arXiv subjects

Jaime de la Cruz Rodriguez

Publications and source records attributed to Jaime de la Cruz Rodriguez.

18 recordsLinked to original sources

arXiv2025

Science Requirement Document (SRD) for the European Solar Telescope (EST) (3rd Edition, December 2025)

The European Strategy Forum on Research Infrastructures (ESFRI) included the European Solar Telescope (EST) as an ESFRI Project in its 2016 Roadmap and confirmed this status in 2021. During the Preparatory Phase (2017 to 2022), the EST Science Advisory Group (SAG) was established in 2017. Its first task was to revise the Science Requirements Document (SRD), originally formulated in 2011. This second edition of the SRD was published in December 2019 (Schlichenmaier et al. 2019, 2019arXiv191208650S). Since 2019, the EST Project Office has advanced the telescope design and developed the Science Instrumentation Suite (SIS). All telescope subsystems and the SIS have now passed their Design Reviews. Aligned with the discussions and resolutions of the SAG, the SIS comprises three categories of first-generation instruments: (1) Tunable Imaging Spectropolarimeters coupled with Fixed Band Imagers (TIS/FBIs), employing large-aperture Fabry-Pérot etalons; (2) Integral Field Spectropolarimeters based on microlens arrays (IFS-M); (3) The near-infrared spectropolarimeter EMBER (spectropolariMeter Based on slicEr-mirrors for the near-infraRed), using image-slicing technology. This configuration enables simultaneous observations of the same two-dimensional solar region across a broad wavelength range (380-2200 nm), giving EST a uniquely powerful multi-wavelength observing capability. This has made it necessary to revise the Observing Programmes so that they accurately reflect the capabilities of the SIS and ensure that all science objectives can be met. This third edition of the EST SRD integrates the outcomes of numerous SAG meetings held between 2020 and 2025 and incorporates all design developments up to 2025. It updates the Observing Programmes accordingly and assesses their alignment with the scientific objectives defined by the SAG.

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arXiv2024

ALMA Memo 628 -- High-cadence observations of the Sun

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic capabilities for studying the Sun, providing complementary insights through high spatial and temporal resolution at millimeter wavelengths. ALMA acts as a linear thermometer for atmospheric gas, aiding in understanding the solar atmosphere's structure, dynamics, and energy balance. Given the Sun's complex emission patterns and rapid evolution, high-cadence imaging is essential for solar observations. Snapshot imaging is required, though it limits available visibility data, making full exploitation of ALMA's capabilities non-trivial. Challenges in processing solar ALMA data highlight the need for revising and enhancing the solar observing mode. The ALMA development study High-Cadence Imaging of the Sun demonstrated the potential benefits of high cadence observations through a forward modelling approach. The resulting report provides initial recommendations for improved post-processing solar ALMA data and explores increasing the observing cadence to sub-second intervals to improve image reliability.

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arXiv2024

Spatial resolution effects on the solar open flux estimates

Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630\,nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution. The results show a significant decrease in the mean magnetic flux density -- related to the open flux observed at the disk center -- with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20\,cm aperture telescope yields a 30\% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle.

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arXiv2022

Prospects and challenges of numerical modelling of the Sun at millimetre wavelengths

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic possibilities that complement other commonly used diagnostics for the study of our Sun. In particular, ALMA's ability to serve as an essentially linear thermometer of the chromospheric gas at unprecedented spatial resolution at millimetre wavelengths and future polarisation measurements have great diagnostic potential. Solar ALMA observations are therefore expected to contribute significantly to answering long-standing questions about the structure, dynamics and energy balance of the outer layers of the solar atmosphere. In this regard, current and future ALMA data are also important for constraining and further developing numerical models of the solar atmosphere, which in turn are often vital for the interpretation of observations. The latter is particularly important given the Sun's highly intermittent and dynamic nature that involves a plethora of processes occurring over extended ranges in spatial and temporal scales. Realistic forward modelling of the Sun therefore requires time-dependent three-dimensional radiation magnetohydrodynamics that account for non-equilibrium effects and, typically as a separate step, detailed radiative transfer calculations, resulting in synthetic observables that can be compared to observations. Such artificial observations sometimes also account for instrumental and seeing effects, which, in addition to aiding the interpretation of observations, provide instructive tools for designing and optimising ALMA's solar observing modes. In the other direction, ALMA data in combination with other simultaneous observations enables the reconstruction of the solar atmospheric structure via data inversion techniques. This article highlights central aspects of the impact of ALMA for numerical modelling for the Sun, their potential and challenges, together with selected examples.

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arXiv2021

On the (mis)interpretation of the scattering polarization signatures in the Ca II 8542 A line through spectral line inversions

Scattering polarization tends to dominate the linear polarization signals of the Ca II 8542 A line in weakly magnetized areas ($B \lesssim 100$ G), especially when the observing geometry is close to the limb. In this paper we evaluate the degree of applicability of existing non-LTE spectral line inversion codes (which assume that the spectral line polarization is due to the Zeeman effect only) at inferring the magnetic field vector and, particularly, its transverse component. To this end, we use the inversion code STiC to extract the strength and orientation of the magnetic field from synthetic spectropolarimetric data generated with the Hanle-RT code. The latter accounts for the generation of polarization through scattering processes as well as the joint actions of the Hanle and the Zeeman effects. We find that, when the transverse component of the field is stronger than $\sim$80 G, the inversion code is able to retrieve accurate estimates of the transverse field strength as well as its azimuth in the plane of the sky. Below this threshold, the scattering polarization signatures become the major contributors to the linear polarization signals and often mislead the inversion code into severely over- or under-estimating the field strength. Since the line-of-sight component of the field is derived from the circular polarization signal, which is not affected by atomic alignment, the corresponding inferences are always good.

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arXiv2020

The Formation Height of Millimeter-wavelength Emission in the Solar Chromosphere

In the past few years, the ALMA radio telescope has become available for solar observations. ALMA diagnostics of the solar atmosphere are of high interest because of the theoretically expected linear relationship between the brightness temperature at mm wavelengths and the local gas temperature in the solar atmosphere. Key for the interpretation of solar ALMA observations is understanding where in the solar atmosphere the ALMA emission originates. Recent theoretical studies have suggested that ALMA bands at 1.2 (band 6) and 3 mm (band 3) form in the middle and upper chromosphere at significantly different heights. We study the formation of ALMA diagnostics using a 2.5D radiative MHD model that includes the effects of ion-neutral interactions (ambipolar diffusion) and non-equilibrium ionization of hydrogen and helium. Our results suggest that in active regions and network regions, observations at both wavelengths most often originate from similar heights in the upper chromosphere, contrary to previous results. Non-equilibrium ionization increases the opacity in the chromosphere so that ALMA mostly observe spicules and fibrils along the canopy fields. We combine these modeling results with observations from IRIS, SDO and ALMA to suggest a new interpretation for the recently reported "dark chromospheric holes", regions of very low temperatures in the chromosphere.

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arXiv2020

The Sun at millimeter wavelengths I. Introduction to ALMA Band 3 observations

We present an initial study of one of the first ALMA Band 3 observations of the Sun with the aim to characterise the diagnostic potential of brightness temperatures measured with ALMA on the Sun. The observation covers 48min at a cadence of 2s targeting a Quiet Sun region at disk-centre. Corresponding time series of brightness temperature maps are constructed with the first version of the Solar ALMA Pipeline (SoAP) and compared to simultaneous SDO observations. The angular resolution of the observations is set by the synthesized beam (1.4x2.1as). The ALMA maps exhibit network patches, internetwork regions and also elongated thin features that are connected to large-scale magnetic loops as confirmed by a comparison with SDO maps. The ALMA Band 3 maps correlate best with the SDO/AIA 171, 131 and 304 channels in that they exhibit network features and, although very weak in the ALMA maps, imprints of large-scale loops. A group of compact magnetic loops is very clearly visible in ALMA Band 3. The brightness temperatures in the loop tops reach values of about 8000-9000K and in extreme moments up to 10 000K. ALMA Band 3 interferometric observations from early observing cycles already reveal temperature differences in the solar chromosphere. The weak imprint of magnetic loops and the correlation with the 171, 131, and 304 SDO channels suggests though that the radiation mapped in ALMA Band 3 might have contributions from a larger range of atmospheric heights than previously assumed but the exact formation height of Band 3 needs to be investigated in more detail. The absolute brightness temperature scale as set by Total Power measurements remains less certain and must be improved in the future. Despite these complications and the limited angular resolution, ALMA Band 3 observations have large potential for quantitative studies of the small-scale structure and dynamics of the solar chromosphere.

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arXiv2019

Is the sky the limit? Performance of the revamped Swedish 1-m Solar Telescope and its blue- and red-beam re-imaging systems

We demonstrate that for data recorded with a solar telescope that uses adaptive optics and/or post-processing to compensate for many low- and high-order aberrations, the RMS granulation contrast is directly proportional to the Strehl ratio calculated from the residual (small-scale) wavefront error. We demonstrate that the wings of the high-order compensated PSF for SST are likely to extend to a radius of not more than about 2 arcsec, consistent with earlier conclusions drawn from straylight compensation of sunspot images. We report on simultaneous measurements of seeing and solar granulation contrast averaged over 2 sec time intervals at several wavelengths from 525 nm to 853.6 nm on the red-beam (CRISP beam) and wavelengths from 395 nm to 484 nm on the blue-beam (CHROMIS beam). These data were recorded with the Swedish 1-m Solar Telescope (SST) that has been revamped with an 85-electrode adaptive mirror and a new tip-tilt mirror, both of which were polished to exceptionally high optical quality. The highest 2-sec average image contrast measured in April 2015 through 0.3-0.9 nm interference filters at 525 nm, 557 nm, 630 nm and 853.5 nm with compensation only for the diffraction limited point spread function of SST is 11.8%, 11.8%, 10.2% and 7.2% respectively. Similarly, the highest 2-sec contrast measured at 395 nm, 400 nm and 484 nm in May 2016 through 0.37-1.3 nm filters is 16%, 16% and 12.5% respectively. The granulation contrast observed with SST compares favorably with that of other telescopes. Simultaneously with the above wideband red-beam data, we also recorded narrow-band continuum images with the CRISP imaging spectropolarimeter. We find that contrasts measured with CRISP are entirely consistent with the corresponding wide-band contrasts, demonstrating that any additional image degradation by the CRISP etalons and telecentric optical system is marginal or even insignificant.

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arXiv2018

Chromospheric condensations and magnetic field in a C3.6-class flare studied via He I D3 spectro-polarimetry

Context. Magnetic reconnection during flares takes place in the corona but a substantial part of flare energy is deposited in the chromosphere. However, high-resolution spectro-polarimetric chromospheric observations of flares are very rare. The most used observables are Ca II 8542 Å and He I 10830 Å. Aims. We aim to study the chromosphere during a C3.6 class flare via spectro-polarimetric observations of the He I D3 line. Methods. We present the first SST/CRISP spectro-polarimetric observations of He I D3. We analyze the data using the inversion code HAZEL, and estimate the LOS velocity and the magnetic field vector. Results. Strong He I D3 emission at the flare footpoints, as well as strong He I D3 absorption profiles tracing the flaring loops are observed during the flare. The He I D3 traveling emission kernels at the flare footpoints exhibit strong chromospheric condensations of up to $\sim$ 60 km/s at their leading edge. Our observations suggest that such condensations result in shocking the deep chromosphere, causing broad and modestly blueshifted He I D3 profiles indicating subsequent upflows. A strong and rather vertical magnetic field of up to $\sim$ 2500 G is measured in the flare footpoints, confirming that the He I D3 line is likely formed in the deep chromosphere at those locations. We provide chromospheric line-of-sight velocity and magnetic field maps obtained via He I D3 inversions. We propose a fan-spine configuration as the flare magnetic field topology. Conclusions. The He I D3 line is an excellent diagnostic to study the chromosphere during flares. The impact of strong condensations on the deep chromosphere has been observed. Detailed maps of the flare dynamics and the magnetic field are obtained.

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arXiv2017

A Hot Downflowing Model Atmosphere For Umbral Flashes And The Physical Properties Of Their Dark Fibrils

We perform NLTE inversions in a large set of umbral flashes, including the dark fibrils visible within them, and in the quiescent umbra by using the inversion code NICOLE on a set of full Stokes high-resolution Ca II 8542 A observations of a sunspot at disk center. We find that the dark structures have Stokes profiles that are distinct from those of the quiescent and flashed regions. They are best reproduced by atmospheres that are more similar to the flashed atmosphere in terms of velocities, even if with reduced amplitudes. We also find two sets of solutions that finely fit the flashed profiles: a set that is upflowing, featuring a transition region that is deeper than in the quiescent case and preceded by a slight dip in temperature, and a second solution with a hotter atmosphere in the chromosphere but featuring downflows close to the speed of sound at such heights. Such downflows may be related, or even dependent, on the presence of coronal loops, rooted in the umbra of sunspots, as is the case in the region analyzed. Similar loops have been recently observed to have supersonic downflows in the transition region and are consistent with the earlier "sunspot plumes" which were invariably found to display strong downflows in sunspots. Finally we find, on average, a magnetic field reduction in the flashed areas, suggesting that the shock pressure is moving field lines in the upper layers.

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arXiv2016

Properties of Supersonic Evershed Downflows

We study supersonic Evershed downflows in a sunspot penumbra by means of high spatial resolution spectropolarimetric data acquired in the Fe I 617.3 nm line with the CRISP instrument at the Swedish 1-m Solar Telescope. Physical observables, such as Dopplergrams calculated from line bisectors and Stokes V zero-crossing wavelengths, and Stokes V maps in the far red wing, are used to find regions where supersonic Evershed downflows may exist. We retrieve the LOS velocity and the magnetic field vector in these regions using two-component inversions of the observed Stokes profiles with the help of the SIR code. We follow these regions during their lifetime to study their temporal behavior. Finally, we carry out a statistical analysis of the detected supersonic downflows to characterize their physical properties. Supersonic downflows are contained in compact patches moving outward, which are located in the mid and outer penumbra. They are observed as bright, roundish structures at the outer end of penumbral filaments that resemble penumbral grains. The patches may undergo fragmentations and mergings during their lifetime, even some of them are recurrents. Supersonic downflows are associated with strong and rather vertical magnetic fields with a reversed polarity compared to that of the sunspot. Our results suggest that downflows returning back to the solar surface with supersonic velocities are abruptly stopped in dense deep layers and produce a shock. Consequently, this shock enhances the temperature and is detected as a bright grain in the continuum filtergrams, which could explain the existence of outward moving grains in the mid and outer penumbra.

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arXiv2016

Fan-shaped jets above the light bridge of a sunspot driven by reconnection

We report on a fan-shaped set of high-speed jets above a strongly magnetized light bridge (LB) of a sunspot observed in the H$α$ line. We study the origin, dynamics and thermal properties of the jets using high-resolution imaging spectroscopy in H$α$ from the Swedish 1-m Solar Telescope and data from the Solar Dynamics Observatory and Hinode. The H$α$ jets have lengths of 7-38 Mm, are impulsively accelerated to a speed of $\sim 100$ km/s close to photospheric footpoints in the LB, and exhibit a constant deceleration consistent with solar effective gravity. They are predominantly launched from one edge of the light bridge, and their footpoints appear bright in the H$α$ wings. AIA data indicates elongated brightenings that are nearly co-spatial with the H$α$ jets. We interpret them as jets of at least transition region temperatures. The magnetic field in the light bridge has a strength of $0.8-2$ kG and it is nearly horizontal. All jet properties are consistent with magnetic reconnection as the driver.

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arXiv2016

Emergence of granular-sized magnetic bubbles through the solar atmosphere. III. The path to the transition region

We study the ascent of granular-sized magnetic bubbles from the solar photosphere through the chromosphere into the transition region and above, for the first time. Such events occurred in a flux emerging region in NOAA 11850 on September 25, 2013. During that time, the first co-observing campaign between the Swedish 1-m Solar Telescope and the IRIS spacecraft was carried out. Simultaneous observations of the chromospheric H$α$ 656.28 nm and \ion{Ca}{2} 854.2 nm lines, plus the photospheric \ion{Fe}{1} 630.25 nm line, were made with the CRISP spectropolarimeter at the SST reaching a spatial resolution of 0."14. At the same time, IRIS was performing a four-step dense raster of the said emerging flux region, taking slit-jaw images at 133 (C~{\sc ii}, transition region), 140 (\ion{Si}{4}, transition region), 279.6 (\ion{Mg}{2} k, core, upper chromosphere), and 283.2 nm (\ion{Mg}{2} k, wing, photosphere). Spectroscopy of several lines was performed by the IRIS spectrograph in the far and near ultraviolet, of which we have used the \ion{Si}{4} 140.3 and the \ion{Mg}{2} k 279.6 nm lines. Coronal images from the Atmospheric Imaging Assembly of the Solar Dynamics Observatory were used to investigate the possible coronal signatures of the flux emergence events. The photospheric and chromospheric properties of small-scale emerging magnetic bubbles have been described in detail in Ortiz et al. (2014). Here we are able to follow such structures up to the transition region. We describe the properties, including temporal delays, of the observed flux emergence in all layers. We believe this may be an important mechanism of transporting energy and magnetic flux from subsurface layers to the transition region and corona.

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arXiv2015

Small-scale magnetic flux emergence in a sunspot light bridge

We analyse a sequence of high-resolution spectropolarimetric observations of a sunspot taken at the 1-m SST, to determine the nature of flux emergence in a light bridge and the processes related to its evolution in the photosphere and chromosphere. Blueshifts of about 2 km/s are seen near the entrance of a granular light bridge on the limbward side of the spot. They lie next to a strongly redshifted patch that appeared 6 mins earlier. Both patches are seen for 25 mins until the end of the sequence. The blueshifts coincide with an elongated emerging granule, while the redshifts appear at the end of it. In the photosphere, the development of the blueshifts is accompanied by a simultaneous increase in field strength and inclination, with the field becoming nearly horizontal. In the redshifted patch, the magnetic field is equally horizontal but of opposite polarity. An intense brightening is seen in the Ca filtergrams over these features, 17 mins after they emerge in the photosphere. The brightening is due to emission in the blue wing of the Ca line, close to its knee. Non-LTE inversions reveal that the asymmetric emission is caused by a temperature enhancement of about 700 K between -5.0<log tau<-3.0 and a blueshift of 3 km/s at log tau=-2.3. The photospheric blueshifts and redshifts seem to be caused by the emergence of a small-scale, flat Omega-loop with highly inclined footpoints of opposite polarity. The gas motions detected in the two footpoints are reminiscent of a siphon flow. The rising loop is probably confined to the lower atmosphere by the overlying sunspot magnetic field and the subsequent interaction may be responsible for temperature enhancements in the upper photosphere/lower chromosphere. This is the first time that magnetic flux is observed to emerge in the strongly magnetised environment of sunspots, pushed upward by the convective flows of a granular light bridge.

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arXiv2013

Emergence of granular-sized magnetic bubbles through the solar atmosphere: I. Spectropolarimetric observations and simulations

We study a granular-sized magnetic flux emergence event that occurred in NOAA 11024 in July 2009. The observations were made with the CRISP spectropolarimeter at the Swedish 1 m Solar Telescope achieving a spatial resolution of 0.14". Simultaneous full Stokes observations of the two photospheric Fe I lines at 630.2 nm and the chromospheric Ca II 854.2 nm line allow us to describe in detail the emergence process across the solar atmosphere. We report here on 3D semi-spherical bubble events, where instead of simple magnetic footpoints, we observe complex semi-circular feet straddling a few granules. The most characteristic signature in these events is the observation of a dark bubble in filtergrams taken in the wings of the Ca II 854.2 nm line. We can infer how the bubble rises through the solar atmosphere as we see it progressing from the wings to the core of Ca II 854.2 nm. In the photosphere, the magnetic bubble shows mean upward Doppler velocities of 2 km/s. In about 3.5 minutes it travels some 1100 km to reach the mid chromosphere, implying an average ascent speed of 5.2 km/s. To aid the interpretation of the observations, we carry out 3D numerical simulations of the evolution of a horizontal, untwisted magnetic flux sheet injected in the convection zone, using the Bifrost code. The computational domain spans from the upper convection zone to the lower corona. In the modeled chromosphere the rising flux sheet produces a large, cool, magnetized bubble. We compare this bubble with the observed ones and find excellent agreement, including similar field strengths and velocity signals in the photosphere and chromosphere, temperature deficits, ascent speeds, expansion velocities, and lifetimes.

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arXiv2013

Short dynamic fibrils in sunspot chromospheres

Sunspot chromospheres display vigorous oscillatory signature when observed in chromospheric diagnostics like the strong Ca II lines and H-alpha. New high-resolution sunspot observations from the Swedish 1-m Solar Telescope show the ubiquitous presence of small-scale periodic jet-like features that move up and down. This phenomenon has not been described before. Their typical width is about 0.3 arcsec and they display clear parabolic trajectories in space-time diagrams. The maximum extension of the top of the jets is lowest in the umbra, a few 100 km, and progressively longer further away from the umbra in the penumbra, with the longest more than 1000 km. These jets resemble dynamic fibrils found in plage regions but at smaller extensions. LTE inversion of spectro-polarimetric Ca II 8542 observations enabled for a comparison of the magnetic field inclination and the properties of these short jets. We find that the most extended of these jets also have longer periods and tend to be located in regions with more horizontal magnetic fields. This is a direct observational confirmation of the mechanism of long-period waves propagating along inclined magnetic fields into the solar chromosphere. This mechanism was identified earlier as the driver of dynamic fibrils in plage, part of the mottles in quiet Sun, and type I spicules at the limb. The sunspot dynamic fibrils that we report here represent a new class of manifestation of this mechanism. They are not the same as the transient penumbral and umbral micro-jets reported earlier.

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arXiv2013

Magnetic tornadoes and chromospheric swirls -- Definition and classification

Chromospheric swirls are the observational signatures of rotating magnetic field structures in the solar atmosphere, also known as magnetic tornadoes. Swirls appear as dark rotating features in the core of the spectral line of singly ionized calcium at a wavelength of 854.2 nm. This signature can be very subtle and difficult to detect given the dynamic changes in the solar chromosphere. Important steps towards a systematic and objective detection method are the compilation and characterization of a statistically significant sample of observed and simulated chromospheric swirls. Here, we provide a more exact definition of the chromospheric swirl phenomenon and also present a first morphological classification of swirls with three types: (I) Ring, (II) Split, (III) Spiral. We also discuss the nature of the magnetic field structures connected to tornadoes and the influence of limited spatial resolution on the appearance of their photospheric footpoints.

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arXiv2012

Temporal Evolution of Velocity and Magnetic Field in and around Umbral Dots

We study the temporal evolution of umbral dots (UDs) using measurements from the CRISP imaging spectropolarimeter at the Swedish 1-m Solar Telescope. Scans of the magnetically sensitive 630 nm iron lines were performed under stable atmospheric conditions for 71 min with a cadence of 63 s. These observations allow us to investigate the magnetic field and velocity in and around UDs at a resolution approaching 0.13". From the analysis of 339 UDs, we draw the following conclusions: (1)UDs show clear hints of upflows, as predicted by magnetohydrodynamic (MHD) simulations. By contrast, we could not find systematic downflow signals. Only in very deep layers we detect localized downflows around UDs, but they do not persist in time. (2) We confirm that UDs exhibit weaker and more inclined fields than their surroundings, as reported previously. However, UDs that have strong fields above 2000 G or are in the decay phase show enhanced and more vertical fields. (3)There are enhanced fields at the migration front of UDs detached from penumbral grains, as if their motion were impeded by the ambient field. (4) Long-lived UDs travel longer distances with slower proper motions. Our results appear to confirm some aspects of recent numerical simulations of magnetoconvection in the umbra (e.g., the existence of upflows in UDs), but not others (e.g., the systematic weakening of the magnetic field at the position of UDs.)

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