166 research outputs found
Measuring X-ray anisotropy in solar flares. Prospective stereoscopic capabilities of STIX and MiSolFA
During the next solar maximum, two upcoming space-borne X-ray missions, STIX
on board Solar Orbiter and MiSolFA, will perform stereoscopic X-ray
observations of solar flares at two different locations: STIX at 0.28 AU (at
perihelion) and up to inclinations of , and MiSolFA in a
low-Earth orbit. The combined observations from these cross-calibrated
detectors will allow us to infer the electron anisotropy of individual flares
confidently for the first time. We simulated both instrumental and physical
effects for STIX and MiSolFA including thermal shielding, background and X-ray
Compton backscattering (albedo effect) in the solar photosphere. We predict the
expected number of observable flares available for stereoscopic measurements
during the next solar maximum. We also discuss the range of useful spacecraft
observation angles for the challenging case of close-to-isotropic flare
anisotropy. The simulated results show that STIX and MiSolFA will be capable of
detecting low levels of flare anisotropy, for M1-class or stronger flares, even
with a relatively small spacecraft angular separation of 20-30{\deg}. Both
instruments will directly measure the flare X-ray anisotropy of about 40 M- and
X-class solar flares during the next solar maximum. Near-future stereoscopic
observations with Solar Orbiter/STIX and MiSolFA will help distinguishing
between competing flare-acceleration mechanisms, and provide essential
constraints regarding collisional and non-collisional transport processes
occurring in the flaring atmosphere for individual solar flares
Positions and sizes of X-ray solar flare sources
<p><b>Aims:</b> The positions and source sizes of X-ray sources taking into account Compton backscattering (albedo) are investigated.</p>
<p><b>Methods:</b> Using a Monte Carlo simulation of X-ray photon transport including photo-electric absorption and Compton scattering, we calculate the apparent source sizes and positions of X-ray sources at the solar disk for various source sizes, spectral indices and directivities of the primary source.</p>
<p><b>Results:</b> We show that the albedo effect can alter the true source positions and substantially increase the measured source sizes. The source positions are shifted by up to ~0.5” radially towards the disk centre and 5 arcsec source sizes can be two times larger even for an isotropic source (minimum albedo effect) at 1 Mm above the photosphere. The X-ray sources therefore should have minimum observed sizes, and thus their FWHM source size (2.35 times second-moment) will be as large as ~7” in the 20-50 keV range for a disk-centered point source at a height of 1 Mm (~1.4”) above the photosphere. The source size and position change is greater for flatter primary X-ray spectra, a stronger downward anisotropy, for sources closer to the solar disk centre, and between the energies of 30 and 50 keV.</p>
<p><b>Conclusions:</b> Albedo should be taken into account when X-ray footpoint positions, footpoint motions or source sizes from e.g. RHESSI or Yohkoh data are interpreted, and we suggest that footpoint sources should be larger in X-rays than in either optical or EUV ranges.</p>
Numerical simulations of chromospheric hard X-ray source sizes in solar flares
X-ray observations are a powerful diagnostic tool for transport,
acceleration, and heating of electrons in solar flares. Height and size
measurements of X-ray footpoints sources can be used to determine the
chromospheric density and constrain the parameters of magnetic field
convergence and electron pitch-angle evolution. We investigate the influence of
the chromospheric density, magnetic mirroring and collisional pitch-angle
scattering on the size of X-ray sources. The time-independent Fokker-Planck
equation for electron transport is solved numerically and analytically to find
the electron distribution as a function of height above the photosphere. From
this distribution, the expected X-ray flux as a function of height, its peak
height and full width at half maximum are calculated and compared with RHESSI
observations. A purely instrumental explanation for the observed source size
was ruled out by using simulated RHESSI images. We find that magnetic mirroring
and collisional pitch-angle scattering tend to change the electron flux such
that electrons are stopped higher in the atmosphere compared with the simple
case with collisional energy loss only. However, the resulting X-ray flux is
dominated by the density structure in the chromosphere and only marginal
increases in source width are found. Very high loop densities (>10^{11}
cm^{-3}) could explain the observed sizes at higher energies, but are
unrealistic and would result in no footpoint emission below about 40 keV,
contrary to observations. We conclude that within a monolithic density model
the vertical sizes are given mostly by the density scale-height and are
predicted smaller than the RHESSI results show.Comment: 19 pages, 9 figures, accepted for publication in Ap
Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop
<p><b>Aims:</b> A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to infer sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density.</p>
<p><b>Methods:</b> Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and centroid positions of hard X-ray sources with sub-arcsecond resolution (~0.2'') for a solar limb flare. We show that the height variations of the chromospheric density and the magnetic flux densities can be found with an unprecedented vertical resolution of ~150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km.</p>
<p><b>Results:</b> Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tubes in the chromosphere with height. The magnetic scale height B(z)(dB/dz)-1 is found to be of the order of 300 km and a strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of ~900 km.</p>
On the variation of solar flare coronal x-ray source sizes with energy
Observations with {\em RHESSI} have enabled the detailed study of the
structure of dense hard X-ray coronal sources in solar flares. The variation of
source extent with electron energy has been discussed in the context of
streaming of non-thermal particles in a one-dimensional cold-target model, and
the results used to constrain both the physical extent of, and density within,
the electron acceleration region. Here we extend this investigation to a more
physically realistic model of electron transport that takes into account the
finite temperature of the ambient plasma, the initial pitch-angle distribution
of the accelerated electrons, and the effects of collisional pitch-angle
scattering. The finite temperature results in the thermal diffusion of
electrons, that leads to the observationally-inferred value of the acceleration
region volume being an overestimate of its true value. The different directions
of the electron trajectories, a consequence of both the non-zero injection
pitch-angle and scattering within the target, cause the projected propagation
distance parallel to the guiding magnetic field to be reduced, so that a
one-dimensional interpretation can overestimate the actual density by a factor
of up to . The implications of these results for the determination of
acceleration region properties (specific acceleration rate, filling factor,
etc.) are discussed.Comment: 45 pages, 9 figures, accepted for publication in Ap
Local re-acceleration and a modified thick target model of solar flare electrons
The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts
has become an almost 'Standard Model' of flare impulsive phase energy transport
and radiation. However, it faces various problems in the light of recent data,
particularly the high electron beam density and anisotropy it involves.} {We
consider how photon yield per electron can be increased, and hence fast
electron beam intensity requirements reduced, by local re-acceleration of fast
electrons throughout the HXR source itself, after injection.} {We show
parametrically that, if net re-acceleration rates due to e.g. waves or local
current sheet electric () fields are a significant fraction of
collisional loss rates, electron lifetimes, and hence the net radiative HXR
output per electron can be substantially increased over the CTTM values. In
this local re-acceleration thick target model (LRTTM) fast electron number
requirements and anisotropy are thus reduced. One specific possible scenario
involving such re-acceleration is discussed, viz, a current sheet cascade (CSC)
in a randomly stressed magnetic loop.} {Combined MHD and test particle
simulations show that local fields in CSCs can efficiently
accelerate electrons in the corona and and re-accelerate them after injection
into the chromosphere. In this HXR source scenario, rapid synchronisation and
variability of impulsive footpoint emissions can still occur since primary
electron acceleration is in the high Alfv\'{e}n speed corona with fast
re-acceleration in chromospheric CSCs. It is also consistent with the
energy-dependent time-of-flight delays in HXR features.Comment: 8 pages, 2 figure
Collisional relaxation of electrons in a warm plasma and accelerated nonthermal electron spectra in solar flares
Extending previous studies of nonthermal electron transport in solar flares
which include the effects of collisional energy diffusion and thermalization of
fast electrons, we present an analytic method to infer more accurate estimates
of the accelerated electron spectrum in solar flares from observations of the
hard X-ray spectrum. Unlike for the standard cold-target model, the spatial
characteristics of the flaring region, especially the necessity to consider a
finite volume of hot plasma in the source, need to be taken into account in
order to correctly obtain the injected electron spectrum from the
source-integrated electron flux spectrum (a quantity straightforwardly obtained
from hard X-ray observations). We show that the effect of electron
thermalization can be significant enough to nullify the need to introduce an
{\it ad hoc} low-energy cutoff to the injected electron spectrum in order to
keep the injected power in non-thermal electrons at a reasonable value. Rather
the suppression of the inferred low-energy end of the injected spectrum
compared to that deduced from a cold-target analysis allows the inference from
hard X-ray observations of a more realistic energy in injected non-thermal
electrons in solar flares.Comment: accepted for publication in Ap
Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations
<p><b>Context:</b> A fundamental problem in astrophysics is the interaction between magnetic turbulence and charged particles. It is now possible to use Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations of hard X-rays (HXR) emitted by electrons to identify the presence of turbulence and to estimate the magnitude of the magnetic field line diffusion coefficient at least in dense coronal flaring loops.</p>
<p><b>Aims:</b> We discuss the various possible regimes of cross-field transport of non-thermal electrons resulting from broadband magnetic turbulence in coronal loops. The importance of the Kubo number K as a governing parameter is emphasized and results applicable in both the large and small Kubo number limits are collected.</p>
<p><b>Methods:</b> Generic models, based on concepts and insights developed in the statistical theory of transport, are applied to the coronal loops and to the interpretation of hard X-ray imaging data in solar flares. The role of trapping effects, which become important in the non-linear regime of transport, is taken into account in the interpretation of the data.</p>
<p><b>Results:</b> For this flaring solar loop, we constrain the ranges of parallel and perpendicular correlation lengths of turbulent magnetic fields and possible Kubo numbers. We show that a substantial amount of magnetic fluctuations with energy ~1% (or more) of the background field can be inferred from the measurements of the magnetic diffusion coefficient inside thick-target coronal loops.</p>
Fast electron slowing-down and diffusion in a high temperature coronal X-ray source
Finite thermal velocity modifications to electron slowing-down rates may be important for the deduction of solar flare total electron energy. Here we treat both slowing-down and velocity diffusion of electrons in the corona at flare temperatures, for the case of a simple, spatially homogeneous source. Including velocity diffusion yields a consistent treatment of both "accelerated" and "thermal" electrons. It also emphasises that one may not invoke finite thermal velocity target effects on electron lifetimes without simultaneously treating the contribution to the observed X-ray spectrum from thermal electrons. We present model calculations of the X-ray spectra resulting from injection of a power-law energy distribution of electrons into a source with finite temperature. Reducing the power-law distribution low-energy cutoff to lower and lower energies only increases the relative magnitude of the thermal component of the spectrum, because the lowest energy electrons simply join the background thermal distribution. Acceptable fits to RHESSI flare data are obtained using this model. These also demonstrate, however, that observed spectra may in consequence be acceptably consistent with rather a wide range of injected electron parameters
The sub-arcsecond hard X-ray structure of loop footpoints in a solar flare
The newly developed X-ray visibility forward fitting technique is applied to
Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) data of a limb
flare to investigate the energy and height dependence on sizes, shapes, and
position of hard X-ray chromospheric footpoint sources. This provides
information about the electron transport and chromospheric density structure.
The spatial distribution of two footpoint X-ray sources is analyzed using
PIXON, Maximum Entropy Method, CLEAN and visibility forward fit algorithms at
nonthermal energies from to keV. We report, for the first
time, the vertical extents and widths of hard X-ray chromospheric sources
measured as a function of energy for a limb event. Our observations suggest
that both the vertical and horizontal sizes of footpoints are decreasing with
energy. Higher energy emission originates progressively deeper in the
chromosphere consistent with downward flare accelerated streaming electrons.
The ellipticity of the footpoints grows with energy from at keV to at keV. The positions of X-ray emission are in
agreement with an exponential density profile of scale height ~km.
The characteristic size of the hard X-ray footpoint source along the limb is
decreasing with energy suggesting a converging magnetic field in the footpoint.
The vertical sizes of X-ray sources are inconsistent with simple collisional
transport in a single density scale height but can be explained using a
multi-threaded density structure in the chromosphere.Comment: 7 pages, 7 figures, submitted to Ap
- …