Collisional relaxation of electrons in a warm plasma and accelerated nonthermal electron spectra in solar flares

Extending previous studies of nonthermal electron transport in solar flares which include the effects of collisional energy diffusion and thermalization of fast electrons, we present an analytic method to infer more accurate estimates of the accelerated electron spectrum in solar flares from observations of the hard X-ray spectrum. Unlike for the standard cold-target model, the spatial characteristics of the flaring region, especially the necessity to consider a finite volume of hot plasma in the source, need to be taken into account in order to correctly obtain the injected electron spectrum from the source-integrated electron flux spectrum (a quantity straightforwardly obtained from hard X-ray observations). We show that the effect of electron thermalization can be significant enough to nullify the need to introduce an {\it ad hoc} low-energy cutoff to the injected electron spectrum in order to keep the injected power in non-thermal electrons at a reasonable value. Rather the suppression of the inferred low-energy end of the injected spectrum compared to that deduced from a cold-target analysis allows the inference from hard X-ray observations of a more realistic energy in injected non-thermal electrons in solar flares.Comment: accepted for publication in Ap

On Certain Two Dimensional Integrals that Appear In Conformal Field Theory

In a first part, we generalize a theorem for an holomorphic $\times$ anti-holomorphic integrand, in the case of 2 dimensional Fourier transform. In the second part, we derive p-uple conformal integrals the integrand of which are linear combination of holomorphic times holomorphic generalized hypergeometric functions. The specific case $p=3$ is relevant to determine the triple Pomeron vertex in QCD.Comment: latex txt.tex, 3 files, 39 pages [SPhT-T00/034], submitted to Comm. Math. Phy

Observations of Reconnection Flows in a Flare on the Solar Disk

Magnetic reconnection is a well-accepted part of the theory of solar eruptive events, though the evidence is still circumstantial. Intrinsic to the reconnection picture of a solar eruptive event, particularly in the standard model for two-ribbon flares ("CSHKP" model), are an advective flow of magnetized plasma into the reconnection region, expansion of field above the reconnection region as a flux rope erupts, retraction of heated post-reconnection loops, and downflows of cooling plasma along those loops. We report on a unique set of SDO/AIA imaging and Hinode/EIS spectroscopic observations of the disk flare SOL2016-03-23T03:54 in which all four flows are present simultaneously. This includes spectroscopic evidence for a plasma upflow in association with large-scale expanding closed inflow field. The reconnection inflows are symmetric, and consistent with fast reconnection, and the post-reconnection loops show a clear cooling and deceleration as they retract. Observations of coronal reconnection flows are still rare, and most events are observed at the solar limb, obscured by complex foregrounds, making their relationship to the flare ribbons, cusp field and arcades formed in the lower atmosphere difficult to interpret. The disk location and favorable perspective of this event have removed these ambiguities giving a clear picture of the reconnection dynamics.Comment: 9 pages, 5 figures, and 1 table. Accepted for publication in ApJ

The development of lower-atmosphere turbulence early in a solar flare

We present the first observational study of the onset and evolution of solar flare turbulence in the lower solar atmosphere on an unprecedented time scale of 1.7 s using the Interface Region Imaging Spectrograph observing plasma at a temperature of 80,000 K. At this time resolution, nonthermal spectral line broadening, indicating turbulent velocity fluctuations, precedes the flare onset at this temperature and is coincident with net blue-shifts. The broadening decreases as the flare brightens and then oscillates with a period of ~10 s. These observations are consistent with turbulence in the lower solar atmosphere at the flare onset, heating that region as it dissipates. This challenges the current view of energy release and transport in the standard solar flare model, suggesting that turbulence partly heats the lower atmosphere.Comment: Published in Science Advances (5th December 2018

A Large k Asymptotics of Witten's Invariant of Seifert Manifolds

We calculate a large $k$ asymptotic expansion of the exact surgery formula for Witten's $SU(2)$ invariant of Seifert manifolds. The contributions of all flat connections are identified. An agreement with the 1-loop formula is checked. A contribution of the irreducible connections appears to contain only a finite number of terms in the asymptotic series. A 2-loop correction to the contribution of the trivial connection is found to be proportional to Casson's invariant.Comment: 51 pages (Some changes are made to the Discussion section. A surgery formula for perturbative corrections to the contribution of the trivial connection is suggested.

Universality in the one-dimensional chain of phase-coupled oscillators

We apply a recently developed renormalization group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and couplings form frequency-synchronized clusters. Although the RG was originally intended for strong randomness, i.e. for distributions with long tails, we find good agreement with numerical simulations even in the regime of weak randomness. We use the RG flow to derive how the correlation length scales with the width of the coupling distribution in the limit of large coupling. This leads to the identification of a universality class of distributions with the same critical exponent $\nu$. We also find universal scaling for small coupling. Finally, we show that the RG flow is characterized by a universal approach to the unsynchronized fixed point, which provides physical insight into low-frequency clusters.Comment: 14 pages, 10 figure

Old and New Fields on Super Riemann Surfaces

The ``new fields" or ``superconformal functions" on $N=1$ super Riemann surfaces introduced recently by Rogers and Langer are shown to coincide with the Abelian differentials (plus constants), viewed as a subset of the functions on the associated $N=2$ super Riemann surface. We confirm that, as originally defined, they do not form a super vector space.Comment: 9 pages, LaTex. Published version: minor changes for clarity, two new reference