Disruption of a heliospheric current sheet fold

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 38,, doi: /2011gl047822, 2011 Disruption of a heliospheric current sheet fold V. G. Merkin, 1 J. G. Lyon, 2 S. L. McGregor, 2 and D. M. Pahud 3 Received 16 April 2011; revised 31 May 2011; accepted 31 May 2011; published 23 July [1] We present results from a new magnetohydrodynamic model of the inner heliosphere. We focus in this study on Carrington rotation 1892 which occurred during solar minimum, and simulate the solar wind and heliospheric magnetic field from 0.1 to 2 AU. We demonstrate the development of small scale ( solar radius) structure, such as folds and ripples, on the surface of the heliospheric current sheet. In particular, we analyze the evolution of a current sheet fold forming by 1 AU, significantly narrowing by 1.5 AU ( 1 in width), and quickly disrupting afterwards. The disruption constitutes a process whereby the lower part of the current sheet fold separates from the main surface and, on a heliocentric spherical surface, appears as an island of outward polarity in the sea of the field of inward polarity. We show that this process is associated with non radial motion of plasma and magnetic field induced inside a stream interaction region. In addition, we discuss evidence of magnetic reconnection in our simulation that involves flux tubes in the vicinity of the heliospheric current sheet. The simulations presented here provide a useful global 3 dimensional context for interpreting multiple current sheet crossings commonly observed by spacecraft as well as observations of magnetic reconnection in the solar wind. Citation: Merkin, V. G., J. G. Lyon,S.L.McGregor,andD.M.Pahud(2011),Disruptionofa heliospheric current sheet fold, Geophys. Res. Lett., 38,, doi: /2011gl Introduction [2] The Heliospheric Current Sheet (HCS) separates regions of solar magnetic field of opposite polarities. Its shape on the large scale is determined by the interplay of the distribution of the magnetic field and plasma velocity at the sun, and the inclination of the sun s magnetic axis with respect to its axis of rotation [e.g., Smith, 2001]. The geometry of the HCS changes dramatically between solar minimum and solar maximum, owing to the fundamentally different structure of the solar magnetic field even in the absence of transients such as Coronal Mass Ejections (CME) [Riley and Linker, 2002]. In this Letter, we are concerned with the HCS structure during solar minimum on the mesoscale defined here as spatial distances much smaller than the size of the heliosphere, limited in this work to a few Astronomical Units (AU), but much larger than the width of the current sheet, 10,000 km at 1 AU [Winterhalter et al., 1994]. More precisely, we will 1 Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA. 2 Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire, USA. 3 Department of Astronomy, Boston University, Boston, Massachusetts, USA. Copyright 2011 by the American Geophysical Union /11/2011GL be dealing with HCS phenomena occurring on spatial scales l such that 1 R ] l <10R, where R is the solar radius. [3] Earlier studies predicted, based on kinematic expansion of the solar wind, that a smooth current sheet near the sun will distort and form folds due to velocity inhomogeneities as the radial distance increases [Suess and Hildner, 1985]. Later, such HCS structures were reproduced in magnetohydrodynamic (MHD) simulations with significant folding developing by 10 AU [Pizzo, 1994] and closer (2.5 5 AU) [Riley and Linker, 2002]. In these previous works, HCS folds formed on scales of >10 in azimuth at the above distances [Pizzo, 1994, Figure 1; Riley and Linker, 2002, Figure 3]. Large scale distortions of the HCS were also discussed in the context of global heliosphere simulations [Czechowski et al., 2010] and simulations of the corona with foot point motion [Lionello et al., 2006]. [4] In this Letter, we present results from a new MHD model of the inner heliosphere with sufficient spatial resolution to study HCS and other heliosphere phenomena at a scale of at least an order of magnitude smaller. We show that the formation and properties of these folds (as well as other mesoscale HCS structures, such as ripples) is highly dependent on the simulation resolution. The resolution also determines the radial distance at which the structure will form. We show a specific example of an HCS fold forming by 1 AU, significantly narrowing by 1.5 AU ( 1 in width), and quickly disrupting afterwards. We suggest that the disruption may occur as a consequence of non radial motion within a narrow stream interaction region, which leads to the formation of an island of magnetic field of one polarity inside a sea of field of the opposite polarity. These simulations provide a modeling context for observations of the local structure of the HCS, such as multiple HCS crossings often registered by spacecraft [e.g., Blanco et al., 2006; Neugebauer, 2008; Foullon et al., 2009], particularly, those occurring on time scales of multiple hours. [5] A complementary result we report here is evidence of magnetic reconnection in our simulations. Reconnection occurs on magnetic field lines in the vicinity of the HCS and results in folding of magnetic field lines on themselves so that segments of opposite polarities become magnetically connected. Although reconnection appears to occur on field lines involved in the HCS fold discussed above, invoking reconnection is not necessary to explain the formation of the fold and its disruption. 2. Simulation Method [6] The MHD code used for this study is a version of the Lyon Fedder Mobarry (LFM) model adapted to the environment of the inner heliosphere. We will refer to this new version of the code as LFM helio. LFM is a well established MHD code that has been primarily used for simulations of the terrestrial magnetosphere. Limited applications to the global 1of6

2 Figure 1. Radial velocity (Figures 1a, 1c, and 1e) and magnetic field (Figures 1b, 1d, and 1f) at (a b) the inner boundary of the simulation (0.1 AU), and at (c f) 1.5 AU. Lower (Figures 1c and 1d) and higher (Figures 1e and 1f) resolution simulations are shown at 1.5 AU. Magnetic field at 0.1 AU is scaled down by a factor 2/3 100 to be shown in the same color range (the field strength is 230 nt). The HCS is calculated as the surface where the radial magnetic field vanishes and is shown as a white contour on the velocity plots and black contour on the magnetic field plots. heliosphere [McNutt et al., 1999] and other planetary magnetospheres [Kallio et al., 1998] have also been carried out. The numerical algorithms underlying the LFM code have been described in detail elsewhere [Lyon et al., 2004]. The distinct feature of the LFM model is its high resolving power leading to the ability to resolve MHD shocks and discontinuities in 1 2 simulation grid cells. The LFM numerical algorithms are used without modification within LFM helio. In brief, LFM helio uses a different grid, modified boundary and initial conditions. [7] The inner boundary condition of LFM helio assumes super sonic and super Alfvénic solar wind and thus must be located beyond the critical point. For the simulations presented below we used a regular spherical grid with the inner boundary located at 21.5 R (0.1 AU) and the outer boundary at 430 R (2 AU). The specification of the boundary condition was obtained from steady state solutions of the Wang Sheeley Arge (WSA) model [Arge and Pizzo, 2000; Arge et al., 2004]. The velocity, Vr, at the inner boundary was calculated from the WSA magnetic field according to McGregor et al. [2011] (equation (2) with V0 = 200 km/s, V1 = 750 km/s, = 3.8, and b = 3.6), who derived a recalibration of the empirical velocity relation previously used by Arge et al. [2004]. The azimuthal magnetic field is inferred by assuming corotation: B = (V /Vr) Br, where V is the solar rotation speed at the radial distance of the boundary, (2p/27days) 0.1 AU. The plasma density was obtained from an empirical fit to Helios data [McGregor, 2011]: n [cm 3] = / (Vr [km/s])2, while the temperature was determined by assuming uniform thermal pressure, nt = n0t 0, where T 0 = K and n0 = 300 cm 3. The latter assumption is commonly used in modeling studies [Odstrcil and Pizzo, 1999; Riley et al., 2001] and is usually justified by the requirement to inhibit non radial plasma flow. [8] Unlike the magnetospheric LFM, the LFM helio grid does not typically extend to the poles. This is not a fundamental limitation of the model and is done to avoid computing small time steps resulting from convergent grid lines near the axis. In the simulations presented here, the grid extended to 10 heliographic colatitude. Free outflow conditions are applied on the side and outward boundaries. Calculations are performed in the inertial reference frame. All results presented here correspond to the same moment of time when the simulation reaches a steady state. Animations S1 and S2, included as auxiliary material, demonstrate the time evolution of simulated structures for 20 days following that moment of time, and show that the simulation remains in steady state to a good accuracy, in particular, the HCS structures considered below.1 3. Results and Discussion [9] We performed two simulations of Carrington rotation (CR) 1892, one with uniform resolution in radial, polar and azimuthal directions, respectively, and the other, at double that, sub degree resolution in both angular directions and 1 solar radius in the radial direction. Figures 1a and 1b show the radial velocity and magnetic field 1 Auxiliary materials are available in the HTML. doi: / 2011GL of 6

3 Figure 2. (a c) Evolution of the HCS fold with radial distance is shown within the area marked with the green square. Color coded is the cosine of the magnetic field declination angle from the radial direction, cosd = ^r B/B; red is outward, blue is inward. (d) The 3 D surface of the HCS (cosd = 0) colored by the plasma velocity magnitude. The semi transparent spherical surface marks the 1.5 AU heliocentric distance and shows cosd in the same format as Figures 2a 2c. The HCS in figure (d) extends to the outer edge of the simulation grid (2 AU), and the outer rim of the HCS is indicated by the white contour. The HCS fold is seen inside the 1.5 AU sphere as a single ridge; beyond that distance a flux tube bundle detached from the main HCS surface can be seen. at the inner boundary of the simulation. Importantly, the boundary condition specification is the same in both lower and higher resolution simulations: the corresponding values are interpolated from the WSA grid ( ) to the LFM helio grid of the corresponding resolution. Figures 1a and 1b show a smooth HCS at 0.1 AU which develops into the warped, structured surface at 1.5 AU shown in Figures 1c and 1d (lower resolution) and Figures 1e and 1f (higher resolution). We note that many smaller scale features evident in the higher resolution simulation are absent in the lower resolution simulation. This is an important observation as our high resolution grid cell size (at 1 AU) in both angular directions is 1 AU 1 4 R km, which is 2 3 orders of magnitude greater than the width of the current sheet. The fact that the MHD simulation with a relatively smooth inner boundary condition self consistently develops structure that is clearly still under resolved, i.e. occurs on the scale of the grid, suggests that there is much to be learned about the dynamics of the solar wind that operate on MHD spatio temporal scales unresolved by current models. [10] Although many smaller scale HCS folds and ripples can be seen in the higher resolution simulation, in this Letter we concentrate on the HCS fold seen around 150 longitude in Figure 1e. Figures 1c and 1d show the formation of this fold, which has a greater width than in the higher resolution case. Although the structure does become narrower with increasing radial distance in the lower resolution simulation, the resolution is never sufficient to capture its subsequent disruption evident in the high resolution case that is discussed below. Thus we will focus on the high resolution simulation hereafter. Figures 2a 2c show the evolution of this fold with radial distance. Comparison with Figure 1 shows that this structure develops in front of a high speed stream from a smooth current sheet at 0.1 AU. Such folding of the HCS associated with velocity inhomogeneities was predicted based on kinematic expansion [Suess and Hildner, 1985] and later reproduced in MHD simulations [Pizzo, 1994; Riley and Linker, 2002], but at larger radial distances. Here we demonstrate that not only can such significant HCS folding develop much closer to the sun, but also that the process is highly dependent on the resolution of the simulation. Furthermore, Figures 2a 2c reveal a remarkable detail: the HCS fold narrows down significantly between 1 and 1.5 AU as the high speed flow behind it runs into the slow flow in front of it, and is eventually disrupted within a short distance from 1.5 to 1.6 AU. The small island of positive polarity in the sea of negative polarity is evident in Figure 2c and is the remainder of the original fold. [11] Figure 2d clarifies the physical picture of the fold disruption. It shows a 3 dimensional depiction of the surface of the HCS, defined here as the iso surface of the zero radial magnetic field. The surface is color coded with the magnitude of the plasma velocity. Also shown is a semi transparent sphere of radius 1.5 AU. One can clearly see a ridge in the 3 of 6

4 Figure 3. A zoom in on the HCS fold shown in Figure 2. The background shows q the ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi magnitude of the non radial plasma velocity V = V 2 þ V 2, while arrows show the corresponding velocity vectors (at 1.5 AU). The white contour is the HCS surface defined as in Figure 2. The background indicates that the fold thickness is essentially one grid cell underscoring the fact that sufficiently fine resolution is required to reproduce such a structure. HCS surface inside the sphere. Outside the sphere, a bundle of magnetic flux tubes of outward polarity separates from the ridge toward south. It is clear that the east side of the ridge (a 3D representation of the HCS fold) has a higher velocity associated with it in accordance with the high speed stream running into the HCS fold seen in Figure 1e. Although this stream does not have extremely high velocity, forces acting within the interaction region are sufficient to considerably distort the shape of the HCS and eventually lead to the disruption of the HCS fold. [12] While Figure 2d shows the evolution of the magnetic field leading to the fold disruption, the physical mechanism of the process remains unclear. The question is, What leads to the north south deflection of a bundle of flux tubes whose foot points back at the corona were just above the smooth current sheet? The formation of the fold is closely associated with a stream interaction region. It has long been known that non radial solar wind flows are induced inside stream interactions [Pizzo, 1982]. Thus we surmise that non radial gradients in thermal and magnetic pressure within the stream interaction lead to the corresponding deflection of the plasma belonging to the flux tubes populating the inside of the HCS fold. To support this conjecture with evidence from the simulation, we plot in Figure 3 a detailed representation of the non radial solar wind flow in the regions surrounding the HCS fold at 1.5 AU. It is clear from Figure 3 that the plasma in the lower and middle parts of the fold experiences substantial motion in the southwest (down and to the right) direction. We hypothesize that this can create a squeezing effect: the outward magnetic flux from the middle of the fold is redistributed and moved southward resulting in the apparent disappearance of outward magnetic field seen in Figure 2d above the detached flux tube bundle. Also included in Figure 3 for comparison are much stronger stream interactions at lower latitudes corresponding to the transitional region from the slow to fast wind. [13] The discussion above offers an explanation of how an HCS fold can break up without a change in the magnetic topology: by non radial deflection of plasma and magnetic field from the interior of the fold. However, further analysis of our simulation results shows a rather complicated topology of magnetic field in the vicinity of the fold. Figure 4a depicts a number of magnetic field lines traced from the lower part of the HCS fold originating at the radial distance of 1.5 AU indicated by the arrow. Figure 4a shows a large number of sigmoid field lines that appear to have been doubly reconnected, once on each side of the current sheet fold. Figure 4b illustrates the picture schematically. The dashed lines in Figure 4b represent a planar cut through the HCS surface (assume the plane to be the ecliptic for simplicity). If reconnection occurs according to the simplistic scenario in Figure 4b, then it cannot be responsible for the disruption of the fold, because the field inside the fold (between the dashed lines) retains outward polarity regardless of whether the fieldlines have been reconnected or not. Therefore, a spherical cut through the simulation will always show a connected fold, as in Figure 2b, not a disconnected one, as in Figure 2c, unless the spherical cut is made at the radial distance of a reconnection site. In addition, unlike the situation in the sketch, the simulated picture is intrinsically 3 dimensional: the outward (red) segment of the sigmoid shaped field lines is located southward of the west side inward (blue) segment and northward of the east side one. Determining whether reconnection occurs at the site of the fold disruption, or, more generally, at any given location in a 3D MHD simulation is a significant challenge [Ouellette et al., 2010], and thus we cannot at this point confirm whether magnetic reconnection Figure 4. (a) Magnetic field topology in the vicinity of the HCS fold in the simulation. The spherical cut shows the cosine of the magnetic field declination angle from the radial direction at 1 AU in the same format as in Figure 2. The magnetic field lines shown are colored by the same quantity (cosd) indicating segments of opposite polarity belonging to the same field line. (b) A 2D schematic representation (not to scale) of the simulated magnetic field topology. The dashed lines show the surface of the zero radial magnetic field, used here to indicate the HCS. 4of6

5 contributed to the fold disruption. In fact, our supposition that reconnection occurs in the simulation is based only on the inferred topology of the magnetic field (the sigmoid field lines as well as closed loops as in Figure 4b). If these field lines are created by reconnection, it is still unclear whether they are created locally at the site of the fold disruption or they have been convected by the flow from smaller radial distances. [14] Evidence of magnetic reconnection at the HCS in our simulations is important for placing the corresponding spacecraft observations [Gosling et al., 2005; Phan et al., 2006] in the global 3D context. However, more work needs to be done. Since the HCS is created at the inner boundary of the simulation as a tangential discontinuity with anti parallel fields on the two sides of the sheet, reconnection is made possible by numerical dissipation mechanisms [Lyon et al., 2004], given a favorable alignment of the plasma flow. Observationally, the magnetic field does not go to zero inside the HCS, suggesting that it is either a rotational discontinuity or that the tangential field rotates through the current sheet without reaching zero [Smith, 2001]. In the former case, our simulation disregards the possibility that the HCS can already be a rotational discontinuity at the inner boundary of the simulation, created, for example, by reconnection in the corona below the boundary, and then convected into the simulation domain. In the latter case, our simulation disregards the presence of a guide field in the reconnection process. Simulating either of these circumstances will necessarily entail more elaborate boundary conditions on the magnetic field, in particular, including a component normal to the current sheet or a shear angle different from 180. Inferring such conditions from a potential coronal magnetic field solution, e.g. WSA, is not possible. However, contrived numerical experiments to this end or simulations driven by MHD coronal solutions are feasible and should be pursued. [15] The work presented here focused on the simulations of CR The simulations were carried out as part of a larger effort [Pahud et al., 2009] to validate LFM helio against Ulysses spacecraft observations during its fast latitude scan, which occurred from January to April of 1995, during solar minimum [e.g., McComas et al., 2000]. Interestingly, our simulation of the following CR (1893) did not form the HCS fold, presented here, owing to the different structure of plasma flows and magnetic fields. Our preliminary analysis of Ulysses data (the spacecraft passed through this region during CR 1893) shows no evidence of the fold formation either. We plan to specifically look for HCS mesoscale features, such as those presented here, in Ulysses observations [e.g., Neugebauer, 2008] and perform comparisons with our simulations during those periods. [16] In summary, we have presented a high resolution (sub degree, solar radius) simulations of the inner heliosphere using an MHD model that is capable of resolving shocks and discontinuities within 1 2 grid cells. A particular feature, a narrow fold in the heliospheric current sheet, has been the focus of this study. We tracked the radial evolution of this fold and its eventual disruption owing to separation of a bundle of outward directed magnetic flux tubes into the southern hemisphere populated by the inward magnetic flux. We discussed two processes associated with the fold formation and disruption: Non radial flows excited within a stream interaction region pushing the heliospheric current sheet and magnetic reconnection which led to sigmoid shaped magnetic field lines. Neither of these processes could be identified definitively as the cause of the fold disruption. [17] Acknowledgments. V.G.M. thanks N. Schwadron for his support and encouragement during the initial development of LFM helio as well as W. J. Hughes, G. Mason, N. E. Raouafi, E. Roelof, M. Sitnov, and A. J. Ukhorskiy for useful discussions. The authors are grateful to C. N. Arge for the use of the WSA model. This research was supported by the National Science Foundation under agreement ATM , which funds the Center for Integrated Space Weather Modeling (CISM) project of the Science and Technology Center (STC) program. The computations were performed on Kraken and visualized partly on Nautilus at the National Institute for Computational Sciences ( through an allocation of advanced computing resources provided by the National Science Foundation. [18] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper. References Arge, C. N., and V. J. Pizzo (2000), Improvement in the prediction of solar wind conditions using near real time solar magnetic field updates, J. Geophys. Res., 105, 10,465 10,479. Arge, C. N., J. G. Luhmann, D. Odstrcil, C. J. Schrijver, and Y. Li (2004), Stream structure and coronal sources of the solar wind during the May 12th, 1997 CME, J. Atmos. Sol. Terr. Phys., 66, Blanco, J. J., J. Rodríguez Pacheco, M. A. Hidalgo, and J. Sequeiros (2006), Analysis of the heliospheric current sheet fine structure: Single or multiple current sheets, J. Atmos. Sol. Terr. Phys., 68, Czechowski, A., M. Strumik, J. Grygorczuk, S. Grzedzielski, R. Ratkiewicz, and K. Scherer (2010), Structure of the heliospheric current sheet from plasma convection in time dependent heliospheric models, Astron. Astrophys., 516, A17. Foullon, C., et al. (2009), The apparent layered structure of the heliospheric current sheet: Multi spacecraft observations, Solar Phys., 259, Gosling,J.T.,R.M.Skoug,D.J.McComas,andC.W.Smith(2005), Magnetic disconnection from the Sun: Observations of a reconnection exhaust in the solar wind at the heliospheric current sheet, Geophys. Res. Lett., 32, L05105, doi: /2005gl Kallio, E., J. G. Luhmann, and J. G. Lyon (1998), Magnetic field near Venus: A comparison between Pioneer Venus Orbiter magnetic field observations and an MHD simulation, J. Geophys. Res., 103, , doi: /97ja Lionello, R., J. A. Linker, Z. Mikic, and P. Riley (2006), The latitudinal excursion of coronal magnetic field lines in response to differential rotation: MHD simulations, Astrophys. J., 642(1), L69 L72. Lyon, J. G., J. A. Fedder, and C. M. Mobarry (2004), The Lyon Fedder Mobarry (LFM) global MHD magnetospheric simulation code, J. Atmos. Sol. Terr. Phys., 66, , doi: /j.jastp McComas, D. J., et al. (2000), Solar wind observations over Ulysses first full polar orbit, J. Geophys. Res., 105, 10,419 10,433, doi: / 1999JA McGregor, S. L. (2011), On tracing the origins of the solar wind, Ph.D. thesis, Boston Univ., Boston, Mass. McGregor, S. L., W. J. Hughes, C. N. Arge, M. J. Owens, and D. Odstrcil (2011), The distribution of solar wind speeds during solar minimum: Calibration for numerical solar wind modeling constraints on the source of the slow solar wind, J. Geophys. Res., 116, A03101, doi: / 2010JA McNutt, R. L., J. Lyon, C. C. Goodrich, and M. Wiltberger (1999), 3D MHD simulations of the heliosphere VLISM interaction, AIP Conf. Proc., 471, , doi: / Neugebauer, M. (2008), Heliospheric sector boundaries: Single or multiple?, J. Geophys. Res., 113, A12106, doi: /2008ja Odstrcil, D., and V. J. Pizzo (1999), Distortion of the interplanetary magnetic field by three dimensional propagation of coronal mass ejections in a structured solar wind, J. Geophys. Res., 104, 28,225 28,239, doi: /1999ja Ouellette, J. E., B. Rogers, M. Wiltberger, and J. Lyon (2010), Magnetic reconnection at the dayside magnetopause in global Lyon Fedder Mobarry simulations, J. Geophys. Res., 115, A08222, doi: / 2009JA Pahud, D. M., V. G. Merkin, W. J. Hughes, J. Lyon, and S. L. McGregor (2009), LFM helio MHD model and comparisons with Ulysses Fast Latitude Scan data, Eos Trans. AGU, 90(52), Fall Meet. Suppl., Abstract SH13B Phan, T. D., et al. (2006), A magnetic reconnection X line extending more than 390 Earth radii in the solar wind, Nature, 439, of6

6 Pizzo, V. J. (1982), A three dimensional model of corotating streams in the solar wind: 3. Magnetohydrodynamic streams, J. Geophys. Res., 87, Pizzo, V. J. (1994), Global, quasi steady dynamics of the distant solar wind: 2. Deformation of the heliospheric current sheet, J. Geophys. Res., 99, Riley, P., and J. Linker (2002), Modeling the heliospheric current sheet: Solar cycle variations, J. Geophys. Res., 107(A7), 1136, doi: / 2001JA Riley, P., J. A. Linker, and Z. Mikic (2001), An empirically driven global MHD model of the solar corona and inner heliosphere, J. Geophys. Res., 106, 15,889 15,902. Smith, E. J. (2001), The heliospheric current sheet, J. Geophys. Res., 106, 15,819 15,831. Suess, S. T., and E. Hildner (1985), Deformation of the heliospheric current sheet, J. Geophys. Res., 90, Winterhalter, D., E. J. Smith, M. E. Burton, N. Murphy, and D. J. McComas (1994), The heliospheric plasma sheet, J. Geophys. Res., 99, J. G. Lyon and S. L. McGregor, Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, USA. (lyon@tinman.dartmouth.edu; sarahlmcgregor@dartmouth.edu) V. G. Merkin, Johns Hopkins University Applied Physics Laboratory, Johns Hopkins Rd., Laurel, MD , USA. (Slava. Merkin@jhuapl.edu) D. M. Pahud, Department of Astronomy, Boston University, 725 Commonwealth Ave., Boston, MA 02215, USA. (dpahud@bu.edu) 6of6