Quasi-periodic with cosine kernel#
This kernel has been introduced by Perger et al. 2021. The kernel has been implemented in PyORBIT
without relying on any other package.
If we define \(\tau = t_i-t_j\) :
where \(\theta\) is equivalent to the rotation period of the star, \(w\) is the coherence scale, and \(\lambda\) is usually associated with the decay time scale of the active regions. Within PyORBIT
, the amplitude of the quasi-periodic part of the kernel \(h_1\) and the amplitude of the cosine part \(h_2\) have been labeled as Hamp
and Camp
respectively.
Important
As for the quasi-periodic kewrnel, mind the possible presence of a factor 2 in the denominator of the aperiodic variation (i.e., \(2 \lambda\) rather than \(\lambda\))
Model definition and requirements#
The only implementation of this kernel relies on numpy
and scipy
.
model name: gp_quasiperiodic_cosine
required common object:
activity
direct implementation relying only on
scipy
Model parameters#
The following parameters will be inherited from the common model (column Common?: common) or a different value will be assigned for each dataset (column Common?: dataset)
Name |
Parameter |
Common? |
Definition |
Notes |
---|---|---|---|---|
Prot |
Rotational period of the star \(\theta\) |
common |
|
|
Pdec |
Decay time scale of active regions \(\lambda\) |
common |
|
|
Oamp |
Coherence scale \(w\) |
common |
|
|
Hamp |
Amplitude of the kernel |
dataset |
|
|
Camp |
Amplitude of the cosine part of the kernel |
dataset |
|
Keywords#
Model-wide keywords, with the default value in boldface.
hyperparameters_condition
accepted values:
True
|False
activate the conditions \( \lambda ^ 2 > (3/4 \pi) \theta ^2 w ^ 2 \) (adapted from Rajpaul 2017 and Rajpaul et al. 2021 to take into account the factor 2 in the denominator of the aperiodic variation) to ensure that the QP function has at least one non-trivial turning point.
rotation_decay_condition
accepted values:
True
|False
if activated, it ensures that the decay time scale of the activity regions \(\lambda\) is at least twice the rotational period of the star \(\theta\)
use_stellar_rotation_period
accepted values:
True
|False
if activated, the parameter
Prot
from theactivity
common model will be replaced by the parameterrotation_period
from thestar_parameters
common model. In this way, a unique parameter can be used by different models, e.g., stellar activity and Rossiter-McLaughlin modeling. It can also be useful if you want to use independent GP hyperparameters over several observational seasons while using a single parameter for the rotational period of the star.