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J/A+AS/108/25 Cepheids fundamental parameters II. (Bersier+, 1994)
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Fundamental parameters of Cepheids: II. Radial velocity data
Bersier D., Burki G., Mayor M., Duquennoy A.
<Astron. Astrophys. Suppl. Ser. 108, 25 (1994)>
=1994A&AS..108...25B (SIMBAD/NED Reference)
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ADC_Keywords: Stars, variable; Radial velocities
Keywords: stars: Cepheids - stars: oscillations - stars: DL Cas, W Sgr
Abstract:
Radial velocity data for 40 Cepheid stars obtained with the CORAVEL
spectrometer are presented. They represent 1203 individual observations.
The mean number of measurements per star is 41, ranging from 10 to 133.
For each star, a Fourier analysis has been made and we searched the period
that gave the best fit for the velocity curve. When the data covered a
sufficiently long time interval, it has been looked for period changes or
phase jumps. The results have been compared to those found in the
literature; the choice of the best periods is discussed, taking into
consideration the uncertainty on the period, the smoothness of the fit and
several other parameters. New orbital elements, based on CORAVEL
measurements only, are given for DL Cas and W Sgr.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table2 58 1641 Radial velocities for 40 Cepheids
table3 597 47 Fourier coefficients of the radial velocity
curves
table3.tex 122 249 LaTeX version of table3
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Byte-by-byte Description of file: table2
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Bytes Format Units Label Explanations
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1- 10 A10 --- Name Star name
12- 30 A19 --- HD HD number or BD number or coordinates 1900
32- 43 F12.4 d JD Date of measurement in Julian day
46- 51 F6.2 km/s RV Radial velocity
54- 57 F4.2 km/s e_RV Rms uncertainty on the radial velocity
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Byte-by-byte Description of file: table3
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Bytes Format Units Label Explanations
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2- 12 A11 --- Name Name
14- 22 F9.7 d-1 Freq. Frequency
27- 32 F6.2 km/s A0 Amplitude A0
33 A1 --- n_A0 A ) indicates that for the binaries and
suspected binaries, the center-of-mass
velocity has been set to zero
41- 44 F4.2 km/s eps(fit) standard deviation around the fit
46- 56 F11.3 d T0 epoch (HJD)
58- 63 F6.3 km/s A1 amplitude of the harmonic Freq.
73- 78 F6.4 --- L1 []? Lanczos coefficient
82- 87 F6.3 rad phi1 phase of Freq.
89- 93 F5.3 km/s A2 []? amplitude of the harmonic 2*Freq.
103-108 F6.4 --- L2 []? Lanczos coefficient
112-117 F6.3 rad phi2 []? phase of the harmonic 2*Freq.
119-123 F5.3 km/s A3 []? amplitude of the harmonic 3*Freq.
133-138 F6.4 --- L3 []? Lanczos coefficient
142-147 F6.3 rad phi3 []? phase of the harmonic 3*Freq.
149-153 F5.3 km/s A4 []? amplitude of the harmonic 4*Freq.
163-168 F6.4 --- L4 []? Lanczos coefficient
172-177 F6.3 rad phi4 []? phase of the harmonic 4*Freq.
179-183 F5.3 km/s A5 []? amplitude of the harmonic 5*Freq.
193-198 F6.4 --- L5 []? Lanczos coefficient
202-207 F6.3 rad phi5 []? phase of the harmonic 5*Freq.
209-213 F5.3 km/s A6 []? amplitude of the harmonic 6*Freq.
223-228 F6.4 --- L6 []? Lanczos coefficient
232-237 F6.3 rad phi6 []? phase of the harmonic 6*Freq.
239-243 F5.3 km/s A7 []? amplitude of the harmonic 7*Freq.
253-258 F6.4 --- L7 []? Lanczos coefficient
262-267 F6.3 rad phi7 []? phase of the harmonic 7*Freq.
269-273 F5.3 km/s A8 []? amplitude of the harmonic 8*Freq.
283-288 F6.4 --- L8 []? Lanczos coefficient
292-297 F6.3 rad phi8 []? phase of the harmonic 8*Freq.
299-303 F5.3 km/s A9 []? amplitude of the harmonic 9*Freq.
313-318 F6.4 --- L9 []? Lanczos coefficient
322-327 F6.3 rad phi9 []? phase of the harmonic 9*Freq.
329-333 F5.3 km/s A10 []? amplitude of the harmonic 10*Freq.
343-348 F6.4 --- L10 []? Lanczos coefficient
352-357 F6.3 rad phi10 []? phase of the harmonic 10*Freq.
359-363 F5.3 km/s A11 []? amplitude of the harmonic 11*Freq.
373-378 F6.4 --- L11 []? Lanczos coefficient
382-387 F6.3 rad phi11 []? phase of the harmonic 11*Freq.
389-393 F5.3 km/s A12 []? amplitude of the harmonic 12*Freq.
403-408 F6.4 --- L12 []? Lanczos coefficient
412-417 F6.3 rad phi12 []? phase of the harmonic 12*Freq.
419-423 F5.3 km/s A13 []? amplitude of the harmonic 13*Freq.
433-438 F6.4 --- L13 []? Lanczos coefficient
442-447 F6.3 rad phi13 []? phase of the harmonic 13*Freq.
449-453 F5.3 km/s A14 []? amplitude of the harmonic 14*Freq.
463-468 F6.4 --- L14 []? Lanczos coefficient
472-477 F6.3 rad phi14 []? phase of the harmonic 14*Freq.
479-483 F5.3 km/s A15 []? amplitude of the harmonic 15*Freq.
493-498 F6.4 --- L15 []? Lanczos coefficient
502-507 F6.3 rad phi15 []? phase of the harmonic 15*Freq.
509-513 F5.3 km/s A16 []? amplitude of the harmonic 16*Freq.
523-528 F6.4 --- L16 []? Lanczos coefficient
532-537 F6.3 rad phi16 []? phase of the harmonic 16*Freq.
539-543 F5.3 km/s A17 []? amplitude of the harmonic 17*Freq.
553-558 F6.4 --- L17 []? Lanczos coefficient
562-567 F6.3 rad phi17 []? phase of the harmonic 17*Freq.
569-573 F5.3 km/s A18 []? amplitude of the harmonic 18*Freq.
583-588 F6.4 --- L18 []? Lanczos coefficient
592-597 F6.3 rad phi18 []? phase of the harmonic 18*Freq.
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Note on the Lanczos coefficients
A finite Fourier series is a sum, n=1,...,N:
f(x) = A0/2 + sum( An*cos(nx) + Bn*sin(nx) )
Originally, the Lanczos coefficients have been introduced to solve divergence
problems that appear when differentiating a Fourier series. The Lanczos
coefficient of order n is defined as
sin(n*pi/N)
Ln = -----------
(n*pi/N)
where n is smaller or equal to N. From the definition, we see that Ln is
always between 0 and 1. A Fourier series with Lanczos factors will be
f(x) = A0/2 + sum( Ln*[An*cos(nx) + Bn*sin(nx)] )
A useful application is the attenuation of the Gibbs phenomenon. At the
points where the function presents a discontinuity, there is a problem
of convergence of the Fourier series, even with a large number of harmonics.
The use of Lanczos factors avoids too large differences between the function
and its finite Fourier series at the discontinuities.
Another example is the fitting of a Fourier series on the light curve of a
variable star. Taking too many harmonics will produce an "overfitting",
that is, the fitted curve will present unphysical features. The Lanczos
coefficients make the curve smoother and more realistic.
A useful reference where the definition and examples can be found:
Arfken G., 1970, Mathematical methods for physicists, 2nd edition,
Academic Press, New York
Another reference, more specialised:
Lanczos C., 1956, Applied Analysis, Prentice-Hall, Englewood Cliffs
(New Jersey)
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(End) Patricia Bauer [CDS] 26-May-1994