Surface grid

When the newly modified code was run, black pixels started to appear on the surfaces of both stars. Their number increases with increasing shear strength and they are not present when no differential rotation is applied. This was also found to happen in the original single star version of the code. This is illustrated in the top panel of Fig. 5.10. The explanation for the null pixels lies in the way the surface grid was sheared.

The vertices of each surface triangular pixel (see _§5.4.2) lie on lines of constant latitude. Therefore, a triangular pixel either has two vertices on the upper latitude and one on the lower latitude or vice-versa. The latitude of each pixel is stored and this is transferred to the subroutine responsible for performing the rotations described above. The problem with this is that when differential rotation is applied, all three vertices of the triangle are sheared by the same amount, irrespective of the small latitude difference that one of the vertices must have to the other two. The result of this is that, as differential rotation is applied, adjacent latitude bands no longer tessellate perfectly. Due to problems of numerical accuracy gaps can then start to appear when this triangular grid is ‘painted’ on to the viewplane (again see _§5.4.2).

1

Figure 5.10: The viewplane surface showing the model of a star after a shear of 90deg has been applied. Top: the original implementation showing black pixels. Bottom: after shearing each vertex individually (see text), note no black pixels.

While the black pixels make up a very small fraction of the total number of pixels, it was feared that they might be introducing noise into the final maximum entropy re- construction. Therefore, when we run a grid of different differential rotation parameters (described in chapter 7) in order to locate the best fitting combination of parameters, the black pixels would be biasing our results. This is particularly worrying as the number of blank pixels is correlated with the rate of differential rotation.

In order to solve this problem the latitude of eachvertexof each triangle was stored and this was transferred to the subroutine responsible for applying the latitudinal de- pendant shear. So now each vertex is sheared individually, rather than the whole pixel. Consequently, neighbouring latitude bands remain in perfect alignment with each other. This is illustrated in the lower panel of Fig. 5.10, where no black pixels are visible. Naively one may think that this changes the area of the pixel. However, given that the area of a triangle is 1₂(base × height) and neither the base nor the height are changing, the area will be preserved. So effectively the triangle becomes progressively more stretched out as the star is subjected to increasing amount of shear.

Unfortunately this solution brings about its own problems. If the rate of differential rotation is extreme, or equivalently the duration of observations is long, then each pixel will become grossly stretched out. Consequently parts of the pixel are no longer representative of the positional dependent parameters that were calculated for the original pixel centre (e.g. the pixel outward normal). Ultimately this can cause the stellar surface to resemble a ‘disco ball’ which is also undesirable. There likely exists a limit on the total shear beyond which the original version with black pixels will again become preferable. In theory, therefore, when this limit is approached the code could pause and resample the pixel grid. In practice, however, this would be computationally expensive and may itself introduce a discontinuity in the reconstruction process.

On a practical level, increasing the number of latitudes of the surface grid will allow a larger shear to be used before the above effects will start to come into effect. In Fig. 5.10, ninety latitudes are used and a total shear (between pole and equator) of 1.5 radians (or approximately 90 ◦_{) is used. Here only very slight distortion of the surface grid occurs} near the bottom of the image (corresponding to mid-to-high latitudes in the largely unseen hemisphere). This level of shear was chosen because it represents the maximum amount of shear that occurs on either star of HD 155555 over 11 nights of observations (see Chapter

7).

The changes described above to the DoTS code were also implemented in our new ZDI code, ZDoTS, allowing us to obtain a separate measurement of the stellar differential rotation from Stokes V spectra.

CHAPTER 6

The first magnetic maps of a pre-main sequence binary system - HD

155555

This chapter is based on a paper accepted for publication in Monthly Notices of the Royal Astronomical Society by:

Dunstone, N.J., Hussain, G.A.J., Collier Cameron, A., Marsden, S.C., Jardine, M., Stem- pels, H.C., Ramirez Vlez, J.C., Donati, J.-F. (2008, In press, MNRAS, astro-ph/0803.0837) All the work described here was carried out by myself with the exception of the spectral synthesis in_§6.3.2 and the coronal field extrapolations in_§6.6. This is clearly highlighted in the text.

6.1 Introduction

The only tidally-locked binary star to date for which published magnetic maps are avail- able is the evolved primary star of the RS CVn system HR 1099. A strong latitudinal dependence on the polarity of the radial field maps is found and HR 1099 often exhibits a unipolar cap (Donati et al. 2003). Also present are strong, and often complete, axisym- metric rings of azimuthal field on the stellar surface. Petit et al. (2004) confirmed the existence of an anti-correlation between the polarity of the radial and azimuthal fields. This is not observed on young rapidly rotating stars but is present on the Sun. Due to the evolved nature of RS CVn primary components, it is difficult to interpret their magnetic maps with respect to those of young rapidly rotating single stars. Therefore in an attempt to establish the relative importance of tidal locking and youth on surface magnetic field distributions, we present observations of the young pre-main sequence binary system HD 155555.

The HD 155555 (V824 Ara) system is composed of a G5 IV primary and a K0 IV secondary and has an orbital period of 1.68 d. This makes it a good target for observing over a five day observing run, as outlined in §6.2. HD 155555 was first discovered as a close binary system by Bennett et al. (1967). It was later classified as an RS CVn binary (Strassmeier et al. 1993) based upon the activity and binarity of the system. Pasquini et al. (1991) suggested that HD 155555 was more likely a young pre-main sequence binary. This was based upon the high Li (6708 ˚A) abundance (re-visited here in §6.3.2) and the presence of a very active dMe companion (LDS587B). More recently Strassmeier & Rice (2000) derived an age of 18 Myr using the Hipparcos distance of 31 pc and the pre-main- sequence evolutionary tracks of D’Antona & Mazzitelli (1997).

HD 155555 is a particularly active system with an X-ray luminosity of 2.7x1030_{erg s}−1

(Dempsey et al. 1993), and both components show CaII H & K core emission and filled in Hα. Therefore given its proximity and activity it is unsurprising that HD 155555 has been the subject of a number of recent papers. In 1996 it was the target of a multi-wavelength study by Dempsey et al. (2001). The authors detected considerable flare activity, with several flares being observed simultaneously in the UV and radio wavelengths. As part of this campaign, optical spectroscopy was also obtained and surface brightness images were produced using Doppler imaging by Strassmeier & Rice (2000). An earlier Doppler image of HD 155555 produced from data obtained in 1990 was published by Hatzes & K¨urster (1999). In addition, a magnetic field detection has also been reported for both components of HD 155555 by Donati et al. (1997).

In this chapter we present new surface brightness maps (_§6.3) and the first magnetic maps of HD 155555 (_§6.4.1). To achieve this we have developed a binary ZDI code in order to model the contribution of each star to the combined Stokes V profiles that are observed during conjunction phases (see Chapter 5). The more recent, and numerous, 2007 observations of HD 155555 are described first. Then in _§6.5 we present a smaller set of observations taken in 2004. In obtaining magnetic maps for both components of a binary system we open up many interesting possibilities to explore the effects of binarity on the magnetic fields of both stars. Possible interaction between the stellar fields are of interest because it will determine many of the system’s X-ray properties and the location of stellar winds. In _§6.6 we use the magnetic maps recovered of both the primary and secondary components in order to perform an initial analysis of the likelihood of interaction between the two stars. We discuss our results in _§6.7 and present our conclusions in _§6.8.