J/A+A/689/A224 Precise Fourier parameters of Cepheids RV curves (Hocde+, 2024)
Precise Fourier parameters of radial velocity curves.
Towards refining the Hertzsprung progression models.
Hocde V., Moskalik P., Gorynya N.A., Smolec R., Singh Rathour R.,
Ziolkowska O.
<Astron. Astrophys. 689, A224 (2024)>
=2024A&A...689A.224H 2024A&A...689A.224H (SIMBAD/NED BibCode)
ADC_Keywords: Stars, variable ; Radial velocities ; Optical
Keywords: techniques: radial velocities - stars: oscillations -
stars: variables: Cepheids
Abstract:
Radial velocity (RV) curves of Classical Cepheids allow precise
determination of the resonant periods, which in turn help to constrain
fundamental parameters of these stars.
The primary goal of this paper is to derive precise Fourier parameters
of the radial velocity (RV) curves for fundamental and
first-overtone Galactic Cepheids. The secondary objectives are then to
analyze progression of the Fourier parameters up to the 7th harmonic
as well as to propose identification of the pulsation modes of the
stars.
For each star, we carefully selected RV measurements available in the
literature which yield the highest precision of Fourier parameters
according to the procedure that follows. We performed a Fourier
decomposition of the RV curves using unweighted least-square method. We
corrected for zero-point differences between data sets. We subtracted
RV modulations caused by binary motion and have removed other residual
trends. Uncertainty of Fourier parameters are derived using the
covariance matrix. Finally, we have displayed and analyzed
qualitatively the progressions found for low- and for high-order
Fourier parameters. We applied a standard identification of their
pulsation mode based on their Fourier phase difference φ21.
We more than doubled the number of Cepheids with published Fourier
parameters of their RV curves, determined together with their
uncertainties. Our sample includes 178 fundamental-mode and 33 first
overtone pulsators, as well as 7 additional Cepheids whose pulsation
mode is uncertain or undetermined according to our criteria. For the
fundamental-mode Cepheids, the precision of the obtained low-order
Fourier phases is about 7 times better and of the low-order Fourier
amplitude ratios about 25% better as compared to precision achieved in
previously published Fourier parameter surveys. The precision of the
first-overtone Fourier parameters is improved by about 50%.With highly
accurate RV Fourier phases φ21, we are able to firmly identify
V495 Cyg as a new first-overtone Cepheid. We confirm first-overtone
nature of several other stars, tentatively identified as such with the
shape of their lightcurves. We also show that α UMi should be
definitely classified as a first-overtone pulsator. In 3 objects
(VY Per, AQ Pup and QZ Nor) we found significant γ-velocity
variations that we attribute to spectroscopic binarity after careful
analysis RV measurements of these stars. Finally, the analysis of the
fundamental mode Fourier parameters up to 7th order reveals very tight
progression of Fourier phases for all pulsation periods. They are also
tightly correlated with each other. For P<10-day we find a very well
defined upper limit for the Fourier amplitude A1.
We have provided new precise Fourier parameters of Cepheid velocity
curves, determined from RV measurements available in the literature
together with unpublished data. The pulsation period coverage and the
precision obtained, in particular for Fourier phase φ21, will be
useful for studying the dynamics of Cepheid pulsations with the help
of hydrodynamical models. Further radial velocity measurements from
modern high-resolution spectroscopic instruments will be important to
improve these results.
Description:
We provide the tables of Fourier parameters of radial velocity curves
of fundamental-mode, first-overtone, and unknown pulsation mode
Cepheids, together with their uncertainties. We also provide all the
references from the literature and additional previously unpublish
radial velocity measurements of Krzesinski, Pont, Balona and O'Toole.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tableb1.dat 52 218 RV data sources used for Fourier decomposition
refs.dat 76 83 References
tabled1.dat 452 85 Fourier parameters of fundamental-mode Cepheids
(Quality 1)
tabled2.dat 452 54 Fourier parameters of fundamental-mode Cepheids
(Quality 1a)
tabled3.dat 323 66 Fourier parameters of fundamental-mode Cepheids
(Quality 2)
tabled4.dat 121 33 Fourier parameters of first-overtone Cepheids
tabled5.dat 101 7 Fourier parameters of Cepheids with uncertain
or unknown pulsation mode
tabled6.dat 56 271 Private communication of RV measurements
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Byte-by-byte Description of file: tableb1.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 9 A9 --- Name Cepheid name
11- 20 F10.7 d Per Pulsation period (1)
22- 52 A31 --- r_Per Sources of data, in refs.dat file
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Note (1): The adopted pulsation period is chosen to minimize the standard
deviation of the fit
--------------------------------------------------------------------------------
Byte-by-byte Description of file: refs.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 2 I2 --- Ref Reference number
4- 22 A19 --- BibCode BibCode
24- 44 A21 --- Aut Author's name
46- 76 A31 --- Com Comments
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tabled1.dat tabled2.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 9 A9 --- Name Cepheid name
11- 15 F5.2 d Per Pulsation period
17- 19 I3 --- Ndat Number of data points
21- 24 A4 --- N Order of the Fourier fit (1)
26- 29 F4.2 km/s sigma Dispersion of the fit
31- 35 F5.2 km/s A1 Fourier amplitude of the first harmonic
37- 40 F4.2 km/s e_A1 Error of A1
42- 46 F5.3 --- phi21 Fourier phase phi21=phi2-2.phi1
48- 52 F5.3 --- e_phi21 Error of phi21
54- 58 F5.3 --- R21 Fourier amplitude ratio R21=A2/A1
60- 64 F5.3 --- e_R21 Error of R21
66- 70 F5.3 --- phi31 ? Fourier phase phi31=phi3-3.phi1
72- 76 F5.3 --- e_phi31 ? Error of phi31
78- 82 F5.3 --- R31 ? Fourier amplitude ratio R31=A3/A1
84- 88 F5.3 --- e_R31 ? Error of R31
91- 95 F5.3 --- phi41 ? Fourier phase phi41=phi4-4.phi1
98-102 F5.3 --- e_phi41 ? Error of phi41
105-109 F5.3 --- R41 ? Fourier amplitude ratio R41=A4/A1
112-116 F5.3 --- e_R41 ? Error of R41
119-123 F5.3 --- phi51 ? Fourier phase phi51=phi5-5.phi1
126-130 F5.3 --- e_phi51 ? Error of phi51
133-137 F5.3 --- R51 ? Fourier amplitude ratio R51=A5/A1
140-144 F5.3 --- e_R51 ? Error of R51
147-151 F5.3 --- phi61 ? Fourier phase phi61=phi6-6.phi1
154-158 F5.3 --- e_phi61 ? Error of phi61
161-165 F5.3 --- R61 ? Fourier amplitude ratio R61=A6/A1
168-172 F5.3 --- e_R61 ? Error of R61
175-179 F5.3 --- phi71 ? Fourier phase phi71=phi7-7.phi1
182-186 F5.3 --- e_phi71 ? Error of phi71
189-193 F5.3 --- R71 ? Fourier amplitude ratio R71=A7/A1
196-200 F5.3 --- e_R71 ? Error of R71
203-207 F5.3 --- phi81 ? Fourier phase phi81=phi8-8.phi1
210-214 F5.3 --- e_phi81 ? Error of phi81
217-221 F5.3 --- R81 ? Fourier amplitude ratio R81=A8/A1
224-228 F5.3 --- e_R81 ? Error of R81
231-235 F5.3 --- phi91 ? Fourier phase phi91=phi9-9.phi1
238-242 F5.3 --- e_phi91 ? Error of phi91
245-249 F5.3 --- R91 ? Fourier amplitude ratio R91=A9/A1
252-256 F5.3 --- e_R91 ? Error of R91
259-263 F5.3 --- phi101 ? Fourier phase phi101=phi10-10.phi1
266-270 F5.3 --- e_phi101 ? Error of phi101
273-277 F5.3 --- R101 ? Fourier amplitude ratio R101=A10/A1
280-284 F5.3 --- e_R101 ? Error of R101
287-291 F5.3 --- phi111 ? Fourier phase phi111=phi11-11.phi1
294-298 F5.3 --- e_phi111 ? Error of phi111
301-305 F5.3 --- R111 ? Fourier amplitude ratio R111=A11/A1
308-312 F5.3 --- e_R111 ? Error of R111
315-319 F5.3 --- phi121 ? Fourier phase phi121=phi12-12.phi1
322-326 F5.3 --- e_phi121 ? Error of phi121
329-333 F5.3 --- R121 ? Fourier amplitude ratio R121=A12/A1
336-340 F5.3 --- e_R121 ? Error of R121
343-347 F5.3 --- phi131 ? Fourier phase phi131=phi13-13.phi1
350-354 F5.3 --- e_phi131 ? Error of phi131
357-361 F5.3 --- R131 ? Fourier amplitude ratio R131=A13/A1
364-368 F5.3 --- e_R131 ? Error of R131
371-375 F5.3 --- phi141 ? Fourier phase phi141=phi14-14.phi1
378-382 F5.3 --- e_phi141 ? Error of phi141
385-389 F5.3 --- R141 ? Fourier amplitude ratio R141=A14/A1
392-396 F5.3 --- e_R141 ? Error of R141
399-403 F5.3 --- phi151 ? Fourier phase phi151=phi15-15.phi1
406-410 F5.3 --- e_phi151 ? Error of phi151
413-417 F5.3 --- R151 ? Fourier amplitude ratio R151=A15/A1
420-424 F5.3 --- e_R151 ? Error of R151
427-431 F5.3 --- phi161 ? Fourier phase phi161=phi16-16.phi1
434-438 F5.3 --- e_phi161 ? Error of phi161
441-445 F5.3 --- R161 ? Fourier amplitude ratio R161=A16/A1
448-452 F5.3 --- e_R161 ? Error of R161
--------------------------------------------------------------------------------
Note (1): The order N is additionally supplemented with an orbital motion
correction or a trend t.
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tabled3.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 9 A9 --- Name Cepheid name
11- 15 F5.2 d Per Pulsation period
17- 19 I3 --- Ndat Number of data points
21- 23 A3 --- N Order of the Fourier fit (1)
25- 28 F4.2 km/s sigma Dispersion of the fit
30- 34 F5.2 km/s A1 Fourier amplitude of the first harmonic
36- 39 F4.2 km/s e_A1 Error of A1
41- 45 F5.3 --- phi21 ? Fourier phase phi21=phi2-2.phi1
48- 52 F5.3 --- e_phi21 ? Error of phi21
55- 59 F5.3 --- R21 ? Fourier amplitude ratio R21=A2/A1
62- 66 F5.3 --- e_R21 ? Error of R21
69- 73 F5.3 --- phi31 ? Fourier phase phi31=phi3-3.phi1
76- 80 F5.3 --- e_phi31 ? Error of phi31
83- 87 F5.3 --- R31 ? Fourier amplitude ratio R31=A3/A1
90- 94 F5.3 --- e_R31 ? Error of R31
97-101 F5.3 --- phi41 ? Fourier phase phi41=phi4-4.phi1
104-108 F5.3 --- e_phi41 ? Error of phi41
111-115 F5.3 --- R41 ? Fourier amplitude ratio R41=A4/A1
118-122 F5.3 --- e_R41 ? Error of R41
125-129 F5.3 --- phi51 ? Fourier phase phi51=phi5-5.phi1
132-136 F5.3 --- e_phi51 ? Error of phi51
139-143 F5.3 --- R51 ? Fourier amplitude ratio R51=A5/A1
146-150 F5.3 --- e_R51 ? Error of R51
153-157 F5.3 --- phi61 ? Fourier phase phi61=phi6-6.phi1
160-164 F5.3 --- e_phi61 ? Error of phi61
167-171 F5.3 --- R61 ? Fourier amplitude ratio R61=A6/A1
174-178 F5.3 --- e_R61 ? Error of R61
181-185 F5.3 --- phi71 ? Fourier phase phi71=phi7-7.phi1
188-192 F5.3 --- e_phi71 ? Error of phi71
195-199 F5.3 --- R71 ? Fourier amplitude ratio R71=A7/A1
202-206 F5.3 --- e_R71 ? Error of R71
209-213 F5.3 --- phi81 ? Fourier phase phi81=phi8-8.phi1
216-220 F5.3 --- e_phi81 ? Error of phi81
223-227 F5.3 --- R81 ? Fourier amplitude ratio R81=A8/A1
230-234 F5.3 --- e_R81 ? Error of R81
237-241 F5.3 --- phi91 ? Fourier phase phi91=phi9-9.phi1
244-248 F5.3 --- e_phi91 ? Error of phi91
251-255 F5.3 --- R91 ? Fourier amplitude ratio R91=A9/A1
258-262 F5.3 --- e_R91 ? Error of R91
265-269 F5.3 --- phi101 ? Fourier phase phi101=phi10-10.phi1
272-276 F5.3 --- e_phi101 ? Error of phi101
279-283 F5.3 --- R101 ? Fourier amplitude ratio R101=A10/A1
286-290 F5.3 --- e_R101 ? Error of R101
293-297 F5.3 --- phi111 ? Fourier phase phi111=phi11-11.phi1
300-304 F5.3 --- e_phi111 ? Error of phi111
307-311 F5.3 --- R111 ? Fourier amplitude ratio R111=A11/A1
314-318 F5.3 --- e_R111 ? Error of R111
320-323 A4 --- Flag [2bcde] Quality of the fit (2)
--------------------------------------------------------------------------------
Note (1): The order N is additionally supplemented with an orbital motion
correction or a trend t.
Note (2): Flag as follows:
b = unstable fit
c = poor coverage
d = low number of data points
e = standard deviation larger than 1.5km/s
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tabled4.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 9 A9 --- Name Cepheid name
11- 14 F4.2 d Per Pulsation period
16- 18 I3 --- Ndat Number of data points
20- 22 A3 --- N Order of the Fourier fit (1)
24- 27 F4.2 km/s sigma Dispersion of the fit
29- 33 F5.2 km/s A1 Fourier amplitude of first harmonic
35- 38 F4.2 km/s e_A1 Error of A1
40- 44 F5.3 --- phi21 Fourier phase phi21=phi2-2.phi1
46- 50 F5.3 --- e_phi21 Error of phi21
52- 56 F5.3 --- R21 Fourier amplitude ratio R21=A2/A1
58- 62 F5.3 --- e_R21 Error of R21
64- 69 F6.3 --- phi31 ? Fourier phase phi31=phi3-3.phi1
71- 76 F6.3 --- e_phi31 ? Error of phi31
78- 83 F6.3 --- R31 ? Fourier amplitude ratio R31=A3/A1
85- 90 F6.3 --- e_R31 ? Error of R31
92- 97 F6.3 --- phi41 ? Fourier phase phi41=phi4-4.phi1
99-104 F6.3 --- e_phi41 ? Error of phi41
106-111 F6.3 --- R41 ? Fourier amplitude ratio R41=A4/A1
113-118 F6.3 --- e_R41 ? Error of R41
120-121 A2 --- Flag Quality of the fit (2)
--------------------------------------------------------------------------------
Note (1): The order N is additionally supplemented with an orbital motion
correction or a trend t.
Note (2): Flag as follows:
1 = good fit with no instabilities and with an excellent phase coverage
(Quality 1)
1a = good fit, but with a slight instability (Quality 1a)
2e = good fit, but with standard deviation larger than 1.5km/s (Quality 2)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tabled5.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 9 A9 --- Name Cepheid name
11- 14 F4.2 d Per Pulsation period
16- 18 I3 --- Ndat Number of data points
20- 22 A3 --- N Order of the Fourier fit (1)
24- 27 F4.2 km/s sigma Dispersion of the fit
29- 33 F5.2 km/s A1 Fourier amplitude of the first harmonic
35- 38 F4.2 km/s e_A1 Error of A1
40- 45 F6.3 --- phi21 ? Fourier phase phi21=phi2-2.phi1
47- 52 F6.3 --- e_phi21 ? Error of phi21
54- 59 F6.3 --- R21 ? Fourier amplitude ratio R21=A2/A1
61- 66 F6.3 --- e_R21 ? Error of R21
68- 73 F6.3 --- phi31 ? Fourier phase phi31=phi3-3.phi1
75- 80 F6.3 --- e_phi31 ? Error of phi31
82- 87 F6.3 --- R31 ? Fourier amplitude ratio R31=A3/A1
89- 94 F6.3 --- e_R31 ? Error of R31
96- 97 A2 --- Flag Quality of the fit (2)
99-101 A3 --- Mode Pulsation mode (3)
--------------------------------------------------------------------------------
Note (1): The order N is additionally supplemented with an orbital motion
correction or a trend t.
Note (2): Flag as follows:
1 = good fit with no instabilities and with an excellent phase coverage
(Quality 1)
2e = good fit, but with standard deviation larger than 1.5km/s (Quality 2)
Note (3): Tentative mode identification implied by the ABL-PL relation of
Ripepi et al. (2023A&A...674A..17R 2023A&A...674A..17R, Cat. J/A+A/674/A17)
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Byte-by-byte Description of file: tabled6.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 9 A9 --- Name Cepheid name
11- 20 F10.4 d Date Observations date (JD-2400000)
22- 28 F7.3 km/s RV Observed radial velocity
30- 35 F6.3 km/s e_RV ? Radial velocity uncertainty
37- 45 A9 --- Inst Instrument (1)
47- 56 A10 --- Observer Observer name
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Note (1): Instrument as follows:
CORAVEL = data collected in the same way as in Pont et al.
(1997A&A...318..416P 1997A&A...318..416P, Cat. J/A+A/318/416)
ELODIE = data collected in the same way as in Pont et al.
(1997A&A...318..416P 1997A&A...318..416P, Cat. J/A+A/318/416)
GIRAFFE = data collected with 1.9m telescope in SAAO (South Africa) with
Fibre-Fed Echelle spectrograph (GIRAFFE)
STROMLO = Collected from Mt Stromlo Observatory on the 74 inch telescope
RADCLIFFE = Collected from two-prism spectrograph of the 1.9-m Radcliffe
telescope in Pretoria
--------------------------------------------------------------------------------
History:
From Vincent Hocde, vincent.hocde(at)oca.eu
Acknowledgements:
We extend our gratitude to Louis Balona, Jurek Krzesinski, Simon
O'Toole, and Frederic Pont for providing their RV data and granting
permission for its publication.
(End) Patricia Vannier [CDS] 26-Jul-2024