How rare are counter Evershed flows?

One of the main characteristics of the penumbra of sunspots is the radially outward-directed Evershed flow. Only recently have penumbral regions been reported with similar characteristics to normal penumbral filaments, but with an opposite direction of the flow. Such flows directed towards the umbra are known as counter Evershed flows (CEFs). We aim to determine the frequency of occurrence of CEFs in active regions (ARs) and to characterize their lifetime and the prevailing conditions in the ARs. We analysed the continuum images, Dopplergrams, and magnetograms recorded by SDO/HMI of 97 ARs that appeared from 2011 to 2017. We followed the ARs for $9.6\pm1.4$ days on average. We found 384 CEFs in total, with a median value of 6 CEFs per AR. CEFs are a rather common feature, they occur in 83.5% of all ARs regardless of the magnetic complexity of the AR. However, CEFs were observed on average only during 5.9% of the mean total duration of all the observations analyzed here. The lifetime of CEFs follows a log-normal distribution with a median value of 10.6$_{-6.0}^{+12.4}$ hr. In addition, we report two populations of CEFs depending on whether they are associated with light bridges, or not. We explain that the rarity of reports of CEFs in the literature is a result of highly incomplete coverage of ARs with spectropolarimetric data. By using the continuous observations now routinely available from space, we are able to overcome this limitation.


Introduction
Sunspots are a manifestation of solar magnetism. The two main constituents of sunspots are the dark umbra, harbouring a strong and relatively vertical magnetic field (B); and the penumbra, highly filamentary in continuous radiation, with a more horizontal B.
A radially outward-directed flow along the penumbral produces Dopplershifted photospheric spectral lines 1 when the sunspot is observed away from disk center. This Evershed flow (see Solanki 2003, for a review) was detected more than a century ago (Evershed 1909). In the past decade, there have been a few reports of peculiar flows directed towards the umbra (Kleint & Sainz Dalda 2013;Louis et al. 2014;Siu-Tapia et al. 2017;Guglielmino et al. 2017Guglielmino et al. , 2019Louis et al. 2020). These socalled counter Evershed flows (CEFs) have also been observed in one magneto-hydrodynamic (MHD) simulation (Siu-Tapia et al. 2018). CEFs studied in the literature have been found in complex active regions (ARs). Recently, Louis et al. (2020) reported the appearance of a light bridge associated with a CEF. Common to these works, which all only analyzed one sunspot each, is that CEFs were described as anomalous, unusual, or atypical flows.
Photospheric CEFs should not be confused with the more commonly reported chromospheric inverse Evershed flows (St. John 1911b,a;Maltby 1975;Choudhary & Beck 2018;Beck & Choudhary 2019). Inverse Evershed flows transport material in e-mail: castellanos@mps.mpg.de 1 In this paper, the radial direction is taken to be parallel to the solar surface and ascribed from the umbra-penumbra boundary, across the penumbra, towards the quiet-sun. the chromospheric penumbrae towards the umbra and they are thought to be driven by pressure gradients (siphon flows, e.g., Thomas 1988).
The few existing reports of CEFs might suggest that this type of photospheric flow is a rare phenomenon in sunspots. However, until now, no study systematically looked at a large set of ARs to quantify how often CEFs occur in ARs, and whether their occurrence depends on the magnetic complexity of the host AR. In this Letter, we fill this gap and present the first analysis of CEFs in a large sample of ARs using 6 years of space-borne data.

Observational data and analysis
We analyzed 97 ARs observed by the Solar Dynamic Observatory (SDO; Pesnell et al. 2012) taken by the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012;Schou et al. 2012). We analyzed the continuum intensity (I c ), Dopplergrams (v LOS ), and magnetograms (B LOS ) with a spatial resolution of 1 . Data were taken with a cadence of 12 minutes and covered the development of each AR over a time ranging from 153 to 278 hr. Table 1 summarizes the observations. Data were processed using standard SSWIDL routines, and temporal series were created by co-aligning the images using cross-correlations between the subsequent frames.
The 97 ARs were observed between 2011 July 30 and 2017 August 24. ARs were tracked continuously while they crossed the solar disk for 9.6 ± 1.4 days on average. The only criteria applied when selecting the ARs was that it had sunspots and could be followed for at least 6 consecutive days, independently of whether individual sunspots within the AR emerge/decay dur-Article number, page 1 of 43 arXiv:2106.05592v1 [astro-ph.SR] 10 Jun 2021 A&A proofs: manuscript no. main ing this period. This criterion excludes many small ARs with only small, short-lived sunspots, also many ARs that are formed when already well on the disc, or ARs that are already decaying when they appear at the East limb. It might also exclude some ARs that appeared during the SDO's eclipsing seasons. We analyzed ∼1.1×10 5 individual time-steps (×3 for the I c , v LOS , B LOS ).
Our sample covers all classification types of ARs, from the most simple to the more complex ones. The magnetic complexity of solar ARs is regularly described by Hale's classification (Hale et al. 1919). In this classification, an AR is assigned to the category α if it contains one or multiple sunspots of unique polarity, β refers to ARs harboring bipolar sunspots or groups, and γ describes complex ARs with sunspots and groups of intermixed polarities. An amendment to Hale's classification was done in the 1960s by adding an extra category, δ, to describe those ARs that harbour umbrae of mixed polarities enclosed by a common penumbra within < 2 • (Künzel 1960(Künzel , 1965. The categories can be appended to describe the complexity of an AR increasing from α to βγδ. In our sample, we take into account the change of the magnetic classification for each AR during their lifetimes. Considering that bipolar-β ARs are the most common type observed on the Sun (∼65%; Jaeggli & Norton 2016), our sample is also dominated by this AR type.
The determination of the zero-level of the line-of-sight velocity measurements requires taking into account the following effects: (1) the line-of-sight velocity of the observatory with respect to the Sun (v SDO LOS ), (2) the large-scale flows (LSF) on the solar surface including solar differential rotation and meridional circulation, (3) the center-to-limb variation of the convective blueshift, and (4) the gravitational redshift. For SDO, the value for v SDO LOS is estimated by combining the keywords OBS_VR, OBS_VW, and OBS_VN in the header of the HMI data files. Following Schuck et al. (2016), v SDO LOS in the helioprojective coordinate system (θ ρ , ψ) is given by v SDO LOS = OBS_VW sin θ ρ sin ψ − OBS_VN sin θ ρ cos ψ + OBS_VR cos θ ρ , (1) where these keywords provide information about the speed of the observatory in the radial direction from the Sun (OBS_VR), westward in direction of Earth orbit (OBS_VW), and northward in the direction of the solar north (OBS_VN). Thompson (2006) provides the conversion between coordinates systems.
An alternative method to account for (1) is based on the HMI Doppler-and magnetograms to estimate the average quietsun velocity calculated from a region ±15 around disk center. Strong magnetic concentrations are avoided by masking regions with |B LOS | > 500 G. The good agreement between the average quiet-sun velocities and the velocity information taken from the header of the data files can be gleaned from Fig. 1a, which shows the diurnal variation of the spacecraft velocity of up to ±3 km s −1 . Note that the peak-to-peak amplitude and mean of v SDO LOS changes in the course of the year. The correction for the large-scale flows (2) has two components: differential solar rotation (v rot ) and the surface meridional flow (v mer ). We calculate their contribution at every pixel in our maps based on its Stonyhurst heliographic coordinates latitude and longitude (Θ, Φ). The line-of-sight component of these −17.7 m s −1 obtained by Hathaway & Rightmire (2011). The contribution of the surface meridional flow is tiny and therefore negligible. Fig. 1b shows examples of the correction for differential rotation for the bottom-left, center, and top-right pixels within the field-of-view (FoV) for the AR 12489. For comparison, the green line shows the average quiet-sun velocity within the FoV. Notice that this average is influenced by the location of the sunspots within the AR inside the observed FoV, which may change as they evolve and change shape over multiple days.
To compensate for the center-to-limb variation of the convective blueshift, we reconstructed the profile by (Löhner-Böttcher & Schlichenmaier 2013, their Fig. 2c), and shifted the profile to match it with the convective blueshift value at disk center measured by the Laser Absolute Reference Spectrograph (LARS; Doerr 2015;Löhner-Böttcher et al. 2017). LARS performed absolute wavelength calibrated observations with a resolving power of ∼700 000 at 6173 Å, determining the convective blueshift for the Fe i 6173.3 Å line at disk center to be -320 m s −1 (Stief et al. 2019). At HMI's resolving power of ∼81 000 this value reduces to -275 m s −1 ). Similar to Stief et al. (2019), we fitted the center-to-limb variation with a fifth degree polynomial, given by (5) where µ = cos θ and θ is the heliocentric angle. To correct for this effect, we obtained the µ-values for all pixels inside FoV and subtract the result of Eq. 5 from the v LOS . An example of this correction, taken at the same three pixels inside the FoV, is shown in Fig. 1c.
The gravitational redshift is a relativistic effect and a direct application of the equivalence principle for the light traveling from the Sun to the Earth. The gravitational Doppler shift is given by, where all the constants have their nominal meaning. Continuum images were corrected for limb darkening following the procedure explained by Castellanos Durán & Kleint (2020). To select the penumbra, we use the continuum images and set the commonly used limits 0.5I qs ≤ I penumbra ≤ 0.97I qs , where I qs is the quiet-sun mean intensity.
Due to the Evershed flow, the limb-side penumbra is observed redshifted, while the center-side is blueshifted. This pattern is reversed if a sector of the penumbra is carrying a CEF. A CEF appears blueshifted if it is located on the limbward side, and redshifted on the center side. When searching for candidates of CEFs, we put the constraint that these events should appear in penumbrae and the penumbral region should have an adjacent umbra. The second condition avoids orphan penumbrae that tend to show strong flows, but where it is non-trivial to establish whether the flow direction corresponds to the normal Evershed flow or not.
Candidates to CEFs were found using the SOBEL edgeenhancement and CANNY edge-detection algorithms, both implemented in the Interactive Data Language IDL8.3 (Exelis Visual Information Solutions, Boulder, Colorado) to detect breaks in the Dopplergrams within the penumbrae. In addition, we calculated the spatial gradient of v LOS , where the position of the maximum gradient often outlines the CEF region very well. However, this method sometimes failed, especially when the CEF was orientated closely parallel to the direction of the closest limb. It is difficult to detect CEFs that are aligned within 10 − 15 • to the direction of the nearest solar limb (these flows are perpendicular to the LOS and hence produce almost no Doppler shift). We, therefore, miss between 5% and 10% of all the CEFs in the studied ARs, if we assume that they are isotropically distributed. We additionally checked all sunspots within the ARs by visual inspection of videos showing their temporal evolution for CEFs which were not identified by the method described above.
We used the Solar Region Summary (SRS) provided by the Space Weather Prediction Center (SWPC) to determine parameters such as the NOAA AR number, the heliographic latitude, longitude, and area of the AR, and magnetic classification of the AR. We completed the records for a few ARs that were excluded from the SRS reports because they emerged on the same day, but after the SRS reports were issued at 00:30 UT.

Results
We found CEFs in 81 out of all 97 studied ARs between 2011 July 30 to 2017 August 24. Fig. 2 shows the distribution of the number of CEFs per AR. The median number of CEFs detected per AR is 6. While 11 ARs presented just one CEF, the peak is found at 4 CEFs, with 15 ARs harbouring that number. There are 6 ARs with 10 or more CEFs, with AR 11520 harbouring 15 CEFs (see Fig. B.69 in the Appendix B), the largest number for any AR in our sample. Some CEFs also appear in nests, i.e., multiple CEFs are observed to form in the same part of the penumbra of a given sunspot. In few cases, multiple CEFs were observed at the same time at different locations of the same sunspot. We observed that the occurrence of CEFs depends on neither the size nor on the number of sunspots belonging to an AR. Table 1 summarizes parameters of the observations and general properties of the hosting ARs such as the NOAA AR, date and time, the total duration of the observation, size of the FoV, the median latitude of the AR, the start and end longitude of the considered observations of the AR, and magnetic classification of the AR during all the days it was observed.
Four examples of CEFs are shown in Fig. 3. From left to right, Fig. 3   We find that CEFs can be categorized into two different groups: (1) CEFs associated with light bridges: Such CEFs originate in a light bridge or in a penumbral intrusion (i.e. a partial light bridge) and extend into the penumbra with the opposite flow direction compared to the adjacent penumbra. We label these CEFs as LB-CEFs. Four examples of such LB-CEFs are plotted in Fig. 4. (2) CEFs completely embedded in the penumbra, labelled as nLB-CEFs (non-light bridge CEFs; Fig. 3). Both types of CEFs are almost equally common in our sample: 198 (51.6%) nLB-CEFs vs. 186 (48.4%) LB-CEFs.
CEFs appeared in all magnetic types of ARs: ranging from simple α ARs to the more complex δ ARs. Similarly, the few ARs not harbouring any CEF also show many complexity categories. The examples of CEFs presented in Figs. 3 and 4 indicate the magnetic classification just above the leftmost image of each row, illustrating the large variety of ARs where CEFs appeared. There is no clear dependence on the occurrence of CEFs on the complexity of the AR. Both types of CEFs appear in all magnetic classes. The 81 ARs that hosted CEFs were observed for a total of ∼1000 days. The percentage of days on which CEFs are observed does seem to depend on the magnetic complexity of an AR. For the simplest, α, regions, CEFs are visible on only 8% of all days. This increases to roughly 1/3 of all days for β and βγ regions and finally becomes slightly more than 50% for the βγδ regions.
We did not observe CEFs in 16 ARs (16.5%), all except one containing only a single sunspot. The magnetic classification of these ARs is dominated by the simple α class (51.8% of all days these regions were observed). In 39.3% of those observed days the ARs without CEFs appear in β configuration, 7.1% in βγ, and 1.8% in βδ. Fig A.1 in Appendix A shows the continuum images of all the ARs without CEFs. The sunspots within these ARs share a similar roundish morphology and are all rather small with a diameter smaller than 40 . The details of these ARs, as well as their evolution through different magnetic classes, are summarized in the top part of Table 1.
The lifetimes of CEFs found in the literature range from 1 hr to approximately 12 hr (e.g., Louis et al. 2014;Siu-Tapia et al. 2018;Louis et al. 2020). Fig. 5 presents the histogram of the lifetimes of CEFs from our study. The median and average lifetime of CEF are 10.6 +12.4 −6.0 hr and 13.5 hr. The total lifetime distribution is reasonably well reproduced by a log-normal function given by, where η = 780.6 ± 0.6, ζ = 11.6 ± 0.4, and ξ = 0.8 ± 0.03. 85.1% of CEFs have a lifetime shorter than 1 day and the peak in the lifetime distribution is found at around ∼7 hr. The previously reported lifetimes of CEFs fall close to the median value, including the MHD-simulated CEF that vanishes after ∼10 hr (Siu- Tapia  In Fig. 5 we differentiate between nLB-CEFs (dark blue) and LB-CEFs (light blue). The mean lifetime of LB-CEFs is 3.5 hr longer (15.4±10.1 hr compared to 11.9±9.3 hr). In addition, the lifetime of CEFs does not depend of the magnetic classification on the AR (not shown).
We found a slight positive trend between the lifetime of CEFs and the total area of the AR, but with a large scatter, so that the trend is not statistically significant at the 1σ confidence level. In addition, ARs are usually formed by a group of many sunspots (e.g., Mandal et al. 2021), while CEFs often appear in just one of the sunspots within the AR. Therefore, we divided the total area of the AR by the number of visible sunspots belonging to the AR. The scatter remains large. The slight positive trend is enhanced, but still not statistically significant.
Most of the CEFs appear as elongated structures, with the B LOS values being lower than in the surrounding penumbra and sometimes even of opposite magnetic polarity (see for example Fig. 4, cf. Lim et al. 2020). As we use line-of-sight magnetograms for this study, this polarity statement is only reliable for CEFs located at µ-values larger than ≈0.8. From the 181 CEFs fulfilling this criterion, ∼42% are of opposite polarity compared to the surrounding penumbra (38/91 nLB-CEF vs. 38/90 LB-CEF).

Summary and conclusions
We presented the first statistical survey of CEFs in a sample of 97 ARs. We tracked the ARs for 9.6 ± 1.4 days days on average using the continuous observations by SDO/HMI. We report the appearance of 384 CEFs in 83.5% of the ARs. CEFs were observed in all magnetic types of ARs catalogued, from α, β to βγδ. The number of CEFs produced by an AR ranges from 1 to 15, with a median value of 6 CEFs per AR.
We distinguished two populations of CEFs, with one of these populations associated with light bridges the other one not. The two populations are almost equal in size, and ∼2 out of 5 of the CEFs within these two populations are of opposite polarity with respect to the surrounding penumbra. Given that not all sunspots have light bridges and these take up only a small part of the sunspot, we conclude that light bridges provide favourable conditions for the formation of CEFs. LB-CEFs have slightly longer lifetimes, but the separation of these two populations based on their lifetime is not statistically significant.
Almost all the CEFs in our sample are long and narrow. We could not find another example as broad as (i.e. covering such a large penumbral segment) as the CEF reported by Siu-Tapia et al. (2017). These results enhance the uniqueness of the AR 11930 and its CEF (Siu-Tapia et al. 2019).
The few reports in the literature of ARs associated with CEFs suggest that this might be a rather rare phenomenon. In this survey, we showed that almost all ARs of all magnetic types harbour CEFs. The reason for this seeming discrepancy most likely lies in the fact that CEFs are narrow and can easily be missed. Additionally, the average lifetime of CEFs is rather short compared to the total duration of the observation. The ratio between these two quantities highlights the observational difficulty of detecting CEFs (see bottom x-axis on Fig. 5): We needed to track continuously the ARs on average for 9.6 ± 1.4 days to detect 6 CEFs in an ARs (median value). From our findings, we expect to see a CEF only on an average of 5.9% of the mean total duration of the observation of an AR. Therefore, to detect CEFs, uninterrupted and stable time series of continuum images and Doppler velocity observations are required. These requirements had not been met until observations became available from space, in particular by HMI.
In this survey, we have shown that CEFs are far more common than the few cases reported in the literature suggest. We find that ∼85% of ARs harbour at least one CEF and typically 6 in the course of the lifetime of an AR. However, only HMI provides the uninterrupted, stable, and relatively high-resolution measurements of velocity needed to identify a high fraction of CEFs. Based on the probability found in this study, the Japanese solar mission Hinode (Kosugi et al. 2007) should have observed more CEFs than those found in the current literature. A quick and simple search in the archive of the Spectro-Polarimeter instrument (SP; Ichimoto et al. 2008) revealed 18 CEFs, indicating that the estimates for the occurrence of CEFs derived in this study are reasonable. The regions harbouring CEFs observed by Hinode/SP were classified from α to δ, and the CEFs belonging to the two categories (LB-and nLB-CEFs), are roughly equal in number, consistent with the results reported in this Letter.
The Polarimetric and Helioseismic Imager (PHI; Solanki et al. 2020) onboard Solar Orbiter (Müller et al. 2020) will allow us to track individual AR for longer periods of time, thanks to the partial corotation of the spacecraft with the Sun near its perihelion and the possibility of combining measurements from PHI, Hinode/SP, and HMI. Such measurements will allow us to accurately measure the flow velocity, magnetic and thermodynamic conditions inside CEFs.

Appendix A: ARs without CEFs
CEFs appear to be a more common phenomenon than was previously conceived. We could not detect CEFs in only 16.5% of the ARs in the sample. Continuum images of the 16 ARs without CEFs are presented in Fig A.1. Most of these ARs are composed of just one sunspot. The top part on Table 1 summarizes the general characteristics of the ARs without CEFs.

Appendix B: All CEFs
All the CEFs found in this study are presented in Figs The layout is the same as in Fig. 3. We remark that CEFs are displayed at the time closest to their maximum contrast with respect to their surroundings in the line-of-sight velocity maps. Hence, for few cases, the association with light bridges and the LB-CEFs is buried.

Total
Magnetic classification of the day (k)