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Large Scale MHD Properties of Interplanetary Magnetic Clouds:  Large Scale MHD Properties of Interplanetary Magnetic Clouds S.Dasso1, C.H.Mandrini1, P.Dèmoulin2, M.L.Luoni1, and A.Gulisano1 1 Instituto de Astronomía y Física del Espacio (IAFE), UBA-CONICET, Buenos Aires, Argentina. 2 Observatoire de Paris, LESIA, 92195 Meudon Cedex, France. ASSE, 23-27 March, 2004, San Jose dos Campos, Brasil Outline:  Outline Brief Introduction to Interplanetary Magnetic Clouds (MCs) Technique and Data Analysis Magnetic Helicity (H) and Flux in Cylindrical Structures Estimation of H for MCs Results of Studied Events and Comparison of H in MCs with estimations of release of H from their coronal source Conclusions Common Signatures of Interplanetary Coronal Mass Ejections (ICMEs) observed in situ at ~ 1AU:  Common Signatures of Interplanetary Coronal Mass Ejections (ICMEs) observed in situ at ~ 1AU Strong magnetic field [Burlaga & King, JGR 1979] Low proton temperature [Gosling et al., JGR 1973; Richardson & Cand, JGR 1995] Large and coherent rotation of the magnetic vector (helix) [Bulaga et al., JGR 1981] Bi-directional flows (E>80eV) electron fluxes [Montgomery et al., JGR 1974; Gosling, JGR 1987] Bi-directional flows (E~KeV-MeV) proton fluxes [Mardsen et al., JGR 1987; Galvin et al., JGR 1987] Highly variable abundance of Helium (0-20%) [Borrini et al., JGR 1982; Galvin et al., JGR 1987] Unusual ionization states [Galvin et al., JGR 1987] Typical speed ~300-600 km/s [Cane & Richardson, JGR 2003] Te>>Tp [Osherovich et al., JGR, 1993; Richardson et al., JGR 1997] Tp//>Tp (Tp//~10Tp) [Galvin et al., JGR 1987] Te//>Te (Te//~3Te) [Pillip et al., JGR 1987; Gosling et al., JGR 1987] Excitation of EM Waves (~p ~1Hz) [Dasso et al., JGR 2003] Level of magnetic fluctuations lower than in SW [Pudovkin et al., JGR 1979; Torsti et al., ApJL 2004] (known as Magnetic Cloud) Slide4:  Spacecraft Observations (MFI/Wind): MC observed on Oct 18-19, 1995 From Lepping et al. [JGR, 1997] Coherent Rotation of B Velocity profile flat (old cloud without significant expansion) Shock wave in front (A) and internal (C) Magnetic hole (B): reconnection? Alfén waves activity after the MC Slide5:  In situ observations indicate that the field of a Magnetic Cloud can be described as a (locally) cylindrical flux tube [Farrugia et al., JGR, 1995] Magnetic Clouds in the Interplanetary Medium How is its detailed magnetic structure? And its magnetic connectivity with the Sun? It is not clear when and how is the magnetic recconection between the MC and the SW What is the right meaning of the observed bidirectional flux of electrons and protons? In situ measurements from spacecrafts (S/C) can only observe linear cuts of the structure of the cloud:  In situ measurements from spacecrafts (S/C) can only observe linear cuts of the structure of the cloud From [Bothmer & Schwenn, AnnGeophys 1998] When p~0 Minimum Variance Method to find the orientation of the tube:  Minimum Variance Method to find the orientation of the tube [e.g., Bothmer & Schwenn, AnnGeophys 1998] The extremes (conditioned |n|=1, Lagrange) of 2n are given by the eigenvectors of M (M•n=n), with i =i2 The orientation of the tube is needed to determine its radius and the trasformations from observed (GSE) to local coordinates (MCs frame) The Magnetic Helicity is extensive, and so it depends on the size Slide8:  Two Crucial Magnetic Quantities in MHD Magnetic Flux () across a surface (S): Magnetic Helicity (H) contained in a volume V: For a given time, =0 when S is closed (Gauss + •B=0), then in=out Ideal MHD  d/dt=0 for a material S (e.g., a material moving slice of a magnetic flux tube) H is an ideal invariant ( is the magnetic diffusivity) H decays more slowly than the total energy Magnetic Helicity: Why?:  Magnetic Helicity: Why? MH is a well conserved quantity on time scales of 105 years (from classical difussion) [Berger, Geophys. Astrophys. Fluid Dyn. 1984] In 3D, in a turbulent regime, it cascades to the largest scales MH allows us to track the flux from its formation to the heliosphere, linking:  the convective zone  the corona  the interplanetary medium It quantifies features of magnetic field structures Recents estimations of MH in corona [e.g., Dèmoulin et al., A&A 2002] MH has not been yet sufficiently analyzed in MCs From Berger [Plasma Phys. Control. Fusion, 1999] But!, because the gauge fredom (A’=A+) H is not always well defined, and H can have different values for a given B configuration:  But!, because the gauge fredom (A’=A+) H is not always well defined, and H can have different values for a given B configuration Magnetic Helicity When Bn= B•n=0  S(V), H is Gauge Invariant Relative Magnetic Helicity:  Relative Magnetic Helicity (Gauge invariant) When Bn0: The Relative Helicity (Hr) is Gauge Invariant [Berger&Field, JFluidMech 1984] Hr does not depend on the extension of B nor of B0 outside V Hr is gauge invariant Slide12:  Cylindrical Fields: B=Bz(r)z + B(r) If we choose B0=Bz(r)z (a non-twisted potential Field) A0=Az(r=R)z + A(r) Exercises: Verify that with this option to B0 and A0: (i) B0,n= Bn on S(V) for a cylindrical volume located and oriented as the symmetrical field, and (ii) xA0=B0 , b) Using the defined reference field (B0) and its vector potential (A0), show the following relationships Thus: Slide13:  Estimation of H from Direct Observations Under this symetry: The Magnetic Helicity can be expressed here as the contribution of the azimuthal field weighted by the accumulated axial Flux ()  and Hr/L can be computed with the only assumption of cylindrical symetry as hypothesis (without any model to the magnetic configuration), from: The direct observations {B(t1), B(t2), ..., B(tN)} (InBound/OutBound) MV (for the rotation matrix R) [Dasso et al., COLAGE, 2004] Cylindrical Helical MHD equilibria:  Cylindrical Helical MHD equilibria Force Free Field (FFF): Non-Force Free Field (NFFF): J is not parallel to B (Lorentz Force not null, it is balanced with p) (r)=d/dz=B/rBz is the amount by which (for a given radius r) a magnetic line is twisted when it advances in dz 0=(r~0) B0 is the field intensitiy at the tube’s axis Cloud’s Frame: Slide15:  Cylindrical equilibria for the ‘local’ flux tube at 1AU Uniform Twist Angle (non-Linear Force Free Field) [Farrugia et al., SW9 1999] Uniform cylindrical Current (non-Force Free Field) [Hidalgo et al., JGR 2002] Linear Force Free Field [Burlaga et al., JGR 1981] Cylindrical Current (non-Force Free Field) [Cid et al., Sol.Phys 2002] Other ... [Berger & Field, 1984] [Demoulin et al., A&A, 2002] Slide16:  Linear Force Free Field (LFFF) [Lundquist, ArkFys 1960] Non-Linear Force Free Field with Uniform Twist (UT-NLFFF) [Gold & Hoyle, 1960] From FFF condition and from 0=B/rBz Once determined the orientation of the MC, the observations are compared with the model (non-linear least square method):  Once determined the orientation of the MC, the observations are compared with the model (non-linear least square method) Minimum Variance Method (geometry) Least Square Method Fit (Physical Parameters) rS/C(t) Mínimize 2 giving freedom only to the physical parameters Orientation of the tube (S/C trajectory in the flux tube coordinates) from MV MC of Oct 18-19, 1995 (Wind):  MV method: int/min~6 Rotation of B (~ 160°) MC of Oct 18-19, 1995 (Wind) [Dasso et al., in preparation, 2004] Slide19:  (see details of coronal level analysis in [Luoni et al., poster COLAGE2004]) [Luoni et al., in press, 2004] Small cloud inside a complex ejecta: 22:00UT on May 15 – 01:50UT on May 16, 1998 (Wind) [From Mandrini et al., A&A, submitted, 2004]:  Small cloud inside a complex ejecta: 22:00UT on May 15 – 01:50UT on May 16, 1998 (Wind) [From Mandrini et al., A&A, submitted, 2004] -3.1x1039Mx2<Hcor<-2.3x1039Mx2  cor ~ 1019Mx Interplanetary Hot Flux Tube (no MC) [From Dasso et al., JGR, 2003]:  Interplanetary Hot Flux Tube (no MC) [From Dasso et al., JGR, 2003] Agreement between 3 models (L, G, H) and 3 methods (MV and SIM) Better Fit with force-free models for this interplanetary hot tube Impact parameter such that: p~R/10 The variance ratio from MV is int/min~10 Analysis of 8 MCs:  Analysis of 8 MCs (More results and details of this statistical study in [Gulisano et al., poster COLAGE2004]) We analyzed 8 MC of quality 1 (well behaved) We model the data using 4 different models (Lundquist, Gold-Hoyle, Hidalgo, and Cid) We found that H is better determined than the Flux We found that H is model-independent From list at http://lepmfi.gsfc.nasa.gov/mfi/mag_cloud_pub1.html Summary and Conclusions:  Summary and Conclusions H is the most important MHD magnitude to gain insight about the physics during the ejection/travel of CMEs We showed a technique/method to analize the content of H in Interplanetary Flux Tubes observed in situ by spacecrafts (in particular in Magnetic Clouds) In spite of the field lines twist is very differently distributed along r, for the different analyzed models, the global value of H resulted to be similar !. And so, H is a well determined MHD quantity for MC (it is almost not sensitive to the model) H is sensitive to the size (radius) of the tube, so it is very important to improve the determination of its orientation and impact parameter. Our comparisons with the release of H from coronal level of the AR associated show a good agreement with H and the Flux in AR H is better determined than the flux when the assumed model is changed Our next steps are: To extend this analysis to a larger set of MCs Elliptical shape to the cross section of MCs Expansion of the MC Multi-spacecrafts analysis End:  End

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