For detecting and measuring the effect of starspots, there are a range of different techniques that can be used. For stellar physicists, their interest stems from wishing to understand better the processes ongoing within a star and how similar they are to one another and to the Sun. In more recent years, stellar activity has also become of interest for those who search for extrasolar planets (see1.5and onwards) where a very small signal needs to be found within a sea of stellar
‘noise’.
1.4.1 Photometry
As has been seen for sunspots, spots cause brightness variations on the surface of a star.
Therefore it is logical that it could be possible to detect their influence by studying the brightness of stars over a long baseline, such as a light curve. The variations expected within the light curve would be periodic and have the same period as the stellar rotation. This naturally depends on the lifetime of the active regions, where those with shorter lifetimes are hard to discern as they decay away too quickly to leave a repetitive trace. By modelling different coloured light curves, it is also possible to estimate likely temperatures and surface distributions of the spots.
To extrapolate properties of the spots from photometry, it is necessary to infer and use models. One example is to generate synthetic light curves using model stars with different sizes and distributions of spots, and compare those to the observed light curves. The models can be comprised of either circular, uniform spots (Budding 1977;Vogt 1981a;Poe & Eaton 1985) or spots with defined umbral/penumbral distributions (Dorren 1987); or the model can also be simple restrictions on the allowed latitude and longitudes of the spots (Bopp & Evans 1973; Eaton & Hall 1979). It is rarely possible for a single-spot model to fit the pattern in a light curve, and it is often unlikely to determine one, single result (with specific spot positions, sizes, temperatures etc.); additional measurements are needed, either photometry in different colours or other complementing techniques. Vogt(1981b,a) was able to determine the temperature and geometry of the spots from light curves in two colours (V and R) with a single, circular spot model with various properties. Since, more advanced computational codes have been developed as the wealth of photometric data has increased from various telescopes and
missions (e.g. Ribárik et al. 2003;Boisse et al. 2012;Oshagh et al. 2013a;Dumusque et al.
2014;Maxted 2016and others).
Due to the variation in the light curve due to spots occurring at the same periodicity as the stellar rotation period, tracking the appearance of spots is a means to measuring the stellar rotation period. For more details, see Chapter5.
1.4.2 Spectroscopy
There are various spectroscopic measurements which can aid in characterising spots; these include line-depth ratios and molecular lines.
Line-depth Ratios
The ratio in the line-depths is a reliable source of determining stellar atmosphere temperatures (with an accuracy of tens of degrees and changes less than 10K,Gray 1994). The same can be done for starspots (Gray 1996;Catalano et al. 2002). By tracking how the spot crosses the face of the star, it introduces depth variations in different lines which probe different temperatures;
therefore by measuring how a temperature-dependent line changes with respect to one which is not temperature-dependent, it is possible to get an estimate of the temperature of the stellar surface feature. Examples can be seen in (Toner & Gray 1988) with respect to rotational mod-ulation, and activity cycles in (Gray et al. 1996).
Molecular Lines
Stars with high effective temperatures have no molecular absorption lines, as they can only form in cooler stellar atmospheres. Therefore, for those stars, there may be molecular lines from starspots. The first time this effect was seen was byVogt(1979) for the star HD224085.
He studied the molecular lines for TiO and VO and concluded they were caused by spots.
This was closely followed by similar detections on other stars fromRamsey & Nations(1980);
Huenemoerder et al.(1989). Later, more developed techniques were proposed for more accur-ately measuring the temperature and filling-factord of the spots themselves by comparing two or more molecular lines (Huenemoerder & Ramsey 1987;Neff et al. 1995;O’Neal et al. 1996, 1998,2004). This method can also be extended to molecular lines in other bands; for example, in the near-infrared, where spots are significantly brighter than the rest of the photosphere and therefore have a larger effect on the molecular lines (O’Neal & Neff 1997).
As well as a means for detecting spots and determining their temperature and filling factor, the molecular lines can also be indicators of the spots’ magnetic field strength. The TiO lines
dFilling-factor: the proportion of spot coverage on a star (f =0.1∼10%).
Figure 1.7:Illustration of the Doppler Imaging method. As a spot crosses the face of the star, it blocks light from portions of the stellar surface. Different areas of the star are red-/blue-shifted by different amounts. By tracking the amount of light blocked over the different shifts over time, it is possible to measure spot properties (adapted fromVogt & Penrod 1983).
at 7055Å are magnetically sensitive and will split by small amounts (Berdyugina & Solanki 2002;Berdyugina et al. 2003;Berdyugina 2002).
1.4.3 Doppler & Zeeman-Doppler Imaging
Ideally, when investigating starspots, knowing their location and size on the surface is important;
as well as how all that evolves over time. Doppler imaging is able to determine that. The first uses of Doppler imaging come from its use for generating surface maps of Ap stars, to see anomalies in the magnetic field strength and element abundance (Deutsch 1958,1970;Falk &
Wehlau 1974;Goncharskii et al. 1977). If a star has surface features then these cause Doppler shifts as the star rotates, line profiles will change shape at certain phases when the surface inhomogeneity appears. The first time it was applied to “seeing” spots was by Vogt(1981c), Vogt & Penrod(1983) andVogt et al.(1987). The theory behind Doppler imaging is shown in Figure 1.7. A rapidly rotating star is split into a number of sections (in line with the rotation
axis) where the Doppler shift induced by the rotating star is taken to be uniform; therefore absorption lines will be shifted by different (but known) amounts in each section. In the case of a non-spotted star, the sum of these line shifts are simply a Doppler-broadened version of the non-shifted line (which can be used to measure the stellar rotation period). However when placing a spot on the surface, as it enters each section, it will reduce the overall brightness of that section. Summing all sections will then reveal the Doppler-broadened line with an additional little ‘bump’. Do this at regular intervals, and the movement of the spot can be tracked; and the size can be measured by the size of the bump in the line. The latitude of the spot can also be determined by establishing the range of wavelengths which were affected by it – a smaller range than the Doppler-broaded line would suggest higher latitudes, for example. Naturally, the reality of Doppler imaging is not as simple as the example in Figure1.7suggests. Additional noise in the stellar spectrum and stars with more than a single spot add complexity to this method. And a key precursor is that the star must rotate sufficiently rapidly that other sources of line broadening are dominated by the Doppler broadening. Additionally, it only functions well for fairly large spots – extrapolating the log-normal spot distribution seen on the Sun to stars with higher levels of activity (and therefore larger spots). Even the smaller spots cannot be resolved by Doppler imaging (Solanki & Unruh 2004) and that comparing the spot coverage observed via photometry and Doppler imaging for particular cases show that there are spots missing from imaging (Unruh et al. 1995).
Zeeman-Doppler imaging is just a further extension of Doppler imaging, and was first suggested bySemel(1989). It has since evolved to include more and more intricate magnetic forms and more detailed field properties by analysing more and more spectral lines at once (Donati & Brown 1997;Donati & Collier Cameron 1997). The Zeeman effect occurs when there is a magnetic field present within an area of stellar atmosphere, and causes the spectral lines to split into component lines at different wavelengths. The pattern of the splitting depends on the strength of the field and the properties of the atomic composition of the stellar atmosphere involved. In the case of a non-rotating star with a static spot, the spectra would show that some lines were split due to there being a magnetic field in the spot. But, add in stellar rotation, the same Doppler-effect will be seen – instead of it applying to simple spectral lines, it shifts the split lines. The same properties as measured through Doppler imaging can be measured, as well as the magnetic field strength by tracking the range of wavelengths involved.
1.4.4 Effect on Exoplanet Observations
Starspots are not just indicators of the behaviour of a star, they can also describe what the conditions are like in space surrounding that star. This is important when considering extrasolar planets (see Section1.5), as their climate and habitability heavily depend on the level of activity
of the star. For Earth, there is evidence of a correlation between climate and the level of activity the Sun is experiencing at the time (see Section 1.2.2). Therefore, it can be understood that with higher levels of activity there may be climate effects on an Earth-like planet around a much more active, Sun-like star – and this could be further amplified for different stellar types and planets in closer orbits (and therefore closer to the ‘action’). Furthermore, even the detection of such celestial bodies strongly relies on the ability to understand the stellar activity (and most significantly, the starspots) so that it can be removed as ‘noise’. Details of this can be found in Sections1.6.1and1.6.2for the effect of starspots on radial velocities and photometry respectively, as well as Chapter6.
‘Science progresses best when observations force us to alter our preconceptions.’
Dr Vera Rubin