J/MNRAS/521/443 Study of TESS LCs RRc stars variation modes (Benko+, 2023)
Time series analysis of bright TESS RRc stars additional modes, phase
variations, and more.
Benko J.M., Plachy E., Netzel H., Bodi A., Molnar L., Pal A.
<Mon. Not. R. Astron. Soc. 521, 443-462 (2023)>
=2023MNRAS.521..443B 2023MNRAS.521..443B (SIMBAD/NED BibCode)
ADC_Keywords: Stars, variable ; Asteroseismology ; Photometry ; Optical
Keywords: asteroseismology - methods: data analysis - space vehicles -
techniques: photometric - stars: oscillations -
stars: variables: RR Lyrae
Abstract:
Using two years of data from the TESS space telescope, we have
investigated the time series of 633 overtone pulsating field RR Lyrae
(RRc) stars. The majority of stars (82.8 per cent) contain additional
frequencies beyond the main pulsation. In addition to the frequencies
previously explained by the l = 8 and 9 non-radial modes, we have
identified a group of stars where the additional frequencies may
belong to the l = 10 non-radial modes. We found that stars with no
additional frequencies are more common among stars with shorter
periods, while stars with longer periods almost always show additional
frequencies. The incidence rate and this period distribution both
agree well with the predictions of recent theoretical models. The
amplitude and phase of additional frequencies are varying in time. The
frequencies of different non-radial modes appearing in a given star
seem to vary on different time-scales. We have determined a 10.4 per
cent incidence rate for the Blazhko effect. For several stars we have
detected continuous annual-scale phase change without significant
amplitude variation. This type of variation offers a plausible
explanation for the 'phase jump' phenomenon reported in many RRc
stars. The main pulsation frequency could show quasi-periodic phase
and amplitude fluctuations. This fluctuation is clearly related to
additional frequencies present in the star: stars with two non-radial
modes show the strongest fluctuations, while stars with no such modes
show no fluctuations at all. The summation of the phase fluctuation
over time may explain the O-C variations that have long been known for
many non-Blazhko RRc stars.
Description:
The analysis of space photometric data is not limited to providing a
better understanding of the additional modes. Continuous space data
series can also answer some long-standing questions such as what
causes the strong and often irregular period (O-C) variations
observed in many RRc stars, which cannot be explained by stellar
evolutionOr, how the so-called 'phase jump' phenomenon happens: the
light curves of some RRc obtained in different observing seasons could
not be folded by a common period. However, if we assume that there was
a phase jump between the observing seasons, the light curves can be
folded nicely. Is this a real, sudden jump or the result of a
continuous phase change during the non-observed time interval ? The
work of Moskalik et al. (2015MNRAS.447.2348M 2015MNRAS.447.2348M) on Kepler RRc stars
suggests the second scenario, but their sample of four stars is too
small for a final answer. Only continuous observation on a larger
sample can decide the question. The observations of the near all-sky
TESS mission gives us a good opportunity to investigate RRc stars
through a large and homogeneous sample of space photometry.
Our primary goal was to detect and analyse the frequency content of
RRc stars on a large and homogeneous space photometric sample. Our
selection is based on the catalogue of Clementini et al.
(2019A&A...622A..60C 2019A&A...622A..60C, Cat. J/A+A/622/A60), which lists more than 40380
RRc stars across the sky as observed by Gaia. Since the additional
modes are usually associated with low amplitude frequencies, we
restrict ourselves to using the best quality data. The brightness of
the brightest observed RRc star is well bellow the saturation limit of
TESS photometry. These brightness limits seemed to be a good
compromise: the resulting sample is large enough (747 stars), as the
noise starts to increase rapidly above 14 mag. More, the correction
of scattered light from the Earth and the Moon make us excluded stars
with strong systematics. The final 670 stars of our sample are listed
in table1.dat. We used the differential-image pipeline developed by
Pal (2012MNRAS.421.1825P 2012MNRAS.421.1825P) to produce the FFI light curves, in which
the key element is an image convolution step that is able to correct
for many of the instrumental effects.
Next as explained in section 3, we ran SigSpec twice on each data set.
First, we determined the dominant pulsation frequency f1 by fitting of
its significant harmonics Fourier quantities are presented in
table2.dat. Secondly, the table3.dat shows 11000 results of the
Fourier analysis from the residual light curves after we subtracted a
non-linear fit containing the main frequency and its harmonics.
Further in our study, in section 5.2.1, we focus on the frequencies in
phase variation functions with help of SigSpec program package.
Results are given in table6.dat. The 670 light curves used for this
analysis are provided in lcs folder and are taken from
(https://www.konkoly.hu/KIK/), images are available in
(https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html).
File Summary:
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FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table1.dat 83 670 Basic parameters of the RRc stars used TESS
selected sample
table2.dat 94 670 *Fourier coefficients as results of the Fourier
analysis of our study
table3.dat 106 11000 *Additional frequencies in TESS RRc Fourier
spectra
table6.dat 68 203 Frequencies detected in the phase variation
function spectra as results of the analysis in
section 5.2.1
lcs/* . 670 Light curves from TESS observations
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Note on table2.dat: Here the amplitudes and phases are derived from sin-based
Fourier as expressed in equation 1 of the section 3.1 The process and
its results.
Note on table3.dat: As discussed in section 3.1, this table shows the results
of the Fourier analysis from the residual light curves after we subtracted
a non-linear fit containing the main frequency and its harmonics. The
consecutive pre-whitening and frequency search was carried out on each data
set separately.
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See also:
J/MNRAS/491/4752 : Modelled parameters of Cepheid and RR Lyrae
(Bellinger+, 2020)
J/MNRAS/487/5584 : First-overtone RR Lyrae stars from OGLE (Netzel+, 2019)
J/MNRAS/480/1229 : Blazhko effect in the first overtone RR Lyrae (Netzel+,2018)
J/MNRAS/478/1425 : Single-mode OGLE Cepheids additional modes (Suveges+, 2018)
J/MNRAS/453/2022 : Double-mode radial-non-radial RR Lyrae stars (Netzel+, 2015)
J/MNRAS/452/4283 : 33 RR Lyrae observed in Pisces with K2-E2 (Molnar+, 2015)
J/MNRAS/419/2173 : Long-term photometry of M3 RR Lyrae (Jursik+, 2012)
J/A+A/622/A60 : Gaia DR2 misclassified RR Lyrae list (Clementini+, 2019)
J/A+A/476/307 : Period variations in galactic RRab stars (Le Borgne+, 2007)
J/ApJS/258/8 : LCs of RR Lyrae stars from TESS (Molnar+, 2022)
J/ApJS/253/11 : TESS observations of Cepheid stars (Plachy+, 2021)
J/ApJS/244/32 : Extended Aperture Photometry of K2 RR Lyrae stars
(Plachy+, 2019)
J/ApJS/213/31 : Blazhko effect from 4yr of Kepler data (Benko+, 2014)
J/AcA/69/321 : OGLE RR Lyrae stars in Galactic bulge and disk
(Soszynski+, 2019)
J/AcA/66/131 : VI light curves of SMC and LMC RR Lyrae (Soszynski+, 2016)
J/AcA/64/177 : VI light curves of Galactic Bulge RR Lyrae (Soszynski+,2014)
J/AcA/60/17 : VI light curves of SMC classical Cepheids (Soszynski+, 2010)
J/AcA/58/163 : VI light curves of LMC classical Cepheids (Soszynski+, 2008)
IV/38 : TESS Input Catalog - v8.0 (TIC-8) (Stassun+, 2019)
I/345 : Gaia DR2 (Gaia Collaboration, 2018)
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 30 A30 --- Star Star name identifier (Star)
32- 46 F15.11 deg RAdeg Right ascension (J2000) (RA)
48- 61 F14.10 deg DEdeg Declination (J2000) (DEC)
63- 72 F10.7 mag RPmag Integrated RP mean magnitude (Vega) from GaiaDR2
(Gaia Collaboration 2018A&A...616A...1G 2018A&A...616A...1G,
Cat. II/345) (GRP)
74- 83 I10 --- TIC TESS Input Catalog identifier from TESS of
(Stassun et al. 2019AJ....158..138S 2019AJ....158..138S, Cat. IV/38)
(TIC_ID)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 30 A30 --- Star Star name identifier (Star)
32- 33 I2 --- Sector TESS sector (Sect.)
35- 41 F7.5 1/d f1 The dominant pulsation frequency (f1)
43- 48 F6.4 mag A1 The first Fourier amplitude coefficient (A1)
50- 54 F5.3 --- R21 Fourier parameter as A2/A1
56- 60 F5.3 --- R31 Fourier parameter as A3/A1
62- 66 F5.3 rad phi21 Fourier phase parameter φ21 defined with
φij = jφi - iφj as
phi21 = phi2-2phi1 (φ21)
68- 73 F6.3 rad phi31 ? Fourier phase parameter φ31 defined
with φij = jφi - iφj as
phi31 = phi3-3phi1 (φ31)
75- 94 A20 --- Note Note for detection in multiple sectors (Remarks)
(1)
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Note (1): If a star was detected in more than one sector, the frequencies,
amplitudes, and Fourier parameters are calculated from the merged
data sets. The meaning of these notations is explained in
Sections 4.1 The Blazhko effect and 4.2 Additional frequencies.
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table3.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 30 A30 --- Star Star name identifier (Star)
32- 33 I2 --- Sector TESS sector (Sect.)
35- 41 F7.5 1/d f1 ? The dominant pulsation frequency (f1)
43- 48 F6.4 mag A1 ? The first Fourier amplitude coefficient (A1)
50- 57 F8.5 1/d fx The associated frequency with the extra peaks
detected in the pre-whitening steps, with
decreasing amplitudes (fx)
59- 64 F6.4 mag Ax The associated amplitude coefficient with the
extra peaks detected in the pre-whitening
steps, with decreasing amplitudes (Ax)
66- 72 F7.4 rad phix The associated Fourier phase with the extra
peaks detected in the pre-whitening steps, with
decreasing amplitudes (phix)
74- 78 F5.3 --- f1/fx The associated period ratio Fourier parameter
(f1/fx)
80- 84 F5.3 --- Rx1 The associated amplitude ratio Fourier
parameter as Ax/A1 (Ax/A1)
86- 106 A21 --- Note Notes on possible identifications of the
frequency (Ident.)
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Byte-by-byte Description of file: table6.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 29 A29 --- Star Star name identifier (Star)
31- 37 F7.5 1/d Freq Frequencies detected in the phase variation
function spectra (Freq)
39- 43 F5.2 --- Sf The spectral significance defined in Reegen
(2007A&A...467.1353R 2007A&A...467.1353R) (Sf)
45- 51 F7.5 1/d e_Freq Error of the frequency (Err) (1)
53- 61 A9 --- Ident Possible identifications of frequencies where i
when we considered the frequency to be
instrumental and * when frequency is significant
in spectrum of the amplitude change curve (Ident)
63- 68 F6.4 --- pI ? The probability 1-p that a given frequency is
instrumental in origin with p as probability of
this situation defined in eq. 2 of sect. 5.1.2
Frequencies in phase variation functions (pI)
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Note (1): The accuracy of the frequencies obtained from a discrete Fourier
analysis is not a simple task to compute. In a semi-empirical study,
Kallinger et al. (2008A&A...481..571K 2008A&A...481..571K) demonstrated that the value
σK = 1/(T*SQRT(Sf)) is a reliable upper estimate for the
frequency determination error so we used this estimate. Here T is the
total time span of the observation.
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Byte-by-byte Description of file: lcs/*
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 13 F13.5 d BJD Barycentric Julian Date of TESS measurements (BJD)
15- 23 F9.6 mag Tmag TESS optical magnitude (mag)
25- 35 F11.9 mag e_Tmag Uncertainty of Tmag (mag_err)
37- 45 F9.3 e-/s Flux TESS flux (flux)
47- 57 F11.6 e-/s e_Flux Uncertainty of Flux (flux_err)
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History:
From electronic version of the journal
License: CC-BY-4.0
(End) Luc Trabelsi [CDS] 22-May-2026