J/MNRAS/488/3274 Kepler stars' surface differential rotation (de Freitas, 2019)
Multifractal detrended moving average analysis of Kepler stars with surface
differential rotation traces.
de Freitas D.B., Nepomuceno M.M.F., Cordeiro J.G., Das Chagas M.L.,
De Medeiros J.R.
<Mon. Not. R. Astron. Soc., 488, 3274-3297 (2019)>
=2019MNRAS.488.3274D 2019MNRAS.488.3274D (SIMBAD/NED BibCode)
ADC_Keywords: Stars, G-type ; Effective temperatures ; Stars, masses ; Optical
Keywords: methods: data analysis - stars: rotation - stars: solar-type
Abstract:
A multifractal formalism is employed to analyse high-precision
time-series data of Kepler stars with surface differential rotation
(DR) traces. The multifractal detrended moving average (MFDMA)
algorithm has been explored to characterize the multiscale behaviour
of the observed time series from a sample of 662 stars selected with
parameters close to those of the Sun (e.g. effective temperature,
mass, effective gravity and rotation period). Among these stars, 141
have surface DR traces, whereas 521 have no detected DR signatures. In
our sample, we also include the Sun in its active phase. Our results
can be summarized in two points. First, our work suggests that
star-spots for time series with and without DR have distinct dynamics.
Secondly, the magnetic fields of active stars are apparently governed
by two mechanisms with different levels of complexity for
fluctuations. Throughout the course of the study, we identified an
overall trend whereby the DR is distributed in two H regimes
segregated by the degree of asymmetry A, where H-index denotes the
global Hurst exponent that is used as a measure of long-term memory of
time series. As a result, we show that the degree of asymmetry can be
considered a segregation factor that distinguishes the DR behaviour
when related to the effect of the rotational modulation on the time
series. In summary, the multifractality signals in our sample are the
result of magnetic activity control mechanisms leading to
activity-related long-term persistent signatures.
Description:
The Kepler mission performed 17 observational runs for ∼90d each, and
these runs, designated as Quarters, were composed of long-cadence
(data sampling every 29.4min) and short-cadence (sampling every 59s)
observations.
Based on a working sample adopted by Reinhold et al.
(2013A&A...560A...4R 2013A&A...560A...4R, Cat. J/A+A/560/A4) with well-determined rotation
periods, we constructed our light curves using only Quarter 3
long-cadence data. All time series have been normalized to the median
value of Q3. Our final working sample consisted of 662 active stars
with physical properties similar to those of the Sun, defined by
Teff between 5579 and 5979K, logg between 3.94 and 4.94dex
(Pinsonneault et al. 2012ApJS..199...30P 2012ApJS..199...30P, Cat. J/ApJS/199/30) and
(primary) rotation periods between 24 and 34d.
Among the total of 662 stars, 141 were detected to have DR traces,
while the rest were identified as having rigid-body rotation. The
period interval for the above-mentioned selection was based on the
results from Lanza et al. (2003A&A...403.1135L 2003A&A...403.1135L), for which the
rotational periods of the Sun are between 24.5d (equator) and 33.5d
(poles). Values for the rotational periods were estimated using an
autocorrelation function and were taken from Reinhold et al.
(2013A&A...560A...4R 2013A&A...560A...4R, Cat. J/A+A/560/A4), and the temperature and
gravity were obtained from Pinsonneault et al. (2012ApJS..199...30P 2012ApJS..199...30P,
Cat. J/ApJS/199/30); that is, the corrected Sloan Digital Sky Survey
(SDSS) temperature and the Kepler Input Catalogue (KIC) surface
gravity.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 77 142 Results of the geometric analysis of the
multifractal spectrum for the indices A,
Δα, ΔfL(α),
ΔfR(α) and H for the Sun and 141
stars with DR, using the SAP4 flux
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See also:
J/A+A/560/A4 : Rotation periods of active Kepler stars (Reinhold+, 2013)
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 8 A8 --- KIC Star name (Sun and NNNNNNNN from KIC)
10- 14 F5.2 d P1 Primary rotation period
16- 20 F5.2 d P2 Secondary rotation period
22- 25 I4 K Teff Effective temperature
27- 30 F4.2 [cm/s2] logg Surface gravity
32- 35 F4.2 Msun Mass Star mass
37- 41 F5.2 d Prot Rotation period
43- 46 F4.2 --- A Degree of asymmetry (1)
48- 51 F4.2 --- Dalpha Degree of multifractality (2)
53- 56 F4.2 --- DfL Singularity parameter ΔfL (3)
58- 62 F5.3 --- DfR Singularity parameter ΔfR (3)
64- 67 F4.2 --- H Hurst exponent (4)
69- 72 F4.2 --- beta Relative shear (5)
74- 77 F4.2 rad/d DOmega Horizontal absolute shear (6)
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Note (1): A=(αmax-α0)/(α0-αmin), where
α0 is the value of α when f(α) is maximal. The
right endpoint αmax and the left endpoint αmin
represent the maximum and minimum values of the singularity strength
function, α(q). The value of this index A indicates one of three
shapes: right-skewed (A>1), left-skewed (0<A<1) or symmetric (A=1).
Note (2): This index represents the broadness
Δα=αmax-αmin
Note (3): The parameters ΔfL(α) and ΔfR(α)
characterize the broadness, which is defined as the difference
between the maximum (fmax(α)=1) and minimum values of the
singularity spectrum, where the left-side endpoint is denoted by
fminL(α) and the right-side endpoint by fminR(α.
Note (4): According to de Freitas et al. (2013ApJ...773L..18D 2013ApJ...773L..18D), the exponent
H denotes Brownian motion when H=1/2. On the one hand, if H>1/2, then
the fluctuations have a tendency to long-term persistence. On the
other hand, if H<1/2, then the fluctuations tend not to continue in
the same direction but instead turn back on themselves, which results
in a less smooth time series.
Note (5): The relative shear β is defined as β=|P1-P2|/max{P1,P2}
Note (6): The absolute horizontal shear is defined as
ΔΩ=2π|1/P1-1/P2|
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History:
From electronic version of the journal
(End) Ana Fiallos [CDS] 14-Dec-2022