J/A+AS/108/25 Cepheids fundamental parameters II. (Bersier+, 1994)
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 1994A&AS..108...25B (SIMBAD/NED Reference)
ADC_Keywords: Stars, variable; Radial velocities
Keywords: stars: Cepheids - stars: oscillations - stars: DL Cas, W Sgr
File Summary:
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File Name 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-per-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-per-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