In this Letter, we develop a self-consistent picture of the time-averaged structure and composition of polar coronal holes L127 1.

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1 The Astrophysical Journal, 51:L127 L131, 1998 July The American Astronomical Society. All rights reserved. Printed in U.S.A. UVCS/SOHO EMPIRICAL DETERMINATIONS OF ANISOTROPIC VELOCITY DISTRIBUTIONS IN THE SOLAR CORONA J. L. Kohl, 1 G. Noci, 2 E. Antonucci, 3 G. Tondello, 4 M. C. E. Huber, 5 S. R. Cranmer, 1 L. Strachan, 1 A. V Panasyuk, 1 L. D. Gardner, 1 M. Romoli, 2 S. Fineschi, 1 D. Dobrzycka, 1 J. C. Raymond, 1 P. Nicolosi, 4 O. H. W. Siegmund, 6 D. Spadaro, 7 C. Benna, 8 A. Ciaravella, 1,5 S. Giordano, 8 S. R. Habbal, 1 M. Karovska, 1 X. Li, 1 R. Martin, 9 J. G. Michels, 1 A. Modigliani, 2 G. Naletto, 4 R. H. O Neal, 1 C. Pernechele, 4 G. Poletto, 1 P. L. Smith, 1 and R. M. Suleiman 1 Received 1997 December 1; accepted 1998 April 3; published 1998 June 18 ABSTRACT We present a self-consistent empirical model for several plasma parameters of a polar coronal hole near solar minimum, derived from observations with the Solar and Heliospheric Observatory Ultraviolet Coronagraph Spectrometer. The model describes the radial distribution of density for electrons, H, and O and the outflow velocity and unresolved most probable velocities for H and O during the period between 1996 November and 1997 April. In this Letter, we compare observations of H i Lya and O vi ll132, 137 emission lines with spatial models of the plasma parameters, and we iterate for optimal consistency between measured and synthesized observable quantities. The unexpectedly large line widths of H atoms and O ions at most radii are the result of anisotropic velocity distributions, which are not consistent with purely thermal motions or the expected motions from a combination of thermal and transverse wave velocities. Above 2 R,, the observed transverse, most probable speeds for O are significantly larger than the corresponding motions for H, and the outflow velocities of O are also significantly larger than the corresponding velocities of H. We discuss the constraints and implications on various theoretical models of coronal heating and acceleration. Subject headings: line: profiles solar wind Sun: corona Sun: UV radiation 1. INTRODUCTION In order to explain comprehensively the heating and acceleration of the solar wind, theories must incorporate detailed empirical knowledge of the physical conditions in the coronal plasma. Obtaining accurate measurements of densities, outflow velocities, and microscopic velocity distributions in the principal acceleration region of the solar corona (between 1 and 5 R, ) is thus of extreme importance. This is a primary goal of the Ultraviolet Coronagraph Spectrometer (UVCS) operating aboard the Solar and Heliospheric Observatory (SOHO) satellite. The UVCS instrument is described in detail by Kohl et al. (1995), and some preliminary first results have been presented by Kohl et al. (1996, 1997a, 1997b), Noci et al. (1997), Raymond et al. (1997), and others. The ultraviolet emission lines and polarized visible light observed by UVCS/SOHO present a rich and varied source of diagnostic information about the solar corona. In this Letter, we utilize a large ensemble of these measurements to construct an empirical model of an average polar coronal hole near solar 1 Harvard-Smithsonian Center for Astrophysics, 6 Garden Street, Cambridge, MA Università di Firenze, I-5125 Firenze, Italy. 3 Osservatorio Astronomico di Torino, Strada Osservatorio, 2, I-125 Pino Torinese, Italy. 4 Università di Padova, I Padova, Italy. 5 Space Science Department, ESA-ESTEC, Astrophysical Division, Postbus 299, 22 AG Noordwijk, The Netherlands. 6 Space Sciences Laboratory, University of California, Berkeley, CA Osservatorio Astrofisico di Catania, Città Universitaria, Viale Andrea Doria 6, I Catania, Italy. 8 Università di Torino, I-1125 Torino, Italy. 9 Institut d Astrophysique Spatiale, Universite Paris XI, Batiment 121, 9145 Orsay Cedex, France. 1 Osservatorio Astrofisico Arcetri, Largo Enrico Fermi 5, I-5125 Firenze, Italy. L127 minimum. The modeling procedure is initiated by deducing various physical quantities (e.g., density, outflow velocity, and velocity distribution) directly from UVCS observations in a fashion similar to that used by Kohl et al. (1997a). However, this simple inverse determination of the plasma parameters is not yet fully self-consistent. Synthetic observables (such as line profiles, intensities, and polarized white light) generated with these initial models often do not agree perfectly with the measured data, and small adjustments must then be made to the plasma parameters. Repeated comparison with the data provides guidance on how to iterate the derived quantities until there is optimal agreement between the empirical model and the observations (for more details, see Cranmer et al. 1998a). It is important to emphasize that the empirical models described here do not specify the processes that maintain the coronal plasma in its assumed steady state. Thus, there is no explicit mention of coronal heating and acceleration mechanisms, waves and turbulent motions, and magnetic field structure within the models themselves. The iterated quantities in the models depend on only observations and well-established theory, such as the radiative transfer inherent in the line formation process. All of the resulting coronal parameters, then, are derived straightforwardly and unambiguously from measurements and can be effectively utilized to constrain theoretical models. In the remainder of this Letter, we outline the UVCS observations that are incorporated into the empirical model ( 2), construct a detailed picture of the dynamics of coronal H atoms ( 3) and O ions ( 4), and discuss the implications of the empirical data on theoretical models of the solar corona and wind ( 5). 2. OBSERVATIONS AND ELECTRON DENSITY MODEL In this Letter, we develop a self-consistent picture of the time-averaged structure and composition of polar coronal holes

2 L128 KOHL ET AL. Vol. 51 during the period between 1996 November and 1997 April. This time interval was very near the minimum of solar activity (see, e.g., Pap et al. 1997). The present empirical model of a representative coronal hole takes advantage of the relatively simple (axisymmetric) structure of the corona observed during this 6 month period, i.e., large polar holes with presumably open magnetic field lines, bounded by equatorial high-density streamers with mainly closed field lines. The open field lines are assumed to follow the large-scale electron density structure, expanding superradially near the solar surface then radially farther out, eventually filling a majority of the volume of the solar wind (Hundhausen 1977; Low 199; Roberts & Goldstein 1998). The specific UVCS observations that have been used in the empirical modeling process will be described by Cranmer et al. (1998a). The UVCS Data Analysis Software was used to remove image distortion, to flat-field the detectors, and to calibrate the data in wavelength and intensity (Gardner et al. 1996; Kohl et al. 1997a, 1997b). Noncoronal sources of emission, such as instrument-scattered stray light from the solar disk, the F-corona, and interplanetary H i Lya, were subtracted from the data (Panasyuk et al. 1998). Note, though, that the straylight characterization and modeling of the instrument is ongoing (see, e.g., Romoli et al. 1998). We model the electron density in the solar corona by measuring the linear polarization due to Thomson-scattered photospheric light (van de Hulst 195) with the UVCS white-light channel (WLC). The methods used to reduce and calibrate the WLC measurements are given by Romoli et al. (1993, 1998), and Figure 1 shows the polarized brightness (pb) as a function of radius over the south heliographic pole. A fraction of the temporal variation in pb at a given height cannot be explained by noise in the data and can be understood as the evolution or rotation of variable-density structures, e.g., polar plumes, across the line of sight (LOS). At the radii observed, we find there is a negligible latitudinal dependence of pb within 6 from the heliographic poles, in agreement with the conclusions of Guhathakurta & Holzer (1994). The measured boundary between the superradially expanding coronal hole and the streamer belt is specified using Kopp & Holzer s (1976) parameterization, with constants fmax 6.5, R1 1.5 R,, and j1.6 R,. The mean polar electron density as a function of radius between 2 and 4 R, is given by ( ) ( ) ne ( r) R, R, , (1) cm r r with relative uncertainties equal to those in the observed pb (which is linearly related to n e ). Because the pb data in Figure 1 were obtained over several nonconsecutive days, the derived electron density represents an average between regions of bright polar plume concentrations and weaker interplume regions. They are not significantly affected by streamer enhancements along the extended LOS. As shown, above 2 R, these densities are in good agreement with other measurements near solar minimum (Guhathakurta & Holzer 1994; Fisher & Guhathakurta 1995). 3. NEUTRAL HYDROGEN VELOCITY DISTRIBUTION The Lyman series lines of neutral hydrogen are some of the most prominent features in coronal ultraviolet spectra. Coronal Fig. 1. UVCS coronal polarization brightness (pb) in units of the mean solar-disk surface brightness B,, over the south pole. Measurements were taken during 1996 December 27 3 (squares) and 1997 April 14 2 (crosses), with error bars reflecting statistical and stray-light uncertainties. Also plotted 2 is the result of a nonlinear x minimization fit (solid line) and the relative uncertainty in the overall radiometric calibration (dashed lines). The coronal hole electron densities of Guhathakurta & Holzer (1994, dot-dashed line) and Fisher & Guhathakurta (1995, gray region) have been translated back into pb and plotted here. H i Lya emission is caused mainly by resonant scattering of chromospheric H i Lya photons and only negligibly by local collisional excitation. The shape and intensity of this line are determined by the density and velocity distribution of H in the solar wind, which is believed to reflect closely the distribution of protons up to about 3 R, (Olsen, Leer, & Holzer 1994; Allen, Habbal, & Hu 1998). In this section, we construct an empirical model of these quantities from UVCS profile measurements of the H i Lya line. The H i Lya specific intensity emergent from an optically thin corona is given by a straightforward integration over the LOS, the incident frequency, and the solid angle of the solar disk (Withbroe et al. 1982). The integrand depends on the coronal H density, the chromospheric H i Lya intensity and profile, the partial redistribution of photons, and the atomic transition strength. In ionization equilibrium, the density of H atoms depends primarily on the electron temperature (Gabriel 1971), which we adopt from models of the in situ chargestate measurements made by the Solar Wind Ion Compositon Sprectrometer instrument on Ulysses (Ko et al. 1997). The redistribution function depends on the velocity distribution of H atoms, which we characterize as an anisotropic bi-maxwellian with independent, most probable 1/e speeds wk that are parallel and perpendicular, respectively, to the superradially diverging 11 magnetic field lines, and a parallel macroscopic outflow velocity u. The most probable speeds 11 For convenience, we model individual flux tubes as all having the same latitudinally invariant Kopp & Holzer (1976) divergence factor; variation of this factor with latitude does not significantly affect the resulting line intensities or widths (for observations over the poles) and therefore has no impact on the results of this Letter.

3 No. 1, 1998 UVCS/SOHO EMPIRICAL DETERMINATIONS L129 Fig. 2. (a) V 1/e and most probable speeds for H i Lya. The line widths are denoted by squares (north polar holes) and triangles (south polar holes). Also plotted is a fit to the data (solid line), the most probable speed we corresponding to thermal distributions at Te (dotted line), for models A1 (dashed line) and A2 (dot-dashed lines). (b) Same as (a), but for O vi l132 (north: squares, south: triangles) and O vi l137 (north: diamonds, south: crosses), and with models B1 and B2 replacing A1 and A2. Also plotted is an empirical upper limit for the O parallel speed w max (dash triple-dotted line). (c) Empirical outflow velocity over the poles, with gray regions corresponding to lower/upper limits on w k in models A1, A2 (for H ) and B1, B2 (for O ). The solid lines denote proton mass flux conservation with f 6.5 (upper line) and f 1 (lower line). max wk correspond to independent kinetic temperatures in the two directions, but we retain the velocity units because these quantities may contain both microscopic random motions as well as any unresolved bulk fluctuations along the LOS (e.g., transverse wave velocities). In the self-consistent empirical model for H, we specify the velocity parameters wk, w, and u as functions of radius over the coronal poles, and we adjust these quantities until the synthesized intensities and line widths agree with the observed values. The total H i Lya intensity depends mainly on the velocity parameters in the directions parallel to the incident solar-disk radiation (i.e., primarily on u and w k ) via the Doppler-dimming effect (Hyder & Lites 197; Beckers & Chipman 1974; Withbroe et al. 1982). The 1/e half-width of the near-gaussian line profiles depends mainly on the velocity parameters along the LOS (i.e., primarily on w for near 9 scattering). In the actual models, however, all three velocity parameters affect both the synthesized intensity and the line shape (Li et al. 1998; Cranmer et al. 1998a). In Figure 2a, we plot UVCS measurements of 1/e half-widths of the Gaussian coronal components of H i Lya lines over the poles, expressed in Doppler velocity units: cdl1/e 2kTK V1/e, (2) l m H where Dl 1/e is the observed 1/e half-width in wavelength and T K is the effective kinetic temperature of particles moving with an assumed most probable speed V 1/e along the LOS. These measurements are consistent, within the 1 3 km s uncertainties, with the V 1/e line width parameters measured at a slightly earlier period in 1996 by Kohl et al. (1997a). Note that the measured V 1/e contains contributions from both the unresolved motions (incorporated into wk ) and the LOS-projected macroscopic wind outflow u; these two types of motion are separated in the modeling process. At all radii, TK greatly exceeds the expected electron temperature Te. We plot the hydrogen thermal speed that would correspond to the 1/2 electron temperature as we (2kT e/m H). Because the Doppler dimming for H i Lya depends on both u and w k, it is difficult to determine both independently. We thus choose plausible extreme limits on and vary both u w k and w in order to construct self-consistent models for each case. In model A1, we set a reasonable lower limit by assuming that the parallel hydrogen motions are in thermal equilibrium with the electrons ( wk we ). In model A2, we set an upper limit by assuming an isotropic distribution ( wk w ). Figure 2a shows the derived w values for models A1 and A2; these are close to, but slightly smaller than, V 1/e because of the linebroadening effect of the LOS component of u along the superradially diverging flux tube. Figure 2c shows the self-consistent model outflow velocities u, which have combined experimental and modeling uncertainties on the order of 3 8 km s (see also Strachan et al. 1993). The expected proton wind speed is also plotted, assuming mass flux conservation over the poles. We use in situ measurements of the time-averaged mass flux to calibrate these 8 2 values, with n pu 2 # 1 cm s at 1 AU (Goldstein et al. 1996), and we assume n p.8ne for a fully ionized plasma with 1% helium. The lower solid line in Figure 2c represents the limit of purely radial expansion, or f 1 at all radii; the upper solid line results from applying the modeled Kopp & Holzer (1976) expansion with fmax 6.5. Above r 2.2 R,, the outflow velocity derived from model A1 is in general agreement with that assuming mass flux conservation and clearly not in agreement with model A2 above 3. R,. The agreement with model A1 represents indirect, but reasonably firm, evidence that the H velocity distribution (along with the protons) is anisotropic, with w 1 w. k 4. IONIZED OXYGEN VELOCITY DISTRIBUTION The most surprising initial results from the first year of operation of UVCS have been the extremely broad coronal profiles of such highly ionized elements as oxygen and magnesium (Kohl et al. 1997a, 1997b). Here we develop an empirical model of the distribution of O ions in coronal holes from the bright O vi ll131.93, emission-line doublet. We utilize the same line-synthesis techniques described in 3 to compute the O vi emission from a given model. Both the oxygen elemental abundance and the frozen-in ionization balance are assumed to be constant in radius, with log 1 (n O/n p) 6.7 (Cranmer et al. 1998a). In Figure 2b, we plot the radial dependence of the 1/e half-

4 L13 KOHL ET AL. Vol. 51 widths of both O vi lines over north and south polar coronal holes. The most striking aspect of these measurements is the unusually large magnitude of V 1/e at most radii, compared with H i Lya. The large spread in the V 1/e velocities at large radii arises from both line width measurement uncertainties and a possible long-timescale variability of this sensitive plasma parameter in the extended corona. The outflow velocity of O ions can be sensitively probed because of the scattering of chromospheric C ii ll136.34, radiation by the O vi l137 line (Noci, Kohl, & Withbroe 1987; Li et al. 1998). The C ii photons interact with coronal O velocity distributions in limited regions of outflowvelocity space, and this Doppler pumping can strengthen the O vi l137 intensity in these regions. However, for large enough values of the most probable speed in the direction of the incoming radiation, the O vi l137 and C ii lines are effectively smeared together, and the localized intensity enhancement grows weaker. Because of this constraint, we are able to use the intensity ratio between the O vi l132 and O vi l137 lines in order to put a firm upper limit, wmax, on wk. For parallel speeds larger than this limit, the intensity ratio could never reach the low values less than 1 observed by UVCS (for details, see Li et al and Cranmer et al. 1998a). As in 3, we specify reasonable lower and upper limits for w k in two self-consistent models. Model B1 is similar to model A1 in that we assume the parallel O motions are in equilibrium with the electrons. Model B2 assumes that w k is equal to the smaller of wmax at each radius, where wmax is the empirical upper limit to w k discussed above. Figure 2b shows the modeled oxygen w values, which are slightly smaller than V 1/e because of LOS components of the outflow velocity. It is thus clear that for r 2.2 R,, w must be larger than wk and that the O motions must be strongly anisotropic. Also, since w for O ions is larger at most radii than for H w atoms, this implies that neither thermal motions (which would imply smaller speeds for heavier ions) nor common bulk-fluid motions (e.g., transverse waves, which would imply speeds independent of mass) dominate the unresolved perpendicular speeds. Figure 2c displays the outflow velocities for models B1 and B2. The modeled outflow velocity for O ions is significantly larger than the proton velocity implied by mass flux conservation and also larger than the H velocity from model A1 (see also Li et al. 1998). The O velocity may pass within the uncertainty limits of the outflow derived from model A2. Note that the derived outflow velocity depends on the direction of the flow vectors with respect to the direction of the incoming radiation; if the empirical Ansatz of superradial divergence were to be replaced by radial expansion, the derived velocities for O (greater than 2 km s ) would be lowered by approx- imately 5 km s. However, it seems improbable that the outflow velocities for hydrogen and oxygen are the same above 2 R, (see Cranmer et al. 1998a for a more detailed uncertainty analysis). Because the outflow velocity of oxygen ions at 1 AU is no more than 1% 15% larger than that of the protons (Schmidt et al. 198), it seems that the only reasonable way for the high speeds in Figure 2c to be consistent with mass flux conservation is for n O/n p to vary with radius in the corona. (Note, however, that the empirical outflow velocity has been determined robustly from the O vi line ratio, and it is completely independent of the abundance and ionization balance.) 5. DISCUSSION AND THEORETICAL IMPLICATIONS In the empirical coronal hole model presented in this Letter, we have attempted to apply as few physical assumptions as possible to the observations and deduce only what can be unambiguously and consistently derived from the data. Thus, for example, we have not attempted to separate observed velocity distributions into various unresolvable components: e.g., thermal motions, other random microscopic motions, and transverse wave motions. We have not attempted to speculate on the underlying heating and acceleration mechanisms that give rise to the observed distributions. However, the significant differences between H and O in both u and w put strong constraints on possible theoretical solar wind models. One theoretical explanation for the preferential ion acceleration may be the dissipation of high-frequency waves via resonance with ion-cyclotron Larmor motions (Isenberg & Hollweg 1983; Isenberg 1984; McKenzie, Banaszkiewicz, & Axford 1995; Tu & Marsch 1997). Because different ions have different resonant frequencies, they receive different amounts of heating and acceleration as a function of radius (see also Fletcher & Huber 1997 and Cranmer et al. 1998b). Also, nonresonant models of nonlinear Alfvén waves (e.g., Ofman & Davila 1997) may be able to model the observed velocity distributions if the wave-particle interactions are able to accelerate heavier ions preferentially. Cranmer et al. (1998a) discuss further implications and constraints of the UVCS/SOHO empirical data on theoretical models of coronal heating and the acceleration of the high-speed solar wind. 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