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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      (SIMBAD/NED Reference)
ADC_Keywords: Stars, variable; Radial velocities

Keywords: stars: Cepheids - stars: oscillations - stars: DL Cas, W Sgr


File Summary:

       FileName      Lrecl  Records   Explanations

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


Byte-by-byte Description of file: table2

   Bytes Format  Units   Label    Explanations

   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


Byte-by-byte Description of file: table3

   Bytes Format  Units   Label    Explanations

   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.
--------------------------------------------------------------------------------
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)

(End)                                        Patricia Bauer [CDS]   26-May-1994