EGU General Assembly 2011 Occurrence Frequency of Interplanetary Magnetic Flux Ropes K. Marubashi, Y.-H. Kim, K.-S. Cho, Y.-D. Park, K.-C. Choi, S. Choi, and J.-H. Baek (KASI: Korea Astronomy and Space Science Institute)

OUTLINE We searched for magnetic field structures which can be well fitted to the force-free flux rope models, in the solar wind data from WIND/ACE (1995 – 2009). The most important finding is: “The number of such structures is far, far, far more than those implied by previous surveys.” Why it happened? How it is possible?  Identification of large impact parameter events  Events that can be explained only by torus model

Lepping et al. (2006) Occurrence frequency: very low MCs and MC-like structures: follow the change of SSN. Previous MC Surveys Klein & Burlaga (1982) Zhang & Burlaga (1988) Lepping et al. (1990) Bothmer & Schwenn (1998) Marubashi (2000) Lynch et al. (2005) Huttunen et al. (2005) Lepping et al. (2006)

Present Result: Year-to-year variation of occurrence number (Conditions: Duration >= 7 hours, Erms < 0.35) torus cylinder (some part: torus) Occurrence : (1) much higher than hitherto believed (2) yearly change in parallel to solar activity CYLINDER, CYLINDER & TORUS: 440

Two mathematical models (cylinder & torus) S/C passing near the apex: Local Structure can be approximated by a cylinder shown by dashed line. S/C passing near the flank: Curvature effects should be taken into account, and the simplest approximation Is given by a torus geometry. Torus model: to describe local geometry, not indicating the whole structure were torus Cylinder model Torus model

An example: Only “torus model” can reproduce the observations (Duration = 43 hours, Rotation of the filed = 330 deg)

Statistical Distribution of “cylinder parameters” (Conditions: Duration >= 7, Erms < 0.35, Cone angle < 10) Finding: Occurrence increases with impact parameter. Note: Circled portions need further consideration.

Further Selection (Exclude extreme cases) 1. Impact parameter (p): |p| < 0.98 Geometries may not be reliable. This condition excludes many events of R > 0.2 AU. 2. Duration (Td): Td < 30 hours Many of long-duration events are better fitted to torus model. 3. Cone Angle (Ac): Ac > 10 degrees (already adopted) Small Ac events need torus-fitting. This condition excludes many events of small R. (Note: Criteria for p, Td, Ac need further consideration.)

Statistical Distribution of Cylinder Parameters (Modified: |p| 10 deg) excluded mostly excluded Increase with |p|: main reason for the large occurrence

Lepping and Wu (2010): occurrence vs. Impact Parameter We need to admit that only small I.P. cases were studied so far. (They are easy to identify due to large angle rotation of B vector)

Possible|p|dependence of detected event number  p (dark blue) < p (light blue)  Cylinder axes correspond to tangent lines to 2 circles. Consider in 2-D (YZ-plane): If angular distributin is uniform, number is propotional to r (p).

Distribution of the cylinder axis direction (Lat. & Long.) N = 325 (to Sun)

Distribution of Cone Angles 7 hrs =< Td < 30 hrs |p| < 0.98 Cone angle > 10 deg If the axis orientation is uniformly distributed, the event numbers should be constant in this diagram. At cone angles 20~75, it looks to be satisfied.

Most probable distribution of MC cylinder radii (241 events: 20 deg =< Cone angle < 75 deg) We expect a similar radius distribution for torus events.

Concluding Remarks 1. We could identify ~ 500 flux rope structures in the solar wind data of , their occurrence frequency changes with sunspot activity. (much, much larger number) 2. The flux rope detection rate increases with the impact parameter, in agreement with simple geometrical consideration. We are preparing a website to provide all the fitting results.

Thank you for your attention!