MHD MODELING FOR HMI JON A. LINKER SCIENCE APPLICATIONS INTL. CORP. SAN DIEGO

Transcription

1 MHD MODELING FOR HMI ZORAN MIKIĆ JON A. LINKER SCIENCE APPLICATIONS INTL. CORP. SAN DIEGO Presented at the HMI Team Meeting Stanford University, Palo Alto, May 1 2, 23

2 USEFULNESS OF MHD MODELS A global evolving solar wind model will be very useful for providing contextual information for HMI observations (e.g., source regions, location and geometry of CIRs and solar wind streams, magnetic field polarity, magnetic field topology in CMEs) The coronal + heliospheric model is useful in particular for connecting in situ measurements with solar source regions and coronal phenomena The heliospheric model is useful for tracking CME propagation through the interplanetary medium New opportunity: coronal models including vector field measurements

3 MHD EQUATIONS (POLYTROPIC MODEL) B = 4π c J E = 1 c B t ρ v t E + 1 c v B = η J ρ t + (ρv) = + v v = 1 c J B p + ρg + (νρ v) p t + (pv) = (γ 1)p v γ = 1.5 for coronal solution; γ = 1.5 for heliospheric solution

4 ρ p t v t MHD EQUATIONS (IMPROVED ENERGY EQUATION MODEL) B = 4π c J E = 1 B c t E + 1 c v B = η J ρ t + (ρv) = + v v = 1 c J B p p w + ρg + (νρ v) + (pv) = (γ 1) p v q nenpq(t) + H γ = 5/3 q = κ bˆ bˆ T (Close to the Sun, r < ~ 1R s ) q = 2αneT bˆ bˆ v/(γ 1) (Far from the Sun, r > ~ 1R s ) + WKB equations for Alfvén wave pressure p w evolution

5 MHD Model of the Corona and Inner Heliosphere: Overview Line-of-sight Photospheric Magnetic field (e.g., Kitt Peak) B r at inner boundary 1 3 Solar radii Coronal Model Density, temperature constant B r Heliospheric Model 3 Solar radii 5 AU Speed from magnetic topology Momentum Flux balance => density Pressure balance => temperature

6 MHD Model of the Corona and Inner Heliosphere: Overview Line-of-sight Photospheric Magnetic field (e.g., Kitt Peak) B r at inner boundary 1 3 Solar radii Coronal Model Density, temperature constant B r Heliospheric Model 3 Solar radii 5 AU Speed from magnetic topology Momentum Flux balance => density Pressure balance => temperature

7 Whole Sun Month Aug. 1 Sep. 8, Kitt Peak Synoptic Chart, B r Latitude (deg.) Smoothed Magnetic Field (used in MHD model) 45 Latitude (deg.) Carrington Longitude (deg.)

8 Whole Sun Month Aug. 1 Sep. 8, 1996 Radial Velocity Open and Closed Field Lines Radial Velocity (km/s) 19 95

9 MHD Modeling of the Solar Corona During Whole Sun Month 9 MHD Model, r = 1.75Rs 9 MLSO MKIII, r = 1.75Rs MHD Model, r = 2.35Rs 9 LASCO C2, r = 2.35Rs Latitude (deg.) MHD Model, r = 5Rs CR 1913 Carrington Longitude (deg.) CR 1912 Latitude (deg.) Coronal Holes LASCO C3, r = 5Rs CR 1913 Carrington Longitude (deg.) CR D MHD Model (Coronal Holes) NSOKP Coronal Hole Map EIT Fe XII Image EIT Fe XV Image Magnetic Field Lines and Heliospheric Current Sheet Ulysses WIND Sources of Solar Wind at the Sun Measured at Ulysses North Pole View Speed [km/s] 7 HCS 6 5 4

10 Field Lines (MHD Model) Eclipse Comparisons Polarization Brightness (MHD Model) Eclipse Image November 3, 1994 October 24, 1995 March 9, 1997 February 26, 1998 August 11, 1999

11 MHD Model of the Corona and Inner Heliosphere: Overview Line-of-sight Photospheric Magnetic field (e.g., Kitt Peak) B r at inner boundary 1 3 Solar radii Coronal Model Density, temperature constant B r Heliospheric Model 3 Solar radii 5 AU Speed from magnetic topology Momentum Flux balance => density Pressure balance => temperature

12 MHD Model of the Corona and Inner Heliosphere: Overview Line-of-sight Photospheric Magnetic field (e.g., Kitt Peak) B r at inner boundary 1 3 Solar radii Coronal Model Density, temperature constant B r Heliospheric Model 3 Solar radii 5 AU Speed from magnetic topology Momentum Flux balance => density Pressure balance => temperature

13 9 O Latitude a O Open Field Lines Closed Field Lines MHD Model of the Corona and Inner Heliosphere: Heliospheric Boundary Conditions at Solar Minimum -9 O Photospheric magnetic field topology Imposed Radial Velocity Profile 65 V (km/s) 65 V (km/s) Mapped Radial Velocity Profile at 3 Solar Radii O 9 O 18 O 27 O 36 O Longitude 265

14 Solar Wind Velocity in the Heliosphere During Whole Sun Month (August September 1996) 5 AU 5 AU 5 AU 5 AU N Radial Velocity in Equatorial Plane 5 AU 5 AU N Radial Velocity in Meridional Plane Latitude Latitude S Longitude Radial Velocity at r = 1 AU S Longitude Radial Velocity at r = 4.2 AU km/s

15 The Heliosphere During Whole Sun Month August September 1996 Ulysses Trajectory Radial Velocity Heliospheric Current Sheet WIND Trajectory Magnetic Field Lines 1 A.U.

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17 Solar Wind Source Regions Determined from a 3D MHD Calculation Compared with ACE Measurements Whole Sun Month 3 (Aug Sep. 14, 1999) Magnetic Field Direction DOY CR1953: Latitude Longitude Out of Sun: F P - F B < 45o Into Sun: F P - F B - 18 o < 45 o

18 WSM3 Comparison Between ACE Measurements* and an MHD Simulation Radial Magnetic Field [nt] Proton Temperature [K] Proton Density [cm -3 ] Solar Wind Speed [km/s] CR1953 ACE Data MHD Sim Day of Year ACE Data MHD Sim. CR Day of Year 1999 CR1953 ACE Data MHD Sim Day of Year ACE Data (avg) MHD Simulation CR Day of Year 1999 *No account has been taken of CMEs

19 AN EVOLVING SOLAR WIND MODEL We can run a time-dependent coronal model with continuous updates of the photospheric magnetic field driven by observations We can use daily or more frequent updates (determined primarily by resources) The boundary magnetic field Bro in the model is updated using an electric field at the boundary The coronal solution and solar wind respond to the boundary condition changes A quasi-real-time model can be developed if a massively parallel computer is used (e.g., a Beowulf cluster with 32 processors) for a medium-resolution run [ ~ O(1 3 ) mesh points]

20 EVOLVING BOUNDARY CONDITIONS The boundary magnetic field Bro (at r = R o ) is updated using an electric field at the boundary: Eto = t Ψ rˆ + t Φ, where Ψ(θ,φ) controls the normal magnetic field Bro, and Φ(θ,φ) controls the transverse magnetic field Ψ is determined from: c t 2 Ψ = B ro t Φ can be determined from a circuit model to match the normal component of the electric current Jr (deduced from measurements of the transverse field): Φ t (Jr Jro)

21 Kitt Peak Magnetogram Field Lines Coronal Cross Sections Temperature 6 Temperature [1 K] Log Density 1.5 Log Density [cm-3] Figure 1. Modeling the magnetic and thermal structure of an active region on August 29, A Kitt Peak magnetogram is used to specify the normal component of the magnetic field. A twist is applied to the field, and the steady state is calculated for a given coronal heating distribution. The temperate and density structure shows that the transition region height varies in different parts of the active region.

22 STANDARD DATA PRODUCTS We are developing WWW site with data for 2.5 solar cycles (~ 35 Carrington rotations, CR 1625 present) Coronal hole maps with magnetic field polarity Field line connectivity (spacecraft to source regions on the Sun) Plasma parameters: B, v, T, n plots vs. latitude, longitude, radius meridional and equatorial cuts Limb pb images at Earth and spacecraft views, movies of pb Synoptic maps of pb at various radii 3D images of the heliospheric current sheet and field lines (VRML) Raw data: B(x,t), v(x,t), T(x,t), n(x,t) Future products: Interactive tools (e.g., field line tracing on demand)

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29 VRML of Coronal Field Lines (CR 1971, Dec. 12, 2 Jan. 17, 21)

30 VRML of Heliospheric Field Lines (CR 1971, Dec. 12, 2 Jan. 17, 21)