SHINE Zermatt Resort, Midway, UT July 31-August 4, 2006 Empirical Solar Wind Forecasting from the Chromosphere: Inclusion of a Potential Field Corona R.J. Leamon, 1 S.W. McIntosh 2 1 ADNET Systems, Inc. at NASA GSFC, Greenbelt MD; 2 Southwest Research Institute, Boulder, CO INTRODUCTION The measured separation in height of the TRACE 1600Å and 1700Å UV band pass filters correlates very strongly with solar wind velocity and inversely with the ratio of ionic oxygen (O 7+ /O 6+ ) densities measured at 1 AU. These correlations suggest that the structure of the solar wind is rooted deeper in the outer solar atmosphere than previously considered. We show here that the value of plasma beta extrapolated from the photosphere up into the chromosphere correlates with TRACE UV band pass separation and thus to in situ solar wind velocity and composition. Initial results of a model developed to so predict interplanetary solar wind conditions, using SOHO/MDI magnetograms with 96 minute cadence as input has recently been submitted to ApJL. The model provides a near continuous range of solar wind speeds and composition quantities from the structure of the chromosphere, and shows good correlation with observations over approximately one solar rotation. At SHINE we discuss the implications and results from including a PFSS model of the corona to trace the sub-terrestrial field line to the photosphere. 5 – Potential Field Source Surface (deRosa & Schrijver’s SSW contributions) extrapolations. The above 4 panels are stills from a QuickTime movie that covers the whole 36-day interval from the “old” disk center results (Fig. 4). The PFSS data are reduced daily. For each MDI magnetogram (441), 33 field lines are traced back to the sun; one at the sub-solar point, and 32 around an ellipse one-third the size used for the disk center ellipse calculations (i.e., 5º  2.5º). Sometimes, the whole ellipse maps to a small region of the photosphere, other times it maps to all over the map! Sometimes the sub-solar point on the source surface is connected to the sub-solar point on the photosphere, other times the footpoint is as much as 35º away from disk center. 6 – (Below Right) Results in the same format as Fig. 4, but using the PFSS footprint mask. First notice the dynamic range increases. The cross-correlation coefficients are now for O 7+ /O 6+ (at +19.6h), and (at +24h) for V SW. Notice the variation in error bar size – small when the whole ellipse maps back to one point in an active region (thus the slowest wind), and large (for the crazy 4th panel, above). 1 – Results from McIntosh & Leamon [2005]: The areas in red in the top "time difference" image show a shallow, dense chromosphere beneath an area with slow, dense solar wind outflow; the areas in blue in the bottom image show a deep, less dense chromosphere below a "coronal hole" with fast, tenuous solar wind outflow. Separation of the formation heights of 1600Å and 1700Å TRACE filters correlates strongly with solar wind speed and inversely with the ratio of oxygen composition. One smooth curve can fit through the observations of Active Regions, Quiet Sun and Coronal Holes. The two filled symbols are for the two EIT/ TRACE images, above. Best-fit Power laws ( A  z B + C ): V SW : A = 1.49 (± 0.19)  B = 4.56 ± 0.33 (1) C = 333 ± 12 O 7+ /O 6+ : A = 1.22 (± 0.11)  B = ± 0.23 (2) C = ± – 2-D histogram showing the correspondence of oscillation travel time and the plasma  at 450 km above the photosphere for the suite of 13 TRACE observations (below left). TT = log 10 (  + 5  10 3 ) The nature of the TRACE UV observations does not lend itself to a predictive tool: each of the 13 solar observations below left is the result of a 1–3 hour time TRACE sequence of interleaved 1600Å and 1700Å images, which then require careful co- alignment to sub-pixel accuracy and removal of the effects of solar rotation. Fortunately, there is the striking relationship between the observed travel times and the plasma  at the mean formation height of the TRACE 1600Å passband. So, we extrapolate a co-aligned line-of-sight magnetogram from MDI to 450 km, and compute the magnetic pressure. By imposing a simple model gas pressure (e.g., VAL3C), we can compute  in the chromospheric region of the TRACE passbands. Using this relationship, we can generate a synthetic full-disk TT map from the extrapolated MDI magnetogram  and then use Eq. (1) to generate a map of predicted wind speed or other in situ quantities. Since the source region of Earth-directed solar wind parcels can be only a fraction of the whole solar disk, we average the predicted wind speed over a ``source window.'' The size of the source window is set somewhat arbitrarily as an ellipse with semi-major axes 0.25  R sun (~15º by 7.5º) at disk center. 4 – Results. Left panels are for ballistic propagation, right panels use Parker’s solar wind model. The blue crosses are for a refined model with an empirically reduced delay, resulting in zero lag for the cross-correlation between model and data. With ballistic propagation, the correlation coefficients are 0.30 for V SW and 0.41 for oxygen, both at a lag of 28.8h. The Spearman rank-order correlation coefficients are comparable: 0.27 and With the Parker model, the cross-correlation coefficients increase to 0.32 and 0.47, and the Spearman coefficients increase significantly to 0.46 and It is perhaps interesting to note that the correlations for O 7+ /O 6+ are consistently higher than for V SW, despite the fact that we use the same V SW to predict the arrival time of the hot oxygen. TTV SW 3 – Derived wind speed and composition maps, and a context EIT image, showing the active regions and coronal holes. In all 3 panels, the white dashed circle has radius ~600 , beyond which the accuracy of the line-of-sight approx for MDI magnetograms degrades significantly. We present two different two empirical solar wind condition “forward-modeling” scenarios. First, we shall consider a simple ballistic propagation model, shifting the predictions derived from MDI observations from the time of MDI observations by the constant velocity travel time (147 million km divided by predicted V SW ). Then, we will adopt a more sophisticated model based on the original solar wind model of Parker [1958] where the accelerating solar wind can be expressed as solutions of We use the method of Cranmer [2004], invoking Lambert's W function, to solve Parker’s equation exactly, with various coronal temperatures as input. We convert these velocity profiles into a look-up table for the time taken for a parcel of plasma to flow from the sun to 1 AU, given the predicted V SW at 1 AU. CONCLUSIONS Including a PFSS model of the corona to track the source of Earth-directed wind improves the correlation and agreement with in situ V SW and O 7+ /O 6+ data, but at the expense (at this point in time) of time lags. We have not yet considered the length of the coronal field lines (i.e., the twisted path from photosphere to Source Surface)… See you next year!