T Tauri stars represent a key transitional period in the life of a star, between the embedded protostellar phase of spherical accretion and the main sequence stage where accretion has ceased. They are low mass pre-main sequence stars, the youngest of which accrete material from dusty circumstellar discs. They possess strong magnetic fields, of order a few kG (e.g. Johns-Krull 2007), which truncate the disc and force in-falling gas to flow along the field lines of the stellar magnetosphere. It is this crucial time, lasting only about 10 Myr, which sets the challengingly brief window in which planets may form (Hartmann et al. 1998). The duration of this period is set by the lifetime of the disc, which in turn depends on the mass accretion rate. It is therefore important to understand how the magnetic field of the central star disrupts the disc and influences the accretion process. In doing so, we gain insight into the formation of all planetary systems including our own.
Previous accretion models assume that T Tauri stars have dipolar magnetic fields. However, recent observational results demonstrate that their fields are much more complex. First, strong fields have been detected from Zeeman broad- ening of photospheric lines, but often with no net circular polarization signal (Valenti & Johns-Krull 2004). This indicates that the stellar surface is covered in many regions of opposite polarity. Second, the detection of rotational modula- tion of X-ray emission cannot be explained in the framework of dipolar magnetic fields (Flaccomio et al. 2005).
In the following Chapters I develop models of the magnetospheres of T Tauri stars using powerful numerical techniques to extrapolate 3D magnetic field struc-
tures from Zeeman-Doppler images. I am currently working with surface maps of T Tauri stars, which have recently become available (Donati et al. 2007), but to date I have used magnetograms of young main sequence stars. In Chapter 2 I describe a method for extrapolating magnetic fields from surface magnetograms, and how observed X-ray emission measures may be used to put constraints on the coronal structure of T Tauri stars. I then go on to develop a simple steady state isothermal accretion model in Chapters 3 and 4, by first considering accre- tion to dipolar fields, then using fields with a realistic degree of complexity. By calculating mass accretion accretion rates I demonstrate that my model produces results which are consistent with the observed correlation between accretion rate and stellar mass. In Chapter 5 I demonstrate that my model reproduces the observed rotational modulation of X-ray emission, and in Chapter 6 I argue that the largest flares detected on T Tauri stars (which have been interpreted as di- rect evidence for magnetic links between stars and their discs) may arise from the reconnection of large extended open field lines within the disc. I summarise the main results from my thesis work in Chapter 7 and discuss future directions for my own research and for the field of low mass star formation as a whole.
Chapter 2
Realistic Magnetic Fields
Parts of the discussion in this chapter are based on the published papers Gregory, Jardine, Simpson, Donati, 2006, MNRAS, 371, 999 and Jardine, Collier Cameron, Donati, Gregory, Wood, MNRAS, 2006, 367, 917. Sections 2.3.1 and 2.3.2 summarise the discussion contained
within the latter paper.
2.1
Zeeman-Doppler imaging
Zeeman-Doppler imaging (ZDI) is a tomographic technique that uses high resolu- tion spectropolometric observations to reconstruct stellar surface magnetic fields. It was introduced by Semel (1989) and further developed by Donati, Semel & Praderie (1989), Brown et al. (1991), Semel, Donati & Rees (1993) and Donati & Brown (1997). ZDI recovers the shape and distribution of surface magnetic re- gions and also, to some extent, the orientation of field lines within those magnetic regions. Surface maps have been obtained for various types of star from young rapid rotators, a wholly convective M-dwarf, a massive B-type star and a star at the red giant phase (e.g. Donati 1999; Donati et al. 2003; Donati et al. 2006a; Donati et al. 2006b). Recently ZDI has been performed on the CTTs V2129 Oph
and BP Tau, which will for the first time allow the magnetic field geometry of CTTs to be determined (Donati et al. 2007).
ZDI combines Doppler imaging with circular polarimetry, and is reviewed in detail by Hussain (1999) and Berdyugina (2005); for our purposes it is sufficient to briefly outline the technique and to highlight some limitations. ZDI is an ad- vancement of conventional polarimetric techniques, which involve measuring the projected line-of-sight field component averaged over an entire visible hemisphere, for it allows the magnetic polarity distribution across the stellar surface to be de- termined. Fig. 2.1 shows an example of what can be determined from ZDI. Note that the meridional component of the field is so small it is not displayed. The magnetic field components can be determined at the stellar surface by analysing the Doppler shifts of Zeeman split spectral line profiles (see Fig. 2.2). In order for the technique to work, sufficient resolution is required in the line profiles; there- fore the star must be sufficiently rapidly rotating so that rotational broadening makes a significant contribution to the line profiles
Typical circular polarisation signatures due to star spots can be extremely small. Zeeman signatures have relative amplitudes of 0.1% with noise levels of order 10−3 in a single line, making the polarisation signal difficult to detect (Do-
nati, Semel & Rees 1992). Multi-line approaches have therefore been developed to increase the signal-to-noise ratio for the measured polarisation. The technique called least squares deconvolution (LSD) was developed by Semel (1989) and Semel & Li (1996) and involves combining the Stokes V profiles (the measure- ment of circular polarisation) for thousands of magnetically sensitive lines. Such a method significantly increases the signal-to-noise ratio.
The radial, azimuthal and meridional field components at the stellar surface are then determined by applying an inversion technique to the Stokes parameters (I,Q, U and V; which measure the intensity of the received signal in unpolarised light, the amount of linear polarisation present determined using filters at 0◦
Figure 2.1: Brightness map of the K0 dwarf star AB Dor (upper panel), with the corresponding magnetic maps (lower panels) reconstructed from Zeeman-Doppler imaging. Field strengths are labelled in G, with positive values corresponding to field vectors directed outward and eastward for the radial and azimuthal maps respectively. The tick marks indicate the phases of observation; reproduced with permission from Donati et al. (2003).
Figure 2.2: The observed circular polarisation signal (b) is the sum of opposite polarity Stokes V profiles due to spots at different Doppler shifts (a). Reproduced with permission from Semel (1989).
and 45◦
, and the amount circular polarisation respectively - see Tinbergen 1996 for details and for the relationships between the different parameters). Several such inversion techniques have been developed (e.g. Brown et al. 1991; Hussain et al. 2000; Piskunov & Kochukhov 2002), although Zeeman-Doppler images are typically constructed using only the Stokes V and I profiles as the magnetic signatures detected in Stokes Q and U are too small to be of use. This lose of information can be accounted for by assuming relationships between the different field components, allowing fields to be reconstructed (e.g. Hussain, Jardine & Collier Cameron 2001).
There are several limitations to ZDI. As was noted above you need enough rotational broadening to get decent resolution in individual lines, but not as much as is required for traditional Doppler imaging. Further, as with all circular polar- isation techniques, the measurements are sensitive to the line-of-sight component of the magnetic field. Circularly polarisation measurements thus suffer from flux cancellation (see the discussion in Hussain 1999), a combined effect of having a low signal from azimuthal fields and poor surface resolution at high latitudes. Hence the overall level of flux received is suppressed. ZDI therefore provides limited information about the field strength, but does provide the best method for detecting changes in field polarity. Another limitation is that one pole of the star is inclined towards the observer, permanently obscuring much of one hemi- sphere. Thus the polarity distribution may only be determined across the visible hemisphere, and a small portion of the other.