The global solar corona derived with time-dependent three-dimensional MHD simulation
using daily-updated SOHO/MDI magnetic field synoptic data

Simulations with choice O : The density and temperature are fixed at the base of the open-field coronal hole. The new plots are usually made 7AM (Pacific Time).
lat-lon map at various distances : click here to enlarge.	l-o-s integration of coronal density
		• csv format: plain text data at the outer corona / inner heliosphere. Vr (in km/s) and Br (in nT) at 30 Rs (please contact us if the data be used for scientific purposes.) • java-applet animation recent 27 plots of lat-lon map and LoS-integrated plasma density with Newkirk filter for r > 1 Rs
• other plots    lat.-lon. plots; since March 1, 2008. part of CR2067, CR2068, CR2069, CR2070, CR2071, CR2072, CR2073, Carrington number here is approximate and based on the date of MDI measurement, not that of the simulation. 2008 Feb. 08∼29 (simulated without polar field correction),
Observations
SOHO's corresponding images (taken two days before the simulations are conducted). * Please mind that automated download is being under test thus the displayed images are not always the intended ones.
Plots with other choices of boundary treatment (c.f. Hayashi (2005) ApJS vol. 161 pp. 480) The daily quasi-real-time simulation shown above assumes fixed density and temperature at the coronal hole base (labeled choice O in my paper (2005)). The coronal simulations with other choices of sub-alfvenic boundary treatment are also conducted. The plots of other two choices are shown below.
Simulation with choice A : density, temperature and bulk velocity at the base of the coronal hole can vary under the constraints; the fixed specific enthalpy and the limited mass flux. The new plots are usually made 8AM (Pacific Time).
		• csv format Vr (in km/s) and Br (in nT) at 30 Rs (please contact us if the data be used for scientific purposes.) • java-applet animation recent 27 plots of lat-lon structures at various heights, and LoS-integrated coronal plasma density and coronal base of open-field regions
• other plots lat.-lon. plots : CR2069, CR2070, CR2071, CR2072, CR2073,
Simulation with choice AB' : density and bulk velocity at the base of the coronal hole can vary under the constraints; the fixed temperature and the limited mass flux. The new plots are usually made 10AM (Pacific Time).
		• csv format Vr (in km/s) and Br (in nT) at 30 Rs (please contact us if the data be used for scientific purposes.) • java-applet animation recent 27 plots of lat-lon structures at various heights, and LoS-integrated coronal plasma density and coronal base of open-field regions
• other plots lat.-lon. plots : CR2073,

modification / change / history

• August 1 : Daily simulations with choice A and AB' start.
• July 1 : Newkirk filter and other modifications are applied to LoS images for choice O.
• June 15 : Newkirk filter and other modifications are applied to LoS images for choice A and AB'.
• May 11 : This page starts.
• May 1 : Simulations with boundary treatment choice A and AB' are started.
• April 21 : Test plots of line-of-sight coronal density integration are added.
• March 1 : Polar field correction is introduced.
• Feb. 8, 2008 : Daily simulation starts.

description

• general : The simulation is scheduled to start 1 AM Pacific Time. It usually takes about 6 hours (in wall clock time, depending on the computational choices such as the boundary treatment and the computation resources available) to conduct this near real-time MHD solution. New plots may appear around 7 AM (P.T.) at earliest.
• data input : The simulation uses the EOF (preliminary) version of SOHO/MDI solar surface magnetic field synoptic data so that the recent state of the corona can be determined. The EOF magnetic field map is regularly updated using the measurement data made 24 hours prior, and the dashed rectangle in the plots above approximately shows the Earth-side heliographic region in which the data is updated.
     The simulation script uses "wget" command to get the magnetic field data that is located at the web-accessible place above, and, for sake of maintaining the regular basis, uses the second newest synoptic data that contains the measurement data from 24 hours to 28 days prior to the start time of the simulation.
• polar field correction : Because of variety of factors such as the apparent inclination of the solar rotation axis, the measurement of the polar field is generally of low quality. The polar field correction is needed to to enhance studies on the solar corona and solar wind.
     Our correction is based on those proposed and tested by Liu, Y. and is implemented with great helps and assists by Sun, X. The correction is based on the spline extrapolation with respect to both time and space. This strategy works pretty well, at least todays at the minimum phase of the solar activity, as the differences between results with and without the correction are significant.
• initial and boundary values of magnetic field : The boundary value and the three-dimensional initial value of the magnetic field are then calculated with the potential-field source-surface (PFSS) model. In this daily simulation, the spherical harmonics decomposition is used in the PFSS model, and the polynomial up to 5th order is used to give the initial and boundary values.
• MHD simulation : To obtain the steady state of the sub/trans-alfvénic solar corona, the time-dependent three-dimensional MHD simulation is conducted. The simulation scheme here is based on the Lax-Friedrich method that is a simplified version of the TVD Roe/Godunov method; the Lax-Friedrich method is much much faster than the Roe/Godunov method. The number of grids are 72, 32 and 64 for the radial, latitudinal and longitudinal direction, respectively. The inner boundary of the simulation is set at 1.01 solar radii, so that we will handle the coronal plasma already heated up to the order of 1 MK though the solar transition region.
     The boundary values of the eight MHD variables at this height are controlled by using the normal projected characteristics method, so that the obtained time-relaxed solution can be fully consistent with the given boundary map, the basic nonlinear hyperbolic MHD equations, and the concept of the characteristics. This is a quite capable mathematical method applicable to any computation scheme; this method re-distribute the calculated temporal derivatives in accordance with the given constraints and the direction of the characteristics curvature. In this method, all three components of plasma flow and the two tangential components of magnetic field can vary in accordance with the concept of the characteristics.
     Three among the possible choices are selected and used in the daily MHD simulations (labeled O, A and AB') to treat the open field region (coronal hole). The choice A and AB' limit the mass flux. For the closed-field region (coronal streamer), the plasma density and temperature can vary responding to the plasma precipitation from the stagnant closed field regions. Whether the plasma will be flowing outward or stagnant is determined by the simulated nonlinear interaction with the magnetic field, thus small or weak closed-field can be open as the results of the MHD process. The radial component of surface magnetic field is fixed all through the computation with any choices above.
     The polytrope plasma with specific heat ratio of 1.05 is assumed to mimic the near-isothermal coronal situation due to the high thermal conduction. This assumption yields somehow small contrast in flow speed and density, and the absolute value of plasma is less reliable. However, the magnetic field quantities and the trends of these plasma variables would be well retrieved.