Uniform model

Uniform model#

UniformModel reproduces a transit over a disk of constant surface brightness. With no limb darkening, the overlap integral reduces to the analytic intersection area of two circles, which makes this the fastest model in PyTransit.

It takes no limb darkening coefficients, so its evaluate signature is shorter than the other models’:

from numpy import pi, linspace
from pytransit import UniformModel

time = linspace(-0.1, 0.1, 1000)

tm = UniformModel()
tm.set_data(time)

flux = tm.evaluate(k=0.1, t0=0.0, p=1.0, a=3.0, i=0.5*pi)

When to use it#

Secondary eclipses. The occulted body is the planet, whose dayside really is close to uniform, so the model is physically correct here rather than merely convenient. Create it with eclipse=True to shift the modelled event to the secondary eclipse.

tm = UniformModel(eclipse=True)

EclipseModel does the same thing while also handling the planet-star flux ratio, and is usually the better choice.

Speed-critical work where transit shape does not matter. Transit searches, injection-recovery tests, and rough duration or depth estimates.

Warning

Do not use this model to measure a radius ratio from real photometry. Ignoring limb darkening biases the depth, and therefore the inferred planet radius, at a level that matters for any modern dataset.

API#

class pytransit.models.ma_uniform.UniformModel(eclipse=False)[source]#

Bases: TransitModel

Transit over a uniform (unlimb-darkened) stellar disk (Mandel & Agol, ApJ 580, L171-L175, 2002).

The uniform model gives the flux blocked by an opaque circular planet crossing a disk of constant surface brightness. Because there is no limb darkening, the model takes no limb darkening coefficients and reduces to the analytic overlap area of two circles, which makes it the fastest model in PyTransit.

The model is used for two things in practice:

Secondary eclipses, where the planet’s dayside is occulted by the star. The planet disk really is close to uniform in this geometry, so the model is physically correct rather than merely convenient. Pass eclipse=True to shift the modelled event to the secondary eclipse.
Transits where limb darkening is negligible or irrelevant, such as very low-precision photometry or transit-search applications where speed matters more than a ppm-accurate shape.

Examples

from pytransit import UniformModel

tm = UniformModel()
tm.set_data(time)
flux = tm.evaluate(k=0.1, t0=0.0, p=1.0, a=3.0, i=0.5*pi)

Uniform model

Contents

Uniform model#

When to use it#

API#