4. Spectral subtraction
Stellar activity is seen most often in the hydrogen Balmer lines and Ca II. The Balmer lines are difficult to model with success since at typical chromospheric temperatures and electron densities the source function is collisionally dominated as opposed to photo-ionization dominated (Fosbury 1974). As chromospheric activity increases the Balmer lines react in an increasingly non-monotonic fashion. For M-dwarfs detailed computations by Cram & Mullan (1979), Cram & Giampapa (1987) and more recently by Houdebine, Doyle & Koscielecki (1995) show that as activity increases the Balmer absorption lines first strengthen, then weaken by filling-in of the core relative to inactive stars and finally become pure emission lines. This behaviour of the Balmer lines has been confirmed both for the Sun (La Bonte 1986) and for late-type dwarfs, sub-giants and giants (Strassmeier et al. 1990). Hence some highly active stars which show strong emission in the cores of Ca II H and K (the phenomenon which generally defines the term chromospherically active) can often show weaker Balmer line absorption than inactive stars of the same spectral type and luminosity class, even though these lines are also formed substantially in the chromosphere. For this reason a good quantitative assessment of the levels of activity in some stars requires an approach more convoluted than simply measuring the strengths or equivalent widths (EWs) of active lines. What is required is a measure of the additional absorption or emission part of the line due to the atmospheric layer responsible for the activity, i.e. the chromosphere.
Spectral subtraction provides a technique of studying the diverse phenomena of stellar activity by isolating that part of the spectroscopic signature due only to chromospheric activity. This involves simulating the inactive spectrum of the star concerned and simply performing a linear subtraction of this from the observed spectrum. Any manifestation of activity is then visible in the subtracted spectrum as emission or absorption features above or below the zero continuum level. Relative changes in these features can then help to determine the time behaviour and spatial locations of any active regions. The problem with the technique then is to simulate the correct spectrum representing the inactive contribution. Two approaches are possible; first to use theoretical spectra based on radiative transfer solutions in model atmospheres or secondly to use observed spectra of inactive stars. Such techniques have been widely used and are becoming more commonplace.
Fraquelli (1984) applied spectral subtraction to spectra of the RS CVn-type star HR 1099 (V711 Tauri). Theoretical absorption H profiles were calculated using standard stellar atmosphere codes and using the known effective temperature and surface gravities of the component stars. These profiles were shifted, broadened and combined and then corrected to match the H cores of observed comparison stars. Although an investigation was made of the effect of spectral type mismatch on the results no use was actually made of the single star comparison spectra in the profile matching. The problem with theoretical line profiles for spectral subtraction lies in the uncertainty and complexity of the atmospheric conditions giving rise to the profile. Without detailed information concerning the dominating effects on the source functions of active lines and the effects of active regions on these lines it is impossible to form an adequate theoretical representation of the inactive contribution. So although radiative transfer codes are readily available for modelling active lines in late-type chromospheres their use is unwarranted in this sort of study.
For observational comparison spectra the usual method is to use a star which is similar to the program star in all respects other than the level of chromospheric activity. In this work the comparison spectra are referred to as the spectral standards or simply standards. Herbig (1985) studied the excess emission EW for 40 F8-G3 dwarfs using the same inactive G0 V comparison star. Young et al. (1989) also used observed spectra of inactive M-dwarfs of the same (R-I) colour index as the program stars to derive estimates of excess emission. Thatcher & Robinson (1993) used two comparison stars of spectral types G6 V and K1 V to isolate excess H emission in a sample of late-G to early-K stars. Recently Montes et al. (1995) used comparison stars in a study of the excess H emission dependence on effective temperature and rotation in a sample of RS CVn binaries. Some authors have chosen to subtract an average or quiescent spectrum of the same object in their analyses (e.g. Young, Rottler & Skumanich 1991; Byrne, Eibe & Rolleston 1996). Such a procedure is often difficult since many targets do not habitually display inactive states and the assumption must be made that the source function of the chromosphere is temporally static. Other authors who have used observational spectra for subtraction include Hall & Ramsey (1992b), Lazaro & Arevalo (1994), Montes et al. (1994) and Frasca & Catalano (1994).
Many assumptions are involved in the spectral subtraction technique. The most important assumption is that there exists a linear radiative transfer relationship between the photosphere and chromosphere in the active star and that there is no significant horizontal radiative coupling between an active region and its neighbouring quiet atmosphere. These are generally not good assumptions for active stars because very large fractional surface coverage by active regions gives rise to extremely non-local radiative transfer. Another important assumption is that the underlying photosphere of the active star is similar to that of the spectral standard. This is also not a good assumption since the observed spectrum of a spectral standard is certainly not due to a simple photosphere with no extra-photospheric contribution. Local and non-local inhomogeneities in the chromospheres and transition regions of a spectral standard will produce some activity signatures in its spectrum. As has been demonstrated by Basri, Wilcots & Stouts (1989) for early-K main sequence stars, some photospheric lines can be affected by magnetic activity. In the solar case, La Bonte (1986) observed broad emission wings in photospheric lines in active regions. The assumption of an underlying photosphere is then only true for very localized or transparent active regions. Consequently the subtraction process will remove some contribution from the chromosphere and transition region of the active star. Nevertheless the application of spectral subtraction often shows excellent cancellation of photospheric lines. Furthermore, analysis of simultaneous optical and UV spectra (which show the photosphere directly) demonstrate the reliability of the technique (Newmark et al. 1990; Huenemoerder, Ramsey & Buzasi 1990; Huenemoerder 1988; Huenemoerder & Barden 1986).
Several questions may be raised concerning the spectral subtraction technique. Firstly is the representation of an inactive spectrum a true depiction of the basal state of the photosphere and inactive chromosphere? Secondly is the linear subtraction of an inactive spectrum justified for a regime where highly non-linear radiation transfer takes place? The work of Cram & Mullan (1979) and Cram & Giampapa (1987) show that in atmospheric models of cool stars with no chromosphere the H equivalent widths are weaker than those found even for the most inactive of stars. Although the effect is less prominent for earlier stars of spectral types F and later is it debatable whether stars exist with so called null chromospheres. No observations have as yet revealed such stars. The conclusion is that the spectral subtraction technique underestimates the degree of chromospheric activity. However in very active stars this effect will be almost negligible and the derived excess emission will fairly well characterise the chromospheric behaviour. This is another point against the use of model calculations to simulate inactive spectra since the results of spectral subtraction will then be model dependent rather than empirical. The technique then provides a consistent set of measurements for comparison and provides the only practical method of studying such stars. It should be realized that the features seen in subtracted spectra reflect differences in the stars as a result of a source function or opacity difference in the line-forming regions. If the source functions of the two stars are equivalent functions of depth, i.e. the optical depth scales are equivalent and only the temperature structures are different, then the subtracted features will be a good measure of the relative degrees of activity. This is because the two atmospheres map onto the line profiles in the same way. An increase in non-radiative heating in one of the stars will increase the source function in the upper atmosphere (assuming LTE) while leaving the deeper layers unaffected. The temperature structure maps onto the line profile with the wings originating at the deeper layer but the core will become filled-in relative to the less active star. This is of course a gross oversimplification since the line core filling could be the effect of a reduced opacity in the line and it may not be reasonable to assume similar source functions in active and inactive stars. The particle densities may be very different (particularly for stars of different surface gravities) leading to very different ionization and excitation equilibria and the dominating processes in line-formation may also be different. Hence the detailed interpretation of subtracted emission or absorption features must await the detailed modelling of stellar atmospheres. Line wing differences may be successfully modelled with the LTE assumption but the structure in active line cores requires detailed NLTE modelling.
Spectral subtraction is thus likely to be an uncertain technique even when used for stars with the same spectral type and luminosity class (or colour and surface gravity) since other parameters will effect the source functions of the lines of interest. The greatest power of the technique is in tracking line variability due to surface activity in a single object or in comparing closely related objects. Even so the technique has had great success in determining consistent phenomena in a wide variety of stars and so has become an acceptable method of deriving first order estimates of activity signatures.
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998