Cool Star Astronomy

Cool stars play a major role in astrophysics; they define the largest stellar class, comprising our Sun as an average example. Most cool stars maintain magnetically confined atmospheres which give rise to particle acceleration and plasma heating. Investigations of the Sun in spatial, spectral, and temporal detail have provided us with a considerable knowledge on energy release, structuring, and evolution of stellar atmospheres. However, the Sun represents a particular state of stellar evolution, for a particular stellar mass. Understanding the full range of phenomena related to stellar activity, mass loss, and evolution requires the study of solar-like phenomena in large samples of stars. Up to the present day, no star at an activity level of the Sun's, believed to be typical for the vast majority of cool stars, has been detected at radio wavelengths. The SKA will drastically change this situation and is certain to yield a major breakthrough in our understanding of stellar atmospheres, by detecting several thousand normal stars in the solar vicinity. A broad range of diagnostic tools is available. ``Solar-stellar connection'' studies will be fruitful means to better understand both the Sun and stars.

Cool stars (typically defined as stars with photospheric temperatures $\;\rlap{\lower 2.5pt \hbox{$\sim$ }}\raise 1.5pt\hbox{$<$ }\;7000$ K, or spectral types later than A) serve as the natural bridge from solar to stellar physics. On the one hand, the Sun is a moderate, average example of a middle-aged main-sequence star, in no ways special nor extreme, believed to well represent the basic phenomena of magnetic activity that are thought to occur in many other star classes with outer convection zones. On the other hand, mid-mass main-sequence stars play, among stellar populations, a major role in our understanding of the dynamo, the long-term evolution, the atmospheric energy release from magnetic fields, and the spin-down history of stars due to transport of angular momentum away from the star by a magnetized stellar wind.

The stellar astronomer's vantage point with a prototypical source close-by sets a particularly exciting task to this part of astronomy. While extremely detailed physical models can be tested on the Sun in spectroscopic, spatial, and temporal detail, the diversity of stellar sources plays also a global role in the evolution of the galaxy, the recycling of matter and enrichment of the interstellar medium, the formation of planetary systems, and perhaps in the acceleration of soft cosmic rays. The Sun presents only a small range of atmospheric behavior; stars with different masses, ages, rotation periods, and chemical composition need to be understood as well to attack many fundamental problems of stellar evolution and galactic structure.

It is the task of the `solar-stellar connection' to build the bridge between the great knowledge gathered from solar observations and modeling, and the diversity of stars. The flow of information is in both directions: Many of the physical principles are known from the Sun, but much about global systematics and stellar (and therefore: solar) evolution can be learned only from stellar observations. This section summarizes how far we have gotten in this endeavour in radio astronomy, and how important a role the SKA will play in solar-stellar connection studies.

Single A or early F stars are usually not detected as radio sources (the same holds for X-ray emission; see gap in Fig. 2.1, bottom right, around $B-V \approx 0.2$). They do not possess strong winds, and their outer convection zone becomes too shallow to maintain a solar-like magnetic dynamo. Notable exceptions are chemically peculiar Bp/Ap stars that do support strong magnetic fields and are radio sources, although the physical mechanisms and geometric structures are probably very unlike the Sun's (Linsky, Drake, & Bastian 1992).

We are in the following mainly concerned with cool stars with outer convection zones and their pre-main-sequence relatives. There is evidence that each cool MS star possesses an outer magnetic atmosphere (e.g., Schmitt 1997) in which radio phenomena described in this chapter are generated.

Toward the optically faintest stars (M dwarfs to the lower right in the HRD) the maximum radio luminosity declines. This trend is not due to a selection effect but is real and parallels observations in the X-rays: The total (non-flaring) X-ray luminosity of a coronal star is bounded by $\sim 10^{-3}$ times its bolometric luminosity. This upper bound is ascribed to a `saturation' effect either intrinsic to the magnetic dynamo, or to the X-ray emitting plasma trapped in the corona. In contrast to the X-ray emission, the radio emission apparently signifies a saturation of the number of relativistic electrons in the corona. The statistics therefore clearly indicate that the most active coronal stars are found in spectral class G, i.e., among analogs to the Sun!

The Radio Sun

The non-flaring Sun has been studied at metric/decimetric/centimetric wavelengths in appreciable detail. Fig. 2.18 shows the Sun observed near its activity maximum with the Very Large Array (VLA) at 20 cm wavelength (Dulk & Gary 1983). Figure 2b illustrates a close-up view of 6 cm radio emission (contours) in the vicinity of a sunspot group (Gary & Hurford 1994). The emission contributions vary strongly during the magnetic activity cycle; at maximum, most of the measured flux stems from active regions. The dominant emission mechanism depends on the observing frequency and on the source location with respect to active region magnetic field structures. The type of dominant emission can be derived in particular from the spectral behavior on the optically thin side of the spectrum, with gyroresonance emission showing a steeper decrease toward higher frequencies; polarization properties are also used as discriminators (e.g., Gary & Hurford 1994; Vourlidas & Bastian 1996). Roughly speaking, the longer-wavelength emission (e.g., at 20 cm, Fig. 2a) is dominated by optically thick coronal free-free emission that correlates well with soft-X-ray features (identical emission mechanism; Dulk & Gary 1983; Gopalswamy, White, & Kundu 1991; Vourlidas & Bastian 1996). At wavelengths $\;\rlap{\lower 2.5pt \hbox{$\sim$ }}\raise 1.5pt\hbox{$<$ }\;$6 cm, active region emission consists of bright compact sources and a diffuse halo. The former, strongly sunspot-related component with a brightness temperature of a few times 10⁶ K is attributed to optically thick gyroresonance emission of coronal plasma in rather strong ($\sim$1 kG) magnetic fields (e.g., Lang et al. 1987; Vourlidas, Bastian, & Aschwanden 1997). The halo component is often due to optically thin thermal free-free emission from the corona, but also from the cooler transition region and the chromosphere.

  

Figure 2.18: The 20 cm radio Sun observed with the VLA during the magnetic activity maximum on September 26, 1981. The patches of enhanced emission are predominantly due to optically thick free-free emission from coronal plasma. (Copyright by the Smithsonian Institution). Right: Radio emission (contours) from above a sunspot group (grayscale plot), observed at 6 cm (4.8 GHz) with the Owens Valley Radio Observatory. Much of the emission is due to optically thick gyroresonance emission in concentrated ($\sim 1$ kG) magnetic fields. (Gary & Hurford 1994; courtesy of D. Gary.)

Both types of emission can be effectively used to derive principal source parameters, namely the electron temperature from either of the optically thick emissions, the electron density $n_{\rm e}$ from the bremsstrahlung components, and the magnetic field strengths from the gyroresonance emission (Gary & Hurford 1994). Somewhat surprisingly, strong magnetic fields up to 2 kG can be present even at coronal levels. Such values are close to photospheric levels; they indicate that the magnetic field divergence from the photosphere to coronal layers is rather small (White, Kundu, & Gopalswamy 1991; Lang et al. 1987; Lang et al. 1993; Vourlidas et al. 1997). This aspect may be much more important still for active stars in which the photospheric filling factor of strong magnetic fields is large, and their divergence is even more confined on geometric grounds.

During flares, the Sun can be a source of copious radio gyrosynchrotron emission for up to tens of minutes. The emission is produced by accelerated, mildly relativistic electrons spiraling around the magnetic field lines. This radiation often reaches its peak flux (transition from optically thick to optically thin) in the 1-10 GHz region. Its spectrum contains rich diagnostic information: The electron energies can be derived from the optically thick portion, magnetic field strengths from the turnover frequency, and the electron energy distribution from the optically thin part. Many of these diagnostic tools have been applied to easily observable, strong stellar flares, albeit with considerably smaller temporal and spectral (and no spatial) resolution. For a comprehensive review of solar radio flares and their diagnostic power, we refer to Bastian, Benz, & Gary (1998).

  

Figure 2.19: Extract from a dynamic spectrum of a solar type U radio burst group (9 July 1980). U bursts are generated by the beam plasma instability. The emission at the plasma frequency traces closed coronal loops. (From the RAG data archive, Institute of Astronomy, ETH Zürich.)

Solar radio astronomy has greatly profited from the diagnostic power of coherent radio emission during flares (Bastian et al. 1998). Traditionally, dynamic spectra (i.e., flux as a function of frequency and time) at a high temporal sampling rate (>1 spectrum per second) with high frequency resolution ( $f/\Delta f \;\rlap{\lower 2.5pt \hbox{$\sim$ }}\raise 1.5pt\hbox{$>$ }\;100$) over a broad frequency band (several 100 MHz) have helped disentangle a veritable zoo of coherent radio emissions. The best studied examples are thought to be due to emission near the plasma frequency or its second harmonic, induced by an electron beam instability (type III). Since the emission frequency is proportional to $\sqrt{n_{\rm e}}$, the time history of the emission on the dynamic spectrum traces the path of the electron beam in density, in cases producing `pseudo-images' of coronal loops as the electrons travel along closed magnetic field lines (Fig. 2.19). Beams traveling along open magnetic field lines eventually end up in interplanetary space. The timing of these bursts provides information on the electron beam acceleration and the possible fragmentation of the accelerator. In cases where simultaneous upward- and downward-moving beams can be identified, information about the density in the acceleration region (represented by the demarcation frequency) are obtained. Shorter, narrow-band emissions (spike bursts) have been interpreted as signatures of energy release fragmentation and may provide insight into the shortest time scales of the energy release (Benz 1985). Meter-wavelength type IV and type II bursts can be associated with coronal mass ejections (CME's) and related shocks and therefore provide important clues on transient coronal mass loss and magnetic field geometry (Kundu et al. 1989).

Observing Solar Analogs at Radio Wavelengths

The non-flaring radio luminosity of the Sun at several GHz is log $L_{\rm R} \approx 10.7$ [erg s^-1Hz^-1] (principally due to gyroresonance and bremsstrahlung emissions) and therefore well below the base level in the logarithmic 3-D diagrams in Fig. 1. No single radio star with $L_{\rm R}$ equaling that of the Sun has ever been detected. The lowest-luminosity radio star found so far, the F5 subgiant Procyon at a distance of 3.5 pc, is at log $L_{\rm R} \approx 11.7$, an order of magnitude higher than the Sun (Drake, Simon, & Brown 1993). Presently, the VLA detects a source like the Sun marginally out to 1.5 pc after 10 hours of integration time. The SKA, in contrast, will detect solar twins at 50 pc distance!

  

Figure 2.20: Radio spectra of the active dMe star UV Cet during quiescence. The left figure shows three optically thin gyrosynchrotron spectra. The right figure additionally reveals optically thick components above 10 GHz interpreted as gyroresonance emission. (Güdel & Zucker 1999.)

Almost all radio detections among cool MS or subgiant stars are interpreted as nonthermal gyrosynchrotron emission, based on their shallow spectra (Fig. 2.20) and on estimates of their brightness temperatures (often reaching 10⁸-10¹⁰ K; e.g., White, Kundu, & Jackson 1989). This sets active stars apart from solar behavior. But since the Sun is also a gyrosynchrotron source during flares, it has been speculated that the steady nonthermal emission from magnetically active stars is the envelope of a large number of unresolved flare contributions. This view is supported by a correlation between quiescent radio and X-ray luminosities of active stars that appears to be similar for time-integrated solar flare gyrosynchrotron and X-ray emissions (Güdel 1994 for a review).

In rare cases, a second spectral component is detected that is compatible with optically thick gyroresonance emission from hot plasma (Fig. 2.20, right panel). It can be used to derive coronal magnetic field strengths (Güdel & Benz 1989; White, Lim, & Kundu 1994). However, most dMe stars do not show this component at a detectable level, providing stringent upper limits to the filling factor of strong, low-coronal magnetic fields that contain hot plasma (White et al. 1994).

Flares on active stars are commonly interpreted in terms of solar flare physics (Bastian 1990 for a review). Their emission is often strongly circularly polarized and rapidly varying in time. Together with the high brightness temperature (up to 10¹⁶ K) this clearly suggests coherent emission mechanisms. Dynamic spectra would therefore provide great diagnostic insights into the timing and temporal fine structures of the accelerator, electron beams (type III or U bursts), mass loss by coronal mass ejections (type II and IV bursts), magnetic field topology, or electron densities. However, non-solar radio astronomers have traditionally been utilizing single-frequency receivers. Only a few dynamic spectra of stellar flares exist so far; their information content is clearly limited given their total bandwidth of typically less than 100 MHz at a frequency of 1400 MHz (Fig. 5; see also Bastian & Bookbinder 1987; Jackson, Kundu, & White 1987; Bastian et al. 1990). A broadband device such as proposed for the SKA could produce dynamic spectra routinely.

  

Figure 2.21: Dynamic spectrum of a very strong ($\sim 700$ mJy) coherent radio burst from the dMe star AD Leo, observed simultaneously at Arecibo (top; time resolution = 0.2 s), Effelsberg (middle; 0.125 s), and Jodrell Bank (bottom; 2 s). Note the narrow frequency range. The Effelsberg range is contained within the Jodrell Bank band. (From Güdel et al. 1989).

Where are the many other Radio Suns?

Why do we have numerous nonthermal radio detections of nearby M dwarfs (with smaller surface areas than the Sun; White, Jackson, & Kundu 1989) while solar analogs have escaped detection until recently despite their clear trend toward a much higher upper envelope of radio luminosity (Fig. 2.2)? Presently, only about a dozen GV stars have radio detections (see list in Güdel, Guinan, & Skinner 1998). Observations show that the spin-down of initially rapidly rotating G stars to projected equatorial surface velocities of vsin $i \approx 10$ km s^-1 occurs within a few tens of Myr, but takes $\sim$10 times longer for M dwarfs (Soderblom et al. 1993). At the Hyades' age (600 Myr), G stars rotate slowly, while M dwarfs easily maintain vsini > 10 km s^-1. The value of vsini is a good measure for magnetic activity (presumably since rotation directly influences the operation of the magnetic dynamo). Further, the space density of field M dwarfs is 8 times higher than for G dwarfs (Allen 1973). Both properties strongly favor M dwarfs for radio detections.

We thus identify two major areas in which the SKA will lead to a breakthrough: 1) The most ``active'' single MS stars are found among solar analogs. These would be the objects of choice for many investigations were they not so rare or weak. The SKA will detect such stars easily out to several hundred pc. 2) By far the largest population of stars in the solar neighborhood is made of spun-down stars that presumably behave grossly like the Sun. Except for the weak detection of the subgiant Procyon, none of these stars has been found at radio wavelengths so far.

   
Prospects for the SKA

Physics of Solar-Like Stars

The SKA will detect solar twins out to $\sim$50 pc as illustrated in Fig. 2.22. Extrapolating from the Gliese & Jahreiss (1991) Catalog of Nearby Stars or Allen's (1973) volume densities of stars in the solar neighborhood, we infer that 30,000 stars (99% of them being cool MS stars) are potentially within reach of a telescope like the SKA if the solar activity level is taken as a lower limit for all MS stars. Clearly, the SKA will open a completely new window to `normal' stars. Numerous physical problems so far studied only on the Sun can be investigated on a wide range of stars; the diagnostic power of bremsstrahlung or gyroresonance components will allow us to infer low-coronal magnetic field strengths, magnetic filling factors, or coronal electron densities and to study these parameters as a function of stellar age, rotation period, mass, or other magnetic activity indicators. The potential for inferring structuring and composition of the (non-flaring) corona and transition region will be considerable. Radio observations will help determine coronal temperatures from the low-coronal optically thick emission and will therefore complement soft X-ray observations. The magnetic filling factor, if identified from radio observations, should be compared with spot coverage maps from simultaneous optical Doppler imaging techniques.

Rotational modulation can be studied at high sensitivity. Apart from providing a unique collection of rotation periods (difficult to measure otherwise), it gives invaluable information on the size and the distribution of active regions. Knowledge of the frequency-dependent source sizes is important for a proper interpretation of the microwave spectra, including variations of the polarization (Bastian et al. 1998). Since the presence of active regions presumably varies with magnetic activity cycles as on the Sun, radio observations will also uncover such cycles. Polarization measurements could perhaps even detect a predominant magnetic polarity!

Nonthermal sources will be detectable out to hundreds of parsecs. This provides the exciting opportunity to study several open stellar clusters at radio wavelengths (Lim & White 1995). Such studies are important to probe systematics in the evolution of coronae. This extends back in time to many star forming regions of which the most important ones will be easily surveyed by the SKA.

If the SKA will be connected with VLBI antennas or will itself contain baselines of Earth-diameter size, its sensitivity will make routine, spatially resolved observations of radio stars at the milliarcsec level possible. So far, only few main-sequence stars reach an appropriate level for VLBI studies, but they begin to yield exciting results on coronal structure, such as global magnetic fields, in active stars not expected before (Benz, Conway, & Güdel 1998).

  

Figure 2.22: Expected sensitivity range of the SKA for detecting cool stars. A number of stars are plotted on the distance-luminosity plane, with the blue dots representing selected bright objects (mostly RS CVn binaries; Drake, Simon, & Linsky 1993) and the red dots F/G-type MS stars so far detected. Many M dwarf flare stars fall within the schematic quadrangle at left (within 10 pc; White et al. 1989). Various other radio detections (Wendker 1995) are plotted as small crosses. The average radio luminosity at 8 GHz of the non-flaring Sun is indicated by the bar at bottom, and the luminosity of a typical solar radio flare is marked by the dotted line. The diagonal lines represent the 3$\sigma$ detection limits for three different continuum integration times (1 min, 1 hr, 10 hrs), both for the VLA (8.4 GHz, 100 MHz bandwidth; upper set) and the projected SKA (maximum bandwidth; lower set) - Right: Light curve simulation for the SKA. Top panel: VLA observation of the flare star UV Cet at X band, 5 min resolution; 2nd panel: same observation, 1 min resolution; 3rd and 4th panel: simulated light curves for the VLA X band and the SKA, respectively, using the input model light curve shown in 5th panel. The numbers in the plot indicate the time binning.

Flares and Microflares

One major aspect of the SKA is its ability to provide high time resolution thanks to its high sensitivity. Coronal energy releases in the Sun and on stars occur on time scales between less than 0.1 s and several tens of minutes. Although the VLA and other modern radio telescopes observe large, energetic flares from many stellar systems, the main physical questions require high time resolution of flare light curves, broad bandwidth with spectral resolution, and observations of small and short events (`microflares'). The limitations to the latter are illustrated in Fig. 2.22. The two upper panels show the light curve from a VLA X-band observation (100 MHz bandwidth) of one of the most productive, most variable, and radio-brightest nearby flare stars, the M dwarf binary UV Cet. About ten flares with characteristics similar to major solar ``gradual'' flares are well visible (Güdel et al. 1996). From simultaneous X-ray observations, their radiated energy has been estimated to be $2\times 10^{30} - 2\times 10^{31}$ ergs, i.e., corresponding to large solar flares.

The thermal noise sets severe limitations. The remaining panels show a simulation of a synthetic light curve (bottom panel) that conforms with the assumption of small-scale events building up part of the ``quiescent'' emission of active stars. About 15,000 flares with a power-law distribution of their energy and duration have been stochastically placed in time (on a constant background level). The middle panels in Fig. 2.22 show the input light curve degraded to the sensitivity of the VLA at X-band (1 min resolution) and to the SKA (in the 5 GHz band with maximum bandwidth).

We expect that SKA easily observes flares on nearby stars 100 times smaller in their total energy (and shorter by a factor of ten) at time resolutions of a few seconds. We note that a typical solar radio flare may reach about 0.1 mJy at a distance of $\alpha$ Cen (1.3 pc). Such fluxes are accurately measurable at sub-second time-resolution with the SKA! The great sensitivity to flares over a very wide range in energy will address the fundamental problem of coronal heating. The energy distribution of a large set of flares can be used to study whether their rate of occurrence suffices to power the corona (the ``microflare/nanoflare'' hypothesis; see Parker 1988). Observations of the Neupert effect (characteristic lag of soft X-ray emission with respect to the flare gyrosynchrotron peak, owing to a causal relation between electron/heat front impact on the chromosphere and plasma heating and expansion) in a large number of such events may yield a qualitative or even quantitative picture of mechanisms that lift cool material into the strongly radiating coronae of magnetically active stars.

Summary of Scientific Objectives

The scientific objectives in stellar astronomy for an instrument with the capabilities of the SKA are manifold; most of the stellar phenomena described above and known on the Sun will for the first time be within reach of a radio telescope. Many scientific objectives so far only addressed in the solar case will be extended to a large variety of stars. Some of the major steps forward are expected in the following areas:

• Routine detection of non-flaring, thermal radio emission from most cool stars in the solar neighborhood, out to approximately 50 pc distance. The SKA will probe the physics and structuring of the lower corona and transition region. This telescope will open a new research area in the `radio solar-stellar connection'.

• Bremsstrahlung and gyroresonance components will yield information on the electron temperature and density and on the magnetic field strengths in active regions for a large sample of stars. In the case of more active stars, optical Doppler imaging can be used to relate the observed coronal emission to surface magnetic features. Rotational modulation provides information on the size and distribution of active regions, while long-term monitoring could uncover magnetic activity cycles.

• By studying the production of nonthermal electrons via their gyrosynchrotron emission in active stars and its fading toward less active stars, the physics of energy release can be studied as a function of stellar evolution. This is relevant to the problem of magnetic field production, the stellar dynamos, and the interaction of high-energy particles with the stellar environment. In terms of solar history, we can study the `Sun in Time' and infer the behavior of the Sun in past times. Extension to pre-main-sequence objects will probe the possible early history of the Sun and provide important information on star formation.

• Luminous nonthermal coronal sources such as young, active main-sequence stars will be detectable out to several hundred pc easily. Many open clusters will be studied to infer important systematics in the evolution of coronal activity.
• High-sensitivity observations will detect numerous small flaring events. Their statistics could yield important clues for the long-standing problem of coronal heating.

• Broad-band observations will provide diagnostics for coronal instabilities and energy release. This field has strongly fostered solar radio astronomy for 50 years but has only been touched by stellar astronomers, even after considerable efforts.

• The SKA can contribute greatly in sensitivity to VLBI studies of normal stars. Such observations will be ground breaking for the study of coronal structure in many types of stars.

Stellar radio astronomy is in urgent need of a new instrument as powerful as the proposed SKA. About 20 years ago, the VLA became operational; it has set new standards in stellar radio astronomy by discovering many stellar classes routinely for the first time, and thus yielding access to new physics at a rapid pace along with leading satellite observatories at other wavelengths. By now, however, most new investigations of stellar chromospheres, transition regions, and coronae rely on data in the ultraviolet, the EUV range, and X-rays from devices that detect moderately active stars out to many parsecs routinely, and active stars out to hundreds of parsecs. But radio astronomy has its own diagnostic power that cannot be replaced by information from other wavelengths. A new suite of space-borne observatories will soon be, or is already, available across the electromagnetic spectrum (e.g., AXAF, XMM, HST, GRO, SIRTF, FIRST), with next-generation follow-up missions already under discussion (NGST, Constellation-X, XEUS, etc). Clearly, radio astronomy needs to keep pace with these exciting developments.