Modeling and forecasting solar energetic particle events at Mars: the event on 6 March 1989

Context. Large solar energetic particle events are able to enhance the radiation intensity present in interplanetary space by several orders of magnitude. Therefore the study, modeling and prediction of these events is a key factor to understand our space environment and to protect manned space missions from hazardous radiation. Aims. We model an intense solar energetic particle event observed simultaneously on the 6 of March 1989 by the near-Earth orbiting spacecraft IMP-8 and by the Phobos-2 spacecraft in orbit around Mars ( located 72. to the East of the Earth and at 1.58 AU from the Sun). This particle event was associated with the second largest X-ray flare in solar cycle 22. The site of this long-duration X15/3B solar flare was N35E69 ( as seen from the Earth) and the onset of the 1 - 8 angstrom X-ray emission occurred at 1350 UT on 6 March 1989. A traveling interplanetary shock accompanied with < 15 MeV proton intensity enhancements was observed by IMP-8 at 1800 UT on 8 March and by Phobos-2 at 2015 UT on 9 March. This shock determines the particle intensities at both spacecraft. Methods. We use an MHD code to model the propagation of the associated shock to both spacecraft and a particle transport code to model the proton intensities measured by IMP-8 and Phobos-2. By assuming that energetic particles are continuously accelerated by the traveling shock, and that the injection rate of these particles, Q, into the interplanetary medium is related to the upstream-to-downstream velocity ratio, VR, at the point of the shock front that connects with the observer, we perform predictions of the solar energetic particle intensities observed at Mars from those measured at Earth. Results. We reproduce not only the arrival times of the shock at both spacecraft but also the measured jump discontinuity of solar wind speed, density and magnetic field. Also, we reproduce the 0.5 - 20 MeV proton intensities measured by both spacecraft. Functional dependences such as the Q( VR) relation deduced here allow us to predict the proton intensities measured at Phobos-2 for this event. Applications of this model for future predictions of solar energetic particle fluxes at Mars are discussed.