687 research outputs found

    Consimilarity and quaternion matrix equations AX−X^B=CAX-\hat{X}B=C, X−AX^B=CX-A\hat{X}B=C

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    L.Huang [Linear Algebra Appl. 331 (2001) 21-30] gave a canonical form of a quaternion matrix AA with respect to consimilarity transformations S~−1AS\tilde{S}^{-1}AS in which SS is a nonsingular quaternion matrix and h~:=a−bi+cj−dk\tilde{h}:=a-bi+cj-dk for each quaternion h=a+bi+cj+dkh=a+bi+cj+dk. We give an analogous canonical form of a quaternion matrix with respect to consimilarity transformations S^−1AS\hat{S}^{-1}AS in which h↦h^h\mapsto\hat{h} is an arbitrary involutive automorphism of the skew field of quaternions. We apply the obtained canonical form to the quaternion matrix equations AX−X^B=CAX-\hat{X}B=C and X−AX^B=CX-A\hat{X}B=C

    Signatures of Steady Heating in Time Lag Analysis of Coronal Emission

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    Among the many ways of investigating coronal heating, the time lag method of Viall & Klimchuk (2012) is becoming increasingly prevalent as an analysis technique complementary to those traditionally used. The time lag method cross correlates light curves at a given spatial location obtained in spectral bands that sample different temperature plasmas. It has been used most extensively with data from the Atmospheric Imaging Assembly on the Solar Dynamics Observatory. We have previously applied the time lag method to entire active regions and surrounding quiet Sun and create maps of the results (Viall & Klimchuk 2012; Viall & Klimchuk 2015). We find that the majority of time lags are consistent with the cooling of coronal plasma that has been impulsively heated. Additionally, a significant fraction of the map area has a time lag of zero. This does not indicate a lack of variability. Rather, strong variability must be present, and it must occur in phase in the different channels. We have shown previously that these zero time lags are consistent with the transition region response to coronal nanoflares (Viall & Klimchuk 2015; Bradshaw & Viall 2016), but other explanations are possible. A common misconception is that the zero time lag indicates steady emission resulting from steady heating. Using simulated and observed light curves, we demonstrate here that highly correlated light curves at zero time lag are not compatible with equilibrium solutions. Such light curves can only be created by evolution.Comment: 10 pages, 3 figures. Accepted to ApJ July 5 201

    Are Chromospheric Nanoflares a Primary Source of Coronal Plasma?

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    It has been suggested that the hot plasma of the solar corona comes primarily from impulsive heating events, or nanoflares, that occur in the lower atmosphere, either in the upper part of the ordinary chromosphere or at the tips of type II spicules. We test this idea with a series of hydrodynamic simulations. We find that synthetic Fe XII (195) and Fe XIV (274) line profiles generated from the simulations disagree dramatically with actual observations. The integrated line intensities are much too faint; the blue shifts are much too fast; the blue-red asymmetries are much too large; and the emission is confined to low altitudes. We conclude that chromospheric nanoflares are not a primary source of hot coronal plasma. Such events may play an important role in producing the chromosphere and powering its intense radiation, but they do not, in general, raise the temperature of the plasma to coronal values. Those cases where coronal temperatures are reached must be relatively uncommon. The observed profiles of Fe XII and Fe XIV come primarily from plasma that is heated in the corona itself, either by coronal nanoflares or a quasi-steady coronal heating process. Chromospheric nanoflares might play a role in generating waves that provide this coronal heating.Comment: 14 pages, 6 figures, accepted by Astrophysical Journa

    A nanoflare based cellular automaton model and the observed properties of the coronal plasma

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    We use the cellular automaton model described in L\'opez Fuentes \& Klimchuk (2015, ApJ, 799, 128) to study the evolution of coronal loop plasmas. The model, based on the idea of a critical misalignment angle in tangled magnetic fields, produces nanoflares of varying frequency with respect to the plasma cooling time. We compare the results of the model with active region (AR) observations obtained with the Hinode/XRT and SDO/AIA instruments. The comparison is based on the statistical properties of synthetic and observed loop lightcurves. Our results show that the model reproduces the main observational characteristics of the evolution of the plasma in AR coronal loops. The typical intensity fluctuations have an amplitude of 10 to 15\% both for the model and the observations. The sign of the skewness of the intensity distributions indicates the presence of cooling plasma in the loops. We also study the emission measure (EM) distribution predicted by the model and obtain slopes in log(EM) versus log(T) between 2.7 and 4.3, in agreement with published observational values.Comment: Paper 2 of 2: Model comparison with observations. Accepted for publication in Ap
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