J/AJ/164/213 Power-law for cumulative flare frequency distributions (Gao+, 2022)
Correcting Stellar Flare Frequency Distributions Detected by TESS and Kepler.
Gao D.-Y., Liu H.-G., Yang M., Zhou J.-L.
<Astron. J., 164, 213 (2022)>
=2022AJ....164..213G 2022AJ....164..213G
ADC_Keywords: Stars, flare; Exoplanets; Photometry; Optical; Spectral types;
Effective temperatures
Keywords: Stellar flares ; Stellar activity ; Habitable zone ; Planet
hosting stars
Abstract:
The habitability of planets is closely connected with stellar
activity, mainly the frequency of flares and the distribution of flare
energy. Kepler and TESS find many flaring stars via precise
time-domain photometric data, and the frequency and energy
distribution of stellar flares on different types of stars are studied
statistically. However, the completeness and observational bias of
detected flare events from different missions (e.g., Kepler and TESS)
vary a lot. We use a unified data processing and detection method for
flare events based on the light curves from Kepler and TESS. Then we
perform injection and recovery tests in the original light curve of
each star for each flare event to correct the completeness and energy
of flares. Three samples of flaring stars are selected from Kepler and
TESS, with rotation periods from 1 to ∼5days. Adopting a hot-blackbody
assumption, our results show that the cumulative flare frequency
distributions (FFDs) of the same stars in Kepler and TESS bands tend
to be consistent after correction, revealing a more natural flaring
frequency and energy distribution. Our results also extend the
low-energy limit in cumulative FFD fitting to 1031.5-33erg on
different types of stars. For solar-type stars, the average power-law
index of cumulative FFD (αcum) is -0.84, which indicates that
low-energy flares contribute less to the total flare energy. With a
piecewise correlation between αcum and Teff, αcum first
rises from M2 to K1 stars, then slightly decreases for stars hotter
than K1.
Description:
In this paper, we use the photometry data from Kepler and Transiting
Exoplanet Survey Satellite (TESS) to study stellar flares because of
their high photometric precision and continuity.
Kepler is a Schmidt telescope design with a 0.95 maperture and a
spectral bandpass from 400 to 900nm.
TESSs four 10cm optical cameras simultaneously observe an entire field
of 24x96deg, with a red-optical bandpass covering the wavelength range
from about 600 to 1000nm. Note the TESS band is redder than the Kepler
band.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 179 121 *Stellar parameters of three selected samples
table2.dat 184 13 *The power-law parameters for fitting cumulative FFDs
table3.dat 202 83 *The power-law parameters for fitting cumulative FFDs
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Note on table1.dat: For stars in Sample-1 and Sample-2, the stellar
parameters are read through astroquery.mast.Catalogs
(http://astroquery.readthedocs.io) from TESS input catalog (TIC v8)
(Paegert+, 2022, IV/39); For Kelper flaring stars in Sample-3, their
stellar parameters are from Berger+, 2020, J/AJ/159/280; We cross
match each star with GAIA DR3 and show the stellar parameters from the
GAIA catalog.
Note on table2.dat: Before and after correction for flaring stars in Sample-1
"RangeAll" means the fitting within the whole energy range;
"Range65" means the fitting within energy range of P_det ≥ 65%;
"Range15" means the fitting within energy range of P_det ≥ 15%;
All energies are in ergs.
Note on table3.dat: Before and after correction for solar-type stars
in Sample-2 and for different type stars (Sample-3).
For the meaning of "Range65" and "Range15", see the notes in
Table 2.
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See also:
IV/39 : TESS Input Catalog version 8.2 (TIC v8.2) (Paegert+, 2021)
J/ApJS/173/673 : M dwarf UV flares in GALEX (Welsh+, 2007)
J/AJ/141/50 : White-light flares cool stars from Kepler (Walkowicz+, 2011)
J/ApJ/743/48 : Stars with Prot & X-ray luminosities (Wright+, 2011)
J/A+A/543/A54 : 61 main-sequence & subgiant oscillations (Appourchaux+, 2012)
J/MNRAS/432/1203 : Rotation periods of M-dwarf stars (McQuillan+, 2013)
J/ApJS/208/9 : Intrinsic colors and temperatures of PMS stars (Pecaut+, 2013)
J/A+A/560/A4 : Rotation periods of active Kepler stars (Reinhold+, 2013)
J/ApJS/209/5 : Superflares of Kepler stars. I. (Shibayama+, 2013)
J/ApJS/211/24 : Rotation periods of Kepler MS stars (McQuillan+, 2014)
J/ApJ/814/35 : Flare events in M dwarf of M37 (Chang+, 2015)
J/AJ/150/133 : Stellar noise 4529 Kepler solar-type dwarfs (Gilliland+, 2015)
J/ApJ/829/23 : Stellar flares from Q0-Q17 Kepler LCs (Davenport, 2016)
J/ApJS/224/37 : White-light flares on close binaries from Kepler (Gao+, 2016)
J/ApJ/822/86 : False positive probabilities Q1-Q17 DR24 KOIs (Morton+, 2016)
J/ApJ/866/99 : Radii of KIC stars & planets using Gaia DR2 (Berger+, 2018)
J/ApJ/858/55 : K2 ultracool dwarfs survey. III. M6-L0 flares (Paudel+, 2018)
J/ApJ/859/87 : Kepler long- and short-cadence flare parameters (Yang+, 2018)
J/ApJS/241/29 : Flare catalog through LC data of Kepler DR25 (Yang+, 2019)
J/AJ/159/280 : Gaia-Kepler stellar properties.I. KIC stars (Berger+, 2020)
J/AJ/159/60 : 8695 flares 1228 stars in TESS sectors 1 & 2 (Gunther+, 2020)
J/ApJ/890/46 : Superflares solar-type stars from TESS first year (Tu+, 2020)
J/A+A/645/A42 : Flares in 5 open clusters (Ilin+, 2021)
J/ApJ/906/72 : 2344 superflares on 266 solar-type stars (Okamoto+, 2021)
J/MNRAS/505/L79 : Characteristic time of stellar flares (Yan+, 2021)
http://astroquery.readthedocs.io : Astroquery coordinated package of astropy
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 8 A8 --- Samples Sample number
10- 18 I9 --- TIC ? TESS Input Catalog ID
20- 27 I8 --- KIC ? Kepler Input Catalog ID
29- 34 F6.2 mag Tmag [7.78/14.56]? TESS magnitude
36- 41 F6.2 mag Kmag [10.9/16.5]? Kepler magnitude
43- 46 I4 K Teff [3286/5955] Effective temperature
48- 53 F6.4 Rsun Rad [0.31/2.53] Stellar Radius
55- 73 I19 --- GAIA GAIA DR3 Catalog ID
75- 82 F8.4 --- RUWE [0.72/28.2]? GAIA DR3 Renormalised Unit
Weight Error
84- 90 F7.3 mag Gmag [8.21/16.4]? GAIA DR3 G-band mean magnitude
92- 95 I4 K Teff-G [3006/5870]? Effective temperature
from GSP-Phot
97-102 F6.3 [cm/s2] logg-G [3.75/4.87]? log surface gravity from GSP-Phot
104-109 F6.3 [-] [Fe/H]-G [-1.33/0.22]? Iron abundance from GSP-Phot
111-117 F7.4 Rsun Rad-G [0.38/2.11]? Radius from GSP-Phot
119 A1 --- SpType ? Spectral type
121-125 F5.2 d Prot [1.01/29.9] Rotation period (1)
127-129 I3 --- Nf-prev [1/491] Number of flares in previous work
131-133 I3 --- Nf-TESS [1/106]? Number of flares detected from TESS
data in this work (2)
135-144 A10 --- Sector ? TESS data used in this work
146-149 I4 --- Nf-Kepler [69/1602]? Number of flares detected from
Kepler data in this work (3)
151-170 A20 --- Quarter ? Kepler data used in this work
172-179 F8.5 arcsec Sep [3.28/6.3]? Distance of nearby star to this
star
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Note (1): Stellar rotation periods are taken from
Gunther+, 2020, J/AJ/159/60 and Yang & Liu, 2019, J/ApJS/241/29,
partly given by Reinhold+, 2013, J/A+A/560/A4 and
McQuillan+, 2014, J/ApJS/211/24M.
Note (2): Taken from Gunther+, 2020, J/AJ/159/60 and Tu+, 2020, J/ApJ/890/46.
Note (3): Taken from Yang & Liu., 2019, J/ApJS/241/29.
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Byte-by-byte Description of file: table2.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 9 I9 --- TIC TESS Input Catalog ID
11- 18 I8 --- KIC Kepler Input Catalog ID
20- 24 F5.2 mag Tmag [12.1/14.5] TESS apparent magnitude
26- 30 F5.2 d Prot [1.4/29.9] Rotation period
32- 35 I4 K Teff [3371/5247] Effective temperature
37- 40 I4 K Teff-G [3371/5128]? Effective temperature
from GSP-Phot
42- 47 F6.4 --- RUWE [0.95/2.05] GAIA DR3 Renormalised Unit Weight
Error
49- 53 F5.2 [10-7J] T-E-Lo [31.3/34.1] log lower limit of TESS detected
flare energy
55- 59 F5.2 [10-7J] T-E-Up [32.8/36.9] log upper limit of TESS detected
flare energy
61- 66 F6.3 --- T-a-Ori [-2.58/-0.48]? alphacum from original
cumulative FFD RangeAll detected by TESS (1)
68- 73 F6.3 --- e_T-a-Ori [0.03/0.7]? Uncertainty in T-a-Ori
75- 80 F6.2 --- T-b-Ori [15.2/83.4]? betacum from original
cumulative FFD in RangeAll detected by TESS
82- 87 F6.2 --- e_T-b-Ori [1/23]? Uncertainty in T-b-Ori
89- 94 F6.3 --- T-a-Cor [-2.37/-0.5] alphacum from corrected
cumulative FFD RangeAll detected by TESS (1)
96-100 F5.3 --- e_T-a-Cor [0.1/0.8] Uncertainty in T-a-Cor
102-106 F5.2 --- T-b-Cor [17.7/79] betacum from corrected cumulative
FFD in RangeAll detected by TESS
108-112 F5.2 --- e_T-b-Cor [3/26] Uncertainty in T-b-Cor
114-118 F5.2 [10-7J] K-E-Lo [29.8/33.4] log Lower limit of Kepler detected
flare energy in RangeAll
120-124 F5.2 [10-7J] K-E-Up [34.5/35.9] log Upper limit of Kepler detected
flare energy in RangeAll
126-131 F6.3 --- K-a-Ori [-1.83/-0.75] alphacum from original
cumulative FFD in Range65 detected by Kepler
133-137 F5.3 --- e_K-a-Ori [0.02/0.3] Uncertainty in K-a-Ori
139-143 F5.2 --- K-b-Ori [23.2/62] betacum from original cumulative
FFD in Range65 detected by Kepler
145-148 F4.2 --- e_K-b-Ori [0.7/8] Uncertainty in K-b-Ori
150-154 F5.2 [10-7J] K-R65 [32.3/34.7] log Lower limit of Kepler detected
flare energy in Range65
156-161 F6.3 --- K-a-Cor [-1.59/-0.99] alphacum from corrected
cumulative FFD in Range15 detected by Kepler
163-167 F5.3 --- e_K-a-Cor [0.01/0.2] Uncertaintyin K-a-Cor
169-173 F5.2 --- K-b-Cor [31.5/51.9] betacum from corrected
cumulative FFD in Range15 detected by Kepler
175-178 F4.2 --- e_K-b-Cor [0.5/4] Uncertainty in K-b-Cor
180-184 F5.2 [10-7J] K-R15 [31.9/34.3] log Lower limit of Kepler detected
flare energy in Range15
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Note (1): Because of the requirement of sufficient energy bins, we only use
the whole energy range to fit the cumulative FFDs obtained from the
TESS data for Sample-1 stars. The fitting of FFD is failed for
"Range65" and "Range15" due to limited number of energy bins.
faint stars in Sample-1, considering their worse photometric
precision from TESS, we correct the flares with Pdet≥0.001 to
enlarge the flare numbers. (see Section 3.4)
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Byte-by-byte Description of file: table3.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 8 A8 --- Samples Sample number
10- 18 I9 --- TIC ? TESS Input Catalog ID
20- 26 I7 --- KIC ? Kepler Input Catalog ID
28- 33 F6.3 --- a-pre [-1.88/-0.49]? alphacum form previous work
(1)
35- 41 F7.3 --- b-pre [15.9/62.9]? betacum form previous work (1)
43- 48 F6.3 --- R-a-Ori [-1.29/-0.3] alphacum from original
cumulative FFD in RangeAll detected by TESS
or Kepler
50- 54 F5.3 --- e_R-a-Ori [0.01/0.4] Uncertainty in R-a-Ori
56- 60 F5.2 --- R-b-Ori [9.33/42.5] betacum from original
cumulative FFD in RangeAll detected by TESS
or Kepler
62- 66 F5.2 --- e_R-b-Ori [0.3/11] Uncertainty in R-b-Ori
68- 73 F6.3 --- R-a-Cor [-1.89/-0.58] alphacum from corrected
cumulative FFD in RangeAll detected by TESS
or Kepler
75- 79 F5.3 --- e_R-a-Cor [0.01/0.4] Uncertainty in R-a-Cor
81- 85 F5.2 --- R-b-Cor [19.3/63.3] betacum from corrected
cumulative FFD in RangeAll detected by TESS
or Kepler
87- 91 F5.2 --- e_R-b-Cor [0.5/14] Uncertainty in R-b-Cor
93- 98 F6.3 --- R15-a-Ori [-1.29/-0.25]? alphacum from original
cumulative FFD in Range15 detected by TESS
or Kepler
100-105 F6.3 --- e_R15-a-Ori [0.003/0.6]? Uncertainty in R15-a-Ori
107-112 F6.2 --- R15-b-Ori [7.74/42.5]? beta_cum from original cumulative
FFD in Range15 detected by TESS or Kepler
114-119 F6.2 --- e_R15-b-Ori [0.1/20]? Uncertainty in R15-b-Ori
121-126 F6.3 --- R15-a-Cor [-1.59/-0.38]? alphacum from corrected
cumulative FFD in Range15 detected by TESS
or Kepler
128-133 F6.3 --- e_R15-a-Cor [0.01/0.4]? Uncertainty in R15-a-Cor
135-140 F6.2 --- R15-b-Cor [12.5/51.9]? betacum from corrected
cumulative FFD in Range15 detected by TESS
or Kepler
142-147 F6.2 --- e_R15-b-Cor [0.4/13.2]? Uncertainty in R15-b-Cor
149-154 F6.3 --- R65-a-Ori [-1.62/-0.35]? alphacum from original
cumulative FFD in Range65 detected by TESS
or Kepler
156-161 F6.3 --- e_R65-a-Ori [0.002/0.4]? Uncertainty in R65-alp-Ori
163-168 F6.2 --- R65-b-Ori [10.9/54]? betacum from original
cumulative FFD in Range65 detected by TESS
or Kepler
170-175 F6.2 --- e_R65-b-Ori [0.07/11]? Uncertainty in R65-b-Ori
177-182 F6.3 --- R65-a-Cor [-1.59/-0.39]? alphacum from corrected
cumulative FFD in Range65 detected by TESS
or Kepler
184-189 F6.3 --- e_R65-a-Cor [0.01/0.3]? Uncertainty in R65-a-Cor
191-196 F6.2 --- R65-b-Cor [12.2/52]? betacum from corrected
cumulative FFD in Range65 detected by TESS
or Kepler
198-202 F5.2 --- e_R65-b-Cor [0.5/9]? Uncertainty in in R65-b-Cor
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Note (1): From Gunther+, 2020A, J/AJ/159/60.
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History:
From electronic version of the journal
(End) Prepared by [AAS], Coralie Fix [CDS], 30-Nov-2022