J/A+A/685/A62 Eclipsing binary parameters (IJspeert+, 2024)
Automated eccentricity measurement from raw eclipsing binary light curves
with intrinsic variability.
IJspeert L.W., Tkachenko A., Johnston C., Prsa A., Wells M.A., Aerts C.
<Astron. Astrophys. 685, A62 (2024)>
=2024A&A...685A..62I 2024A&A...685A..62I (SIMBAD/NED BibCode)
ADC_Keywords: Binaries, eclipsing ; Ephemerides ; Binaries, orbits
Keywords: asteroseismology - methods: data analysis - methods: statistical -
ephemerides - binaries: eclipsing
Abstract:
Eclipsing binary systems provide the opportunity to measure
fundamental parameters of their component stars in a stellar-model
independent way. This makes them ideal candidates for testing and
calibrating theories of stellar structure and (tidal) evolution. Large
photometric (space) surveys provide a wealth of data for both the
discovery and the analysis of these systems. Even without
spectroscopic follow up there is often enough information in their
photometric time series to warrant analysis, certainly if there is an
added value present in the form of intrinsic variability like
pulsations.
Our goal is to implement and validate a framework for the homogeneous
analysis of large numbers of eclipsing binary light curves such as the
numerous high duty-cycle observations from space missions like TESS.
The aim of this framework is to be quick and simple to run and to
limit the user's time investment in obtaining, amongst other
parameters, orbital eccentricities.
We develop a new and fully automated methodology for the analysis of
eclipsing binary light curves with or without additional intrinsic
variability. Our method includes a fast iterative prewhitening
procedure resulting in a list of extracted sinusoids that is broadly
applicable for purposes other than eclipses. After eclipses are
identified and measured, orbital and stellar parameters are measured
under the assumption of spherical stars of uniform brightness.
We test our methodology in two settings: a set of synthetic light
curves with known input and the catalogue of Kepler eclipsing
binaries. The synthetic tests show that we can reliably recover the
frequencies and amplitudes of the sinusoids included in the signal as
well as the input binary parameters, albeit to varying degrees of
accuracy. Recovery of the tangential component of eccentricity is most
accurate and precise. Kepler results confirm a robust determination of
orbital periods, with 81.8% of periods matching the catalogued ones.
We present the eccentricities for this analysis and show that they
broadly follow the theoretically expected pattern as a function of the
orbital period.
Our analysis methodology is shown to be capable of analysing large
numbers of eclipsing binary light curves with no user intervention,
and provide in that a basis for the further in-depth analysis of
systems of particular interest as well as for statistical analysis at
the sample level. Furthermore the computational performance of the
frequency analysis, extracting hundreds of sinusoids from Kepler light
curves in a few hours, demonstrates its value as a tool for a field
like asteroseismology.
Description:
The file contains the results for the 2983 binaries in the Kepler EB
Catalog obtained by analysing their 30-minute detrended light curves
with the automated pipeline STAR SHADOW (see
https://github.com/LucIJspeert/star_shadow). Targets are identified by
their KIC numbers, and the columns correspond to the summarised output
of the mentioned pipeline.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
results.dat 2873 2978 Kepler results for the 2827 binaries in the
Kepler EB Catalog
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See also:
V/133 : Kepler Input Catalog (Kepler Mission Team, 2009)
Byte-by-byte Description of file: results.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 14 A14 --- Id Target identifier (KIC) (NNNNNNNN.0N.lc)
(id)
16 I1 --- Stage [1/9] Stage the analysis reached (stage)
18- 37 F20.15 d Ttot Total time base of observations in days
(t_tot)
39- 56 F18.12 d Tmean Time series mean time reference point
(t_mean)
58- 80 F23.18 d Per Orbital period in days (period)
82- 103 E22.16 d s_Per ?=-1 Error in the orbital period (p_err)
105- 108 F4.1 d e_Per [-1/1] Lower HDI error estimate in period
(perrl) (1)
110- 113 F4.1 d E_Per [-1/1] Upper HDI error estimate in period
(perru) (1)
115- 121 F7.1 --- Nparprew Free parameters after prewhitening
(nparamprew)
123- 143 F21.12 --- BICprew BIC after the prewhitening phase (bic_prew)
145- 166 E22.16 --- noislprew Noise level after prewhitening
(noiss_lev e_prew)
168- 189 F22.17 d t1 ?=-1 Time of primary minimum (t_1) (2)
191- 212 F22.17 d t2 ?=-1 Time of secondary minimum (t_2) (2)
214- 237 F24.19 d t1-1 ?=-1 Time of primary first contact
(t11) (2)
239- 260 F22.17 d t1-2 ?=-1 Time of primary last contact
(t12) (2)
262- 283 F22.17 d t2-1 ?=-1 Time of secondary first contact
(t21) (2)
285- 306 F22.17 d t2-2 ?=-1 Time of secondary last contact
(t22) (2)
308- 329 F22.17 d tb1-1 ?=-1 Start (flat) eclipse bottom primary
(tb1_1) (2)
331- 352 F22.17 d tb1-2 ?=-1 End (flat) eclipse bottom primary
(tb1_2) (2)
354- 375 F22.17 d tb2-1 ?=-1 Start (flat) bottom secondary
(tb2_1) (2)
377- 398 F22.17 d tb2-2 ?=-1 End (flat) eclipse bottom secondary
(tb2_2) (2)
400- 422 E23.16 --- depth1 ?=-1 Depth of primary minimum (depth_1)
424- 446 E23.16 --- depth2 ?=-1 Depth of secondary minimum (depth_2)
448- 469 E22.16 d s_t1 ?=-1 Error in t1 (t1err)
471- 492 E22.16 d s_t2 ?=-1 Error in t2 (t2err)
494- 515 E22.16 d s_t1-1 ?=-1 Error in t1-1 (t11_err)
517- 538 E22.16 d s_t1-2 ?=-1 Error in t1-2 (t12_err)
540- 561 E22.16 d s_t2-1 ?=-1 Error in t2-1 (t21_err)
563- 584 E22.16 d s_t2-2 ?=-1 Error in t2-2 (t22_err)
586- 607 E22.16 d s_tb1-1 ?=-1 Error in tb1-1 (tb11err)
609- 630 E22.16 d s_tb1-2 ?=-1 Error in tb1-2 (tb12err)
632- 653 E22.16 d s_tb2-1 ?=-1 Error in tb2-1 (tb21err)
655- 676 E22.16 d s_tb2-2 ?=-1 Error in tb2-2 (tb22err)
678- 699 E22.16 --- s_depth1 ?=-1 Error in depth of primary minimum
(d1err)
701- 722 E22.16 --- s_depth2 ?=-1 Error in depth of secondary minimum
(d2err)
724- 745 E22.16 d ei_t1 ?=-1 Individual error in t1 (t1ind_err)
747- 768 E22.16 d ei_t2 ?=-1 Individual error in t2 (t2ind_err)
770- 791 E22.15 d ei_t1-1 ?=-1 Individual error in t1-1
(t11inderr)
793- 814 E22.15 d ei_t1-2 ?=-1 Individual error in t1-2
(t12inderr)
816- 837 E22.16 d ei_t2-1 ?=-1 Individual error in t2-1
(t21inderr)
839- 860 E22.15 d ei_t2-2 ?=-1 Individual error in t2-2
(t22inderr)
862- 883 E22.16 d ei_tb1-1 ?=-1 Individual error in tb1-1
(tb11ind_err)
885- 906 E22.16 d ei_tb1-2 ?=-1 Individual error in tb1-2
(tb12ind_err)
908- 929 E22.16 d ei_tb2-1 ?=-1 Individual error in tb2-1
(tb21ind_err)
931- 952 E22.16 d ei_tb2-2 ?=-1 Individual error in tb2-2
(tb22ind_err)
954- 975 E22.16 --- ei_depth1 ?=-1 Individual error in depth1
(d1ind_err)
977- 998 E22.16 --- ei_depth2 ?=-1 Individual error in depth2
(d2ind_err)
1000-1022 E23.16 --- ecosw ?=-1 e*cos(w) from timing formulae
(ecosw_form)
1024-1046 E23.15 --- esinw ?=-1 e*sin(w) from timing formulae
(esinw_form)
1048-1069 E22.16 --- cosi ?=-1 Cosine inclination from timing formulae
(cosi_form)
1071-1092 F22.19 --- phi0 ?=-1 phi0 angle from timing formulae
(phi0form)
1094-1116 E23.16 --- logrr ?=-1 log10 r2/r1 from timing formulae
(logrrform)
1118-1140 E23.16 --- logsb ?=-1 log10 sb2/sb1 from timing formulae
(logsbform)
1142-1163 E22.15 --- e ?=-1 Eccentricity from timing formulae
(s_form)
1165-1185 F21.18 --- w ?=-1 omega from timing formulae
(w_form)
1187-1205 F19.16 rad i ?=-1 Inclination from timing formulae
(i_form)
1207-1228 F22.19 --- rsum ?=-1 Sum of radii from timing formulae
(rsumform)
1230-1253 F24.19 --- rrat ?=-1 r2/r1 from timing formulae (rratform)
1255-1278 F24.19 --- sbrat ?=-1 sb2/sb1 from timing formulae
(sbratform)
1280-1301 E22.16 --- s_ecosw ?=-1 Formal uncorrelated error in ecosw
(ecosw_sig)
1303-1324 E22.16 --- s_esinw ?=-1 Formal uncorrelated error in esinw
(esinw_sig)
1326-1346 F21.18 --- s_cosi ?=-1 Error estimate for cosi (cosi_sig)
1348-1369 E22.16 --- s_phi0 ?=-1 Formal uncorrelated error in phi0
(phi0sig)
1371-1392 E22.16 --- s_logrr ?=-1 Scaled error estimate for logrr
(logrrsig)
1394-1415 E22.16 --- s_logsb ?=-1 Scaled error estimate for logsb
(logsbsig)
1417-1438 E22.16 --- s_e ?=-1 Formal uncorrelated error in e (e_sig)
1440-1461 E22.16 --- s_w ?=-1 Formal uncorrelated error in w (w_sig)
1463-1468 F6.3 rad s_i ?=-1 Error estimate for i (i_sig)
1470-1491 E22.16 --- s_rsum ?=-1 Formal uncorrelated error in rsum
(rsumsig)
1493-1514 E22.16 --- s_rrat ?=-1 Scaled error formal estimate for rrat
(rratsig)
1515 A1 --- nsrrat [i] i for infinity
1516-1537 E22.16 --- s_sbrat ?=-1 Scaled error formal estimate for sbrat
(sbratsig)
1538 A1 --- nssbrat [i] i for infinity
1539-1560 E22.16 --- e_ecosw ?=-1 Lower error estimate in ecosw
(ecosw_low)
1562-1583 E22.16 --- E_ecosw ?=-1 Upper error estimate in ecosw
(ecosw_upp)
1585-1610 F26.20 --- e_esinw ?=-1 Lower error estimate in esinw
(esinw_low)
1612-1637 F26.20 --- E_esinw ?=-1 Upper error estimate in esinw
(esinw_upp)
1639-1659 F21.18 --- e_cosi ?=-1 Lower error estimate in cosi
(cosi_low)
1661-1681 F21.18 --- E_cosi ?=-1 Upper error estimate in cosi
(cosi_upp)
1683-1705 F23.20 --- e_phi0 ?=-1 Lower error estimate in phi0
(phi0low)
1707-1729 F23.20 --- E_phi0 ?=-1 Upper error estimate in phi0
(phi0upp)
1731-1752 E22.16 --- e_logrr ?=-1 Lower error estimate in logrr
(logrrlow)
1754-1775 E22.16 --- E_logrr ?=-1 Upper error estimate in logrr
(logrrupp)
1777-1798 E22.16 --- e_logsb ?=-1 Lower error estimate in logsb
(logsblow)
1800-1821 E22.16 --- E_logsb ?=-1 Upper error estimate in logsb
(logsbupp)
1823-1848 F26.20 --- e_e ?=-1 Lower error estimate in e (s_low)
1850-1875 F26.20 --- E_e ?=-1 Upper error estimate in e (s_upp)
1877-1901 F25.19 --- e_w ?=-1 Lower error estimate in w (w_low)
1903-1927 F25.19 --- E_w ?=-1 Upper error estimate in w (w_upp)
1929-1949 F21.18 rad e_i ?=-1 Lower error estimate in i (i_low)
1951-1971 F21.18 rad E_i ?=-1 Upper error estimate in i (i_upp)
1973-1994 E22.16 --- e_rsum ?=-1 Lower error estimate in rsum
(rsumlow)
1996-2017 E22.16 --- E_rsum ?=-1 Upper error estimate in rsum
(rsumupp)
2019-2040 E22.16 --- e_rrat ?=-1 Lower error estimate in rrat
(rratlow)
2041 A1 --- nerrat [i] i for infinity
2042-2063 E22.16 --- E_rrat ?=-1 Upper error estimate in rrat
(rratupp)
2064 A1 --- nErrat [i] i for infinity
2065-2086 E22.16 --- e_sbrat ?=-1 Lower error estimate in sbrat
(sbratlow)
2087 A1 --- nesbrat [i] i for infinity
2088-2109 E22.16 --- E_sbrat ?=-1 Upper error estimate in sb_rat
(sbratupp)
2110 A1 --- nEsbrat [i] i for infinity
2111-2133 E23.16 --- ecoswphys ?=-1 ecos(w) of the physical model
(ecosw_phys)
2135-2157 E23.16 --- esinwphys ?=-1 esin(w) of the physical model
(esinw_phys)
2159-2180 E22.16 --- cosiphys ?=-1 cos(i) of the physical model
(cosi_phys)
2182-2203 E22.16 --- phi0phys ?=-1 phi0 of the physical model
(phi0phys)
2205-2227 E23.16 --- logrrphys ?=-1 log10 r2/r1 of the physical model
(logrrphys)
2229-2251 E23.16 --- logsbphys ?=-1 log10 sb2/sb1 of the physical model
(logsbphys)
2253-2274 E22.16 --- ephys ?=-1 Eccentricity of the physical model
(s_phys)
2276-2297 F22.19 --- wphys ?=-1 omega of the physical model (w_phys)
2299-2317 F19.16 rad iphys ?=-1 Inclination of the physical model
(i_phys)
2319-2340 E22.16 --- rsumphys ?=-1 Sum of radii of the physical model
(rsumphys)
2342-2365 F24.19 --- rratphys ?=-1 r2/r1 of the physical model
(rratphys)
2367-2390 F24.19 --- sbratphys ?=-1 sb2/sb1 of the physical model
(sbratphys)
2392-2395 F4.1 --- s_ecoswphys ?=-1 Lower HDI error in ecosw
(ecoswerrl) (1)
2397-2400 F4.1 --- E_ecoswphys ?=-1 Upper HDI error in ecosw
(ecoswerru) (1)
2402-2405 F4.1 --- s_esinwphys ?=-1 Lower HDI error in esinw
(esinwerrl) (1)
2407-2410 F4.1 --- E_esinwphys ?=-1 Upper HDI error in esinw
(esinwerru) (1)
2412-2415 F4.1 --- s_cosiphys ?=-1 Lower HDI error in cosi
(cosierrl) (1)
2417-2420 F4.1 --- E_cosiphys ?=-1 Upper HDI error in cosi
(cosierru) (1)
2422-2425 F4.1 --- s_phi0phys ?=-1 Lower HDI error in phi0
(phi0err_l) (1)
2427-2430 F4.1 --- E_phi0phys ?=-1 Upper HDI error in phi0
(phi0err_u) (1)
2432-2435 F4.1 --- s_logrrphys ?=-1 Lower HDI error in logrr
(logrrerr_l) (1)
2437-2440 F4.1 --- E_logrrphys ?=-1 Upper HDI error in logrr
(logrrerr_u) (1)
2442-2445 F4.1 --- s_logsbphys ?=-1 Lower HDI error in logsb
(logsberr_l) (1)
2447-2450 F4.1 --- E_logsbphys ?=-1 Upper HDI error in logsb
(logsberr_u) (1)
2452-2455 F4.1 --- s_ephys ?=-1 Lower HDI error in e (eerrl) (1)
2457-2460 F4.1 --- E_ephys ?=-1 Upper HDI error in e (serru) (1)
2462-2465 F4.1 --- s_wphys ?=-1 Lower HDI error in w (werrl) (1)
2467-2470 F4.1 --- E_wphys ?=-1 Upper HDI error in w (werru) (1)
2472-2475 F4.1 rad s_iphys ?=-1 Lower HDI error in i (ierrl) (1)
2477-2480 F4.1 rad E_iphys ?=-1 Upper HDI error in i (ierru) (1)
2482-2485 F4.1 --- s_rsumphys ?=-1 Lower HDI error in rsum
(rsumerr_l) (1)
2487-2490 F4.1 --- E_rsumphys ?=-1 Upper HDI error in rsum
(rsumerr_u) (1)
2492-2495 F4.1 --- s_rratphys ?=-1 Lower HDI error in rrat
(rraterr_l) (1)
2497-2500 F4.1 --- E_rratphys ?=-1 Upper HDI error in rrat
(rraterr_u) (1)
2502-2505 F4.1 --- s_sbratphys ?=-1 Lower HDI error in sbrat
(sbraterr_l) (1)
2507-2510 F4.1 --- E_sbratphys ?=-1 Upper HDI error in sbrat
(sbraterr_u) (1)
2512-2518 F7.1 --- Nparphys ?=-1 Number of parameters after physical
model optimisation (nparamphys)
2520-2540 F21.12 --- BICphys ?=-1 BIC after physical model optimisation
(bic_phys)
2542-2563 E22.16 --- noislphys ?=-1 Noise level after physical model
optimisation (noiss_lev e_phys)
2565-2570 F6.1 --- TotFreqs ?=-1 Total number of frequencies
(total_freqs)
2572-2577 F6.1 --- PasSigma ?=-1 Number of frequencies that passed the
sigma test (passed_sigma)
2579-2584 F6.1 --- PasSNR ?=-1 Number of frequencies that passed the
S/R test (passed_snr)
2586-2591 F6.1 --- PasBoth ?=-1 Number of frequencies that passed both
tests (passed_both)
2593-2598 F6.1 --- PasHarm ?=-1 Number of harmonics that passed both
tests (passed_harmonics)
2600-2621 E22.16 --- std1 ?=-1 Standard deviation of the residuals of
the linear+sinusoid+eclipse model (std_1)
2623-2644 E22.16 --- std2 ?=-1 Standard deviation of the residuals of
the linear+eclipse model (std_2)
2646-2667 E22.15 --- std3 ?=-1 Standard deviation of the residuals of
the linear+harmonic 1 and 2+eclipse model
(std_3)
2669-2690 E22.16 --- std4 ?=-1 Standard deviation of the residuals of
the linear+non-harmonic sinusoid+eclipse
model (std_4)
2692-2712 F21.16 --- ratio1-1 ?=-1 Ratio of the first depth to std1
(ratio11)
2714-2735 F22.17 --- ratio1-2 ?=-1 Ratio of the second depth to std1
(ratio12)
2737-2758 F22.18 --- ratio2-1 ?=-1 Ratio of the first depth to std2
(ratio21)
2760-2781 F22.18 --- ratio2-2 ?=-1 Ratio of the second depth to std2
(ratio22)
2783-2804 F22.18 --- ratio3-1 ?=-1 Ratio of the first depth to std3
(ratio31)
2806-2827 F22.18 --- ratio3-2 ?=-1 Ratio of the second depth to std3
(ratio32)
2829-2850 F22.18 --- ratio4-1 ?=-1 Ratio of the first depth to std4
(ratio41)
2852-2873 F22.18 --- ratio4-2 ?=-1 Ratio of the second depth to std4
(ratio42)
--------------------------------------------------------------------------------
Note (1): HDI errors are negative one because the corresponding MCMC sampling
optimisation was not performed, and this is standardised output of
the STAR_SHADOW code.
Note (2): Times are measured with respect to the time series mean.
--------------------------------------------------------------------------------
Acknowledgements:
Luc IJspeert, luc.ijspeert(at)kuleuven.be
(End) Luc IJspeert [KU Leuven], Patricia Vannier [CDS] 08-Jan-2024