A first step towards proton flux forecasting

Advances in Space Research xxx (2005) xxx xxx www.elsevier.com/locate/asr A first step towards proton flux forecasting A. Aran a, *, B. Sanahuja a, D. Lario b a Departament dõastronomia i Meteorologia, Martí i Franquès 1, E-08028 Barcelona, Spain b Applied Physics Laboratory, The Johns Hopkins University, 11100 Johns Hopkins Road, Laurel MD 20723, USA Received 19 October 2002; received in revised form 8 March 2004; accepted 21 June 2004 Abstract We present a preliminary version of a potential tool for real time proton flux prediction which provides proton flux profiles and cumulative fluence profiles at 0.5 and 2 MeV of solar energetic particle events, from their onset up to the arrival of the interplanetary shock at the spacecraft position (located at 1 or 0.4 AU). Based on the proton transportation model by Lario et al. [Lario, D., Sanahuja, B., Heras, A.M. Energetic particle events: efficiency of interplanetary shocks as 50 kev E < 100 MeV proton accelerators. Astrophys. J. 509, 415 434, 1998] and the magnetohydrodynamic shock propagation model of Wu et al. [Wu, S.T., Dryer, M., Han, S.M. Non-planar MHD model for solar flare-generated disturbances in the Heliospheric equatorial plane. Sol. Phys. 84, 395 418, 1983], we have generated a database containing synthetic profiles of the proton fluxes and cumulative fluences of 384 solar energetic particle events. We are currently validating the applicability of this code for space weather forecasting by comparing the resulting synthetic flux profiles with those of several real events. Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Space weather; Proton flux forecasting; Interplanetary shock; Solar protons 1. Introduction At present the engineering codes for particle flux and fluence predictions of solar energetic particle (SEP) events are unable to assess the source of the order-ofmagnitude variation of the observed fluxes. Most probably the main deficiency is the failure of including the effects of interplanetary shocks because operational codes were developed under the old paradigm that particle acceleration occurs only at the site of the associated solar event (usually the flare site). Large gradual SEP events are generated by shocks driven by coronal mass ejections (CMEs) (see, for example, Reames, 1999), and they can occur with no associated flares. That failure and the scarce number of proton flux observations out of 1 AU are responsible of our poor knowledge of * Corresoponding author. Tel.: +34 93 402 1131; fax: +34 93 402 1133. E-mail address: aaran@am.ub.es (A. Aran). the radial variations of solar SEP fluxes; in many engineering applications a simple inverse square law is used. Therefore, a more complete physical approach in modeling the solar particle generation and propagation in interplanetary space is required, and this approach must be translated into an operational code. We have been developing a very first version of an engineering tool that takes into account the contribution of shock-accelerated protons in the flux and fluences of gradual SEP events, in the upstream part of the shock. At present, we only consider the contribution of protons although helium ions can account for a ten to fifteen percent of the total equivalent dose (Turner, 2001). To obtain proton flux profiles, we combine a MHD shock propagation model and a particle transport model. From them, we derive a functional relationship between the injection rate of protons and the strength of the shock at the point on the shock front magnetically connected to the observer, i.e., the cobpoint (after Heras et al., 1995). We assume that the injection of particles takes 0273-1177/$30 Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2004.06.023

2 A. Aran et al. / Advances in Space Research xxx (2005) xxx xxx place at the cobpoint, which changes of location and properties as the shock expands. We represent the strength of the shock at this point by the normalized jump of plasma velocity (VR). The particles injected at the cobpoint travel to the observerõs position spiraling along the interplanetary magnetic field (IMF) lines. The effects of this travel on the particles are modeled by means of a transport equation that considers the effects of streaming, scattering, convection and adiabatic deceleration (Heras et al., 1992; Lario et al., 1998). It is well-known that the evolution of the flux profiles differs from one SEP event to another (Cane et al., 1988), therefore, modeling the proton flux profiles of each SEP event is an iterative task which demands skills, and hence, preventing to obtain results in real time. We have built up a database containing synthetic proton flux and fluence profiles upstream of the shock for 384 interplanetary scenarios. In this way, the desired profiles can be obtained in less than a minute; intermediate scenarios are fast calculated by interpolation from those contained in the dataset. This procedure, once validated, will allow us to make predictions useful for forecasting and nowcasting. 2. Building the database Flux profiles for different SEP events greatly vary depending on: (1) the characteristics of the interplanetary shock, (2) the observerõs location with respect to the parent solar transient event, and (3) the different conditions for particle transport. For details see discussion and description of Fig. 15 in Cane et al. (1988). According to this, we have generated a database which contains the flux and cumulative fluence profiles of 288 interplanetary scenarios for a spacecraft located at 1 AU, and 96 for a probe at 0.4 AU. We assume averaged values for several parameters describing these scenarios, taken from the former modeling of real SEP events. The shape of flux profiles is very different depending on the angular position of the observer relative to the heliolongitude of the parent solar activity (Cane et al., 1988). Consequently, we have simulated nine angular positions for a spacecraft located at 1 AU: W45, W30, W22.5, W15, W00, E15, E22.5, E30 and E45. Further, taking into account that there are planned missions to the inner heliosphere (i.e., Beppi Colombo, MESSENGER or Solar Orbiter) we have included a spacecraft located at 0.4 AU. In this way, we can study the capability of our code to obtain useful proton flux profiles and fluences for such heliocentric distances. At 0.4 AU, we have considered three angular positions: W45, W00 and E30. We have simulated the propagation of eight interplanetary shocks using the model of Wu et al. (1983). These shocks are characterized by the initial pulse velocity at the inner boundary of the integration grid, the speeds considered are: v s = 750, 900, 1050, 1200, 1350, 1500, 1650 and 1800 km s 1. The initial pulse angular amplitude of the shock has been fixed at x = 140. We characterize the proton transport conditions by means of the proton mean free path; the code offers two possible choices: k i = 0.2 and 0.8 AU at 0.5 MeV (taken as the reference energy). To reproduce the flux enhancement observed in some large gradual SEP events, we consider the existence of a turbulent foreshock region along the shock front. It is characterized by a mean free path, k ic = 0.01 AU for 0.5 MeV protons, and with a given width of 0.1 AU, in front of the shock. The main factor that permits us to derive synthetic proton flux profiles is a parametric relationship between the injection rate of shock-accelerated particles, Q, and the normalized downstream-to-upstream plasma velocity ratio at the cobpoint, VR (Lario et al., 1999). We adopt (Lario, 1997) log Q ¼ log Q 0 þ kvr; ð1þ where Q 0 =1 10 35 (cm 6 s 3 s 1 ) at 0.5 MeV and 5 10 41 (cm 6 s 3 s 1 ) at 2 MeV. We have considered k = 0.5 for all events, except for western events at energies higher than 2 MeV where we consider k = 3.0 in order to reproduce the decrease of the flux profile usually observed at high energies in many western events. Note that the injection of particles at the cobpoint is only assumed if VR > 0.1. The database contains the proton cumulative fluences for energies above 0.5 MeV and above 2 MeV, for each scenario. The fluence is the result of the integration over time of the fluxes, from the onset of the event up to the shock arrival, and the integration over the energy starting from a threshold energy (E > 0.5 or >2 MeV). 3. The engineering model The input parameters of the code, in its present stage, are the position of the observer, the initial pulse velocity, the proton mean free path, the existence of a foreshock region and the energy of the protons. The code permits to choose between 1.0 and 0.4 AU for the heliocentric radial distance of the spacecraft, and it asks to introduce an initial pulse velocity for the shock (from 750 to 1800 km s 1 ). Next, the user has to choose an angular position for the observer (from W45 to E45 at 1 AU; W45, W00 or E30 at 0.4 AU), the proton mean free path (0.2 or 0.8 AU), and the existence of a turbulent foreshock region (YES/NO). Finally, the energy of the particles has to be specified (0.5 or 2.0 MeV). Once all the input parameters are specified, the code searches in the database for those events with the closest characteristics to the userõs selection. For intermediate values of initial shock velocity and observerõs angular position (at 1 AU), flux and fluence profiles are calculated performing

A. Aran et al. / Advances in Space Research xxx (2005) xxx xxx 3 Fig. 1. Examples of resulting profiles for a western event at 1.0 AU and central meridian event at 0.4 AU. a linear interpolation from those searched profiles. In spite of the simplicity of the interpolation procedure, the relative differences between the interpolated flux profiles and those obtained from computing the same event specified by the user are usually less than a ten per cent. We have checked that these differences can be decreased by reducing the scale of the grid of simulated events The outputs of the code are the transit time and velocity of the shock from the Sun to the spacecraft for the selected event, as well as the total fluence above the chosen energy, calculated throughout the upstream region of the event. Besides, the code displays the resulting plots of the flux and/or cumulative fluence versus time and allows the user to save them in JPEG format. Fig. 1 shows two examples of the outputs; in each case, the left upper panel presents the list of parameters selected and the right panel provides the transit time and velocity, and also the total fluence. Dashed vertical lines indicate the time of the shock arrival at the spacecraft. 4. Starting with the validation of the code To validate this engineering tool it is necessary: (1) to compare the outputs of the code with observational data, (2) and further modeling of more SEP events. We present here the results derived for the SEP event on 12 15 September 2000. The CME that drove the event was temporally associated with a Ha flare located at S17W09, starting at 1240 UT on September 12 (doy 256). The CME-driven shock was detected by the Advanced Composition Explorer (ACE) at 0359 UT on September 15 (doy 259), thus this is a slow Central Meridian event with a transit time of 63.33 h (average transit velocity of 649 km s 1 ). Fig. 2 shows the simultaneous fitting of the proton flux and first order anisotropy profiles of this SEP event, when running the particle transport code of Lario et al. (1998). Flux data are obtained from the Electron Proton and Alpha Monitor (EPAM) instrument on ACE (Gold et al., 1998) and the first order anisotropy is computed using the sectored data from the Low Energy Magnetic Spectrometers (LEMS) of the EPAM instrument by transforming the measurements into the solar wind frame of reference and fitting them by spherical harmonic functions (details of this method are described in Sanderson et al., 1985). To simultaneously fit proton fluxes and anisotropy profiles we considered a constant mean free path of 0.2 AU for protons of 0.8 MeV; that is, k i = 0.18 AU for protons of 0.5 MeV and k i = 0.25 AU for protons of 2 MeV, assuming a dependence of the mean free path on the proton magnetic rigidity as in Hasselman and Wibberenz (1970). Besides, we considered a foreshock region with a width of 0.04 AU. Therefore, the closest parameters in our database to reproduce this specific SEP event are 0.2 AU for the proton mean free path and NO inclusion of a foreshock turbulent region. In Figs. 3 and 4, we compare the observed flux profiles with those derived from our operational code. Considering an initial pulse velocity equal of 750 km s 1,we reproduce the time of arrival of the shock within 1 h less

4 A. Aran et al. / Advances in Space Research xxx (2005) xxx xxx Fig. 2. September 15 2000 SEP event. Observed (dotted lines) and fitted (dashed thick lines) proton flux and first order anisotropy profiles. Flux data are obtained from the LEMS telescope of the ACE/EPAM instrument (Gold et al., 1998). First order anisotropy profiles were calculated as in Sanderson et al. (1985) and applied to LEMS data. The arrow indicates the time of the solar activity and the vertical solid line the time of shock arrival at ACE. Also, the solar wind velocity from Solar Wind Electron Proton Alpha Monitor, (SWEPAM) on ACE (McComas et al., 1998) is shown at the left bottom panel; and the local interplanetary magnetic field magnitude and directions in GSE coordinates from data of the ACE magnetometer (MAG) (Smith et al., 1998). of the actual time. The evolution of the flux profile at 0.5 MeV is similar to the equivalent energy channel of ACE/ EPAM instrument (P5 and P 0 5). We cannot compare directly the flux profile obtained at 2 MeV and the 1.9 4.8 MeV channel (P8 and P 0 8) because of the different energy windows of the ACE/EPAM instrument and that used in our database. A narrower channel centered at 2 MeV would be necessary to directly compare the measured flux profile with that obtained from our database. In order to compare observed fluences above a certain energy threshold with those derived from our code, it is necessary to assume an energy dependence above those energies not simulated and not measured. We have assumed a power law spectrum with a slope c =2(Turner, 2001) above our highest simulated energy (8 MeV) and above the highest energy observed by the LEMS detectors of the ACE/EPAM instrument (4.8 MeV). The observed total fluence derived is 6.2 10 8 cm 2 sr 1 for E > 0.59 MeV and 1.0 10 8 cm 2 sr 1 for E > 1.9 MeV. Comparing these values with those derived from the engineering code, we conclude that the values obtained for the total fluence for this SEP event are good, since they are only a factor 3.0 (for E > 0.5 MeV) and 3.4 (for E > 2 MeV) lower than those observed. 5. Conclusions We have presented an engineering code which allows the user to obtain in less than 1 min the proton flux and cumulative fluence profiles at 0.5 and 2 MeV for SEP events at radial distances of 1 and 0.4 AU. The database

A. Aran et al. / Advances in Space Research xxx (2005) xxx xxx 5 Fig. 3. Flux and fluence profiles resulting from the engineering tool (right panel) for the 12 15 September 2000 SEP event at 0.5 MeV compared with the flux observed by EPAM instrument onboard ACE (left panel). Fig. 4. Flux and fluence profiles resulting from the engineering tool (right panel) for the 12 15 September 2000 SEP event at 2.0 MeV compared with the flux observed by EPAM instrument onboard ACE (left panel). comprises a variety of interplanetary scenarios considering slow and fast shocks, i.e., with times of arrival ranging from 25.0 h for the fastest to 72.4 h for the slowest, and heliolongitudes from W45 to E45 for spacecraft at 1 AU. We plan to expand this database to other scenarios in order to increase the number of SEP events available and to compare them with real events (both at 1 and 0.4 AU). Intermediate events are obtained by linear interpo-

6 A. Aran et al. / Advances in Space Research xxx (2005) xxx xxx lation from those in the dataset. Further the averaged difference between computed and interpolated profiles is less than a 10% and can be improved by reducing the intergrid size of the database. We are currently modeling SEP events to check in deep the parametric dependence of the injection rate with the upstream-to-downstream plasma velocity ratio (VR) and to study the potential application of this code to space weather forecasting. Acknowledgements We acknowledge the financial support of ESA/ES- TEC Contract 14098/99/NL/MM and of the Ministerio de Ciencia y Tecnología (Spain), under the project AYA2001-3304. Partial computational support has been provided by the Centre de Supercomputació de Catalunya (C 4 ). D.L. was supported by NASA Grant NAG5-10787. We acknowledge the use of ACE/EPAM data and the ACE Science Center for providing the ACE data. References Cane, H.V., Reames, D.V., von Rosenvinge, T.T. The role of interplanetary shocks in the longitude distribution of solar energetic particles. J. Geophys. Res. 93, 9555 9567, 1988. Gold, R.E., Krimigis, S.M., Hawkins III, S.E., et al. Electron, proton, and alpha monitor on the advanced composition explorer spacecraft. Space Sci. Rev. 86 (1 4), 541 562, 1998. Hasselman, K., Wibberenz, G. A note on the parallel diffusion coefficient. Astrophys. J. 162, 1049 1051, 1970. Heras, A.M., Sanahuja, B., Smith, Z.K., et al. The influence of the large-scale Interplanetary shock structure on a low-energy particle event. Astrophys. J. 391, 359 369, 1992. Heras, A.M., Sanahuja, B., Lario, D., et al. Three low-energy particle events: modeling the influence of the parent interplanetary shock. Astrophys. J. 445, 497 508, 1995. Lario, D. Propagation of low-energy particles through the interplanetary medium: modeling their injection from interplanetary shocks. PhD thesis, Universitat de Barcelona, 1997.. Lario, D., Sanahuja, B., Heras, A.M. Energetic particle events: efficiency of interplanetary shocks as 50 kev < E < 100 MeV proton accelerators. Astrophys. J. 509, 415 434, 1998. Lario, D., Sanahuja, B., Heras, A.M. A tool to model solar energetic particle events. ESA Workshop on Space Weather, ESA WPP-155, pp. 343 346, 1999.. McComas, D.J., Bame, S.J., Barker, P., et al. Solar wind electron proton alpha monitor (SWEPAM) for the advanced composition explorer. Space Sci. Rev. 86 (1 4), 563 612, 1998. Reames, D.V. Particle acceleration at the Sun and in the heliosphere. Space Sci. Rev. 90, 413 491, 1999. Sanderson, T.R., Reinhard, R., van Nes, P., et al. Observations of three-dimensional anisotropies of 35- to 1000-keV protons associated with interplanetary shocks. J. Geophys. Res. 90, 19 27, 1985. Smith, C.W., LÕHeureux, J., Ness, N.F., et al. The ACE magnetic fields experiment. Space Sci. Rev. 86 (1 4), 613 632, 1998. Turner, R. What we must know about solar particle events to reduce risk to astronauts, in: Song, P., et al. (Eds.), Space Weather, Geophysical Monograph 125. American Geophysical Union, Washington, DC, pp. 39 44, 2001.. Wu, S.T., Dryer, M., Han, S.M. Non-planar MHD model for solar flare-generated disturbances in the Heliospheric equatorial plane. Sol. Phys. 84, 395 418, 1983.