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Modeling and predicting the 6 March 1989 SEP event at Mars. 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) - PowerPoint PPT Presentation
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Angels Aran1, David Lario2 and Blai Sanahuja1,3
(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, 16-11-2006
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?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 1989.
● 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)
ObservationsObservations
● 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
● Hα 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, vs
Main outputs:
COBPOINT’s location
MHD variables (VR, BR and θBn) 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 s3 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 = Vr(d)/Vr (u) -1 BR: the downstream/upstream magnetic field intensity ratio, BR = |B|(d)/|B|(u)θBn: 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:
vsw (km s-1) n (cm-3) |B| (nT)
1.0 AU 434 4.8 6.9
1.58 AU 435 1.9 4.0
● 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-8 52.1 51.1 hours
Phobos-2 78.4 77.4 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)
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 = Vr(d)/Vr(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/R0)0.5
0 = 0.6 AU R0 = 75.52 MV
( E0= 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/R0)-0.8 AU
● Initial injection (t<tc)
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 Q0 + 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) <E> Q0 (cm-6 s3 s-1) k ------------------------------------------------------------ a 0.50 - 0.96 0.69 4.91 10-36 1.18 b 0.96 - 2.0 1.39 7.10 10-37 1.30 c 2.0 - 4.6 3.03 2.20 10-38 2.19 d 4.6 -15.0 8.31 2.48 10-40 3.33 e 15.0 - 25.0 19.36 1.28 10-41 2.19 f 25.0 - 48.0 34.64 1.20 10-42 2.19
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/R0)0.5
0 = 0.6 AU R0 = 75.52 MV
( E0= 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/R0)0.2 AU
● Initial injection (t<tc)
Reid-Axford profile
β = 20 h and τ = 15 h
Modeling
Figure 3
M1
IMP-8
From the MHD, model at the cobpointVR(t)
Q(VR): log Q = log Q0 + 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 Q0 values as the energy channels of both instruments are different
Fc2
● IMP-8 simulation:
E(MeV) <E> Q0 (cm-3 s3 s-1) k coef. Corr.-------------------------------------------------------------------0.5-0.96 0.69 4.91 10-36 1.18 0.930.96-2.0 1.39 7.10 10-37 1.30 0.952.0-4.6 3.03 2.20 10-38 2.19 0.98 4.6-15.0 8.31 2.48 10-40 3.33 0.9715.0-25.0 19.36 1.28 10-41 2.19 0.9825.0-48.0 34.64 1.20 10-42 2.19 0.98
● Phobos-2: Prediction. Transport conditions from the fitting of figure 2.
E(MeV) <E> Q0 (cm-3 s3 s-1) k-high k-low k-Phobos (figure 5)-------------------------------------------------------------------------------------0.9-1.2 1.04 1.63 10-36 1.30 1.18 1.30 1.8-3.8 2.62 4.25 10-38 2.19 1.30 2.193.8-8.0 5.51 2.02 10-39 3.33 2.19 3.33/2.19 (dashed)9.0-19.0 13.08 5.90 10-41 2.19 3.33 3.33
Q(VR) relation from the IMP-8 fitting
log Q = logQ0 + 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.
Fluences and peak fluxes at Mars. Observed and forecasted (Fc2 and Fc3)
values.
E (MeV) Obvs. Fc2 Fc3
0.9 - 1.2 1.8 1.5 1.5 (x 108) 1.8 - 3.8 2.1 1.8 2.3 (x 107)3.8 - 8.0 3.1 2.4 3.8 (x 106)8.0 - 19.0 5.5 1.7 2.2 (x 105)
Fluence [p (cm2 sr MeV) -1]
E (MeV) Obvs. Fc2 Fc3
0.9 - 1.2 3412.7† 4266.6 3909.01.8 - 3.8 443.8† 487.0 453.43.8 - 8.0 66.4 64.3 58.98.0 - 19.0 9.2 6.8 6.8
Peak fux [p (cm2 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 8.0 -19 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 4.6 -15 MeV of IMP-8, for example).
● For E < 8 MeV channels, predictions
give values similar to observed values.
● For the 9.0 - 19 MeV channel, the peak flux is underestimated a factor of about1.4.
Conclusions (and caveats)
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”
ModelingObservation Problem