Intermittent and Scale-Invariant Intensity Fluctuations in Hot Coronal Loops

ABSTRACT BODY: To resolve outstanding questions on heating of coronal loops, we study intensity fluctuations in inter-moss portions of active region core loops as observed with AIA/SDO. The 94Å fluctuations (Figure 1) have structure on timescales shorter than radiative and conductive cooling times. Each of several strong 94Å brightenings is followed after ~8 min by a broader peak in the cooler 335Å emission. This indicates that we see emission from the hot component of the 94Å contribution function. No hotter contributions appear, and we conclude that the 94Å intensity can be used as a proxy for energy injection into the loop plasma. The probability density function of the observed 94Å intensity has 'heavy tails' that approach zero more slowly than the tails of a normal distribution. Hence, large fluctuations dominate the behavior of the system. The resulting 'intermittence' is associated with power-law or exponential scaling of the related variables, and these in turn are associated with turbulent phenomena. The intensity plots in Figure 1 resemble multifractal time series, which are common to various forms of turbulent energy dissipation. In these systems a single fractal dimension is insufficient to describe the dynamics and instead there is a spectrum of fractal dimensions that quantify the self-similar properties. Figure 2 shows the multifractal spectrum from our data to be invariant over timescales from 24 s to 6.4 min. We compare these results to outputs from theoretical energy dissipation models based on MHD turbulence, and in some cases we find substantial agreement, in terms of intermittence, multifractality and scale invariance. Figure 1. Time traces of 94A intensity in the inter-moss portions of four AR core loops. Figure 2. Multifractal spectra showing timescale invariance. The four cases of Figure 1 are included.

Search for Rapid Changes in the Visible-Light Corona during the 21 June 2001 Total Solar Eclipse

Some 8000 images obtained with the Solar Eclipse Coronal Imaging System (SECIS) fast-frame CCD camera instrument located at Lusaka, Zambia, during the total eclipse of 21 June 2001 have been analysed to search for short-period oscillations in intensity that could be a signature of solar coronal heating mechanisms by MHD wave dissipation. Images were taken in white-light and Fe xiv green-line (5303 ) channels over 205 seconds (frame rate 39 s(-1)), approximately the length of eclipse totality at this location, with a pixel size of four arcseconds square. The data are of considerably better quality than those that we obtained during the 11 August 1999 total eclipse (Rudawy et al.: Astron. Astrophys. 416, 1179, 2004), in that the images are much better exposed and enhancements in the drive system of the heliostat used gave a much improved image stability. Classical Fourier and wavelet techniques have been used to analyse the emission at 29 518 locations, of which 10 714 had emission at reasonably high levels, searching for periodic fluctuations with periods in the range 0.1 -aEuro parts per thousand 17 seconds (frequencies 0.06 -aEuro parts per thousand 10 Hz). While a number of possible periodicities were apparent in the wavelet analysis, none of the spatially and time-limited periodicities in the local brightness curves was found to be physically important. This implies that the pervasive Alfv,n wave-like phenomena (Tomczyk et al.: Science 317, 1192, 2007) using polarimetric observations with the Coronal Multi-Channel Polarimeter (CoMP) instrument do not give rise to significant oscillatory intensity fluctuations.

Propagating Wave Phenomena Detected in Observations and Simulations of the Lower Solar Atmosphere

We present high-cadence observations and simulations of the solar photosphere, obtained using the Rapid Oscillations in the Solar Atmosphere imaging system and the MuRAM magnetohydrodynamic (MHD) code, respectively. Each data set demonstrates a wealth of magnetoacoustic oscillatory behavior, visible as periodic intensity fluctuations with periods in the range 110–600 s. Almost no propagating waves with periods less than 140 s and 110 s are detected in the observational and simulated data sets, respectively. High concentrations of power are found in highly magnetized regions, such as magnetic bright points and intergranular lanes. Radiative diagnostics of the photospheric simulations replicate our observational results, confirming that the current breed of MHD simulations are able to accurately represent the lower solar atmosphere. All observed oscillations are generated as a result of naturally occurring magnetoconvective processes, with no specific input driver present. Using contribution functions extracted from our numerical simulations, we estimate minimum G-band and 4170 Å continuum formation heights of 100 km and 25 km, respectively. Detected magnetoacoustic oscillations exhibit a dominant phase delay of −8◦ between the G-band and 4170 Å continuum observations, suggesting the presence of upwardly propagating waves.More than 73% of MBPs (73% from observations and 96% from simulations) display upwardly propagating wave phenomena, suggesting the abundant nature of oscillatory behavior detected higher in the solar atmosphere may be traced back to magnetoconvective processes occurring in the upper layers of the Sun’s convection zone.

Nanoflare Activity In the Solar Chromosphere

We use ground-based images of high spatial and temporal resolution to search for evidence of nanoflare activity in the solar chromosphere. Through close examination of more than 1 x 10(9) pixels in the immediate vicinity of an active region, we show that the distributions of observed intensity fluctuations have subtle asymmetries. A negative excess in the intensity fluctuations indicates that more pixels have fainter-than-average intensities compared with those that appear brighter than average. By employing Monte Carlo simulations, we reveal how the negative excess can be explained by a series of impulsive events, coupled with exponential decays, that are fractionally below the current resolving limits of low-noise equipment on high-resolution ground-based observatories. Importantly, our Monte Carlo simulations provide clear evidence that the intensity asymmetries cannot be explained by photon-counting statistics alone. A comparison to the coronal work of Terzo et al. suggests that nanoflare activity in the chromosphere is more readily occurring, with an impulsive event occurring every similar to 360 s in a 10,000 km(2) area of the chromosphere, some 50 times more events than a comparably sized region of the corona. As a result, nanoflare activity in the chromosphere is likely to play an important role in providing heat energy to this layer of the solar atmosphere.

Evolution of Hot Loops in an Active Region Core Observed with the SDO Atmospheric Image Assembly

Evidence has accumulated of high temperature (> 4 MK) coronal emission in active region cores that corresponds to structures in equilibrium. Other studies have found evidence of evolving loops. We investigate the EUV intensity and temperature variations of short coronal loops observed in the core of NOAA Active Region 11250 on 13 July 2011. The loops, which run directly between the AR opposite polarities, are first detectable in the 94Å band of Fe XVIII, implying an effective temperature ~ 7 MK. The low temperature component of the 94 Å signal is modeled in terms of a linear superposition of the 193 Å and 171 Å signals in order to separate the hot component. After identifying the loops we have used contemporaneous HMI observations to identify the corresponding inter-moss regions, and we have investigated their time evolution in six AIA EUV channels. The results can be separated into two classes. Group 1 (94Å, 335Å, 211Å) is characterized by hotter temperatures (~2-7 MK), and Group 2 (193Å, 171Å, 131Å) by cooler temperatures (0.4 - 1.6 MK). For Group 1 the intensity peaks in the 94Å channel are followed by maxima in the 335 Å channel with a time lag of ~8 min, suggestive of a cooling pattern with an exponential decay. While the 211Å maxima follow those in the 335 Å channel, there is no systematic relation which would indicate a progressive cooling process through the lower temperatures, as has been observed in other investigations. In Group 2 the signals in the 171 and 131Å channels track each other closely, and lag behind the 193Å. In the inter-moss region of the loop the peak temperature and peak emission measure have opposite trends. The hot 94Å brightenings occur in the central part of the loops with maximum temperatures ~7 MK. Subsequently the loops appear to fill with plasma with an emission measure compatible with the 193 Å signal and temperature in the range ~ 1.5-2 MK. Although the exact details of the time evolution are still under investigation, these non static loops show high levels of intermittency in the 94Å signal (please see poster "Intermittent and Scale-Invariant Intensity Fluctuations in Hot Coronal Loops," by Lawrence et al. in this session).

Coupled Effects of a Perturbation in a Complex Structure Observed with SDO/AIA, SDO/HMI and ROSA/HARDcam

We study properties of intensity fluctuations in NOAA Active Region 11250 observed on 13 July 2011 starting at UT 13:32. Included are data obtained in the EUV bands of the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO/AIA) as well as nearly simultaneous observations of the chromosphere made, at much higher spatial and temporal resolution, with the Rapid Oscillations in the Solar Atmosphere (ROSA) and Hydrogen-Alpha Rapid Dynamics camera (HARDcam) systems at the Dunn Solar Telescope. A complex structure seen in both the ROSA/HARDcam and SDO data sets comprises a system of loops extending outward from near the boundary of the leading sunspot umbra. It is visible in the ROSA Ca II K and HARDcam Hα images, as well as the SDO 304 Å, 171 Å and 193 Å channels, and it thus couples the chromosphere, transition region and corona. In the ground-based images the loop structure is 4.1 Mm long. Some 17.5 Mm, can be traced in the SDO/AIA data. The chromospheric emissions observed by ROSA and HARDcam appear to occupy the inner, and apparently cooler and lower, quarter of the loop. We compare the intensity fluctuations of two points within the structure. From alignment with SDO/HMI images we identify a point "A" near the loop structure, which sits directly above a bipolar magnetic feature in the photosphere. Point "B" is characteristic of locations within the loops that are visible in both the ROSA/HARDcam and the SDO/AIA data. The intensity traces for point A are quiet during the first part of the data string. At time ~ 19 min they suddenly begin a series of impulsive brightenings. In the 171 Å and 193 Å coronal lines the brightenings are localized impulses in time, but in the transition region line at 304 Å they are more extended in time. The intensity traces in the 304 Å line for point B shows a quasi-periodic signal that changes properties at about 19 min. The wavelet power spectra are characterized by two periodicities. A 6.7 min period extends from the beginning of the series until about 25 minutes, and another signal with period ~3 min starts at about 20 min. The 193 Å power spectrum has a characteristic period of 5 min, before the 20 min transition and a 2.5 min periodicity afterward. In the case of HARDcam Hα data a localized 4 min periodicity can be found until about 7 min, followed by a quiet regime. After ~20 min a 2.3 min periodicity appears. Interestingly a coronal loop visible in the 94 Å line that is centrally located in the AR, running from the leading umbra to the following polarity, at about time 20 min undergoes a strong brightening beginning at the same moment all along 15 Mm of its length. The fact that these different signals all experience a clear-cut change at time about 20 min suggests an underlying organizing mechanism. Given that point A has a direct connection to the photospheric magnetic bipole, we conjecture that the whole extended structure is connected in a complex manner to the underlying magnetic field. The periodicities in these features may favor the wave nature rather than upflows and interpretations will be discussed.

Rapid Oscillations in the Solar Atmosphere: Spectra and Physical Effects

High-frequency fluctuations are observed with the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument (Jess et al. 2010, Solar Phys, 261, 363) at the Dunn Solar Telescope. This can produce simultaneous observations in up to six channels, at different heights in the photosphere and chromosphere, at an unprecedentedly high cadence of 0.5 seconds, and at a spatial resolution of 100 km after photometrically correct speckle reconstruction. Here we concentrate on observations at two levels. The first is in the G-band of the CH radical at 4305.5Å, bandpass 9.2Å, with height of formation z <250 km at a cadence of 0.525 sec corresponding to Nyquist frequency 950 mHz. The second is in the Ca II K-line core at 3933.7Å, bandpass 1.0Å, with height of formation z <1300 km, and cadence 4.2 sec giving Nyquist frequency 120 mHz. The data span 53 min, and the maximum field of view is 45 Mm. The data were taken on 28 May 2009 in internetwork and network near disk center. Using both Fourier and Morlet wavelet methods we find evidence in the G-band spectra for intensity fluctuations above noise out to frequencies f >> 100 mHz. The K-line signal is noisier and is seen only for f <50 mHz. With wavelet techniques we find that G-band spectral power with 20 <f <100 mHz is clearly concentrated in the intergranular lanes and especially at the locations of magnetic elements indicated by G-band bright points. This wavelet power is highly intermittent in time. By cross-correlating the data we find that pulses of high-frequency G-band power in the photosphere tend to be followed by increases in K-line emission in the chromosphere with a time lag of about 2 min.

Dynamics of Gompertzian tumour growth under environmental fluctuations

We investigate the effect of correlated additive and multiplicative Gaussian white noise oil the Gompertzian growth of tumours. Our results are obtained by Solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In Our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under Study. We perform simulations to analyze various aspects, of the probability distribution. of the tumour cell populations in the transient- and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (tau) to the steady-state distribution as a function of (i) of the correlation strength (lambda) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (alpha). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.

Rapid Fluctuations in the Lower Solar Atmosphere

The Rapid Oscillations in the Solar Atmosphere instrument reveals solar atmospheric fluctuations at high frequencies. Spectra of variations of the G-band intensity (IG ) and Ca II K-line intensity (IK ) show correlated fluctuations above white noise to frequencies beyond 300 mHz and 50 mHz, respectively. The noise-corrected G-band spectrum for f = 28-326 mHz shows a power law with exponent -1.21 ± 0.02, consistent with the presence of turbulent motions. G-band spectral power in the 25-100 mHz ("UHF") range is concentrated at the locations of magnetic bright points in the intergranular lanes and is highly intermittent in time. The intermittence of the UHF G-band fluctuations, shown by a positive kurtosis ?, also suggests turbulence. Combining values of IG , IK , UHF power, and ? reveals two distinct states of the solar atmosphere. State 1, including almost all the data, is characterized by low IG , IK , and UHF power and ? ˜ 6. State 2, including only a very small fraction of the data, is characterized by high IG , IK , and UHF power and ? ˜ 3. Superposed epoch analysis shows that the UHF power peaks simultaneously with spatio-temporal IG maxima in either state. For State 1, IK shows 3.5 minute chromospheric oscillations with maxima occurring 21 s after IG maxima implying a 150-210 km effective height difference. However, for State 2 the IK and IG maxima are simultaneous; in this highly magnetized environment sites of G-band and K-line emission may be spatially close together.

Turbulent Fluctuations in G-band and K-line Intensities Observed with the Rapid Oscillations in the Solar Atmosphere (ROSA) Instrument

Using the Rapid Oscillation in the Solar Atmosphere (ROSA) instrument at the Dunn Solar Telescope we have found that the spectra of fluctuations of the G-band (cadence 1.05 s) and Ca II K-line (cadence 4.2 s) intensities show correlated fluctuations above white noise out to frequencies beyond 300 mHz and up to 70 mHz, respectively. The noise-corrected G-band spectrum presents a scaling range (Ultra High Frequency “UHF”) for f = 25-100 mHz, with an exponent consistent with the presence of turbulent motions. The UHF power, is concentrated at the locations of magnetic bright points in the intergranular lanes, it is highly intermittent in time and characterized by a positive kurtosis κ. Combining values of G-band and K-line intensities, the UHF power, and κ, reveals two distinct “states” of the internetwork solar atmosphere. State 1, with κ ≍ 6, which includes almost all the data, is characterized by low intensities and low UHF power. State 2, with κ ≍ 3, including a very small fraction of the data, is characterized by high intensities and high UHF power. Superposed epoch analysis shows that for State 1, the K-line intensity presents 3.5 min chromospheric oscillations with maxima occurring 21 s after G-band intensity maxima implying a 150-210 km effective height difference. For State 2, the G-band and K-line intensity maxima are simultaneous, suggesting that in the highly magnetized environment sites of G-band and K-line emission may be spatially close together. Analysis of observations obtained with Hinode/SOT confirm a scaling range in the G-band spectrum up to 53 mHz also consistent with turbulent motions as well as the identification of two distinct states in terms of the H-line intensity and G-band power as functions of G-band intensity.

A comparison of theoretical line intensity ratios for Ni XII with extreme ultraviolet observations from the JET tokamak

Recent R-matrix calculations of electron impact excitation rates in Ni XII are used to derive the emission line ratios R-1 = I(154.17 Angstrom)/I(152.15 Angstrom), R-2 = I(152.95 Angstrom)/I(152.15 Angstrom) and R-3 = 1(160.55 Angstrom)/I(152.15 Angstrom). This is the first time (to our knowledge) that theoretical emission line ratios have been calculated for this ion. The ratios are found to be insensitive to changes in the adopted electron density (N-e) when N-e greater than or equal to 5 x 10(11) cm(-3), typical of laboratory plasmas. However, they do vary with electron temperature (T-e), with for example R-1 and R-3 changing by factors of 1.3 and 1.8, respectively, between T-e = 10(5) and 10(6) K. A comparison of the theoretical line ratios with measurements from the Joint European Tents (JET) tokamak reveals very good agreement between theory and observation for R-1, with an average discrepancy of only 7%. Agreement between the calculated and experimental ratios for R-2 and R-3 is less satisfactory, with average differences of 30 and 33%, respectively. These probably arise from errors in the JET instrument calibration curve. However, the discrepancies are smaller than the uncertainties in the R-2 and R-3 measurements. Our results, in particular for R-1, provide experimental support for the accuracy of the Ni XIII line ratio calculations, and hence for the atomic data adopted in their derivation.

Observations of H alpha intensity oscillations in a flare ribbon

High-cadence Halpha blue wing observations of a C9.6 solar flare obtained at Big Bear Solar Observatory using the Rapid Dual Imager are presented. Wavelet and time-distance methods were used to study oscillatory power along the ribbon, finding periods of 40 - 80 s during the impulsive phase of the flare. A parametric study found statistically significant intensity oscillations with amplitudes of 3% of the peak flare amplitude, periods of 69 s (14.5 mHz) and oscillation decay times of 500 s. These measured properties are consistent with the existence of flare-induced acoustic waves within the overlying loops.