Techniques d'observation spectroscopique d'astéroïdes

CHAPTER 2. WHY SPECTROSCOPY? 49
0.6
Flux [arbitrary units]
(a)
1
0.8
0.6
0.4
0.2
0
400 450 500 550 600 650 700
Wavelength [nm]
Correlation coefficient
(b)
0.4
0.2
0
−0.2
−0.4
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
z
Figure 2.4: a) PG1634 + 706 spectrum obtained after data reduction and continuum subtraction; b) the correlation
coefficient between quasar spectrum and the template spectrum shifted with different z [Popescu et al., 2012a].
tel-00785991, version 1 - 7 Feb 2013
varying background to zero and essentially has the same effect as filtering out the long-period
Fourier components of the spectra. Without continuum subtraction, the intensities of spectral
lines are not clearly detectable. The continuum was removed by dividing the spectrum with
a fifth order polynomial curve fitting. The obtained result after data reduction and continuum
subtraction is given in Fig. 2.4.
The redshift is defined as the ratio of the change in wavelength (∆λ = λ obs − λ 0 ) to the
non-shifted wavelength (λ 0 ) from a stationary source:
z= λ √
obs− λ 0 c+v
=
λ 0 c−v − 1 (2.8)
where c is the speed of light in free space and v is the recession speed of the object. The analysis
of the obtained spectrum of PG1634+706 consists in redshift determination and application of
Hubble law to determine its distance.
The most common technique [Tonry & Davis, 1979] 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 the article of [Francis et al.,
1991] obtained using data from Large Bright Quasar Survey (LBQS). Thus for determining the
redshift of our spectrum the following steps were taken:
• 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.
• At each step, the correlation coefficient between the quasar spectrum and the shifted template
spectrum is computed (Fig. 2.4).
• Choose the redshift corresponding to the best correlation coefficient found.
In this way, it was obtained z = 1.340 corresponding to the peak value of the correlation