A Quantitative, Topological Model of Reconnection and Flux Rope Formation in a Two-Ribbon Flare † Dana Longcope & Colin Beveridge Montana State University I. Sheared Arcade II. Infinite Arcade III. Finite Arcade IV. Energy V. Rconnection † Work supported by NSF 1
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A Quantitative, TopologicalModel of Reconnection andFlux Rope Formation in a
Two-Ribbon Flare†
Dana Longcope & Colin Beveridge
Montana State University
I. Sheared Arcade
II. Infinite Arcade
III. Finite Arcade
IV. Energy
V. Rconnection
† Work supported by NSF
1
The 2-ribbon flare
◦ Classical (2d) CSHKP model — (a)
(Carmichael 1964; Sturrock 1968; Hirayama 1974; Kopp and Pneuman 1976)
(b)(a)
A
X
CS XA
RR
S FR
P
C
CC
C
PIL
PIL
◦ 3d generalization (b) — (Gosling 1990; Gosling et al. 1995)
◦ Recon’n flux: magnetic flux swept by flare ribbons (R)
(Forbes & Priest 1984; Poletto & Kopp 1986; Fletcher et al. 2001; Qiu et al. 2002)
◦ Ejected flux rope (FR) → Magnetic Cloud (MC) at 1 AU
(Burlaga et al. 1981; Lepping et al. 1990)
We seek a 3d model quantifying. . .
? Energy storage (vs. shear)
? Reconnected flux (vs. shear)
? Flux in twisted rope (vs. shear)
? Twist in rope (vs. shear)
2
I. The Sheared Arcade
θ
aS/2
a/2
PIL
Photopsheric Flux:◦ Parallel bands of opposing flux
◦ Separated by a◦ Each with Φ′ flux per length◦ Some distribution (profile)within bands◦ May have finite extent L (§III)or L = ∞ (§II)◦ Shear: relative ‖ disp’ment: aS.◦ θ = cot−1S.
- Isolated arcade (Klimchuk et al. 1988, Choe & Lee 1996)
◦ Free magnetic energy: ∆W = W −Wpot
◦ ∆W increases with shearing S — errupts for S ∼> 5
◦ Klimchuk et al. 1988 derive empirical expression:
∆W = Wpot c1 ln(1 + c2S2) , (1)
c1 ' 0.7684 and c2 ' 0.5530
◦ Potential energy depends on profile (through K)
Wpot
L=
K
8π(Φ′)2 , (2)
Gaussian profile: K = 1; Lorentzian profile: K = π/4
3
A Topological Model
θ
x
aS/2
N5
P6
N6
a/2
PIL
N9N8N7
P3 P4 P5 P7
∆
◦ Break bands into segments: ∆x◦ Each contains ψ0 = Φ′∆x◦ Field from source: mutlipoleexpansion ◦ Before shear:1. Pi and Ni are opposite2. B is potential◦ Shear separates Pi from Ni
◦ Domain i–j: connects Pi to Nj.◦ Flux in domain: Ψi–j
◦ shaded: P6—N7Potential Field:◦ Nulls (4 & 5) between sources◦ B6/7 between P6 and P7 (5)
◦ Flux:Ψ(v)i–j
◦ Separators connect nullpoints —enclose domains
◦ Initial field: Ψ(v)i–j = ψ0 δij
Pi connected 100% to Ni — nothing else
◦ Shearing changes potential field — P6 and N7 approach
Ψ(v)6−7 ' S
a
∆xψ0 = SaΦ′
4
II. The Infinite Arcade — energy storage
◦ w/o reconnection actual field does not chage: Ψ6−7 = 0
- Self-helicity remaining after mutual helicity is gone
up to Hselfi /2πΨ2
i ∼ 10 turns
- Compare to (cot−1S)/2π = 0.15 turns from shear
17
Reconnection: — The consequences
spines: rims of
reconnected domains
B. Flare ribbons
◦ Total reconnection: ∆ψσ depends on S (approx’ by MCC)
◦ Subsequent generations increase in height
◦ Ribbon motion NOT approximated
Actual reconnection (2d)
MCC reconnection (2d)
18
References
Biskamp, D., & Welter, H. 1989, Solar Phys., 120, 49Burlaga, L., Sittler, E., Mariani, F., & Schwenn, R. 1981, JGR, 86, 6673Carmichael, H. 1964, in AAS-NASA Symposium on the Physics of Solar Flares, ed. W. N. Hess
(Washington, DC: NASA), 451Choe, G. S., & Lee, L. C. 1996, ApJ, 472, 360Fletcher, L., Metcalf, T. R., Alexander, D., Brown, D. S., & Ryder, L. A. 2001, ApJ, 554, 451Forbes, T. G., & Priest, E. R. 1984, in Solar Terrestrial Physics: Present and Future, ed.
D. Butler & K. Papadopoulos (NASA), 35Gosling, J. T. 1990, in Geophys. Monographs, Vol. 58, Physics of Magnetic Flux Ropes, ed.
C. T. Russel, E. R. Priest, & L. C. Lee (AGU), 343Gosling, J. T., Birn, J., & Hesse, M. 1995, GRL, 22, 869Hirayama, T. 1974, Solar Phys., 34, 323Klimchuk, J. A., Sturrock, P. A., & Yang, W.-H. 1988, ApJ, 335, 456Kopp, R. A., & Pneuman, G. W. 1976, Solar Phys., 50, 85Lepping, R. P., Burlaga, L. F., & Jones, J. A. 1990, JGR, 95, 11957Longcope, D. W. 1996, Solar Phys., 169, 91Longcope, D. W., & Magara, T. 2004, ApJ, 608, 1106Mikic, Z., Barnes, D. C., & Schnack, D. D. 1988, ApJ, 328, 830Poletto, G., & Kopp, R. A. 1986, in The Lower Atmospheres of Solar Flares, ed. D. F. Neidig
(National Solar Observatory), 453Qiu, J., Lee, J., Gary, D. E., & Wang, H. 2002, ApJ, 565, 1335Sturrock, P. A. 1968, in IAU Symp. 35: Structure and Development of Solar Active Regions,
471Wright, A. N., & Berger, M. A. 1989, JGR, 94, 1295