Magnetic structure of the disk corona Slava Titov, Zoran Mikic, Alexei Pankin, Dalton Schnack SAIC,...

Magnetic structureMagnetic structureof the disk coronaof the disk corona

Slava Titov, Zoran Mikic, Alexei Pankin, Dalton SchnackSAIC, San Diego

Jeremy Goodman, Dmitri UzdenskyPrinceton University

CMSO General Meeting, October 5-7, 2005Princeton

2

2D case: field line connectivity and topology

normal field line

NP separtrix field line

BP separtrix field line

Flux tubes enclosing separatrices split at null points or "bald-patch" points. They are topological features, because splitting cannot be removed by a continous deformation of the configuration. Current sheets are formed at the separatrices due to footpoint displacements or instabilities.

All these 2D issues can be generalized to 3D!

3

Differences compared to nulls and BPs: •squashing may be removed by a continuous deformation, •=> QSL is not topological but geometrical object, •metric is needed to describe QSL quantitatively, •=> topological arguments for the current sheet formation at QSLs are not applicable;

other approach is required.

Extra opportunity in 3D: squashing instead of splitting

Nevertheless, thin QSLs are as important as genuine separatrices for this process.

4

Definition of Q in coordinates:                                                           

where a, b, c and d are the elements of the Jacobian matrix                                                                          

D and then Q can be determined by integrating field line equations.

  Geometrical definition:

Infinitezimal flux tube such that a cross-section at one foot is curcular,

then circle  ==>   ellipse:

      Q = aspect ratio of the ellipse;

Q is invariant to direction of mapping.

Squashing factor Q

(Titov, Hornig & Démoulin, 2002)

5

  Geometrical definition:

Infinitezimal flux tube such that a cross-section at one foot is curcular,

then circle  ==>   ellipse:      K = lg(ellipse area / circle area);

K is invariant (up to the sign) to the direction of mapping.

Expansion-contraction factor K

Definition of K in coordinates:                                                           

where a, b, c and d are the elements of the Jacobian matrix                                                                          

D and then Q can be determined by integrating field line equations.

6

What can we obtain with the help of Q and K?

1. Identify the regions subject to boundary effects.

2. Understand the effect of resistivity.

3. Identify the reconnecting magnetic flux tubes.

7

Example (t=238)Exact ideal MHD Numerical MHD

log Q

1 2

-10 0 10

From the initial B(r)and vdsk(rdsk,t) only!

From thecomputed B(r,t).

8

Example (t=238)Exact ideal MHD Numerical MHD

K

-1 0 1

-10 0 10

9

Example (t=238)Exact ideal MHD Numerical MHD

log Q

1 2

-10 0 10

K

-1 0 1

10

Helical QSL (t=238)

Magnetic field lines Launch footpoints

11

Conclusions

Evolving Q and K distributions make possible:

1. to identify the regions subject to boundary effects,

2. to understand the effect of resistivity,

3. to identify the reconnecting magnetic flux tubes (helical QSL).