Many problems in the experimental estimation of parameters for models can be solved through use of the likelihood ratio test. Applications of the likelihood ratio, with particular attention to photon counting experiments, are discussed. The procedures presented solve a greater range of problems than those currently in use, yet are no more difficult to apply. The procedures are proved analytically, and examples from current problems in astronomy are discussed.

Parameter estimation in astronomy through application of the likelihood ratio. [satellite data analysis techniques

Data Reduction And Error Analysis For The Physical Sciences

We present an overview of solar flares and associated phenomena, drawing upon a wide range of observational data primarily from the RHESSI era Following an introductory discussion and overview of the status of observational capabilities, the article is split into topical sections which deal with different areas of flare phenomena (footpoints and ribbons, coronal sources, relationship to coronal mass ejections) and their interconnections We also discuss flare soft X-ray spectroscopy and the energetics of the process The emphasis is to describe the observations from multiple points of view, while bearing in mind the models that link them to each other and to theory The present theoretical and observational understanding of solar flares is far from complete, so we conclude with a brief discussion of models, and a list of missing but important observations

An Observational Overview of Solar Flares

We present version 8 of the CHIANTI database. This version includes a large amount of new data and ions, which represent a significant improvement in the soft X-ray, extreme UV (EUV) and UV spectral regions, which several space missions currently cover. New data for neutrals and low charge states are also added. The data are assessed, but to improve the modelling of low-temperature plasma the effective collision strengths for most of the new datasets are not spline-fitted as previously, but are retained as calculated. This required a change of the format of the CHIANTI electron excitation files. The format of the energy files has also been changed. Excitation rates between all the levels are retained for most of the new datasets, so the data can in principle be used to model high-density plasma. In addition, the method for computing the differential emission measure used in the CHIANTI software has been changed.

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CHIANTI – An atomic database for emission lines. Version 8

Solar flares are observed at all wavelengths from decameter radio waves to gamma-rays beyond 1 GeV. This review focuses on recent observations in EUV, soft and hard X-rays, white light, and radio waves. Space missions such as RHESSI, Yohkoh, TRACE, SOHO, and more recently Hinode and SDO have enlarged widely the observational base. They have revealed a number of surprises: Coronal sources appear before the hard X-ray emission in chromospheric footpoints, major flare acceleration sites appear to be independent of coronal mass ejections, electrons, and ions may be accelerated at different sites, there are at least 3 different magnetic topologies, and basic characteristics vary from small to large flares. Recent progress also includes improved insights into the flare energy partition, on the location(s) of energy release, tests of energy release scenarios and particle acceleration. The interplay of observations with theory is important to deduce the geometry and to disentangle the various processes involved. There is increasing evidence supporting magnetic reconnection as the basic cause. While this process has become generally accepted as the trigger, it is still controversial how it converts a considerable fraction of the energy into non-thermal particles. Flare-like processes may be responsible for large-scale restructuring of the magnetic field in the corona as well as for its heating. Large flares influence interplanetary space and substantially affect the Earth’s ionosphere. Flare scenarios have slowly converged over the past decades, but every new observation still reveals major unexpected results, demonstrating that solar flares, after 150 years since their discovery, remain a complex problem of astrophysics including major unsolved questions.

Flare Observations

Aims. To demonstrate the capabilities of regularized inversion to recover differential emission measures (DEMs) from multiwavelength observations provided by telescopes such as Hinode and SDO. Methods. We develop and apply an enhanced regularization algorithm, used in RHESSI X-ray spectral analysis, to constrain the ill-posed inverse problem that is determining the DEM from solar observations. We demonstrate this computationally fast technique applied to a range of DEM models simulating broadband imaging data from SDO/AIA and high resolution line spectra from Hinode/EIS, as well as actual active region observations with Hinode/EIS and XRT. As this regularization method naturally provides both vertical and horizontal (temperature resolution) error bars we are able to test the role of uncertainties in the data and response functions. Results. The regularization method is able to successfully recover the DEM from simulated data of a variety of model DEMs (single Gaussian, multiple Gaussians and CHIANTI DEM models). It is able to do this, at best, to over four orders of magnitude in DEM space but typically over two orders of magnitude from peak emission. The combination of horizontal and vertical error bars and the regularized solution matrix allows us to easily determine the accuracy and robustness of the regularized DEM. We find that the typical range for the horizontal errors is ΔlogT ≈ 0.1−0.5 and this is dependent on the observed signal to noise, uncertainty in the response functions as well as the source model and temperature. With Hinode/EIS an uncertainty of 20% greatly broadens the regularized DEMs for both Gaussian and CHIANTI models although information about the underlying DEMs is still recoverable. When applied to real active region observations with Hinode/EIS and XRT the regularization method is able to recover a DEM similar to that found via a MCMC method but in considerably less computational time. Conclusions. Regularized inversion quickly determines the DEM from solar observations and provides reliable error estimates (both horizontal and vertical) which allows the temperature spread of coronal plasma to be robustly quantified.

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Differential Emission Measures from the Regularized Inversion of Hinode and SDO data

We present the first statistical analysis of the thermal and nonthermal X-ray emission of all 25,705 microflares (RHESSI) observed between 2002 March and 2007 March. These events were found by searching the 6-12 keV energy range (see Paper I) and are small active region flares, from low (GOES) C class to below A class. Each microflare is automatically analyzed at the peak time of the 6-12 keV emission: the thermal source size is found by forward-fitting the complex visibilities for 4-8 keV, and the spectral parameters (temperature, emission measure, power-law index) are found by forward-fitting a thermal plus nonthermal model. The resulting wealth of information we determine about the events allows a range of the thermal and nonthermal properties to be investigated. In particular, we find that there is no correlation between the thermal loop size and the flare magnitude, indicating that microflares are not necessarily spatially small. We present the first thermal energy distribution of RHESSI flares and compare it to previous thermal energy distributions of transient events. We also present the first nonthermal power distribution of RHESSI flares and find that a few microflares have unexpectedly large nonthermal powers up to 1028 erg s−1. The total microflare nonthermal energy, however, is still small compared to that of large flares as it occurs for shorter durations. These large energies and difficulties in analyzing the steep nonthermal spectra suggest that a sharp broken power law and thick-target bremsstrahlung model may not be appropriate for microflares.

https://iopscience.iop.org/article/10.1086/529012/pdf

RHESSI Microflare Statistics. II. X-Ray Imaging, Spectroscopy, and Energy Distributions

We present X-ray imaging and spectral analysis of all microflares the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observed between March 2002 and March 2007, a total of 25,705 events. These microflares are small flares, from low GOES C Class to below A Class (background subtracted) and are associated with active regions. They were found by searching the 6-12 keV energy range during periods when the full sensitivity of RHESSI's detectors was available (see paper I). Each microflare is automatically analyzed at the peak time of the 6-12 keV emission: the thermal source size is found by forward-fitting the complex visibilities for 4-8 keV, and the spectral parameters (temperature, emission measure, power-law index) are found by forward fitting a thermal plus non-thermal model. The combination of these parameters allows us to present the first statistical analysis of the thermal and non-thermal energy at the peak times of microflares.

RHESSI Microflare Statistics II. X-ray Imaging, Spectroscopy & Energy Distributions

The fan-spine magnetic topology is believed to be responsible for many curious emission signatures in solar explosive events. A spine field line links topologically distinct flux domains, but direct observation of such structure has been rare. Here we report a unique event observed by the Solar Dynamic Observatory (SDO) where a set of hot coronal loops (over 10 MK) that developed during the rising phase of a flare connected to a quasi-circular ribbon at one end and a remote brightening at the other. Magnetic field extrapolation suggests these loops are partly tracers of the evolving spine field line. The sequential brightening of the ribbon, the apparent shuffling loop motion, and the increasing volume occupied by the hot loops suggest that continuous slipping- and null-point-type reconnections were at work, energizing the loop plasma and transferring magnetic flux within and across the dome-shaped, fan quasi-separatrix layer (QSL). We argue that the initial reconnection is of the “breakout” type, which then transitioned to a more violent flare reconnection nearing the flare peak with an eruption from the fan dome. Significant magnetic field changes are expected and indeed ensued, which include a change of the horizontal photospheric field, a shift of the QSL footprint, and reduction in shear of the coronal loops. This event also features an extreme-ultraviolet (EUV) late phase, i.e. a secondary emission peak observed in warm EUV lines (about 2‐7 MK) as much as 1‐2 hours after the soft X-ray peak. We show that this peak comes from the large post-reconnection loops beside and above the compact fan dome, a direct product of eruption in such topological settings. Cooling of these “late-phase arcades” naturally explains the sequential delay of the late-phase peaks in increasingly cooler EUV lines. The long cooling time of the large arcades contributes to the long delay; additional heating may also be required. Our result demonstrates the critical nature of cross-scale magnetic coupling ‐ minor topological change in a sub-system may lead to explosions on a much larger scale. Subject headings: Sun: activity — Sun: corona — Sun: flares — Sun: surface magnetism — Sun: magnetic topology

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Hot spine loops and the nature of a late-phase solar flare

We present the first in-depth statistical survey of all X-ray microflares observed by RHESSI between 2002 March and 2007 March, a total of 25,705 events, an order of magnitude larger then previous studies. These microflares were found using a new flare-finding algorithm designed to search the 6-12 keV count rate when RHESSI's full sensitivity was available in order to find the smallest events. The peak and total count rate are automatically obtained along with count spectra at the peak and the microflare centroid position. Our microflare magnitudes are below GOES C class, on average GOES A class (background subtracted). They are found to occur only in active regions, not in the quiet Sun, and are similar to large flares. The monthly average microflaring rate is found to vary with the solar cycle and ranges from 90 to 5 flares a day during active and quiet times, respectively. Most flares are found to be impulsive (74%), with rise times shorter than decay times. The mean flare duration is ~6 minutes with a 1 minute minimum set by the flare-finding algorithm. The frequency distributions of the peak count rate in the energy bands, 3-6, 6-12, and 12-25 keV, can be represented by power-law distributions with a negative power-law index of -->1.50 ± 0.03, -->1.51 ± 0.03, and -->1.58 ± 0.02, respectively. We find that these power-law indices are constant as a function of time. The X-ray photon spectra for individual events can be approximated with a power-law spectrum [ -->dJ/d(hν) ~ (hν)−γ]. Using the ratio of photon fluxes between 10-15 and 15-20 keV, we find -->4 -1.7 ± 0.1. We estimate the total energy flux deposited in active regions by microflare-associated accelerated electrons (>10 keV) over the five years of observations to be, on average, below 1026 erg s−1.

https://iopscience.iop.org/article/10.1086/529011/pdf

Iain G. Hannah

Papers

Differential Emission Measures from the Regularized Inversion of Hinode and SDO data

RHESSI Microflare Statistics. II. X-Ray Imaging, Spectroscopy, and Energy Distributions

RHESSI Microflare Statistics II. X-ray Imaging, Spectroscopy & Energy Distributions

Hot spine loops and the nature of a late-phase solar flare

RHESSI Microflare Statistics. I. Flare-Finding and Frequency Distributions