Sunspot Umbra Research Articles

A Data-constrained Analysis for Joule Heating as a Solar Active Region Atmosphere Heating Mechanism. I. Sunspot Umbral Light Bridge

Understanding the mechanisms underlying the heating of the solar atmosphere is a fundamental problem in solar physics. The lower atmosphere of the Sun (i.e., photosphere and chromosphere) is composed of weakly ionized plasma. This results in anisotropic dissipation of electric currents by Coulomb and Cowling resistivities. Joule heating due to dissipation of currents perpendicular to the magnetic field by Cowling resistivity has been demonstrated to be the main mechanism for the heating of a sunspot umbral light bridge located in NOAA AR 12002 on 2014 March 13. Here, we focus on the same target region and demonstrate the importance of further constraining our Joule heating model using observational data in addition to magnetic field, namely plasma temperature calculated from the inversion of spectroscopic data obtained from the Interferometric BI-dimensional Spectrometer instrument of the ground-based Dunn Solar Telescope. As a parameter in our analysis, temperature is demonstrated to have the highest sensitivity after magnetic field. We show that the heating of the light bridge is a highly dynamic event that necessitates utilization of 3D spatially resolved observational data for temperature rather than a 1D temperature stratification based on theoretical/semiempirical solar atmosphere models. Our improved data-constrained analysis using spatially resolved temperatures shows that the entire light bridge is heated by the proposed mechanism, and yields heating rate values that are consistent with our previous study.

Effect of area divergence and frequency on damping of slow magnetoacoustic waves propagating along umbral fan loops

ABSTRACT Waves play an important role in the heating of solar atmosphere; however, observations of wave propagation and damping from the solar photosphere to corona through chromosphere and transition region are very rare. Recent observations have shown propagation of 3-min slow magnetoacoustic waves (SMAWs) along fan loops from the solar photosphere to corona. In this work, we investigate the role of area divergence and frequencies on the damping of SMAWs propagating from the photosphere to the corona along several fan loops rooted in the sunspot umbra. We study the Fourier power spectra of oscillations along fan loops at each atmospheric height which showed significant enhancements in 1–2, 2.3–3.6, and 4.2–6 min period bands. Amplitude of intensity oscillations in different period bands and heights are extracted after normalizing the filtered light curves with low-frequency background. We find damping of SMAW energy flux propagating along the fan loop 6 with damping lengths $\approx 170$ and $\approx 208$ km for 1.5- and 3-min period bands. We also show the decay of total wave energy content with height after incorporating area divergence effect, and present actual damping of SMAWs from photosphere to corona. Actual damping lengths in this case increases to $\approx 172$ and $\approx 303$ km for 1.5- and 3-min period bands. All the fan loops show such increase in actual damping lengths, and thus highlight the importance of area divergence effect. Results also show some frequency-dependent damping of SMAW energy fluxes with height where high-frequency waves are damped faster than low-frequency waves.

Multi-wavelength Observations of Umbral Oscillations above a Sunspot

We investigate the umbral oscillation at multi-height solar atmospheres above a sunspot in the active region of National Oceanic and Atmospheric Administration 12680 on 2017 September 15. In this study, the extreme ultraviolet images were measured by the Atmospheric Imaging Assembly (AIA), while the ultraviolet spectral lines and images were observed by the Interface Region Imaging Spectrograph. At the sunspot umbra, the AIA 1700 Å intensity curve shows the primary oscillation with a long period of ∼(4.2±0.8) minutes, while the intensity curves in AIA 1600 Å, 171 Å, and 193 Å exhibit an apparent oscillation with a short period of ∼(2.8±0.3) minutes. Meanwhile, a short period of ∼(3.1±0.5) minutes is found in the Mg II h & k lines and the slit-jaw image at 2796 Å, a short period of ∼(2.9±0.4) minutes is detected in the Si IV 1393.76 Å line. Our observations suggest that the oscillatory periods at the sunspot umbra decrease with the height of solar outer atmospheres. The short period is roughly equal to 3 minutes, which could be interpreted as the propagating slow magnetoacoustic wave above the sunspot umbra, and it might originate from the temperature minimum region and then propagate up to the corona. While the long period is close to 5 minutes oscillation in the photosphere, which might be regarded as the solar P-mode wave.

Carrington Maps in H i Lyα and Their Relationships with Extreme-ultraviolet and Magnetic-field Maps

H i Lyα emission in the chromosphere and transition region is a key ingredient of the incident radiation to coronal neutral hydrogen for modeling corona Lyα emission. The Lyα emission distribution across the solar disk can be obtained from a Lyα Carrington map. Before the launch of the Advanced Space-based Solar Observatory (ASO-S), such a Lyα Carrington map was derived from the Carrington map at He ii 30.4 nm and sometimes is even assumed to be uniform. We construct the first Lyα Carrington map based on full-disk Lyα images acquired by the Solar Disk Imager (SDI) on board ASO-S and present two versions: the standard one is for a CR, and the other is daily updated. For modeling Lyα intensities during eruptions, the Carrington map with incorporated flare region is produced. Furthermore, we evaluate the difference between the Lyα Carrington map derived with SDI observations and that synthesized from the 30.4 nm data based on an empirical relationship between Lyα and He ii 30.4 nm intensities, particularly extended to flare intensities that have not been investigated before. The average difference of 38% proves the importance of the Lyα Carrington map built from observations directly. However, the synthetic Lyα Carrington map can be used as an approximation before SDI data are available. The comparison between the SDI Lyα Carrington map and the corresponding magnetic field synoptic map indicates that active regions in general are brighter in Lyα, while the sunspot umbras with strong magnetic field strength are usually weaker in Lyα.

Correction for the Weakening Magnetic Field Within the Sunspot Umbra Observed by ASO-S/FMG

Correction for the Weakening Magnetic Field Within the Sunspot Umbra Observed by ASO-S/FMG

Efficiency of solar microflares in accelerating electrons when rooted in a sunspot

Context. The spectral shape of the X-ray emission in solar flares varies with the event size, with small flares generally exhibiting softer spectra than large events, indicative of a relatively lower number of accelerated electrons at higher energies. Aims. We investigate two microflares of GOES classes A9 and C1 (after background subtraction) observed by STIX onboard Solar Orbiter with exceptionally strong nonthermal emission. We complement the hard X-ray imaging and spectral analysis by STIX with co-temporal observations in the (E)UV and visual range by AIA and HMI to investigate what makes these microflares so efficient in high-energy particle acceleration. Methods. We made a preselection of events in the STIX flare catalog based on the ratio of the thermal to nonthermal quicklook X-ray emission. The STIX spectrogram science data were used to perform spectral fitting to identify the non-thermal and thermal components. The STIX X-ray images were reconstructed to analyze the spatial distribution of the precipitating electrons and the hard X-ray emission they produce. The EUV images from SDO/AIA and SDO/HMI LOS magnetograms were analyzed to better understand the magnetic environment and the chromospheric and coronal response. For the A9 event, EOVSA microwave observations were available, allowing for image reconstruction in the radio domain. Results. We performed case studies of two microflares observed by STIX on October 11, 2021 and November 10, 2022, which showed unusually hard microflare X-ray spectra with power-law indices of the electron flux distributions of δ = (2.98 ± 0.25) and δ = (4.08 ± 0.23), during their non-thermal peaks and photon energies up to 76 keV and 50 keV, respectively. For both events under study, we found that one footpoint is located within a sunspot covering areas with mean magnetic flux densities in excess of 1500 G, suggesting that the hard electron spectra are caused by the strong magnetic fields the flare loops are rooted in. Additionally, we revisited a previously published unusually hard RHESSI microflare and found that in this event, there was also one flare kernel located within a sunspot, which corroborates the result from the two hard STIX microflares under study in this work. Conclusions. The characteristics of the strong photospheric magnetic fields inside the sunspot umbrae and penumbrae where flare loops are rooted play an important role in the generation of exceptionally hard X-ray spectra in these microflares.

Spatial structure of resonance cavities in sunspots

ABSTRACT We present a study of wave processes in sunspots from active regions NOAA 11131 on 2010 December 10 and NOAA 12565 on 2016 July 14 observed by SDO/AIA in the 1600, 304, and 171 Å temperature channels. To study the spatial structure of the resonance cavities previously found by Jess et al., we applied spectral data processing techniques such as pixelized wavelet filtering and mode decomposition. For the first time, we found stable regions as waveguides of the oscillations in the sunspot umbra, occupying specific frequency ranges without spatial overlap. The sizes of these regions depend on the frequency oscillations, and the maximum frequency coincides with the values of the harmonics of the main oscillation mode. Frequency drifts were observed in the band occupied by these regions, with different spectral slopes depending on the location of the sources in the sunspot umbra. We suggest that the observed distribution of wave sources in the umbra is a set of resonant cavities where successive amplification of oscillations at selected multiple harmonics is observed. The distribution of sources at low frequencies indicates the influence of the atmospheric cut-off due to the inclinations of the magnetic field lines.

Identifying footpoints of pre-eruptive and coronal mass ejection flux ropes with sunspot scars

Context. The properties of pre-eruptive structures and coronal mass ejections (CMEs) are characterized by those of their footpoints, the latter of which attract a great deal of interest. However, the matter of how to identify the footpoints of pre-eruptive structures and how to do so with the use of ground-based instruments still remains elusive. Aims. In this work, we study an arc-shaped structure intruding in the sunspot umbra. It is located close to the (pre-)eruptive flux rope footpoint and it is expected to help identify the footpoint. Methods. We analyzed this arc-shaped structure, which we call a “sunspot scar”, in a CME event on July 12, 2012, and in two CME events from observationally inspired magnetohydrodynamic simulations performed by OHM and MPI-AMRVAC. Results. The sunspot scar displays a more inclined magnetic field with a weaker vertical component and a stronger horizontal component relative to that in the surrounding umbra and is manifested as a light bridge in the white light passband. The hot field lines anchored in the sunspot scar are spatially at the transition between the flux rope and the background coronal loops and temporally in the process of the slipping reconnection which builds up the flux rope. Conclusions. The sunspot scar and its related light bridge mark the edge of the CME flux rope footpoint and particularly indicate the edge of the pre-eruptive flux rope footpoint in the framework of “pre-eruptive structures being flux ropes”. Therefore, they provide a new perspective for the identification of pre-eruptive and CME flux rope footpoints, as well as new methods for studying the properties and evolution of pre-eruptive structures and CMEs with photospheric observations only.

The Decay of Two Adjacent Sunspots Associated with Moving Magnetic Features

The relationship between the decay of sunspots and moving magnetic features (MMFs) plays an important role in understanding the evolution of active regions. We present observations of two adjacent sunspots, the gap between them, and a lot of MMFs propagating from the gap and the sunspots' outer edges in NOAA Active Region 13023. The MMFs are divided into two types based on their magnetic field inclination angle: vertical (0° < γ < 45°) and horizontal (45° ≤ γ < 90°) MMFs (V-MMFs and H-MMFs, respectively). The main results are as follows: (1) the mean magnetic flux decay rates of the two sunspots are −1.7 × 1020 and −1.4 × 1020 Mx day−1; (2) the magnetic flux generation rate of all MMFs is calculated to be −1.9 × 1021 Mx day−1, which is on average 5.6 times higher than the total magnetic flux loss rate of the sunspots; (3) the magnetic flux of V-MMFs (including a pore separated from the sunspots) is 1.4 times larger than the total lost magnetic flux of the two sunspots, and in a later stage when the pore has passed through the reference ellipse, the magnetic flux generation rate of the V-MMFs is almost the same as the magnetic flux loss rate of the sunspots; and (4) within the gap, the magnetic flux of V-MMFs is one-third of the total magnetic flux. Few V-MMFs stream out from the sunspots at the nongap region. All observations suggest that MMFs with vertical magnetic fields are closely related to the disintegration of the sunspot, and most of the MMFs from the gap may originate directly from the sunspot umbra.

A Statistical Analysis of Spiral-shaped Wave Patterns in Sunspot Umbrae

Spiral-shaped wave patterns (SWPs) observed in sunspot umbrae represent the superposition of axisymmetric patterns and nonaxisymmetric patterns of umbral oscillations. These patterns give us physical information about the source of oscillations below the surface. Here we present the statistics of their observational properties determined from the 304 Å line-intensity data obtained with the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory. From the 2013 to 2018 data set, we examined each of the 496 sunspots near the disk center for 2 hr. As a result, we identified 241 SWPs from 140 sunspots, which corresponds to the detection rate of 0.24 per hour in each sunspot. Most of the SWPs had one spiral arm, 48 SWPs had two arms, and only one had three. The oscillation period was estimated at 151 ± 27 s and the lifetime, at 770 ± 250 s, being comparable to those of conventional umbral oscillations. The rotation period of the SWPs was estimated at 190 ± 69 s for the one-armed SWPs and 299 ± 115 s for the two-armed SWPs. We found that the properties of the SWPs have no dependence on hemisphere, latitude, and sunspot size. From the apparent radial speeds of the SWPs and a simple model of wave propagation, we infer that the SWPs may be generated between 2 and 11 Mm below the photosphere with a mean value of about 6 Mm.

Exploring Magnetic Coupling of Solar Atmosphere Through Frequency Modulations of 3-min Slow Magnetoacoustic Waves

Coronal fan loops rooted in sunspot umbra show outward propagating waves with subsonic phase speed and a period around 3 min. However, their source region in the lower atmosphere is still ambiguous. We performed multi-wavelength observations of a clean fan loop system rooted in a sunspot utilizing data from the Interface Region Imaging Spectrograph (IRIS) and the Solar Dynamics Observatory (SDO). We explored the less studied property of frequency modulation of these 3-min waves from the photosphere to the corona, and identified periodicities in the ranges of 14-20 min, and 24-35 min. Based on our findings, we interpret that the 3-min slow waves observed in the coronal fan loops are driven by 3-min oscillations observed at the photospheric footpoints of these fan loops in the umbral region. We also investigated possible connections between the 3-min and 5-min oscillations observed at the photosphere, which are still poorly understood. Our results provide clear evidence of magnetic coupling of the solar umbral atmosphere through the propagation of 3-min waves along the fan loops at different atmospheric heights.

The Influence of Eruptive Processes in Active Regions on Oscillations of the Magnetic Field Parameters in Sunspot Umbrae

The Influence of Eruptive Processes in Active Regions on Oscillations of the Magnetic Field Parameters in Sunspot Umbrae

Intensity and velocity oscillations in a flaring active region

ABSTRACT Chromospheric oscillations can give us insight into the physical environment in the solar atmosphere, both in quiet Sun and flaring conditions. Many authors have reported increases in the prevalence of 3-minute oscillations which are thought to be excited by events which impact the chromosphere such as flares. In this study, we utilized the Ca ii 8542 Å line to study the oscillatory behaviour of the chromosphere in an active region which underwent two B-class flares. We analysed oscillations in both intensity and velocity, and found different behaviours in both. Intensity oscillations were most prevalent over the umbrae of sunspots and magnetic pores in the active region, and the extent of the area which contained significant oscillations was found to decrease when comparing times after the flares to before. By measuring the evolution of the magnetic field, we found that this could be because the areas surrounding the umbrae were becoming more ‘penumbral’ with an increase to the magnetic field inclination. Velocity oscillations were found across the active region both before and after the flares but were observed clearly in areas which were brightened by the second flare. By comparing to EUV imaging, it was seen that strong chromospheric velocity oscillations with 3–4-minute periods occurred at the same time and location as a flare loop cooling 30 min after the second flare peak. This could be evidence of disturbances in the loop exciting a response from the chromosphere at its acoustic cut-off frequency.

Propagation Properties of Sunspots Umbral Oscillations in Horizontal and Vertical Directions

We present a study on investigating the propagation characteristics of umbral oscillations in sunspots. In sunspot 1 (located in NOAA AR 12127) with four umbrae, the analysis shows that the oscillations in different umbrae are correlated. The weak correlation (<20%) is attributed to the propagation of umbral oscillations across the umbral boundary to its adjacent umbra in the horizontal direction. We speculate that oscillations in two of the umbrae have a common origin in the sub-photosphere, resulting in a stronger correlation (>30%). Additionally, utilizing the TiO (photosphere), Hα (chromosphere) images provided by BBSO/GST, and the 304 Å (upper chromosphere and lower transition region), 171 Å (upper transition region), 193 Å (corona), and 211 Å (active region corona) images acquired by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO), we analyze the vertical propagation of oscillations in the sunspot umbra. Multi-channel observation shows that the umbral oscillations observed in the lower atmosphere of sunspot 1 cannot be detected in the upper atmosphere. However, in sunspot 2 (located in NOAA AR 12132), oscillations in the lower atmosphere can propagate to the upper atmosphere. Using photospheric magnetic field data provided by the Helioseismic and Magnetic Imager on board SDO, potential field extrapolation of the magnetic field for the two sunspots shows that open magnetic field structures allow sunspot oscillations to propagate to higher heights, while closed magnetic field structures do not.

Relationships Between Physical Parameters of Umbral Dots Measured for 12 Sunspot Umbras with the Goode Solar Telescope

Relationships Between Physical Parameters of Umbral Dots Measured for 12 Sunspot Umbras with the Goode Solar Telescope

Exploring source region of 3-min slow magnetoacoustic waves observed in coronal fan loops rooted in sunspot umbra

ABSTRACT Sunspots host various oscillations and wave phenomena like umbral flashes, umbral oscillations, running penumbral waves, and coronal waves. All fan loops rooted in sunspot umbra constantly show a 3-min period propagating slow magnetoacoustic waves in the corona. However, their origin in the lower atmosphere is still unclear. In this work, we studied these oscillations in detail along a clean fan loop system rooted in active region AR 12553 for a duration of 4 h on 2016 June 16 observed by Interface Region Imaging Spectrograph and Solar Dynamics Observatory. We traced foot-points of several fan loops by identifying their locations at different atmospheric heights from the corona to the photosphere. We found presence of 3-min oscillations at foot-points of all the loops and at all atmospheric heights. We further traced origin of these waves by utilizing their amplitude modulation characteristics while propagating in the solar atmosphere. We found several amplitude modulation periods in the range of 9–14, 20–24, and 30–40 min of these 3-min waves at all heights. Based on our findings, we interpret that 3-min slow magnetoacoustic waves propagating in coronal fan loops are driven by 3-min oscillations observed at the photospheric foot-points of these fan loops in the umbral region. We also explored any connection between 3- and 5-min oscillations observed at the photospheric foot-points of these loops and found them to be weakly coupled. Results provide clear evidence of magnetic coupling of the solar atmosphere through propagation of 3-min waves along fan loops at different atmospheric heights.

Magnetic field fluctuations in the shocked umbral chromosphere

Context. Umbral chromospheric observations show the presence of magnetoacoustic shocks. Several recent studies have reported magnetic field fluctuations associated with these shock waves. The mechanism behind these periodic magnetic field changes is still an unresolved question. Aims. We aim to study the properties and origin of magnetic field fluctuations in the umbral chromosphere. Methods. Temporal series of spectropolarimetric observations were acquired with the GREGOR telescope on 2017 June 18. The chromospheric and photospheric conditions, including the temporal evolution of the magnetic field, were derived from simultaneous inversions of the He I 10 830 Å triplet and the Si I 10 827 Å line using the HAZEL2 code. The oscillations were interpreted using wavelet analysis and context information from ultraviolet observations acquired with the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO/AIA) and the Interface Region Imaging Spectrograph (IRIS). Results. The chromospheric magnetic field shows strong fluctuations in the sunspot umbra, with peak field strengths of up to 2900 G. This inferred field strength is comparable to the magnetic field strength in the upper photosphere. Magnetic field and velocity umbral oscillations exhibit a strong coherence, with the magnetic field lagging the shock fronts detected in the velocity fluctuations. This points to a common origin of the fluctuations in both parameters, and the analysis of the phase shift between photospheric and chromospheric velocity is consistent with upward wave propagation. These results suggest that the strong inferred magnetic field fluctuations are caused by changes in the response height of the He I 10 830 Å line to the magnetic field, which is sensitive to the high photosphere during and right after the shock. The analysis of extreme ultraviolet data shows a weak brightening in a coronal loop rooted in the umbra around the time of the measured magnetic field fluctuations. This coronal activity could possibly have some impact on the inferred fluctuations, but it is not the main driver of the magnetic field oscillations since they are found before the extreme ultraviolet event takes place. Conclusions. Chromospheric magnetic field fluctuations measured with the He I 10 830 Å triplet arise due to variations in the opacity of the line. After strong shocks are produced by the propagation of slow magnetoacoustic waves, the response of the line to the magnetic field can be shifted down to the upper photosphere. This is seen as remarkably large fluctuations in the line-of-sight magnetic field strength.

The source of unusual coronal upflows with photospheric abundance in a solar active region

Context. Upflows in the corona are of importance, as they may contribute to the solar wind. There has been considerable interest in upflows from active regions (ARs). The coronal upflows that are seen at the edges of active regions have coronal elemental composition and can contribute to the slow solar wind. The sources of the upflows have been challenging to determine because they may be multiple, and the spatial resolution of previous observations is not yet high enough. Aims. In this article, we analyse coronal upflows in AR 12960 that are unusually close to the sunspot umbra. We analyse their properties, and we attempt to determine if it is possible that they feed into the slow solar wind. Methods. We analysed the activity in the upflow region in detail using a combination of Solar Orbiter EUV images at high spatial and temporal resolution, Hinode/EUV Imaging Spectrometer data, and observations from instruments on board the Solar Dynamics Observatory. This combined dataset was acquired during the first Solar Orbiter perihelion of the science phase, which provided a spatial resolution of 356 km for two pixels. Doppler velocity, density, and plasma composition determinations, as well as coronal magnetic field modelling, were carried out to understand the source of the upflows. Results. We observed small magnetic fragments, called moving magnetic features (MMFs), moving away from the sunspot in the active region. Specifically, they moved towards the sunspot from the edge of the penumbra where a small positive polarity connects to the umbra via small-scale and very dynamic coronal loops. At this location, small dark grains are evident and flow along penumbral filaments in continuum images. The magnetic field modelling showed small low-lying loops anchored close to the umbral magnetic field. The high-resolution data of the Solar Orbiter EUV Imagers showed the dynamics of these small loops, which last on time scales of only minutes. The edges of these small loops are the location of the coronal upflow that has photospheric abundance.

First Observation of Chromospheric Waves in a Sunspot by DKIST/ViSP: The Anatomy of an Umbral Flash

The Visible Spectro-Polarimeter of the NSF Daniel K. Inouye Solar Telescope collected its Science Verification data on 2021 May 7–8. The instrument observed multiple layers of a sunspot atmosphere simultaneously, in passbands of Ca ii 397 nm (H line), Fe i 630 nm, and Ca ii 854 nm, scanning the region with a spatial sampling of 0.″041 and an average temporal cadence of 7.76 s, for a duration of 38.8 minutes. The slit moved southward across the plane of sky at 3.83 km s−1. The spectropolarimetric scans exhibit prominent oscillatory “ridge” structures that lie nearly perpendicular to the direction of slit motion (north to south). These ridges are visible in the maps of line intensity, central wavelength, line width, and both linear and circular polarization. Contemporaneous Atmospheric Imaging Assembly observations indicate that these ridges are purely temporal in character and are likely attributed to the familiar chromospheric 3 minute umbral oscillations. We observe in detail a steady umbral flash near the center of the sunspot umbra. Although bad seeing limited the spatial resolution, the unique high signal-to-noise ratio data enable us to estimate the shock Mach numbers (≈2), propagation speeds (≈9 km s−1), and their impacts on the longitudinal magnetic field (ΔB ≈ 50 G), gas pressure, and temperature (ΔT/T ≈ 0.1) of subshocks over 30 s. We also find evidence for rarefaction waves situated between neighboring wave train shocks. The Ca ii 854 nm line width is fairly steady throughout the umbral flash, except for a sharp 1.5 km s−1 dip immediately before, and a comparable spike immediately after, the passage of the shock front. This zigzag in line width is centered on the subshock and extends over 0.″4.

Why Do Chromospheric Oscillations in Sunspot Umbrae Appear to Propagate Downward?

Umbral oscillations constitute the most noticeable chromospheric feature of sunspot umbrae—large-amplitude oscillations of intensity (umbral flashes, if very strong) and line-of-sight velocity, with periods of about 3 minutes. These umbral oscillations are usually interpreted as acoustic waves propagating upward under the effect of gravity. However, there have been observational reports that intensity peaks tend to occur in downflowing phases of umbral oscillations, and this appears to be more compatible with downward propagation. We investigate whether this intensity–velocity correlation occurs persistently or not, by determining the vertical flux of the wave energy, based on Hα line measurements of the temperature and velocity. As a result, we find that the wave flux is persistently negative in sunspot umbrae, confirming the discrepancy specified above. We attribute this discrepancy to the nonzero fluctuation of net radiative heating. We find that when this effect is taken into account in the energy equation, the pressure is peaked during upflowing phases, being compatible with the notion of upward propagation. We conclude that temperature (and intensity) peaks occur during downflowing phases, not because of downward propagation, but because of radiative heat transport.