Geo-effective transients and their solar causes during solar cycle 23

Transcription

1 Indian Journal of Radio & Space Physics Vol. 37, December 2008, pp Geo-effective transients and their solar causes during solar cycle 23 Santosh Kumar 1,$ *,1, 2,# & Simranjit Kaur 1 Department of Physics and Electronics, Rani Durgawati University, Jabalpur (MP) , India 2 Department of Physics, University of Utah, Salt Lake City, UT, USA $ s_kumar123@rediffmail.com; # simranhanspal@hotmail.com Received 20 December 2006; revised 23 August 2007; accepted 28 August 2007 During nine-year period of the current solar cycle 23 from July 1996 to January 2005, geomagnetic storms (GMSs) of Intense if (Dst < -100nT), Major if (-50nT Dst -100nT) and Minor if (-20nT Dst -50nT) have been investigated. It is observed that maximum number of GMSs are associated with coronal mass ejections (CMEs) followed by individual Hα and X-ray solar flare events. When accumulated effect of Hα and X-ray solar flare events are considered, these solar flares are better associated with GMSs than CMEs. A significant decline in the number of Intense and Minor GMSs have been observed from 1998 to 1999, however, there is an increase in Major GMSs. On the contrary, during , Intense and Minor GMSs have increased with the ascending phase of solar activity and Major GMSs have decreased. It is observed that an overall northern bias apparently prevails for solar flares and active prominences and disappearing filaments. Hα and X- ray solar flares occurring over the western limb of the solar disk cause larger disturbances in magnetosphere leading to occurrence of Intense GMSs, whereas, solar flares occurring on eastern limb of the solar disk lead to occurrence of Major and Minor GMSs. It is observed that coronal intensity (CI) is maximum for Minor GMSs followed by Major and Intense GMSs, whereas, mean CI is maximum for Intense GMSs followed by Major and Minor GMSs. The results show that the product of solar wind velocity (Vsw) with minimum Bz component (Bz min ) of interplanetary magnetic field (Vsw.Bz min ), product of linear velocity of CMEs (Vcme) with Bz min (Vcme.Bz min ) along with minimum Dst of the sudden storm commencement day are the reliable indicators of intensity of GMSs. Keywords Geomagnetic storms, Solar flares, Active prominences and disappearing filaments, Coronal mass ejections, Coronal intensity, Disturbance storm time PACS No.: Qx; ph; qe; qf 1 Introduction The geospheric environment is highly affected by the Sun and its features such as solar flares, active prominences and disappearing filaments (APDFs), CMEs, etc. which are responsible for some large/small geomagnetic storms 1,2. The disturbances in the geomagnetic fields are caused by fluctuations in solar wind impinging on the Earth 3. The degree of equatorial magnetic field deviation, measure of magnitude of GMSs is usually given by disturbance storm time (Dst) index. Dst is the hourly average of the deviations of the H (horizontal) component of magnetic field measured by several ground stations in mid to low latitudes. Geomagnetic storms events are characterized by Dst index measured in terms of nano Tesla (nt). The solar flare is a spectacular short-lived phenomenon that occurs on the solar disc and is responsible for solar energetic particle (SEP) event and geomagnetic storm. Many workers have shown the association of different types of geomagnetic storms with solar flares and APDFs 2,4,5. The mechanism of flare energy released is associated with magnetic reconnection. During magnetic reconnection of the flares, there is rapid heating of coronal and chromo-spheric material, which expands outward into interplanetary medium and produces interplanetary shocks causing GMSs. CMEs are large scale magneto-plasma structures that erupt from the Sun and propagate through interplanetary medium with speed ranging from a few kms -1 to 3000 kms -1. CMEs carry typically g of coronal material 6. CMEs originate from active, filament or complex (containing filament and active) regions. When CMEs occur, the closed magnetic structures are flown off and expand into the inner

2 380 INDIAN J RADIO & SPACE PHYS, DECEMBER 2008 heliosphere following a CME. The coronal near the sun restructures itself, producing post eruption arcades or flare loops. CMEs originating on the visible solar disk are known as Earth directed CMEs. GMSs occur when the interplanetary magnetic field (IMF) associated with CMEs (ICMEs) impinges upon the Earth s magnetosphere and reconnect. There is statistical evidence favouring the association of GMSs with magnetic clouds produced by CMEs 7,8. Coronal holes are darker regions of lower density and temperature than the rest of solar corona. About 10% of the coronal area seems to be occupied by coronal holes. Data spanning 21 years made it possible to recognize some of the coronal holes that are permanently visible on solar poles, except at the time of maximum of the solar cycle when polarity inversion occurs. It is very common that coronal holes on solar poles expand to lower solar latitudes following a sector of equal polarity. Moreover, isolated coronal holes appear at several latitudes at any time. High-speed solar wind particles streaming out of the hole and streaming towards the earth result in striking the Earth s magnetic field and triggering GMSs 9,10. The coronal intensities are given in millionths of intensity of solar disk (coronal units) and converted to photometrical scale of Lomnicky Stit Station at a height of 40" above the solar limb. The GMSs generally occur one to four days later than onset / explosion of solar features on the solar disk 2. It is generally accepted that initial phase of the resulting geomagnetic storm is triggered by an increase in plasma pressure accompanied by an increase in density and speed of solar wind at and behind the interplanetary shock. The main phase is governed, on the other hand, by the southward component of the IMF 11. In recent years, a number of investigations have been carried out to understand the solar-terrestrial relationship and to ascertain factors that are responsible for geomagnetic storms In the present analysis, the sudden storm commencements (SSCs) and the minimum Dst of the SSC day for categorizing the GMSs have been considered. A storm is said to be Intense if (Dst < -100nT), Major if (-50nT Dst -100nT) and Minor if (-20nT Dst -50nT). In the present paper, a systematic statistical analysis has been made to study geoeffective transients and their solar causes during the nine-year period of current solar cycle 23 from July1996 to January Data Analysis In the present data analysis for the period July 1996 to January 2005, geomagnetic storm events are characterized by the minimum Dst index of the SSC day. Solar Geophysical and Interplanetary Data and SOHO/LASCO CME catalog are used to study the manifestations of CMEs causing GMSs. The values of Dst indices are obtained from the geomagnetic activity web page of the World Data Center, Japan ( Coronal intensities data is obtained from Lomnicky Stit, Slovak Republic online catalogue. In order to determine the solar source of a geomagnetic storm, a criterion similar to that of Kumar and Yadav 2 has been followed. On the basis of solar wind velocity (Vsw), solar features have been investigated 1 t 5 days prior to the occurrence of GMSs on the earth. Here, time t, taken by the solar wind in reaching the Earth from the Sun, depends upon Vsw. 3 Results and discussion It is observed from Fig. 1 that during the year of maximum solar activity, i.e. 2000, Minor GMSs have occurred larger in number as compared to Intense and Major GMSs by different types of solar features and this holds for entire period of investigation. During the following year (2001), it is observed that more Intense and Major GMSs are caused by different types of solar features as compared to the preceding year of maximum solar activity, i.e It is apparent from Fig. 1 that in 1996, i.e. during solar minimum, only one Minor GMSs is observed, whereas 21 Minor GMSs are observed during solar maximum year in Further, nine Intense and 11 Major GMSs (largest in number) occurred during the Fig. 1 Occurrence frequency of Intense, Major and Minor GMSs from July 1996 to January 2005

3 KUMAR & KAUR: GEO-EFFECTIVE TRANSIENTS/SOLAR CAUSES DURING SOLAR CYCLE solar cycle 23, have been observed during 2001, which is close to the solar maximum year The results are in agreement with Richardson et al. 15 and Shrivastava et al. 11 that large number of Intense GMSs occur close to the solar maximum. It is observed that during the ascending phase of the solar cycle 23, the number of Intense GMSs increased from one (in 1997) to five (in 2000). Further, Major GMSs increase from seven (in 1997) to 10 (in 2000) and furthermore, Minor GMSs increased from one (in 1996) to 21 (in 2001), thereby, an increase with the progress of the solar activity cycle. Further, a significant decline in the number of Intense and Minor GMSs have been observed from 1998 to 1999, and Major GMSs from 1997 to This decline is consistent with Cane et al. 16 on the overall decline in the solar activity and related interplanetary activity in Richardson et al. 15 observed temporary decline in the number of GMSs which is attributed to the restructuring of the near ecliptic solar wind. Hα solar flares, X-ray solar flares, APDFs, CMEs, CI and accumulated solar features (Hα, X-ray - solar flares + APDFs + CMEs + CI) associated with Intense, Major, Minor and Total GMSs have been investigated from the period July 1996 to January It is observed from Table 1 that maximum number of GMSs are associated with CI followed by CMEs and further by individual Hα and X-ray solar flare events. However, when the accumulated effect of Hα and X-ray solar flare events are considered, these solar flares are better associated with GMSs than CMEs. This is in agreement with Kumar & Yadav 14 and Cliver et al. 17. The correlation coefficients between the yearly occurrence of Total (Intense + Major + Minor) GMSs and solar features such as Hα solar flares, X-ray solar flares, Hα + X-ray solar flares, APDFs, CMEs, CI and accumulated solar features, respectively have been calculated for Total GMSs. It is observed that CI posses an excellent correlation coefficient value, i.e. 1, with the occurrence of Total GMSs, followed by accumulated solar features, i.e and further 0.95 for Hα + X-ray solar flares and 0.94 for CMEs. These outcomes are in agreement with Shrivastava & Venkatakrishnana 11 and Temmer, et al. 18. However, this is not in agreement with the findings of Yermolaev and Yearmolaev 19. In many individual events, travel time between the explosion on the Sun and the maximum activity lies between and h for Intense, and Table 1 Different solar origins and their association causing Intense, Major, Minor and Total (Intense + Major + Minor) GMSs during July Jan 2005 S.No. Solar Features Intense (35) Major (58) Minor (76) Total (169) 1 Hα solar flares X-ray solar flares 3 APDFs CMEs CI Hα, X-ray solar flares 7 X-ray solar flares, APDFs 8 APDFs, CMEs APDFs, CMEs, CI 10 Hα solar flares, CMEs 11 Hα, X-ray solar flares, CMEs 12 Hα, X-ray solar flares, CMEs, CI 13 Hα, X-ray solar flares, APDFs 14 X-ray solar flares, APDFs, CMEs 15 Hα solar flares, APDFs, CMEs 16 Hα, X-ray solar flares, APDFs, CMEs 17 Hα, X-ray solar flares, APDFs, CMEs, CI h for Major and and h for Minor GMSs. This result is consistent with Kumar and Yadav 2. Several studies have dealt with the N-S spatial asymmetry of various kinds of manifestations of solar activity. Investigations of the N-S asymmetry of solar flares have been carried out by many workers 20,21. Most of the papers reveal the existence of a N-S asymmetry, however, there are different outcomes when evolution of the N-S asymmetry is correlated with the solar cycle. For the entire period of investigation, Hα, X-ray solar flares and APDFs distribution in heliographic

4 382 INDIAN J RADIO & SPACE PHYS, DECEMBER 2008 latitude for Intense, Major and Minor GMSs have been observed and results indicate that the Hα, X-ray solar flares and APDFs in the northern hemisphere are more in numbers than those in the southern hemisphere (except the APDFs causing Intense GMSs) for Intense, Major, Minor and Total GMSs. The ratio of total number of Hα, X-ray solar flares in the northern hemisphere and southern hemisphere have been evaluated for Hα, X-ray solar flare events causing different types of storms. It is observed that an overall northern bias apparently prevailed in the solar cycle 23. The flare events in the northern hemisphere exceeded the events in the southern hemisphere by 56.2% and APDFs by 18.3% during the investigated period. This shows a strong N-S asymmetry, which supports the findings of Temmer et al. 18. The longitude asymmetry of the Hα, X-ray solar flares and APDFs distribution has also been investigated during the period of study. It is observed that for Intense GMSs, Hα, X-ray solar flares occur mostly in western hemisphere. However, for Major and Minor GMSs, Hα, X-ray solar flares occur mostly in eastern hemisphere. Further, for Total GMSs, X-ray solar flare events are distributed equally in western and eastern hemispheres. However, Total (Hα + X-ray) solar flares exceeded in eastern region. APDFs causing Intense GMSs occur equally in both eastern and western regions. For Major GMSs, APDFs occurring in eastern region are more than in the western region. However, for Minor and Total GMSs, APDFs events are exceeded in the western region than those in the eastern region. The ratio of total number of Hα, X-ray solar flares in the western hemisphere and eastern hemisphere have been evaluated for Hα, X-ray solar flare events causing different types of storms. It may be inferred from the investigations that Hα and X-ray solar flare occurring over the western limb of the solar disk cause larger disturbances in magnetosphere leading to occurrence of Intense GMSs, whereas, solar flares occurring over the eastern limb of the solar disk lead to occurrence of Major, Minor and Total GMSs. These findings are in agreement with Temmer et al. 18 for Hα solar flares for the rising phase of solar cycle 23. CMEs are energetically the most important transient phenomenon on the Sun causing geomagnetic disturbances 6,22. For various properties of CMEs, the statistical study has been performed for different types of GMSs during the period of investigation of solar cycle 23 and the results are presented in Table 2. The mean angular width is wider for Intense GMSs followed by Minor and Major GMSs. Similar observations have been found for the one-sigma error in the distribution of points for angular width. It is observed from Table 2 that maximum linear fit speed for CMEs is largest causing the Intense GMSs followed by Major and Minor Table 2 Statistical characteristics of CMEs causing GMSs from July 1996 to Jan 2005 Storms Properties Max Min Mean Median σ Intense Angular Width Speed from linear fit (km/s) Second order speed at final height (km/s) Second order speed at 20 Rs (km/s) Acceleration Polar Angle Major Angular Width Speed from linear fit (km/s) Second order speed at final height (km/s) Second order speed at 20 Rs (km/s) Acceleration Polar Angle Minor Angular Width Speed from linear fit (km/s) Second order speed at final height (km/s) Second order speed at 20 Rs (km/s) Acceleration Polar Angle

5 KUMAR & KAUR: GEO-EFFECTIVE TRANSIENTS/SOLAR CAUSES DURING SOLAR CYCLE GMSs. However, one sigma error contained for Intense GMSs in the distribution of points of linear fit speed is largest for Intense GMSs followed by Major and Minor GMSs. Similarly, the mean linear fit speed, second order speed at final height and second order speed at 20 Rs (solar radius) is also observed to be largest for Intense followed by Major and Minor GMSs. However, the second order speed at final height of Major GMSs is largest. The tricohotomy suggests that CMEs associated with GMSs undergo severe changes in their evolution. The mean acceleration of CMEs is found to be 0.5, and 6.1 ms -1 for Intense, Major and Minor GMSs, respectively. It was observed that halo CMEs causing Intense, Major and Minor GMSs have negative acceleration i.e., they decelerated in the LASCO C2-C3 field of view. This result is in consistent with Zhao et al. 23. The polar angles of CMEs are observed from 5 to 325 for Intense, 8 to 323 for Major and 0 to 355 for Minor GMSs. It is observed that total number of CMEs caused dominating role in creating Minor GMSs followed by Major and Intense GMSs. The coronal intensities are given in millionths of intensity of the solar disk (coronal units) streaming towards the earth resulting in striking the Earth s magnetic field and triggering the geomagnetic storms. For the CI, the statistical study has been carried out for different types of GMSs during the period of investigation of solar cycle 23. It is observed from Table 1 that total CI is maximum for Minor GMSs followed by Major and Intense GMSs, whereas mean CI is maximum for Intense followed by Major and Minor GMSs. It is observed that maximum number of maximum CI (CI max ) occurred in the range degree, whereas minimum number of CImax occurred in the range 0-50 degree. It is observed from Figs 2 and 3 that CI with Vsw and Vcme do not posses better correlation. Furthermore, it is observed that for Intense and Major GMSs, CI, Vsw and Vcme are maximum during 2001 (close to solar maximum), whereas, for Minor GMSs CI, Vsw and Vcme are maximum during the solar maximum year (2000). These solar features are observed as minimum during the solar minimum year. It is observed that there are many occasions when eruptive streams and shock are unaccompanied by flare of filament activity and CMEs anywhere on the disc. Somehow, CI was observed during the interval. Hewish and Bravo 9 found that GMSs are more associated with coronal holes than solar flares. Thus it is concluded that high speed solar wind streams (HSSWS) and CMEs originated from the coronal holes have much greater ability to produce GMSs. Earlier studies suggest that the geoeffectiveness of solar wind depends upon the speed and the embedded southward magnetic field 3,24. It is the coupling between the solar wind plasma and magnetic field orientation that defines the magnitude of a geomagnetic storm. The variation of Bz plays a crucial role in determining the amount of solar wind energy, which is transferred to the magnetosphere 3,25. It is observed that the maximum solar wind velocity is not the binding condition for the intensity of occurrence of GMSs. Similarly the maximum decrease in the IMF Bz component is also not a binding condition for the intensity of GMSs to occur. It is also observed that Intense and Major GMSs occur even when value of IMF Bz is even larger than 10nT. Thus it seems that the relationship pointed out by Tsurutani and Gonzalez 25 is not the binding condition for the Intense GMSs to occur where Bz < -10nT. The Pearson s correlation coefficient between Dst and Bz for all types of GMSs from July 1996 to January 2005 have been found to be Wu and Leeping 26 using hourly average OMNI data for 135 events from 1965 to 1998 have obtained the correlation to be 0.86 and Cane et al. 16 have obtained the correlation to be 0.74 for the period 1996 to 1999 for 83 events. A very good correlation between Dst and Bz for the solar cycle 23 reveals that Bz and Dst play an important role in the occurrence of GMSs. For Intense, Major and Minor GMSs, product of solar wind velocity (Vsw) with Bz min (Vsw.Bz min ) and linear velocity of CMEs (Vcme) with Bz min Fig. 2 Occurrence frequency of CI for Intense, Major and Minor GMSs from July 1996 to January 2005

6 384 INDIAN J RADIO & SPACE PHYS, DECEMBER 2008 Fig. 3 Plot of CI with Vsw and Vcme for Intense, Major and Minor GMSs from July 1996 to January 2005 Table 3 Significance of Bz min, Dst, Vsw and Vcme on GMSs during July Jan 2005 Storms Dst Bz min Vsw Vcme Vsw. Bz min Vcme. Bz min Intense Major Minor (Vcme.Bz min ) have been presented in Table 3. It is observed that values of these products along with Dst are largest minimum for Intense GMSs followed by Major and Minor GMSs, respectively. Thus, it is deduced that product of Bz min with Vsw and Vcme (Vsw.Bz min and Vcme.Bz min ) along with minimum Dst of the SSC day are the reliable indicators of the intensity of GMSs. 4 Conclusions The following have been observed: (i) Maximum number of GMSs are associated with CMEs followed by individual Hα and X-ray solar flare events. However, when the (ii) (iii) (iv) (v) accumulated effect of Hα and X-ray solar flare events are considered, these solar flares are better associated with GMSs than CMEs. Intense and Minor GMSs increase with the ascending phase of solar activity, however, Major GMSs decrease during Somehow, significant decline in the number of Intense and Minor GMSs have been observed from 1998 to Correlation coefficient obtained between Total GMSs and CMEs and different solar features indicate that CMEs and accumulated (Hα + X-ray) solar flares are equally significant in initiating the GMSs. There is strong N-S asymmetry for solar cycle 23. An overall northern bias apparently prevailed for solar flares and APDFs. Hα and X-ray solar flares occurring over the western limb of the solar disk cause larger disturbances in magnetosphere leading to

7 KUMAR & KAUR: GEO-EFFECTIVE TRANSIENTS/SOLAR CAUSES DURING SOLAR CYCLE (vi) occurrence of Intense GMSs, whereas, solar flares occurring on the eastern limb of the solar disk lead to occurrence of Major and Minor GMSs. The mean angular width of CMEs is wider for Intense GMSs followed by Minor and Major GMSs. The linear fit speed for CMEs is largest causing Intense GMSs followed by Major and Minor GMSs. The mean linear fit speed, second order speed at final height and second order speed at 20 Rs are largest for Intense followed by Major and Minor GMSs. However, the second order speed at final height of the Major GMSs is largest. (vii) Halo CMEs causing Intense, Major and Minor GMSs have negative acceleration, i.e. they decelerate in the LASCO C2-C3 field of view. (viii) Total CI is maximum for Minor GMSs followed by Major and Intense GMSs, whereas, mean CI is maximum for Intense GMSs followed by Major and Minor GMSs. (ix) (x) (xi) Maximum number of CI max occurred in the range degree whereas minimum number of CI max occurred in the range 0-50 degree. HSSWS and CMEs originated from the coronal holes have much greater ability to produce GMSs. Product of Bz min with solar wind velocity Vsw and Vcme (Vsw.Bz min and Vcme.Bz min ) along with minimum Dst of the SSC day are reliable indicators of the intensity of the GMSs. Acknowledgements The authors are thankful to various experimental groups for providing data. The authors are also thankful to the anonymous referees for their valuable suggestions. References 1 Gonzalez W D, Joslyn J A, Kamide Y, Kroehl H W, Rostoker G, Tsurutani B T & Vasylinus V M, What is a geomagnetic storm?, J Geophys Res (USA), 99 (1994) Kumar S & Yadav M P, Study of solar features causing GMSs with 250γ < H <400γ, Pramana (India), 61 (2003) Kane R P, Sun earth relation: Historical development and present status - A brief review, Adv Space Res (UK), 35 (2005) Lockwood J A, Forbush decreases in the cosmic radiation, Space Sci Rev (Netherlands), 12 (1971) Garcia H A & Dryer M, The solar flares of February 1986 and the ensuing intense geomagnetic storm, Sol Phys (Netherlands), 109 (1987) Gopalswamy N, Lara A, Yashiro S, Kaiser M L & Howard R A, Predicting the 1-AU arrival times of coronal mass ejections, J Geophys Res (USA), 106 (2001) Hewish A & Bravo S, The sources of large-scale heliospheric disturbances, Sol Phys (Netherlands), 106 (1986) Wilson R M & Hildner E, On the association of magnetic clouds with disappearing filaments, J Geophys Res (USA), 91 (1986) Sheely N R, Harvey J W & Feldman W C, Coronal holes, solar wind streams and recurrent geomagnetic disturbances , Sol Phys (Netherlands), 49 (1976) Nolte J T, Gerassimenko M, Kriegar A S & Solodyna C V, Coronal hole evolution by sudden large scale changes, Sol Phys (Netherlands), 56 (1978) Srivastava N & Venkatakrishnana P, Solar and interplanetary sources of major geomagnetic storms during , J Geophys Res (USA), 109 (2004) Feynman J & Gabriel S B, On space weather consequences and predictions, J Geophys Res (USA), 105 (2000) Plunkett S P, Thompson B J, St Cyr O C & Howard R A, Solar source regions of coronal mass ejections and their geomagnetic effects, J Atmos Sol-Terr Phys (UK), 63 (2001) Kumar S & Yadav M P, Geoeffectiveness of solar features, 28th International Cosmic Ray Conference, SH 2.2 (Tsukuba, Japan), 2003, p Richardson I G, Cane H V & Cliver E W, Sources of geomagnetic activity during nearly three solar cycles ( ), J Geophys Res (USA), 107 (2000) Cane H V, Richardson I G & St Cyr O C, Coronal mass ejections, ejecta and geomagnetic storms, Geophys Res Lett (USA), 27 (2000) Cliver E W, Webb D F & Howard H A, On the origin of solar metric type II bursts, Sol Phys (Netherlands), 187 (1999) Temmer M, Verong A & Hanslmeier A, Soft X-ray flares for the period , Sol Phys (Netherlands), 477 (2002) Yermolaev Y I & Yermolaev M Y, Statistical relationships between solar, interplanetary and geomagnetic disturbances , Cosm Res (USA), 41 (2) (2003) Verma V K, On the increase of solar activity in the southern hemisphere during solar cycle 21, Sol Phys (Netherlands), 114 (1987) Atac T & Ozguc A, Flare index during the rising phase of solar cycle 23, Sol Phys (Netherlands), 198 (2001) Low B C, Coronal mass ejections, magnetic flux ropes and solar magnetism, J Geophys Res (USA), 106 (2001) Hyashi K, Zhao X P & Liu Y, Solar corona obtained with MHD simulation using various boundary treatments based on characteristic projection method, AGU Fall Meeting, SH42B (San Francisco, USA, 8-12 December 2003). 24 Kumar S & Yadav M P, Solar causes of geomagnetic storms, Indian J Radio Space Phys, 31 (2002) Tsurutani B T & Gonzalez W D, The interplanetary causes of magnetic storms, in Magnetic Storms, Geophys Monogr, Vol 98, edited by B T Tsurutani, W D Gonzalez & Y Kamide (AGU, Washington D C, USA), 1997, p Wu C C & Leeping R P, Effect of solar wind velocity on magnetic cloud-associated magnetic storm intensity, J Geophys Res (USA), 107 (2002) 1346.