TY - JOUR

T1 - Estimating activity cycles with probabilistic methods II

T2 - The Mount Wilson Ca H&K data

AU - Olspert, N.

AU - Lehtinen, J. J.

AU - Käpylä, M. J.

AU - Pelt, J.

AU - Grigorievskiy, A.

PY - 2018

Y1 - 2018

N2 - Debate over the existence versus nonexistence of trends in the stellar
activity-rotation diagrams continues. Application of modern time series
analysis tools to study the mean cycle periods in chromospheric activity
index is lacking. We develop such models, based on Gaussian processes,
for one-dimensional time series and apply it to the extended Mount
Wilson Ca H&K sample. Our main aim is to study how the previously
commonly used assumption of strict harmonicity of the stellar cycles
affects the results. We introduce three methods of different complexity,
starting with the simple harmonic model and followed by Gaussian Process
models with periodic and quasi-periodic covariance functions. We confirm
the existence of two populations in the activity-period diagram. We find
only one significant trend in the inactive population, namely that the
cycle periods get shorter with increasing rotation. This is in contrast
with earlier studies, that postulate the existence of trends in both of
the populations. In terms of rotation to cycle period ratio, our data is
consistent with only two activity branches such that the active branch
merges together with the transitional one. The retrieved stellar cycles
are uniformly distributed over the R'HK activity index, indicating that
the operation of stellar large-scale dynamos carries smoothly over the
Vaughan-Preston gap. At around the solar activity index, however,
indications of a disruption in the cyclic dynamo action are seen. Our
study shows that stellar cycle estimates depend significantly on the
model applied. Such model-dependent aspects include the improper
treatment of linear trends and too simple assumptions of the noise
variance model. Assumption of strict harmonicity can result in the
appearance of double cyclicities that seem more likely to be explained
by the quasi-periodicity of the cycles.

AB - Debate over the existence versus nonexistence of trends in the stellar
activity-rotation diagrams continues. Application of modern time series
analysis tools to study the mean cycle periods in chromospheric activity
index is lacking. We develop such models, based on Gaussian processes,
for one-dimensional time series and apply it to the extended Mount
Wilson Ca H&K sample. Our main aim is to study how the previously
commonly used assumption of strict harmonicity of the stellar cycles
affects the results. We introduce three methods of different complexity,
starting with the simple harmonic model and followed by Gaussian Process
models with periodic and quasi-periodic covariance functions. We confirm
the existence of two populations in the activity-period diagram. We find
only one significant trend in the inactive population, namely that the
cycle periods get shorter with increasing rotation. This is in contrast
with earlier studies, that postulate the existence of trends in both of
the populations. In terms of rotation to cycle period ratio, our data is
consistent with only two activity branches such that the active branch
merges together with the transitional one. The retrieved stellar cycles
are uniformly distributed over the R'HK activity index, indicating that
the operation of stellar large-scale dynamos carries smoothly over the
Vaughan-Preston gap. At around the solar activity index, however,
indications of a disruption in the cyclic dynamo action are seen. Our
study shows that stellar cycle estimates depend significantly on the
model applied. Such model-dependent aspects include the improper
treatment of linear trends and too simple assumptions of the noise
variance model. Assumption of strict harmonicity can result in the
appearance of double cyclicities that seem more likely to be explained
by the quasi-periodicity of the cycles.

KW - Astrophysics - Solar and Stellar Astrophysics

KW - Statistics - Applications

KW - Statistics - Machine Learning

U2 - 10.1051/0004-6361/201732525

DO - 10.1051/0004-6361/201732525

M3 - Article

VL - 619

SP - 1

EP - 20

JO - Astronomy & Astrophysics

JF - Astronomy & Astrophysics

SN - 0004-6361

M1 - A6

ER -