Differential Emission Measure Distribution Research Articles

Solar plasma temperature diagnostics in flares and active regions from spectral lines in the range 280–330 Å in the SPIRIT/CORONAS-F experiment

Plasma temperature diagnostics in solar flares and active regions has been carried out using data from the SPIRIT spectroheliograph onboard the CORONAS-F satellite. The temperature distribution of the differential emission measure (DEM) has been determined from the relative intensities of spectral lines recorded in the spectral range 280–330 A in the period from 2001 to 2005. Analysis of these distributions has led to the conclusion about the existence of active regions with various “characteristic” temperature compositions. The presence of a hot plasma with temperatures logT = 6.8−7.2 in active regions has been established for the first time from XUV spectroscopic data and monochromatic X-ray line images. The DEM distribution for intense long-decay flares has also been obtained for the first time and a similarity of the temperature compositions for flares of different classes at the decay phase has been found. The spectra have been modeled on the basis of the calculated DEMs. The systematic discrepancies between the calculated and measured line intensities are discussed.

THE HYDRODYNAMIC EVOLUTION OF IMPULSIVELY HEATED CORONAL LOOPS: EXPLICIT ANALYTICAL APPROXIMATIONS

We derive simple analytical approximations (in explicit form) for the hydrodynamic evolution of the electron temperature T(s, t) and electron density n(s, t), for one-dimensional coronal loops that are subject to impulsive heating with subsequent cooling. Our analytical approximations are derived from first principles, using (1) the hydrodynamic energy balance equation, (2) the loop scaling laws of Rosner–Tucker–Vaiana and Serio, (3) the Neupert effect, and (4) the Jakimiec relationship. We compare our analytical approximations with 56 numerical cases of time-dependent hydrodynamic simulations from a parametric study of Tsiklauri et al., covering a large parameter space of heating rates, heating timescales, heating scale heights, loop lengths, for both footpoint and apex heating, mostly applicable to flare conditions. The average deviations from the average temperature and density values are typically ≈20% for our analytical expressions. The analytical approximations in explicit form provide an efficient tool to mimic time-dependent hydrodynamic simulations, to model observed soft X-rays and extremeultraviolet light curves of heated and cooling loops in the solar corona and in flares by forward fitting, to model microflares, to infer the coronal heating function from light curves of multi-wavelength observations, and to provide physical models of differential emission measure distributions for solar and stellar flares, coronae, and irradiance.

HINODE/EXTREME-ULTRAVIOLET IMAGING SPECTROMETER OBSERVATIONS OF THE TEMPERATURE STRUCTURE OF THE QUIET CORONA

We present a Differential Emission Measure (DEM) analysis of the quiet solar corona on disk using data obtained by the Extreme-ultraviolet Imaging Spectrometer (EIS) on {\it Hinode}. We show that the expected quiet Sun DEM distribution can be recovered from judiciously selected lines, and that their average intensities can be reproduced to within 30%. We present a subset of these selected lines spanning the temperature range $\log$ T = 5.6 to 6.4 K that can be used to derive the DEM distribution reliably. The subset can be used without the need for extensive measurements and the observed intensities can be reproduced to within the estimated uncertainty in the pre-launch calibration of EIS. Furthermore, using this subset, we also demonstrate that the quiet coronal DEM distribution can be recovered on size scales down to the spatial resolution of the instrument (1$$ pixels). The subset will therefore be useful for studies of small-scale spatial inhomogeneities in the coronal temperature structure, for example, in addition to studies requiring multiple DEM derivations in space or time. We apply the subset to 45 quiet Sun datasets taken in the period 2007 January to April, and show that although the absolute magnitude of the coronal DEM may scale with the amount of released energy, the shape of the distribution is very similar up to at least $\log$ T $\sim$ 6.2 K in all cases. This result is consistent with the view that the {\it shape} of the quiet Sun DEM is mainly a function of the radiating and conducting properties of the plasma and is fairly insensitive to the location and rate of energy deposition. This {\it universal} DEM may be sensitive to other factors such as loop geometry, flows, and the heating mechanism, but if so they cannot vary significantly from quiet Sun region to region.

FIRST THREE-DIMENSIONAL RECONSTRUCTIONS OF CORONAL LOOPS WITH THESTEREO A+BSPACECRAFT. III. INSTANT STEREOSCOPIC TOMOGRAPHY OF ACTIVE REGIONS

Here we develop a novel three-dimensional (3D) reconstruction method of the coronal plasma of an active region by combining stereoscopic triangulation of loops with density and temperature modeling of coronal loops with a filling factor equivalent to tomographic volume rendering. Because this method requires only a stereoscopic image pair in multiple temperature filters, which are sampled within 1 minute with the recent STEREO/EUVI instrument, this method is about four orders of magnitude faster than conventional solar rotation-based tomography. We reconstruct the 3D density and temperature distribution of active region NOAA 10955 by stereoscopic triangulation of 70 loops, which are used as a skeleton for a 3D field interpolation of some 7000 loop components, leading to a 3D model that reproduces the observed fluxes in each stereoscopic image pair with an accuracy of a few percents (of the average flux) in each pixel. With the stereoscopic tomography we infer also a differential emission measure distribution over the entire temperature range of T 104-107, with predictions for the transition region and hotter corona in soft X-rays. The tomographic 3D model provides also large statistics of physical parameters. We find that the extreme-ultraviolet loops with apex temperatures of Tm 3.0 MK tend to be super-hydrostatic, while hotter loops with Tm 4-7 MK are near-hydrostatic. The new 3D reconstruction model is fully independent of any magnetic field data and is promising for future tests of theoretical magnetic field models and coronal heating models.

HINODE X-RAY TELESCOPE DETECTION OF HOT EMISSION FROM QUIESCENT ACTIVE REGIONS: A NANOFLARE SIGNATURE?

The X-Ray Telescope (XRT) on the Japanese/USA/UK Hinode (Solar-B) spacecraft has detected emission from a quiescent active region core that is consistent with nanoflare heating. The fluxes from 10 broadband X-ray filters and filter combinations were used to construct differential emission measure (DEM) curves. In addition to the expected active region peak at log T = 6.3-6.5, we find a high-temperature component with significant emission measure at log T > 7.0. This emission measure is weak compared to the main peak—the DEM is down by almost three orders of magnitude—which accounts of the fact that it has not been observed with earlier instruments. It is also consistent with spectra of quiescent active regions: no Fe XIX lines are observed in a CHIANTI synthetic spectrum generated using the XRT DEM distribution. The DEM result is successfully reproduced with a simple two-component nanoflare model.

Highly Efficient Modeling of Dynamic Coronal Loops

Observational and theoretical evidence suggests that coronal heating is impulsive and occurs on very small cross-field spatial scales. A single coronal loop could contain a hundred or more individual strands that are heated quasi-independently by nanoflares. It is therefore an enormous undertaking to model an entire active region or the global corona. Three-dimensional MHD codes have inadequate spatial resolution, and one-dimensional (1D) hydrodynamic codes are too slow to simulate the many thousands of elemental strands that must be treated in a reasonable representation. Fortunately, thermal conduction and flows tend to smooth out plasma gradients along the magnetic field, so zero-dimensional (0D) models are an acceptable alternative. We have developed a highly efficient model called enthalpy-based thermal evolution of loops (EBTEL), which accurately describes the evolution of the average temperature, pressure, and density along a coronal strand. It improves significantly on earlier models of this type—in accuracy, flexibility, and capability. It treats both slowly varying and highly impulsive coronal heating; it provides the time-dependent differential emission measure distribution, DEM(T), at the transition region footpoints; and there are options for heat flux saturation and nonthermal electron beam heating. EBTEL gives excellent agreement with far more sophisticated 1D hydrodynamic simulations despite using 4 orders of magnitude less computing time. It promises to be a powerful new tool for solar and stellar studies.

RHESSITiming Studies: Multithermal Delays

We investigate the energy-dependent timing of thermal emission in solar flares using high-resolution spectra and demodulated time profiles from the RHESSI instrument. We model for the first time the spectral-temporal hard X-ray flux f(,t) in terms of a multitemperature plasma governed by thermal conduction cooling. In this quantitative model we characterize the multitemperature differential emission measure distribution (DEM) and nonthermal spectra with power-law functions. We fit this model to the spectra and energy-dependent time delays of a representative data set of 89 solar flares observed with RHESSI during 2002-2005. Eliminating weak flares, we find 65 events suitable for fitting and obtain in 44 events (68%) a satisfactory fit that is consistent with the theoretical model. The best-fit results yield a thermal-nonthermal crossover energy of th = 18.0 ± 3.4 keV, nonthermal spectral indices of γnth = 3.5 ± 1.1 (at ≈30-50 keV), thermal multispectral indices of γth = 6.9 ± 0.9 (at ≈10-20 keV), and thermal conduction cooling times of τc0 = 101.6±0.6 s at th = 1 keV (or T0 = 11.6 MK), which scale with temperature as τc(T) ∝ T-β with β = 2.7 ± 1.2, consistent with the theoretically expected scaling of τc(T) ∝ T-5/2 for thermal conduction cooling. The (empirical) Neupert effect is consistent with this theoretical model in the asymptotic limit of long cooling times. This study provides clear evidence that all analyzed flares are consistent with the model of a multitemperature plasma distribution and with thermal conduction as dominant cooling mechanism (at flare temperatures of T 10 MK). Our modeling of energy-dependent time delays provides an alternative method for separating multithermal from nonthermal spectral components based on information in the time domain, in contrast to previous spectral fitting methods.

Differential emission measure distributions in X-ray solar flares

X-ray spectrometer RESIK has observed spectra in the four wavelength bands from 3.3 Å to 6.1 Å. This spectral range contains many emission lines of H- and He-like ions for Si, S, Ar and K. These lines are formed in plasma of coronal temperatures ( T > 3 MK). Analysis of their intensities allows studying differential emission measure distributions (DEM) in temperature range roughly between 3 MK and 30 MK. The aim of present study was to check whether any relationship exists between the character of DEM distribution, the event phase and the X-ray flare class. To do this we have calculated and analyzed the DEM distributions for a set of flares belonging to different GOES classes from the range B5.6–X1. The DEM distributions have been calculated using “Withbroe–Sylwester” multiplicative, maximum likelihood iterative algorithm. As the input data we have used absolute fluxes observed by RESIK in several spectral bands (lines + continuum). Respective emission functions have been calculated using the CHIANTI v. 5.2 atomic data package.

ChandraHigh‐Resolution X‐Ray Spectroscopy of AM Herculis

We present the results of high-resolution spectroscopy of the prototype Polar AM Herculis observed with Chandra High Energy Transmission Grating . The X-ray spectrum contains hydrogen-like and helium-like lines of Fe, S, Si, Mg, Ne, and O, with several Fe L-shell emission lines. The forbidden lines in the spectrum are generally weak, whereas the hydrogen-like lines are stronger suggesting that emission from a multitemperature, collisionally ionized plasma dominates. The helium-like line flux ratios yield a plasma temperature of 2 MK and a plasma density 1-9 × 1012 cm-3, whereas the line flux ratio of Fe XXVI to Fe XXV gives an ionization temperature of 12.4 keV. We present the differential emission measure distribution of AM Her, whose shape is consistent with the volume emission measure obtained by a multitemperature APEC model. The multitemperature plasma model fit to the average X-ray spectrum indicates the mass of the white dwarf to be ~1.15 M☉. From phase-resolved spectroscopy, we find the line centers of Mg XII, S XVI, resonance line of Fe XXV, and Fe XXVI emission modulated by a few hundred to 1000 km s-1 from the theoretically expected values, indicating bulk motion of ionized matter in the accretion column of AM Her. The observed velocities of Fe XXVI ions are close to the expected shock velocity for a 0.6 M☉ white dwarf. The observed velocity modulation is consistent with that expected from a single pole accreting binary system.

Coronal Diagnostic Spectrometer Observations of Isothermal and Multithermal Coronal Loops

A data set obtained on 2003 January 17 with the Coronal Diagnostic Spectrometer (CDS) shows two loops sitting side by side on the solar disk. These loops are oriented along the CDS slit, so all pixels in each loop were observed simultaneously. So, although the instrument has a relatively slow time cadence, changes as a function of time that may occur during the CDS raster buildup will not affect the loop temperature results. Differential emission measure (DEM) analysis using a forward-folding technique shows different results for the two loops. For the first loop, the intensities of the lines that remain after background subtraction are well fit with a DEM curve that collapses to a single spike. In other words, the loop plasma at this location is isothermal. This analysis is confirmed with an emission measure loci method and agrees with the results obtained recently by other authors that show that the moderate spatial resolution of CDS can detect isothermal structures. For the second loop, the background-subtracted line intensities require a broad DEM, not consistent with isothermal plasma. This conclusion is confirmed with an automatic-inversion DEM method. In this Letter, we specifically address some of the concerns raised about CDS temperature analysis: the slow CDS temporal resolution, the moderate CDS spatial resolution, the inherent smoothing associated with DEM inversion, and line-of-sight effects on the DEM distribution.

Determination of differential emission measure from X-ray solar spectra registered by RESIK aboard CORONAS-F

The differential emission measure (DEM) describes the temperature distribution of the emitting plasma. The DEM distribution allows one to study the physical conditions and the energy of flares in detail (including the mean temperature and the total emission measure). In this paper, we analyze the time changes of the DEM distributions for a selected flare, which has been observed with the RESIK instrument. To calculate the differential emission measure, we used the Withbroe-Sylwester (W-S) iterative algorithm corresponding to the maximum likelihood procedure. The required emission functions were calculated with the CHIANTI package. We calculated the DEM for four available estimates of the ionization equilibrium and coronal composition of plasma.

The Intercalibration of SOHO EIT, CDS‐NIS, and TRACE

Using coordinated observations of a quiet coronal region, we study the intercalibration of the CDS and EIT instruments on board the Solar and Heliospheric Observatory (SOHO) and the Transition Region and Coronal Explorer (TRACE). We derive the differential emission measure (DEM) distribution from CDS spectral line intensities and convolve it with EIT and TRACE temperature response functions, calculated with the latest atomic data from the CHIANTI database, to predict count rates in their observing channels. We examine different analysis methods and briefly discuss some more advanced aspects of atomic modeling such as the density dependence of the ionization fractions. We investigate the implications for our study using data from the ADAS database. We find that our CDS DEM can predict the TRACE and EIT 171 and 195 A channel count rates to within 25%. However, the accuracy of the predictions depends on the ionization fractions and elemental abundances used. The TRACE 284 A and EIT 284 and 304 A filter predictions do not agree well with the observations, even after taking the contribution from the optically thick He II 304 A line to the TRACE 284 A channel into account. The different CDS DEM solutions we derive using different ionization fractions produce fairly similar results: the majority of the CDS line intensities used are reproduced to within 20% with only around one-fifth reproduced to worse than 50%. However, the comparison provides us with further clues with which to explain the discrepancies found for some lines, and highlights the need for accurate equilibrium ionization balance calculations even at low density.

NRLEUV 2: A new model of solar EUV irradiance variability

NRLEUV represents an independent approach to modeling the Sun’s EUV irradiance and its variability. Instead of relying on existing irradiance observations, our model utilizes differential emission measure distributions derived from spatially and spectrally resolved solar observations, full-disk solar images, and a database of atomic physics parameters to calculate the solar EUV irradiance. Recent updates to the model include the calculation of a new quiet Sun differential emission measure distribution using data from the CDS and SUMER spectrometers on SOHO and the use of a more extensive database of atomic physics parameters. Here, we present comparisons between the NRLEUV quiet Sun reference spectrum and solar minimum irradiance observations. Although there are many areas of agreement between the modeled spectrum and the observations, there are some major disagreements. The computed spectra cannot reproduce the observed irradiances at wavelengths below about 160 Å. The observed irradiances appear to overstate the magnitude of the EUV continua. We also present some initial comparisons between the NRLEUV irradiance variability model and TIMED/SEE data. We find that the NRLEUV model tends to overpredict the absolute magnitude of the irradiance at many wavelengths. The model also appears to underpredict the magnitude of the solar-cycle and solar rotational variation in transition region emission lines.

Three Criteria to Discriminate between Elementary and Composite Coronal Loops

In this Letter, we establish three simple criteria to discriminate between elementary and composite loop structures, based on observations from high-resolution (TRACE) and low-resolution (EIT) imagers. Both data sets contain triple-filter data with a temperature diagnostic in the range of T ≈ 0.7-2.8 MK, which we use for forward-fitting of a differential emission measure (DEM) distribution to constrain the temperature range of each structure. From the TRACE data set, we find for the finest structures a mean width of w = 1.4 ± 0.3 Mm, a flux-to-background contrast of c ≈ 0.18 ± 0.13, and a temperature range of dT = 0.07 ± 0.10 MK, which we identify as elementary strands, defined in terms of their thermal homogeneity. The loop structures observed with EIT have loop widths w, flux contrasts c, and temperature ranges dT that are all about an order of magnitude larger and thus clearly constitute composite structures, consisting of many loop strands. These two contrasting observations resolve previous controversies about the basic thermal structure of coronal loops and yield a simple discrimination rule: elementary loop strands (1) are near-isothermal (dT 0.2 MK), (2) have a small width (w 2 Mm), and (3) have a faint contrast (c 0.3), while virtually all wider and higher contrast loop features are most likely multithermal composites and have a broad DEM.

Elementary Loop Structures in the Solar Corona Analyzed fromTRACETriple‐Filter Images

This study represents the first quantitative analysis of the multithread structure of coronal loops. We analyzed a set of 234 fine loop threads observed with TRACE triple-filter images at wavelengths of 171, 195, and 284 Å. The cross-sectional flux profiles are simultaneously forward fitted in all three filters with the superposition of a cospatial Gaussian and linear background functions. We fit a general multitemperature differential emission measure (DEM) distribution to each cross section, as well as the special case of a single-temperature or isothermal DEM. We perform these forward fits at ≈18,000 loop positions and find that this geometric model could be fitted in ≈3500 cases (within a χred ≤ 1.5), while all other cases require more complex geometric models of the loop cross section, secondary loops, and background. The major result of this study is that the vast majority (84%) of the acceptable DEM fits are isothermal. Temperatures are measured over the whole sensitivity range of 0.7-2.8 MK, but with a higher probability near the peak sensitivities of the three filters. We conclude that we indeed resolve "elementary" or "monolithic" loop strands with TRACE, in terms of isothermal homogeneity. Virtually all earlier studies detected ensembles of multiple strands, while our detected loop strands exhibit much smaller widths (w ≈ 1.4 ± 0.3 Mm) and also smaller signal-to-background ratios (14% ± 10%). We suggest that the temperature homogeneity of coronal loops up to widths of w ≲ 2000 km is related to their magnetic mapping to photospheric granulation (convection) cells.

Ion‐by‐Ion Differential Emission Measure Determination of Collisionally Ionized Plasma. II. Application to Hot Stars

In a previous paper we have described a technique to derive constraints on the differential emission measure (DEM) distribution, a measure of the temperature distribution, of collisionally ionized hot plasmas from their X-ray emission line spectra. We apply this technique to the Chandra HETGS spectra of all of the nine hot stars available to us at the time that this project was initiated. We find that DEM distributions of six of the seven O stars in our sample are very similar, but that θ1 Ori C has an X-ray spectrum characterized by higher temperatures. The DEM distributions of both of the B stars in our sample have lower magnitudes than those of the O stars, and one, τ Sco, is characterized by higher temperatures than the other, β Cru. These results confirm previous work in which high temperatures have been found for θ1 Ori C and τ Sco and taken as evidence for channeling of the wind in magnetic fields, the existence of which is related to the stars' youth. Our results demonstrate the utility of our method for deriving temperature information for large samples of X-ray emission-line spectra.

The Coronae of AB Doradus and V471 Tauri: Primordial Angular Momentum versus Tidal Spin‐up

The zero-age main-sequence star AB Dor and the K dwarf component of the V471 Tau close binary have essentially identical rotation rates and spectral types. An analysis of their high-resolution Chandra X-ray spectra reveals remarkably similar coronal characteristics in terms of both temperature structure and element abundances. Both stars show depletions of low first ionization potential (FIP) elements by factors of ~3, with higher FIP elements showing more mild depletions. No evidence for enhancements of very low FIP (<7 eV) elements, such as Na, Al, and Ca, as compared to other low-FIP elements, was found. The abundance anomaly pattern for AB Dor and V471 Tau is similar to, although less extreme than, the abundance anomalies exhibited by active RS CVn-type binaries. While we find statistically significant structure in the underlying differential emission measure distributions of these stars over narrow temperature intervals, this structure is strongly dependent on the lines used in the analysis and is probably spurious. On the basis of their X-ray similarities, we conclude that the exact evolutionary state of a star has little effect on coronal characteristics and that the parameters that dominate coronal structure and composition are simply the rotation rate and spectral type.

A Solar Minimum Irradiance Spectrum for Wavelengths below 1200 A

NRLEUV represents an independent approach to modeling the Sun's EUV irradiance and its variability. Our model utilizes differential emission measure distributions derived from spatially and spectrally resolved solar observations, full-disk solar images, and a database of atomic physics parameters to calculate the solar EUV irradiance. In this paper we present a new solar minimum irradiance spectrum for wavelengths below 1200 A. This spectrum is based on extensive observations of the quiet Sun taken with the CDS and SUMER spectrometers on the Solar and Heliospheric Observatory (SOHO) and the most recent version of the CHIANTI atomic physics database. In general, we find excellent agreement between this new irradiance spectrum and our previous quiet-Sun reference spectrum derived primarily from Harvard Skylab observations. Our analysis does show that the quiet-Sun emission measure above about 1 MK declines more rapidly than in our earlier emission measure distribution and that the intensities of the EUV free-bound continua at some wavelengths are somewhat smaller than indicated by the Harvard observations. Our new reference spectrum is also generally consistent with recent irradiance observations taken near solar minimum. There are, however, two areas of persistent disagreement. Our solar spectrum indicates that the irradiance measurements overestimate the contribution of the EUV free-bound continua at some wavelengths by as much as a factor of 10. Our model also cannot reproduce the observed irradiances at wavelengths below about 150 A. Comparisons with spectrally resolved solar and stellar observations indicate that only a small fraction of the emission lines in the 60-120 A wavelength range are accounted for in CHIANTI.

Ion‐by‐Ion Differential Emission Measure Determination of Collisionally Ionized Plasma. I. Method

We describe a technique to derive constraints on the differential emission measure (DEM) distribution, a measure of the temperature distribution, of collisionally ionized hot plasmas from their X-ray emission-line spectra. This technique involves fitting spectra using a number of components, each of which is the entire X-ray emission-line spectrum for a single ion. It is applicable to high-resolution X-ray spectra of any collisionally ionized plasma, and it is particularly useful for spectra in which the emission lines are broadened and blended, such as those of the winds of hot stars. This method does not require that any explicit assumptions about the form of the DEM distribution be made and is easily automated.

First Determinations of Differential Emission Measure Distribution from RESIK X-ray Spectra

RESIK Bragg spectrometer aboard CORONAS-F solar observatory collected spectra of hundreds of solar flares in the unique spectral range between 3.3 A and 6.1 A. The instrument’s absolute and relative calibrations are now finished which allows for the first time to interpret the observations in terms of the differential emission measure (DEM) distribution. With known DEM shape it is possible to derive and study in detail flaring plasma composition and energy balance. Here we report results of using an improved Maximum Likelihood iterative algorithm (WithbroeSylwester) for determination of the DEM distributions for 7 January 2003 flare at 23:30 UT. The study is based on the absolute flux values observed in a number of strong Hand He-like transitions of K xviii, Ar xviii, Ar xvii, S xvi, S xv, Si xiv and Si xiii ions. In this respect, we use line and continuum X-ray emissivities as provided by CHIANTI package from SolarSoft.