The topology of the coronal magnetic field is essential for understanding solar energetic events and properties of the solar wind. Magnetic null points, separatrix and quasi-separatrix surfaces are likely preferred sites for magnetic reconnection. (Quasi-)separatrix surfaces serve as boundaries between topologically distinct flux systems having different properties. Knowledge of the magnetic topology of the corona is useful to the solar and space physics research community, as well as for space-weather forecasting.
It is possible to identify topological regions in the corona where the magnetic field configuration may be unstable to perturbation. Q, a geometrical parameter that describes the squashing factor of elemental flux tubes, is useful for understanding the coronal configurations that are relevant to space weather. Q-maps provide intuitive visualization of the topological magnetic features where reconnection may preferably occur. Such structures are thought to be important for launching the slow solar wind and have been used to support the S-Web theory for the slow wind.
Q-maps are computed from the results of a 3D coronal field model applied to photospheric magnetic field observations. The general method developed by Titov et al. (2008, 2011) is applied to current observations from the HMI (Helioseismic and Magnetic Imager) instrument on SDO (Solar Dynamics Observatory) and to archival observations from the MDI (Michelson Doppler Imager) instrument on SOHO (the Solar and Heliospheric Observatory).
|For a given field line, an infinitesimal circle is mapped along
field lines into an infinitesimal ellipse. The circle and ellipse are on
the boundary surfaces of a finite volume defined by curvilinear coordinates
(U1,U2) and (W1,W2) -- for example the photosphere and the source surface of a
coronal field model.
The aspect ratio of the resulting ellipse defines the squashing factor of the elemental flux tube enclosing the given field line. Q=N^2/delta where N is the generalized norm and delta is the expansion / contraction factor (Titov et al, 2008).
When N is large and/or delta is very small, Q can become large.
slog Q is especially convenient for analyzing the structure of magnetic configurations
We have calculated slog Q at ten heights above the photosphere for each solar rotation from 1996 to the present.
|The figure shows the photosphere and corona for one complete solar rotation in August 2010, Carrington Rotation 2099. There are four panels. The values are computed from HMI observations of the photospheric field. Each panel is a map of the whole Sun at some height at or above the photosphere. These figures are frames of a movie.
|The upper left panel is the smoothed radial magnetic field in the photosphere from which the coronal field is calculated. Positive field is white and negative black. The Sun was not too active in mid 2010.
|Upper right: Foot points near the photosphere that open to the solar wind. Blue points indicate where the magnetic field polarity is positive (out of the Sun). Red points have negative polarity.
|Lower left: slog Q map at 1.10 solar radii showing complex structures. Blue and red show positive and negative polarity. Dark colors are high values of Q.
|Lower right: slog Q at 2.499 Rs showing simplified structure higher in the corona. The neutral line separating blue and red is the base of the heliospheric current sheet.
Synoptic maps of Q are available from the Solar Dynamics Observatory Joint Science Operations Center (JSOC). JSOC data series can be exported like any other SDO HMI or AIA data. The primary data series are described below.
Click on the button to go to the JSOC lookdata program for the indicated data series.
A movie of the synoptic Q-maps, photospheric field, and open-field lines footpoint can be found in HMI Synoptic Q-Maps
The data series hmi.Q_synop has three map segments for each Carrington Rotation starting with CR 2097 in May 2010.
The data series hmi.pfss_synop has six data segments for each Carrington Rotation.
The data series hmi.polar_db has, once each year, the best measurement of the high-latitude field above 60 degrees made during the time of optimal viewing. The polar field can best be observed when it is most tipped toward Earth. Due to the inclination of the ecliptic this happens in early March in the south and in September in the north. The series has four data segments.
In order to compute the coronal field, the magnetic field over the entire solar surface must be known, including the polar regions that are always difficult to observe and often obscured due to Earth's orbit. Using the method of Sun et al. (2011), we infer the polar field above 60 degrees from annual observations of the poles when most visible (See hmi.polar_db above). The smoothed field is interpolated for earlier years and extrapolated for the most recent months to provide a good estimate of the large-scale field above 60 degrees for any time interval.
The data series hmi.synoptic_mr_polfil_720s has a single data segment for each Carrington Rotation. The standard synoptic maps of the radial magnetic field inferred from line-of-sight magnetic observations taken every 720 seconds are merged with interpolated values of the polar field above 62 degrees. The field above 75 degrees consists of only the smoothed interpolated values.
The Michelson Doppler Imager instrument on SOHO began observing the Sun in 1996 and stopped taking synoptic magnetic observations in 2011. Data are available for most rotations from CR 1911 -- CR 2107. The data quality and original resolution are different for MDI than for HMI. The two instruments overlap from CR 2097 - CR 2107 in 2010 - 2011.
A movie of the MDI synoptic Q-maps, photospheric field, and open-field lines footpoint can be found in MDI Synoptic Q-Maps.
Like the hmi data product, mdi.Q_synop has three data segments for each Carrington Rotation, the Q-map data cube in slogQ, the foot-point map in chmap, and the radial field data cube in Brq. The resolution is the same, and the Q-maps and Br are computed at the same 10 heights in the corona.
Like the hmi data product, mdi.pfss_synop has six data segments for each Carrington Rotation: Br, Bt, Bp are the three components of the coronal field computed using the PFSS model with one-degree spatial resolution at the 51 heights. Brq is the higher-resolution radial field data cube at the 10 heights, Br0 is the smoothed radial field at the photosphere used as input to the PFSS model, and gh has the harmonic coefficients of the coronal field between the photosphere and source surface computed up to order 121 using the PFSS model.
Like the hmi data product, mdi.polar_db has the best measurement of the polar field above 60 degrees taken during the time interval each year that the pole is best viewed from Earth. Each pole is measured once per year. There are four data segments: data_raw and data are the original and smoothed values of the 97 polemost pixels of the synoptic maps at 3600 longitudes points; image_raw and image are 600*600 stereoscopic projections of the original and smoothed polar field above 60 degrees.
mdi.synoptic_mr_polfil_96m, like it's hmi counterpart, has a single data segment per Carrington Rotation. The standard synoptic map is merged, poleward of 62 degrees, with the interpolated, smoothed best-annual measurement of the polar field. The resolution is the same 3600*1440 longitude/sine-latitude as for HMI. The radial field is inferred from the MDI 96-minute line-of-sight measurements.
Daily Q-maps are computed using a better measure of the global magnetic field for each particular day.
Standard synoptic maps are observed over a ~27.27-day time span and are assembled using only central meridian observations as they rotate beneath the Earth. Each longitude is observed at a different time. A synoptic frame, used for this product, is constructed for each day using 120 degrees of longitude from one magnetogram to replace the leftmost edge of the usual synoptic map. At least the left-most third of the Sun is observed simultaneously on that day. There are some issues associated with time-evolution and proper motion of magnetic features, but daily Q-maps can better reflect dynamic conditions as they evolve on the solar surface and in the corona.
The colorful figure shows the Q-map for August 25, 2018 at 1.001 Rs.
The map is 360 degrees wide and extends from pole to pole
The left 120 degrees of the input map has been constructed from a magnetogram taken at 12 UT on that day.
The rest of the input frame is the standard synoptic map observed a few to many days earlier at central meridian.
A map is computed each day by extending the map to the left by about 13 degrees.
The color bar for slogQ is at the bottom, with blue (yellow) representing negative (positive) magnetic polarity.
Click on Figure to compare the Q-Maps for 2018 August 25 and 26.
Annual movies of daily Q-maps can be found in Yearly Synoptic Frames.
Like the other Q_Synop series, hmi.q_synframe has three segments slogQ, chmap, and Brq, but computed each day with the synchronic frame that includes 120 degrees of data observed that day.
hmi.pfss_synframe has the same contents as the other PFSS data series, but computed each day: low-resolution Br, Bt, Bp at 51 heights, daily higher-resolution Brq at 10 heights, Br0 with the smoothed Br at the photosphere, and gh with the PFSS harmonic coefficients to order 121.
We have computed high-resolution Q-Maps above a limited number of active regions using a non-linear force-free field (NLFFF) model applied to HMI vector magnetic field measurements. The figure shows results for a portion of AR 12673 on 6 September 2017 at 11:35 UT.
We may be able to fulfill requests for certain active regions of interest. Currently the processing runs in IDL and must be tailored for each application.
|Panel (a) shows the radial component of the photospheric field in a portion of AR 12673 observed 6 September 2017. The neutral line, in orange, is crossed by four green lines labeled (b) - (e). The lines are the bottom boundaries of vertical slices of log-Q maps shown in panels (b) - (e). In this case the field was determined using a Non-Linear Force-Free Field (NLFFF) model. See Zhao et al, 2014) for model details.