Charini Perera
Advisor: Prof. Robert Harmon

Site Map

Introduction
The Solar Dynamo
Rotation and Convection
Characteristics of sunspots
Starspots
Using MLI to map starspots
My Research
Conclusion
Acknowledgments

Introduction

The Sun is driven by a dynamo that is believed to be the cause of solar activity.

Similar activity has been revealed on stars, as well as the presence of a stellar magnetic field.

A key ingredient to understanding stellar magnetic fields and their interaction with moving plasmas is the study of starspots.

The Solar Dynamo

Energy is transported within in the Sun in three ways:

Hydrogen burning core ~ which is within the inner third of the Sun's radius

Radiation ~ which takes place within the next third of the Sun's radius

Convective zone ~ which takes place within the outer third of the Sun's radius, which is about 200,000 km.

Magnetic activity takes place within the convective zone.

Magnetic activity is believed to be driven by the interaction of rotation and convection, and this is the "dynamo."

http://science.msfc.nasa.gov/ssl/pad/solar/interior.htmI

Rotation and Convection

Richard Carrington was the first to discover Differential Rotation.

Differential rotation is when sunspots at the equator rotate ~2% faster than those at mid-latitudes.

During differential rotation field lines get pulled forward at the equator by the faster rotation and are deformed in an east-west direction.

Ultimately these lie parallel to the equator and float to the surface, erupting as sunspots.

The following picture best illustrates how sunspots are believed to occur. This model was defined by Horace Babcock, and is called the "Babcock Model."

(a) Here the Sun rotates differentially, with an initial global field flowing from south to north, with the equator rotating faster than the poles.

(b) As the equator rotates faster, the field lines get wound around, into a spiral field with a strong toroidal component.

(c) As the winding increases 'omega' shaped loops and kinks form in the toroid and float to the surface as active regions giving rise to sunspot groups and other forms of activity before decaying. As this decaying occurs, a flux loop forms connecting the leader and follower spots. The magnetic axis between leader and follower is tilted towards the equator. If the leader and follower spots move apart as the flux loop is decaying, the follower flux will move polewards and the leader flux will move equatorwards. These fluxes would then cancel with the existing polar fields, and a trans-equatorial poloidal loop would form, connecting follower flux from one hemisphere with that of the other.

(d) Accumulation of such loops would cancel the existing field, and create a new one, which is of an opposite polarity to the original, and this occurs every 11 years.

Carroll and Ostlie, Introduction to Modern Astrophysics

Characteristics of sunspots

Sunspots form when strong magnetic fields suppress the convective flow of gases, which prevents internal heat from being carried to the surface.

A typical sunspot consists of an dark central region, called the umbra, which is surrounded by a lighter region of alternating dark and light filaments, called the penumbra.

Sunspots appear dark as they are ~1500K cooler than surrounding surface.

Field lines emerge from the surface of one sunspot and re-enter the sun at the surface of another, linking the spots in pairs of opposite polarity that are oriented roughly in an east-west direction.

Sunspots tend to appear in groups consisting of one leader and several follower spots with the leader and the follower spots having opposite polarities.

An interesting aspect of sunspots is their 11-year variation of their annually averaged number count - which is known as the sunspot cycle.

The polarity patterns of this cycle reverse every 11 years, so the total magnetic cycle takes 22 years to complete.

This image is a close-up of a sunspot, and you can clearly see the umbra surrounded by the penumbra.
	G. Scharmer, L.H.M. Rouppe van der Voort (KVA) et. al., SVST

Starspots

Main sequence-stars, those that are still burning hydrogen in their cores, have been found to exhibit signs of magnetic activity.

From these, stars younger in age than the sun have fast rotation periods, and show higher levels of dynamo activity, and thus have erratic fluctuations of magnetic activity and no well-defined cycles.

A consistent dynamo cycle does begin to appear as the star ages

Similar to the sun, the rotation rate (period) and the presence and depth of a convection zone are what feature in the study of stellar magnetic cycles.

The degree of spottedness of a star varies with time and some stars exhibit cyclic spot activity.

Differential Rotation

Young Solar Analogs, stars similar to the Sun, but younger in age, may appear to exhibit features of a magnetic cycle that is similar to the Sun's.

In particular, stars similar to the Sun may show differential rotation, where starspots at different latitudes will show different rotation periods.

By monitoring and mapping starspots on young solar analogs, it may be possible to examine the existence of differential rotation on stars.

Using MLI to map starspots

The Matrix light-curve inversion (MLI) method is an indirect way of inverting photometric light curves of a given star such that its surface features may be discerned.

The surface of the star can be divided into spherically rectangular patches that are assumed to radiate uniformly across their surfaces

The goal of MLI is to find a light-curve that corresponds to the patch intensities and may be fitted to the light-curve obtained through observation

When fitting the modeled light-curve to the observed light-curve, it is not ideal to have an exact fit.

This is because real data have scatter due to noise, and a surface that is covered with small spots will have variations in its light-curve that is similar to noise.

A computer program that is searching for the exact fit to a light-curve will instead try to mimic the noise and pepper the surface of the star with lots of little spots, which is not good!

Instead constrained minimization is utilized, which looks for the smoothest solution possible that will suppress the noise artifacts and yet still fit the overall shape of the light curve.

The advantage of MLI is that it makes no a priori assumptions in regard to the number of spots on a star's surface or their locations.

Light-curve inversions of Pluto's surface that were made using MLI were later found to correspond to maps obtained via direct imaging using the Hubble Telescope, thus showing that MLI works!

My Research

For my research, I used data obtained by the 0.4-m Automatic Photometric Telescope (APT), a joint project of the Vanderbilt University Department of Physics and Astronomy and the Tennessee State University Center of Excellence in Information Systems, for Young Solar Analogs.

The stars I analyzed analyzed: HD 1835 (constant period), HD 20630, HD 206860, HD 30495, HD 97334 and HD 72905 (all variable period).

The purpose of this research was to use MLI to map stellar surfaces of stars with variable periods to examine differential rotation on these stars.

Prelimary results obtained for HD 20630 don't appear to show any differential rotation on the star. As can be seen in the images below, the spot appears to be at the same latitudes for the star in the two seasons analyzed. If the spot had appeared at different latitudes, this would be evidence for differential rotation!

Conclusion

The appearance of the spot at the same latitude as the inclination angle given to the program is not a coincidence.

The program tends to place spots at the given inclination angles, thus evidence for differential rotation is not shown.

This is due to the program trying to search for the smoothest possible solution to fit the observed light curve to the generated light curve and it seeks to generate the smallest possible spot that will give a good fit to the light curve.

This would occur when the spot passes directly in the line of sight.

As a larger spot near the the pole would produce a similar light curve variation as a smaller spot at a latitude near the inclination angle, the solution process may tend to model a larger spot a different latitude with a smaller spot whose latitude is equal to the inclination.

Thus a smaller spot will be favored by the minimization algorithm, as long as it fits the light curve well enough.

Additionally, the spots on this star appear to be small in size, and the program is not as sensitive to resolving smaller spots as it would be for larger spots.

Simulations that have been carried out by Robert Harmon show that for larger spots on the surface of a star, the differences in latitude may be resolved.

By modifying the program so as to better resolve latitude differences, differential rotation may successfully be resolved in the future.

Acknowledgments

Prof. Robert Harmon, for his guidance and support, throughout this project as well as over the course of the past four years.

The Department of Physics and Astronomy at Ohio Wesleyan University, that became a home away from home!

My parents for always supporting my dreams, and my sisters for always being there for me.

Greg Henry of the Tennessee State University.

Thanks for visiting. I hope you learnt alot about starspot research! For further information, you may access my research paper at the following link:

Examining Differential Rotation using Matrix Light-Curve Inversion

Examining Differential Rotation of Stars using Matrix Light-Curve Inversion