# Presentation: 684240

## The Role of Sunspot Rotation in Driving Sigmoid Eruptions

**The Role of Sunspot Rotation in Driving Sigmoid Eruptions**
**David Alexander and Richard Nightingale **
**Lockheed Martin Solar and Astrophysics Lab.**

## Introduction

- In an on-going study, several sunspots, rotating about their umbral centers, have been identified in the TRACE photospheric white light (WL) images (at a 1 arcsec resolution).
- In many cases the rotation can be seen in the corresponding TRACE UV (1600 A) and/or EUV (171, 195A) images, as well as in the MDI data (for 1 case).
- The observations have been derotated and clipped so that all images are co-aligned, and despiking has been performed on the data to remove cosmic ray and particle hits.
- The white light data (for 8-10 August 2000) about the rotating sunspot were ‘uncurled’ using the geometry shown and displayed as r-plots.

## Introduction II:

** ****In this study we investigate the role of**
**   ****the energization of the corona by sunspot **
**   ****rotation.**
** ****The question we want to ask is what, if **
**   ****any, part does the sunspot rotation play **
**   ****in driving a sigmoid to erupt.**
** ****In particular, we will investigate `helicity  charging’ (e.g. ****Rust **
**    ****and Kumar, 1994a****) as a means of energizing and destabilizing **
**   ****the sigmoid.**
** ****We consider two distinct observational periods each **
**   ****associated with a well-defined rotation and a sigmoid: 1. Aug  **
**   ****8-10 2000 – sigmoid displayed a wide rangel of activity but no **
**   ****obvious eruption, and 2. Aug15-18 1999 – dynamic sigmoid **
**   ****development with eruption at ~1700 UT on Aug17 (****Gibson et **
**    ****al., 2002****).**

## August 8-10, 2000   (1600 A,   171 A,   WL, SOHO/MDI)

- Some apparently rotating EUV loops at 171 A caught our attention originally. Then we saw the rotation at several wavelengths.

## Introduction

- Time slices at different radii were utilized to better display the rotation of other features in and near the sunspot, as appears in this figure at a radius of 15 arcsec for the August 2000 data.

- By tracking these features, the rotational speeds at the different times and positions have been calculated. The rotational speed versus radius is shown below for the August 8-10, 2000 event .

## The rotational speed versus time and angular spacing are displayed in figures 8 and 9 for August 8-10, 2000.

## Yohkoh SXT on August 8-10, 2000

- A selection of corresponding Yohkoh/SXT observations showing that the active region is initially unstressed, but as the rotation occurs a sigmoid forms and then dims, probably due to a small flare followed by cooling, after the bulk of the rotation takes place.

## Energization

- We can estimate the changes in the electromagnetic energy flux in the twisted loops by using the integral of the Poynting Flux Density **S** through some area of the photosphere represented by a vector **ds** normal to the surface:
- where **v** is the rotational velocity, which is in the azimuthal direction and counter clockwise; **B** is the magnetic field vector (Bz, Br, B); and **E** is the electric field vector; rb, ra are the radii of the outer and inner sides of the annulus defining the approximate region of the foot points of the twisting loops.
- The average rotational speed v comes from our August 8-10, 2000 rotational speed analysis in the penumbra, assumed now to move as a rigid body with the magnetic fields frozen in. We use the penumbral speeds because the foot points appear to be in the penumbral region of maximum speed, as shown in the next figure by the light blue circles of radii rb = 12’’,  ra = 8’’.
- We obtained the magnetic field values from Mees vector magnetograph data using a magnetogram at 19:12 on August 8. We averaged the product of Bz B within the penumbral annulus between ra and rb.

## Energization

- v

## Helicity Injection

**	****Rate of Helicity Injection:**** ****from**** ****Kusano et al., 2002**** **
**	****Total Injected Helicity:**
**	****Helicity charging and instability:**
**	****	****Rust and Kumar (1994a)**** ****find a simple relationship between the helicity,**
**	****	****H****t**** and the flux, ********,                         for a helical fluxrope model.**
**	****	****where L is the loop length and ******** is the force-free parameter.**
**	****	****Rust and Kumar (1994b)**** calculated that a constant ******** fluxrope **
**	****	****becomes unstable for L******** > 3.7******** or  ****H****t****>1.85********2**** **** .  This compares**
**	****	****favorably with the criterion for MHD instability at  ****H****t****>1.25********2****  of**
**	****	****Hood (1991)****.**
**	****	****In the figures we show both limits and their relationship to the**
**	****	****injected helicity.**

****** ****~ 6 x 10****19**** Mx**

## Aug 8-10 2000: Energization and Helicity Charging

**SXT Flux determined from**
**composite (long+short exps.)**
**images**

**Cumulative energy storage **
**and helicity for X-ray sigmoid**

**As helicity injection exceeds the critical limit of ****Hood (1991)****, H****crit****=1.25********2****, sigmoid reaches maximum spatial extent (Frame C).  However, the upper limit corresponding to the ****Rust and Kumar (1994a)**** instability criterion is not attained.**

****** ****= magnetic flux**

**A**

**B**

**C**

**D**

## August 15-18, 1999  (WL, 1600 A,  171 A)

## August 15-18, 1999      (WL, 1600 A,  171 A)

## August 15-18, 1999

- A sigmoid structure can be seen in the Yohkoh/SXT images (top and third row), which are compared to H-alpha images (second and last rows) from Big Bear Solar Observatory. The images are for the six August days of 16-21 at ~14:00-16:00 UT. (Figure taken from Yohkoh/SXT Science Nugget of December 17, 1999.)

## Aug 15-18 1999: Energization and Helicity Charging

**Cumuulative energy storage and helicity for X-ray sigmoid**

**In this case, helicity injection exceeds the ****Rust and Kumar (1994b)**** instability criterion, H****t**** > 1.85********2****.  At this time the X-ray sigmoid exhibits a substantial growth in brightness and erupts (see ****Gibson et al., 2002****).**

**Aug 17   13:35         Aug 17   16:51          Aug 17   19:02          Aug 18  08:44**

**HOUR               61.5                             65                                67                             81**

## Conclusions

** ****Results are preliminary but seem to indicate that helicity charging **
**   ****generated by sunspot rotation is critical to the eruption (or `not’) of their **
**   ****associated X-ray sigmoids.**
** ****For both sigmoids considered the helicity injection due to the observed **
**   ****sunspot rotation exceeded the critical limit for instability defined by ****Hood **
**    ****(1991)****, H****crit**** = 1.25********2****.  But only in the sigmoid spanning Aug 17 1999 did the **
**   ****helicity injection exceed the instability limit identified by ****Rust and Kumar **
**    ****(1994b) ****(RK), H****crit**** = 1.85********2****.  The attainment of the Hood critical helicity was **
**   ****accompanied by a brightening of the sigmoid in the Aug 2000 case, while **
**   ****the attainment of the RK critical helicity in the Aug 1999 case resulted in **
**   ****an eruption of the sigmoid.**
** ****The evolution of a sigmoid prior to eruption typically shows significant but **
**   ****low level activity (C-flares, X-ray brightness variations).  This needs **
**   ****further investigation but may be a result of quasi-steady dissipation of the **
**   ****type described by ****Somov and Syrovatskii (1979)****, which `bleeds’ energy from **
**   ****the sigmoid, heating it to X-ray temperatures, without significantly **
**   ****impacting its overall growth in growth in free energy and helicity.**