FENRIR: A statistical model of stellar variability - I. A physics-based, fast Gaussian process model to represent stellar activity and perform statistical Doppler imaging

Open Access

Table C.1

Kernels (k^W) obtained for different window shapes (W), normalized such that k^W(0) = 1.

	W (t)	k^W (τ)	kernel type	rank
Sudden appearing and exp. decay	1_t>0 exp(−t/ρ)	exp(−\|τ\|/ρ)	Matérn 1/2	1
Asymmetric exp. (dis)appearing	1_t<0 exp(t/ρ₋) + 1_t>0 exp(−t/ρ₊)	$\frac{ρ_{+} \exp (- \| τ \| / ρ_{+}) - ρ_{-} \exp (- \| τ \| / ρ_{-})}{ρ_{+} - ρ_{-}}$ ${{{{\rho _ + }\exp \left( { - \|\tau \|/{\rho _ + }} \right) - {\rho _ - }\exp \left( { - \|\tau \|/{\rho _ - }} \right)} \over {{\rho _ + } - {\rho _ - }}}}$	Sum of Matérn 1/2	2
Symmetric exp. (dis)appearing	exp(−\|t\|/ρ)	$(1 + \frac{\| τ \|}{ρ}) \exp (- \| τ \| / ρ)$ ${\left( {1 + {{\|\tau \|} \over \rho }} \right)\exp ( - \|\tau \|/\rho )}$	Matérn 3/2	3

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