Fast solar wind after the rapid acceleration

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003ja010247, 2004 Fast solar wind after the rapid acceleration M. Kojima, 1 A. R. Breen, 2 K. Fujiki, 1 K. Hayashi, 3 T. Ohmi, 4 and M. Tokumaru 1 Received 25 September 2003; revised 18 January 2004; accepted 13 February 2004; published 20 April [1] We have studied the radial dependence of the velocity of high-latitude fast solar wind in the heliocentric distance range of AU. For this study a new tomographic analysis method which can evaluate uncertainties was developed to obtain velocity distribution maps on two reference spheres at 0.13 and 0.3 AU using interplanetary scintillation (IPS) observations. First of all, it is tested that this tomographic method has enough sensitivity and reliability to investigate the radial dependence of the wind velocity. The analysis was made for the IPS observations during 3 years, from 1995 to 1997, when solar activity was minimum. From this analysis, average velocities of km s 1 were obtained at distances of AU, which were 19 ± 17 km s 1 lower than those at AU. The results from this work, taken together with measurements of SOHO/ LASCO, EISCAT and MERLIN [Breen et al., 2002], Helios [Schwenn et al., 1978], and Ulysses [McComas et al., 2000], indicate that the fast wind is accelerated almost to its final flow velocity within 20 R s and a small but not negligible acceleration exists beyond 30 R s which tends to become smaller at farther heliocentric distances. INDEX TERMS: 2164 Interplanetary Physics: Solar wind plasma; 7511 Solar Physics, Astrophysics, and Astronomy: Coronal holes; 6982 Radio Science: Tomography and imaging; 6969 Radio Science: Remote sensing; KEYWORDS: solar wind, interplanetary scintillation, acceleration Citation: Kojima, M., A. R. Breen, K. Fujiki, K. Hayashi, T. Ohmi, and M. Tokumaru (2004), Fast solar wind after the rapid acceleration, J. Geophys. Res., 109,, doi: /2003ja Introduction [2] Interplanetary scintillation (IPS) observations by Grall et al. [1996] have revealed that the fast solar wind emanating from a polar coronal hole is rapidly accelerated to its final flow velocity within 20 R s. This rapid acceleration was confirmed by IPS observations made using the EISCAT (932 MHz) and MERLIN (5 GHz) facilities by Breen et al. [2000, 2002]. Closer to the Sun, the Solar and Heliospheric Observatory (SOHO) spacecraft observed the acceleration of the fast solar wind taking place within several solar radii [Kohl et al., 1998; Axford et al., 1999; Cranmer et al., 1999; Breen et al., 2000; Giordano et al., 2000; Patsourakos and Vial, 2000; Miralles et al., 2001; Breen et al., 2002; Teriaca et al., 2003]. These observations revealed that the fast solar wind attains 50% of its cruising speed by 4 5 R s and the acceleration is almost completed inside 10 R s. [3] Based on these observational facts of the wind velocity and an extremely high kinetic temperature at a few solar radii [Kohl et al., 1997, 1998], new acceleration models for 1 Solar-Terrestrial Environment Laboratory, Nagoya University, Toyokawa, Japan. 2 Institute of Mathematical and Physical Sciences, University of Wales, Aberystwyth, UK. 3 W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, California, USA. 4 Science and Technology Department, CTI Co., Ltd., Nagoya, Japan. Copyright 2004 by the American Geophysical Union /04/2003JA protons have been proposed to explain the rapid acceleration by several authors [e.g., Esser and Habbal, 1996; Esser et al., 1997; McKenzie et al., 1997; Axford et al., 1999]. In the early acceleration models, Alfvén wave pressure has been introduced in the momentum equation as an additional force to accelerate the fast wind from a low-temperature corona [e.g., Hollweg, 1973; Barnes, 1992]. However, the pressure gradient associated with Alfvén waves does not play an important role in the acceleration inside of 10 R s because of the small Alfvén wave velocity amplitude, in the inner corona, compared with the thermal velocity. Therefore Alfvén wave pressure cannot accelerate the fast wind rapidly within 10 R s and a more efficient acceleration mechanism is required. The newly proposed acceleration models have introduced an additional heating term in the energy equation, and this term is ascribed to cyclotron heating by high-frequency Alfvén waves released from network nanoflares [McKenzie et al., 1997; Axford et al., 1999]. These rapid acceleration models can accelerate the solar wind to 400 km s 1 by 4 R s and to its final flow velocity by 10 R s. [4] The wind velocities measured by IPS at distances between 10 and 20 R s have a large velocity spread with some measurements being over 1000 km s 1 at closer distances to the Sun (see Figure 3 in the work of Grall et al. [1996]). These velocities may not be the bulk flow velocity alone but may be biased by Alfvén wave velocity. Coles and Harmon [2001] have shown that density fluctuations produced by oblique Alfvén waves can cause a large overestimation of flow velocities especially within 20 R s. They attribute the wide spread of radial velocities obtained 1of10

2 in IPS measurements near the Sun to this biasing effect. If their observed wind velocities are caused by outward propagating waves, the lower envelope of the velocity spread may indicate the radial dependence of a bulk flow velocity. This means that the fast wind does not necessarily have to be accelerated to the final speed within 10 R s as the model proposed by McKenzie et al. [1997] and Axford et al. [1999]. Miralles et al. [2001] found that the acceleration profiles of the fast wind within 4 R s are different depending on their origins, i.e., the acceleration of the fast solar wind from a large equatorial coronal hole is more gradual than that from a polar coronal hole. It should be noted that velocities larger than 500 km s 1 have not been reported from SOHO observations within 4 R s. These facts mean that the solar wind acceleration profile around 10 R s is still not clear, and the rapid acceleration of the fast solar wind may not be completed within 10 R s. Also the acceleration model proposed by Esser et al. [1997], in which the solar wind is accelerated to 50% of its cruising speed by 4 R s and gradually approaches its final speed by a few tens of solar radii, can be a possible acceleration model. [5] In interplanetary space the Helios and Ulysses spacecraft have observed radial dependence of the wind velocity and temperature at heliocentric distances beyond 0.3 AU. Schwenn et al. [1978] have reported that the velocity change of the fast wind is small in the distance range of AU, but not zero. The existence of a small acceleration rate of 7 ± 16 km s 1 AU 1 is reported. At farther distances of AU, McComas et al. [2000] reported from Ulysses observations that an acceleration is still continuing at a smaller rate of 1.5 km s 1 AU 1. Thus a slight acceleration is present after the initial rapid acceleration at least up to 5 AU. Considering together with nonadiabatic cooling of the fast solar wind, T R 0.808±0.169 for speeds of km s 1 at heliocentric distances of AU [Freemann, 1988] and R 1.02 at AU [McComas et al., 2000], some energy and momentum supplies may remain after the rapid acceleration. [6] Therefore it is important to elucidate how the rapidly accelerated solar wind approaches asymptotically to the final flow velocity beyond the major acceleration region. We analyze the radial dependence of the wind velocity in the distance range of 0.13 to 0.9 AU ( R s ) using IPS data obtained at the Solar-Terrestrial Environment Laboratory (STELab) at a frequency of 327 MHz [Asai et al., 1995]. Although the IPS method has been used to measure the radial dependence of the solar wind from the near-sun region to 1 AU, it has several potential biases. One of them is a line-of-sight integration effect, which reduces both the velocity of the fast solar wind and the spatial resolution. This drawback can be overcome by applying the computerassisted tomography method which will be introduced in the following sections. First, we introduce the tomographic analysis method which is modified from the previous version developed by Kojima et al. [1998] so that it can evaluate uncertainties involved in the analysis. Then we discuss the sensitivity and reliability of this analysis method for investigation of the distance dependence of the wind velocity. Using the tomographic analysis method, we reanalyze the data obtained in 1995 which were already analyzed by Kojima et al. [1998] and extend the analysis to the years of 1996 and 1997 when the solar activity was at its minimum and the solar wind structure was not complicated. Finally, we do a statistical analysis of velocities derived for the fast wind at high latitudes and compare with other observations. 2. Tomographic Analysis 2.1. Tomography With Two Reference Spheres [7] In the tomographic analysis developed by Kojima et al. [1998], an initial model of wind velocity distribution is first introduced on the reference sphere and then expanded radially outward with a constant velocity to make a threedimensional solar wind model. IPS observations are simulated in this three-dimensional solar wind model and compared with actual observations. The amount of wind velocity discrepancy between the simulated and observed IPS data is distributed on the reference sphere along a projected line of sight with a weighting factor to modify the velocity distribution model on the reference sphere. After completing the simulations for all observations, the initial solar wind model is modified and the IPS simulations are restarted. This process is iterated until the residuals become small enough. Usually, this process converges after several iterations. [8] For this study we derive two velocity maps in Carrington longitude and heliographic latitude from IPS data obtained at distances of AU. One is the inner velocity map which represents the average wind velocity structure at AU (28 64 R s ), and the other one is the outer map representing the solar wind structure at AU ( R s ). To derive these two maps, the tomographic analysis is modified. The modified analysis uses two reference spheres at 0.13 and 0.3 AU. Initial velocity distribution maps are introduced on these reference spheres independently, and then the solar wind within and outside of 0.3 AU were modeled by expanding these maps outwardly with an assumption of radial and constant velocity flow. IPS observations are simulated in the solar wind model and compared with actual observations. The iteration process to modify the initial velocity maps by comparing the simulated and observed IPS data is made as follows. When the elongation angle of a given line of sight is larger than 17, all portions on the line of sight are outside of 0.3 AU. In this case, velocity data on the line of sight are all referred to the outer sphere at 0.3 AU (Figure 1). When the elongation angle is less than 17, a part of the line of sight near the closest point to the Sun is within 0.3 AU, while the other parts are outside of 0.3 AU. In such cases two reference spheres are used: velocity data at portions on the line of sight within 0.3 AU are referred to the inner sphere at 0.13 AU, while the rest of the data are referred to the outer reference sphere at 0.3 AU. When making the inner map, IPS data observed at elongations less than 7.5, at which the closest distance of a line of sight to the Sun is 0.13 AU, are not used because the IPS at a frequency of 327 MHz saturates within this elongation angle in the polar regions [Manoharan, 1993]. [9] The velocity maps in Figure 2 are examples of the two-sphere tomography obtained from the IPS observations during Carrington rotations (CR) in the year Since data from one solar rotation period was sparse, data of five rotations were used to get sufficient latitudinal 2of10

3 Figure 1. Tomographic analysis using two reference spheres. Data at portions on the line of sight within 0.3 AU are referred to the inner sphere at 0.13 AU, while the rest of the data are referred to the outer reference sphere at 0.3 AU. coverage. A black narrow belt above the equator in the inner map is the region in which there were not enough lines of sight. Comparing the inner and outer maps, one can see that the inner map is noisier because of less number of lines of sight which traverse the inner region Reliability of Analysis [10] Since the IPS observation is a line-of-sight integration in the structured solar wind, spatial structure of the solar wind is blurred and measured velocities are biased in the IPS observation. The tomographic analysis is to deconvolve this line-of-sight integration. However, since the lineof-sight integration is a nonlinear convolution, it cannot be solved by linear inverse process and we use the iteration process to find the best-fit solution. The purpose of this section is to test that the iteration process converges to a unique solution in which the original solar wind structure and unbiased velocities are retrieved. [11] Kojima et al. [1998, 1999, 2001] have discussed the reliability of the IPS tomographic observations in several cases. Reconstruction of the global solar wind structure during the solar activity minimum phase was tested by applying the tomographic analysis for noise-free IPS measurements which were synthesized by simulating IPS data using a solar wind model [Kojima et al., 1998]. In this test it was shown that the tomographic analysis can retrieve the original solar wind structure which is blurred by line-of-sight integration. A reconstruction test for a compact low-speed stream structure was made by Kojima et al. [1999]. Kojima et al. [2001] showed that the IPS tomographic analysis can detect latitudinal velocity structures such as a sharp wind velocity gradient between low-speed and high-speed regions, a velocity increase with latitude in the high-speed region and the north-south asymmetry in wind velocity which were observed by Ulysses [e.g., Goldstein et al., 1996; Woch et al., 1997]. Here we discuss the reliability of the tomographic analysis from viewpoints different from those. First, we introduce a method to estimate the uncertainty contained in each resolution bin in a wind velocity map. Second, we discuss the velocity resolution when there is a small acceleration at distances of AU Analysis of Uncertainty [12] After several iterations to modify the solar wind model in the tomographic analysis, there still remains some discrepancy between the actual observed velocity and the simulated one in the solar wind model. After the last iteration, discrepancy residuals d(k)=v obs (k) V sim (k) are calculated for each line of sight, where V obs (k) and V sim (k) are observed and simulated velocities for the k-th line of sight, respectively. Then a weighted means of the discrepancy residuals, s(i, j), is calculated in each resolution bin of the map at latitude and longitude (i, j)bys(i, j)=s k (d(k)w(i, j; k))/s k w(i, j; k), where w(i, j; k) is a weighting factor assigned to a resolution bin at (i, j) through which the k-th line of sight traverses (see Kojima et al. [1998] for a formula of the weighting function). The summation S k is made for all the lines of sight which traverse through the (i, j) bin. The calculated s(i, j) is used as the uncertainty of the wind velocity analyzed by the tomographic method. In this analysis we use a resolution bin size of 1 1 in longitude and latitude, but the actual resolution is a twodimensional running mean made with a circular weighting window of angular radius 7.5. Using this analysis, we can find and remove less reliable bins in the velocity map Sensitivity [13] We test the tomographic analysis to determine whether it can detect the wind velocity difference between Figure 2. Examples of the two-sphere IPS tomography. (a) An inner map and (b) an outer map. Contour lines are for every 100 km s 1 from 400 to 700 km s 1. These solar wind velocity maps were derived from the IPS observations made during five Carrington rotations, , in the year A black belt along the equator in the inner map is the region where no line-of-sight data were available. 3of10

4 the heliocentric distance ranges AU (inner region) and AU (outer region) if the solar wind is accelerated in these distance ranges. This test used a synthetic IPS data set simulating observations in a typical solar minimum solar wind model with a latitudinal structure of VðR; qþ ¼ V max for jqj > 30 ; VðR; qþ ¼ V min þ ðv max V min Þsin 4 ð3qþ for jqj < 30 ; with heliocentric distance dependence of velocity VðR; qþ ¼ V o þ ar: V max and V min are the velocities of fast wind at high latitudes and of low-speed wind along the equator, respectively, while q is the heliographic latitude, V o is a velocity at 0.1 AU, and R is the heliocentric distance in AU. The test is made for the following two models. Model-1: a = 20 km s 1 AU 1 for V o < 500 km s 1, and a =50km s 1 AU 1 for V o > 500 km s 1. Model-2: a = 50 km s 1 AU 1 for V o < 500 km s 1, and a = 100 km s 1 AU 1 for V o > 500 km s 1. The average velocity differences of the fast wind between inner and outer regions are 20 km s 1 in Model-1 and 40 km s 1 in Model-2, respectively. IPS observations are simulated in these solar wind models with the 1,984 lines of sight which were actually observed during CR in the year of [14] Having generated this synthetic dataset, the tomographic analysis is applied to these noise-free synthetic IPS observations and the inner and outer velocity maps are derived. The tomography analysis does not assume beforehand the wind velocity changes with heliocentric distance. If the analysis is successful, velocities in the inner map will be different from those in the outer map. Figures 3a and 3b are the latitudinal dependence of velocity derived by taking the longitudinal average in the inner (thin line) and outer (thick line) velocity maps, respectively. We examined how well original velocities were retrieved for the fast solar wind at high latitudes by comparing velocities averaged in the latitudinal range and obtained a velocity difference of 21 ± 8 km s 1 for the test of Model-1 solar wind and 42 ± 7kms 1 for Model-2. These are very close to the velocity differences between the inner and outer distance ranges in each model. [15] Thus the tomographic analysis has enough sensitivity to determine the wind velocity differences as small as 20 km s 1 between the inner and outer regions. It should be noted that the result from the tomographic analysis does not depend on the initial model given on the reference sphere to start the iteration process Applicable Distance Range of the Tomographic Analysis [16] The tomographic analysis is based on the Born approximation which is valid in radio weak scattering region. The level of radio scattering intensity depends on the level of electron density fluctuation and a radio frequency. As an IPS radio source approaches the Sun, the level of electron density fluctuation increases and then the radio scattering goes into the strong scattering region. Therefore we have to decide the heliocentric distance range Figure 3. Sensitivity test of the two-sphere tomographic analysis applied to synthetic IPS observations using two solar wind models in which the wind velocity was increased with the heliocentric distance: An average velocity difference of high latitude solar wind between distance ranges of AU (inner region) and AU (outer region) is 20 km s 1 in Model-1 and 40 km s 1 in Model-2, respectively. (a) The latitudinal structures were derived from the inner and outer velocity maps which were obtained applying the tomographic analysis for the synthetic IPS observations in the solar wind Model-1, and (b) for those in the Model-2, respectively. Average velocity differences between the inner and outer maps in the latitudinal range of are 21 ± 8 km s 1 for Model-1 and 42 ± 7 km s 1 for Model-2. in which the tomographic analysis is applicable for the IPS observations at a frequency of 327 MHz. [17] Manoharan [1993] has reported that the density fluctuation level in the polar regions is about 2.5 times less than that in the equatorial regions during solar activity minimum phase and the IPS at a frequency of 327 MHz saturates at an elongation angle of 12 (0.2 AU) in the equatorial zone and at 7.5 (0.13 AU) in the polar regions. On the basis of this observational report we decide to use the data obtained in distance range of AU during the solar minimum phase and at high latitudes, which are expected to be observed in the weak scattering region. [18] Although we selected a distance range of AU to avoid the strong scattering region, there is some risk that the near-sun region might be affected by strong scattering. We therefore apply two tests to determine the validity of the tomographic application. For the first test we compare the spatial resolution of the analysis between the inner and outer regions of 0.3 AU using the data obtained in the solar minimum phase. If the IPS observations at a frequency of 327 MHz in the distance range of of10

5 Figure 4. (a) Solar wind velocity distribution on the reference sphere at 0.13 AU derived from observations during CR at elongations less than 17 ( AU), and (b) from observations at elongations larger than 17 ( AU). Contour lines are for every 100 km s 1 from 400 to 700 km s 1. Black-colored regions at high latitudes are bins with no data. (c) Latitudinal dependence of the solar wind velocity in the two maps. The thick line is for the outer map while the thin one is for the inner map. The similarity of the structure indicates that the tomographic analysis can be used in the distance range of AU. 0.3 AU were in the strong scattering region, the Born approximation is not valid in the tomographic analysis and then the line-of-sight integration effects cannot be deconvolved adequately. As a result, spatial structure of the solar wind could not be retrieved well. If the tomographic analysis is applicable, the tomography results from inner and outer regions should be similar to each other because the solar wind velocity does not evolve significantly at distances beyond 0.1 AU. For this test we used the tomographic method which made use of one reference sphere at 0.13 AU because the method which uses two reference spheres has poor data coverage at low latitudes as shown in Figure 2. [19] Inner and outer velocity maps were derived in Figures 4a and 4b from observations during CR in the year of Since the latitudinal structure is simple in this year, latitudinal dependences of velocity were obtained by averaging the maps in longitude and are plotted together for the inner and outer maps in Figure 4c for comparison. It should be noted that the inner and outer maps were derived from independent data sets: the inner map was derived with the lines of sight whose closest point to the Sun were at AU, while the outer map used lines of sight whose closest points were farther than 0.3 AU. Although the two maps were derived from different data sets, both latitudinal profiles have good similarities especially at low latitudes and at the northern high latitudes. The similarity of the latitudinal profiles between two maps indicates that the tomographic analysis is applicable for the IPS observations at AU at a frequency of 327 MHz. However this does not mean that the tomographic analysis is applicable to the strong scattering region. This has two possible meanings: the radio scattering was not strong in this distance range or the strong scattering effect was not serious in this distance range in the solar minimum phase at a frequency of 327 MHz. [20] The second test is to see how much bias will be produced in a velocity derived by the tomographic analysis in strong scattering region. Since there have been no in situ measurements of wind velocity at distances within 0.3 AU, we cannot judge adequateness of a velocity derived from the tomographic analysis within 0.3 AU. Therefore we applied the two-sphere tomographic analysis to IPS observations at a frequency of VHF, which were made by the groups at the University of California at San Diego (74 MHz) and the Research Institute of Atmospherics (the former institute of STELab) (69 MHz) in the years of 1976 and 1977 when the solar activity was minimum. Since the strong scattering region at these frequencies are within 0.5 AU of the Sun, where Helios observations were available, we can compare velocities derived from the tomographic analysis with those from in situ measurements in distances of AU. In this tomographic analysis we use two reference spheres at 0.24 and 0.5 AU, and all data obtained in a year are used because IPS data at VHF is quite sparse. However, detrimental effect caused by solar wind structure change during a year will be small because these years were in the solar minimum phase. Even though all data obtained in a year were used, there are less data coverage in the Southern Hemisphere within 0.5 AU and at high latitudes in the Northern Hemisphere at AU. Therefore latitudinal dependences of velocity for the Northern Hemisphere are shown in Figure 5, and average velocities shown in Table 1 were calculated for latitudes These averages were calculated after removing less reliable bins from the map as follows. Assuming the latitudes of are in the highspeed region, bins with velocities less than 600 km s 1 or larger than 900 km s 1 are discarded. An average velocity value and a variance is calculated for each latitude, and then bins which have velocities more than 1s larger than the average are also discarded. The global latitudinal structures obtained in this manner are similar to each other except for the polar region where the number of lines of sight traversing through is quite small. [21] If the tomographic analysis is applicable to the observations in the strong scattering regime, velocities should be similar to those observed by spacecraft. Table 1 shows that the velocities are in a range observed by Ulysses 5of10

6 Figure 5. Strong scattering test using VHF IPS data. Latitudinal solar wind velocity dependences are derived from the two-sphere tomographic analysis using IPS data observed at VHF (a) for CR in 1976 and (b) for CR in The thick line is for the heliocentric distances AU, while the thin one is for distances AU. [e.g., Phillips et al., 1995] and the differences between velocities inside and outside of 0.5 AU are small. However, the differences are larger than that reported by Schwenn et al. [1978] from Helios observations at heliocentric distances AU. According to the Helios observation, the acceleration rate is 7 ± 16 km s 1 AU 1, that is the velocity difference between the distances of AU and AU is 2 ± 5 km s 1. However the tomographic analysis obtained a larger velocity difference, 16 to 25 km s 1.Ifthis is the bias caused from tomographic analysis applied for the strong scattering region, the measured velocity tends to be biased toward a smaller value than the intrinsic wind velocity by an amount of 20 km s 1. [22] Consequently, in solar activity minimum phase, the tomographic analysis is applicable to the IPS observations at a frequency of 327 MHz at heliocentric distances of AU. If the distance range of AU were in the strong scattering region, the velocity measurement will be biased low about by 20 km s Data and Analysis Results [23] We analyzed IPS data from observations centered on a frequency of 327 MHz made during the 3 years from 1995 to 1997 at STELab. Since this period was in the solar minimum phase, polar high-speed regions were developed toward lower latitudes and analysis of the latitudinal structure was simple. Since the number of data in one rotation is not enough for the tomographic analysis, especially for making an inner map, data obtained during four Carrington rotations are used to derive one velocity map, and the inner and outer maps are derived by shifting the analysis period by one rotation as follows: , ,..., , Thus a total of 21 data sets are analyzed, and a sample from them is shown in Figure 6. Black colored areas in the maps are either less reliable bins that have been removed or bins through which less than six lines of sight pass. [24] Latitudinal dependence is calculated by averaging bins in longitude. In this calculation we discard bins with velocities outside the km s 1 range and beyond 3s of the average. Since solar wind velocities in the polar regions are less reliable compared with those at midlatitudes because of the sparsity of coverage of lines of sight, we compare wind velocities averaged for latitudes between the inner and outer maps. Differences of the averaged velocities between the inner and outer maps are calculated for each of the 21 maps, and then their average and the variance are calculated. Finally, we used 19 maps for the analysis discarding two maps which had velocity differences 2s larger than the average. A sample of them is shown by its latitudinal dependence in Figure 6 for each hemisphere separately. A vertical bar on the latitudinal plot is ±1s at every five degrees. The latitudinal dependences in the inner (thin line) and outer (thick line) maps are plotted together for comparison. 4. Radial Distance Dependence [25] The averaged velocity from each map and the total average for 19 maps are shown in Table 2. Columns with no data in the table mean that there are no good data at the latitudes which satisfy the data selection conditions discussed above. These averages are plotted as a function of heliocentric distance in Figure 7. Since there might be north-south asymmetry in velocity, data are plotted separately for each hemisphere. The horizontal bars represent a distance range for data used, and the vertical bar is a superposition of all error bars for all data indicating the amount of variance in the data. Diamond marks are averages of all datasets with the center of the mark being the average velocity and the height being equal to 2s. [26] Wind velocity differences between the inner and outer maps are plotted all together in Figure 8 with open and filled circles for the Southern and Northern Hemisphere, respectively. A vertical solid line at 19 km s 1 is the total average, and dashed lines indicate a ±1s range of 17 km s 1. From this analysis it is statistically significant that the solar wind velocity is slightly slower at AU than at AU. 5. Comparison With Other Observations [27] The observational result from this work is plotted in Figure 9 by a short dashed line. The wind velocity differ- Table 1. Average Solar Wind Velocities at Latitudes Measured by the VHF IPS in 1976 and 1977 Rotation Number AU AU ± 5 km s ± 10 km s ± ± 18 6of10

7 from a large low-latitude coronal hole that appeared in the years 1999 and 2000, while this work analyzed the fast wind from a high-latitude polar coronal hole in The LASCO velocity measurements were determined from cross-correlation analysis between large irregularities observed by C2 and C3 coronagraphs at different distance range, and thus obtained LASCO velocity has been regarded as the bulk flow velocity of the solar wind [e.g., Sheeley et al., 1997; Breen et al., 2000]. This figure shows large velocity spread at R s as reported by Grall et al. [1996], but data spread and measurement uncertainties become small at distances beyond 30 R s. [28] Although the observational results from this work is several tens km s 1 higher than the EISCAT observations, the acceleration profile agrees very well with each other when it is shifted on the EISCAT data (long-dashed line). The single data point from MERLIN at 8 R s shows a velocity significantly higher than the LASCO measurements. This velocity difference is very close to the half of the spread velocities measured by Grall et al. [1996]. This is consistent with the suggestion by Coles and Harmon [2001] that turbulent-scale irregularities may be boosted above the bulk flow speed by wave activity. If so, the lower limit on the uncertainty bar for this provides the best estimate of bulk flow speed. When we take the lower envelope of velocity measurements by LASCO and MERLIN within 20 R s, it can be asymptotically connected to the IPS measurements at R > 30 R s. This indicates that the fast wind is accelerated almost to its final flow velocity within 20 R s, but a small but not negligible acceleration exists beyond 30 R s. [29] The result from this work is plotted together with the acceleration profiles from Schwenn et al. [1978] and McComas et al. [2000] in Figure 10. Relative vertical positions of the three profiles are adjusted so that velocity is continuous at the all distance ranges. This figure indicates that the acceleration rate tends to become smaller at farther distances, and Table 3 compares those acceleration rates after converting to per AU. Figure 6. Solar wind velocity distribution maps derived from observations during CR using the twosphere tomography on the reference spheres at (a) 0.13 AU and (b) 0.3 AU. Contour lines are for every 100 km s 1 from 400 to 700 km s 1. Black colored regions are bins with no data. (c) Latitudinal dependence of the solar wind velocity in the two maps. The top and bottom panels are for the Northern and Southern Hemispheres, respectively. The thick line is for the outer map while the thin one is for the inner map. ence of 19 km s 1 between distance ranges of AU and AU is attributed to the acceleration within 0.3 AU because the acceleration reported from Helios observations beyond 0.3 AU is small. The coordinated IPS and LASCO observations made by Breen et al. [2002] are superimposed in the figure. Observations with LASCO, EISCAT, and MERLIN were made for the flow 6. Discussion [30] We have studied the radial dependence of the wind velocity of the high-latitude fast solar wind in distance range of AU ( R s ). For this study we have developed the new tomographic analysis method, which can derive velocity distributions on the sphere at different distances of 0.13 and 0.3 AU, and shown that it has enough sensitivity to find velocity differences as little as 20 km s 1 between and AU. Since the observations were made in the last solar minimum phase ( ), solar wind structure was not complicated and the IPS observations were in weak scattering region for which the tomographic analysis is applicable. [31] The tomographic analysis obtained velocities in the range km s 1 with an average of km s 1 at distances between 0.13 and 0.9 AU. This result agrees with IPS observations by Grall et al. [1996] and Breen et al. [2002] and Ulysses observations at high latitudes [e.g., Phillips et al., 1995]. The results from this work taking together with measurements of SOHO/LASCO and EISCAT and MERLIN [Breen et al., 2002], Helios [Schwenn et al., 1978] and Ulysses [McComas et al., 7of10

8 Table 2. Average Solar Wind Velocities at Latitudes in the Years Rotation Number AU km s 1 Northern Hemisphere AU km s AU km s 1 Southern Hemisphere AU km s ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 29 Total Average 768 ± ± ± ± ] indicate that the fast wind is accelerated almost to its final flow velocity within 20 R s, and a small but not negligible acceleration exists beyond 30 R s which tends to become smaller at farther distances (Table 3). Freemann [1988] has reported that the temperature of the fast wind decreases as R 0.808±0.169 for speeds between 700 and 800 km s 1 at distances of AU, and a larger cooling rate of T = R 1.02 is derived from Ulysses observations at AU by McComas et al. [2000]. This nonadiabatic cooling is caused by some heating mechanism which damps with heliocentric distance. This heat source may sustain the gradual acceleration beyond the rapid acceleration region, which also damps with heliocentric distance. Axford et al. [1999] estimated that the energy flux of low-frequency waves should not be damped fully in the corona and the remnant will be more than 4% of the observed streaming energy so that the acceleration does not get completed by 10 R s. For another reason why the acceleration does not complete by 10 R s we note the spectral line analysis of SOHO/UVCS measurements by Esser et al. [1999], which shows that the proton temperature is not more than K below 2 R s and not more than K in the range R s. This is not high enough temperature to accelerate the high-speed solar wind rapidly with high proton temperatures as proposed in the models such as by Esser and Habbal [1996], McKenzie et al. [1997], Axford et al. [1999], and Esser et al. [1997], and might indicate that the acceleration is caused by direct momentum addition rather than proton heating [Esser et al., 1999]. [32] There are some discrepancies in the wind velocity measurements between this work and that of Breen et al. [2002]. Several reasons can be attributed for this. One is the difference in the analysis method: this work used the tomographic analysis method, while EISCAT analysis used the least-squares fitting method of the results of a theoretical scattering model to the observed autospectra and crossspectra [Klinglesmith, 1997; Massey, 1998]. Another reason is the difference between the observation periods: the STELab observations were made during the minimum phase of solar activity when fast solar wind prevailed, while the MERLIN, LASCO, and EISCAT observations were made in 1999 and 2000 when low-speed wind was dominant. One more reason is the difference of the source region: The STELab results are from observations of the fast wind from a high-latitude polar coronal hole, while the results from MERLIN, LASCO, and EISCAT were for observations of the flow from a large low-latitude coronal hole. Hereto we note the work of Miralles et al. [2001], which found that the acceleration of the fast solar wind from a large equatorial coronal hole is more gradual than that from a polar coronal hole in the 1.5 to 3.5 R s range. [33] The data set which we analyzed in this work includes those which had been analyzed by Kojima et al. [1998]. They analyzed the IPS data observed in the year 1995 using the similar tomographic analysis method as used in this work, but they obtained the result of velocity increase Figure 7. Radial distance dependence of the fast solar wind velocity. Velocities at latitudes are averaged for each of the inner and outer maps. Each horizontal bar represents the heliocentric distance range of the IPS data used, and a vertical bar is the superposition of all error bars of all data. Diamond marks represent the averages of all datasets with the center of the mark being the average wind velocity and the height being equal to 2s. 8of10

9 Figure 10. Radial dependence of the velocity of the fast solar wind. The solid line is from this work, while Helios [Schwenn et al., 1978] and Ulysses [McComas et al., 2000] observations are shown by dotted and dash-dotted lines, respectively. Figure 8. Solar wind velocity differences between the Southern (open circle) and Northern Hemispheres (filled circle). Carrington rotations of the data set are shown at the left side. The vertical solid line at 19 km s 1 is the total average, and dashed lines indicate a ±1s range of 17 km s 1. toward the Sun. Although their result is marginal, it is different from that of this work. We think this difference was caused from data quality. The velocities derived by Kojima et al. [1998] have large uncertainties about km s 1, while those from this work have small uncertainties less than 50 km s 1 (Table 2). This work used data obtained during four Carrington rotations to derive one Figure 9. The acceleration profile from this work is superimposed on the measurements made by Breen et al. [2002] using LASCO, EISCAT (932 MHz), and MERLIN (5 GHz) facilities. The short dashed line is from the average velocities in Table 2, while the long dashed one is the same line shifted vertically downward on the EISCAT measurements. Observations with LASCO, EISCAT, and MERLIN were made for the flow from a large low-latitude coronal hole appeared in the years 1999 and 2000, while this work was made for the fast wind from a high-latitude polar coronal hole in velocity map, while Kojima et al. [1998] used data of three rotations for one map. This is one of the reasons why it was possible to derive reliable velocity maps. Another reason is that with the development of the evaluation method of the uncertainties included in the tomographic analysis, it has become possible to remove less reliable bins in the velocity map, as discussed in section 3. [34] Although our results are statistically significant, the data scattering is still rather large. This is partly caused from not enough IPS data, especially at high latitudes and within 0.3 AU. The construction of a more powerful IPS facility with a larger antenna will make this type of analysis more reliable. Although the IPS data used in this analysis were obtained in distances anticipated to be in the weak scattering region, it should be mentioned that the obtained velocity difference of 19 km s 1 may be biased by strong scattering or density waves. In the strong scattering test using VHF IPS data, we found that the strong scattering effect tends to bias velocity measurement toward lower values by about 20 km s 1 (see Table 1). However we think that the strong scattering effect on our analysis is very small because of two reasons: the first reason is that the latitudinal velocity profiles obtained from UHF IPS data at and AU (Figure 4) are quite similar, and the second one is that the velocity profile is quite similar to the IPS observations made at a higher frequency using EISCAT facility. To discard the strong scattering effect, it is necessary to make IPS observations at a higher frequency than 327 MHz at distances between 0.1 and 0.3 AU where there will be little effects of waves. Future coordinated IPS observations at different frequencies using such as EISCAT (932 MHz) and STELab (327 MHz) antennas are necessary to investigate the velocity discrepancies between this work and the work by Breen et al. [2002]. [35] Finally, we note that the wave bias is harder to dismiss in the observations because we have no other way Table 3. Radial Distance Dependence of the Acceleration Rate of the Fast Solar Wind Distances, AU Acceleration Rate, km s 1 AU 1 49±44 7±16 a 1.5 b a Schwenn et al. [1978]. McComas et al. [2000]. 9of10

10 to confirm the presence of density waves at this time. The large velocity spread in IPS measurements are explained by irregularity motions boosted by wave activity [Coles and Harmon, 2001]. Irregularities observed by the IPS using EISCAT and MERLIN facilities are turbulent scale size less than 50 km, while the LASCO measured the drift velocity of very large scale irregularities. In spite of the large difference in the scale size of the irregularities, the velocity spread around R s in the IPS and LASCO measurements is quite similar to each other. If the LASCO measurements are also boosted by waves, why does its velocity spread becomes small within 10 R s? This question should be made clear in future study. The rough approximation of the wave bias by Coles and Harmon [2001] shows that it might decrease from 130 to 20 km s 1 over 0.13 to 0.9 AU. If the IPS measurements were boosted up by the outward propagating wave motion, the intrinsic wind velocity at AU should be lower than that measured by the IPS method, and the acceleration in the distance range of AU should be larger than 19 km s 1. [36] Acknowledgments. We would like to thank W. A. Coles for his valuable comments on this work. IPS data observed at VHF was kindly provided by W. A. Coles group at the University of California, San Diego. We would like to thank the director and staff of EISCAT and Jodrell Bank for use of the EISCAT and MERLIN data and the LASCO consortium and S. J. Tappin for the LASCO data and analysis. The programs used to analyze the EISCAT and MERLIN IPS data were originally developed at University of California, San Diego and are used thanks to W. A. Coles and B. Rickett. Our thanks are also to Bernie Jackson, Paul Hick, and Andrew Buffington at UCSD for their collaboration with us in developing the CAT analysis method. 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