TTV2Fast2Furious

Tools for TTV analysis and parameter inference.

ttv2fast2furious.MultiplanetSystemLinearModelAmplitudes(Nplanets, Periods, T0s, masses, eccs, pomegas, **kwargs)

Compute amplitudes for linear model basis functions for user-specified planet parameters.

Parameters:

• Nplanets (int) – The number of planets in the system.
• Periods (ndarray) – Periods of the planets.
• T0s (ndarray) – Times of first transit
• masses (ndarray) – Planet masses, in units of host-star mass.
• eccs (ndarray) – Eccentricities.
• pomegas (ndarray) – Longitudes of periapse.

Returns:

List of model amplitudes

Return type:

list of ndarrays

ttv2fast2furious.MultiplanetSystemBasisFunctionMatrices(Nplanets, Periods, T0s, Ntransits, **kwargs)

Compute basis function matrices for the transit times of an Nplanet system.

Parameters:

• Nplanets (int) – The number of transting planets to model.
• Periods (ndarray) – Array listing planets’ orbital periods.
• T0s (ndarray) – Array listing the times of planets’ first transits
• Ntransits (ndarray) – Array listing the number of transits to compute for each planet.

Keyword Arguments:  

InteractionMatrix – Specify the interactions between planets as a matrix. By default, all planets are assumed to interact with one antoher.

Returns:

List of ndarrays with columns containing TTV basis functions of each planet.

Return type:

list

class ttv2fast2furious.PlanetTransitObservations(transit_numbers, times, uncertainties)

Object to store transit timing measurement information.

__init__(transit_numbers, times, uncertainties)

Parameters:

• transit_numbers (ndarray) – List that numbers the series of transit observations
• times (ndarray) – List of transit mid-times
• uncertainties (ndarray) – List of tramsit mid-time measurement \(1\sigma\) uncertainties

basis_function_matrix()

Generate the basis function matrix for a linear transit ephemeris.

Returns:basis function matrix Return type:ndarray

classmethod from_times_only(times, unc=0)

Initialize transit observation object diectly from list of transit times.

Return a PlanetTransitObservations object initialized from a list of transit times. Transit numbers are automatically assigned sequentially. Uniform uncertainties are assigned to the observations according to the user-specified unc.

Parameters:

• times (array_like) – List of transit mid-times
• unc (float, optional) – Uncertainty assigned to transit observations

function_mask(func)

Mask out transit times by applying function func to the times.

Parameters:func (callable) – Function to mask times. func should return False for times that are to be masked out. Otherwise func should return True.

linear_best_fit()

Determine the best-fit period and initial transit time for a linear transit ephemeris.

linear_fit_design_matrix()

Generate the design matrix for a linear transit ephemeris.

linear_fit_residuals()

Return the transit timing residuals of a best-fit linear transit ephemeris.

times

List of transit mid-times

Type:ndarray

transit_numbers

List of transit epoch numbers.

Type:ndarray

uncertainties

List of \(1\sigma\) transit mid-time measurement uncertainties.

Type:ndarray

class ttv2fast2furious.TransitTimesLinearModels(observations_list)

Object representing a collection of transit time linear models in a system of interacting planets.

observations : list

A list of transit time observation objects representing the transit observations for a system

basis_function_matrices: list

List of each planet’s transit itme basis function matrix

periods : ndarray

Best-fit periods of all planets

T0s : ndarray

Best-fit initial times of transit for all planets

best_fit : list of ndarray

List of ndarray best fit amplitudes of each planets’ TTV basis functions.

covariance_matrices : list of ndarray

List of ndarray covariance matrices for each planets’ TTV basis functions.

Parameters:observations_list (list of PlanetTransitObservations) – Set of transit observations to model.

N

Number of planets with transit observations.

Type:int

__init__(observations_list)

Initialize self. See help(type(self)) for accurate signature.

design_matrices

Design matrices for each planet’s TTV model.

Type:list of ndarrays

interaction_matrix

Matrix with elements that record whether pair-wise interactions are in each planet’s set of TTV basis functions. If \(I_{ij}=\) True, then the basis functions accounting for perturbations by planet j on planet i are included in the model for planet i’s TTV.

Type:ndarray

maximum_interaction_period_ratio

Maximum period ratio above which planet-planet interactions are ignored in the TTV model.

Type:float

reset()

Reset TTV model.

All TTV basis functions are erased and a linear ephemeris is re-fit to each planet’s transit times. The interaction matrix is reset so that all pair-wise interactions are considered.