb832e6b4c0>]

coverage of 1. means a period that has been fully covered. For this particular simulation (4 hours per night observations) the minima corresponds to the day/night cycle.

Note

In many scenarios, two events need to be observed in order to be detected (such as exoplanet transits). For that reason you can specify the coverage for n events using coverage(n=...). See an example here.

Application

portrait is particularly useful to understand how much a periodic orbit is covered by certain observations. It can be used to know if a planet with a certain orbital period was susceptible to be observed or not. If \(c\) is the coverage at a certain period \(P\), of particular interest is the quantity

\[C = \int_0^P c\,dP\]

which corresponds to how much orbits with periods up to \(P\) have been observed given certain observation times.

Note

Keep in mind that phase coverage is a mean quantity, and that actual phase coverage highly depend on the phase of an event during its orbit (such as the transit mid-time for a transiting exoplanet)