Quasi-periodic plus squared-exponential kernel

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The quasi-periodic plus squared-exponential kernel combines the usual stellar-rotation term with an additional long-timescale squared-exponential component. It is intended for activity signals where the rotationally modulated covariance and a slower cycle-like covariance should be fitted together.

\[\gamma(t_i,t_j) = H_\mathrm{amp}^2 G_\mathrm{QP}(t_i,t_j) + C_\mathrm{amp}^2 G_\mathrm{SE}(t_i,t_j; P_\mathrm{cyc})\]

where G_QP is the quasi-periodic kernel and G_SE is a squared-exponential kernel with scale Pcyc.

Model definition and requirements

model name: tinygp_quasiperiodicsquaredexponential

• required common object: activity

• implemented with tinygp

• read Caveats on the use of tinyGP carefully

model alias

• tinygp_quasiperiodic_squaredexponential

Keywords

Model-wide keywords, with the default value in boldface.

hyperparameters_condition

• accepted values: True | False

• activates the quasi-periodic hyperparameter condition described in the quasi-periodic kernel.

rotation_decay_condition

• accepted values: True | False

• if activated, requires Pdec > 2 Prot.

halfrotation_decay_condition

• accepted values: True | False

• if activated, requires Pdec > 0.5 Prot.

decay_rotation_factor or rotation_decay_factor

• accepted values: float | not used

• if provided, requires Pdec to be larger than the specified factor times Prot.

use_stellar_rotation_period

• accepted values: True | False

• replaces Prot with rotation_period from star_parameters.

use_stellar_activity_decay

• accepted values: True | False

• replaces Pdec with activity_decay from star_parameters.

Example

inputs:
  LCdata:
    file: datasets/lightcurve_PyORBIT.dat
    kind: Phot
    models:
      - gp_qp_cycle
common:
  activity:
    boundaries:
      Prot: [10.0, 20.0]
      Pdec: [20.0, 1000.0]
      Pcyc: [100.0, 5000.0]
      Oamp: [0.001, 1.0]
models:
  gp_qp_cycle:
    model: tinygp_quasiperiodicsquaredexponential
    common: activity
    hyperparameters_condition: True
    rotation_decay_condition: True
    boundaries:
      Hamp: [0.0, 1.0]
      Camp: [0.0, 1.0]

Model parameters

Name	Parameter	Common?	Definition	Notes
Prot	Rotational period of the star	common	activity	Replaced by rotation_period when use_stellar_rotation_period: True
Pdec	Decay timescale of active regions	common	activity	Replaced by activity_decay when use_stellar_activity_decay: True
Pcyc	Timescale of the squared-exponential component	common	activity
Oamp	Coherence scale	common	activity
Hamp	Amplitude of the quasi-periodic component	dataset	activity
Camp	Amplitude of the squared-exponential component	dataset	activity