Angels Aran 1, David Lario 2 and Blai Sanahuja 1,3 (1) Departament d’Astronomia i Meteorologia. Universitat de Barcelona (Spain) (2) Applied Physics Laboratory. The Johns Hopkins University (Maryland, USA) (3) Institut de Ciències del Cosmos, UB. Barcelona (Spain) 3rd ESWW, Brussels, Modeling and predicting the 6 March 1989 SEP event at Mars Modeling and predicting the 6 March 1989 SEP event at Mars

Outline ● Why this SEP event? ● Observations at 1 AU (IMP-8) and at 1.58 AU (Phobos-2) ● Modeling the 1 AU SEP event of 6-10 March 1989 ● Deriving the empirical relation Q(VR) at 1 AU ● Predicting SEP flux profile at Phobos-2 ● Conclusions Outline ● Why this SEP event? ● Observations at 1 AU (IMP-8) and at 1.58 AU (Phobos-2) ● Modeling the 1 AU SEP event of 6-10 March 1989 ● Deriving the empirical relation Q(VR) at 1 AU ● Predicting SEP flux profile at Phobos-2 ● Conclusions

Why this SEP event? ● There are a few observational analysis on the dependence of particle flux and fluences of SEP events with radial distance (see, Lario et al., 2006) ● No studies dealing with forecasting individual SEP events exist at Mars orbit, from SEP Earth-orbit observations. In fact, it does not exist any study dealing with modeling of an individual SEP event observed by separate spacecraft. Phobos-2 was launched on July 1988, reached Mars on 29 January 1989, and it was inserted into orbit around the planet. It was lost on 27 March ● This SEP event was, fortunately observed by spacecraft orbiting around Earth and by spacecraft orbiting around Mars. Therefore, the opportunity to study this particle event is quite unique. (Even thought, this is not a text-book case because at Phobos-2: (1) there is a relevant data gap (2) the low-accuracy of the available solar wind data (3) the lack of useful measurements (4) there are no anisotropies measurements of the magnetic field(neither at IMP-8)

Observations ● A traveling interplanetary (IP) shock Detected at ~18:00 UT on 8 March at IMP-8 (McKenna-Lawlor et al., 2005) at ~20:15 UT on 9 March at Phobos-2 (Marsden et al., 1990) ● Energetic particles The IP shock was accompanied with proton (< 15 MeV) intensity enhancements observed by both spacecraft Mars’ orbit Earth’s orbit ● A fast CME observed the 6 of March (Solar Max Mission) Observed over the northeast limb at 14:15 UT. ● X-Ray emission (X15) The onset was 13:50 UT, with the maximum 14:05 UT ● H α 3B flare The onset was at 13:54 UT (N35E69) (Feynman and Hundhausen, 1994; Marsden et al., 1990; and Kurt et al., 2004) The second largest of the Solar Cycle 22 (Watari et al., 2001)

IP Shock (McKenna-Lawlor et al., 2005) IP Shock Solar Activity Transit time of the shock: 52.1 hours Average transit speed: 798 km s -1 (1 AU)

IP Shock Due to fluctuations, it is not possible to use magnetic field values (McKenna-Lawlor et al., 2005) IP Shock Solar Activity Transit time of the shock: 78.4 hours Average transit speed: 837 km s -1 Solar Activity IP shock (1.58 AU ) (R. Marsden, 2006)

The flare was located at N35E69 (as seen from the Earth). Therefore, this is a Far eastern SEP event (E69) as seen at 1 AU by IMP-8 Phobos-2 was located at 1.58 AU from the Sun and 72º eastward from the Earth Central Meridian SEP event (W02) as seen by Phobos-2 IMF lines IMF line that connects IMP-8 to the Sun IMF connection between IMP-8 and Phobos-2 with the Sun, respectively

● The simulation of in-ecliptic multi-spacecraft observations requires the use of al least 2-dimensional models of shock propagation. A radial magnetic field cannot reproduce the longitudinal dependence of the SEP intensity profiles observed by multi-spacecraft observations Shock-and-Particle model (D. Lario, B. Sanahuja and A. M. Heras, 1998) ● We use a 2.5-D MHD model to simulate the expansion of the IP shock and we solve the focused-transport equation to describe the propagation of energetic particles along the IMF. ● We assume that shock-accelerated particles are injected onto the IMF lines at the point of the shock front magnetically connected with the observer (the cobpoint: Connecting with the OBserver POINT). ● The variable that links both models is Q: the injection rate of shock- accelerated particles in phase space, at a given time and radial distance.

2,5-D MHD model (Wu et al., 1983) Main inputs for the initial shock pulsation: the initial speed, v s Main outputs:  COBPOINT’s location  MHD variables (VR, BR and θ Bn ) at the COBPOINT Proton propagation model (Lario, 1997; Lario et al., 1998) Using a focused-diffusion transport equation + solar wind convection + adiabatic deceleration Main parameters: Q (cm -6 s 3 s -1 ), the injection rate of shock-accelerated particles at the COBPOINT λ ║, proton mean free path Main outputs (observations):  Proton differential flux at several energies  First order anisotropy Any relation between MHD variables and Q should be independent of the shock particle acceleration mechanism. ● At the cobpoint VR: the downstream/upstream normalized velocity ratio, VR = V r (d)/V r (u) -1 BR: the downstream/upstream magnetic field intensity ratio, BR = |B|(d)/|B|(u) θ Bn : the shock front normal – upstream magnetic field angle

Interplanetary shock simulation ● We have used the 2.5-D MHD model by Wu et al. (1983). The outer boundary of code up to 2 AU. Steady-state background solar wind that reproduces the plasma and magnetic field observations prior to the shock arrival. ● Background solar wind conditions at: v sw (km s -1 )n (cm -3 ) |B| (nT) 1.0 AU AU ● Initial conditions for the shock pulse at 18 R  (Smith and Dryer, 1990) Speed Vs = 1260 km s -1 Angular width ω =131º Duration  = 1 hour Shock-and-Particle model.I: The shock

Simulation (grey traces) of the solar wind and magnetic field conditions at IMP-8. Observations: black traces Simulation (black traces) of the solar wind and magnetic field conditions at Phobos-2. Observations: open circles Transit time of the shock observed modeled IMP hours Phobos hours

Phobos-2/Mars is magnetically connected to the front of the shock, but not IMP-8/Earth Mars Cobpoint (Connecting with the OBserver POINT; in red Heras et al., 1995) Front of the shock Three snapshot of the evolution of the IMF connection between the observers (at 1 AU and at 1.58 AU) and the front of the shock

Phobos-2/Mars magnetically connected to the front of the shock (red cobpoint) IMP-8 already connected to the front of the shock (orange cobpoint) Both, IMP-8 and Mars cobpoints move to the right (toward the MHD stronger central part of the shock), scanning different regions of the shock front

The shock is arriving to IMP-8/Earth (flux peak at low energy) Mars cobpoint is moving closer to the nose of the shock (red cobpoint)

The shock is arriving to Mars/Phobos-2

Evolution of the position of the two cobpoints: VR and BR values VR is the downstream (d) to upstream (u) normalized velocity ratio (radial velocity jump acroos the front) VR = V r (d)/V r (u) -1 and BR the magnetic field ratio BR = |B|(d)/|B|(u) Observer Front of the shock Sun Upstream IMF line Angle Distance Cobpoint (calculate VR, BR…) (d) (u) IMP-8 Phobos-2 Shock IMP-8 Shock Phobos-2

Particle transport equation (Ruffolo, 1995) used by Lario et al. (1998) Streaming + Convection Focusing Differential convection Scattering Adiabatic deceleration Source term (Directly related to the injection rate, Q, in velocity space) Shock-and-particle model. II: The particles

18 Simulation of the SEP Event observed by IMP-8 ● From MHD shock model Time of connection: 21.6 h Time of shock arrival: 52.1 h ● Transport conditions Mean free path No radial dependence Energy: ║ = 0 (R/R 0 ) = 0.6 AU R 0 = MV ( E 0 = 3.03 MeV for protons) Turbulent foreshock At work for E < 15 MeV t = 21.8 h width = 0.07 AU ║ c = 0.03 (R/R 0 ) -0.8 AU ● Initial injection (t<t c ) Reid-Axford profile β = 50 h and τ = 15 h

IMP-8 Q(t) From the MHD, model at the cobpoint From the fitting of SEP event, at the cobpoint VR(t) Q(VR): log Q = log Q 0 + k VR The SEP event observed by IMP-8: the Q(VR) relation This is the key figure: it allows forecasting IMP-8 E (MeV) Q 0 (cm -6 s 3 s -1 ) k a b c d e f

Fitting the SEP event observed by Phobos-2 ● From MHD shock model Time of connection: 12.6 h Time of shock arrival: 78.4 h ● Transport conditions Mean free path No radial dependence Energy: ║ = 0 (R/R 0 ) = 0.6 AU R 0 = MV ( E 0 = 3.03 MeV for protons) Turbulent foreshock At work for E < 9 MeV t = 12.0 h width = 0.05 AU ║ c = 0.03 (R/R 0 ) 0.2 AU ● Initial injection (t<t c ) Reid-Axford profile β = 20 h and τ = 15 h Modeling Figure 3 M1

IMP-8 Q(t) From the MHD, model at the cobpoint From the fitting of SEP event, at the cobpoint VR(t) Q(VR): log Q = log Q 0 + k VR Phobos-2 Reverse procedure: Predicting the SEP event at Phobos-2 (1) Then, combining ● this Q(VR) relation and ● the VR(t)-values at the cobpoint of Phobos-2 spacecraft allow us (2) to derive the evolution of Q, Q(t), at Phobos-2 cobpoint. (3) Next step is to use these Q(t)- values as input values for the source term in the particle transport equation Finally, (4) solving the transport equation yield the synthetic flux profiles (for each energy channel) at Phobos-2 position.

Predicting the SEP event at Phobos-2 (W02) Flux profile prediction at Phobos-2 derived: ● Assuming that the Q(VR) relation derived from IMP-8 data is also valid at Phobos-2 cobpoint. ● IP transport conditions derived from the fitting of IMP-8 data. [Results are very similar if the IP transport conditions derived from fitting Phobos-2 data are used profiles.] ● Initial injection derived from Phobos-2 modeling. Phobos-2 ‘sees’ a W02 event: the IMF connection is established earlier than at IMP-8 and a larger initial injection occurs. Calibration of the Q 0 values as the energy channels of both instruments are different Fc2

● IMP-8 simulation: E(MeV) Q 0 (cm -3 s 3 s -1 ) k coef. Corr ● Phobos-2: Prediction. Transport conditions from the fitting of figure 2. E(MeV) Q 0 (cm -3 s 3 s -1 ) k-high k-low k-Phobos (figure 5) /2.19 (dashed) Q(VR) relation from the IMP-8 fitting log Q = logQ 0 + k VR

Figure 5 Predicting the SEP event at Phobos-2 (W02) Flux profile prediction at Phobos-2 derived: ● Assuming that the Q(VR) relation derived from IMP- 8 data is also valid at Phobos-2 cobpoint. ● IP transport conditions: same as for fit to Phobos- 2 data. ● Stronger initial (solar) injection: a Reid-Axford profile with β = 20 h and τ = 5 h ( 1) High efficient particle- acceleration near the Sun (2) The data gap prevents a more complete study Fc3

Fluences and peak fluxes at Mars. Observed and forecasted (Fc2 and Fc3) values. E (MeV) Obvs. Fc2 Fc (x 10 8 ) (x 10 7 ) (x 10 6 ) (x 10 5 ) Fluence [p (cm 2 sr MeV) -1 ] E (MeV) Obvs. Fc2 Fc † † Peak fux [p (cm 2 s sr MeV) -1 ] † Values at the time assumed for the shock passage (peak flux shortly after the shock, within the resolution of the solar wind data at Phobos-2) ● For E < 8 MeV channels, predictions give values similar to observed values. ● For the MeV channel, the predicted values are smaller, a factor ~3, than observed values. Predictions can be improved if: - A MHD shock propagation model from a few ~3R  can be used - High energy detectors have small window energy channels (not as the MeV of IMP-8, for example ). ● For E < 8 MeV channels, predictions give values similar to observed values. ● For the MeV channel, the peak flux is underestimated a factor of about1.4.

Conclusions (and caveats) ● Particle flux profile predictions derived for different space locations, from SEP events observed at 1 AU may be affected by: - Different IP transport conditions that particles might encounter en route to other observers (…it does not seem to be the case for this SEP event) - Different pre-existing particle seed populations filling flux tubes to be swept by the shock (for example, at early stages of the shock propagation). … and in spite of the observational/instrumental problems found. Thus, guess what is possible to do with more/new/well tailored multi-spacecraft SEP events (textbook-case, please!), from STEREO, for example,... but also out of 1 AU (Solar Orbiter?). ● Comparison between predicted and measured flux profiles at Mars leads us to conclude that the Q(VR) relation performs well in forecasting the flux profiles at Phobos-2, for this SEP event…....there where it can be reasonably applied (that means after the gap).

To be confident that the Q(VR) relation holds for a large variety of SEP events observed at different solar-interplanetary scenarios it is necessary to model a large set of isolated SEP events observed by spacecraft located at different heliocentric distances and longitudes that detect the passage of the same IP shock. ● The main constraint for this type of analysis is the scarce number of SEP events that can be detected by different spacecraft at distances around Mars (for example, in this case). In fact, this is the sole case we have found, able to be modeled under rather “reasonable conditions”. ● Differences between measured and predicted fluxes are – for this event – of less relevance, - For the fluence, because all flux profiles monotonically increase up to the shock passage - For the peak flux because due to the data gap we don’t know where the peak flux really occurs. That is not necessarily true in general. In many SEP events, at low energy the flux peaks at shock passage while at high energy the peak flux (or a plateau) appears early in the event.

Moltes gràcies! ¡Muchas gracias! “The two extremes” Modeling ObservationProblem

Spectral index,  : Q(E) = Q 0 (E/E 0 ) -  E 0 = 3.03 MeV E < 1 MeV t < h,  = 3.4 t > h,  = ≤ E < 15.0 MeV: t < h,  = 4.0 t > h,  = 3.5 E > 15 MeV:  = 4.0 E (MeV) Q 0 (cm -6 s -3 s -1 ) k Corr. coef e e e e e e SEP Event March, as seen at Earth (E69): Fit to IMP-8 data (II) Q(t) Q(VR)

Spectral index,  : Q(E) = Q 0 (E/E 0 ) -  E 0 = 2.62 MeV E < 1.8 MeV t < 53.0 h,  = 3.15 t > 53.0 h,  = 3.00 E > 1.8 MeV: t < 53.0 h,  = 3.40 t > 53.0 h,  = 3.00 Figure 4 SEP Event March, as seen at Mars (W02): Fit to Phobos2 data (III) using solar injection as derived from Figure 3 and transport conditions derived from the fitting of IMP-8 data (Figure 1).

32 SEP Event March, as seen at Earth (E69): Fit to IMP-8 data (I) Time of connection: 21.6 h Time of shock arrival: h Transport conditions: Constant mean free path: ║ = 0 * (p/p 0 ) = 0.6 AU, p 0 = MeV E 0 = 3.03 MeV Turbulent foreshock for E < 15 MeV): t = 21.8 h; width = 0.07 AU ║ c = 0.03 * (p/p 0 ) -0.8 (AU) Solar injection: Reid-Axford profile, β = 50 h and τ = 15 h Energy dependence: p -8.6

Solar injection: Reid-Axford profile, β = 20 h and τ = 5 h Energy dependence: p -5.0 Figure 7a Figure 7b Aran, Lario, Sanahuja et al., A&A in preparation