I had to modify the original pipeline to extract all the orders (the red orders were particu- larly challenging) and to not average all the spectra of each science target. At the end of running the MagE pipeline script, one is left with a "multispec" FITS file, in which is contained, for every order of each spectrum: Sum of the sky over the extraction aperture, sum of the object over the extraction aperture, expected noise from sum of object and sky plus the read noise, signal-to- noise spectrum (per pixel) and the sum of the lamp spectrum over the extraction aperture. The multi.fits files are not very user friendly, so I generated a series of scripts to store the results of each order of a single target in “molly”1files. Figure 2.8 shows an example of data before and after the reduction process. This is the spectrum of the CV V4041 Sgr. The two visible lines are He I and Hα. The Figure shows a raw image at the top, followed by the 10th order spectrum before and after flux calibration. Flux calibration may be considered as the final step of spectral reduction, but depending on the kind of analysis that will be performed on the spectra, one might want to normalise instead. To flux calibrate the spectrum of the target, we need to observe a spectro pho- tometric standard star during the observation night, using the same instrumental configuration than used for the target. The spectrum of the standard star is reduced and extracted in the same way than the science target spectra and compared to a known flux data (usually in the form of a flux table and available from the observatories web page). The ratio between the standard star and the flux table is calculated by fitting splines to determine flux to count ratio for each pixel. Finally, this conversion is applied to the science spectra to calibrate it by flux.The flux calibration or normalisation of the science spectra were made manually with “molly”.
2.2 Radial Velocity Analysis
The most common analysis of the overall radial velocity measurements of a binary components is performed with a Gaussian fit to the line profiles. Radial velocity measurements of the primary and secondary stars can be used to determine the masses in a CB (see Equations 1.4 and 1.5).
To estimateK1, as the primary star is rarely visible, we rely on the emission lines from the
accretion disc (Kd i sc) since it shares the motion of the primary in orbit. One of the problems with this assumption are the asymmetries among the disc. The standard methods rely on the assump- tion that the asymmetries will be confined to the outer region of the disc and try to obtain radial velocity curves from the wings of the emission lines which are created closer to the primary. One such method that is commonly used for CBs is the double Gaussian fit, developed by Schneider & Young (1980). This method consist of convolving the data with a Gaussian template. Having a spectrumS(Λ), we can find the mean position of the emission line by solving the equation:
Z +∞
−∞
f(Λ)K(Λ−λ)dΛ=0 (2.10)
38 CHAPTER 2. METHODS
To calculate the wavelength at any position of the line, withK usually of the form:
K(x)=exp · −(x−a) 2 2σ2 ¸ −exp · −(x+a) 2 2σ2 ¸ (2.11)
where the Gaussians separation,a, and width,σ, can be adjusted to measure the velocity at the base of the emission line. These radial velocities are then fitted with an equation of the form of equation 2.15 to obtain an estimate of the orbital parameters of the system.
2.2.1 Diagnostic Diagram
The width and separations of the Gaussians used in the method described above can be adjusted to measure the velocity at any position in the line profile. The measured radial velocities then, will depend on the choice ofaandσ. As the asymmetries of the disc may persist out to the emis- sion line wings, a way to investigate the extent of these was developed by Shafter et al. (1986). The idea behind this technique is to map the line profile in radial velocity space, by using differ- ent Gaussian separations to measure the lines. These results are then plotted in what is called a diagnostic diagram, Figure 2.9. The diagnostic diagram shows the variation ofK1, its associ-
ated error,σK/K, the systemic velocityγand the phase zeroΦ0as functions of the Gaussian
separation a. The expectation is that the solution forK1 should asymptotically approach the
correct value whenais large enough and then diverge when the Gaussians hit the continuum noise instead of the spectral profile. Similarly, whenareaches the extreme wings and the signal is lost, the error should rise sharply. In practise, diagnostic diagrams do not always behave this way since in many systems asymmetries occur throughout the whole disc. In the case of Figure 2.9, we had more than one line available to perform this technique, allowing us to compare the results for three different lines. In this case, the diagnostic diagrams reach convergence between a=2000 and 2500 km/s. So, even though the value ofK1 is consistent among these three lines,
the value ofγshows a dispersion of over 100 km/s from one line to the other. Discrepancies on the value ofγbetween the emission lines is commonly observed among CVs and it is often as- sociated with blending with neighbouring lines (as is potentially the case of CaII, blended with Paschen in our example), wing asymmetries or even deviations from the flatness of the contin- uum. So, even when the simultaneous study of more than one emission line with diagnostic diagrams could lead to better constrained values ofK1, the constraints onγare still rather poor.
In the next Section, we will study alternative methods to constrain the system parameters based on Doppler tomography and compare these with the results delivered by the diagnostic diagram.
2.2. RADIAL VELOCITY ANALYSIS 39
Figure 2.9: Diagnostic diagram for CC Scl with their respective radial velocity curve for the Gaus- sian separationain the convergence zone. For emission lines from top to bottom: Hα, Hβand CaII 8662 Å
40 CHAPTER 2. METHODS