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Self-similar evolution of fast magnetic reconnection in free-space: A new model for astrophysical reconnection Shin-ya Nitta The Graduate University for Advanced Studies, Hayama Center for Advanced Studies E-mail:

  1. Self-similar evolution of fast magnetic reconnection in free-space: A new model for astrophysical reconnection Shin-ya Nitta 新田 伸也 The Graduate University for Advanced Studies, Hayama Center for Advanced Studies E-mail: snitta@koryuw02.soken.ac.jp §Introduction Magnetic reconnection is ・ Very powerful energy converter ・ Very common in the universe e.g., Solar Flares

  2. §§Astrophysical Reconnection Astrophysical Reconnection is characterized by huge dynamic range of expansion e.g., Solar flares Initial system scale (Initial Current Sheet Thickness ) Final system scale (Maximum scale of reconnection system ) ⇩ intrinsically Time-Dependent Should be treated as Spontaneous Evolution in Free Space Cannot be described by previous models! Aim of this work Suitable reconnection model for astrophysical application? ⇩ Self-Similar Evolution

  3. §Evolution Process 1) Onset (Resistive Stage) Sweet-Parker-like or tearing ⇩ Formation of Fast-mode Rarefaction Wave , - )*+) . !"##$%& ! '($$& ./00"1/2% ! *$3/2% 2) Induction of Inflow Propagation of FRWF ⇩ Induction of Inflow !"#$%& 3) Similarity Stage (Petschek-like at center) Formation of Slow-Shock ⇩ Fast-mode Rarefaction Dominated (Petschek-like) Fast Reconnection

  4. §Numerical Approach y Initial Equilibrium （ Harris solution ） Resistive � Region 2D D: � Initial � Current � Sheet � Depth x Current � Sheet Code: 2-step Lax-Wendroff Parameters & Normalization Parameters Normalization ⇨

  5. §§Simulation Result Self-Similarly Expanding ！ with Fast-mode Rarefaction Wave Front

  6. §Analytical Approach §§Inflow Region Zoom-out coordinate Linear perturbation method Equilibrium (0th)+Deviation (1st) by reconnection Grad-Shafranov Eq.

  7. § § Solution for Inflow Region Fairly Consistent!

  8. §§Reconnection Outflow Quasi-1D structure divided by several discontinuities Reconnection jet collides with current sheet plasma " !!! %2-:*2:-8 ! '@ ! -8*'118*24'1 ! ':2@&'( %&'( ! %)'*+ 7898-58 ! ,.52 ! %)'*+ #$%&'( ! %)'*+ 0'12.*2 ! 345*'16 -8;4'1 ! < 0:--812 ! -8;4'1 ! = -8;4'1 ! > -8;4'1 ! ? %)882 ! @ ! * ! 5 ! ⇩ ,'-(.-/ ! %&'( ! %)'*+ Shock tube approximation 22 eqs. (junction conditions) for 22 unknowns ⇩ Quantities in outflow spontaneously determined!!

  9. §§Reconnection Rate Reconnection Rate vs. beta !"!( !"!' !"!& -Vyp*Bxp !"!% !"!$ !"!# ! !"!!!# !"!!# !"!# !"# # #! #!! #!!! Beta0 Rec. rate R ~ 0.05 for low β (almost const. indep. of β ) ⇧ Spontaneous inhalation of inflow (induced by fast-mode rarefaction)

  10. Reconnection Rate vs. Mag. Reynolds Num. !"# -Vyp*Bxp+Vxp*Byp !"!# #! #!! Rem* (Rem* ≡V A0 /V dif *) converging inflow: |Vxp| ↑ as Rem* ↑ ⇨ Vp, Bp → parallel at inflow region ! S S L S S D R R ≡ Vp × Bp ∝ Rem*^(-1) "

  11. §Observational Inspection We can inspect Self-Similar Model by Solar-B “Dimming” around reconnection point ⇧ Rarefied region by FRW Emission Measure 1.00 1.000 0.80 0.60 0.930 y 0.40 1.040 0.20 0.715 1.185 0.00 0.00 0.20 0.40 0.60 0.80 1.00 Existence of inflow ~1 0[km/s] x Expanding in V A0 ~1 000[km/s] Duration ~1 00[s]

  12. §Summary Spontaneous Evolution of Fast Magnetic Reconnection in Free Space ⇩ Self-Similar Solution （ verified by numerical simulation/analytical study ） A new model of Magnetic Reconnection Self-Similar Evolution of Fast Reconnection Properties ・ Expanding with propagation of FRW ・ Petschek-like structure in central region （ Fast-mode rarefaction dominated ） ・ Reconnection rate R ~ 0.05 (for small Rem*<20, insensitive to β ) ⇦ spontaneous inhalation of inflow ・ Reconnection rate R ∝ Rem*^(-1) (for large Rem* ≫2 0, insensitive to β ) References Nitta, Tanuma, Shibata, Maezawa ApJ, 550, 1119 (2001) Nitta, Tanuma, Maezawa ApJ, 580, 538 (2002) Nitta ApJ, 610, 1117 (2004)

  13. §§Simulation Result Evolution in Zoom-Out Coordinate Features of reconnection system Self-Similarly Expanding ！ with propagation of Fast-mode Wave Front

  14. Reconnection Rate vs. Mag. Reynolds Num. !"# -Vyp*Bxp+Vxp*Byp !"!# #! #!! Rem* R ≡ Vp × Bp ∝ Rem*^(-1) (Rem* ≡ V A0 /V dif *) ⇧ converging inflow: |Vxp| ↑ as Rem* ↑ ⇨ Vp, Bp → parallel at inflow region ⇨ R ≡ Vp × Bp ↓

  15. A new model of magnetic reconnection: Self-similar evolving model Shin-ya Nitta 新田 伸也 The Graduate University for Advanced Studies, Hayama Center for Advanced Studies E-mail: snitta@koryuw02.soken.ac.jp §Introduction Magnetic reconnection is ・ Very powerful energy converter ・ Very common in the universe e.g., Solar Flares

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