- Email: [email protected]
KET
Advances in Space Research 35 (2005) 605–610 www.elsevier.com/locate/asr
On the determination of energy spectra of MeV electrons by the Ulysses COSPIN/KET B. Heber a
a,*
, A. Kopp
b,c
, H. Fichtner c, S.E.S Ferreira
d
Fachbereich Physik, Universita¨t Osnabru¨ck, Barbarastr. 7, 49069 Osnabru¨ck, Germany b Max-Planck Institut fu¨r Sonnensystemforschung, Katlenburg-Lindau, Germany c Ruhr-Universita¨t Bochum, Bochum, Germany d North-West University, Campus Potchefstroom, South Africa
Received 29 October 2004; received in revised form 12 January 2005; accepted 13 January 2005
Abstract The Ulysses mission has provided a wealth of data, particularly regarding the transport of low-energy cosmic ray electrons. These data have been used to derive significant constraints for the anisotropic spatial diffusion of these particles. Detailed model simulations allowed, in addition, to determine the relative contributions of galactic and Jovian electrons to the total flux at a given time and position in the heliosphere. Despite these insights, energy spectra have not been reliably determined as yet. This is a consequence of the uncertainty due to a background connected to proton interactions with the spacecraft. Recently, however, it was demonstrated that this uncertainty can, with some difficulty, be reduced, thus opening the opportunity to understand such spectra in the energy range 3–30 MeV, i.e., the part mostly dominated by Jovian electrons. We present results of a corresponding re-analysis of COSPIN/ KET data. Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Instrumentation; GEANT-simulation; MeV-Electrons
1. Introduction and motivation The COsmic and Solar Particle INvestigation Kiel Electron Telescope (COSPIN/KET) on-board Ulysses measures protons and a-particles in the energy range from 4 to >2000 MeV/n and electrons in the range from 2 to >300 MeV in different energy channels. Fig. 1 shows a sketch of the KET sensor. The telescope as described in Simpson et al. (1992) consists in principal of two parts: (1) an entrance telescope and (2) the calorimeter, a lead fluoride Cherenkov detector C2 and a scintillation detector S2. The entrance telescope comprises a silica-aerogel Cherenkov detector with an index of refraction of 1.066 inserted between *
Corresponding author. E-mail address: [email protected] (B. Heber).
semi-conductor detectors. It defines the geometry, selects particles with speeds v/c = b > 0.938 and determines the magnitude of the particle charge but not its sign. Below the entrance telescope is a 2.5 radiation length lead-fluoride (PbF2) crystal calorimeter located above a curved-shaped scintillator detector that counts the number of particles leaving the calorimeter. This part of the detector system characterizes electromagnetic showers. Based on measured signals, data from KET are classified into ‘‘channels’’ with a count rate available for each channel (Rastoin (1995); Ferrando et al. (1996)). The channel E12 counts particles, normally electrons in the energy range between 7 and 170 MeV, with speeds v > 0.938c that do not trigger the lowest scintillator but interact in the calorimeter. The channels labeled P190 and P4000 count particles that do not interact with the calorimeter yet do trigger the Cherenkov C2 and the
0273-1177/$30 Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.01.054
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Fig. 1. Sketch of the KET sensor.
scintillator. Nominally these particles are protons above 250 MeV (Heber, 1997). From the in-flight energy loss distribution in D1 vs. D2, as displayed in Fig. 2, it became evident that a fraction of counts can be attributed to a simultaneous crossing of two electrons in D1, C1 and D2 within a 1-ls (Ferrando et al., 1996). These contributions are identified by the entries in the upper right corner in Fig. 2. Heber et al. (1999) interpreted these background due to electrons moving from the back to the front of the instrument. Energetic c-rays, which are generated locally by hadronic interactions of galactic cosmic rays (GCRs) with the spacecraft material, may enter the lead-fluoride (PbF2) crystal calorimeter unseen
Fig. 3. Four-day averaged raw count rate of 7–170 MeV electrons (e) and >2000 MeV protons (upper curves) and 7–170 MeV electrons, identified as background (bg) as well as >2000 MeV protons (lower curves). Adapted from Heber et al. (1999).
by the scintillator. There they are either converted into an electron–positron pair or give rise to photoelectric or Compton electrons inside the calorimeter. These electrons either escape the instrument through the front aperture, or do not leave a signal sufficient to trigger the anti-coincidence. Fig. 3 displays the 4-day averaged background (lower curve) and the count rate of 7– 170 MeV electrons (upper curve), as proposed by Ferrando et al. (1996), together with >2 GeV protons. The proton and electron curves are normalised to each other during Ulyssess rapid pole-to-pole passage. As discussed in Ferrando et al. (1993) and Simpson et al. (1993) the sharp increases in 1992/1993 of the electron intensity are due to special propagation conditions of electrons from Jupiter to Ulysses. Except for such periods the count rate of the background and of the 7– 170 MeV electron, follows that of the protons. Since the intensity of >2000 MeV protons exceeds that of 7– 170 MeV electrons, we conclude that this channel has a strong contribution induced by GCR-protons.
2. KET data analysis
Fig. 2. Electron energy loss matrix (E12) of D1 and D2.
In what follows we will derive a better estimation of the c-ray contamination empirically. This can be done because the particles responsible for most of the contamination are measured at KET. Using the photon-distribution in the lead fluoride detector, the knowledge from measurements at accelerator beams and a GEANT 3 simulation we show that electron spectra from 8 to 40 MeV can be determined from the KET measurements.
B. Heber et al. / Advances in Space Research 35 (2005) 605–610
2.1. Background subtraction The contribution of the c-ray generated background to the ‘‘1-electron’’ 7–170 MeV electron channel is expected to be dependent on the electromagnetic shower in C2. In order to check on our expectation we analyse the information of the number of generated photons in C2 available for a subset of particles registered. Fig. 4 shows such 52-day averaged photon distributions in C2 during quiet times mid-1994 (left) and during a solar particle event in August 1991 (right). Since solar energetic electron events are characterised by a soft energy spectrum I(E) µ Ec the number of low energy energy electrons and, therefore, the number of smaller showers in C2 is higher than in the background. Thus, such differences were expected. In the next step of our analysis we defined four different subchannels as indicated in Fig. 4. The definition for these subchannels are:
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distribution measured in 1994 as displayed in the left panel of Fig. 4. In order to determine the background distribution B(t), we make use of >2 GeV proton measurements P(t). First we determine the normalisation factor f in T = 1994 by using the ratio of P(T) and the count rate in the C2 > 150 A(T): f = A(T)/P(T). The background at any other time is then given by: A*(t) = f Æ P(t). The count rate A*(t) corresponds to the grey curve in Fig. 5(A) and determines the normalisation. As an example we have plotted in Fig. 6 the result of this procedure for a photon distribution in August 1991 (a) during a solar electron event (Heber et al., 2002). The distribution (b) corresponds to the normalised background distribution, and (c) gives the residual one. From that figure it is evident that corrections are small for the subchannel (D), become important for (C) and are crucial for (B). 2.2. Calibration at different accelerator beams
A: E12, 1 electron, C2 P 150 B: E12, 1 electron, 120 6 C2 6 140 C: E12, 1 electron, 80 6 C2 6 110 D: E12, 1 electron, 20 6 C2 6 70 The corresponding time histories of the 26-day averages are displayed in Fig. 5(A)–(D) together with the variation of >2 GeV/n protons and helium (grey curves, P(t)), respectively. The variation of the background is smallest for the E12, 20 6 C26 70 electrons and is better approximated by the helium channel, which has been used in Fig. 5(D) only. Comparing Fig. 5(A) and (B) on the one side and (C) and (D) on the other we conclude that electrons counted in a channel number above 120 in C2 are dominated by the c-ray background produced by high energy protons. The time profiles of the two other subchannels displayed in (C) and (D) do not follow the time profile of the protons except for a short period in 1994. From this fact we conclude that the maximum background distribution can be estimated by the
Several calibration runs at different electron accelerator beams have been performed. In this analysis we use runs from the Deutsche Elektronen SYnchroton (DESY, Germany) in 1984, the Physikalisches Institut der Universita¨t Bonn (Germany) in 1985, and the Acce´le´rateur Line´aire, in Gif sur Yvette (France) in 1985. At these institutions electron beams in the energy range from 7.5 MeV to 5 GeV were available. Fig. 7 shows the smoothed normalised photon distributions obtained with energies of 7.5, 10, 30, 50, and 100 MeV. From that figure it follows that the energy resolution of the calorimeter is not perfect; e.g., the signal of a 7.5 and a 10-MeV electron beam have a strong overlap. Thus, in order to deconvolute the measured calorimeter spectra correctly a complicated fitting process would be necessary. Such a procedure, however, is beyond the scope of this paper and is foreseen in the future. A simpler interpretation of the C2-spectra can be derived when assuming an ideal detector. In such a
Fig. 4. Fiftytwo-day averaged photon distribution in C2 in mid-1994 (left) and during a August 1991 event (right). The areas (B), (C) and (D) correspond to different electron energies. The corresponding time histories are displayed in Fig. 5.
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Fig. 5. Time profiles of 26-day averaged count rates of the four different electron subchannels (A)–(D), together with the variation of the >2 GeV/n proton and helium channels (grey curves, P(t)).
detector each monoenergetic electron would only give a signal in one C2-channel. The result of such a simplified inversion should be regarded more in the nature of an upper limit. In the next step we determined the accelerator energy as a function of the mean value C of the photon distribution, as shown in Fig. 8. The line through the points is a three parameter (p1, p2, p3) fit of the function " 2 !# 1 C p2 EðCÞ ¼ exp p1 exp : ð1Þ 2 p3
Using this function it is possible to convert the photon distribution into an electron energy distribution. For the last step of the inversion we need to determine the response function of the KET instrument to electrons in space. 2.3. Monte-Carlo simulations The required response functions cannot be obtained directly from accelerator measurements. Therefore Sierks (1988) developed a Monte-Carlo code using the GEANT 3 package (Brun et al., 1987) in order to model
10
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(a) Solar electron event
(c) Residual
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(b) Distribution mid 1994
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Fig. 6. Normalised photon distributions in mid-1994 and during a solar particle event in 1991.
Fig. 7. Smoothed photon distribution in C2 obtained at different accelerator beams for energies between 7.5 and 100 MeV.
B. Heber et al. / Advances in Space Research 35 (2005) 605–610
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Fig. 8. Mean energy as function of the mean median channel of the photon distribution in C2.
the KET instrument. Results of this simulation have been used before by Rastoin (1995) to derive the energy spectra of GeV-electrons. The response function and from that the geometrical factor G has been calculated using the same energies as above. The geometrical factor in [cm2 sr] is shown in Fig. 9. We used these calculations and the function ! 2 1 logðEðCÞÞ p 2 G ¼ p1 exp ; ð2Þ 2 p3 to determine the geometrical factor G as function of the mean energy E(C) of the photon distribution. Eq. (1) gives E as a function of C. The result of the three parameter fit of Eq. (2) to the calculations is displayed in Fig. 9. 2.4. Energy spectra In order to obtain the physical energy spectra from the corrected photon distribution as displayed in Fig. 6, the physical energy spectra the x-axis (Channel num0.6 0.5 G (cm2sr)
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Fig. 10. Energy spectra (1) during quiet times in early 1991, (2) during a solar particle event in August 1991, and during a Jovian electron event early 1992, when the spacecraft was close to Jupiter.
ber) has to be transformed into an energy axis by Eq. (1). The intensity in each of these channel bins is than that given by the following procedure: (1) The distribution (a) in Fig. 6 is normalised to unity. (2) This normalisation factor is applied to the residual distribution (c). (3) The residual distribution (c) will be multiplied by the count rate measured in the 7–170 MeV channel during that time period. (4) Each bin is divided with the corresponding geometrical factor times the energy width of the bin. The result of this procedure is displayed in Fig. 10. The spectra exhibit the expected form. For Jovian electrons the result can be further checked by a comparison of the intensity level at the lower energy end (about 5 MeV): del Peral et al. (2003) have analysed the electron spectrum in the overlapping interval 0.15–10 MeV, measured with the EPHIN sensor on board SOHO during 1996. Their independent findings fit nicely to the intensity level found from our analysis.
3. Conclusion
0.2 0.1 0
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Fig. 9. Geometrical factor as function of the mean median channel in C2.
Using results from the calibration of the KET at accelerators and a GEANT 3 simulation of the instrument, we have developed a simple deconvolution of the C2 photon distribution in order to obtain a reasonable first order approximation of the electron energy spectrum. The results, taking into account a proton induced background is in good agreement with observations by del Peral et al. (2003), who derived the
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electron spectra below 10 MeV from EPHIN/SOHO measurements. We have, thus, successfully demonstrated that there is a real potential in deriving energy spectra of MeV-electrons from the COSPIN/KET aboard the Ulysses spacecraft using a sophisticate but complicate mathematical procedure in the future.
Acknowledgements This work was funded within the framework of the bi-lateral collaboration programme between South Africa and Germany by the Deutsche Forschungsgemeinschaft (DFG). A.K. and S.E.S.F. acknowledge financial support via the project SCHL 201/14-1/2. The work of all authors benefitted from their participation in the UCRJET workshop sponsored via DFG 445-SUA122/1/03. B.H. acknowledges the support from the DFG enabling him to participate in the 35th COSPAR Assembly in Paris, July 2004, where this work was presented.
References Brun, R., Bruyant, F., Maire, M., McPherson, A.C., Zanarini, P. GEANT3. CERN Data Handling Divison (DD/EE/84-1), 1987. del Peral, L., Go´mez-Herrero, R., Rodrı´guez-Frı´as, M.D., Gutie´rrez, J., Mu¨ller-Mellin, R., Kunow, H. Jovian electrons in the heliosphere: new insights from EPHIN on board SOHO. Astropart. Phys. 20, 235–245, 2003. Ferrando, P., Ducros, R., Rastoin, C., Raviart, A., Kunow, H., Mu¨ller-Mellin, R., Sierks, H., Wibberenz, G. Propagation of Jovian electrons in and out of the Ecliptic. Adv. Space Res. 13 (6), 107–110, 1993.
Ferrando, P., Raviart, A., Haasbroek, L.J., Potgieter, M.S., Dro¨ge, W., Heber, B., Kunow, H., Mu¨ller-Mellin, R., Sierks, H., Wibberenz, G., Paizis, C. Latitude variations of 7 MeV and >300 MeV cosmic ray electron fluxes in the heliosphere: ULYSSES COSPIN/ KET results and implications. Astron. Astrophys. 316 (2), 528–537, 1996. Heber, B. Modulation galaktischer kosmischer Protonen und aTeilchen in der inneren dreidimensionalen Heliospha¨re: Ulysses COSPIN/KET Ergebnisse. Ph.D. thesis, Universita¨t Kiel, Germany, 1997. Heber, B., Ferrando, P., Raviart, A., Paizis, C., Posner, A., Wibberenz, G., Mu¨ller-Mellin, R., Kunow, H., Potgieter, M.S., Ferreira, S.E.S., Burger, R.A., Fichtner, H., Schlickeiser, R. 3–20 MeV electrons in the inner three-dimensional heliosphere at solar maximum: Ulysses COSPIN/KET observations. Astrophys. J. 579, 888–894, 2002. Heber, B., Raviart, A., Ferrando, P., Sierks, H., Paizis, C., Kunow, H., Mu¨ller-Mellin, R., Bothmer, V., Posner, A. Determination of 7– 30 MeV electron intensities: Ulysses COSPIN/KET results, in: Proceedings of the 16th International Cosmic Ray Conference, Salt Lake City, Utah, USA, August 17–25, vol. 7, p. 186, 1999. Rastoin, C. Les e´lectrons de Jupiter et de la Galaxie dans lhe´liosphe`re dapre`s lexpe´rience KET a bord de la sonde spatiale ULYSSE. Ph.D. thesis, Saclay, France, 1995. Sierks, H. Auswertungen der Eichmessungen des Kieler ElektronenTeleskops zur Erstellung von Energiespektren an Bord der Raumsonde ULYSSES (International Solar Polar Mission). Masters thesis, Christian-Albrechts-Universita¨t Kiel, Germany, 1988. Simpson, Wibberenz, Anglin, J., Barlogh, A., Bercovitch, M., Bouman, J., Budzinski, E., Burrows, J., Carvell, R., Connell, J., Ducros, R., Ferrando, P., Firth, J., Garcia-Munoz, M., Henrion, J., Hynds, R., Iwers, B., Jacquet, R., Kunow, H., Lentz, G., Marsden, R., McKibben, R., Mu¨ller-Mellin, R., Page, D., Perkins, M., Raviart, A., Sanderson, T., Sierks, H., Treguer, L., Tuzzolino, A., Wenzel, K.-P., Wibberenz, G. The Ulysses cosmic-ray and Solar particle investigation. Astron. Astrophys. Suppl. 92 (2), 365– 399, 1992. Simpson, J.A., Smith, D.A., Zhang, M. Jovian electron propagation in three dimensions of the heliosphere: the ULYSSES investigations. J. Geophys. Res 98, 21129–21144, 1993.
On the determination of energy spectra of MeV electrons by the Ulysses COSPIN/KET B. Heber a
a,*
, A. Kopp
b,c
, H. Fichtner c, S.E.S Ferreira
d
Fachbereich Physik, Universita¨t Osnabru¨ck, Barbarastr. 7, 49069 Osnabru¨ck, Germany b Max-Planck Institut fu¨r Sonnensystemforschung, Katlenburg-Lindau, Germany c Ruhr-Universita¨t Bochum, Bochum, Germany d North-West University, Campus Potchefstroom, South Africa
Received 29 October 2004; received in revised form 12 January 2005; accepted 13 January 2005
Abstract The Ulysses mission has provided a wealth of data, particularly regarding the transport of low-energy cosmic ray electrons. These data have been used to derive significant constraints for the anisotropic spatial diffusion of these particles. Detailed model simulations allowed, in addition, to determine the relative contributions of galactic and Jovian electrons to the total flux at a given time and position in the heliosphere. Despite these insights, energy spectra have not been reliably determined as yet. This is a consequence of the uncertainty due to a background connected to proton interactions with the spacecraft. Recently, however, it was demonstrated that this uncertainty can, with some difficulty, be reduced, thus opening the opportunity to understand such spectra in the energy range 3–30 MeV, i.e., the part mostly dominated by Jovian electrons. We present results of a corresponding re-analysis of COSPIN/ KET data. Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Instrumentation; GEANT-simulation; MeV-Electrons
1. Introduction and motivation The COsmic and Solar Particle INvestigation Kiel Electron Telescope (COSPIN/KET) on-board Ulysses measures protons and a-particles in the energy range from 4 to >2000 MeV/n and electrons in the range from 2 to >300 MeV in different energy channels. Fig. 1 shows a sketch of the KET sensor. The telescope as described in Simpson et al. (1992) consists in principal of two parts: (1) an entrance telescope and (2) the calorimeter, a lead fluoride Cherenkov detector C2 and a scintillation detector S2. The entrance telescope comprises a silica-aerogel Cherenkov detector with an index of refraction of 1.066 inserted between *
Corresponding author. E-mail address: [email protected] (B. Heber).
semi-conductor detectors. It defines the geometry, selects particles with speeds v/c = b > 0.938 and determines the magnitude of the particle charge but not its sign. Below the entrance telescope is a 2.5 radiation length lead-fluoride (PbF2) crystal calorimeter located above a curved-shaped scintillator detector that counts the number of particles leaving the calorimeter. This part of the detector system characterizes electromagnetic showers. Based on measured signals, data from KET are classified into ‘‘channels’’ with a count rate available for each channel (Rastoin (1995); Ferrando et al. (1996)). The channel E12 counts particles, normally electrons in the energy range between 7 and 170 MeV, with speeds v > 0.938c that do not trigger the lowest scintillator but interact in the calorimeter. The channels labeled P190 and P4000 count particles that do not interact with the calorimeter yet do trigger the Cherenkov C2 and the
0273-1177/$30 Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.01.054
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B. Heber et al. / Advances in Space Research 35 (2005) 605–610
Fig. 1. Sketch of the KET sensor.
scintillator. Nominally these particles are protons above 250 MeV (Heber, 1997). From the in-flight energy loss distribution in D1 vs. D2, as displayed in Fig. 2, it became evident that a fraction of counts can be attributed to a simultaneous crossing of two electrons in D1, C1 and D2 within a 1-ls (Ferrando et al., 1996). These contributions are identified by the entries in the upper right corner in Fig. 2. Heber et al. (1999) interpreted these background due to electrons moving from the back to the front of the instrument. Energetic c-rays, which are generated locally by hadronic interactions of galactic cosmic rays (GCRs) with the spacecraft material, may enter the lead-fluoride (PbF2) crystal calorimeter unseen
Fig. 3. Four-day averaged raw count rate of 7–170 MeV electrons (e) and >2000 MeV protons (upper curves) and 7–170 MeV electrons, identified as background (bg) as well as >2000 MeV protons (lower curves). Adapted from Heber et al. (1999).
by the scintillator. There they are either converted into an electron–positron pair or give rise to photoelectric or Compton electrons inside the calorimeter. These electrons either escape the instrument through the front aperture, or do not leave a signal sufficient to trigger the anti-coincidence. Fig. 3 displays the 4-day averaged background (lower curve) and the count rate of 7– 170 MeV electrons (upper curve), as proposed by Ferrando et al. (1996), together with >2 GeV protons. The proton and electron curves are normalised to each other during Ulyssess rapid pole-to-pole passage. As discussed in Ferrando et al. (1993) and Simpson et al. (1993) the sharp increases in 1992/1993 of the electron intensity are due to special propagation conditions of electrons from Jupiter to Ulysses. Except for such periods the count rate of the background and of the 7– 170 MeV electron, follows that of the protons. Since the intensity of >2000 MeV protons exceeds that of 7– 170 MeV electrons, we conclude that this channel has a strong contribution induced by GCR-protons.
2. KET data analysis
Fig. 2. Electron energy loss matrix (E12) of D1 and D2.
In what follows we will derive a better estimation of the c-ray contamination empirically. This can be done because the particles responsible for most of the contamination are measured at KET. Using the photon-distribution in the lead fluoride detector, the knowledge from measurements at accelerator beams and a GEANT 3 simulation we show that electron spectra from 8 to 40 MeV can be determined from the KET measurements.
B. Heber et al. / Advances in Space Research 35 (2005) 605–610
2.1. Background subtraction The contribution of the c-ray generated background to the ‘‘1-electron’’ 7–170 MeV electron channel is expected to be dependent on the electromagnetic shower in C2. In order to check on our expectation we analyse the information of the number of generated photons in C2 available for a subset of particles registered. Fig. 4 shows such 52-day averaged photon distributions in C2 during quiet times mid-1994 (left) and during a solar particle event in August 1991 (right). Since solar energetic electron events are characterised by a soft energy spectrum I(E) µ Ec the number of low energy energy electrons and, therefore, the number of smaller showers in C2 is higher than in the background. Thus, such differences were expected. In the next step of our analysis we defined four different subchannels as indicated in Fig. 4. The definition for these subchannels are:
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distribution measured in 1994 as displayed in the left panel of Fig. 4. In order to determine the background distribution B(t), we make use of >2 GeV proton measurements P(t). First we determine the normalisation factor f in T = 1994 by using the ratio of P(T) and the count rate in the C2 > 150 A(T): f = A(T)/P(T). The background at any other time is then given by: A*(t) = f Æ P(t). The count rate A*(t) corresponds to the grey curve in Fig. 5(A) and determines the normalisation. As an example we have plotted in Fig. 6 the result of this procedure for a photon distribution in August 1991 (a) during a solar electron event (Heber et al., 2002). The distribution (b) corresponds to the normalised background distribution, and (c) gives the residual one. From that figure it is evident that corrections are small for the subchannel (D), become important for (C) and are crucial for (B). 2.2. Calibration at different accelerator beams
A: E12, 1 electron, C2 P 150 B: E12, 1 electron, 120 6 C2 6 140 C: E12, 1 electron, 80 6 C2 6 110 D: E12, 1 electron, 20 6 C2 6 70 The corresponding time histories of the 26-day averages are displayed in Fig. 5(A)–(D) together with the variation of >2 GeV/n protons and helium (grey curves, P(t)), respectively. The variation of the background is smallest for the E12, 20 6 C26 70 electrons and is better approximated by the helium channel, which has been used in Fig. 5(D) only. Comparing Fig. 5(A) and (B) on the one side and (C) and (D) on the other we conclude that electrons counted in a channel number above 120 in C2 are dominated by the c-ray background produced by high energy protons. The time profiles of the two other subchannels displayed in (C) and (D) do not follow the time profile of the protons except for a short period in 1994. From this fact we conclude that the maximum background distribution can be estimated by the
Several calibration runs at different electron accelerator beams have been performed. In this analysis we use runs from the Deutsche Elektronen SYnchroton (DESY, Germany) in 1984, the Physikalisches Institut der Universita¨t Bonn (Germany) in 1985, and the Acce´le´rateur Line´aire, in Gif sur Yvette (France) in 1985. At these institutions electron beams in the energy range from 7.5 MeV to 5 GeV were available. Fig. 7 shows the smoothed normalised photon distributions obtained with energies of 7.5, 10, 30, 50, and 100 MeV. From that figure it follows that the energy resolution of the calorimeter is not perfect; e.g., the signal of a 7.5 and a 10-MeV electron beam have a strong overlap. Thus, in order to deconvolute the measured calorimeter spectra correctly a complicated fitting process would be necessary. Such a procedure, however, is beyond the scope of this paper and is foreseen in the future. A simpler interpretation of the C2-spectra can be derived when assuming an ideal detector. In such a
Fig. 4. Fiftytwo-day averaged photon distribution in C2 in mid-1994 (left) and during a August 1991 event (right). The areas (B), (C) and (D) correspond to different electron energies. The corresponding time histories are displayed in Fig. 5.
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Fig. 5. Time profiles of 26-day averaged count rates of the four different electron subchannels (A)–(D), together with the variation of the >2 GeV/n proton and helium channels (grey curves, P(t)).
detector each monoenergetic electron would only give a signal in one C2-channel. The result of such a simplified inversion should be regarded more in the nature of an upper limit. In the next step we determined the accelerator energy as a function of the mean value C of the photon distribution, as shown in Fig. 8. The line through the points is a three parameter (p1, p2, p3) fit of the function " 2 !# 1 C p2 EðCÞ ¼ exp p1 exp : ð1Þ 2 p3
Using this function it is possible to convert the photon distribution into an electron energy distribution. For the last step of the inversion we need to determine the response function of the KET instrument to electrons in space. 2.3. Monte-Carlo simulations The required response functions cannot be obtained directly from accelerator measurements. Therefore Sierks (1988) developed a Monte-Carlo code using the GEANT 3 package (Brun et al., 1987) in order to model
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Fig. 6. Normalised photon distributions in mid-1994 and during a solar particle event in 1991.
Fig. 7. Smoothed photon distribution in C2 obtained at different accelerator beams for energies between 7.5 and 100 MeV.
B. Heber et al. / Advances in Space Research 35 (2005) 605–610
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Fig. 8. Mean energy as function of the mean median channel of the photon distribution in C2.
the KET instrument. Results of this simulation have been used before by Rastoin (1995) to derive the energy spectra of GeV-electrons. The response function and from that the geometrical factor G has been calculated using the same energies as above. The geometrical factor in [cm2 sr] is shown in Fig. 9. We used these calculations and the function ! 2 1 logðEðCÞÞ p 2 G ¼ p1 exp ; ð2Þ 2 p3 to determine the geometrical factor G as function of the mean energy E(C) of the photon distribution. Eq. (1) gives E as a function of C. The result of the three parameter fit of Eq. (2) to the calculations is displayed in Fig. 9. 2.4. Energy spectra In order to obtain the physical energy spectra from the corrected photon distribution as displayed in Fig. 6, the physical energy spectra the x-axis (Channel num0.6 0.5 G (cm2sr)
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-6
1
10 E [MeV]
10
2
Fig. 10. Energy spectra (1) during quiet times in early 1991, (2) during a solar particle event in August 1991, and during a Jovian electron event early 1992, when the spacecraft was close to Jupiter.
ber) has to be transformed into an energy axis by Eq. (1). The intensity in each of these channel bins is than that given by the following procedure: (1) The distribution (a) in Fig. 6 is normalised to unity. (2) This normalisation factor is applied to the residual distribution (c). (3) The residual distribution (c) will be multiplied by the count rate measured in the 7–170 MeV channel during that time period. (4) Each bin is divided with the corresponding geometrical factor times the energy width of the bin. The result of this procedure is displayed in Fig. 10. The spectra exhibit the expected form. For Jovian electrons the result can be further checked by a comparison of the intensity level at the lower energy end (about 5 MeV): del Peral et al. (2003) have analysed the electron spectrum in the overlapping interval 0.15–10 MeV, measured with the EPHIN sensor on board SOHO during 1996. Their independent findings fit nicely to the intensity level found from our analysis.
3. Conclusion
0.2 0.1 0
10
-4
40
60 80 100 120 Channel number in C2
140
Fig. 9. Geometrical factor as function of the mean median channel in C2.
Using results from the calibration of the KET at accelerators and a GEANT 3 simulation of the instrument, we have developed a simple deconvolution of the C2 photon distribution in order to obtain a reasonable first order approximation of the electron energy spectrum. The results, taking into account a proton induced background is in good agreement with observations by del Peral et al. (2003), who derived the
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electron spectra below 10 MeV from EPHIN/SOHO measurements. We have, thus, successfully demonstrated that there is a real potential in deriving energy spectra of MeV-electrons from the COSPIN/KET aboard the Ulysses spacecraft using a sophisticate but complicate mathematical procedure in the future.
Acknowledgements This work was funded within the framework of the bi-lateral collaboration programme between South Africa and Germany by the Deutsche Forschungsgemeinschaft (DFG). A.K. and S.E.S.F. acknowledge financial support via the project SCHL 201/14-1/2. The work of all authors benefitted from their participation in the UCRJET workshop sponsored via DFG 445-SUA122/1/03. B.H. acknowledges the support from the DFG enabling him to participate in the 35th COSPAR Assembly in Paris, July 2004, where this work was presented.
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