Abstract. We have developed a computer-assisted tomography (CAT) technique that iteratively modifies a kinematic solar wind model to least-squares fit heliospheric remote sensing observations (interplanetary scintillation and Thomson-scattering observations). These remote sensing data cover a large range of solar elongations, and access high-latitude regions over the solar poles. The technique can be applied to a time-independent solar wind model, assuming strict co-rotation, or, when sufficient remote sensing observations are available, to a time-dependent model. For the time-dependent case the technique depends primarily on outward motion of structures in the solar wind to provide the perspective views required for a tomographic reconstruction. We show results of corotating tomographic reconstructions primarily using IPS velocity observations from the Solar-Terrestrial Environment Laboratory (STELab, Nagoya, Japan), and include comparisons with in situ velocity data out of the ecliptic (Ulysses) and in the ecliptic (ACE).
Keywords: heliosphere, solar wind, tomography
Heliospheric remote sensing observations probe the global extent of the solar wind. Lines of sight cover a large range of solar elongations, sometimes extending across the high-latitude regions over the solar poles, which are difficult to access by any other means. Studies of the solar wind density use e.g. white-light Thomson-scattering observations (from the zodiacal light photometers on the Helios spacecraft) and interplanetary scintillation (IPS) index observations (from e.g. the radio array in Cambridge, UK). The velocity is studied using IPS velocity observations from multi-station radio telescopes (e.g. from STELab in Nagoya, Japan). As these data represent a line-of-sight integral through the solar wind, drawing unambiguous conclusions about the solar wind structure is often challenging. Assumptions such as the ‘point-P’ or ‘plane-of-the-sky’ assumption, stating that the action takes place closest to the Sun along the line of sight, introduce an unwelcome bias. To avoid this we have developed a tomographic technique: observations sampling solar wind structures from many different directions are combined to construct a solar wind model that best reproduces the observations based on a least-squares criterion. The reconstruction takes into account that line of sight observations are dominated by contributions from material closest to the Sun, but no explicit assumptions are made about the distribution of velocity and density along the lines of sight. The solar wind model is purely kinematic using simple assumptions about the solar wind outflow: given the velocity and density on a ‘source surface’ at 2.5 solar radii, a fully 3D solar wind model follows by assuming radial outflow and enforcing conservation of mass and mass flux (Jackson et al., 1998).
A reconstruction of the solar wind is based on observations obtained during a specific interval. Typically a month-long stretch, covering a full solar rotation is used. Solar rotation provides different perspectives of the ‘quiet’, corotating part of the solar wind. If structures do not evolve (except for corotation) on a time scale of a solar rotation period, then this is sufficient for a reconstruction of the quiet or corotating solar wind. This type of corotating tomographic reconstruction has also been applied to coronal X-ray and coronagraph observations. For heliospheric remote sensing observations the large range of elongations covered provides additional perspective information: as a structure rotates or flows past the observer it is seen from widely different directions. Corotating tomographic reconstructions using IPS and Helios data are usually performed with angular resolution of 10º in heliographic coordinates and 0.1 AU in heliocentric distance.
Near solar maximum solar transients cause changes in the solar wind on time scales of hours to days, much shorter than a solar rotation. The assumption of corotation breaks down and a time-dependent approach is required. The reconstruction of transients depends almost exclusively on the different perspectives derived from solar wind outflow past the observer. To the extent that the transient outflow is consistent with the kinematic solar wind model, the changing perspective can be used to reconstruct transient features. Current data sets are sparse, with low angular and time resolution. This limits the time-dependent tomography to time steps on the order of one day. Consequently the spatial resolution is limited to 20º in heliographic coordinates and 0.2 AU in heliocentric distance.
One way to test the validity of the tomographic technique is to compare solar wind parameters derived from the reconstructions with values observed in situ by spacecraft. In the next section we show results from corotating reconstuctions in the high-latitude heliosphere (at the location of Ulysses) and in the ecliptic near Earth (using ACE observations).
IPS is caused by scattering of the radio signal from compact radio sources by small-scale (100-1000 km) density variations in the solar wind. In the IPS tomography the density variations dn are related empirically to the solar wind density n by:
Figure 1. Comparison of in situ solar wind velocity observed by the SWOOPS instrument on Ulysses (dashed) and the velocity derived from a tomographic reconstruction from IPS velocity observations. Ulysses covered the latitude range on the horizontal axis between December 1994 and July 1995.
An important use for heliospheric tomographic reconstructions lies in its application to space weather studies: remote sensing observations towards the east of the Sun sample corotating structures that have not yet reached Earth. Thus, corotating tomographic reconstructions based on remote sensing data, processed in real time, can be used to forecast the arrival of corotating structures at Earth. Similarly, observations at small elongations will pick up transient solar events such as coronal mass ejections, before they reach Earth. An analysis in real time using time-dependent tomography makes it possible to reconstruct and track transient solar events, and predict their arrival at Earth.
We are currently testing a near-real-time forecast system using the STELab IPS data. Daily IPS data obtained with the STELab system are processed within hours and are sent to UCSD where they are used to update a tomographic reconstruction based on the most recent 30-days stretch of data. Figure 2 shows a forecast run at 04:00 UT on 7 September 2000 using corotating tomography. The reconstruction is based on IPS data prior to this time. The tomographic time series at Earth (solid line) extends about 7 days past the forecast time: these correspond to corotating structures that have not yet reached Earth. A comparison with ACE data (after smoothing using a running mean of 0.75 days) obtained during this time shows a good agreement with the tomographic result.
Figure 2. Velocity time series for the solar wind velocity near Earth from the corotating tomography (solid) and from ACE at the L1 Lagrange point (dashed). The vertical dashed line marks the forecast time. Note that the part of the ACE time series to the right of this line was not available yet at the time of the forecast.
This work was supported at the University of California by grants NAG5 -6475 and AFOSR- 97-0070. The SWOOPS data were obtained from the ESA archive for Ulysses data at http://helio.estec.esa.nl/Ulysses/archive/.
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