Energy and Helicity in Emerging Active Regions Yang Liu, Peter Schuck, and HMI vector field data team

Outline Energy and helicity in three emerging active regions; Test with Demoulin & Berger’s model (2003; DB03).

Calculation of energy and helicity fluxes emerging termshear term emerging term shear term B h, B n (obs), and V h, V n (obs + DAVE4VM)

Case 1: AR11072—a simple AR

B_n (image) + V_h (arrows)

B_n (image) + V_n (contours)

B_n (image) + B_h (arrows)

Summary (For AR11072, a simple bipolar AR): 1.Helicity flux from shear term is dominant. It follows magnetic flux emergence, but with a lag in phase; 2.Helicity flux from emergence term is small during flux emergence, implying that the emerging field is initially close to potential field; 3.Helicity fluxes from both terms have the same sign.

Summary: 1.Energy flux from shear term varies following flux emergence, and approaches to zero after emergence stops; 2.Energy flux from emergence term has a delay in phase with the flux emergence, but keeps certain level after the emergence stops.

Summary (AR11072-simple AR) Helicity Flux across the photosphere –Helicity flux from shear term is dominant, varying with magnetic flux emergence, but with a small lag in phase, approaching to zero after emergence stops; –Helicity flux from emergence term is rather small, implying the initial emerging field is close to potential; –The signs of the helicity fluxes from both terms are the same. Energy Flux across the photosphere –Energy flux from shear term varies with flux emergence, and approaches to zero after emergence stops; –Energy flux from emergence term has a delay in phase with the flux emergence, and keeps substantial level after emergence stops. Major contribution is from the strong upflows surrounding sunspots.

Case 2: AR11117—multipole AR

B_z (image) + V_h (arrows)

B_z (image) + V_n (contours)

B_z (image) + B_h(arrows)

Summary (For AR11117, a multipole AR): 1.Helicity flux from shear term is dominant. It follows magnetic flux emergence; 2.Helicity flux from emergence term is small during flux emergence, implying that the emerging field is initially close to potential field; 3.Helicity fluxes from both terms have the same sign in most of time.

Summary: 1.Energy flux from shear term varies following flux emergence; 2.Energy flux from emergence term has an outstanding delay in phase with the flux emergence.

Summary (AR11117-multipole AR) Helicity flux –Helicity flux from shear term is dominant, and variation of the helicity flux follows flux emergence; –Helicity flux from emergence term is small, implying emerging field is originally close to potential field; –Both fluxes are the same sign during flux emergence. Energy flux –Energy flux from shear term follows flux emergence; –Energy flux from emergence term shows a delay in phase with flux emergence. Major contribution is from the upflows surrounding sunspots.

Case 3: AR11158-a very complex AR

Summary (For AR11158, a very complex AR): 1.Helicity flux from shear term is dominant. It follows magnetic flux emergence with a lag in phase. It becomes even higher after emergence stops. It implies that strong surface flows still work then. 2.Helicity flux from emergence term is small during flux emergence, implying that the emerging field is initially close to potential field; 3.Helicity fluxes from both terms have the same sign in most time.

Summary: 1.Energy flux from shear term varies following flux emergence; 2.Energy flux from emergence term has a delay in phase with the flux emergence. It keeps fairly high flux level after emergence stops.

Summary (AR11158-complex AR) Helicity flux –Helicity flux from shear term is dominant, and variation of the helicity flux follows flux emergence with a phase lag. It becomes even higher after emergence stops. –Helicity flux from emergence term is small during flux emergence, implying emerging field is initially close to potential field. –Both fluxes are the same sign during flux emergence. Energy flux –Energy flux from shear term follows flux emergence; –Energy flux from emergence term shows a delay in phase with flux emergence. It keeps fairly high level after emergence stops. Major contribution is from the upflows surrounding sunspots.

Test with Demoulin & Berger’s model (2003)—DB03 model Using DAVE (Schuck 2006)  u

Summary (DB03 model) Horizontal velocity derived by tracking the photospheric footpoints of magnetic flux tubes is close to horizontal plasma velocity, but may not be the combination of horizontal and vertical velocities, as predicted in DB03 model; However, as helicity flux from shear term is dominant, the helicity computed from DB03 model is close to the total helicity; The energy from DB03 model cannot be deemed as the total energy—significant difference is seen.

Conclusions Helicity flux across the photosphere: –Helicity flux from shear term is dominant. Its variation is consistent with flux emergence (may has a phase lag). – Helicity flux from emerging term is small. It implies that the emerging field is initially close to potential. –Both fluxes have the same sign during emergence. Energy flux across the photosphere –Energy flux from shear term is consistent with the flux emergence in phase. It approaches to zero after emergence stops. –Energy flux from emerging term shows an outstanding delay in phase with the flux emergence, and it keeps fairly high level after emergence stops. Upflows surrounding sunspots contributes substantially energy flux. DB03 model –The horizontal velocity derived by tracking the photospheric footpoints of magnetic tubes is close to the horizontal plasma velocity; –The helicity estimated by DB03 model is close to total helicity, while the energy from DB03 model is significantly away from the total energy.