Global structure of the out-of-ecliptic solar wind

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110,, doi: /2004ja010875, 2005 Global structure of the out-of-ecliptic solar wind Y. C. Whang Department of Mechanical Engineering, Catholic University of America, Washington, D. C., USA Y.-M. Wang and N. R. Sheeley Jr. Naval Research Laboratory, Washington, D. C., USA L. F. Burlaga NASA Goddard Space Flight Center, Greenbelt, Maryland, USA Received 31 October 2004; revised 15 December 2004; accepted 17 January 2005; published 18 March [1] We use the observed photospheric field maps and the wind speed observed from Ulysses to study the out-of-ecliptic solar wind. The model calculates the wind speed from the rate of magnetic flux tube expansion factors using a conversion function that is determined by least squares fit of all currently available data from Ulysses. Using the best fit conversion function, we investigate the global solar wind covering a 36-year period from 1968 through The results complement and expand upon earlier studies conducted with interplanetary scintillation and other in situ spacecraft observations. The rotationally averaged wind speed is a function of two parameters: the heliolatitude and the phase of the solar cycle. The out-of-ecliptic solar wind has a recurrent stable structure, and the average wind speed varies like a sine square of latitude profile spanning more than 5 years during the declining phase and solar minimum in each solar cycle. Ulysses has observed this stable structure in its first polar orbit in Near solar maximum the structure of the out-of-ecliptic solar wind is in a transient state lasting 2 3 years when the stable structure breaks down during the disappearance and reappearance of the polar coronal holes. Citation: Whang, Y. C., Y.-M. Wang, N. R. Sheeley Jr., and L. F. Burlaga (2005), Global structure of the out-of-ecliptic solar wind, J. Geophys. Res., 110,, doi: /2004ja Introduction Copyright 2005 by the American Geophysical Union /05/2004JA [2] This paper studies the long-term averages of the outof-ecliptic solar wind covering a 36-year period, We follow the coronal expansion factor model of Wang and Sheeley [1990] to calculate the solar wind speed from the observed photospheric field maps. We first obtain a best fit conversion function to calculate the Carrington rotation averages (CRA) of wind speed from the rate of magnetic flux tube expansion factors; all currently available data from Ulysses are used to carry out the minimization process. We then investigate the solar cycle and heliographic latitude dependence of the wind speed. [3] Hundhausen et al. [1971] have reported the detection of heliographic latitude dependence in the solar wind speed during the interval from mid-1964 through mid-1967 using in situ data from Vela satellites. Because the Sun s equator is inclined approximately ±7 1 4 to the ecliptic plane, the small excursion of Earth-orbiting satellites provides an opportunity to examine the latitude variation of the wind speed between ±7 1 4 from the equator. They found that high average wind speeds were observed in the ecliptic plane near the extremes of the heliolatitude excursion. The observation implies a heliolatitude dependence of the solar wind flow. Zhao and Hundhausen [1981] have examined the variation in solar wind speed observed from in situ spacecraft in 1974 in a heliomagnetic coordinate system tilted with respect to the solar equator; they found that the wind speed increased with heliomagnetic latitude. They have also studied the increase in the solar wind speed observed from interplanetary scintillation (IPS) in 1976 with the angular displacement from interplanetary neutral sheet [Zhao and Hundhausen, 1983]. [4] From a combined analysis of 5 months of Mariner 5 and Explorer 33, 34, and 35 data taken in mid-1967, Rhodes and Smith [1976a, 1976b] reported that the latitude gradient in the wind speed is 15 km s 1 deg 1 at low northern latitudes. Gazis et al. [1988] have compared wind speed from Pioneer 11 and Voyager 2 data over years , when both spacecraft were very close in heliocentric distance and longitude but Pioneer 11 was at high latitude while Voyager 2 was near the solar equator; the data showed latitudinal variations in wind speed in the distant heliosphere. [5] IPS measurements provide another source of data to study the out-of-ecliptic solar wind speed over a wider range of latitudes. The method was pioneered by A. Hewish and colleagues, who first showed how multistation observations of radio sources could be used to estimate the solar 1of8

2 [6] In this paper we use the coronal expansion factor model to study the long-term averages of out-of-ecliptic solar wind speed. We use two sets of solar wind data: (1) the direct in situ measurements of the solar wind from Ulysses covering heliolatitudes between 80.2 and 80.2 over a 13-year period from 1991 through 2003 [McComas et al., 2000, 2003] and (2) the simulated wind speed calculated from the coronal expansion factor model of Wang and Sheeley [1990]. The results complement and expand upon earlier studies conducted with IPS and other in situ spacecraft observations. [7] The simulated wind speeds calculated from the observed photospheric field maps have a continuous coverage at all latitudes (from 90 S to90 N) over a period of 36 years ( ). The results suggest that the yearly average speed of the out-of-ecliptic solar wind has a recurrent stable structure spanning more than 5 years during the declining phase and solar minimum in each solar cycle and the structure of the wind speed is in a transient state lasting 2 3 years near solar maximum. Figure 1. Least squares fit study of the conversion function to determine the three parameters a, b, and c in equation (1). We first determine a and b when the RMS deviation along the Ulysses orbit achieves a minimum for a given c. Then we obtain the best fit conversion function when a = 394.6, b = 460.0, and c = 8.9. wind speed [Dennison and Hewish, 1967; Hewish and Symonds, 1969]. In 1966 they found a speed increase with increasing latitude, and in 1967 they did not; these observations were made near the maximum of cycle 20 that is in November The University of California, San Diego, group and the Nagoya group have examined IPS wind speed observations from 1972 to 1987 [Coles and Rickett, 1976; Coles et al., 1978, 1980; Rickett and Coles, 1983, 1991; Kojima and Kakinuma, 1986, 1987, 1990]. These data presented valuable estimates of the solar wind speed over latitudes from 60 S to 60 N. They have established that the IPS method gives a reliable measure of the solar wind speed for large-scale slowly evolving structures. They showed that at times of low and declining solar activity, there is a strong increase in average speed with latitude (north and south) whereas at maximum solar activity the average speed is uniformly low. The average equatorial wind speed is constant over the solar cycle. The standard deviation of their data is 100 km s 1 independent of latitude and time. They have also introduced a cosine square of colatitude profile (same as sine square of latitude) as a guide to examine the speed versus latitude plot. Sheeley et al. [1991] compared the simulated wind speed derived from the coronal expansion factor model with the wind speed inferred from IPS measurements during and with in situ speed measured by Pioneer 11 during ; the three sets of wind speed show the same overall variation with latitude and phase of the solar cycle. 2. Conversion Function [8] The coronal expansion factor model provides another source of data to study the out-of-ecliptic solar wind speed. The model was developed on the basis of the inverse relation between solar wind speed near Earth and flux tube divergence rate in the corona obtained from observations during 2 months of the Skylab mission in This relation shows that the more slowly a coronal flux tube expands in areal cross section, the higher the asymptotic wind speed along that flux tube [Levine et al., 1977; Wang and Sheeley, 1990]. For each Carrington rotation, Wang and Sheeley calculate the rate of magnetic flux tube expansion in the corona for the observed photospheric field maps at every 5 of longitude and latitude at the source surface. The expansion factors f s are then converted into the simulated wind speed V w using an empirically determined table. [9] The original conversion table of Wang and Sheeley [1990] was developed before the Ulysses era; it consists of a series of step functions. The table was periodically upgraded as more observational data became available [Wang and Sheeley, 1994, 1997]. Various versions of the table suggest that the conversion function between the expansion factor f s and the simulated wind speed V w resembles a Gaussian distribution function. In this paper we try to represent the conversion function by a continuous function of the form h i V w ¼ a þ b exp ðf s =cþ 2 ; ð1þ where a, b, and c are constants to be determined. [10] We currently have 13 years of the Ulysses data. Along the Ulysses orbit we can calculate the deviation between the simulated wind speed and the Ulysses wind speed. We carry out a least squares fit study of the conversion function using data along the Ulysses orbit. We can determine a, b, and c for the best fit conversion function when the minimum standard deviation between the two sets of speed is reached. [11] Let V 0 denote the CRA of V w, and let U be the CRA of the wind speed obtained from Ulysses observation at a 2of8

3 given Carrington rotation. Since V w is a linear function of exp [ (f s /c) 2 ] in equation (1), V 0 is a linear function of the CRA of exp [ (f s /c) 2 ], D h ie V 0 ¼ a þ b exp ðf s =cþ 2 : ð2þ We carry out the minimization process in two steps. We first develop the solution for a given scale factor c. We can calculate the CRA hexp [ (f s /c) 2 ]i from the expansion factors derived from the photospheric field data for the same Carrington rotation and at the same latitude as the Ulysses spacecraft. The deviation between V 0 and U is now a function of the adjustable parameters a and b. Taking all data along the Ulysses orbit over the 13-year period from 1991 through 2003, we can determine a and b when the standard deviation along the Ulysses orbit achieves a minimum for a given c. In this manner we have calculated the standard deviation s and the two parameters a and b as functions of the scale factor c. In the second step we study the deviation as a function of the parameter c. As shown in Figure 1, the minimum standard deviation s = 65.5 km s 1 is obtained when a = 394.6, b = 460.0, and c = 8.9. [12] In addition to the conversion tables originally developed by Wang and Sheeley [1990, 1994, 1997], Arge and Pizzo [2000] used another empirical relation to represent the conversion function. Every one of them produces standard Figure 3. (top) CRA wind speed (thin line) and yearly average wind speed (thick line) at northerly latitudes (middle) Wind speed at (bottom) Sunspot number. The wind speed is lower than the long-term average speed for 3 years near the solar maximums and higher than the long-term average during the remaining years of each solar cycle. deviations much greater than 65.5 km s 1 along the Ulysses orbit. In this paper we use the best fit conversion function h i V w ¼ 394:6 þ 460:0 exp ðf s =8:9Þ 2 ð3þ Figure 2. (top) Sunspot number. (middle) Ulysses wind speed. The solid squares are daily averages of the Ulysses wind speed, and the solid line is the Carrington rotation average (CRA) of the simulated wind speed along the Ulysses orbit over a 13-year period. The two speeds agree quite well; the standard deviation is 8% of the maximum speed. (bottom) Heliolatitude of the Ulysses orbit. to study the out-of-ecliptic solar wind. [13] In this research we use the calculated flux tube expansion factors for the observed photospheric field maps from Mount Wilson Observatory, National Solar Observatory, and Wilcox Solar Observatory. The combined data set now covers a 36-year period from 1968 through We can now use the best fit conversion function (equation (3)) to calculate the simulated wind speed. We obtain the longitudinally averaged wind speeds for each Carrington rotation for every 5 of heliographic latitude. The data set has a continuous coverage of the CRA wind speed at all latitudes (from 90 to 90 ) over the 36-year period. [14] In Figure 2 we compare the Ulysses wind speed with the simulated wind speed between 80.2 and 80.2 latitudes over a 13-year period. In Figure 2 (middle) the solid squares are daily averages of the Ulysses wind speed, and the solid line is the CRA of the simulated wind speed calculated using the best fit conversion function along the Ulysses orbit. The standard deviation between the two sets is 8% of the maximum speed. Figure 2 (top) shows the 3of8

4 Figure 4. Alternating pattern of high- and low-speed solar wind in each solar cycle. All latitudes have slow wind at solar maximum. At decreasing latitudes the duration of high-speed wind decreases, and the duration of low-speed wind increases. sunspot number, and Figure 2 (bottom) shows the heliolatitude of the Ulysses orbit. [15] Although pickup proton effect can cause a decrease of the solar wind speed outside the ionization radius [Whang, 1998], since the ionization radius is located near 5 AU, this deceleration process has negligible effects on the wind speed between 1 AU and the Ulysses orbit. Stream interaction also causes the fast wind to slow down and the slow wind to speed up [Whang, 1991]; its effect on the average wind speed between 1 AU and the Ulysses orbit is not included in this analysis. 3. Solar Cycle and Latitude Variations of the Wind Speed [16] Figure 3 shows one example of solar cycle variation of the wind speed. In Figure 3 (top) the thin line is for CRA wind speed, and the thick line is for the yearly average wind speed at northerly latitudes 57.5 (between 55 and 60 ). Figure 3 (middle) is for wind speed at 57.5 (between 55 and 60 ). Figure 3 (bottom) shows the sunspot number. The yearly average wind speed at 1 AU is particularly good in showing the alternating pattern of highand low-speed solar wind in each solar cycle. The wind speed is solar cycle-dependent. Near the solar maximums the wind speed is lower than the long-term average over three solar cycles for 3 years, and during the remaining years of each solar cycle the wind speed is higher than the long-term average. [17] In Figure 4 we use yearly averages to demonstrate the solar cycle dependence of the wind speed at different latitudes. The alternating pattern of high- and low-speed solar wind at 1 AU in each solar cycle is unambiguously clear at all latitudes, particularly at mid and high latitudes. Low-speed wind occurs at polar regions near the solar maximum, lasting 1 year during disappearance of the polar coronal holes. Polar holes reappear at the pole regions and then extend equatorward to cover mid and low latitudes. In each solar cycle the duration of high-speed wind increases, and the duration of low-speed wind decreases with latitude in both hemispheres. The long-term average speed and the magnitude of the maximum yearly average speeds also increase with latitude from the equator to the poles. The result is consistent with IPS observations as discussed by Sheeley et al. [1991, Figure 6]. 4. Recurrent Structure of the Solar Wind [18] Now we use a speed-latitude plot in 5 bins to examine the global structure of the solar wind speed from 4of8

5 Figure 5. Wind speed as a function of latitude in each solar cycle during the declining phase and solar minimum. The thick lines are the 5-year average wind speed, and the thin lines are the yearly average. The long-term averages of the wind speed have a recurrent stable slowly varying structure; the wind speed varies like sin 2 of latitude. the coronal expansion factor model. Figure 5 shows the plots of wind speed as a function of latitude in a solar cycle over a 5-year period during the declining phase and solar minimum. The thick lines are the 5-year average wind speed, and the thin lines are the yearly average. This result suggests that the yearly average wind speed at 1 AU has a recurrent stable slowly varying structure. The long-term averages of the wind speed vary like a sine square of latitude profile spanning more than 5 years during the declining phase and solar minimum in each solar cycle. We may describe this structure as having a sin 2 profile in speed-latitude plot. [19] The stable sin 2 structure of the out-of-ecliptic solar wind always breaks down during the disappearance and reappearance of the polar coronal holes near solar maximum. As shown in Figure 6, the wind speed has a transient 5of8

6 Figure 6. Wind speed, which has a transient structure lasting 2 3 years near solar maximum. The stable structure of the out-of-ecliptic solar wind always breaks down during the disappearance and reappearance of the polar coronal holes near solar maximum. structure lasting 2 3 years near solar maximum. Very large speed changes occur in mid and high latitudes; the changes can reach ±300 km s 1 near the poles. 5. Ulysses Observations of the Recurrent Stable Structure [20] This study suggests that the global solar wind has a recurrent stable sin 2 structure spanning more than 5 years during the declining phase and solar minimum in every solar Figure 7. Observation of the sin 2 structure of the out-ofecliptic solar wind from Ulysses in its first polar orbit. The dotted line is for the period , the dashed line is for the period , and the solid line is for the period of first fast latitude scan. Figure 8. Wind speed and number flux observed from Ulysses in Light shading is for spacecraft at high latitudes (60 < jlatitudej < 90 ), dark shading is for midlatitudes (30 < jlatitudej < 60 ), and no shading is for low latitudes (jlatitudej < 30 ). cycle. In its first polar orbit over a 6-year period, , Ulysses has observed the out-of-ecliptic solar wind during the declining phase and minimum of the solar cycle [Phillips et al., 1996; Goldstein et al., 1996; McComas et al., 2000; Smith et al., 2003]. The solid line in Figure 7 shows the CRA of observed wind speed during the period of first fast latitude scan when Ulysses moved rapidly from 80.2 to 80.2 in 323 days ( ); the CRA of the observed speed rapidly dropped from 772 to 431 km s 1 and then rose to 785 km s 1 again. The dotted line is for the period , and the dashed line is for the period The speed profile resembles the recurrent stable sin 2 structure shown in Figure 5; note that the wind speeds plotted in Figure 5 are yearly and 5-year averages. Goldstein et al. [1996, Figure 3] have shown part of this plot up to This result shows the first Ulysses observation of the recurrent stable sin 2 structure. [21] Figure 8 shows the CPA of the wind speed and proton number flux observed from Ulysses in its first polar orbit when the spacecraft was cruising through the recurrent stable structure of the solar wind. Light shading in the background indicates that the spacecraft was at high latitudes (60 < jlatitudej < 90 ), dark shading indicates midlatitudes (30 < jlatitudej < 60 ), and no shading indicates low latitudes (jlatitudej < 30 ). Table 1 gives the wind speed and number flux obtained from the first Ulysses observation of the recurrent stable structure. The average wind speed is 740 km s 1 at midlatitudes and 770 km s 1 at high latitudes; the proton number flux is about cm 2 s 1 at midlatitudes and cm 2 s 1 at high latitudes. At low latitudes the wind speed is much lower, and the number flux is much higher, as shown in Figure 8. [22] The long-term average of the wind speed is a function of two parameters: the heliolatitude and the phase of the solar cycle. Because the orbital period of the 6of8

7 Table 1. Wind Speed and Number Flux Observed From Ulysses in the Recurrent Stable Structure Wind Speed, km s 1 Number Flux at 1 AU, 10 7 cm 2 s 1 jlatitudej Average SD Average SD 30 < jlatitudej < < jlatitudej < spacecraft is out of phase with the solar cycle, the observed wind speed during the second polar orbit of Ulysses was strikingly different from that observed at similar latitudes during the first polar orbit. The plasma instrument did not observe the same stable structure in When Ulysses made the second fast latitude scan on near the maximum of cycle 23, the spacecraft was, in fact, observing the transient state of the solar wind structure. [23] Ulysses will make another fast scanning of the sin 2 structure in 2007 as the spacecraft moves rapidly from 80.2 to 80.2 near the solar minimum. In the 2 years before the third fast latitude scan the spacecraft will observe half of the recurrent stable structure from the equator to Ulysses will be cruising through the stable structure of the out-of-ecliptic solar wind in the mid and high latitudes in the Southern Hemisphere; the spacecraft is expected to observe high-speed solar wind similar to that observed in [24] Ulysses will make its fourth fast latitude scanning in 2013 during the declining phase. We estimate that in the spacecraft will be cruising, first from 80.2 to 80.2 and then from 80.2 to the equator through the recurrent stable structure of the out-of-ecliptic solar wind. In the 2 years after the fourth fast scan the spacecraft will observe wind speed similar to that observed in in the Northern Hemisphere. 6. Summary and Discussion [25] We use the simulated wind speed calculated from the coronal expansion factor model to study the long-term averages of solar wind speed at all latitudes. This model calculates the wind speed near 1 AU from the rate of magnetic flux tube expansion factors in the corona using a best fit conversion function which is determined by least squares fit of the Ulysses data over 13 years. We investigate the solar cycle and heliographic latitude dependence of the solar wind speed over 36 years from 1968 through The results complement and expand upon earlier studies conducted with IPS and other in situ spacecraft observations. [26] This model treats the flux tube expansion factor as the best single predictor of the wind speed, although we believe that the wind speed also depends on other parameters. A conversion function is used to calculate the simulated wind speeds from the observed photospheric field maps. Because we use all currently available Ulysses data to determine the best fit conversion function, the simulated wind speed calculated from this model is probably more accurate than the IPS-inferred speed. Also, the simulated wind speed should be more accurate in mid and high latitudes where the effects of stream interactions are essentially absent. The solar wind speeds used in this paper are the average speeds over a Carrington rotation or over a year. The averaging process should have minimized any possible error introduced in the calculation of the Carrington longitude of the source point and the calculation of the solar wind transit time from Sun to Earth. [27] This research is motivated by the current interest in the out-of-ecliptic solar wind in the outer heliosphere and the termination shock [Whang et al., 2003, 2004]. In the past few years the encounter of Voyager 1 with the termination shock has been predicted to occur during the declining phase of cycle 23 [Stone, 2001, and references therein]. Recently, Krimigis et al. [2003] reported that the first crossing of Voyager 1 with the termination shock may have occurred on 1 August 2002 at 85.5 AU; others analyzing data from Voyager 1 disagree as to whether the probe had crossed the termination shock [Burlaga et al., 2003; McDonald et al., 2003]. However, all researchers seem to agree that if the crossing did not occur in 2002, Voyager 1 would cross the shock soon. The encounter of Voyager 2 with the termination shock is also expected to occur before Because the crossing points will be near 34 latitude for Voyager 1 and near 30 for Voyager 2, it is important to investigate the solar wind and the termination shock out of the ecliptic plane. [28] This research provides a baseline for the out-ofecliptic solar wind, from which we can begin to study the global solar wind in the outer heliosphere and then study the motion and global geometry of the termination shock. The solar wind is highly latitude-dependent; the solar wind in mid and high latitudes is quite different from that observed near the equator. The Ulysses mission has provided the direct, in situ measurements of the solar wind since February 1992; the data provide outstanding information along the Ulysses orbit. However, unlike the Ulysses data, the simulated wind speeds calculated from the coronal expansion factor model have a continuous coverage at all latitudes over a 36-year period from 1968 through [29] One important finding of this research is about the global structure of the out-of-ecliptic solar wind near 1 AU: The wind speed has a recurrent stable structure spanning more than 5 years during the declining phase and solar minimum in each solar cycle. The stable structure has a sine square of latitude profile (sin 2 profile) in speed-latitude plot. At mid and high latitudes the speed of the recurrent stable structure is maintained at >700 km s 1. Near solar maximum the global structure of the wind speed is in a transient state lasting 2 3 years when the stable structure breaks down during the disappearance and reappearance of the polar coronal holes. Although some latitudinal transport may occur because of dynamic effects, it is small enough that these results will still be valid in the distant heliosphere. The wind transit time from 1 AU to the location of the termination shock is of the order of 1 year. We can expect that the recurrent stable structure of the solar wind would remain relatively stable in the outer heliosphere and the location of the termination shock embedded in the stable structure should also be relatively stable. On the other hand, for the shock embedded in the transient wind structure its location should also change rapidly, lasting 2 3 years around solar maximum. 7of8

8 [30] This study explains how the solar cycle and latitude variations affect the wind speed observed from Ulysses and why the observed wind speeds were strikingly different during the first two polar orbits of Ulysses. This model also predicts that in the 2 years before the third fast latitude scan of 2007, Ulysses will be cruising through the stable structure of the solar wind in the mid and high latitudes in the Southern Hemisphere. Thus the spacecraft will observe high-speed solar wind similar to that observed in [31] Acknowledgments. We thank D. J. McComas for the Ulysses solar wind plasma data. The work at Catholic University was supported under NSF grant ATM and NASA grant NNG04GG58G. At NRL, financial support was provided by the NASA Sun-Earth Connection Program and by an NRL/ONR Accelerated Research Initiative. [32] Shadia Rifai Habbal thanks Bala Poduval and another referee for their assistance in evaluating this paper. References Arge, C. N., and V. J. 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Res., 86, Zhao, X.-P., and A. J. Hundhausen (1983), Spatial structure of solar wind in 1976, J. Geophys. Res., 88, 451. L. F. Burlaga, NASA Goddard Space Flight Center, Code 692, Greenbelt, MD 20771, USA. (burlaga@lepvax.gsfc.nasa.gov) N. R. Sheeley Jr. and Y.-M. Wang, E. O. Hulburt Center for Space Research, Naval Research Laboratory, Code 7672, Washington, DC 20375, USA. (sheeley@spruce.nrl.navy.mil; ywang@yucca.nrl.navy.mil) Y. C. Whang, Department of Mechanical Engineering, Catholic University of America, Washington, DC 20064, USA. (whang@cua.edu) 8of8