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We present the SWAP Filter: an azimuthally varying, radial normalizing filter specifically developed for EUV images of the solar corona. We discuss the origins of our technique, its implementation and key user-configurable parameters, and highlight its effects on data via a series of examples. We discuss the filter's strengths in a data environment in which wide field-of-view observations that specifically target the low signal-to-noise middle corona are newly available and expected to grow in the coming years.

The Sun Watcher with Active Pixels and Image Processing (SWAP) instrument onboard ESA’s PRoject for On Board Autonomy 2 (PROBA2) has provided the first uncompressed, high-cadence, continuous, large field-of-view observations of the extended extreme-ultraviolet (EUV) corona for over a complete solar cycle. It has helped shape our understanding of this previously understudied region, and pioneered research into the middle corona. In this article, we present a review of all publications that have utilized these observations to explore the extended EUV corona, highlighting the unique contributions made by SWAP. The review is broadly divided into three main sections of SWAP-based studies about: i) long-lived phenomena, such as streamers, pseudo-streamers, and coronal fans; ii) dynamic phenomena, such as eruptions, jets, EUV waves, and shocks; iii) coronal EUV emission generation. We also highlight SWAP’s imaging capabilities, techniques that have been applied to observations to enhance the off-limb observations and its legacy.

These dark blemishes on stars are key to understanding the interaction of strong magnetic fields and dynamic plasma.

We observed the 2 July 2019 total solar eclipse with a variety of imaging and spectroscopic instruments recording from three sites in mainland Chile: on the centerline at La Higuera, from the Cerro Tololo Inter-American Observatory, and from La Serena, as well as from a chartered flight at peak totality in mid-Pacific. Our spectroscopy monitored Fe X, Fe XIV, and Ar X lines, and we imaged Ar X with a Lyot filter adjusted from its original H-alpha bandpass. Our composite imaging has been compared with predictions based on modeling using magnetic-field measurements from the pre-eclipse month. Our time-differenced sites will be used to measure motions in coronal streamers.

We investigate the effects of the evolutionary processes in the internal magnetic structure of two interplanetary coronal mass ejections (ICMEs) detected in situ between 2020 November 29 and December 1 by the Parker Solar Probe (PSP). The sources of the ICMEs were observed remotely at the Sun in EUV and subsequently tracked to their coronal counterparts in white light. This period is of particular interest to the community as it has been identified as the first widespread solar energetic particle event of solar cycle 25. The distribution of various solar and heliospheric-dedicated spacecraft throughout the inner heliosphere during PSP observations of these large-scale magnetic structures enables a comprehensive analysis of the internal evolution and topology of such structures. By assembling different models and techniques, we identify the signatures of interaction between the two consecutive ICMEs and the implications for their internal structure. We use multispacecraft observations in combination with a remote-sensing forward modeling technique, numerical propagation models, and in situ reconstruction techniques. The outcome, from the full reconciliations, demonstrates that the two coronal mass ejections (CMEs) are interacting in the vicinity of the PSP. Thus, we identify the in situ observations based on the physical processes that are associated with the interaction and collision of both CMEs. We also expand the flux rope modeling and in situ reconstruction technique to incorporate the aging and expansion effects in a distorted internal magnetic structure and explore the implications of both effects in the magnetic configuration of the ICMEs.

Context.The Extreme Ultraviolet Imager (EUI) is part of the remote sensing instrument package of the ESA/NASA Solar Orbiter mission that will explore the inner heliosphere and observe the Sun from vantage points close to the Sun and out of the ecliptic. Solar Orbiter will advance the “connection science” between solar activity and the heliosphere.Aims.With EUI we aim to improve our understanding of the structure and dynamics of the solar atmosphere, globally as well as at high resolution, and from high solar latitude perspectives.Methods.The EUI consists of three telescopes, the Full Sun Imager and two High Resolution Imagers, which are optimised to image in Lyman-αand EUV (17.4 nm, 30.4 nm) to provide a coverage from chromosphere up to corona. The EUI is designed to cope with the strong constraints imposed by the Solar Orbiter mission characteristics. Limited telemetry availability is compensated by state-of-the-art image compression, onboard image processing, and event selection. The imposed power limitations and potentially harsh radiation environment necessitate the use of novel CMOS sensors. As the unobstructed field of view of the telescopes needs to protrude through the spacecraft’s heat shield, the apertures have been kept as small as possible, without compromising optical performance. This led to a systematic effort to optimise the throughput of every optical element and the reduction of noise levels in the sensor.Results.In this paper we review the design of the two elements of the EUI instrument: the Optical Bench System and the Common Electronic Box. Particular attention is also given to the onboard software, the intended operations, the ground software, and the foreseen data products.Conclusions.The EUI will bring unique science opportunities thanks to its specific design, its viewpoint, and to the planned synergies with the other Solar Orbiter instruments. In particular, we highlight science opportunities brought by the out-of-ecliptic vantage point of the solar poles, the high-resolution imaging of the high chromosphere and corona, and the connection to the outer corona as observed by coronagraphs.

We use The Sun Watcher with Active Pixel System detector and Image Processing (SWAP) imager onboard the Project for Onboard Autonomy 2 (PROBA2) mission to study the evolution of large-scale EUV structures in the solar corona observed throughout Solar Cycle 24 (from 2010 to 2019). We discuss the evolution of the on-disk coronal features and at different heights above the solar surface based on EUV intensity changes. We also look at the evolution of the corona in equatorial and polar regions and compare them at different phases of the solar cycle, as well as with sunspot number evolution and with the PROBA2/Lyman-Alpha Radiometer (LYRA) signal. The main results are as follows: The three time series (SWAP on-disk average brightness, sunspot number and LYRA irradiance) are very well correlated, with correlation coefficients around 0.9. The average rotation rate of bright features at latitudes of +15, 0, and -15 degrees was around 15 degree/day throughout the period studied. A secondary peak in EUV averaged intensity at the Poles was observed on the descending phase of SC24. These peaks (at North and South poles respectively) seem to be associated with the start of the development of the (polar) coronal holes. Large-scale off-limb structures were visible from around March 2010 to around March 2016, meaning that they were absent at the minimum phase of solar activity. A fan at the North pole persisted for more than 11 Carrington rotations (February 2014 to March 2015), and it could be seen up to altitudes of 1.6 Rs.

Most space weather phenomena originate in the solar atmosphere. To ensure forecasters have access to the most up-to-date information about solar conditions that can influence space weather, the Solar Ultraviolet Imager (SUVI) on the Geostationary Operational Environmental Satellites (GOES)-R Series observes the Sun’s chromosphere and corona in six extreme ultraviolet passbands, 94, 131, 171, 195, 284, and 304 A. SUVI observations reveal layers of the corona with temperatures between about 50,000 and 10 million K. SUVI observations are used to identify coronal holes, the quiet sun, filaments and prominences, active regions and solar flares. These phenomena are linked to fast solar wind streams, solar eruptions, and outbursts of energetic particles and electromagnetic radiation that can disrupt technological systems on Earth and in near-Earth space. SUVI images also support the generation of a variety of products that help track dynamic activity in the corona and generate thematic maps of phenomena that could influence space weather.

Between 4 and 10 September 2017, multiple solar eruptions occurred from active region AR12673. NOAA and NASA’s well-instrumented spacecraft observed the evolution of these geoeffective events from ...

The GOES-R series is the latest in a long line of American geostationary weather satellites operated by NOAA (National Oceanic and Atmospheric Administration). The Solar Ultraviolet Imager (SUVI) is an instrument onboard Geostationary Operational Environmental Satellites, GOES-R series, part of NOAA's (National Oceanic and Atmospheric Administration) space weather monitoring fleet. GOES-16 SUVI is in operation and the GOES-17 SUVI has completed initial calibrations. SUVI is a generalized Cassegrain telescope with a large field of view that employs multilayer coatings optimized to operate in six extreme ultraviolet (EUV) narrow bandpasses centered at 9.4, 13.1, 17.1, 19.5, 28.4 and 30.4 nm. The SUVI EUV line set provides the best comprehensive feature and dynamics information for revealing and correlating both the low coronal signatures of coronal mass ejections (CME) triggers (for example, flares) and the high coronal signatures of the actual CME. SUVI acquires full disk images in EUV band pass every few minutes and telemeters the data to the ground for digital processing. These data will enable NOAA to monitor solar activity and to issue accurate near real-time alerts when space weather may possibly affect the performance and reliability of space-borne and ground-based technological systems and human endeavors. This paper describes key design drivers in the development of SUVI, methods used in the autonomous on-orbit calibration of the instrument, and the automated monitoring of the health and safety of the instrument during operations.

We investigate the coronal imaging capabilities of the Solar UltraViolet Imager (SUVI) on board the Geostationary Operational Environmental Satellite-R series spacecraft. Nominally Sun-pointed, SUVI provides solar images in six extreme ultraviolet (EUV) wavelengths. On-orbit data indicated that SUVI had sufficient dynamic range and sensitivity to image the corona to the largest heights above the Sun to date while simultaneously imaging the Sun. We undertook a campaign to investigate the existence of the EUV signal well beyond the nominal Sun-centered imaging area of the solar EUV imagers. We off-pointed the SUVI line of sight by almost one imaging area around the Sun. We present the details of the campaign we conducted when the solar cycle was at near the minimum and some results that confirm that EUV emission is present to beyond three solar radii.

The Sun Coronal Ejection Tracker (SunCET) is an extreme ultraviolet imager and spectrograph instrument concept for tracking coronal mass ejections through the region where they experience the majority of their acceleration: the difficult-to-observe middle corona. It contains a wide field of view (0–4 R⊙) imager and a 1 Å spectral-resolution-irradiance spectrograph spanning 170–340 Å. It leverages new detector technology to read out different areas of the detector with different integration times, resulting in what we call “simultaneous high dynamic range”, as opposed to the traditional high dynamic range camera technique of subsequent full-frame images that are then combined in post-processing. This allows us to image the bright solar disk with short integration time, the middle corona with a long integration time, and the spectra with their own, independent integration time. Thus, SunCET does not require the use of an opaque or filtered occulter. SunCET is also compact – ~15 × 15 × 10 cm in volume – making it an ideal instrument for a CubeSat or a small, complementary addition to a larger mission. Indeed, SunCET is presently in a NASA-funded, competitive Phase A as a CubeSat and has also been proposed to NASA as an instrument onboard a 184 kg Mission of Opportunity.

We present composite white-light images of the 2019 July 2, total solar eclipse, from the minimum of the solar-activity cycle. We exhibit high-resolution high dynamic range composites from three observation sites in Chile, including one made of 646 individual ground-based images and with such a wide field it exceeds the field of view of the Naval Research Laboratory's C2 and C3 coronagraphs aboard ESA's Solar and Heliospheric Observatory. We compare the resolution of the coronal streamers and other magnetic phenomena of the corona. We also show continuity of features on the solar surface as observed from NOAA's GOES-16 and GOES-17 Solar Ultraviolet Imager.

Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models., 29 pages, 11 figures, accepted for publication in Space Science Reviews

Context: ASPIICS is a novel externally occulted solar coronagraph, which will be launched onboard the PROBA-3 mission of the European Space Agency. The external occulter will be placed on the first satellite approximately 150 m ahead of the second satellite that will carry an optical instrument. During 6 hours per orbit, the satellites will fly in a precise formation, constituting a giant externally occulted coronagraph. Large distance between the external occulter and the primary objective will allow observations of the white-light solar corona starting from extremely low heights 1.1RSun. Aims: To analyze influence of optical ghost images formed inside the telescope and develop an algorithm for their removal. Methods: We implement the optical layout of ASPIICS in Zemax and study the ghost behaviour in sequential and non-sequential regimes. We identify sources of the ghost contributions and analyze their geometrical behaviour. Finally we develop a mathematical model and software to calculate ghost images for any given input image. Results: We show that ghost light can be important in the outer part of the field of view, where the coronal signal is weak, since the energy of bright inner corona is redistributed to the outer corona. However the model allows to remove the ghost contribution. Due to a large distance between the external occulter and the primary objective, the primary objective does not produce a significant ghost. The use of the Lyot spot in ASPIICS is not necessary., Comment: 14 pages, 13 figures

We present observations of a powerful solar eruption, accompanied by an X8.2 solar flare, from NOAA Active Region 12673 on 2017 September 10 by the Solar Ultraviolet Imager (SUVI) on the GOES-16 spacecraft. SUVI is noteworthy for its relatively large field of view, which allows it to image solar phenomena to heights approaching 2 solar radii. These observations include the detection of an apparent current sheet associated with magnetic reconnection in the wake of the eruption and evidence of an extreme-ultraviolet wave at some of the largest heights ever reported. We discuss the acceleration of the nascent coronal mass ejection to approximately 2000 km/s at about 1.5 solar radii. We compare these observations with models of eruptions and eruption-related phenomena. We also describe the SUVI data and discuss how the scientific community can access SUVI observations of the event., Supplementary online material for several channels can be found under the event_movies directory in each of the channel directories via this: https://data.ngdc.noaa.gov/platforms/solar-space-observing-satellites/goes/goes16/l1b/

The PROBA2 mission has been launched on 2nd November2009 with a Rockot launcher to a Sunsynchronous orbit at an altitude of 725 km. Its nominal operation duration is two years with possible extension of 2 years. PROBA2 is a small satellite developed under an ESA General Support Technology Program (GSTP) contract to perform an in-flight demonstration of new space technologies and support a scientific mission for a set of selected instruments. The mission is tracked by the ESA Redu Mission Operation Center.

© 2017 E. D'Huys et al., Published by EDP Sciences. On August 14, 2010 a wide-angled coronal mass ejection (CME) was observed. This solar eruption originated from a destabilized filament that connected two active regions and the unwinding of this filament gave the eruption an untwisting motion that drew the attention of many observers. In addition to the erupting filament and the associated CME, several other low-coronal signatures that typically indicate the occurrence of a solar eruption were associated with this event. However, contrary to what was expected, the fast CME (v > 900 km s-1) was accompanied by only a weak C4.4 flare. We investigate the various eruption signatures that were observed for this event and focus on the kinematic evolution of the filament in order to determine its eruption mechanism. Had this solar eruption occurred just a few days earlier, it could have been a significant event for space weather. The risk of underestimating the strength of this eruption based solely on the C4.4 flare illustrates the need to include all eruption signatures in event analyses in order to obtain a complete picture of a solar eruption and assess its possible space weather impact. ispartof: Journal of Space Weather and Space Climate vol:7 status: published

In order to utilize solar imagery for real-time feature identification and large-scale data science investigations of solar structures, we need maps of the Sun where phenomena, or themes, are labeled. Since solar imagers produce observations every few minutes, it is not feasible to label all images by hand. Here, we compare three machine learning algorithms performing solar image classification using Extreme Ultraviolet (EUV) and Hα images: a maximum likelihood model assuming a single normal probability distribution for each theme from Rigler et al. (2012) [Space Weather 10(8): 1–16], a maximum-likelihood model with an underlying Gaussian mixtures distribution, and a random forest model. We create a small database of expert-labeled maps to train and test these algorithms. Due to the ambiguity between the labels created by different experts, a collaborative labeling is used to include all inputs. We find the random forest algorithm performs the best amongst the three algorithms. The advantages of this algorithm are best highlighted in: comparison of outputs to hand-drawn maps; response to short-term variability; and tracking long-term changes on the Sun. Our work indicates that the next generation of solar image classification algorithms would benefit significantly from using spatial structure recognition, compared to only using spectral, pixel-by-pixel brightness distributions.

We calculated the temperature response of the 171 A passbands of the Sun Watcher using APS detectors and image Processing (SWAP) instrument onboard the PRoject for OnBoard Autonomy 2 (PROBA2) satellite. These results were compared to the temperature responses of the Extreme Ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO), the Transition Region and Coronal Explorer (TRACE), the twin Extreme Ultraviolet Imagers (EUVI) onboard the Solar TErrestrial RElations Observatory (STEREO) A and B spacecraft, and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). Multiplying the wavelength-response functions for each instrument by a series of isothermal synthetic spectra and integrating over the range 165 – 195 A produced temperature-response functions for the six instruments. Each temperature response was then multiplied by sample differential emission-measure functions for four different solar conditions. For any given plasma condition (e.g. quiet Sun, active region), it was found that the overall variation with temperature agreed remarkably well across the six instruments, although the wavelength responses for each instrument have some distinctly different features. Deviations were observed, however, when we compared the response of any one instrument to different solar conditions, particularly for the case of solar flares.

International audience; We present the lessons learned about the degradation observed in several space solar missions, based on contributions at the Workshop about On-Orbit Degradation of Solar and Space Weather Instruments that took place at the Solar Terrestrial Centre of Excellence (Royal Observatory of Belgium) in Brussels on 3 May 2012. The aim of this workshop was to open discussions related to the degradation observed in Sun-observing instruments exposed to the effects of the space environment. This article summarizes the various lessons learned and offers recommendations to reduce or correct expected degradation with the goal of increasing the useful lifespan of future and ongoing space missions.

Many natural processes exhibit power-law behavior. The power-law exponent is linked to the underlying physical process and therefore its precise value is of interest. With respect to the energy content of nanoflares, for example, a power-law exponent steeper than 2 is believed to be a necessary condition to solve the enigmatic coronal heating problem. Studying power-law distributions over several orders of magnitudes requires sufficient data and appropriate methodology. In this paper we demonstrate the shortcomings of some popular methods in solar physics that are applied to data of typical sample sizes. We use synthetic data to study the effect of the sample size on the performance of different estimation methods and show that vast amounts of data are needed to obtain a reliable result with graphical methods (where the power-law exponent is estimated by a linear fit on a log-transformed histogram of the data). We revisit published results on power laws for the angular width of solar coronal mass ejections and the radiative losses of nanoflares. We demonstrate the benefits of the maximum likelihood estimator and advocate its use.

The statistical examination of solar flares is crucial to revealing their global characteristics and behaviour. Such examinations can tackle large-scale science questions or give context to detailed single-event studies. However, they are often performed using standard but basic flare detection algorithms relying on arbitrary thresholds. This arbitrariness may lead to important scientific conclusions being drawn from results caused by subjective choices in algorithms rather than the true nature of the Sun. In this paper, we explore the effect of the arbitrary thresholds used in the GOES (Geostationary Operational Environmental Satellite) event list and LYRA (Large Yield RAdiometer) Flare Finder algorithms. We find that there is a small but significant relationship between the power law exponent of the GOES flare peak flux frequency distribution and the flare start thresholds of the algorithms. We also find that the power law exponents of these distributions are not stable, but appear to steepen with increasing peak flux. This implies that the observed flare size distribution may not be a power law at all. We show that depending on the true value of the exponent of the flare size distribution, this deviation from a power law may be due to flares missed by the flare detection algorithms. However, it is not possible determine the true exponent from GOES/XRS observations. Additionally we find that the PROBA2/LYRA flare size distributions are artificially steep and clearly non-power law. We show that this is consistent with an insufficient degradation correction. This means that PROBA2/LYRA should not be used for flare statistics or energetics unless degradation is adequately accounted for. However, it can be used to study variations over shorter timescales and for space weather monitoring., Comment: 14 pages, 8 figures, 1 table

We present AIA observations of a structure we interpret as a current sheet associated with an X4.9 flare and coronal mass ejection that occurred on 2014~February~25 in NOAA Active Region 11990. We characterize the properties of the current sheet, finding that the sheet remains on the order of a few thousand km thick for much of the duration of the event and that its temperature generally ranged between $8-10\,\mathrm{MK}$. We also note the presence of other phenomena believed to be associated with magnetic reconnection in current sheets, including supra-arcade downflows and shrinking loops. We estimate that the rate of reconnection during the event was $M_{A} \approx 0.004-0.007$, a value consistent with model predictions. We conclude with a discussion of the implications of this event for reconnection-based eruption models., Comment: Animation accompanying Figure 2 available at https://figshare.com/articles/SDO_AIA_131_2014-Feb-25_Current_Sheet/4052061

The \textit{Sun Watcher using Active Pixel system detector and Image Processing}(SWAP) on board the \textit{PRoject for OnBoard Autonomy\todash 2} (PROBA\todash 2) spacecraft provides images of the solar corona in EUV channel centered at 174 \AA. These data, together with \textit{Atmospheric Imaging Assembly} (AIA) and the \textit{Helioseismic and Magnetic Imager} (HMI) on board \textit{Solar Dynamics Observatory} (SDO), are used to study the dynamics of coronal bright points. The evolution of the magnetic polarities and associated changes in morphology are studied using magnetograms and multi-wavelength imaging. The morphology of the bright points seen in low-resolution SWAP images and high-resolution AIA images show different structures, whereas the intensity variations with time show similar trends in both SWAP 174 and AIA 171 channels. We observe that bright points are seen in EUV channels corresponding to a magnetic-flux of the order of $10^{18}$ Mx. We find that there exists a good correlation between total emission from the bright point in several UV\todash EUV channels and total unsigned photospheric magnetic flux above certain thresholds. The bright points also show periodic brightenings and we have attempted to find the oscillation periods in bright points and their connection to magnetic flux changes. The observed periods are generally long (10\todash 25 minutes) and there is an indication that the intensity oscillations may be generated by repeated magnetic reconnection.

Observations of the early rise and propagation phases of solar eruptive prominences can provide clues about the forces acting on them through the behavior of their acceleration with height. We have analyzed such an event, observed on 13 April 2010 by SWAP on PROBA2 and EUVI on STEREO. A feature at the top of the erupting prominence was identified and tracked in images from the three spacecraft. The triangulation technique was used to derive the true direction of propagation of this feature. The reconstructed points were fitted with two mathematical models: i) a power-law polynomial function and ii) a cubic smoothing spline, in order to derive the accelerations. The first model is characterized by five degrees of freedom while the second one is characterized by ten degrees of freedom. The results show that the acceleration increases smoothly and it is continuously increasing with height. We conclude that the prominence is not accelerated immediately by local reconnection but rather is swept away as part of a large-scale relaxation of the coronal magnetic field., 15 Pages, Accepted for publication in Solar Physics, PROBA2 Topical Issue

The existence of coronal plasmoids has been postulated for many years in order to supply material to streamers and possibly to the solar wind (SW). The W-L SoHO C2 Lasco coronagraph observations were made under the 2.2 solar radii (R0) occulting disk to look at the ultimate sources of the SW; EUV imagers are preferably devoted to the analysis of the corona on and very near the solar disk. Here, in addition to eclipse white-light (W-L) snapshots, we used the new SWAP space-borne imager designed for the systematic survey of coronal activity in the EUV lines near 17.4 nm, over a field of view (FOV) up to 2 R0. Using summed and co-aligned images, the corona can then be evaluated for the 1st time up to the limit of this FOV. At the time of the July 11, 2010, solar total eclipse a 20h continuous run of observations was collected, including images taken during eclipse totality from several ground observing locations where W-L data were collected. A plasmoid-like off-limb event was followed using the SWAP summed

Using a recently developed analytical procedure, we determine the rate of magnetic reconnection in the "standard" model of eruptive solar flares. During the late phase, the neutral line is located near the lower tip of the reconnection current sheet, and the upper region of the current sheet is bifurcated into a pair of Petschek-type shocks. Despite the presence of these shocks, the reconnection rate remains slow if the resistivity is uniform and the flow is laminar. Fast reconnection is achieved only if there is some additional mechanism that can shorten the length of the diffusion region at the neutral line. Observations of plasma flows by the X-Ray Telescope (XRT) on Hinode imply that the diffusion region is in fact quite short. Two possible mechanisms for reducing the length of the diffusion region are localized resistivity and MHD turbulence.

We develop a model that predicts the velocity, density, and temperature of coronal reconnection jets in the presence of thermal conduction. Our model is based on the quasi-one-dimensional treatment of reconnecting current sheets developed by B. Somov and V. S. Titov using the magnetohydrodynamics nozzle equations. We incorporate thermal conduction into the Somov-Titov framework using slow-shock jump conditions modified to include losses due the conduction of thermal energy along field lines mapping to the chromosphere. We find that thermal conduction has a significant effect on the fast-mode Mach number of the reconnection outflow, producing Mach numbers possibly as high as 7 for some solar-flare conditions. This value is three times greater than previously calculated. We conclude that these termination shocks are considerably more efficient at producing particle acceleration than previously thought since the efficiency of particle acceleration at shocks increases dramatically with Mach number. We compare this model with numerical simulations by T. Yokoyama and K. Shibata and find good agreement.