Imaging the Surfaces of Stars

Imaging the surfaces/atmospheres of other stars is one of the major frontiers in stellar astronomy. Because red giant and supergiant stars present the largest angular diameters in the sky, they are the first stars apart from the Sun to have been imaged, albeit so far with angular resolution just sufficient to resolve their disks. These observations confirm that red giant and supergiant stars have highly extended atmospheres, which from millimeter and infrared observations are known to give rise to a massive outflow. The SKA will be able to image the structure and directly measure the temperature of these stellar atmospheres over a relatively large range of heights, leading to more accurate empirical models of their physical properties as well as a better understanding of the mechanisms that drive the stellar atmosphere outwards.

Optical images of both red giant and supergiant stars reveal the common occurrence of asymmetric photospheric structures on these stars. Examples are shown in Fig. 2.5 for the red giant Mira and the red supergiant Betelgeuse. Their asymmetric photospheric structures are attributed to bright spots produced by large convection cells distributed inhomogenously over the stellar surface, or intrinsic stellar distortions possibly produced by nonradial pulsations.

**Figure 2.5:** Left panel shows a false color near-ultraviolet image of Mira made with the HST with an angular resolution of $\sim$ 45 mas (from Karovska et al. 1997). The optical photosphere of Mira is clearly asymmetric, perhaps as a consequence of nonradial pulsations. Right panel shows a contour plot of Betelgeuse's optical photosphere made with aperture-masking interferometry (from Tuthill et al. 1997). The two apparent bright spots may be produced by large convection cells distributed inhomogeneously over the stellar surface.
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Red giant and supergiant stars are ubiquitous ultraviolet emitters. An ultraviolet image of the red supergiant Betelgeuse made by the Hubble Space Telescope (HST) reveals a hot chromosphere that extends to many stellar radii and is apparently asymmetric (Gilliland & Dupree 1996a,b), as shown in Fig. 2.6. Acoustic waves, Alf ${\'{v}}$ en waves, and radial pulsations have all been proposed for heating thereby greatly extending the stellar atmosphere as well as driving its mass outflow, but the available observations do not permit us to choose between the various possibilities.

**Figure 2.6:** Left panel shows a false color ultraviolet continuum image of Betelgeuse's chromosphere made with the HST with an angular resolution of $\sim$ 38 mas (from Gilliland & Dupree et al. 1996b). Right panel shows a fitted model image comprising an offset hot spot superposed on a circular disk. The black circle has an angular diameter of 55 mas, somewhat larger than the typically inferred optical photospheric diameter of $\sim$ 45 mas. The chromosphere seen here in the ultraviolet continuum extends to a height of nearly 3 R_*, but that seen in the line of Mg II extends to at least twice this height (Gilliland & Dupree 1996a).
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Both red giant and supergiant stars lose mass at a prodigious rate of $\sim$ 10^-7- $10^{-6} M_{\odot} {\rm\ yr^{-1}}$ . On red giant stars, radiation pressure on dust grains condensed from dense gas in the lower stellar atmosphere is thought to drive the mass outflow (Kwok 1975). The situation is less clear for red supergiant stars as dust is not expected to form in a hot chromosphere, but the mechanisms involved presumably also operate in the lower regions of the extended stellar atmosphere. This mass loss has important consequences for it significantly affects the evolution of the star, forms a circumstellar shell that later helps shape the structure of protoplanetary and planetary nebulae (on post red giant stars) and supernova remnants (on post red supergiant stars), and is one of the most important sources of enrichment for the interstellar medium. Thus, study of the properties and dynamics of the stellar atmosphere leading to a better understanding of the mechanisms responsible for their large extents and mass outflows is one of the important topics in red giant and supergiant star research.

The large radio photospheres of red giant and supergiant stars give rise to detectable thermal radio emission. From a sample of 6 stars, Reid & Menten (1997) showed that the radio flux density spectrum of late-M giant stars such as Mira follows a $S \propto \nu^2$ dependence at centimeter wavelengths (8-22 GHz), suggesting that their radio photosphere has a sharp opacity edge. Fig. 2.7 (left panel) shows the expected flux density from Mira-like giant stars as a function of radio frequency at various distances, and for comparison the sensitivity of the SKA for an 8-hr integration over a range of radio frequencies. As is apparent, the SKA will be able to detect the radio photospheres of these stars out to many kiloparsecs at high frequencies, and right across the entire galaxy at 20 GHz.

**Figure 2.7:** The flux density (left panel) and angular diameter (right panel) expected for a Mira-like (late-M) red giant star as a function of radio frequency and distance, assuming $S_{{\mu}Jy} = 5.1 \times \nu_{GHz}^2$ and an absolute diameter of 8 AU as found by Reid & Menten (1997). The 3 $\sigma$ continuum sensitivity of the SKA is plotted for an integration time of 8 hrs in one polarization (left panel), as is the angular resolution of the telescope (right panel).
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Although the radio photospheres of red giant stars have yet to be imaged, Reid & Menten (1997) have partially resolved the radio photosphere of the red giant W Hydra. They find an average diameter of $0\hbox{\raisebox{.9ex}{\scriptsize$\prime$$\prime$ }}.080 \pm 0\hbox{\raisebox{.9ex}{\scriptsize$\prime$$\prime$ }}.015$ (corresponding to $\sim$ 8 AU), and a brightness temperature of $1500 \pm 570 {\rm\ K}$ . This corresponds to a disk size approximately twice that measured in the optical, and a temperature two-thirds that of the optical photosphere. This relative dimension and temperature, when applied to the other red giant stars in the sample of Reid & Menten (1997), also suitably explain their observed flux density. With a brightness sensitivity of $\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}10 {\rm\ K}$ at frequencies above 300 MHz (for an integration time of 8 hrs in one polarization), far below the brightness temperature of the stellar radio disk, the SKA will be able to image with high fidelity the radio photospheres of all red giant stars with angular sizes large enough to be resolved. Assuming a radio photosphere of diameter 8 AU, Fig. 2.7 (right panel) shows the angular diameter a Mira-like giant star will subtend at various distances compared to the angular resolution of the SKA as a function of frequency. At the highest frequency of 20 GHz, it will be possible to resolve the radio photosphere of Mira-like red giant stars to distances of up to $\sim$ 1.5 kpc. For these stars, comparison of the radio photospheric structure to the optical photospheric structure will provide important constraints or help elucidate the mechanism(s) responsible for driving the stellar atmosphere outwards.

Early-M supergiant stars have a flatter radio flux density spectrum of $S \propto \nu^{1.0-1.3}$ as observed for Betelgeuse (Newell & Hjellming 1982) and Antares (Hjellming & Newell 1983). Fig. 2.8 (left panel) shows the expected flux density from Betelgeuse-like supergiant stars as a function of radio frequency at various distances, and for comparison the sensitivity of the SKA for an 8-hr integration over a range of radio frequencies. As is apparent, the SKA will be able to detect the radio photospheres of all red supergiant stars in our Galaxy, and at 20 GHz even those in the Large and Small Magellanic Clouds.

**Figure 2.8:** The flux density (left panel) and angular diameter (right panel) expected for a Betelgeuse-like (early-M) red supergiant star as a function of radio frequency and distance, assuming $S_{{\mu}Jy} = 240 \times \nu_{GHz}^{1.3}$ as found by Newell & Hjellming (1982) and the radio photospheric diameters measured by Lim et al. (1998). The 3 $\sigma$ continuum sensitivity of the SKA is plotted for an integration time of 8 hrs in one polarization (left panel), as is the angular resolution of the telescope (right panel).
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Using the VLA, Lim et al. (1998) have imaged the radio photosphere of Betelgeuse at 7 mm. As shown in Fig. 2.9 (left panel), the star appears to be asymmetric. Measurements taken simultanously at cm-wavelengths partially resolve the stellar atmosphere, and directly measure its radial temperature profile. As shown in Fig. 2.9 (right panel), these measurements reveal that the stellar atmosphere has a temperature close to the photospheric value at a height of $\sim$ R_*, and from there decreases in temperature with height. The height range probed in radio is identical to that probed in the ultraviolet by the HST, but the latter reveals a hot chromosphere at temperatures $\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ } }}5000 {\rm\ K}$ . Although these two components must therefore coexist in the lower stellar atmosphere, the much lower radio opacity per particle of the cooler radio atmosphere implies that it must be much more abundant than the hotter chromospheric component and forms the dominant component in the stellar atmosphere. Lim et al. (1998) suggested that the elevation of photospheric gas by large convection cells distributed inhomogeneously over the stellar surface naturally explains the observed temperatures and asymmetric structure of the stellar atmosphere. Shock waves produced by the elevated gas, particularly strong over the convection cells, may be responsible for heating a small fraction of the atmosphere to chromospheric temperatures. These measurements resolve the previous puzzling observations of episodic dust formation at heights of $\sim$ 3 R_* (Bester et al. 1996), difficult to explain in the presence of a pervasive hot chromosphere. Instead, the measured dominant gas temperature of $\sim$ 2000 K at this height is just sufficiently low for dust grains to condense. Radiation pressure on these dust grains could further elevate the stellar atmosphere, and ultimately drive its mass outflow.

**Figure 2.9:** A false color image of Betelgeuse made at a wavelength of 7 mm with the VLA (left panel). The radio photosphere at $\lambda$ 7 mm has a size approximately twice the optical photosphere (45 mas), and is asymmetric. Simultaneous observations at longer wavelengths partially resolve the radio photosphere, which increases in size with increasing wavelength, and are used to deduce the radial temperature profile of the atmosphere (right panel). From Lim et al. (1998). With surface brightness sensitivity of a few 10's of K at angular resolution below 10 mas, the SKA will directly image the surfaces of red giant and supergiant stars beyond a kpc distance.
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Finally, an exciting prospect not yet studied numerically is the possibility of detecting and imaging circularly polarized radio emission from red giant and supergiant stars from regions of relatively strong and ordered magnetic fields. The detection of polarization in circumstellar SiO maser emission demonstrates that at least some red giant stars possess significant magnetic fields (10-100 G at the observed heights), which furthermore appears to be relatively well ordered on a global scale (Kemball & Diamond 1997). It is not known whether red supergiant stars possess significant magnetic fields. Such magnetic fields, if strong and pervasive on red giant and supergiant stars, may play an important role in shaping the structure of the stellar surface and influencing both the rate and direction of the mass loss.

Complementarity to Planned Optical-IR Interferometers

By the time the Square Kilometer Array is constructed, a number of powerful optical and IR interferometers (OIRI) will also be in operation. Some of the major efforts are summarized in Table 2.1. Names of the interferometers are given in column 1. Column 2 shows the maximum number of baselines existing or planned for that instrument. The maximum baselines (in meters) is shown in column 3 while column 4 shows the diameters of the elements in the array. Some instruments, like COAST, NPOI and SUSI are already operational.

Consideration of angular resolution suggests that the SKA and OIRI will be quite compatible. Fig. 2.10 shows a plot of SKA operating wavelength plotted against those of the planned VLTI.

Table 2.1: Some Current and Planned Optical-IR Interferometers

Name	Max No. Baselines	Max Baseline length	Element Diameter
LBT	1	20 m	8 m
ISI	1	35 m	1.7 m
GI2T	1	60 m	1.5 m
Magellan	1	60 m	6.5 m
PTI	1	110 m	0.4 m
I2T	1	140 m	0.3 m
SUSI	1	640 m	0.2 m
IOTA	1-3	45 m	0.5 m
Keck	1-15	180 m	10/1.5 m
COAST	3-6	100 m	0.4 m
NPOI	3-15	250 m	0.4 m
VLTI	> 6	200 m	8/1.8 m

**Figure 2.10:** Angular Resolution of the SKA and the VLTI Optical-IR Inteferometer. The diagonal line indicates for which radio wavelengths the SKA produces the same angular resolution. There is an excellent match for IR wavelength range 5 - 50 microns and the radio range of 1 to 20 cm.
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The angular resolution of the VLTI which scales inversely with wavelength is shown across the top of the graph. The diagonal line indicates for which radio wavelengths the SKA produces the same angular resolution. We see that the match is excellent for the IR wavelength range 5 - 50 microns and the radio range of 1 to 20 cm. Since the SKA is not planned to operate below 1 cm, the match with the optical resolution capabilities of the OIRI is not as good, although the latter can always be reduced to match the radio capabilities.

Because of the common angular resolution and the common sensitivity to thermal sources the most obvious science overlap is in the study of stellar surfaces. At its highest operating frequency the SKA can approach an angular resolution of 5 milliarcseconds and can therefore resolve the 400 or so stars whose angular diameters are greater than about 10 milliarcseconds. The largest stars have angular diameters approaching 0.1 seconds of arc. Thus, in the best cases SKA will produce stellar images with as many as a couple of hundred resolution elements. Such imaging can record surface features like hot spots and starspots as has been seen in the extensively studied supergiant Betelgeuse. The OIRI will match or exceed the (1 cm) SKA resolution from the optical up to about a wavelength of 5 microns. The availability of common-resolution imaging at optical, IR and radio wavelengths should provide the ability to image the atmospheres of these stars in 3-dimensions because the optical depth is a strong function of observing frequency. This type of imaging should allow the investigation of the vertical structure of the photospheres and via long term monitoring of surface and stellar wind features make it possible to correlate surface activity with changes in the stellar wind (e.g. Lim, 1998). Such studies of the atmosphere-wind interface will not only lead to a better understanding of the wind phenomenon but may also shed light on the dynamo that drives surface activity (e.g. Güedel, 1997). Additionally, such data place important constraints on convection models leading to a better understanding of energy transport in these stars.

Imaging the Surfaces of Stars

Red Giants and Supergiant Stars

Complementarity to Planned Optical-IR Interferometers