Differential Emission Measure Model Research Articles

Soft X-Ray Spectral Diagnostics of Multithermal Plasma in Solar Flares with Chandrayaan-2 XSM

Spectroscopic observations in X-ray wavelengths provide excellent diagnostics of the temperature distribution in solar flare plasma. The Solar X-ray Monitor (XSM) on board the Chandrayaan-2 mission provides broadband disk-integrated soft X-ray solar spectral measurements in the energy range of 1–15 keV with high spectral resolution and time cadence. In this study, we analyze the X-ray spectra of three representative GOES C-class flares obtained with the XSM to investigate the evolution of various plasma parameters during the course of the flares. Using the soft X-ray spectra consisting of the continuum and well-resolved line complexes of major elements like Mg, Si, and Fe, we investigate the validity of the isothermal and multithermal assumptions on the high-temperature components of the flaring plasma. We show that the soft X-ray spectra during the impulsive phase of the high-intensity flares are inconsistent with isothermal models and are best fitted with double-peaked differential emission measure distributions where the temperature of the hotter component rises faster than that of the cooler component. The two distinct temperature components observed in differential emission measure models during the impulsive phase of the flares suggest the presence of the directly heated plasma in the corona and evaporated plasma from the chromospheric footpoints. We also find that the abundances of low first ionization potential elements Mg, Si, and Fe reduce from near coronal to near photospheric values during the rising phase of the flare and recover back to coronal values during the decay phase, which is also consistent with the chromospheric evaporation scenario.

The Mega-MUSCLES Spectral Energy Distribution of TRAPPIST-1

Abstract We present a 5 Å–100 μm spectral energy distribution (SED) of the ultracool dwarf star TRAPPIST-1, obtained as part of the Mega-MUSCLES Treasury Survey. The SED combines ultraviolet and blue-optical spectroscopy obtained with the Hubble Space Telescope, X-ray spectroscopy obtained with XMM-Newton, and models of the stellar photosphere, chromosphere, transition region, and corona. A new differential emission measure model of the unobserved extreme-ultraviolet spectrum is provided, improving on the Lyα–EUV relations often used to estimate the 100–911 Å flux from low-mass stars. We describe the observations and models used, as well as the recipe for combining them into an SED. We also provide a semiempirical, noise-free model of the stellar ultraviolet spectrum based on our observations for use in atmospheric modeling of the TRAPPIST-1 planets.

ANALYSIS OF CORONAL RAIN OBSERVED BY IRIS, HINODE/SOT, AND SDO/AIA: TRANSVERSE OSCILLATIONS, KINEMATICS, AND THERMAL EVOLUTION

ABSTRACT Coronal rain composed of cool plasma condensations falling from coronal heights along magnetic field lines is a phenomenon occurring mainly in active region coronal loops. Recent high-resolution observations have shown that coronal rain is much more common than previously thought, suggesting its important role in the chromosphere-corona mass cycle. We present the analysis of MHD oscillations and kinematics of the coronal rain observed in chromospheric and transition region lines by the Interface Region Imaging Spectrograph (IRIS), the Hinode Solar Optical Telescope (SOT), and the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA). Two different regimes of transverse oscillations traced by the rain are detected: small-scale persistent oscillations driven by a continuously operating process and localized large-scale oscillations excited by a transient mechanism. The plasma condensations are found to move with speeds ranging from few km s−1 up to 180 km s−1 and with accelerations largely below the free-fall rate, likely explained by pressure effects and the ponderomotive force resulting from the loop oscillations. The observed evolution of the emission in individual SDO/AIA bandpasses is found to exhibit clear signatures of a gradual cooling of the plasma at the loop top. We determine the temperature evolution of the coronal loop plasma using regularized inversion to recover the differential emission measure (DEM) and by forward modeling the emission intensities in the SDO/AIA bandpasses using a two-component synthetic DEM model. The inferred evolution of the temperature and density of the plasma near the apex is consistent with the limit cycle model and suggests the loop is going through a sequence of periodically repeating heating-condensation cycles.

THE ABSOLUTE CALIBRATION OF THE EUV IMAGING SPECTROMETER ON HINODE

We investigate the absolute calibration of the EUV Imaging Spectrometer (EIS) on Hinode by comparing EIS full-disk mosaics with irradiance observations from the EUV Variability Experiment (EVE) on the Solar Dynamics Observatory. We also use ultra-deep (>10^5s) exposures of the quiet corona above the limb combined with a simple differential emission measure model to establish new effective area curves that incorporate information from the most recent atomic physics calculations. We find that changes to the EIS instrument sensitivity are a complex function of both time and wavelength. We find that the sensitivity is decaying exponentially with time and that the decay constants vary with wavelength. The EIS short wavelength channel shows significantly longer decay times than the long wavelength channel.

ON THE ACCURACY OF THE DIFFERENTIAL EMISSION MEASURE DIAGNOSTICS OF SOLAR PLASMAS. APPLICATION TO SDO /AIA. II. MULTITHERMAL PLASMAS

The Differential Emission Measure (DEM) analysis is one of the most used diagnostic tools for solar and stellar coronae. Being an inverse problem, it has limitations due to the presence of random and systematic errors. We present in theses series of papers an analysis of the robustness of the inversion in the case of AIA/SDO observations. We completely characterize the DEM inversion and its statistical properties, providing all the solutions consistent with the data along with their associated probabilities, and a test of the suitability of the assumed DEM model. While Paper I focused on isothermal conditions, we now consider multi-thermal plasmas and investigate both isothermal and multithermal solutions. We demonstrate how the ambiguity between noises and multi-thermality fundamentally limits the temperature resolution of the inversion. We show that if the observed plasma is multi-thermal, isothermal solutions tend to cluster on a constant temperature whatever the number of passbands or spectral lines. The multi-thermal solutions are also found to be biased toward near isothermal solutions around 1 MK. This is true even if the residuals support the chosen DEM model, possibly leading to erroneous conclusions on the observed plasma. We propose tools to identify and quantify the possible degeneracy of solutions, thus helping the interpretation of DEM inversion.

SOLAR CORONA LOOP STUDIES WITH THE ATMOSPHERIC IMAGING ASSEMBLY. I. CROSS-SECTIONAL TEMPERATURE STRUCTURE

We present a first systematic study on the cross-sectional temperature structure of coronal loops using the six coronal temperature filters of the Atmospheric Imaging Assembly (AIA) instrument on the Solar Dynamics Observatory (SDO). We analyze a sample of 100 loop snapshots measured at 10 different locations and 10 different times in active region NOAA 11089 on 2010 July 24, 21:00-22:00 UT. The cross-sectional flux profiles are measured and a cospatial background is subtracted in 6 filters in a temperature range of $T \approx 0.5-16$ MK, and 4 different parameterizations of differential emission measure (DEM) distributions are fitted. We find that the reconstructed DEMs consist predominantly of narrowband peak temperature components with a thermal width of $\sigma_{log(T)} \le 0.11\pm0.02$, close to the temperature resolution limit of the instrument, consistent with earlier triple-filter analysis from TRACE by Aschwanden and Nightingale (2005) and from EIS/Hinode by Warren et al. (2008) or Tripathi et al. (2009). We find that 66% of the loops could be fitted with a narrowband single-Gaussian DEM model, and 19% with a DEM consisting of two narrowband Gaussians (which mostly result from pairs of intersecting loops along the same line-of-sight). The mostly isothermal loop DEMs allow us also to derive an improved empirical response function of the AIA 94 \ang\ filter, which needs to be boosted by a factor of $q_{94} = 6.7\pm 1.7$ for temperatures at $log(T) \lapprox 6.3$. The main result of near-isothermal loop cross-sections is not consistent with the predictions of standard nanoflare scenarios, but can be explained by flare-like heating mechanisms that drive chromospheric evaporation and upflows of heated plasma coherently over loop cross-sections of $w \approx 2-4$ Mm.

Suzaku observations of X-ray excess emission in the cluster of galaxies A 3112

We analysed the Suzaku XIS1 data of the A3112 cluster of galaxies in order to examine the X-ray excess emission in this cluster reported earlier with the XMM-Newton and Chandra satellites. The best-fit temperature of the intracluster gas depends strongly on the choice of the energy band used for the spectral analysis. This proves the existence of excess emission component in addition to the single-temperature MEKAL in A3112. We showed that this effect is not an artifact due to uncertainties of the background modeling, instrument calibration or the amount of Galactic absorption. Neither does the PSF scatter of the emission from the cool core nor the projection of the cool gas in the cluster outskirts produce the effect. Finally we modeled the excess emission either by using an additional MEKAL or powerlaw component. Due to the small differencies between thermal and non-thermal model we can not rule out the non-thermal origin of the excess emission based on the goodness of the fit. Assuming that it has a thermal origin, we further examined the Differential Emission Measure (DEM) models. We utilised two different DEM models, a Gaussian differential emission measure distribution (GDEM) and WDEM model, where the emission measure of a number of thermal components is distributed as a truncated power law. The best-fit XIS1 MEKAL temperature for the 0.4-7.0 keV band is 4.7+-0.1 keV, consistent with that obtained using GDEM and WDEM models.

DETERMINING THE GALACTIC HALO'S EMISSION MEASURE FROM UV AND X-RAY OBSERVATIONS

We analyze a pair of Suzaku shadowing observations in order to determine the X-ray spectrum of the Galaxy's gaseous halo. We simultaneously fit the spectra with models having halo, local, and extragalactic components. The intrinsic intensities of the halo OVII triplet and OVIII Lyman alpha emission lines are 9.98^{+1.10}_{-1.99} LU (line unit; photons cm^-2 s^-1 Sr^-1) and 2.66^{+0.37}_{-0.30} LU, respectively. Meanwhile, FUSE OVI observations for the same directions and SPEAR CIV observations for a nearby direction indicate the existence of hot halo gas at temperatures of ~10^{5.0} K to ~10^{6.0} K. This collection of data implies that the hot gas in the Galactic halo is not isothermal, but its temperature spans a relatively wide range from ~10^{5.0} K to ~10^{7.0} K. We therefore construct a differential emission measure (DEM) model for the halo's hot gas, consisting of two components. In each, dEM/dlog T is assumed to follow a power-law function of the temperature and the gas is assumed to be in collisional ionizational equilibrium. The low-temperature component (LTC) of the broken power-law DEM model covers the temperature range of 10^{4.80}-10^{6.02} K with a slope of 0.30 and the high-temperature component (HTC) covers the temperature range of 10^{6.02}-10^{7.02} K with a slope of -2.21. We find that a simple model in which hot gas accretes onto the Galactic halo and cools radiatively cannot explain both the observed UV and X-ray portions of our broken power-law model. It can, however, explain the intensity in the Suzaku bandpass if the mass infall rate is 1.35*10^{-3} Msun yr^-1 kpc^-2. The UV and X-ray intensities and our broken power-law model can be well explained by hot gas produced by supernova explosions or by supernova remnants supplemented by a smooth source of X-rays.

AD Leonis: Flares observed by XMM-Newton and Chandra

The M-dwarf AD Leonis has been observed with the Reflection Grating Spectrometers and the European Photon Imaging Camera aboard XMM-Newton and also with the Low Energy Transmission Grating Spectrometer aboard the Chandra X-ray Observatory. In the observation taken with XMM-Newton five large flares produced by AD Leo were identified and only one in the observation taken with Chandra. A quiescent level to the lightcurves is difficult to define, since several smaller flares mutually overlap each other. However, we defined a quasi-steady state outside of obvious flares or flare decays. The spectra from the flare state and the quasi-steady state are analysed separately. From these spectra the temperature structure was derived with a multi-temperature model and with a differential emission measure model. The multi-temperature model was also used to determine the relative abundances of C, N, O, Ne, Mg, Si, S, and Fe. He-like ions, such as O VII and Ne IX, produce line triplets which are used to determine or constrain the electron temperature and electron density of the corresponding ion. During the flare state a higher emission measure at the hottest temperature is found for both XMM-Newton and Chandra observations. The derived abundances suggest the presence of an inverse First Ionization Potential effect in the corona of AD Leo.

Temperature and Density Measurements in a Quiet Coronal Streamer

Many previous studies have used emission line or broadband filter ratios to infer the presence of temperature gradients in the quiet solar corona. Recently it has been suggested that these temperature gradients are not real, but result from the superposition of isothermal loops with different temperatures and density scale heights along the line of sight. A model describing this hydrostatic weighting bias has been developed by Aschwanden & Acton. In this paper we present the application of the Aschwanden & Acton differential emission measure model to Solar and Heliospheric Observatory Solar Ultraviolet Measurement of Emitted Radiation (SUMER) observations of a quiet coronal streamer. Simultaneous Yohkoh soft X-ray telescope (SXT) observations show increases in the filter ratios with height above the limb, indicating an increase in temperature. The application of the Aschwanden & Acton model to these SUMER data, however, show that the temperature is constant with height and that the distribution of temperatures in the corona is much too narrow for the hydrostatic weighting bias to have any effect on the SXT filter ratios. We consider the possibility that there is a tenuous hot component (~3 MK) that accounts for the SXT observations. We find that a hot plasma with an emission measure sufficient to reproduce the observed SXT fluxes would also produce significant count rates in the high-temperature emission lines in the SUMER wavelength range. These lines are not observed, and we conclude that the SUMER spectra are not consistent with the SXT filter ratio temperatures. Calculations from a hydrodynamic loop model suggest that nonuniform footpoint heating may be consistent with the temperatures and densities observed at most heights, consistent with the recent analysis of relatively cool (~1 MK) active region loops. We also find, however, that at the lowest heights the observed densities are smaller than those predicted by uniform or footpoint heating.

Tempurature Tomography of the Soft X‐Ray Corona: Measurements of Electron Densities, Tempuratures, and Differential Emission Measure Distributions above the Limb

We analyze long-exposure and off-pointing Yohkoh/SXT data of the solar corona observed on 1992 August 26. We develop a new (temperature) tomography method that is based on a forward-fitting method of a four-parameter model to the observed soft X-ray fluxes F1(h) and F2(h) of two SXT wavelength filters as a function of height h. The model is defined in terms of a differential emission measure (DEM) distribution dEM(h, T)/dT, which includes also a temperature dependence of density scale heights ?n(T) = q??T and allows us to quantify deviations (q? ? 1) from hydrostatic equilibrium (q? = 1). This parametrization facilitates a proper line-of-sight integration and relates the widely used filter ratio temperature TFR to the peak of the DEM distribution. A direct consequence of the multi-scale height atmosphere is that the filter ratio temperature TFR(h) is predicted to increase with height, even if all magnetic field lines are isothermal. Our model fitting reveals that coronal holes and quiet-Sun regions are in perfect hydrostatic equilibrium but that coronal streamers have a scale height that exceeds the hydrostatic scale height by a factor of up to q? 2.3, which underscores the dynamic nature of coronal streamers. Our density measurements in coronal holes are slightly lower than most of the white-light polarized brightness inversions and seem to come closer to the requirements of solar wind models. Our DEM model provides also a physical framework for the semiempirical Baumbach-Allen formula and quantifies the temperature ranges and degree of hydrostaticity of the K, L, and F coronae.

Deriving solar X ray irradiance from Yohkoh observations

The soft X ray telescope (SXT) on Yohkoh produces calibrated images which are used to derive X ray irradiance and coronal temperature. In this paper we compute the mean temperature and spectral irradiance for 25 coronal differential emission measure (DEM) models ranging from very quiet solar conditions to the main phase of large flares. These results are compared to what would have been derived from an SXT observation of the solar conditions represented by the DEM models. After applying an empirical correction algorithm, derived as part of this work, 24 of 25 SXT filter‐ratio temperatures fall within 0.1 in log10(T) of the mean DEM temperatures. The irradiance error depends both on the chosen spectral band and the spectrum, here represented by a single plasma temperature. As expected, the irradiance is more accurate and less sensitive to spectrum for bands that match the band pass of the sensor. Even a crude color temperature approximation to the coronal X ray spectrum greatly improves the accuracy of derived radiance over values derived for an assumed temperature of 3 × 106 K: the mean temperature of all DEM. An RMS improvement of a factor of 12–17 was found for the cases studied. For two bands, which match the sensor band pass, the RMS accuracy is better than 10%. Yohkoh X ray irradiance data, converted with SXT color temperatures, will be placed in the National Geophysical Data Center for use by the solar and atmospheric physics communities.

Coronal temperature diagnostics from high-resolution soft X-ray spectra

The Flat Crystal Spectrometer (FCS) on the Solar Maximum Mission has accumulated over 300 spectral atlas scans of the soft X-ray spectrum (1.4 to 23Å). We present here the results of a study which compares these data with theoretical predictions of the relative intensities of some of the brighter lines to determine which line intensity ratios give the most reliable temperature diagnostics for the coronal plasma. The soft X-ray spectrum contains a vast selection of bright lines formed by a variety of elements and their various ionisation stages. The atomic physics is comparatively well understood, since these transitions originate from ions stripped of most of their electrons (e.g, H-like and He-like ions, which dominate this part of the spectrum). For this reason, soft X-ray lines are often used to characterise the temperature and emission measure of the coronal plasma. The purpose of this study is to investigate how accurately and consistently the temperature of the coronal plasma can be derived from soft X-ray spectra. For derivation of coronal temperatures, the plasma is often assumed to be isothermal, sometimes even for flares! While this is a convenient assumption, a full differential emission measure model is the best way of representing the distribution of temperatures in the plasma. Unfortunately, it is not always possible to get enough data to calculate a differential emission model. Using these data, we investigate under what circumstances the isothermal assumption becomes invalid. However, we find that the accuracy of the atomic data and the measured elemental abundances limit the interpretation of the observations.