Phase curves

pytransit.utils.phasecurves.doppler_boosting_alpha(teff: float, flt)[source]

The photon weighted bandpass-integrated boosting factor.

Parameters:
  • teff – Effective temperature of the star [K]
  • flt – Passband transmission
Returns:

The photon weighted bandpass-integrated boosting factor.
Return type:

float
pytransit.utils.phasecurves.doppler_boosting_amplitude(mp: Union[float, numpy.ndarray], ms: Union[float, numpy.ndarray], period: Union[float, numpy.ndarray], alpha: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray][source]

The amplitude of the doppler boosting signal.

Calculates the amplitude of the doppler boosting (beaming, reflex doppler effect) signal following the approach described by Loeb & Gaudi in [Loeb2003] . Note that you need to pre-calculate the photon-weighted bandpass-integrated boosting factor (alpha) [Bloemen2010] [Barclay2012] for the star and the instrument using doppler_boosting_alpha.

Parameters:
  • mp (float or ndarray) – Planetary mass [MJup]
  • ms (float or ndarray) – Stellar mass [MSun]
  • period (float or ndarray) – Orbital period [d]
  • alpha (float or ndarray) – Photon-weighted bandpass-integrated boosting factor
Returns:

Doppler boosting signal amplitude
Return type:

float or ndarray

References

[Loeb2003]Loeb, A. & Gaudi, B. S. Periodic Flux Variability of Stars due to the Reflex Doppler Effect Induced by Planetary Companions. Astrophys. J. 588, L117–L120 (2003).
[Bloemen2010]Bloemen, S. et al. Kepler observations of the beaming binary KPD 1946+4340. MNRAS 410, (2010).
[Barclay2012]Barclay, T. et al. PHOTOMETRICALLY DERIVED MASSES AND RADII OF THE PLANET AND STAR IN THE TrES-2 SYSTEM. AspJ 761, 53 (2012).
pytransit.utils.phasecurves.ellipsoidal_variation_amplitude(mp: Union[float, numpy.ndarray], ms: Union[float, numpy.ndarray], a: Union[float, numpy.ndarray], i: Union[float, numpy.ndarray], u: Union[float, numpy.ndarray], g: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray][source]

The amplitude of the ellipsoidal variation signal.

Calculates the amplitude of the ellipsoidal variation signal following the approach described by Lillo-Box et al. in [Lillo-Box2014], page 11.

Parameters:
  • mp (float or ndarray) – Planetary mass [MJup]
  • ms (float or ndarray) – Stellar mass [MSun]
  • a (float or ndarray) – Semi-major axis of the orbit divided by the stellar radius
  • i (float or ndarray) – Orbital inclination [rad]
  • u (float or ndarray) – Linear limb darkening coefficient
  • g (float or ndarray) – Gravity darkening coefficient
Returns:

ev_amplitude – The amplitude of the ellipsoidal variation signal
Return type:

float or ndarray

References

[Lillo-Box2014]Lillo-Box, J. et al. Kepler-91b: a planet at the end of its life. A&A 562, A109 (2014).
pytransit.utils.phasecurves.ellipsoidal_variation_signal(f: Union[float, numpy.ndarray], theta: Union[float, numpy.ndarray], e: float) → Union[float, numpy.ndarray][source]
Parameters:
  • f – True anomaly [rad]
  • theta – Angle between the line-of-sight and the star-planet direction
  • e – Eccentricity
pytransit.utils.phasecurves.emission(tp: Union[float, numpy.ndarray], tstar: Union[float, numpy.ndarray], k: Union[float, numpy.ndarray], flt) → Union[float, numpy.ndarray][source]

Thermal emission from the planet.

Parameters:
  • tp (float or ndarray) – Equilibrium temperature of the planet [K]
  • tstar (float or ndarray) – Effective temperature of the star [K]
  • k (float or ndarray) – Planet-star radius ratio
  • flt (Filter) – Passband transmission
Returns:

  • float or ndarray
  • References
pytransit.utils.phasecurves.equilibrium_temperature(tstar: Union[float, numpy.ndarray], a: Union[float, numpy.ndarray], f: Union[float, numpy.ndarray], ab: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray][source]

Planetary equilibrium temperature [K].

Parameters:
  • tstar – Effective stellar temperature [K]
  • a – Scaled semi-major axis [Rsun]
  • f – Redistribution factor
  • ab – Bond albedo
Returns:

Teq – Equilibrium temperature [K]
Return type:

float or ndarray
pytransit.utils.phasecurves.flux_ratio(tstar: Union[float, numpy.ndarray], a: Union[float, numpy.ndarray], f: Union[float, numpy.ndarray], ab: Union[float, numpy.ndarray], l: Union[float, numpy.ndarray], r: Union[float, numpy.ndarray] = 1.5, ti: Union[float, numpy.ndarray] = 0) → Union[float, numpy.ndarray][source]

Total flux ratio per projected area element.

Parameters:
  • tstar – Effective stellar temperature [K]
  • a – Scaled semi-major axis [Rs]
  • f – Redistribution factor
  • ab – Bond albedo
  • l – Wavelength [m]
  • r – Inverse of the phase integral
  • ti – Temperature [K]
Returns:

fr – Total flux ratio
Return type:

float
pytransit.utils.phasecurves.planck(t: Union[float, numpy.ndarray], l: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray][source]

Radiance of a black body as a function of wavelength.

Parameters:
  • t – Black body temperature [K]
  • l – Wavelength [m]
Returns:

L – Back body radiance [W m^-2 sr^-1]
Return type:

float or ndarray
pytransit.utils.phasecurves.reflected_fr(a: Union[float, numpy.ndarray], ab: Union[float, numpy.ndarray], r: Union[float, numpy.ndarray] = 1.5) → Union[float, numpy.ndarray][source]

Reflected flux ratio per projected area element.

Parameters:
  • a – Scaled semi-major axis [Rsun]
  • ab – Bond albedo
  • r – Inverse of the phase integral
Returns:

fr – Reflected flux ratio
Return type:

float
pytransit.utils.phasecurves.solve_ab(fr, tstar, a, f, l, r=1.5, ti=0)[source]

Solve the Bond albedo.

Parameters:
  • fr – Flux ratio [-]
  • tstar – Effective stellar temperature [K]
  • a – Scaled semi-major axis [Rs]
  • A – Bond albedo [-]
  • l – Wavelength [m]
  • r – Inverse of the phase integral [-]
  • ti – Temperature [K]
Returns:

A
Return type:

Bond albedo
pytransit.utils.phasecurves.solve_redistribution(fr, tstar, a, ab, l)[source]

Solve the redistribution factor.

Parameters:
  • fr – Flux ratio [-]
  • tstar – Effective stellar temperature [K]
  • a – Scaled semi-major axis [Rs]
  • ab – Bond albedo [-]
  • l – Wavelength [m]
  • r – Inverse of the phase integral [-]
  • Ti (t) – Temperature [K]
Returns:

f
Return type:

Redistribution factor
pytransit.utils.phasecurves.solve_teq(fr, tstar, a, ab, l, r=1.5, ti=0)[source]

Solve the equilibrium temperature.

Parameters:
  • fr – Flux ratio
  • tstar – Effective stellar temperature [K]
  • a – Scaled semi-major axis [Rs]
  • ab – Bond albedo
  • l – Wavelength [m]
  • r – Inverse of the phase integral
  • ti – Temperature [K]
Returns:

Teq – Equilibrium temperature
Return type:

float or ndarray