Exponential-sine periodic kernel (S+LEAF)

Exponential-sine periodic kernel (S+LEAF)#

The S+LEAF exponential-sine periodic (ESP) kernel is a fast approximation of the quasi-periodic kernel. It is useful when one wants an independent covariance matrix for each dataset while sharing the stellar-activity hyperparameters.

The hyperparameters use the same names as the quasi-periodic models:

  • Prot: stellar rotation period

  • Pdec: decay timescale of active regions

  • Oamp: coherence scale of the periodic component

  • Hamp: dataset-specific covariance amplitude

Note

If you use this model, please cite S+LEAF: Delisle et al. 2020 and Delisle et al. 2022.

Model definition and requirements#

model name: spleaf_esp

  • required common object: activity

  • implemented with the S+LEAF package

  • default implementation for the one-dimensional ESP kernel

model aliases

  • spleaf_exponentialsineperiodic

  • spleaf_esp_slow

  • spleaf_exponentialsineperiodic_slow

The slow implementation builds the S+LEAF covariance directly at each likelihood call. The default spleaf_esp implementation keeps a reusable covariance object and is normally preferred.

Keywords#

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

n_harmonics

  • accepted values: integer | 4

  • number of harmonics used by the ESP approximation.

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.

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#

 1inputs:
 2  LC_K2:
 3    file: datasets/K2_lightcurve_PyORBIT.dat
 4    kind: Phot
 5    models:
 6      - spleaf_esp
 7common:
 8  activity:
 9    boundaries:
10      Prot: [10.0, 20.0]
11      Pdec: [20.0, 1000.0]
12      Oamp: [0.001, 1.0]
13models:
14  spleaf_esp:
15    model: spleaf_esp
16    common: activity
17    n_harmonics: 4
18    hyperparameters_condition: True
19    rotation_decay_condition: True
20    boundaries:
21      Hamp: [0.0, 1.0]

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

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

Oamp

Coherence scale

common

activity

Hamp

Amplitude of the kernel

dataset

activity