The Second Flight of the Sunrise Balloon-borne Solar Observatory: Overview of Instrument Updates, the Flight, the Data, and First Results

Gondola. Structural protective elements on the gondola, such as the crush pad assembly below the core gondola frame or the front and rear roll cages, needed to be replaced, as they were designed to deform and thus to take most of the impact energy to protect the rest of the payload. In addition to such refurbishment, modifications were implemented to the gondola, as described below.

The average power consumption during the first flight was much lower than previously estimated, so that the number of solar cells could be reduced to only six panels with 80 SunPower A-300 cells each (from originally 10 panels in 2009). The panels were mechanically re-arranged, reducing the overall width of the instrument. This modification allowed a pre-installation of the solar panels in the integration hall before roll-out, saving precious time on the day of the launch. Additional benefits are reduced mass and a lower aerodynamic cross section.

The mounting of the electronics racks, carrying all the instrument computers, pointing system computer and power distribution units, was modified for the 2013 flight. Instead of having a 20° tilt toward cold sky as in the previous configuration, the racks were now mounted vertically and were directly attached to the gondola side trusses, providing higher overall stiffness and reduced mass. The reduction in thermal efficiency of this configuration was seen to be acceptable, as results from the 2009 flight indicated that the size of the radiating surfaces are sufficiently large to dump all dissipated heat at moderate temperatures even in this slightly less efficient configuration.

As part of the on-ground testing before the flight, a modal survey test was performed to determine the first natural eigenmodes of the complete instrument. A set of externally mounted accelerometers recorded the impulse and frequency response to an impact on the gondola structure. It was verified that the 10 Hz oscillation observed in the pointing data of the 2009 science flight corresponds to the first torsional bending mode of the gondola core framework. Modifications of software filters were then implemented into the pointing system control loops, preventing excitation of this mode during the 2013 flight. Pointing system housekeeping data taken during the 2013 flight clearly demonstrated their efficiency, as almost no 10 Hz oscillations were present during the time spent at float altitude and in particular not when pointing at the Sun.

Telemetry. The 2009 flight operations and commissioning were hampered by the early loss of the E-Link high-speed telemetry provided by ESRANGE,¹¹ which ceased operation after only a few hours when switching from one ground station to another. For the rest of the 2009 mission commanding and health status information was transmitted through a 6 kbit s^–1 TDRSS link, where TDRSS is the Tracking and Data Relay Satellite System, a NASA network of communication satellites on geosynchronous orbits and associated ground stations used for space-to-ground communication. This was found to be clearly insufficient.

In preparation for the 2013 science flight the Sunrise team helped to qualify the Iridium Pilot/OpenPort system for balloon flights. A dedicated test set-up was flown on 2011 September 28 and October 7 from Ft. Sumner on balloons of the Columbia Scientific Ballooning Facility (CSBF) of NASA for several hours each, to verify system integrity during launch, ascent, and operational conditions. The bandwidth transmitted to ground was more than ten times higher than with the TDRSS Omni link. Sunrise  II was one of the first scientific missions to be supported with this new telemetry system. The antenna system on top of the gondola was re-arranged to provide the required 6 ft clearance to the dome-shaped Iridium transmitter. Sunrise  II reached an average data rate of 100 kbit s^–1, and downlink of science data continued even after the payload landed, although the antenna was partly buried in Canadian soil.

Telescope and structure. The telescope and instrumentation needed a thorough cleaning and refurbishment. All mechanisms were disassembled, inspected, cleaned, lubricated, re-assembled, and requalified. The motor and gears of the telescope aperture mechanism were replaced and the mechanism was improved to provide a more reliable detection of the open or closed position. Key elements of the carbon-fiber based structure were inspected, strength tested, and found to be still fully intact. The thermal subsystem consisting of the heat rejection wedge and its radiators needed to be refurbished. New second surface mirrors were attached. All telescope mirror coatings were stripped, the mirrors cleaned, their optical quality interferometrically verified and recoated. The secondary mirror needed to be replaced completely, as the Zerodur mirror substrate was damaged during the landing and recovery after the 2009 flight. The mirror was refabricated by the Lytkarino Optical Glass Factory in Moscow, with a performance identical to the original one.

The telescope alignment proved to be a challenge, because a sufficiently large reference flat mirror provided by SAGEM for the 2009 flight was not available this time. Since on the launch site a misalignment of the telescope was detected (the telescope had been tested before departure to Kiruna without a 1 m reference flat, making the performance assessment ambiguous), a readjustment of the M2 position was necessary.

Figure 1 shows two views of the Sunrise  II payload (telescope with instruments and electronics mounted in the gondola) hanging from the launch crane at the ESRANGE balloon launch facility. More details about the whole system are provided by Barthol et al. (2011).

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The instrumentation mounted within the PFI platform survived the landing and recovery in good shape. Some cleaning was necessary, but almost all elements could be re-used. The PFI was refurbished, but remained technically identical to the one used during the 2009 flight. The scientific instruments were also refurbished and subsequently integrated and realigned.

ISLiD. The ISLiD system (Gandorfer et al. 2011) was not modified relative to the first flight. In order to optimize the end-to-end optical performance of the combined ISLiD–IMaX path, an additional plane-parallel plate was introduced into the converging IMaX feed path in front of the IMaX interface focus. By choosing the inclination and orientation of this plate, residual astigmatism in the ISLiD/IMaX path could be minimized. The plate was coated with high-efficiency anti-reflective layers on both sides, which were tuned to be unpolarizing at the selected angle of incidence.

CWS. The main improvement to the CWS (Berkefeld et al. 2011) for the 2013 flight consisted of a second operating mode. By reading out only the two sub-apertures in the center row (marked red in Figure 2), the bandwidth could be substantially increased and the residual image jitter decreased. Table 1 compares the two modes.

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Due to the better performance, the two-sub-aperture mode was used exclusively during the 2013 flight. Further software improvements included better data logging capabilities and much faster focusing after closing the CWS control loop.

SuFI. The SuFI (Gandorfer et al. 2011) was changed very little compared to the Sunrise  I flight. Thus, the mechanical shutter, which had seen more than 150,000 releases during the 2009 flight, was replaced. For the SuFI CCD camera a new power supply unit with very low output noise was developed. This led to an improvement in signal-to-noise performance by a factor of more than ten. In addition, three of the wavelength filters were exchanged. The filter set for observations in the 2140 Å region was replaced by a combination of two different filters, both of which had a FWHM of 210 Å, but had different side band characteristics, which ensured sufficient blocking of longer wavelength radiation. The 3120 Å channel of Sunrise  I was replaced by a combination of a 2795 Å filter with 4.8 Å width and two blockers of 300 Å and 110 Å width, respectively. This combination of filters, whose profile is plotted in Figure 1 of Riethmüller et al. (2013a), is centered on the Mg ii k line and gets minimal contribution from the Mg ii h line located in the filter profile's wings. Observations in the Ca ii H line were possible through two different filters centered at 3968 Å. In addition to the 1.8 Å wide filter already used in Sunrise  I, a 1.1 Å wide filter was available, which provided better isolation of the contributions from higher atmospheric layers. In the following, these channels are referred to as the 3968w ("w" for wide wavelength band) and 3968n ("n" for narrow band) channels. The 3880 Å channel, which was used in Sunrise  I, was sacrificed for this purpose.

IMaX. The IMaX (Martínez Pillet et al. 2011a) on the 2013 flight was also very similar to the version flown on Sunrise  I, although a number of smaller changes and updates had been made. The parts replaced included the Field Programmable Gata Array (FPGA) in the proximity electronics, the LiNbO₃ etalon, one of the CCD cameras, the collimator doublet, the liquid crystal variable retarders (LCVRs), the power supply for the LCVR heaters (the heaters on the Sunrise I flight did not have enough power to bring the instrument to its nominal operational temperature) and the phase-diversity (PD) plate (the original broke upon landing after the Sunrise I flight). Most of these parts were replaced by nearly identical ones. In addition, the windows of both CCD cameras were removed in order to avoid fringes that had been observed during the Sunrise  I flight.

The SuFI data, as on the first flight, were acquired in PD mode, i.e., one half of the sensor was located in the focal plane, while the other half imaged the same part of the solar surface as the first half, but with a fixed offset in the focus direction. This configuration is necessary, since aberrations of the telescope, although small enough to allow for diffraction limited performance at visible wavelengths, are not negligible at the much shorter UV wavelengths. The PD technique in principle allows for the determination and subsequent removal of these aberrations, provided one of the pair of images is in or very near focus according to Gonsalves & Chidlaw (1979) and Paxman et al. (1992).

Therefore, after the traditional darkfield and flatfield corrections, the data were restored using the Multi-Frame Blind Deconvolution (MFBD) wavefront sensing code (van Noort et al. 2005), which allows for an arbitrary PD term to be present in the data. Due to the highly non-telecentric configuration of the beam, however, the image scale of the defocused image was slightly different from the image scale in the focal plane, so that the influence of the tip-tilt components of the wavefront aberrations in the defocused channel differed from those in the focal plane. This effect was accommodated by restoring the frames in the "calibration mode" of the MFBD code, where all fitted wavefront modes are constrained to be the same for the two channels, with the exception of the tip-tilt and focus terms, which are allowed to vary, but with the difference between the focus and defocus channels constrained to have the same value for all PD pairs in the data set. Due to the relatively low frame rate of the SuFI camera, only four PD pairs, recorded in approximately twenty seconds, could be combined to restore each frame, beyond which the solar evolution started to degrade the result.

Although this method worked well on some of the data, it did not always restore the data to the same quality. This is believed to be the result of residual pointing errors during the relatively long exposure time, that blurred the image in a way that is not consistent with the model, which assumes the point-spread function (PSF) to be produced by a single, static wavefront. The azimuthally averaged Fourier power spectrum of the best frames, however, shows power significantly above the noise floor, at wave numbers up to 85% of the true diffraction limit of ${D}_{\mathrm{telescope}}/\mathrm{lambda}$ (DL, see for instance Paxman et al. 1996), which is slightly better than the criterion of ${D}_{\mathrm{telescope}}/(1.22\lambda )$ proposed by Rayleigh (1879) and generally adopted for considering individual features to be resolved.

The reduction applied to the data from the 2009 flight was explained in detail by Martínez Pillet et al. (2011a). Consequently, here we focus on changes in the data reduction with respect to the reduction of the first flight's data, necessitated by the replacement of several components of IMaX (described in Section 2.2). These replacements influenced various instrumental effects of IMaX such as the occurrence of fringes, ghost images, and the instrument's stray-light behavior.

After the data were corrected for dark current and flat-field effects, residual excess power due to interference fringes was filtered out in the Fourier domain. Before and after each observing run during the flight, a PD measurement was obtained by inserting a glass plate into the optical path of the first camera in order to record pairs of defocusd and focused images, which then allowed retrieval of the system's PSF. The observational data were reconstructed by applying a modified Wiener filter constructed from the PD PSF. By spatially replicating the images before performing operations in the Fourier domain, a reduction of the fields of view (FOVs) as a side effect of a necessary apodization could be avoided. Hence the effective FOV of the IMaX data from Sunrise  II is $51^{\prime\prime} \times 51^{\prime\prime}$.

The instrumental polarization was removed from the observations by a demodulation matrix determined from the pre-flight polarimetric calibration. In contrast to the first flight, this time the FOV dependence of that matrix was taken into account. Since the on-ground polarimeric calibration did not include the main mirror of the telescope and because the thermal environment during calibration was different to the in-flight situation, cross-talk with Stokes I had to be removed from the data. Then the images of the two cameras were co-aligned and merged.

In addition, a slight periodic motion of the image was removed, that was not present in the data of the first flight and correlated well with the switching period of the heating power of the LCVRs, which were mounted near one of the folding mirrors. We also added a further step to the data reduction pipeline that interpolated the spectral scans with respect to time in order to compensate for the solar evolution during the IMaX cycle time of 36.5 s.

Finally, we determined the spatial mean Stokes I profile and subtracted 25% of the mean profile from the individual profiles to correct the data for 25% global stray light. This is equivalent to deconvolving the IMaX data with a constant stray light not varying over the FOV. Details of the stray-light properties of IMaX can be found in Riethmüller et al. (2017).

The physical quantities of the solar atmosphere were then retrieved from the reconstructed Stokes images via the Stokes-Profiles-INversion-O-Routines (SPINOR; Frutiger 2000; Frutiger et al. 2000), which uses the STOPRO routines to solve the Unno–Rachkovsky equations (Solanki 1987). A relatively simple inversion strategy was applied to get robust results: three optical depth nodes for the temperature (at $\mathrm{log}\tau =-2.5,-0.9,0$) and a height-independent magnetic field vector, line of sight velocity, and micro-turbulence. The synthetic spectra were not only calculated for the Fe i 5250.2 Å line but also for its neighboring lines (Co i line at 5250.0 Å and the Fe i line at 5250.6 Å) to include their influence. The spectral resolution of IMaX was taken into account by convolving the synthesized spectra with the spectral transmission profile of IMaX measured in the laboratory during a pre-flight calibration campaign (see the bottom panel of Figure 1 in Riethmüller et al. 2014).

The SPINOR inversion code was run for ten iterations, then the output maps of the individual parameters were spatially smoothed and used as the initial guess parameters to a further run of ten iterations. The intermediate smoothing of the free parameters of the inversion was introduced to get rid of spatial discontinuities in the physical quantities that can occur if the inversion gets stuck in local minima of the merit function at individual pixels or groups of pixels. This procedure was repeated five times (implying 50 iterations in all), with a gradually decreasing amount of smoothing. Finally, the resulting LOS velocity maps were corrected for the etalon blueshift, which is caused by the collimated setup (see Martínez Pillet et al. 2011a).

The longest time series obtained by Sunrise  II was focused on NOAA AR 11768 at $\cos \theta =\mu =0.93$, where θ is the heliocentric angle. The observations were made on 2013 June 12, starting at 23:39 UT, about 1.5 days after the initial appearance of the active region, at a time when magnetic flux was still emerging. At that time the active region had developed a full-fledged leading polarity sunspot, while the following polarity was mainly concentrated in a string of pores.

The active region is illustrated in Figure 4 at the time of the Sunrise  II observations. The IMaX and SuFI FOVs are overplotted on a Helioseismic and Magnetic Imager (HMI) continuum image and an HMI magnetogram and are indicated by the blue boxes.¹² IMaX covered most of the following magnetic polarity pores, including the largest one. The largest pore had a complex structure and on one side showed a feature with a roughly penumbral brightness exhibiting elongated structures. In the course of the further development, however, this feature did not develop into a proper penumbra (as can be deduced from the animation of Figure 4). The IMaX FOV also contained some of the leading polarity flux, mainly in the form of facular magnetic elements. Sunrise  II also caught a region of emerging flux, to be found in the central southern part of the IMaX FOV and partly in the much smaller SuFI FOV, which captured mainly the region between the two polarities, including one of the emergence events.

The animated Figure 4 shows the evolution of the active region from the very first emergence 1.5 days prior to the start of Sunrise  II observations of this region to approximately 1.5 days after the end of the observations of this region. A significant amount of flux appeared in the day after the Sunrise  II observations, which led to the formation of a proper following polarity sunspot, as well as to an increased size of the leading polarity spot, mainly through the coalescence of pores, many of which already carried a piece of penumbra on one side prior to merging. The blue boxes overlaid on the images in the animated figure are tilted by the rotation angle relative to solar north and the roughly 5° of rotation during the course of the SuFI time series is taken into account. Note that the animated Figure 4 runs at a slower speed during the time of the Sunrise  II observations of this region.

The SuFI instrument during the second flight of Sunrise provided diffraction-limited images at 3000 Å and at 3968 Å in both the broader and the narrower channel centered on the core of the Ca ii H line. An image at each of these wavelengths is plotted in Figure 5. Note that during this, the longest time series obtained by SuFI, no data in Mg ii k, nor in the 2140 Å channel were obtained due to the low solar elevation at that time and the consequent high atmospheric absorption at these wavelengths.

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Strongly different structures are seen at 3000 Å and in the Ca ii H line, with the shorter wavelength displaying granulation (as had already been noticed in the Sunrise I data, e.g., Hirzberger et al. 2010; Solanki et al. 2010), but also bright points (Riethmüller et al. 2010), pores with internal fine structure, and a bright elongated granule located at approximately 30''–32'' in the x-direction and 15''–16'' in the y-direction. This last feature is found to be associated with magnetic flux emergence. The two brightest features in the 3000 Å image are located near the two ends of this structure; on its left it brightens to the level of a strong bright point, while there is a bright facular region right at the edge of the FOV in the continuation of the elongated granule on its right side.

The surprising lack of difference between the broader and narrower Ca ii H channels in Figure 5 suggests that they were observing very similar layers of the Sun. Possibly, the filter selecting the narrower channel had drifted in wavelength (e.g., due to temperature changes in the instrument) and was not centered exactly on Ca ii H₃. Due to the similarity between the broad and the narrow Ca ii H channels, in the following the discussion will concentrate on the narrower channel.

In the Ca ii H images the dominant structures are slender fibrils directed roughly across the SuFI FOV, many of which seem to emanate from the large pore just to the left of the SuFI image. They appear to be similar to those observed earlier by Pietarila et al. (2009). Although most of the filaments seem to roughly follow the same direction, a number of them do cross each other. This is particularly clearly seen close to the location of the emerging magnetic flux mentioned above, at around (30''–34'', 13''–15''). Very likely this is due to fibrils belonging to previously existing magnetic field overlying those associated with the emerging flux that are directed differently. The lengths of these fibrils are hard to determine, due to inhomogeneities that may be present in the background, but some seem to extend over a fair portion of the width of the SuFI images. Strikingly, the fibrils are also constantly evolving and in motion. The lengths, along with other properties of these fibrils, are studied in a further paper in this special issue (Gafeira et al. 2017b), while the dynamics of the fibrils, in particular wave modes travelling along them, are investigated by Jafarzadeh et al. (2017b) and by Gafeira et al. (2017a).

The brightenings seen at 3000 Å in connection with the flux emergence are also visible in Ca ii H. The magnetic flux emergence caught by IMaX and SuFI is investigated by Centeno et al. (2017) and Danilovic et al. (2017). At a later stage during the time series this brightening develops further into a small flare that engulfs the emerging flux region and is prominently visible in the Ca ii H line.

SuFI on board Sunrise  II also obtained the first high-resolution images in the Mg ii k line, which have already been published in two earlier papers (Riethmüller et al. 2013a; Danilovic et al. 2014). Images taken in the Mg ii k filter were found to have considerable similarity with nearly simultaneously recorded Ca ii H images, although some distinct differences were also found. These included a 1.4–1.7 times larger intensity contrast and a more smeared appearance. Exampls of Mg ii k images of the quiet Sun and of a weak plage/enhanced network region are shown in Figure 6. These images were exposed for 50 s to counter the strong atmospheric absorption at this wavelength and to obtain a sufficient signal-to-noise ratio. The images are based on SuFI level 3 data, i.e., data that have been PD reconstructed using wave-front errors averaged over the whole time series of images. See Hirzberger et al. (2011) for more details on reduction and PD reconstruction of SuFI data.

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It was concluded that some of these differences may be caused by the much longer integration time needed to record the Mg ii k images due to the strong ozone absorption at that wavelength, while others are likely intrinsic. Possible reasons for the intrinsic differences given by Danilovic et al. (2014) include greater formation height and greater formation height range of the Mg line (the latter due to the rather broad Mg filter) and the stronger response of the emission peaks of Mg ii k to temperature.

The continuum intensity in the visible recorded by IMaX at +227 mÅ from the line center is plotted in Figure 7(a). IMaX images contain a larger number of pores than SuFI due to the bigger FOV. As expected for the continuum intensity at 5250 Å, bright points are much less prominent than at 3000 Å (Figure 5(a)), although the fine structure in the largest pore is clearly visible, with some of the bright "umbral dots" being among the brighter structures in the image. Also clesrly visible in that figure is the long elongated granule already pointed out in the 3000 Å image (located at (30'', 15'') in the IMaX FOV). Another similar granule is found to its right. Both are associated with magnetic flux emergence.

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The bright points in the line core image displayed in Figure 7(b), often forming connected chains filling the intergranular lanes, possess a high contrast. Here, what we refer to as the line core intensity is simply the intensity at the central IMaX wavelength point, which is nominally located at the wavelength of the Fe i 5250.2 Å line core. Chains of such bright points surround most of the pores, but the most prominent bright feature in this image is the strong brightening located between the two elongated granules, i.e., between the two small flux emergence events. The line core of Fe i 5250.2 Å obviously forms below the height of formation of the radiation sampled by either of the two SuFI Ca ii H filters, as the iron line core image still shows faint vestiges of granulation and no signs of fibrils. All quantities in Figure 7 are normalized to the respective intensity averaged over two areas within the joint IMaX and SuFI FOV with near-quiet-Sun conditions, i.e., a relatively low magnetic flux density. We call this averaged "quiet-Sun" intensity, ${I}_{\mathrm{QS}}$. Note that the granule pattern changes to that of reversed granulation if instead of being divided by ${I}_{\mathrm{QS}}$, as is the case in Figure 7(b), the line core intensity is divided by the local continuum intensity, i.e., ${I}_{+227}$, at each pixel (Kahil et al. 2017).

Stokes I, Q, U, and V in the red flank of 5250.2 are plotted in Figures 7(c)–(f). The differences between Figure 7(c) and Figures 7(a) and b are due to the formation height of the line flank (at +40 mÅ) lying between those of the other two wavelengths and the fact that the intensity in the line flank, i.e., in Figure 7(c), is very sensitive to the Doppler shift of the spectral line. The intensity in the line core, as plotted in Figure 7(b), is also affected by Doppler shifts, but to a much lesser extent than the line flanks.

Maps of the best-fit parameters obtained from the inversion of the IMaX Stokes vectors illustrated in Figure 7, are presented in Figure 8. The panels in the upper row display the temperature at the three nodes at which it was determined, $\mathrm{log}(\tau )=0$, $\mathrm{log}(\tau )=-0.9$ and $\mathrm{log}(\tau )=-2.5$; the lower panels give the magnetic field strength, B, the inclination of the magnetic field relative to the line of sight, γ, and the line-of-sight velocity, ${v}_{\mathrm{LOS}}$.

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The results of the inversions reveal some conspicuous features. Among these are the strong blue- and redshifts in the granulation (note that we have not removed the p-modes from the inverted data, so the velocities are influenced by such oscillations). The velocity amplitude is larger than in the granulation shown by Solanki et al. (2010). An important reason for this is that scattered light has been removed from the present data, while the data analyzed by Solanki et al. (2010) were still affected by scattered light. Some discrepancy can also be introduced because the velocities displayed by Solanki et al. (2010) were obtained from a Gaussian fit to line profiles sampled at four wavelengths, while the velocities presented here were provided by the SPINOR inversions of line profiles sampled at seven wavelength points. One of the emerging flux patches is found to be associated with a strong blueshift, much stronger than the other emerging flux feature.

One noticeable feature of the inversion results is that the photospheric field strength in pores often reaches 2500 G (comparable with the highest values found from Hinode data after deconvolving with the PSF; Quintero Noda et al. 2016). In some places higher field strengths are reached, but these cannot be trusted due to the limited wavelength range of the observations and the fact that the continuum point at +227 mÅ starts to be affected.

Another striking feature is that, whereas all pores are clearly cooler than their surroundings at the two lower heights ($\mathrm{log}\tau =0,-0.9$), only the larger pores are clearly distinguishable from their surroundings in the temperature map at $\mathrm{log}\tau =-2.5$. The smaller pores can hardly be separated from their surroundings. In contrast, the line core image in Figure 7 shows a darkening also at the locations of the smallest pores. However, this is mainly due to the lower continuum intensity at these locations. Also, the line core is affected by the Zeeman effect and to a smaller extent also Doppler shifts, so that it is not an unalloyed measure of the temperature. In order to test whether the inversions are giving a reasonable representation of the temperature stratification in pores we consider the SuFI Ca ii H channel.

To compare SuFI and IMaX data the images at individual SuFI wavelengths were aligned to sub-pixel accuracy with the most similar IMaX images. For 3000 Å this is the 5250.4 Å continuum, while the Ca ii H channel is compared with the IMaX line core, normalized to ${I}_{+227}$ at each pixel individually (then the images look more similar). More information on the procedure are provided by Kaithakkal et al. (2017); see also Jafarzadeh et al. (2017b).

Thumbnails of T at $\mathrm{log}\tau =0,-0.9$ and −2.5 as well as of IMaX continuum intensity, ${I}_{+227}$, and the intensity in SuFI 3000 and 3968n Å channels ("n" is for the narrow Ca ii H channel introduced in Section 2.2) are plotted in Figure 9 for two small pores in the top-right part of the SuFI FOV, and in Figure 10 for a single, very small, somewhat weaker pore in the lower part of the SuFI FOV. Overlaid on both pores are contours of the 1400 G level of the magnetic field. In the following, we consider this contour as an independent boundary of the pore, or more exactly of the magnetic concentration underlying the pore.

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1400 G is found to be a good compromise, on the one hand, to isolate a pore from the bright points in its neighborhood while, on the other hand, keeping as much of the pore as possible within the contour. For example, if we take 1200 G or 1300 G, then the bright points often found in the immediate vicinity of pores are included in the contours of some of the pores. If, however, we use a larger value, such as 1500 G or 1600 G, then we include less of the dark part of the pore in the contour. To illustrate this we have added also contours of 1200 G and 1600 G besides those of 1400 G in Figure 9. The 1200 G contour includes bright extensions from the smaller (lower left) pore in this image, while the 1600 G contour misses a significant fraction of the upper right pore.

Interestingly, the 1400 G contour often lies outside the actual pores as seen in, e.g., ${I}_{+227}$ or the SuFI 3000 Å channel. When comparing with ${I}_{+227}$, a part of this difference may have to do with the expansion of the field with height. However, the difference in size is just as large when considering the temperature at $\mathrm{log}\tau =-0.9$, which is much closer to the height at which the magnetic field is determined. Hence, these images demonstrate that pores are surrounded by regions of strong magnetic field that extend well beyond the visible boundaries of the individual pores (see also Martinez Pillet 1997). Of course, the magnetic field, being determined from multiple recordings, is more susceptible to jitter, and may not have the same high resolution as the individual images it is compared with. This extension of strong fields beyond the boundary of the pore still holds even if we consider a threshold of 1500 G or even 1600 G, even though some of the dark parts of the pores no longer lie within the 1600 G contour.

Figures 9 and 10 confirm that the temperature in the lower two inversion nodes are clearly lower than in the surroundings, but are rather similar in the upper node. Similarly, in ${I}_{+227}$ and at 3000 Å the pores are all clearly dark, while in Ca ii H the picture is more mixed. Whereas the pore in Figure 10 is clearly as bright as its surroundings and even has a particularly bright intrusion, the pores seen in Figure 9 both appear to be somewhat darker than their immediate surroundings.

We note, however, that the immediate surroundings of the pores in the Ca images are relatively bright (see Figure 5). The pores are often surrounded by considerable magnetic flux that produces a local brightening. In radiation coming from the lower photosphere, some of this is visible as bright points, or particularly bright granules or granule walls (similar to faculae near the limb, e.g., Carlsson et al. 2004; Keller et al. 2004; Lites et al. 2004). In the low chromosphere, however, this concentration of magnetic flux produces enhanced brightenings in the form of mainly short fibrils surrounding the pores. The pores are not substantially darker than other, less bright parts of the solar surface in the Ca ii H filter (see Figure 5).

To study this more quantitatively, we plot the corresponding histograms in Figures 11 and 12. Each set of histograms represents either the three temperatures, at $\mathrm{log}\tau =0,-0.9,-2.5$ (left panels), or the three intensities (IMaX ${I}_{+227}$, SuFI 3000 Å, SuFI 3968n Å; right panels) studied here. All intensities and temperatures in Figures 11 and 12 are normalized to patches of comparatively quiet Sun (i.e., with low amounts of magnetic flux) near the top left and the bottom of the SuFI FOV.

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In all pores the temperatures in the two lower layers and the intensities at the wavelengths formed deeper (IMaX ${I}_{+227}$ and SuFI 3000 Å) are predominantly lower than in the quiet Sun. The pixels in which they are higher are often the hot walls of neighboring granules that are seen through a strong magnetic field. The same is true for the intensities in the two deeper-forming wavelengths. The temperature at the top node and the brightness in the Ca ii H channel behave quite differently, however. The temperature lies below the quiet-Sun value for only a small fraction of the points. The same is also true for the Ca intensity, for which the ratio of hotter and brighter points to cooler and darker ones is even more extreme.

Hence, although the small pores partly remain visible as dark features relative to their immediate surroundings in the lower chromosphere, they are approximately as bright as, or even brighter than, the quiet Sun at those layers. The most extreme enhancement is displayed by the smallest of the three pores, with the largest being the coolest and darkest (by a small amount) of these three.

The largest pore in the IMaX FOV (and partly in the SuFI FOV) does remain considerably darker than the quiet Sun, even in the Ca images, which unfortunately cover only a small part of the whole pore. Nonetheless, the behavior of the various pores taken together suggests that the difference in the vertical temperature gradient within these pores to that in the quiet Sun depends significantly on the size of the pore. The photospheric temperature gradient is flattest for the smallest pores, with the temperature starting nearly 1000 K below the average quiet-Sun value at the solar surface and reaching the quiet-Sun value in the upper photosphere. For large pores, however, the temperature gradient appears to be more similar to that in the quiet Sun.

Inhomogeneities in brightness and temperature within the pores also decrease with height. Thus, in Figure 9 the umbral dot-like brightenings in the pore at the upper right of the frame are clearly visible in the ${I}_{+227}$ at 5250.4 Å, but only very weakly visible at 3000 Å, which is formed only about 50 km higher, and cannot be seen at all at 3968 Å. This suggests that such inhomogeneities are likely of convective origin, as proposed by Parker (1979), Choudhuri (1986), and Schüssler & Vögler (2006) for umbral dots. In sunspot umbrae a similar restriction to low heights of the thermal enhancements/brightenings associated with umbral dots has been found by, e.g., Socas-Navarro et al. (2004) and Riethmüller et al. (2008, 2013b).