The Solar-Stellar Connection
If the Sun is peculiar in some way, or if we have fine-tuned our models to reproduce its unique properties, we will never know without studying other stars and attempting to match the diverse observations with the same models. For this reason, HAO is committed to maintaining a connection to stellar astrophysics. By observing magnetic activity cycles in other stars, we can improve our understanding of the solar cycle. By measuring the interior properties of different stars that result in a variety of stellar dynamos, we can place our knowledge of the solar dynamo into a broader context. By modeling the effects of rapid rotation on stellar structure, we can learn about the forces that shaped our own star in the past. Our models must be able to reproduce the wide array of behaviors observed in stars at every stage of their evolution, or their validation must be considered incomplete.
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Figure 1: Periods of stellar activity cycles in years, plotted as a function of rotation periods in days. The data follow two sequences: a relatively young, active A sequence (red dashed line) and an older less active I sequence (blue dash-dotted line). The letter H indicates Hyades group stars, crosses indicate stars on the A sequence, and asterisks indicate stars on the I sequence. Squares around the crosses show stars with B-V<0.62. Triangles indicate secondary periods for some stars on the A sequence. The peculiar solar point is shown in yellow (adapted from Böhm-Vitense 2007). |
Stellar Magnetic Activity Cycles
Astronomers have been making telescopic observations of sunspots since the time of Galileo, gradually building an historical record showing a periodic rise and fall in the number of sunspots every 11 years. We now know that sunspots are regions with an enhanced local magnetic field, so this 11-year cycle actually traces a variation in surface magnetism. Attempts to understand this behavior theoretically often invoke a combination of differential rotation, convection, and meridional flow to modulate the field through a magnetic dynamo (e.g., see Rempel 2006; Dikpati & Gilman 2006).
Although we cannot observe spots on other solar-type stars directly, these areas of concentrated magnetic field produce strong emission in the Ca II H (396.8nm) and K (393.4nm) spectral lines. The intensity of the emission scales with the amount of non-thermal heating in the chromosphere, making these lines a useful spectroscopic proxy for the strength of, and fractional area covered by, magnetic fields (Leighton 1959). Wilson (1978) was the first to demonstrate that many solar-type stars exhibit long-term cyclic variations in their Ca II H and K emission, analogous to the solar variations. Early analysis of these data revealed an empirical correlation between the mean level of magnetic activity and the rotation period normalized by the convective timescale (Noyes et al. 1984a), as well as a relation between the rotation rate and the period of the observed activity cycle (Noyes et al. 1984b; Saar & Brandenburg 1999), which generally supports a dynamo interpretation.
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Figure 2: Examples of stellar magnetic activity cycles documented from long-term measurements of Ca II H and K emission in several Sun-like stars observed by the Mount Wilson survey (Baliunas et al. 1995) including the Sun measured with stellar techniques. The complete sample includes cycle periods ranging from 2.5 to more than 25 years, as well as some stars that currently appear to be in a Maunder Minimum phase. |
In 2007, scientists at HAO initiated a survey of the brightest solar-type stars in the southern hemisphere, to complement the existing data from the northern surveys at the Mount Wilson and Lowell Observatories. With collaborators at Yale, Georgia State University, and the Space Telescope Science Institute, more than 50 stars are monitored monthly from the SMARTS 1.5m telescope at Cerro Tololo Interamerican Observatory in Chile, to monitor their Ca II H and K emission. Over the long term, these data will provide important new constraints on the physical mechanisms that drive the solar dynamo.
Asteroseismology and Stellar Interiors
Significant progress in dynamo modeling could only occur after helioseismology provided meaningful constraints on the Sun's interior structure and dynamics (Brown et al. 1989; Schou et al. 1998). Later observations, with the capability of detecting helioseismic signatures of solar cycle effects, established that variations in the mean strength of the solar magnetic field lead to significant shifts (~0.5 μHz) in the frequencies of even the lowest-degree p-modes (Libbrecht & Woodard 1990; Salabert et al. 2004). These shifts can provide independent constraints on the physical mechanisms that drive the solar dynamo, through their influence on the outer boundary condition for the pulsation modes. They are thought to arise either from changes in the near-surface propagation speed due to a direct magnetic perturbation (Goldreich et al. 1991), or from a slight decrease in the radial component of the turbulent velocity in the outer layers and the associated changes in temperature (Dziembowski & Goode 2004, 2005).
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Figure 3: Turbulent convection near the surface of the Sun and other stars excites acoustic oscillations that can be observed from the resulting surface motions and brightness variations. The characteristics of these oscillations probe both the global properties and the interior conditions of the star. |
Space-based asteroseismology missions, such as MOST (Walker et al. 2003), COROT (Baglin et al. 2006), and Kepler (Borucki et al. 2007) are now providing additional tests of dynamo models using other solar-type stars (see Chaplin et al. 2007). The continuous long-term monitoring from these satellite missions and from future ground-based networks like the Stellar Oscillations Network Group (SONG) are expected to yield the precision necessary for asteroseismic measurements of stellar convection zone depths (Monteiro et al. 2000; Verner, Chaplin & Elsworth 2006). By combining such observations with measurements of stellar differential rotation (see below) and the magnetic activity cycles documented from long-term surveys of the Ca II H and K emission (see above), we can extend the calibration of dynamo models from the solar case to many independent sets of physical conditions.
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Figure 4: An echelle diagram for the Sun observed as a star, where we divide the oscillation spectrum into segments of a fixed length and plot them against the oscillation frequency. Colored symbols show the observations while open points show the best stellar model from the automated pipeline of Metcalfe et al. (2009). Only the points with l=0-2 between the dashed lines were used for the fit, but the model also provides a good match to the data outside this frequency range and the l=3 points. |
Scientists at HAO are directly involved in the analysis of asteroseismic data from NASA's Kepler mission, including the development of an innovative stellar model-fitting pipeline using a parallel genetic algorithm. As part of an international collaboration known as the Kepler Asteroseismic Science Consortium (KASC), which is being organized through the University of Aarhus in Denmark, HAO scientists have early access to the Kepler data and are characterizing the properties of thousands of solar-type stars. A small sample of the brightest Kepler targets are also being monitored for Ca II H and K emission throughout the lifetime of the mission from the Nordic Optical Telescope in La Palma, Spain.
Stellar Differential Rotation
Even without the short cadence data that is obtained for asteroseismology, the Kepler mission will yield high precision time-series photometry for many stars that will be sufficient to characterize the surface differential rotation through detailed spot modeling. The photometry will be precise enough to reveal the signature of individual star-spots rotating into view, and the continuous monitoring will show spots at different stellar latitudes lapping each other so their locations and rotation rates can be derived without ambiguity. The Kepler data will allow surface differential rotation measurements for up to 100,000 solar-type stars, and over the lifetime of the mission this may even allow the construction of rudimentary "butterfly diagrams" showing the migration of activity belts through some fraction of the stellar magnetic cycles.
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Figure 5: The rotation period of spots at various latitudes on the young solar-type star κ1 Ceti from observations by the MOST satellite in 2003 (green), 2004 (blue), and 2005 (pink), showing the same pattern of surface differential rotation as the Sun (red lines). The rotation period from ground-based observations of Ca II H and K emission is in the range shown by vertical dashed lines (adapted from Walker et al. 2007). |
For the brighter asteroseismic targets where the individual oscillation frequencies are detectable, the time series should be long enough to resolve rotational splitting of the modes into multiplets for stars with rotation rates between about 2 and 10 times the solar rate (Ballot et al. 2008). Slower rotation makes it difficult to resolve the individual components of each multiplet from their strongly overlapping Lorentzian profiles, while faster rotation produces a splitting that is comparable to the small separation, creating some ambiguity in the mode identification. Measurements of the rotational splitting as a function of radial overtone can indirectly probe radial differential rotation, since the various modes sample slightly different (but overlapping) regions of the star. More directly, even with the limited set of low-degree oscillation frequencies that are available for distant stars, it is possible to construct inversion kernels that might detect a rapidly rotating core (Gough & Kosovichev 1993), although more recent work suggests that a significant detection may require unrealistically strong differential rotation (Chaplin et al. 1999).
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Figure 6: A theoretical H-R diagram showing the positions of various models of rotating stars with the same mass as the Sun. Some of the rapidly rotating models appear near the locations of zero age main sequence models for non-rotating stars (dotted line) creating a potential source of confusion. The inset shows the surface topology and convection zones for a rotating model with observable properties similar to the Sun (adapted from MacGregor et al. 2007). |
The effects of rotation can modify many stellar properties, altering the luminosities, surface temperatures, sizes, and shapes of stars in ways that are unaccounted for in non-rotating models of stars. HAO scientists have developed methods for constructing self-consistent models of differentially rotating, chemically homogeneous stars, whereby the equations of stellar structure and Poisson's equation for the gravitational potential are iteratively solved for an assumed conservative internal rotation law. Such models provide a means of interpreting observations of stars that are known to be rapid rotators.