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Register a new userStatistical Signatures of Nanoflare Activity. I. Monte Carlo Simulations and Parameter-space Exploration
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Small-scale magnetic reconnection processes, in the form of nanoflares, have become increasingly hypothesized as important mechanisms for the heating of the solar atmosphere, for driving propagating disturbances along magnetic field lines in the Suns corona, and for instigating rapid jet-like bursts in the chromosphere. Unfortunately, the relatively weak signatures associated with nanoflares places them below the sensitivities of current observational instrumentation. Here, we employ Monte Carlo techniques to synthesize realistic nanoflare intensity time series from a dense grid of power-law indices and decay timescales. Employing statistical techniques, which examine the modeled intensity fluctuations with more than 10^7 discrete measurements, we show how it is possible to extract and quantify nanoflare characteristics throughout the solar atmosphere, even in the presence of significant photon noise. A comparison between the statistical parameters (derived through examination of the associated intensity fluctuation histograms) extracted from the Monte Carlo simulations and SDO/AIA 171{AA} and 94{AA} observations of active region NOAA 11366 reveals evidence for a flaring power-law index within the range of 1.82 - 1.90, combined with e-folding timescales of 385 +/- 26 s and 262 +/- 17 s for the SDO/AIA 171{AA} and 94{AA} channels, respectively. These results suggest that nanoflare activity is not the dominant heating source for the active region under investigation. This opens the door for future dedicated observational campaigns to not only unequivocally search for the presence of small-scale reconnection in solar and stellar environments, but also quantify key characteristics related to such nanoflare activity.
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Several studies have documented periodic and quasi-periodic signals from the time series of dMe flare stars and other stellar sources. Such periodic signals, observed within quiescent phases (i.e., devoid of larger-scale microflare or flare activity), range in period from $1-1000$ seconds and hence have been tentatively linked to ubiquitous $p$-mode oscillations generated in the convective layers of the star. As such, most interpretations for the observed periodicities have been framed in terms of magneto-hydrodynamic wave behavior. However, we propose that a series of continuous nanoflares, based upon a power-law distribution, can provide a similar periodic signal in the associated time series. Adapting previous statistical analyses of solar nanoflare signals, we find the first statistical evidence for stellar nanoflare signals embedded within the noise envelope of M-type stellar lightcurves. Employing data collected by the Next Generation Transit Survey (NGTS), we find evidence for stellar nanoflare activity demonstrating a flaring power-law index of $3.25 pm 0.20 $, alongside a decay timescale of $200 pm 100$ s. We also find that synthetic time series, consistent with the observations of dMe flare star lightcurves, are capable of producing quasi-periodic signals in the same frequency range as $p$-mode signals, despite being purely comprised of impulsive signatures. Phenomena traditionally considered a consequence of wave behaviour may be described by a number of high frequency but discrete nanoflare energy events. This new physical interpretation presents a novel diagnostic capability, by linking observed periodic signals to given nanoflare model conditions.
A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have no rigorous statistical meaning. Subsequently, we associate each nuclear physics quantity entering in the calculation of reaction rates with a specific probability density function, including Gaussian, lognormal and chi-squared distributions. Based on these probability density functions the total reaction rate is randomly sampled many times until the required statistical precision is achieved. This procedure results in a median (Monte Carlo) rate which agrees under certain conditions with the commonly reported recommended classical rate. In addition, we present at each temperature a low rate and a high rate, corresponding to the 0.16 and 0.84 quantiles of the cumulative reaction rate distribution. These quantities are in general different from the statistically meaningless minimum (or lower limit) and maximum (or upper limit) reaction rates which are commonly reported. Furthermore, we approximate the output reaction rate probability density function by a lognormal distribution and present, at each temperature, the lognormal parameters miu and sigma. The values of these quantities will be crucial for future Monte Carlo nucleosynthesis studies. Our new reaction rates, appropriate for bare nuclei in the laboratory, are tabulated in the second paper of this series (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this series (Paper III). In the fourth paper of this series (Paper IV) we compare our new reaction rates to previous results.
We utilize magnetohydrodynamic (MHD) simulations to develop a numerical model for GMC-GMC collisions between nearly magnetically critical clouds. The goal is to determine if, and under what circumstances, cloud collisions can cause pre-existing magnetically subcritical clumps to become supercritical and undergo gravitational collapse. We first develop and implement new photodissociation region (PDR) based heating and cooling functions that span the atomic to molecular transition, creating a multiphase ISM and allowing modeling of non-equilibrium temperature structures. Then in 2D and with ideal MHD, we explore a wide parameter space of magnetic field strength, magnetic field geometry, collision velocity, and impact parameter, and compare isolated versus colliding clouds. We find factors of ~2-3 increase in mean clump density from typical collisions, with strong dependence on collision velocity and magnetic field strength, but ultimately limited by flux-freezing in 2D geometries. For geometries enabling flow along magnetic field lines, greater degrees of collapse are seen. We discuss observational diagnostics of cloud collisions, focussing on 13CO(J=2-1), 13CO(J=3-2), and 12CO(J=8-7) integrated intensity maps and spectra, which we synthesize from our simulation outputs. We find the ratio of J=8-7 to lower-J emission is a powerful diagnostic probe of GMC collisions.
The theory of radiative transfer provides the link between the physical conditions in an astrophysical object and the observable radiation which it emits. Thus accurately modelling radiative transfer is often a necessary part of testing theoretical models by comparison with observations. We describe a new radiative transfer code which employs Monte Carlo methods for the numerical simulation of radiation transport in expanding media. We discuss the application of this code to the calculation of synthetic spectra and light curves for a Type Ia supernova explosion model and describe the sensitivity of the results to certain approximations made in the simulations.
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two exemplary applications of many. These tasks can only be performed reliably and efficiently with Monte Carlo methods, which involve good samplings of the parameter space in accordance with the relevant target distribution. We show how the standard strategies of rejection sampling, importance sampling, and Markov-chain sampling can be adapted to this context, where the samples must obey the constraints imposed by the positivity of the statistical operator. For a comparison of these sampling methods, we generate sample points in the probability space for two-qubit states probed with a tomographically incomplete measurement, and then use the sample for the calculation of the size and credibility of the recently-introduced optimal error regions [see New J. Phys. 15 (2013) 123026]. Another illustration is the computation of the fractional volume of separable two-qubit states.
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