The basal limit of stellar activity

In the study of stellar activity, the Mount Wilson survey provided early evi- dence for a lower limit of chromospheric Ca ii H & K emission (Schrijver 1987

sion lines (including Ca ii H & K and Mg ii h & k) against stellar colour show clearly defined lower boundaries, with very few outliers below the lower limits. The minimum Ca ii H & K line core flux, seen for the most inactive stars, has a chromospheric component that is independent of stellar cycle variability and referred to as “basal” emission. This means there are three contributions to mea- sured S-values: the photospheric flux, the non-variable basal chromospheric component, and the magnetic activity related, time-variable chromospheric contribution (Schrijver et al. 1989).

The basal emission appears to be completely independent of large-scale stellar fields driven via the global magnetic dynamo. It was immediately sus- pected to arise from the dissipation of non-magnetic energy, via acoustic waves. This hypothesis is supported by detailed theoretical work (e.g. hydrodynamic modelling in Buchholz et al. 1998). However, there is still some debate and ongoing work on the exact mechanisms responsible for basal heating of the chromosphere (Hall 2005 and references therein). It now appears likely that both acoustic and small-scale magnetic mechanisms, unrelated to the stellar dynamo and its activity cycle, are at play (Hall 2005).

An important observational contribution was made bySchröder et al.(2012), who measured the solar S-index during the very pronounced activity mini- mum of 2008-2009. At several epochs, the solar disk was completely free from plages9_{, and the overall emission from this “quiet sun” state was exactly at}

the basal limit observed in large stellar samples. This is evidence for the basal limit as a universal phenomenon for sun-like stars that is reached when they are devoid of active regions.

There have been a series of efforts to quantify the basal limit and investigate its dependencies on fundamental stellar parameters. Divergent methodologies are used, and results are quoted in terms of S-values, log(R0_HK) and F0

HK (e.g.

Isaacson & Fischer 2010, Wright 2004, Perez Martinez et al. 2014). The latter parameter is the chromospheric line core surface flux in absolute flux units, i.e. without normalisation to the total bolometric flux. The approaches used typically rely on empirical fits to the lower envelopes of the distribution of a given parameter, via large stellar samples (Isaacson & Fischer 2010; Mittag

et al. 2013). Some works employ subtraction of best-fit synthetic spectra from

observed stellar spectra (e.g. Takeda et al. 2012; Perez Martinez et al. 2014). This allows a more precise calculation of the full photospheric contribution via the synthetic spectra, and more robust use of absolute flux units. Due to this diversity of approaches, there is no unique agreed upon basal limit in the literature. Modern approaches do yield quite consistent results however (e.g.

Perez Martinez et al. 2014).

For the purposes of this thesis the exact value of the basal limit (and which units it is given in) is of secondary importance. As will be discussed in Sec-

tion 1.4.3, I am primarily interested in outliers significantly below the lower

envelope of the distribution of chromospheric emission values. I will use large stellar samples to illustrate this lower envelope in Chapter2, clearly revealing outliers below this empirical limit. It is convenient to use the most widely avail- able metrics in the literature, i.e. S-values and log(R0HK). The more physically

meaningful, colour-independent metric is log(R0_HK), which can be converted from S-values where necessary. As shown in Section 1.3.1 the conversion only requires the widely available stellar B−V colour index. The more precise methodology of calculating the basal limit of F0

HKinPerez Martinez et al.(2014)

relies on the knowledge of precise stellar effective temperatures (Teff). These

measurements are not widely available, significantly limiting any sample size. While Teff can be estimated directly from B−V, the conversion is not precise

without knowledge of stellar metallicity and stellar surface gravity (g∗), which

A complication in the basal limits of S-values and log(R0_HK) is that both quan- tities show diverging distributions for the different stellar luminosity classes (see e.g. Wright 2004; Jenkins et al. 2008; Mittag et al. 2013and Section 2.3). This is due to changing photospheric contributions in all S-index bandpasses as a function of g∗, and different magnetic activity behaviour as a star moves

through its major evolutionary phases.

Main sequence, subgiant and giant stars should therefore be separated into different samples when analysing log(R0

HK) distributions. An accurate way to

do this is placing stars with precise parallax measurements on the Hertzsprung Russell (HR) diagram (Wright 2004), as will be done in this thesis (Section2.3).

Wright (2004) provided the first analysis along these lines, and I will adopt a

very similar methodology here. In essence, main sequence stars are defined as objects that have not evolved significantly above the average main sequence (for details, see Section2.3).

Following Wright (2004), objects with log(R0_HK) < -5.1 are either evolved, or main sequence stars with extremely rare anomalously low activity levels. The adopted main sequence basal limit is thereforelog(R0_HK) = −5.10. More evolved stars often fall below this level. This exact value of the basal limit is somewhat arbitrary, but in practice provides a conservative, useful threshold between anomalous outliers and the pronounced lower envelope seen in large samples of main sequence stars. This will be illustrated in Section 2.4 for the stellar sample investigated in my thesis. Note that only 9 main sequence stars below this basal limit in a sample of thousands of objects were identified by

Wright(2004). With such a low occurance rate, large stellar samples are clearly