57 Cyg: A spectroscopic binary star

This page describe the observation of the spectroscopic binary star 59 Cyg.
 
57 Cyg characteristics:

RA: 20h53.2
DEC: +44°23'
Magnitude: 4.72
Spectral type: B5V+B5V
Period: 2.8548 days
Half amplitude of the radial velocity curve: 111.9 km/s (primary) and 126.0 km/s (secondary)
Instrumentation:

Flat-field camera 19-cm F/D=4
Audine CCD camera (CCD KAF-0401E)
R3000 spectrograph (dispersion of 0.93 A/pixel)
Observatory location: Ramonville Saint Agne (near Toulouse, France)
 
Journal of observations:

               Date                          JD
25/07/1999  20H56UT    2451385.370  (your phase 0 point)
01/08/1999  20H08UT    2451392.337
20/08/1999  21H30UT    2451411.396
21/08/1999  19H51UT    2451412.327
22/08/1999  20H15UT    2451413.343
23/08/1999  20H19UT    2451414.347
24/08/1999  20H24UT    2451415.350
29/08/1999  20H52UT    2451420.369
31/08/1999  20H06UT    2451422.337
01/09/1999  20H07UT    2451423.338
02/09/1999  20H28UT    2451424.352
11/09/1999  19H54UT    2451433.329

 
Animation of the 57 Cyg spectrum. One can see the separation of the H-alpha (6563A) and HeI (6678A) lines according to the configuration of the orbital couple. The small lines visibles particularly on the left side of H-alpha correspond to telluric lines (H2O). The variation of their intensity is caused by the evolution of the content of moisture of the atmosphere.
 


Graphics of the relative radial speed between two stars in km/s (the whole of the observations made between July 1999 and September 1999 were gathered here). The rotation period adopted is 2.8548 days. The maximum amplitude radial velocity measured is about 450 km/s, whereas the value raised in the catalogues is of 2*(111.9*126.0)=475.8 km/s. The agreement is reasonably correct! A simple sinusoidal curve (in red) is fitted.

Tips:

The phase of a periodical phenomena is given by:

Phase = frac ((JD - JD0) / Period)

where frac() define the fractional part, JD is the Julian Day of the observation, JD0 is an arbitrary starting time (called the Epoch), and Period the period of the phenomena. The following C code show how this is done:

t = (jd - jd0) / period;
phase = (t - floor(t));