Gelu M. Nita

Statistical Study of Two Years of Solar Flare Radio Spectra Obtained with the Owens Valley Solar Array

We present results of analysis of 412 flares during 2001-2002 as detected by the Owens Valley Solar Array (OVSA). This is an in-depth study to investigate some results suggested by a previous study of solar bursts (Nita et al. 2002), which was limited to the peak time of the bursts at a few frequency bands. The new study includes the temporal dependence, at 4 s time resolution, of parameters measured at 40 frequencies in the range 1-18 GHz. We investigate distributions of burst parameters such as maximum flux density in the spectra, peak frequency, spectral slopes below and above the peak frequency (optically thick and thin slopes, respectively), and burst durations. We classify the microwave bursts according to their spectral properties and provide tables of averaged spectral parameters for each spectral type and for different frequency and intensity ranges.

The Peak Flux Distribution of Solar Radio Bursts

We have investigated the peak flux distribution of 40 years of solar radio burst data as a function of frequency and time over a wide range of frequencies. The bursts were reported by observing stations around the world during 1960-1999, as compiled by the National Geophysical Data Center (NGDC) of the National Oceanic and Atmospheric Administration (NOAA). This period covers three full and two partial solar cycles. We have analyzed the data set to find correction factors for missed events, and find evidence that nearly half of the events were missed by the worldwide network. We obtain power-law fits to the differential (density) (dN/dS in events sfu-1) and cumulative [N(> S) in events] distributions as a function of frequency, time, and phase of the solar cycle. The typical power-law index, ~-1.8, is similar to that found in many hard X-ray studies. The average waiting time between bursts with flux density exceeding 1000 sfu was found to be 6 days at solar maximum, and 33 days at solar minimum. Taking account of missed events, the expected waiting time decreases to 3.5 and 18.5 days, respectively. Bursts of this flux level can cause problems with wireless communication systems. We present tables of fit parameters that can be used to find burst occurrence rates in a number of frequency ranges. We find no significant variation of power-law index from one solar cycle to the next, or with phase of the solar cycle, but we do find significant changes of power-law index with frequency.

Radio frequency interference excision using spectral-domain statistics

A radio frequency interference (RFI) excision algorithm based on spectral kurtosis, a spectral variant of time‐domain kurtosis, is proposed and implemented in software. The algorithm works by providing a robust estimator for Gaussian noise that, when violated, indicates the presence of non‐Gaussian RFI. A theoretical formalism is used that unifies the well‐known time‐domain kurtosis estimator with past work related to spectral kurtosis, and leads naturally to a single expression encompassing both. The algorithm accumulates the first two powers of M power spectral density (PSD) estimates, obtained via Fourier transform, to form a spectral kurtosis (SK) estimator whose expected statistical variance is used to define an RFI detection threshold. The performance of the algorithm is theoretically evaluated for different time‐domain RFI characteristics and signal‐to‐noise ratios η. The theoretical performance of the algorithm for intermittent RFI (RFI present in R out of M PSD estimates) is evaluated and shown to depend greatly on the duty cycle, d = R/M. The algorithm is most effective for d = 1/(4 + η), but cannot distinguish RFI from Gaussian noise at any η when d = 0.5. The expected efficiency and robustness of the algorithm are tested using data from the newly designed FASR Subsystem Testbed radio interferometer operating at the Owens Valley Solar Array. The ability of the algorithm to discriminate RFI against the temporally and spectrally complex radio emission produced during solar radio bursts is demonstrated.

Three-dimensional Radio and X-Ray Modeling and Data Analysis Software: Revealing Flare Complexity

Many problems in solar physics require analysis of imaging data obtained in multiple wavelength domains with differing spatial resolution in a framework supplied by advanced three-dimensional (3D) physical models. To facilitate this goal, we have undertaken a major enhancement of our IDL-based simulation tools developed earlier for modeling microwave and X-ray emission. The enhanced software architecture allows the user to (1) import photospheric magnetic field maps and perform magnetic field extrapolations to generate 3D magnetic field models; (2) investigate the magnetic topology by interactively creating field lines and associated flux tubes; (3) populate the flux tubes with user-defined nonuniform thermal plasma and anisotropic, nonuniform, nonthermal electron distributions; (4) investigate the spatial and spectral properties of radio and X-ray emission calculated from the model; and (5) compare the model-derived images and spectra with observational data. The package integrates shared-object libraries containing fast gyrosynchrotron emission codes, IDL-based soft and hard X-ray codes, and potential and linear force-free field extrapolation routines. The package accepts user-defined radiation and magnetic field extrapolation plug-ins. We use this tool to analyze a relatively simple single-loop flare and use the model to constrain the magnetic 3D structure and spatial distribution of the fast electrons inside this loop. We iteratively compute multi-frequency microwave and multi-energy X-ray images from realistic magnetic flux tubes obtained from pre-flare extrapolations, and compare them with imaging data obtained by SDO, NoRH, and RHESSI. We use this event to illustrate the tools use for the general interpretation of solar flares to address disparate problems in solar physics.

Decimetric Spike Bursts versus Microwave Continuum

We analyze properties of decimetric spike bursts occurring simultaneously with microwave gyrosynchrotron continuum bursts. We found that all of the accompanying microwave bursts were highly polarized in the optically thin range. The sense of polarization of the spike clusters is typically the same as that of the optically thin gyrosynchrotron emission, implying preferential extraordinary wave-mode spike polarization. Optically thick spectral indices of the continuum in spike-producing events were not observed to be larger than 2.5, suggesting low or absent Razin suppression. This implies that the plasma frequency-to-gyrofrequency ratio is systematically lower in the spike-producing bursts than in other bursts. The spike cluster flux density is found to be tightly correlated with the high-frequency spectral index of the microwave continuum for each event, while the flux-to-flux correlation may not be present. We discovered strong evidence that the trapped fast electrons producing the microwave gyrosynchrotron continuum have an anisotropic pitch-angle distribution of the loss cone type in the spike-producing bursts. The spike clusters are mainly generated when the trapped electrons have the hardest and the most anisotropic distributions. The new properties are discussed against the currently available ideas about emission processes and models for spike generation. We conclude that the findings strongly support the electron cyclotron maser mechanism of spike emission, with characteristics agreeing with expectations from the local-trap model.

Hard X-Ray and Microwave Observations of Microflares

In this paper, we study solar microflares using the coordinated hard X-ray and microwave observations obtained by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) during its open-shutter operation mode and the Owens Valley Solar Array (OVSA). The events in our study are selected in the energy range of 12-25 keV and are relatively large microflares with an average GOES soft X-ray incremental flux at the B2.0 level. A total of 760 microflares are identified from the RHESSI burst catalog. Of the 200 microflares that fall into the OVSA observing window, about 40% are detected in microwaves. Using these hundreds of events as samples, we study the event distribution with respect to the flux, the solar activity, and active regions, in comparison with flares of larger scales. Nonthermal properties of microflares are investigated through spectral analysis of X-rays and microwaves. (1) We find that the event frequency distribution with respect to the RHESSI peak count rates at 12-25 keV can be accurately described with a power-law function down to 8 counts s-1, the power-law index being 1.75 ± 0.03, consistent with previous studies. (2) Similar to large flares, the occurrence rate of microflares is correlated with solar activity. The studied samples of microflares are mostly produced by active regions, as suggested by the large percentage of events detected by OVSA, which observes target active regions. However, all active regions do not have equal productivity, and certain active regions are a lot more productive than other regions. (3) While some large and complex active regions are predominantly productive in both very weak and strong events, we also find an active region that produces many microflares and C-class events but does not produce powerful events. (4) Analysis of energy-dependent time profiles suggests that there is a pronounced temporal correlation between the time derivative of soft X-rays and 14-20 keV hard X-rays, i.e., the Neupert effect, in about one-half the studied events. (5) Albeit small, many microflares exhibit hard X-ray emission at over 10 keV and microwave emission at around 10 GHz. Spectral analysis in these two wavelengths corroborates the nonthermal nature of these emissions. (6) In a limited number of samples, the RHESSI spectral fitting yields a photon spectral index of 4.5-7, and microwave spectral analysis on the same events shows that the power-law index of the electron spectrum is in the range of 2-5. The discrepancy in the electron spectrum index derived from hard X-rays and microwaves is substantially greater than previously reported in big flares, hinting at the existence of high-energy, microwave-emitting electrons that have a much hardened spectrum compared with electrons emitting hard X-rays.

Statistics of the Spectral Kurtosis Estimator

Spectral kurtosis (SK) is a statistical approach for detecting and removing radio-frequency interference (RFI) in radio astronomy data. In this article, the statistical properties of the SK estimator are investigated and all moments of its probability density function are analytically determined. These moments provide a means to determine the tail probabilities of the estimator that are essential to defining the thresholds for RFI discrimination. It is shown that, for a number of accumulated spectra M≥24, the first SK standard moments satisfy the conditions required by a Pearson type IV probability density function (pdf), which is shown to accurately reproduce the observed distributions. The cumulative function (CF) of the Pearson type IV is then found, in both analytical and numerical forms, suitable for accurate estimation of the tail probabilities of the SK estimator. This same framework is also shown to be applicable to the related time-domain kurtosis (TDK) estimator, whose pdf corresponds to Pearson type IV when the number of time-domain samples is M≥46. The pdf and CF also are determined for this case.

A COLD, TENUOUS SOLAR FLARE: ACCELERATION WITHOUT HEATING

We report the observation of an unusual cold, tenuous solar flare, which reveals itself via numerous and prominent non-thermal manifestations, while lacking any noticeable thermal emission signature. RHESSI hard X-rays and 0.1-18 GHz radio data from OVSA and Phoenix-2 show copious electron acceleration (1035 electrons s-1 above 10 keV) typical for GOES M-class flares with electrons energies up to 100 keV, but GOES temperatures not exceeding 6.1 MK. The imaging, temporal, and spectral characteristics of the flare have led us to a firm conclusion that the bulk of the microwave continuum emission from this flare was produced directly in the acceleration region. The implications of this finding for the flaring energy release and particle acceleration are discussed.

Three-dimensional Simulations of Gyrosynchrotron Emission from Mildly Anisotropic Nonuniform Electron Distributions in Symmetric Magnetic Loops

Microwave emission of solar flares is formed primarily by incoherent gyrosynchrotron radiation generated by accelerated electrons in coronal magnetic loops. The resulting emission depends on many factors, including pitch-angle distribution of the emitting electrons and the source geometry. In this work, we perform systematic simulations of solar microwave emission using recently developed tools (GS Simulator and fast gyrosynchrotron codes) capable of simulating maps of radio brightness and polarization as well as spatially resolved emission spectra. A three-dimensional model of a symmetric dipole magnetic loop is used. We compare the emission from isotropic and anisotropic (of loss-cone type) electron distributions. We also investigate effects caused by inhomogeneous distribution of the emitting particles along the loop. It is found that the effect of the adopted moderate electron anisotropy is the most pronounced near the footpoints and it also depends strongly on the loop orientation. Concentration of the emitting particles at the looptop results in a corresponding spatial shift of the radio brightness peak, thus reducing effects of the anisotropy. The high-frequency ( 50 GHz) emission spectral index is specified mainly by the energy spectrum of the emitting electrons; however, at intermediate frequencies (around 10-20 GHz), the spectrum shape is strongly dependent on the electron anisotropy, spatial distribution, and magnetic field nonuniformity. The implications of the obtained results for the diagnostics of the energetic electrons in solar flares are discussed.

A Wideband Spectrometer with RFI Detection

We report on the design and construction of a wideband spectrometer of 500 MHz instantaneous bandwidth that includes automatic radio frequency interference (RFI) detection. The implementation is based on hardware developed at the Center for Astronomical Signal Processing and Electronics Research (CASPER). The unique aspect of the spectrometer is that it accumulates both power and power-squared, which are then used to develop a spectral kurtosis (SK) estimator. The SK estimator statistics are used for real-time detection and excision of certain types of RFI embedded in the received signal. We report on the use of this spectrometer in the Korean Solar Radio Burst Locator (KSRBL). This instrument utilizes four of these 500 MHz bandwidth SK spectrometers in parallel, to achieve a 2 GHz instantaneous bandwidth that is time multiplexed over the entire 0.24-18 GHz radio frequency range, to study solar bursts. The performance of the spectrometers for excising RFI over this range is presented. It is found that the algorithm is especially useful for excising highly intermittent RFI but is less successful for RFI due to digital signals. A method we call multiscale SK is presented that addresses the known blindness of Kurtosis-based estimators to 50% duty-cycle RFI. The SK algorithm can also be applied to spectral channels prior to correlation to remove unwanted RFI from interferometer data.