Author: Peter Zelina and Silvia Dalla (University of Central Lancashire).
Violent eruptions at the Sun, solar flares and coronal mass ejections, occur with frequency correlated with the 11-year solar cycle. They are sometimes accompanied by energetic particles up to GeV energies observed in situ in the interplanetary medium, by particle instruments onboard spacecraft. Such particles are termed solar energetic particles (SEPs). Protons and electrons are the most abundant species but SEP events also contain small fractions of heavy ions, such as oxygen, carbon, silicon and iron.
The intensity profiles of SEP events observed at 1 AU typically show a rather rapid increase and a more gradual decrease, depending on the relative position of the flare with respect to the observer. When different elements at equal kinetic energy per nucleon (i.e. speed) are considered, an intensity ratio, e.g. Fe/O may be calculated. Often the Fe/O ratio shows a decrease over time over the duration of an SEP event.
Time dependence in previous studies, observations and simulations
Observations of time dependence in ionic ratios have been reported since the 1970’s  and the data have improved with every new generation of spacecraft. Two major ideas proposed to explain the observed temporal evolution of ionic ratios involve SEP acceleration and transport, or their combination. SEP heavy ions, which are partially ionised in the space environment , can take a number of charge states, hence the mass-to-charge (M/Q) ratio for a given species can obtain a range of values.
Scholer et al.  noted that Fe/O decreased over time while O/C remained remarkably steady during SEP events. They explained the observed time dependence as a result of a M/Q-dependent mean free path, where SEP ions with large M/Q values scatter less frequently. Later, Tylka et al.  considered a number of heavy ion ratios and explained the observed Fe/O decrease as due to the acceleration mechanism. Here Fe ions escape the acceleration region at a CME-driven shock earlier than oxygen, due to their larger Larmor radius. More recently, a consensus emerged that the observations of Fe/O at near Earth [4,5] and from Ulysses at high heliolatitudes  are the result of propagation through the interplanetary medium.
Recently, we studied  heavy ion data for 4 SEP events between 2006 and 2014 where the Fe/O ratio showed a decrease. We used data from the ACE, SOHO, and STEREO spacecraft at 4–15 MeV/nucleon. We quantified the time dependence in Fe/O, shown in Figure 1c for event #1 (2012 DOY 244–248), and 35 other ionic ratios by fitting the time profile of the ionic ratios. For each ratio a time constant B (in units day-1) describing a decay or an increase over time was derived from the fit. For Fe/O in event #1 B=-0.92 day-1.
For each ionic ratio we calculated S, the ratio of the mass-to-charge values of the two elements. When we plotted values of B for all 36 elemental ratios as a function of their S, we saw a clear monotonic dependence for heavy ions, as shown for event #1 in Figure 2. One can see that ratios with S ∼ 1, which means that the two elements have similar M/Q values, have B-values close to zero, i.e. show overall very little temporal variation during the SEP event. Ratios with large S-values, such as Fe/O and Fe/Si, decay at a higher rate than ratios with small values of S. Similar behaviour was observed in other three studied SEP events.
A discontinuity in the B vs. S dependence was observed in 3 out of 4 studied events. The data points with S>2.0 belong to ratios with hydrogen, i.e. X/H, where X stands for a heavy ion element. As of now, it is not clear what causes this discontinuity.
Modelling of SEP propagation
Decreases in Fe/O profiles have been also studied using a 3D test particle model  simulating the propagation of SEPs in the interplanetary magnetic field. In our experiment , equal number of Fe (QFe=15) and O (QO=7) SEPs were injected close to the Sun at 2RS, allowed to propagate in a unipolar Parker spiral magnetic field , and counted at 1 AU from the Sun.
The particle flux time profiles are shown in the top row of Figure 3 as a function of longitudinal separation of the source region, 0,10,20 and 30 degrees west of the observer. The noted locations of observers relative to the injection region are at the time of the injection. The calculated Fe/O ratio values are shown in the bottom row of Figure 3.
We observed that energetic particles propagated parallel along the field lines on which they were injected as well as perpendicular to the magnetic field, mainly due to gradient and curvature drifts. The drifts that contributed to the observed intensity time profiles depend on the M/Q value of an ion, therefore, the time profiles for O and Fe are different.
Initially, for an observer directly connected to the injection region at [0,0] (left panels in Figure 3), Fe and O ions were detected at the observer at nearly equal rate (Fe/O ratio value is 1). After approximately 10 hours, the Fe intensity becomes higher than that of O (Fe/O increases), because Fe can propagate across the mean magnetic field towards the observer more efficiently than O, due to the drift.
Early in the event, at locations other than [0,0], there were more Fe than O ions detected at 1 AU. Thus, the Fe/O ratio values showed decreases at the beginning of the events, similar to those in the observed data. The increase in Fe/O later in the events is due to the fact that O occupies a narrower longitudinal extent than Fe, therefore O leaves the 1 AU sphere and decays earlier than Fe.
From this combination of observations and modelling of SEPs at 1 AU we can conclude that:
- Decreases observed in Fe/O are a common feature in SEP events;
- Time-dependent behaviour is also observed in other ionic ratios, and scales with S, the ratio of the mass-to-charge values;
- Significant perpendicular transport is observed in simulations as a result of drifts, which are M/Q-dependent;
- Fe/O decreases can be qualitatively explained by drifts.
A discontinuity in the B vs. S dependence was observed in 3 out of 4 studied events in . The data points with S>2.0 belong to ratios with hydrogen, i.e. X/H, where X stands for a heavy ion element. As of now, it is not clear what causes this discontinuity.
We are keenly awaiting the launch of the Solar Orbiter carrying the EPD particle telescope, which will measure energetic particles close to the Sun, and might potentially disentangle contributions from acceleration and transport to the observed intensity profiles.
-  Scholer, M., Hovestadt, D., Klecker, B., et al. 1978, JGR 83, 3349
-  Luhn, A., Hovestadt, D., Klecker, B., et al. 1985, 19th ICRC, vol. 4, 241
-  Tylka, A.J., Reames, D.V. & Ng, C.K. 1999, GRL 26, 2141
-  Mason, G.M., Desai, M.I., Cohen, C.M.S., et al. 2006, ApJL 647, L65
-  Mason, G.M., Li, G., Cohen, C.M.S., et al. 2012, ApJ 761, 104
-  Tylka, A.J., Malandraki, O.E., Dorrian, G., et al. 2013, SolPhys 285, 251
-  Zelina, P., Dalla, S., Cohen, C.M.S., et al. 2017, ApJ 835, 71
-  Marsh, M.S., Dalla, S., Kelly, J., et al. 2013, ApJ 774, 4
-  Dalla, S., Marsh, M.S., Zelina, P., et al. 2017, A&A 598, A73
-  Parker, E.N. 1958, ApJ 128, 664