Transit Models¶

PyTransit implements five of the most important exoplanet transit light curve models, each with model-specific optimisations to make their evaluation efficient. The models come in two flavours

Numba-accelerated implementations for CPU computing. These implementations are multi-threaded, and can be the best choice when modelling large amounts of short-cadence observations where the data transfer between the GPU and main memory would create a bottleneck.
OpenCL implementations for GPU computing. These can be orders of magnitude faster than the CPU implementations if ran in a powerful GPU, especially when modelling long cadence data where the amount of computation per observation dominates over the time for data transfer.

The CPU and GPU implementations aim to offer equal functionality, but, at the moment of writing, they have some variation in the available features.

Transit model interface¶

The transit models share a unified interface with small variations to account for model-specific parameters and settings. Some of the models have also special evaluation methods aimed for specific science cases, such as transmission spectroscopy where the light curves have been created from a spectroscopic time series.

The models are made to work with heterogeneous photometric time series. That is, a single model evaluation can model observations in different passbands (with different limb darkening), different exposure times, and different supersampling rates.

Model initialisation¶

Model initialisation is straightforward. The Mandel-Agol model with quadratic limb darkening can be imported and initialised by

from pytransit import QuadraticModel

tm = QuadraticModel()

After the initialisation, the model still needs to be set up by giving it the observation centre-times, and optionally other information, such as passbands, exposure times, supersampling rates, etc.

Data setup¶

Basics¶

At its simplest, the data setup requires the mid-observation times. If no other other information is given, the model assumes that all the data have been observed in a single passband and that the exposure time is short enough so that supersampling is not needed.

tm.set_data(time)

Heterogeneous light curves¶

PyTransit can be used to model heterogeneous time series. That is, the time array can consist of many transit light curves observed in different passbands and with different exposure times (requiring different supersampling rates). For this to work, the model first needs to assign each individual exposure to a single light curve. This is done by passing the model an integer array of light curve indices (lcids), where each element maps an exposure to a light curve.

tm.set_data(time=[0,1,2,3,4], lcids=[0,0,0,1,1])

Just setting the light curve indices doesn’t do anything by itself, but it is necessary to use the more advanced features described below.

The model doesn’t need to be told explicitly how many light curves the dataset contains, since the number of light curves is obtained from the unique lcids elements.

Multiple passbands¶

PyTransit can model transits observed in multiple passbands, where each passband has a different stellar limb darkening profile. For this, the model needs to be given an integer array of passband indices (pbids), where each element maps a light curve to a single passband. Expanding the previous example, we can tell the model that the two light curves belong to different passbands as

tm.set_data(time=[0,1,2,3,4], lcids=[0,0,0,1,1], pbids=[0,1])

After this, the model expects to get a two-dimensional array of limb darkening coefficients when evaluated, as explained later in more detail.

Supersampling¶

If the exposure time is long (Kepler and TESS long cadence mode, for example), supersampling can be set up by giving the exposure time (exptime) and supersampling rate (nsamples), where exptime and nsamples are either floats or arrays.

A single float can be given when modelling a homogeneous time series

tm.set_data(time, exptime=0.02, nsamples=10)

in which case the whole time series will have a constant supersampling rate. An array of per-light-curve values can be given when modelling heterogeneous time series

tm.set_data(time=[0,1,2,3,4], lcids=[0,0,0,1,1], exptime=[0.0007, 0.02], nsamples=[1, 10])

in which case each light curve will have a separate supersampling rate.

Advanced example¶

For a slightly more advanced example, a set of three light curves, two observed in one passband and the third in another passband, with times

times_1 (lc = 0, pb = 0, sc) = [1, 2, 3, 4]
times_2 (lc = 1, pb = 0, lc) = [3, 4]
times_3 (lc = 2, pb = 1, sc) = [1, 5, 6]

would be set up as

tm.set_data(time  = [1, 2, 3, 4, 3, 4, 1, 5, 6],
            lcids = [0, 0, 0, 0, 1, 1, 2, 2, 2],
            pbids = [0, 0, 1],
            nsamples = [  1,  10,   1],
            exptimes = [0.1, 1.0, 0.1])

Model evaluation¶

tm.evaluate_ps()

tm.evaluate_pv()

OpenCL¶

The OpenCL versions of the models work identically to the Python version, except that the OpenCL context and queue can be given as arguments in the initialiser, and the model evaluation method can be told to not to copy the model from the GPU memory. If the context and queue are not given, the model creates a default context using cl.create_some_context().

import pyopencl as cl
from src import QuadraticModelCL

ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)

tm = QuadraticModelCL(cl_ctx=ctx, cl_queue=queue)