arXiv subjects

B. De Pontieu

Publications and source records attributed to B. De Pontieu.

At least 19 recordsLinked to original sources

arXiv2025

Coronal energy release by MHD avalanches III. Identification of a reconnection outflow from a nanoflare

Outflows perpendicular to the guide field are believed to be a possible signature of magnetic reconnection in the solar corona and specifically a way to detect the occurrence of ubiquitous small-angle magnetic reconnection. The aim of this work is to identify possible diagnostic techniques of such outflows in hot coronal loops with SDO/AIA and the forthcoming MUltislit Solar Explorer (MUSE), in a realistically dynamic coronal loop environment in which an MHD avalanche is occurring. We consider a 3D MHD model of two magnetic flux tubes, including a stratified, radiative and thermal-conducting atmosphere, twisted by footpoint rotation. The faster rotating flux tube becomes kink-unstable and soon involves the other one in the avalanche. The turbulent decay of this magnetic structure on a global scale leads to the formation, fragmentation, and dissipation of current sheets driving impulsive heating akin to a nanoflare storm. We captured a clear outflow from a reconnection episode soon after the initial avalanche and synthesized its emission as detectable with AIA and MUSE. The outflow has a maximum temperature around 8 MK, a total energy of 1024 erg, a velocity of a few hundred km/s, and a duration of less than 1 min. We show the emission in the AIA 94 A channel (Fe XVIII line) and in the MUSE 108 A Fe XIX spectral line. his outflow shares many features with nanojets recently detected at lower temperatures. Its low emission measure makes, however, its detection difficult with AIA, but Doppler shifts can be measured with MUSE. Conditions become different in a later steady state phase when the flux tubes are filled with denser and relatively cooler plasma.

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arXiv2024

Time-Adaptive PIROCK Method with Error Control for Multi-Fluid and Single-Fluid MHD Systems

The solar atmosphere is a complex environment with diverse species and varying ionization states, especially in the chromosphere, where significant ionization variations occur. This region transitions from highly collisional to weakly collisional states, leading to complex plasma state transitions influenced by magnetic strengths and collisional properties. These processes introduce numerical stiffness in multi-fluid models, imposing severe timestep restrictions on standard time integration methods. New numerical methods are essential to address these computational challenges, effectively managing the diverse timescales in multi-fluid and multi-physics models. The widely used time operator splitting technique offers a straightforward approach but requires careful timestep management to avoid stability issues and errors. Despite some studies on splitting errors, their impact on solar and stellar astrophysics is often overlooked. We focus on a Multi-Fluid Multi-Species (MFMS) model, which presents significant challenges for time integration. We propose a second-order Partitioned Implicit-Explicit Runge-Kutta (PIROCK) method that combines efficient explicit and implicit integration techniques with variable time-stepping and error control. Compared to a standard third-order explicit method and a first-order Lie splitting approach, the PIROCK method shows robust advantages in accuracy, stability, and computational efficiency. Our results reveal PIROCK's capability to solve multi-fluid problems with unprecedented efficiency. Preliminary results on chemical fractionation represent a significant step toward understanding the First-Ionization-Potential (FIP) effect in the solar atmosphere.

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arXiv2024

Coronal energy release by MHD avalanches II. EUV line emission from a multi-threaded coronal loop

MHD kink instability can trigger the fragmentation of a twisted magnetic flux tube into small-scale current sheets that dissipate as aperiodic impulsive heating events. This instability propagates as an avalanche to nearby flux tubes and leads to a nanoflare storm. Our previous work was devoted to related 3D MHD numerical modeling with a stratified and realistic atmosphere. This work addresses predictions for the EUV imaging spectroscopy of such structure and evolution of a loop, with an average temperature of 2.5 MK in the solar corona. We set a particular focus on the forthcoming MUSE mission. From the output of the numerical simulations, we synthesized the intensities, Doppler shifts, and non-thermal line broadening in 3 EUV spectral lines in the MUSE passbands: Fe IX 171A, Fe XV 284 A, and Fe XIX 108 A, at 1 MK, 2 MK, and 10 MK, respectively, according to the MUSE expected pixel size, temporal resolution, and temperature response functions. We provide maps showing different view angles and realistic spectra. Finally, we discuss the relevant evolutionary processes from the perspective of possible observations. We find that the MUSE observations might be able to detect the fine structure determined by tube fragmentation. In particular, the Fe IX line is mostly emitted at the loop footpoints, where we track the motions that drive the magnetic stressing and detect the upward motion of evaporating plasma from the chromosphere. In Fe XV, we see the bulk of the loop with increasing intensity. The Fe XIX line is very faint within the chosen simulation parameters; thus, any transient brightening around the loop apex may possibly be emphasized by the folding of sheet-like structure. In conclusion, we show that coronal loop observations with MUSE can pinpoint some crucial features of MHD-modeled ignition processes, such as the related dynamics, helping to identify the heating processes.

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arXiv2022

Multi-Fluid Simulations of Upper Chromospheric Magnetic Reconnection with Helium-Hydrogen mixture

Our understanding of magnetic reconnection (MR) under chromospheric conditions remains limited. Recent observations have demonstrated the important role of ion-neutral interactions in the dynamics of the chromosphere. Furthermore, the comparison between spectral profiles and synthetic observations of reconnection events suggest that current MHD approaches appear to be inconsistent with observations. First, collisions and multi-thermal aspects of the plasma play a role in these regions. Second, hydrogen and helium ionization effects are relevant to the energy balance of the chromosphere. This work investigates multi-fluid multi-species (MFMS) effects on MR in conditions representative of the upper chromosphere using the multi-fluid Ebysus code. We compare an MFMS approach based on a helium-hydrogen mixture with a two-fluid MHD model based on hydrogen only. The simulations of MRs are performed in a Lundquist number regime high enough to develop plasmoids and instabilities. We study the evolution of the MR and compare the two approaches including the structure of the current sheet and plasmoids, the decoupling of the particles, the evolution of the heating mechanisms, and the composition. The presence of helium species leads to more efficient heating mechanisms than the two-fluid case. This scenario, which is out of reach of the two-fluid or single-fluid models, can reach transition region temperatures starting from upper chromospheric thermodynamic conditions, representative of a quiet Sun scenario. The different dynamics between helium and hydrogen species could lead to chemical fractionation and, under certain conditions, enrichment of helium in the strongest outflows. This could be of significance for recent observations of helium enrichment in the solar wind in switchbacks and CMEs.

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arXiv2022

Quiet Sun Center to Limb Variation of the Linear Polarization Observed by CLASP2 Across the Mg II h & k Lines

The CLASP2 (Chromospheric LAyer SpectroPolarimeter 2) sounding rocket mission was launched on 2019 April 11. CLASP2 measured the four Stokes parameters of the Mg II h & k spectral region around 2800 Angstroms along a 200 arcsecond slit at three locations on the solar disk, achieving the first spatially and spectrally resolved observations of the solar polarization in this near ultraviolet region. The focus of the work presented here is the center-to-limb variation of the linear polarization across these resonance lines, which is produced by the scattering of anisotropic radiation in the solar atmosphere. The linear polarization signals of the Mg II h & k lines are sensitive to the magnetic field from the low to the upper chromosphere through the Hanle and magneto-optical effects. We compare the observations to theoretical predictions from radiative transfer calculations in unmagnetized semi-empirical models, arguing that magnetic fields and horizontal inhomogeneities are needed to explain the observed polarization signals and spatial variations. This comparison is an important step in both validating and refining our understanding of the physical origin of these polarization signatures, and also in paving the way toward future space telescopes for probing the magnetic fields of the solar upper atmosphere via ultraviolet spectropolarimetry.

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arXiv2022

Chromospheric emission from nanoflare heating in RADYN simulations

Heating signatures from small-scale magnetic reconnection events in the solar atmosphere have proven to be difficult to detect through observations. Numerical models that reproduce flaring conditions are essential in the understanding of how nanoflares may act as a heating mechanism of the corona. We study the effects of non-thermal electrons in synthetic spectra from 1D hydrodynamic RADYN simulations of nanoflare heated loops to investigate the diagnostic potential of chromospheric emission from small-scale events. The Mg II h and k, Ca II H and K, Ca II 854.2 nm, H-alpha and H-beta chromospheric lines were synthesised from various RADYN models of coronal loops subject to electron beams of nanoflare energies. The contribution function to the line intensity was computed to better understand how the atmospheric response to the non-thermal electrons affects the formation of spectral lines and the detailed shape of their spectral profiles. The spectral line signatures arising from the electron beams highly depend on the density of the loop and the lower cutoff energy of the electrons. Low-energy (5 keV) electrons deposit their energy in the corona and transition region, producing strong plasma flows that cause both redshifts and blueshifts of the chromospheric spectra. Higher-energy (10 and 15 keV) electrons deposit their energy in the lower transition region and chromosphere, resulting in increased emission from local heating. Our results indicate that effects from small-scale events can be observed with ground-based telescopes, expanding the list of possible diagnostics for the presence and properties of nanoflares.

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arXiv2021

A new view of the solar interface region from the Interface Region Imaging Spectrograph (IRIS)

The Interface Region Imaging Spectrograph (IRIS) has been obtaining near- and far-ultraviolet images and spectra of the solar atmosphere since July 2013. The unique combination of near and far-ultraviolet spectra and images at subarcsecond resolution and high cadence allows the tracing of mass and energy through the critical interface between the solar surface and the corona or solar wind. IRIS has enabled research into the fundamental physical processes thought to play a role in the low solar atmosphere such as ion-neutral interactions, magnetic reconnection, the generation, propagation, and dissipation of various types of waves, the acceleration of non-thermal particles, and various small-scale instabilities. These new findings have helped provide novel insights into a wide range of phenomena including the discovery of non-thermal particles in coronal nanoflares, the formation and impact of spicules and other jets, resonant absorption and dissipation of Alfvenic waves, energy release associated with braiding of magnetic field lines, the thermal instability in the chromosphere-corona mass and energy cycle, the contribution of waves, turbulence, and non-thermal particles in the energy deposition during flares and smaller-scale events such as UV bursts, and the role of flux ropes and other mechanisms in triggering CMEs. IRIS observations have also advanced studies of the connections between solar and stellar physics. Advances in numerical modeling, inversion codes, and machine learning techniques have played a key role in driving these new insights. With the advent of exciting new instrumentation both on the ground (e.g., DKIST, ALMA) and space-based (e.g., Parker Solar Probe, Solar Orbiter), we aim to review new insights based on IRIS observations or related modeling, and highlight some of the outstanding challenges that have been brought to the fore.

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arXiv2020

Observations and modeling of the onset of fast reconnection in the solar transition region

Magnetic reconnection is a fundamental plasma process that plays a critical role not only in energy release in the solar atmosphere, but also in fusion, astrophysical, and other space plasma environments. One of the challenges in explaining solar observations in which reconnection is thought to play a critical role is to account for the transition of the dynamics from a slow quasi-continuous phase to a fast and impulsive energetic burst of much shorter duration. Despite the theoretical progress in identifying mechanisms that might lead to rapid onset, a lack of observations of this transition has left models poorly constrained. High-resolution spectroscopic observations from NASA's Interface Region Imaging Spectrograph (IRIS) now reveal tell-tale signatures of the abrupt transition of reconnection from a slow phase to a fast, impulsive phase during UV bursts or explosive events in the Sun's atmosphere. Our observations are consistent with numerical simulations of the plasmoid instability, and provide evidence for the onset of fast reconnection mediated by plasmoids and new opportunities for remote-sensing diagnostics of reconnection mechanisms on the Sun.

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arXiv2020

High-resolution observations of the solar photosphere, chromosphere and transition region. A database of coordinated IRIS and SST observations

NASA's Interface Region Imaging Spectrograph (IRIS) provides high resolution observations of the solar atmosphere through UV spectroscopy and imaging. Since the launch of IRIS in June 2013, we have conducted systematic observation campaigns in coordination with the Swedish 1-m Solar Telescope (SST) on La Palma. The SST provides complementary high-resolution observations of the photosphere and chromosphere. The SST observations include spectro-polarimetric imaging in photospheric Fe I lines and spectrally-resolved imaging in the chromospheric Ca II 8542 A, H-alpha, and Ca II K lines. We present a database of co-aligned IRIS and SST datasets that is open for analysis to the scientific community. The database covers a variety of targets including active regions, sunspots, plage, quiet Sun, and coronal holes.

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arXiv2019

The multi-thermal chromosphere: inversions of ALMA and IRIS data

Numerical simulations of the solar chromosphere predict a diverse thermal structure with both hot and cool regions. Observations of plage regions in particular feature broader and brighter chromospheric lines, which suggest that they are formed in hotter and denser conditions than in the quiet-Sun, but also implies a non-thermal component whose source is unclear. We revisit the problem of the stratification of temperature and microturbulence in plage now adding millimeter continuum observations provided by ALMA to inversions of near-ultraviolet IRIS spectra as a powerful new diagnostic to disentangle the two parameters. We fit cool chromospheric holes and track the fast evolution of compact mm brightenings in the plage region. We use the STiC non-LTE inversion code to simultaneously fit real ultraviolet and millimeter spectra in order to infer the thermodynamic parameters of the plasma. We confirm the anticipated constraining potential of ALMA in non-LTE inversions of the solar chromosphere. We find significant differences between the inversion results of IRIS data alone compared to the results of a combination with the mm data: the IRIS+ALMA inversions have increased contrast and temperature range, and tend to favor lower values of microturbulence in the chromosphere of plage. The average brightness temperature of the plage region at 1.25 mm is 8500 K, but the ALMA maps also show much cooler ($\sim3000$ K) and hotter ($\sim11\,000$ K) evolving features partially seen in other diagnostics. To explain the former, the inversions require the existence of localized, low temperature regions in the chromosphere where molecules such as CO could form. The hot features could sustain such high temperatures due to non-equilibrium hydrogen ionization effects in a shocked chromosphere - a scenario that is supported by low-frequency shock wave patterns found in the MgII lines probed by IRIS.

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arXiv2018

First high-resolution look at the quiet Sun with ALMA at 3 mm

We present an overview of high resolution quiet Sun observations, from disk center to the limb, obtained with the Atacama Large mm and sub-mm Array (ALMA) at 3 mm. Seven quiet Sun regions were observed with resolution of up to 2.5" by 4.5". We produced both average and snapshot images by self-calibrating the ALMA visibilities and combining the interferometric images with full disk solar images. The images show well the chromospheric network, which, based on the unique segregation method we used, is brighter than the average over the fields of view of the observed regions by $\sim 305$ K while the intranetwork is less bright by $\sim 280$ K, with a slight decrease of the network/intranetwork contrast toward the limb. At 3 mm the network is very similar to the 1600 Å images, with somewhat larger size. We detected for the first time spicular structures, rising up to 15" above the limb with a width down to the image resolution and brightness temperature of $\sim$ 1800 K above the local background. No trace of spicules, either in emission or absorption, was found on the disk. Our results highlight ALMA's potential for the study of the quiet chromosphere.

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arXiv2018

CLASP Constraints on the Magnetization and Geometrical Complexity of the Chromosphere-Corona Transition Region

The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a suborbital rocket experiment that on 3rd September 2015 measured the linear polarization produced by scattering processes in the hydrogen Ly-$α$ line of the solar disk radiation, whose line-center photons stem from the chromosphere-corona transition region (TR). These unprecedented spectropolarimetric observations revealed an interesting surprise, namely that there is practically no center-to-limb variation (CLV) in the $Q/I$ line-center signals. Using an analytical model, we first show that the geometrical complexity of the corrugated surface that delineates the TR has a crucial impact on the CLV of the $Q/I$ and $U/I$ line-center signals. Secondly, we introduce a statistical description of the solar atmosphere based on a three-dimensional (3D) model derived from a state-of-the-art radiation magneto-hydrodynamic simulation. Each realization of the statistical ensemble is a 3D model characterized by a given degree of magnetization and corrugation of the TR, and for each such realization we solve the full 3D radiative transfer problem taking into account the impact of the CLASP instrument degradation on the calculated polarization signals. Finally, we apply the statistical inference method presented in a previous paper to show that the TR of the 3D model that produces the best agreement with the CLASP observations has a relatively weak magnetic field and a relatively high degree of corrugation. We emphasize that a suitable way to validate or refute numerical models of the upper solar chromosphere is by confronting calculations and observations of the scattering polarization in ultraviolet lines sensitive to the Hanle effect.

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arXiv2018

A Statistical Inference Method for Interpreting the CLASP Observations

On 3rd September 2015, the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) successfully measured the linear polarization produced by scattering processes in the hydrogen Lyman-$α$ line of the solar disk radiation, revealing conspicuous spatial variations in the $Q/I$ and $U/I$ signals. Via the Hanle effect the line-center $Q/I$ and $U/I$ amplitudes encode information on the magnetic field of the chromosphere-corona transition region (TR), but they are also sensitive to the three-dimensional structure of this corrugated interface region. With the help of a simple line formation model, here we propose a statistical inference method for interpreting the Lyman-$α$ line-center polarization observed by CLASP.

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arXiv2018

Investigating the response of loop plasma to nanoflare heating using RADYN simulations

We present the results of 1D hydrodynamic simulations of coronal loops which are subject to nanoflares, caused by either in-situ thermal heating, or non-thermal electrons (NTE) beams. The synthesized intensity and Doppler shifts can be directly compared with IRIS and AIA observations of rapid variability in the transition region (TR) of coronal loops, associated with transient coronal heating. We find that NTE with high enough low-energy cutoff (E$_\textrm{C}$) deposit energy in the lower TR and chromosphere causing blueshifts (up to~$\sim$~20 km/s) in the \emph{IRIS} \siiv~lines, which thermal conduction cannot reproduce. The E$_\textrm{C}$ threshold value for the blueshifts depends on the total energy of the events ($\approx$~5 keV for 10$^{24}$ ergs, up to 15 keV for 10$^{25}$ ergs). The observed footpoint emission intensity and flows, combined with the simulations, can provide constraints on both the energy of the heating event and E$_\textrm{C}$. The response of the loop plasma to nanoflares depends crucially on the electron density: significant \siiv~intensity enhancements and flows are observed only for initially low-density loops ($<$~10$^{9}$~cm$^{-3}$). This provides a possible explanation of the relative scarcity of observations of significant moss variability. While the TR response to single heating episodes can be clearly observed, the predicted coronal emission (AIA 94Å) for single strands is below current detectability, and can only be observed when several strands are heated closely in time. Finally, we show that the analysis of the IRIS \mgii~chromospheric lines can help further constrain the properties of the heating mechanisms.

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arXiv2017

First analysis of solar structures in 1.21 mm full-disc ALMA image of the Sun

Various solar features can be seen on maps of the Sun in the mm and sub-mm wavelength range. The recently installed Atacama Large Millimeter/submillimeter Array (ALMA) is capable of observing the Sun in that wavelength range with an unprecedented spatial, temporal and spectral resolution. To interpret solar observations with ALMA the first important step is to compare ALMA maps with simultaneous images of the Sun recorded in other spectral ranges. First we identify different structures in the solar atmosphere seen in the optical, IR and EUV parts of the spectrum (quiet Sun (QS), active regions (AR), prominences on the disc, magnetic inversion lines (IL), coronal holes (CH) and coronal bright points (CBPs)) in a full disc solar ALMA image. The second aim is to measure the intensities (brightness temperatures) of those structures and compare them with the corresponding QS level. A full disc solar image at 1.21 mm obtained on December 18, 2015 during a CSV-EOC campaign with ALMA is calibrated and compared with full disc solar images from the same day in Hα, in He I 1083 nm core, and with SDO images (AIA at 170 nm, 30.4 nm, 21.1 nm, 19.3 nm, and 17.1 nm and HMI magnetogram). The brightness temperatures of various structures are determined by averaging over corresponding regions of interest in the ALMA image. Positions of the QS, ARs, prominences on the disc, ILs, CHs and CBPs are identified in the ALMA image. At 1.21 mm ARs appear as bright areas (but sunspots are dark), while prominences on the disc and CHs are not discernible from the QS background, although having slightly less intensity than surrounding QS regions. ILs appear as large, elongated dark structures and CBPs correspond to ALMA bright points. These results are in general agreement with sparse earlier measurements at similar wavelengths. The identification of CBPs represents the most important new result.

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arXiv2017

Intermittent reconnection and plasmoids in UV bursts in the low solar atmosphere

Magnetic reconnection is thought to drive a wide variety of dynamic phenomena in the solar atmosphere. Yet the detailed physical mechanisms driving reconnection are difficult to discern in the remote sensing observations that are used to study the solar atmosphere. In this paper we exploit the high-resolution instruments Interface Region Imaging Spectrograph (IRIS) and the new CHROMIS Fabry-Perot instrument at the Swedish 1-m Solar Telescope (SST) to identify the intermittency of magnetic reconnection and its association with the formation of plasmoids in so-called UV bursts in the low solar atmosphere. The Si IV 1403A UV burst spectra from the transition region show evidence of highly broadened line profiles with often non-Gaussian and triangular shapes, in addition to signatures of bidirectional flows. Such profiles had previously been linked, in idealized numerical simulations, to magnetic reconnection driven by the plasmoid instability. Simultaneous CHROMIS images in the chromospheric Ca II K 3934A line now provide compelling evidence for the presence of plasmoids, by revealing highly dynamic and rapidly moving brightenings that are smaller than 0.2 arcsec and that evolve on timescales of order seconds. Our interpretation of the observations is supported by detailed comparisons with synthetic observables from advanced numerical simulations of magnetic reconnection and associated plasmoids in the chromosphere. Our results highlight how subarcsecond imaging spectroscopy sensitive to a wide range of temperatures combined with advanced numerical simulations that are realistic enough to compare with observations can directly reveal the small-scale physical processes that drive the wide range of phenomena in the solar atmosphere.

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arXiv2017

Comparison of Solar Fine Structure Observed Simultaneously in Ly-α and Mg II h

The Chromospheric Lyman Alpha Spectropolarimeter (CLASP) observed the Sun in H I Lyman-α during a suborbital rocket flight on September 3, 2015. The Interface Region Imaging Telescope (IRIS) coordinated with the CLASP observations and recorded nearly simultaneous and co-spatial observations in the Mg II h&k lines. The Mg II h and Ly-α lines are important transitions, energetically and diagnostically, in the chromosphere. The canonical solar atmosphere model predicts that these lines form in close proximity to each other and so we expect that the line profiles will exhibit similar variability. In this analysis, we present these coordinated observations and discuss how the two profiles compare over a region of quiet sun at viewing angles that approach the limb. In addition to the observations, we synthesize both line profiles using a 3D radiation-MHD simulation. In the observations, we find that the peak width and the peak intensities are well correlated between the lines. For the simulation, we do not find the same relationship. We have attempted to mitigate the instrumental differences between IRIS and CLASP and to reproduce the instrumental factors in the synthetic profiles. The model indicates that formation heights of the lines differ in a somewhat regular fashion related to magnetic geometry. This variation explains to some degree the lack of correlation, observed and synthesized, between Mg II and Ly-α. Our analysis will aid in the definition of future observatories that aim to link dynamics in the chromosphere and transition region.

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arXiv2017

A First Comparison of Millimeter Continuum and Mg II Ultraviolet Line Emission from the Solar Chromosphere

We present joint observations of the Sun by the Atacama Large Millimeter/submillimeter Array (ALMA) and the Interface Region Imaging Spectrograph (IRIS). The observations were made of a solar active region on 2015 December 18 as part of the ALMA science verification effort. A map of the Sun's continuum emission of size $2.4' \times 2.3'$ was obtained by ALMA at a wavelength of 1.25 mm (239 GHz) using mosaicing techniques. A contemporaneous map of size $1.9'\times 2.9'$ was obtained in the Mg II h doublet line at 2803.5Å by IRIS. Both mm/submm$-λ$ continuum emission and ultraviolet (UV) line emission are believed to originate from the solar chromosphere and both have the potential to serve as powerful and complementary diagnostics of physical conditions in this poorly understood layer of the solar atmosphere. While a clear correlation between mm-$λ$ brightness temperature $T_B$ and the Mg II h line radiation temperature $T_{rad}$ is observed the slope is $<1$, perhaps as a result of the fact that these diagnostics are sensitive to different parts of the chromosphere and/or the Mg II h line source function includes a scattering component. There is a significant offset between the mean $T_B$(1.25 mm) and mean $T_{rad}$(Mg II), the former being $\approx 35\%$ greater than the latter. Partitioning the maps into "sunspot", "quiet regions", and "plage regions" we find that the slope of the scatter plots between the IRIS Mg II h line $T_{rad}$ and the ALMA brightness temperature $T_B$ is 0.4 (sunspot), 0.56 (quiet regions), and 0.66 (plage regions). We suggest that this change may be caused by the regional dependence of the formation heights of the IRIS and ALMA diagnostics, and/or the increased degree of coupling between the UV source function and the local gas temperature in the hotter, denser gas in plage regions.

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