Techniques d'observation spectroscopique d'astéroïdes

114 M. Popescu, M. Birlan , R. M. Gherase , A. B. Sonka , M. Naiman , C. P. Cristescu
their spectra of the emission lines (example: hydrogen Balmer lines - Hα, Hβ, Hγ)
reveals that a large Doppler redshift exists for this type of objects. This redshift is
defined as the ratio of the change in wavelength (Δλ = λ obs – λ 0 ) to the non-shifted
wavelength from a stationary source:
Δλ
c + v
z = = −1
(3)
λ0
c − v
where c is the speed of light and v is the recession speed of the object.
tel-00785991, version 1 - 7 Feb 2013
Fig 6. Correlation coefficient between quasar spectrum and the template spectrum shifted with
different z.
The analysis of the obtained spectrum of the quasar PG1634+706 consists
in redshift determination and application of Hubble law to determine the distance.
The most common technique [14] to determine the redshift is the crosscorrelation
of the observed spectrum with a template spectrum. The redshift is
determined by the location of the largest peak in the cross-correlation functions.
Several rest frame composite quasar spectra exists for the optical region like the
one from article [15] obtained using data from Large Bright Quasar Survey
(LBQS) and form article [16] based on Sloan Digital Sky Survey (SDSS). Thus
for determining the redshift of our spectrum the following steps were taken: 1.)
shift the template spectrum with a z varying from 0.4 to 1.8 using the step of
0.001. This is a reasonable assumption made after visual inspection of our data;
2.) at each step, the correlation coefficient between the quasar spectrum and the
shifted template spectrum is computed (Fig. 6); 3.) choose the redshift
corresponding to the best correlation coefficient found.
In this way, we obtained z = 1.340 corresponding to the peak value of the
correlation coefficient equal with 0.5416. Our determination is at ~ 3σ (where σ =
0.1987 is the standard deviation of the correlation coefficient values plotted in
Fig. 6).
Considering the value found for the redshift - z = 1.340, the emission lines of
known chemical elements could be identified in the spectrum of PG1634+706