The is a typical picture that NASA uses to illustrate a context of solar flares. particles acceleration occurred somewhere for some reason, and stream down to radiate some other places, either loop-top and foot points in this case.(We have to put all the observed radiations back into such a picture.)  Here are some specific issues that we need to address: colored orange is the most often discussed issues, the green is a rarely discsuused, the puple—never discussed-isotropy assumed.: First (indicate the left picture) we want to know how much the observed radiation properties are due to acceleration properties  (ultimate goal) and not due to any transport effect. Often talked about Transport—could be trap and precipitation, and etc. Good precipitation could meaning pitch angle diffusion and good trapping—weak diffusion or strong magnetic mirroring, etc. In some cases all the things in the left column could be related to each other while all the things in the right could be, but not always. In many cases we would not really know, for instance, how much is due to acceleration effect and how much is due to the transport effect.  So we got to make use of the microwave spectrum to help sorting out these issues.  So we tried to relate the spectral observation made at OVSA to the science listed up there. The orange stuff are usually stuff, commonly mentioned issues, The green—rarely mentioned, and the purple would be never … in my knowledge. I will mention it for the first time in this workshop.

As you know the OVSA is a solar-dedicated but with small number of baselines, so not as powerful in imaging as NoRH or other telescopes, but has unique spectral ability in the u.s., and these are the events we have recently studied and the main sciences addressed.

Let me go on this event in some detail and the other ones I’ll go through more quickly.  It was a strong limb flare, and observed as a part of the Max Millennium campaign. The OVSA was run at a high time cadence mode, 1 s resolution, instead at a reduced number of frequencies. The red/orange colors are microwave fluxes as a function of time & the white one is HXR from BATSE. What interested me most was the simple exponential decay curves similar at all frequencies. Note that flux is in log-scale while the time-axis is linear. Looked like a sort of uniformly varying decay time with frequency, which could be uniform variation in electron energy distribution. The HXR in this event was short-lived, which could mean that the injection was short this much (otherwise why HXR is short). Microwaves are OK to be longer if they are trapped in the corona as usual. So the usual injection and trap model would be appropriate, and looking for the morphology.

The red background here is Yohkoh SXT AlMg, and the blue contours are hard X ray images at four diff. Energy channels. , increasing from L to H to the right. The dashed lines here are the solar limb and the active region was in the south-eastern part. With these HXR alone it looks like there is only a small loop, and this is the loop top & foot-points depending on energy. But we still suspect that SXT (on a large FOV)’s extended structure might be representing a large loop.

So we check the microwave source hoping to see a somewhat different result. In this case we are not doing full imaging, and use a more fundamental relationship between the observed phase of the visibility and the source position on the sky. At the time of flare, the OVSA array looked up the sun in a way that the baseline of this combination has spatial resolution along the red line shown here, while the N-S baseline combination has direction along the blue line.  The top panel here shows that a sudden large change occurred in the phase at the time of flare, later comes back to the original position to some extent. Thus indicates a large loop source, a source centered high above the surface/limb by 80 arcsec. So we premise a large loop acting as a trap. Together with the previous HXR images we interpret that the whole system is like a trap-plus-precipitation, like the next famous figure by Aschwanden.

Probably Aschwanden, Kosugi,  Hanaoka, Nishio, & Melrose (1999).  More specifically, the radio comes from the trap and the HXR from the precipitating—these are related to long and short temporal behaviors too. It itself shows two loops  interacting. But the small one is really small compared with the larger one.  Treat them as a point source function, and one large trap.

Having that picture in mind, we look at the light-curves again. If we really consider there is one good trap region and electrons are injected in to the region, and if the HXR represents the injection and microwaves represent the trapped ptls, then a typical relationship in time we normally expect is like (a) where red is HXR, microwave = green: the peak of the radio would have to be delayed and  smooth and gradual all the way. But in the observation it was not, there were both gradual component and impulsive peaks superimposed on the slow envelope and the peaks are simultaneous in our time resolution. So the next picture is the idea we finally brought up with. For some reason there was bifurcation into two component. Namely there are two components: the tail represents the trapped population, but instantly passing-by component (precipitation) and they are never trapped and therefore could look like HXRs. Also they should somehow stand out by themselves. The red-colored part is that. So we wanted to address the idea more quantitatively, and the problem becomes injection vs. trapping, but mixed together with two component-direct precipitation and remaining in the trap, subject to common injection. *we want to address this problem more quantitatively. Three components: 1. Injection as rep. By HXR and 2. Trapped, 3. Passing-by component.

In the analysis: First we had to determine the injection function, which usually is taken as an unknown and found after extensive simulation. But in this case we postulated that it represents injection (based on the time behaviors). The Yohkoh HXT count rate is in this form. We assume a single power law for the photon spectrum, and simulate the observed count rate using the response function P_I to derive the A and gamma factors. Once we get these A and gamma factors we can, using Brown’s formula, reconstruct the electron spectrum at any time and energy (of course under a single power law assumption). As a  result we found the injection spectrum in a time-dependent form not only amplitude but also the spectral slope. The spectral slope change itself could make the inversion problem difficult to solve.

As shown by Melrose & Brown in 1976, the trapped electrons can be expressed as a convolution of the injection function with some kernel representing the trapp processes. We could find a simple analytic solution for the trapped electrons under an assumption that the loss mechanism in the corona is only  the escape-like term. Use the solution to calculate microwave emissivity, and applied here to fit the gradual part. The left frame: the observed flux at three fre vs time. The smooth curves are the model fit to the observed. The rest, spiky part are regarded as due to primary precipitation not trapped and therefore leave them unfit.  Used only the optically thin flux, I.e. the emissivity. Flux at different frequency changes and this depends on the energy-dependent term in the escape term. We found \nu\propto velocity is good enough. Meaning that bounce frequency,i.e.,strong diffusion case.One may think if strong diffusion the trap may loose particles so rapidly, but it was not, because of the small loss cone angle, only the energy dependence tells that it is strong diffusion. Matching this relavtive fluxes at different frequencies is equilvalent to matching the spectral index. The right panel shows the spectral index a good coincidence, mainly determined by the energy dependence of the trap kernel, the strong diffusion in this case. \propto \beta The spectral slope in the right = mainly beta dependence. The proportional constant is related to the loop property as: \nu_0=0.5*alpha0^2(c/L). Alpha0 is a small value, meaning a very good trap in other words.

The electrons pass through all part of the loop will be timely-correlated with the HXR assumed to be injection function. Qualitatively that’s it. However, for quantitative comparison the is one complication.  Now we assumed inhomogeity and so radiation at different field strength varies and for flux we need the cross section variation along the loop, with B in other words.  Therefore needed to consider magnetic field variation (three different cases) . Qualitatively The up-left panel-depening on where they are the radiation efficiency differs although same electrons. The bottom right, and also in some part it is optically thick and in some part optically thin. Thus a full expression is used. The right column show final model fit to the observation: different curves -> different magnetic field tube models how the tube cross section varies with B.

To summarize we have obtained some new results as listed here. In many cases we talked about Coulomb collisions and weak diffusion. But using the relative spectral variation fo the flux, we figured that it should have opposite energy dependence than Coulomb collisions, the decay rate is explicable if we use a very small loss cone angle, i.e. highly inhomogeneous loop. And so on. This tells that some new aspect of the problem could be revealed when microwave spectral and HXR spectral are analyzed in detail together. So we want to close the argument. By far the model was self-consistent. But except one parameter. We found that the gradual population is larger than that of impulsive population. This is not possible under the traditional up-down picture. But quite possible under the opposite case, I.e. down-up picture The small loop has both thick target and the accelerator. This is quite a surprising result in HXR studies, but relatively common in optical observations, nowadays. The number in the thick target was higher than the trapped one—suggests alternative scenario, namely down-up scenario. The right panel: SXT large loop, small loop retain the thick target bremsstrahlung, Radio was just sensitive to this trapped electrons. HXR—again one example to demonstrate the complementary nature. and This was one event in which the spectral and spatial informations are combined to address the electron transport problem and time-dependent injection.

The next one is a counter example to the previous one. The one was strong diffusion case, here is an example which we identified with a weak diffusion case. First of all the morphology of radio w,r,t, the magnetic field was asymmetric, Suggesting a case of weak diffusion. Note the right foot-point has strong magnetic field than the other.  Second, the spectral hardening in the decay phase. If acceleration dominated, usually soft-hard-soft. That it it keeps hardening throughout the decay could mean that the electron dynamics were modulated by Coulomb collisions, as one possibility. This could be a weak pitch angle diffusion and in contrast with the previous example, which was found to be a strong diffusion.

So what did we learn from these two examples? First impulsive/gradual nature? Not sure whether impulsive or gradual categies, but in these cases we inferred injection time and trapping time. So how about taking the ratio between trap vs. inj><2 as a criterion. Concerning the injection properties: as usual there are of cases of conveneint isotropic pitch angle distribution and time-constant energy. But there seems to be other cases like anisotropic injection momentum distribution or time-dependent spectrum are indeed needed in order to explain the spectral observations. And this result may be interesting for study of acceleration mechanisms. If you ask how was the pitch angle diffusion going?, I can simply answer it was weak diffusion in one case and strong in another. But in both cases trapping was rather good, but because of diffusion efficiency but because of either density or magnetic field inhomogeneity. For precipitation-usually talked about is secondary-escape from once-trapped population.  What is the role of magnetic fields in the flare? At least they guide the electrons, charged particles.   This is known and may be called passive roles. What’s the active role in the flare process? I mean, magnetic energy release via reconnection. This is a difficult question because it is in the regime of MHD, not plasma physics that helps radio and electron dynamics. But we try some

This was not a particulary strong flare, but under special observation in H-alpha. The BBSO (Haimin) made a particulary high resolution H-alpha observations. Originally meant to study the elementary bursts. The elementary bursts is like a quantum of the energy release process. How small & how fast are unknown, therefore  requires as fastest and most detail images as possible.  We then adapted the data to other purpose, as typical in solar study: I.e. test the reconnection theory (usually known as Kopp&Pneuman model for erupting filament) and particle acceleration in DC electric fields. (a) H-alpha and radio contours, (b) magnetogram, © HXR/yohkoh., Conclusion. In favor of the DC field acceleration model. (The electric field is strenght was kind of too high, compared with previous speculation—just a result of increased time/spatial resolution)

The march 22 flare is one of the strongest flare in this solar maximum. This move was made by me and used in a public talk in Science Park in NY-NJ. The talk was for warning for the how harmful a solar flare could be. In science,  what this event interested me was that the time profile was surprisingly short. Why it should not? Well, A thumb rule is that  a large flare has everything: large-area, complex magnetic fields, and long-duration of radiation. I related this event to a case of spontaneous reconnection, based on the magnetic field configuration, EUV, radio Ha images. Thus it becomes a paper that addresses the MHD aspect of the solar flare.

The first two cases are intensively analyzed with particular emphasis in the microwave spectral variation, and the results address the usual stuff. The things in green boxes are unusual stuff in this area, radio-physics, namely how we can address or just relate the radio observations to the theoretical ideas based on the recent MHD field. In some case we could say something like these, but in many cases it was not so obvious.