Granulation, Oscillation, Rotation kernels

Granulation, Oscillation, Rotation kernels#

This model provides multi-component Gaussian Process regression to account for stellar oscillation, granulation, annd rotational modulation, as proposed by Barros et al. 2020, with some modifications as detailed in Section 5.1 of Nardiello et al. 2022. The former also provides a practical example of its application.

The kernel comprises:

If you use this model, please cite the celerite2 Foreman-Mackey et al. 2017 and Foreman-Mackey 2018

Model definition and requirements#

model name: celerite2_rotation

required common object: activity
rotation term only

model name: celerite2_granulation_rotation

required common object: activity
one granulation SHO term plus one rotation term

model name: celerite2_granulation_oscillation_rotation

required common object: activity
configurable number of granulation and oscillation SHO terms plus one rotation term

Model parameters#

`celerite2_rotation`#

Name	Parameter	Common?	Definition	Notes
`Prot`	Primary period of variability	common	`activity`	Replaced by `rotation_period` when `use_stellar_rotation_period: True`
`rot_Q0`	Base quality factor of the secondary oscillation	common	`activity`
`rot_deltaQ`	Difference between the quality factors of the two modes	common	`activity`
`rot_fmix`	Fractional amplitude of the secondary mode	common	`activity`
`rot_sigma`	Standard deviation of the process	dataset	`activity`	Common when `use_shared_hyperparameters: True`

`celerite2_granulation_rotation`#

Name	Parameter	Common?	Definition	Notes
`grn_period`	Granulation SHO timescale	common	`activity`
`Prot`	Primary period of variability	common	`activity`	Replaced by `rotation_period` when `use_stellar_rotation_period: True`
`rot_Q0`	Base quality factor of the secondary oscillation	common	`activity`
`rot_deltaQ`	Difference between the quality factors of the two modes	common	`activity`
`rot_fmix`	Fractional amplitude of the secondary mode	common	`activity`
`grn_sigma`	Granulation amplitude	dataset	`activity`
`rot_sigma`	Rotation amplitude	dataset	`activity`

`celerite2_granulation_oscillation_rotation`#

Name	Parameter	Common?	Definition	Notes
`Prot`	Primary period of variability	common	`activity`	Replaced by `rotation_period` when `use_stellar_rotation_period: True`
`rot_Q0`	Base quality factor of the secondary oscillation	common	`activity`
`rot_deltaQ`	Difference between the quality factors of the two modes	common	`activity`
`rot_fmix`	Fractional amplitude of the secondary mode	common	`activity`
`rot_sigma`	Rotation amplitude	dataset	`activity`	Common when `common_amplitudes: True`
`grn_k*_period`	Timescale of each granulation SHO term	common	`activity`	`*` is the kernel index, starting at 0
`grn_k*_sigma`	Amplitude of each granulation SHO term	dataset	`activity`	Common when `common_amplitudes: True`
`osc_k*_period`	Timescale of each oscillation SHO term	common	`activity`	`*` is the kernel index, starting at 0
`osc_k*_Q0`	Quality factor of each oscillation SHO term	common	`activity`
`osc_k*_sigma`	Amplitude of each oscillation SHO term	dataset	`activity`	Common when `common_amplitudes: True`

Keywords#

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

use_stellar_rotation_period

accepted values: True | False
replaces Prot with rotation_period from star_parameters.

use_shared_hyperparameters

accepted values: True | False
for celerite2_rotation, also makes rot_sigma a common parameter.

rotation_kernels

accepted values: integer | 1
used by celerite2_granulation_oscillation_rotation. Only one rotation kernel is currently supported.

granulation_kernels

accepted values: integer | 2
used by celerite2_granulation_oscillation_rotation. Adds parameters named grn_k0_period, grn_k0_sigma, grn_k1_period, grn_k1_sigma, and so on.

oscillation_kernels

accepted values: integer | 1
used by celerite2_granulation_oscillation_rotation. Adds parameters named osc_k0_period, osc_k0_sigma, osc_k0_Q0, and so on.

common_amplitudes

accepted values: True | False
used by celerite2_granulation_oscillation_rotation. If activated, the *_sigma amplitudes are common parameters instead of dataset-specific parameters.

Examples#

Rotation-only model:

inputs:
  LCdata:
    file: datasets/lightcurve_PyORBIT.dat
    kind: Phot
    models:
      - celerite2_rotation
common:
  activity:
    boundaries:
      Prot: [10.0, 20.0]
      rot_Q0: [0.1, 100.0]
      rot_deltaQ: [0.1, 100.0]
      rot_fmix: [0.01, 1.0]
models:
  celerite2_rotation:
    model: celerite2_rotation
    common: activity
    boundaries:
      rot_sigma: [0.0, 1.0]

Granulation, oscillation, and rotation model:

models:
  celerite2_activity:
    model: celerite2_granulation_oscillation_rotation
    common: activity
    granulation_kernels: 2
    oscillation_kernels: 1
    common_amplitudes: False
    boundaries:
      rot_sigma: [0.0, 1.0]
      grn_k0_sigma: [0.0, 1.0]
      grn_k1_sigma: [0.0, 1.0]
      osc_k0_sigma: [0.0, 1.0]

Granulation, Oscillation, Rotation kernels

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