Flux Rope from Eruption Data FRED and its

Flux Rope from Eruption Data (FRED) and its Interplanetary Counterpart Nat Gopalswamy NASA Goddard Space Flight Center S. Yashiro, S. Akiyama, H. Xie The Catholic University of America ISEST/Mini. Max 24 Jeju Sep 18 -22, 2017

Motivation • All CMEs reaching 1 -AU seem to have flux rope structure (irrespective of observed MC or non. MC structure of ICMEs) • All ICMEs are associated with post-eruption arcades at the Sun; similar in MC and non-MC sources (Yashiro et al. 2013) • near-Sun and 1 - AU flux rope fits (Marubashi et al. 2015) to MC and non-MC events • Similar heavy-ion charge states requiring flare plasma injection into flux ropes (Gopalswamy et al. 2013) • On the other hand CME arrival models use a pressure pulse or ad hoc magnetic structures as input • Needed: a realistic flux rope input – Flux Rope from Eruption Data (FRED) Mouschovias and Poland, 1978 • Both geometrical and magnetic properties of a coronal flux rope can be obtained from eruption data • Post-eruption arcade, LOS magnetogram, white-light CME data under the assumption of cylindrical force-free flux rope

Simultaneous Onset of Flare & CME Reconnection at * ** * * • van Ballegooijen & • Martens, 1989 • Gosling 1990 • Longcope et al. 2007 • Qiu et al. 2007 • Two magnetic structures during eruption: • Post eruption arcade • Flux rope (CME) Gopalswamy 2009

Flux Rope Fit to White-light CMEs • Krall & St Cyr (2006) single view (SOHO/LASCO) • Thernisien (2011) Multiview (STEREO/SECCHI) • Geometrical properties: flux rope radius, leading-edge height, aspect ratio • Main parameter we use: R 0/Rtip • Related to the kappa parameter in the GCS model (Thernsien 2011) Λ = 2 R 1/d = R 1/R 0 Rtip Krall & St Cyr (2006); Krall (2007)

Magnetic Properties • Coronal flux rope can be constructed using Φr and CME flux rope fit • If CME flux ropes are formed during eruption, then the total reconnected (RC) flux (Φr) is same as the poloidal flux (Φp) of the resulting FR: Φr ≈ Φp (Longcope et al. 2007; Qiu et al. 2007; Hu et al. 2014; Gopalswamy et al. 2017) • Φr can be computed using the photospheric B underlying cumulative ribbon area (Longcope et al. 2007; Qiu et al. 2007; Kazachenko et al. 2017) • CME and flare properties closely related to Φr • Coronal flux ropes can be tracked and compared with 1 -au flux ropes P • Φr can also be computed in a simpler way as half the flux underlying post eruption arcades (Gopalswamy et al. 2017) r ribbons Longcope et al. 2007

Reconnected Flux fro PEA Photospheric flux in the area under the post eruption arcade in the flare decay phase gives 2Φr. A GOES C 4. 1 flare There is good agreement between RC fluxes obtained from Ribbon (Φr. R) and Arcade (Φr. A) methods: Φr. A = 1. 24(Φr. R)0. 99 ΦP = 1. 29(Φr)0. 85 Cumulative flare-ribbon area (A) is projected on photospheric magnetogram to get the reconnected (RC) flux Φr. R =BA, where B is the average magnetic field (Qiu et al. 2007) The RC flux (Φr) is also significantly correlated with the poloidal flux (ΦP) of the associated magnetic clouds Gopalswamy et al. 2017, Solar Phys. 292, 65

Soft X-ray Flare Size and Fluence Kazachenko et al. 2017 • The RC flux is well correlated with flare size and flare fluence • The flare fluence has a better correlation • True for both MCs and Ejecta Gopalswamy et al. 2017 JASTP

CME Speed and Kinetic Energy (a) (a ) • Both speed and kinetic energy of the CMEs are well correlated with the RC Flux (r = 0. 60, 0. 69) • The higher the RC Flux, the faster are the CMEs • KE has the second highest correlation with RC flux (the highest was with soft X-ray flare fluence) One event (2000 October 2) was excluded from the correlations because the arcade was ill-defined. Diamonds – no mass data, so 1016 g assumed Gopalswamy et al. 2017 JASTP • True when the CMEs ended up as MCs or ejecta

Force-free Flux Ropes • Φp = (L/x 01)B 0 R 0 L-FR length; R-radius; Ba-axial field strength • Φt = (B 0 R 02/x 01) 2πJ 1(x 01) - 1 st order Bessel function; J 1 (x 01) =0. 5192 • Bp = HB 0 J 1(αr) with H = ± 1 (helicity sign) • Bt = B 0 J 0(αr); J 0 – zeroth order Bessel, x 01 - its zero; α = x 01/R 0 • Hr/L = 0. 7 B 02 R 03 Φt /Φp = (R/L) 2πJ 1(x 01) = 1. 63 R/Rtip • Φp from Φr • L, R 0 from FR fit to white-light data • H from PEA skew or hemisphere rule • Get flux rope B 0 in the corona or any other heliospheric location

Helicity sign: positive (RH) tilt angle -47 deg Example: 2012 July 12 Area = 7. 2× 1019 cm 2, <B> = 392 G; RC Flux = 1. 42× 1022 Mx Gopalswamy et al. 2017 IAU 335

Flux Rope Fit to white-light CME Direction: S 15 W 01 tilt = -53 deg Aspect ratio = 0. 31 R 0/Rtip = 0. 26 At Rtip = 10 Rs, R 0 = 2. 6 Rs At Rtip = 1 AU R 0 = 0. 26 AU Hess & Jang 2014 B 0 = Φrx 01/R 0 L = 0. 13 G axial field strength (L = 2 Rtip =20 Rs) Self-similar expansion B 01 au = B 0 (10/214)2 = 28. 3 n. T

Consistency Check • V = 298φr 0. 75 (Gopalswamy et al. 2017 JASTP) • V = 1548 km/s • φr = 9. 0× 1021 Mx vs. observed 1. 42× 1022 Mx • Hr/L = 0. 7 B 02 R 03 • Coronal FR: Hr = 9. 98 × 1043 Mx 2

1 - AU Flux Rope Bt ~ 30 n. T, not too different from the estimate from coronal value MC size at 1 AU =0. 26 AU (self similar expansion) MC duration = 0. 26 AU/500 km/s = 22 h (average MC speed 500 km/s) Similar to GS size (Hu et al. 2016) Hess & Zhang 2014

Coronal Flux Rope B 0 vs. 1 -AU Bt • Cycle 23 Eruptions (CDAW) • Krall & St Cyr flux rope • MCs and non-MCs considered • Correlation significant with p = 0. 005 Btot = 21. 9 logφr− 453. 2 n. T For φr = 1. 42× 1022 Mx Btot = 31. 9 n. T - another consistency check Gopalswamy et al. 2017 IAU 335

Summary • Flux ropes can be completely defined near the Sun using eruption data (photospheric B, PEA, and ME in white-light or EUV), RC flux being the fundamental quantity • RC flux is highly correlated with Flare fluence and CME kinetic energy • Possibility of flux rope formation during eruption: the flux of pre-existing flux rope if any is very small • Axial field magnitude and direction determine asymptotic flux rope properties