Disc-integrated spectra

For the spectral lines presented in this section, the numerical disc-integration method presented in Sect. 6.1 was applied assuming a homogeneous large-scale distribution of the magnetic field over the visible stellar surface. The consequences of this somewhat unrealistic assumption are discussed in Sect. 7.2.

Figure 6.20 shows disc-integrated line profiles for a few combinations of spectral lines and spectral types. The dashed curves represent the profiles without rotation. For the solid curves the profiles were broadened with the solar differential rotation (α = 0.2) at a rotation velocity of υ_rotsin i = 7.5 km s⁻¹ and an inclination of i = 60^◦. This is a reasonable rotation rate for moderately active stars of spectral type F and G, as well as for relatively young and active K and M dwarfs.

In the F3V simulation, both iron lines are shallower and narrower in the 500 G runs than in the non-magnetic runs. Moreover, the lines are considerably shifted to the red and their red wings become more prominent. As already discussed in Sects. 6.3.1 and 6.3.2,

Figure 6.19: Same as Fig. 6.18 but for the difference of the line wing Doppler shift.

the line weakening³ and the modified flows play a more important role in this star than the Zeeman effect (cf. Figs. 6.11 and 6.15). The modifications of both iron lines by the magnetic field look thus very similar although the sensitivity to the Zeeman effect is rather different. In the cooler K0V star, the line weakening is unimportant for the iron lines, but still important for the titanium line (cf. Fig. 6.10). Although the Zeeman broadening is stronger in the infrared titanium line than in the 617.3 nm iron line, the EW of the Tii line is slightly reduced in the magnetic run and its FWHM similar to the non-magnetic run without rotation. The Zeeman effect, however, shifts some line flux to the extreme wings (cf. Fig. 6.11). For the Fei line at 617.3 nm, the line weakening does not play a role. Therefore, EW and FWHM are larger in the line profiles of the 500 G run at any rotation rate. In the M2V simulations, there is no line weakening, thus EW and FWHM are higher in the 500 G runs than in the non-magnetic runs for all lines owing to the Zeeman effect. Owing to the larger wavelength and high g_eff, the titanium line shows the strongest Zeeman broadening in this star.

3The line weakening is less obvious in the disc-integrated profile without rotation because its effect is mainly on the EW and not so much on the line depth.

6.3 Effects of the magnetic fields

Figure 6.20: Disc-integrated line profiles of six combinations of spectral lines and spectral types. In all panels the black curves correspond to the non-magnetic run and the violet curves correspond to the 500 G runs. The dashed curves represent the disc-integrated line profiles without rotation, while the solid curves include broadening by a differential rotation (solar,α=0.2) atυrotsin i=7.5 km s⁻¹seen at an inclination of 60^◦.

Figure 6.21 presents the values of the EW and FWHM of all disc-integrated line pro-files without stellar rotation. The line weakening shows up very clearly in the EW of the hotter end of the model sequence, while the broadening due to the Zeeman effect is best visible in the FWHM of the cooler end of the model sequence. The Zeeman broadening shows the strongest effect in the titanium line, as expected, while it is almost not present in the Fei line at 616.5 nm with its low effective Landé factor of g_eff = 0.69. The virtual absence of the Zeeman effect in this line renders the whole extent of the line weaken-ing visible, while it is partly compensated by the Zeeman effect in the other two spectral lines. It is important to note that the Zeeman broadening appears to be roughly propor-tional to B₀(in both EW and FWHM), which is well visible for the M stars, while the line weakening increases less than linearly with B₀.

As shown in terms of bisectors in Figs. 6.5 – 6.7 in Sect. 6.2.3, stellar rotation can distort already asymmetric line profiles and thus have an impact on the line shape, in

Figure 6.21: Equivalent width (left panels) and full width at half maximum (FWHM, right panels) of the profiles of the three investigated lines for all 24 simulation runs.

6.3 Effects of the magnetic fields

Figure 6.22: Doppler shift of the line profile cores (solid curves) and wings (dashed curves) of all three spectral lines investigated in the F3V, K0V, and M2V simulations as function of υ_rotsin i (for the same plot for the G2V, K5V, and M0V simulations see Fig. B.26). In all cases, i= 60^◦andα=0.2 was assumed.

particular on the effective Doppler shift of the line core and its wings. Figure 6.22 illus-trates the impact of stellar rotation on the effective Doppler shift of the lines as function of the rotational velocity. In Sect. 6.3.2 it was illustrated that the Doppler shifts of the lines are strongly affected by the magnetic field near the disc centre in the F- and G-star simulations (cf. Figs. 6.18 and 6.19). As expected, the highly redshifted line wings of the disc-centre spectrum also have an effect on the disc-integrated spectrum. For the 616.5 nm Feiline in the F3V simulation for instance, line wings and core are shifted by approximately 800 and 600 m s⁻¹, respectively, to the red in the 500 G run compared to the non-magnetic run. As Fig. 6.22 illustrates, simulations with different B₀ have differ-ent effective Doppler shifts of the lines and, more importantly, a differdiffer-ent dependence on υ_rot. If the simulated stars had large-scale structures in the magnetic field (analogous to active and quiet region on the Sun), the Doppler shift would become time dependent in a non-trivial fashion (also see Sect. 7.2). Reiners et al. (2013) proposed an effect of the Zee-man effect on radial velocity signals by a combination of the Doppler and ZeeZee-man effects similar to the Rossiter-McLaughlin effect (Rossiter 1924, McLaughlin 1924). Fig. 6.22 shows, that the effect of the magnetic field is even more pronounced and probably more complicated than that and not exclusively caused by the Zeeman effect but also by the modified convective flow patterns.