Doppler imaging (DI) is a spectroscopic technique that requires frequent observations of a star over one or ideally many rotation periods. Fig. 1.3 shows a schematic representation of the principle behind Doppler imaging. Cool starspots are detected as asymmetric distortions in certain spectral line features. The line profile is shallower where the starspot is located relative to rotation axis. This asymmetry moves from the blue to the red side of the line profile as the star’s rotation carries the starspot from the preceding to the receding stellar limb. The starspot latitude is directly proportional to the velocity amplitude, or the length the distortion propagates through the line profile. The major limitations to Doppler imag- ing include precise information of stellar parameters, accurate stellar atmosphere models, and accurate atomic and molecular line lists. Inaccurate line profiles, rotational velocities, and stellar effective temperatures can lead to artifacts in the surface maps such as polar starspots and/or latitudinal starspot belts (Unruh & Collier Cameron 1997; Berdyugina & Tuominen 1998). While these concerns have been largely addressed (Unruh 1996; Rice 2002), a more direct method for imaging starspots would bolster confidence in the present results. A related technique known as Zeeman Doppler Imaging, introduced by Semel (1989) and
Figure 1.3: A schematic demonstrating the principle behind Doppler imaging. The dashed line indicates the rotationally broadened spectral line profile of an unspotted rapidly rotating star. The solid line indicates the effect on this spectral line as a cool starspot moves across the stellar surface. (Berdyugina 2005)
further developed by Donati et al. (1989), Semel et al. (1993), Brown et al. (1991), and Donati & Brown (1997), produces maps of the stellar magnetic field distribution as opposed to starspots. This is done by inverting the Stokes V parameter is an analogous way to traditional DI. Inverting the Stokes I parameter provides a surface map of the temperature distribution.
These techniques have provided a picture of starspots which in many cases is contrary to the behavior of spots on the Sun. In terms of lifetimes, the large starspots responsible for sinusoidal-like photometric variability can persist from months to years. For the Sun, typical sunspots live on average for only days to weeks. The covering factor, or percentage of the visible surface covered by spots, is far larger for active stars (10% to 50%) than for the Sun where the covering factor never exceeds 0.2% (Cox 2000). In addition, at times where the covering factor is largest, the overall luminosity of active stars decreases substantially
(∆ V ≤ 0.6) whereas the overall luminosity of the Sun actually increases. The activity cycle in the Sun corresponds to the time from one period of sunspot minimum to the next. The cycle length ranges between 9 to 13.5 yrs with an average period of 11.1 yr. Activity cycles in active stars have been detected through photometric and Ca II emission variability. These cycles are periodic on time scales from 3 to 21 years although some active stars have been known to exhibit double periodic cycles or not cycle at all (Baliunas et al. 1995; Frick et al. 2004; Lockwood et al. 2007). Perhaps the most dramatic differences between starspot and sunspot behavior are the locations where the spots emerge on the photosphere. At the beginning of a solar cycle, sunspots appear an approximate latitude of 30◦ symmetric about the equator. As the cycle progresses, sunspots migrate toward the equator stopping at an approximate latitude of 8◦ (Babcock 1961 and references therein). Starspots have been observed to reside anywhere from low to high latitudes or at the poles (Strassmeier 2009a and references therein). Unfortunately imaging efforts do not yet have the temporal baseline to investigate starspot position as a function of activity cycle.
Models have been created to reconcile the differences in spot behavior between the Sun and active stars, particularly in formation location. A nonlinear flux tube instability has been used to explain high latitude starspots (Schuessler & Solanki 1992; Schuessler et al. 1996). For rapid rotators, the dynamo generating the magnetic field responsible for the starspots operates at the base of the convection zone providing the time necessary for the Coriolis force to carry the flux tube toward the pole as the tube is carried to the photosphere via magnetic buoyancy. Increasing the rotation rate has the effect of shifting the emergent starspots to higher latitudes with an absence of equatorial starspots (Granzer et al. 2000). However these models are not able to explain adequately polar sunspots in main-sequence
stars. Berdyugina (2005) notes the flux tube concept in these models for heavily spotted stars implicitly assumes that the large identified starspots are not monolithic, but represent starspot groups. These groups are composed of Sun-like spots created by smaller flux tubes. To help verify the present understanding of starspots and to explore magnetic activity from active stars to the Sun, a direct method of determining starspot properties is required. The best strategy would be to actually image the stellar surface. Fortunately this is possible via long baseline optical/infrared interferometry (LBI). By combining the light, akin to Young’s double slit experiment, from multiple, widely spaced telescopes, angular resolutions down to less than 1 mas can be achieved. Images of stellar surfaces, rapidly rotating stars, binary stars, and star+disk systems are growing more commonplace over the past decade (Tuthill et al. 2001; Monnier et al. 2007; Kloppenborg et al. 2010; Che et al. 2011; Baron et al. 2012). Bright, convection-induced starspots have been imaged using LBI on the surfaces of Betelgeuse and T Per (Haubois et al. 2009; Baron et al. 2014). At present, the angular resolution of the longest baseline interferometer is ∼0.4 mas in the H band. The median angular diameter for surveys of A, F, and G main sequence stars is 0.991 mas or ∼ 2.5 resolution elements (Baines et al. 2008; Boyajian et al. 2012). Therefore this technique is currently only viable for giant stars and close early type dwarfs.
In Chapter 2, the photometric survey of ρ Ophiuchi cluster will be discussed. This will include descriptions of the sample selection, criteria for variability, and time series analysis methods for both periodic and long time scale variability. Chapter 3 will discuss both the morphology and potential mechanisms for the variability identified in ρ Oph. A primer on long baseline interferometry is located in Chapter 4 including how the presence of starspots will affect interferometric observables. Chapter 5 is a discussion of both the interferometric
and photometric observations obtained for λ Andromedae. This chapter also describes the two methods used to create images of the stellar surface and how starspot characteristics (e.g. size, location, temperature) are measured. Chapter 6 discusses the results from the observations spanning 2007 to 2011 including the potential tracing of stellar rotation via starspot motion. A complete summary of this dissertation is located in Chapter 7.
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THE PHOTOMETRIC SURVEY OF ρ OPHIUCHI CLUSTER
This dissertation begins with a broad perspective on stellar variability. This perspective is gained through a high cadence, long baseline, multiwavelength photometric survey of young stars in theρ Ophiuchi cluster. This survey has the potential to investigate numerous forms of stellar variability, many of which operate concurrently in a single star system (Herbst et al. 1994). This chapter discusses the observations and the stars to be surveyed for variability. It goes on to identify 3 methods for identifying stellar variability and describes the final variability catalog. The effect of the observing strategy on identifying fully and measuring the full amplitude of variability is explored. The chapter concludes with discussions on 2 methods used to identify variability timescales within the final variable catalog.