1. Why does the temperature of the Sun’s atmosphere increase with height? Evidence strongly suggests that magnetic waves carry energy into the chromosphere. We are investigating the dynamics of magnetic and acoustic waves near strongly magnetic regions on the Sun’s surface, such as sunspots. Convection cells under the visible surface of the Sun excite acoustic waves at the photosphere. These can transform into magnetic waves in the overlying chromosphere. We analyze data from 3D magnetohydrodynamic (MHD) simulations, to track changes in density and velocity in the chromosphere.We use IDL software to Fourier analyze data which vary in space and time. The resultant plots of wavenumber versus frequency can reveal details about MHD waves as they rise through the solar atmosphere. Our analyses focus on a region where sound waves and magnetic waves have similar speeds. In this region, acoustic and magnetic waves mix and exhibit complicated, non-linear behavior. Understanding these wave interactions can lead to a more complete model of the role of magnetic fields in heating the solar atmosphere. This work is supported by NASA’s Sun-Earth Connection Guest Investigator Program, NRA 00-OSS-01 SEC. Abstract

2. Why does the temperature of the solar atmosphere increase with height?

3. Background  The temperature of the Sun’s interior decreases from millions of degrees K at the core to ~5800 K at the photosphere  The upper atmosphere reaches ~10 5 K and the corona’s temperature exceeds 10 6 K.  The connection between energy released at the photosphere and the temperature increase in the solar atmosphere is unclear.

4. About the code  Developed in High Performance Fortran for massively parallel computers by Galsgaard and Nordlund, 1995  Solves the magnetohydrodynamic (MHD) equations in 2D or 3D.

5. The MHD equations

6. References and Acknowledgements  Bogdan, T.J., et al. (2003), Waves in the magnetized solar atmosphere II. Waves from localized sources in magnetic flux concentrations.,ApJ, 597,2  Johnson, M., Petty-Powell, S., & Zita, E.J. (2002), Energy transport by MHD waves above the photosphere numerical simulations. http://192.211.16.13/z/zita/MHD8a.pdf  Thanks to fellow TESC students Night Song and Andrew White, and Dr. Tom Bogdan of the High Altitude Observatory in Boulder, CO.  This work is supported by NASA’s Sun-Earth Connection Guest Investigator Program, NRA 00-OSS-01 SEC.

7. The Sun, as seen by SOHO Fe IX/X 171 Å, full disk, at 13:00 UT, courtesy NASA (http://sohowww.nascom.nasa.gov/cgi- bin/get_soho_images?summary+040518)Fe IX/X 171 Å, full disk, at 13:00 UT

8. MHD simulation models changes in plasma parameters Fig.2: Variation of plasma density at t=0 in the z-x plane. Light lines are magnetic field lines. Dark lines are plasma-β contours.

9. Plasma density varies with position and altitude Fig.3: Variation of plasma density at t=?? in the z-x plane. Light lines are magnetic field lines. Dark lines are plasma-β contours.

10. Fig.4: Plasma density at a given x varies in altitude and time.

11. Fig.5: Plasma density at a given altitude varies in position and time.

12. Summary  Why does the temperature of the Sun’s atmosphere increase with height?  We seek deeper understanding of dynamics in the solar atmosphere.  This can help scientists predict solar weather.  Methods: FFT analysis of 3D MHD simulation data and generation of  -k diagrams to characterize waves in the solar atmosphere

13. The “magnetic canopy” Plasma-β  β > 1: sound waves are faster than magnetic waves  β < 1: Alfvén (magnetic) waves are faster than sound waves  β ~ 1: Sound speed and magnetic speed are comparable. Hybrid waves can demonstrate both acoustic and Alfvénic properties.

14. Acoustic waves  prominent in β > 1 regions, e.g. near the photosphere  propagate and oscillate along magnetic field lines  compressions & expansions of gas, e.g. due to a driver beneath the photosphere  channeled along unperturbed field lines MHD waves come in different flavors

15. Alfvén waves  fast in β < 1 regions, where the field is strong  “pluck” field lines  propagate along field lines  oscillate perpendicular to field lines

16. Magnetosonic waves  compress and expand magnetic field lines  propagate and oscillate perpendicular to magnetic field lines  caused by restoring force of magnetic pressure for longitudinal waves across field lines

17. Dispersion (  -k) diagrams We transform signals varying in space to power series in wavenumber, using Fourier Transformations We transform signals varying in time to power series in frequency. We can then compare our data with known analytic dispersion relations and characterize waves in complicated areas such as the “magnetic canopy”, where β = 1

18. Method We generate dispersion diagrams to identify waves 1D FFT 2D FFT

21. Future Plans write a program in IDL to make the generation of  -k diagrams simple and intuitive use the  -k diagrams to characterize non-linear waves in the MHD simulation compare  -k diagrams to observational data from SOHO, SUMER, etc.