Resultados de las Encuestas

If we assume the wavelength shifts are caused solely by freely falling gas near the white dwarf, we first recall that when we observe the stream perpendicularly to its motion, there will be no Doppler shift in the measured wavelengths. From that, we use our measured wavelength at phase 0.4 to assume we are seeing gas in a 13.75 MG field 0.13Rwd above the

white dwarf surface.

We can then use our phase-resolved measurements to calculate the velocity of the infalling gas. Our fit will account for both orbital motion and the free-fall velocity. Since the gas we observe is stationary in position with respect to the white dwarf, we take the orbital motion of the gas to be the same as the white dwarf. Given our calculated masses in section 3.5 and our measurement of Ksec, we make a prediction of Kwd = 72 km s−1.

The σ− transition of H α in a magnetic field of 13.75 MG will have a wavelength of

λB = 6284.7 ˚A(Landstreet, 1980). We calculated the velocity of each measurement relative

to that wavelength. We fitted our measurements to

vmeasured=γ+Kwdsin 2π(φ−0.5) +vf fcos α , (3.6.3) where cos α = cos i cos β + sin i sin β cos φ+ψ (3.6.4)

is the viewing angle between the observer and the magnetic field axis (Imamura & Durisen, 1983).

We fit the systemic velocity γ and the free-fall velocity vf f. The phasing of the free-

fall amplitude is determined by our selection of system inclination and the co-latitude and longitude of the accretion spot. Our best-fitting measurements givevf f = 1869±120km s−1

and γ =−58±29 km s−1_{. Our results are shown in Figure 3.8.}

Figure 3.8: Assuming we are observing material in a 13.75 MG field, we have calculated the velocity of the data in Figure 3.7. The data have been fitted to Equation 3.6.3 to account for the motion of the white dwarf and the radially infalling accreting material. The best-fitting model has a free-fall velocity of 1869±120 km s−1.

Two points of evidence encourage us to believe the wavelength shifts are caused by the motion of freely falling gas. The motion of the absorption profile is most red-shifted around phase 0.72, when, based on the geometry presented in section 3.3, the accretion spot is most directly facing us. The accreting material at this phase would be most red-shifted, which is in line with what we observe.

The theoretical free-fall velocity, vf f = 2GM_wd Rwd 1/2 , (3.6.5)

is about 4800 km s−1. The correction for the material not falling from infinity is negligible (Busschaert et al., 2015). This theoretical free-fall velocity gives the velocity at the surface of the white dwarf, so we can correct this amount by our assumed height of 0.13 Rwd. This

impliesvf f(1.13Rwd) = 4500km s−1, which is still larger than our measured value. Detailed

modelling of the geometry and structure of the accretion shock are needed to confirm this suggestion.

3.7 Conclusions

We have presented new measurements of the eclipsing magnetic cataclysmic variable CTCV1928-50. Time-resolved spectroscopy reveals two emission-line components - a broad component from the accretion stream falling towards the white dwarf and a narrow compo- nent from the heated face of the secondary. We measure the radial velocity amplitude at the center of mass of the secondary to be 393±13km s−1_{. Assuming the secondary follows the}

Knigge et al. (2011) mass-radius relationship for secondary stars in cataclysmic variables, we estimate binary parameters of the system. In particular, we find a white dwarf mass of 0.67±0.08M.

We also detect absorption in our spectra that we associate as arising from cool halo gas close to the accretion spot on the white dwarf. The absorption centroid moves with phase which must come either from changes in the magnetic field strength of the absorbing region or from velocity motion of the infalling gas. Based on phasing of the centroid, possible magnetic field strength measurements, and possible radial velocity measurements we suggest the motion is due primarily to the motion of the infalling gas. From this we estimate a free-fall velocity of 1869±120 km s−1 approximately 0.13 Rwd above the white dwarf photosphere.

The geometry of this system, with a clean and well-defined view of the accretion shock, makes it an intriguing object to search for quasi-periodic oscillations. Quasi-periodic oscilla- tions were first seen in polars in V834 Cen and AN UMa by Middleditch (1982) and have also been found in VV Pup (Larsson, 1989) and IGRJ14536-5522 (Potter et al., 2010). Detection in the optical, X-ray, or polarization and modelling of these oscillations would help provide insight into the stability of the accretion column, cooling processes, and homogeneity of the accretion stream (see Bonnet-Bidaud et al. 2015 and Busschaert et al. 2015).

This chapter concludes our study of white dwarf properties in magnetic cataclysmic variables. In the next chapter, we will turn our attention to single pulsating white dwarfs and describe a survey we have completed to estimate Teff and logg from spectroscopy.

CHAPTER 4: A SPECTROSCOPIC SURVEY OF DAVs

The profession I follow will not allow or suffer me to go in any other manner. The dance, the banquet, and the bed of down, were

invented for soft and effeminate courtiers; but toil, disquietude, and arms, were designed for those whom the world calls knights-errant, of which number I.

— Don Quixote

We have completed a spectroscopic survey of 122 white dwarfs with the goal of deter- mining Teff and logg in a consistent manner and with very low systematic errors to enable seismological studies of DAVs. We will obtain atmospheric parameters for each white dwarf by comparing normalized observed Balmer line profiles to normalized model Balmer line profiles (see section 4.4). This is difficult because the Balmer lines in white dwarfs are wide, defining the normalization region between lines is not straight forward because of the lack of true continuum, and small modulations from flat fielding or flux calibration, for example, can change the final determined atmospheric parameters. We will take care to understand, char- acterize, and measure as many of these systematics as possible so that they can be limited by us and others. One of the benefits of our survey is the homogeneity of the observations, data reductions, and spectral fitting processes. Using the same spectrograph and telescope for all observations reduces some of the systematics that can arise from using different spec- trographs, telescopes, or observers. We have also made significant improvements to the data reduction and fitting process (see section 4.3 and section 4.4). The resulting set of Teff and

logg provides priors to constrain future seismology of the DAVs. In addition, we hope to use relative positions in the Teff-logg plane to examine relative structural differences.

has helped discover thousands of new DAs, of which there were a significant number of DAVs (e.g. Kleinman et al. 2004 and Kleinman et al. 2013). More recently, the K2 mission has made observations of many new DAVs. Since over 200 DAVs are now known, looking at the statistical properties of the DAV class can now yield meaningful results. Previous ensemble studies of DAVs (Clemens 1994, Mukadam et al. 2006) have provided hints of structure in the pulsation spectra but suffered from having relatively few white dwarfs to include and atmospheric parameters determined inconsistently. Given the number of DAVs that are now known, it is time for a thorough and systematic study of this class of stars (Clemens et al., 2016).

We have spectroscopically observed 103 DAVs and 19 NOVs. While many of these have existing spectroscopy, much of that spectroscopy is from SDSS. As noted in Kepler et al. (2006), most DAVs observed by SDSS have low signal-to-noise ratios that give systemati- cally different atmospheric parameters when compared to higher signal-to-noise observations. Kepler et al. (2006) compared signal-to-noise ratio≈100 Gemini GMOS spectra to signal-to- noise ratio ≈ 21 SDSS spectra. They found a systematic difference in effective temperature of 320 K lower in the SDSS spectra and a difference of 0.24 dex in logg larger in the SDSS spectra. This difference was attributed primarily to a correlation of Balmer line shape in the Teff - logg plane, a decrease in Teff can be partially compensated by an increase in logg.

Additionally, higher signal-to-noise spectra are beneficial for the higher order Balmer lines, which are relatively shallow. Since these lines are more sensitive to pressure, they help significantly in the determination of logg. As pointed out in Gianninas et al. (2005), the signal-to-noise of the spectrum determines the errors on Teff and logg. We sought to get

higher signal-to-noise spectra of these targets to more precisely determine the atmospheric parameters.

While large surveys of white dwarfs have been done before (e.g. Gianninas et al. 2011), they generally employ multiple telescopes and spectrographs. We sought to use the same telescope and spectrograph for all of our observations. This allows us to probe and limit

the systematics that affect our determination of Teff and logg. In this chapter, we present

the results from our survey. In section 4.1, we will describe the selection of our survey targets then detail our observing strategy in section 4.2. Following that, we will explain our data reduction and fitting methods in section 4.3 and section 4.4. Then, in section 4.5, we carefully go through 10 choices that can change the final atmospheric parameters and offer guidance to future observers. In section 4.7, we will present our chosen method of a uniform effective temperature scale and show some initial comparisons and uses of this data set in section 4.8.