Quantifying Properties of Photospheric Magnetic Cancellations in the Quiet Sun Internetwork

We analyzed spectropolarimetric data from the Swedish 1-meter Solar Telescope to investigate physical properties of small-scale magnetic cancellations in the quiet Sun photosphere. Specifically, we looked at the full Stokes polarization profiles along the Fe I 557.6 nm and of the Fe I 630.1 nm lines measured by CRisp Imaging SpectroPolarimeter (CRISP) to study temporal evolution of the line-of-sight (LOS) magnetic field during 42.5 minutes of quiet Sun evolution. From this magnetogram sequence, we visually identified 38 cancellation events. We then used Yet Another Feature Tracking Algorithm (YAFTA) to characterize physical properties of these magnetic cancellations. We found on average $1.6\times10^{16}$ Mx of magnetic flux cancelled in each event with an average cancellation rate of $3.8\times10^{14}$ Mx s$^{-1}$. The derived cancelled flux is associated with strong downflows, with an average speed of $V_\mathrm{LOS}\approx1.1$ km s$^{-1}$. Our results show that the average lifetime of each event is $9.2$ minutes with an average $44.8\%$ of initial magnetic flux being cancelled. Our estimates of magnetic fluxes provide a lower limit since studied magnetic cancellation events have magnetic field values that are very close to the instrument noise level. We observed no horizontal magnetic fields at the cancellation sites and therefore can not conclude whether the events are associated structures that could cause magnetic reconnection.


INTRODUCTION
The Sun has historically been divided into two domains: the active Sun and the quiet Sun (QS). The active Sun is commonly defined as areas of the Sun occupied by active regions, plage, and sunspots while the quiet Sun represents the remaining areas. It is reported that in the early stages of Solar Physics, scientists believed the QS to be non-magnetic because only granular convection could be seen in continuum images (e.g. Bellot Rubio & Orozco Suárez 2019). However, early measurements showed that magnetic features are ubiquitous on the Sun. For example, using the Kitt Peak magnetograph, Livingston & Harvey (1971) reported a background internetwork field level of 2-3 G. Recent spectropolarimetric measurements allow magnetic structures to be observed down to scales at the limits imposed by current spatial resolution (e.g. Danilovic et al. (2010)). These can be analyzed by using new inversion techniques to interpret the Zeeman and Hanle effects (e.g. del Toro Iniesta & Ruiz Cobo (2016)). Quite the opposite of non-magnetic, the QS displayed a reticular pattern of intense kilogauss fields, the magnetic network (NE), and a varied distribution of smaller-scale (sub-arcsec) magnetic flux concentrations in the areas between them -the solar internetwork (e.g. Gošić et al. 2014).
State-of-the-art, threedimensional magnetohydrodynamic simulations of the solar atmosphere (e.g. Rempel 2014) indicate that large part of the solar surface magnetic features is still unresolved.
Studies by Gošić et al. (2016) and others (e.g. Sánchez Almeida 2004) have indicated that internetwork (IN) fields are essential contributors to the Sun's overall magnetic flux output, with transport of magnetic flux to the solar photosphere at a rate of 120 Mx cm −2 day −1 , which is significantly higher than the 1 Mx cm −2 day −1 transported by active regions (Thornton & Parnell 2011). A large portion of that flux is transported to neighboring intergranular lanes via convective motions (Martínez González & Bellot Rubio 2009) and then to the NE supergranular boundaries (Livingston & Harvey 1975;Zirin 1985;Bellot Rubio & Orozco Suárez 2012). These motions make the IN capable of generating a complete magnetic flux re-supply of the surrounding NE within only ≈ 10 hours (Gošić et al. 2014) indicating that they are an important contributor to the greater flux output of the solar photosphere. QS magnetism has in fact been suggested to affect global solar properties such as limb darkening (e.g. Criscuoli & Foukal 2017), photospheric temperature gradient (e.g. Faurobert et al. 2016) and global radiative output (e.g. Rempel 2020, and references therein).
The transient nature of the IN manifests in frequent instances of magnetic flux emergence, dissipation, and cancellation events. IN magnetic flux cancellation is one of three processes (flux decay, cancellation, and interaction with network) in which flux is removed from the photosphere, and is a mechanism that leads to the maintenance of the flux budget in the photosphere (Lamb et al. 2013;Schrijver et al. 1997;Gošić et al. 2016). A physical cancellation event results in an in-situ disappearance of magnetic flux from the solar photosphere as a result of the interactions between two opposite-polarity magnetic elements Martin et al. 1985). Cancellations are a contributor to QS magnetic behavior and have been observed to play a critical role in many dynamic upper-atmosphere solar phenomena, such as coronal mass ejections, flares, and filament eruptions (Chintzoglou et al. 2019;Yardley et al. 2016;Wang et al. 1996;Zhang et al. 2001;Zuccarello et al. 2007) as well as the formation of prominences (Denker & Tritschler 2009), coronal jets (Panesar et al. 2016), and Ellerman bombs (Schmieder et al. 2002).
IN cancellations may also partially drive the heating of the chromosphere. Gošić et al. (2018) identified 51 cancellation events using data from the Swedish 1meter Solar Telescope (SST, Scharmer et al. 2003a) and compared these with chromospheric temperature diagnostics using IRIS data (De Pontieu et al. 2014). Magnetic cancellations were found to release enough energy to provide local brightening in the chromosphere (Gosic et al. 2017(Gosic et al. , 2018. The derivation of statistical properties of IN cancellations is among the most important steps in further understanding their role in other solar phenomena. This is somewhat challenging due to the relatively low signal-to-noise ratio in current polarimetric measurements of QS. IN fields are particularly difficult to observe because they are arranged on small spatial scales, evolve rapidly, and individually, produce very weak signals. Thus, major advances in this research area have mainly been brought upon by advances in observing technologies (instruments with higher spectropolarimetric sensitivity and spatial and temporal resolutions) and new computational modeling, meaning that many of the fundamental aspects of IN cancellations have been discovered recently and are still widely disputed and incomplete.
In this paper, we analyzed a small area of the QS observed at the SST with high spatial resolution and high cadence spectropolarimetric data. In these data, we noted numerous signatures of magnetic cancellation events, and we describe in the following their statistical properties. Our results complement a growing list of publications focusing on QS magnetism and the important process of cancellations that pervade its surface (e.g. Chae et al. 2002Chae et al. , 2004Kaithakkal & Solanki 2019a;Guglielmino et al. 2012;Nisenson et al. 2003) The outline of this paper is as follows: In Section 2 we describe SST observations and our analysis in Section 3. In Section 4.1 we describe a single cancellation event in detail. In Section 4.2 we summarized statistical parameters of the physical quantities estimated for all 38 cancellation events. In Section 5 we discussed our findings and their implications in the broader field of QS research. In Appendix A we describe four additional cancellation events in detail.

OBSERVATIONS
We employed the full Stokes polarization profiles along the Fe I 557.6 nm and the Fe I 630.1 nm lines to analyze the temporal evolution of the magnetic field and the dynamic properties of plasma at cancellation sites.
Specifically, for our analysis we used data acquired at the Swedish 1-meter Solar Telescope (SST; Scharmer et al. 2003a) in La Palma, Spain, with the CRisp Imaging SpectroPolarimeter (CRISP; Scharmer et al. 2008), as part of a two weeks long campaign (August 6-18, 2011). These observations captured a quiet-Sun region at disk center on August 6, 2011, beginning at 07:57:39 UTC and lasting for 42.5 minutes.
CRISP acquired data along the Fe I 630.1, 630.2 and 557.6 nm lines spectral ranges. Only data acquired along the 630.1 and 557.6 nm lines were used in this study. The pixel scale was ≈ 0. 059/pixel with a fieldof-view of 57.5 × 57.3 . A total of 100 scans were acquired with a temporal cadence of 28 s. Raw data were calibrated using an early version of the standard CRISP calibration pipeline (CRISPRED, de la Cruz Rodríguez et al. 2015). The SST adaptive optics system (Scharmer et al. 2003b) was able to make continuous corrections to the wavefront, effectively operating in a 100% lock rate. The combination of the use of adaptive optics and of the application of the Multi-Object Multi-Frame Blind Deconvolution image restoration technique (MOMFBD, van Noort et al. 2005) allowed for effective minimization of seeing induced aberrations. The images studied here had an angular resolution of ≈ 0.15 at 557.6 nm, which is close to the diffraction-limit of the SST. The estimated spectropolarimetric sensitivity was ≈ 3 × 10 −3 . This dataset has been employed in previous studies to investigate the dynamics (Stangalini et al. 2015(Stangalini et al. , 2017 and thermal properties (Cristaldi & Ermolli 2017;Viavattene et al. 2021) of plasma in the quiet Sun regions. These studies were made possible in part due to the high resolution of the SST and its instruments, inspiring us to analyze the same data to investigate small magnetic features on the QS surface.
We derived information about the magnetic properties of the plasma using the four Stokes parameters, I, Q, U and V observed in the Fe I 630.1 nm line. Specifically, we derived the line-of-sight magnetic field B LOS from the separation of the centroids of the I+V and I-V signals, estimated with the center-of-gravity method (Rees & Semel 1979;Uitenbroek 2003): where g L was the line's effective Landé factor, m and e were the electron mass and charge, respectively, λ 0 was the central wavelength of the line, and λ ± were defined as: where I c was the line's nearby continuum intensity. The Total Circular Polarization signal (TCP, del Toro Iniesta 2007) was computed as: , and the Total Linear Polarization signal (TLP, del Toro Iniesta 2007) as: To estimate the line-of-sight velocities (V LOS ), we used the Doppler shift of the core of the magneticallyinsensitive Fe I 557.6 nm line. The line core was estimated by fitting the observed line profiles with a Gaussian function, and the Doppler shift was computed taking as reference the core position of the average line profile computed over the whole time-series. The resulting average velocity over the whole field of view is -0.07 ± 0.035 km s −1 . Indeed, this value is around "convective upflow" value for the line found in Dravins et al. (1981). This is approximately -0.15 km s −1 to -0.2 km s −1 at disk center.
Examples of the data and data-products used in our analysis are shown in Figure 1: the continuum intensities in the Fe I 557.6 and 630.1 nm continua (left column) and the derived V LOS and B LOS (right column).

DATA ANALYSIS
We used the TCP sequence to visually identify 38 cancellation events for our analysis. We defined the following criteria for our selection. First, for visual detection simplicity, we have chosen cancellations that involve two opposite-sign polarities of roughly equal size. While choice of same-size polarities simplifies the process of cancellation search, it leads to an underestimation of canceled magnetic flux. Second, we avoided selecting events where same-signed flux recombined or emerged in the same location. Finally, we only selected cancellations where the polarities involved were visually identifiable. The average size of a region of interest (ROI) was ≈ 2 × 10 5 km 2 . Given these criteria, we identified 38 cancellation regions of interest (ROI), shown as squares in Figure 1.
Examples of the three steps are illustrated in Figure 2 for five events. For context, the PIL is the boundary between opposite-polarity features. In the first step (second column in Figure 2), to identify individual magnetic features we used "Yet Another Feature Tracking Algorithm" (YAFTA) solar magnetic tracking algorithm (Welsch et al. 2004). YAFTA has been shown to reliably indentify small and short-lived magnetic features. It identifies magnetic features using a gradient based "downhill" method which dilates local flux maxima by expanding down the gradient toward zero flux density. To discriminate the false-positives, YAFTA allows the user to control the following parameters: a threshold for a minimum magnetic field to consider (B min ), a saddle threshold for a minimum magnetic field to merge the already selected features (B saddle ), and a minimum area size for feature identification (S min ). In our analysis we chose B min = 40 G, B saddle = 80 G, and S min = 4 pixels. This parameter set resulted in tracking runs that consistently identified features above the noise level without false-positives. Use of lower thresholds for B min resulted in incorrect feature identification in the noisy areas and larger values of feature magnetic fluxes. The thresholds were set based on many tests and visual inspection of results. DeForest et al. (2007) reports the effects of various thresholds used with YAFTA and their implications on feature tracking. After features are identified, YAFTA arbitrarily labels them based on its first pass through the data. In the second step (third column in Figure 2), since occasionally YAFTA incorrectly assigned multiple labels to one feature, we had to manually re-label all the features after the initial tracking. This incorrect assignment is due to the fact that YAFTA struggles with very large or strong and very small or weak magnetic elements, reflecting imperfections of our approach. After the second pass the feature masks could be referenced and magnetic properties could be analyzed for each polarity independently. Finally, to describe Doppler velocities associated with each cancellation event, we examined the Doppler velocity properties within the PIL. To define PIL location (fourth column in Figure  2), we dilated the masks of the two cancelling polarities by 2 pixels and defined the PIL as the region where these two masks overlapped.
To describe each cancellation event we used the following set of parameters: magnetic flux, Φ B , flux cancellation rate, R, specific cancellation rate, r, convergence speed, V conv , and Doppler velocity, V LOS . We used these parameters as a foundation for our analysis.
For each observation at time t in the image sequence we defined the unsigned magnetic flux of positive (+) and negative (−) polarities in each pair, i, as where N i is the number of magnetic field values in the polarity pair, B j is the magnetic field value at each pixel, j, and ds is the pixel size (0. 059/pixel). The position at time t of each positive and negative polarity in the pair was defined as the center of gravity COG i (t) = [x i (t), y i (t)], i.e. the mean position of the feature weighted by the magnetic flux: (6) We then used these to calculate the separation distance, g(t), and the convergence velocity, v conv (t), between positive and negative polarities in each pair (Chae et al. 2002): dt .
(7) To describe the amount of flux cancelled we defined the flux cancellation rate, R i , and the specific cancellation rate (rate per unit PIL length), r i : where l i was the length of the PIL separating positive and negative polarities of each pair i. Finally, we found the cancelled flux as the difference between the flux values at the start time (t start ) and end time (t end ) of a cancellation event, so that the positive values indicated cancelled flux: To describe variability of R i (t) over time we also calculated the average and peak cancellation rates, R avg and R peak , respectively, over duration, T , of each cancellation event.
In the case of complete disappearance of the feature we defined the last frame before disappearance as tend, when the magnetic flux was above zero.
To define the duration, T , of each cancellation event, we used the time when the PIL was defined, which occurred when opposite polarities were in close proximity to one another. In the events we observed, while the general trend of the polarities' fluxes was characterized by a decay, sometimes flux momentarily increased during the event, so the PIL was defined in the aforementioned way in order to capture the entire event as a whole. If, during a cancellation event, one of the polarities dipped below the detection threshold for fewer than 5 frames but was seen thereafter, we considered it as one cancellation event.
To calculate V LOS , we averaged the Doppler velocity across the PIL region. Positive values were plasma submergence or downflows, while negative values were emergences or upflows. To describe the V LOS variability, we used the mean and the peak values of V LOS , V LOS,avg and V LOS,peak , respectively. To describe the change in Doppler velocity from the start to the end of the cancellation event we used This formalism allowed us to account for cancellations taking place in intergranular lanes where plasma was already flowing downward or in areas where plasma was already flowing upwards.   (3) shows the re-labeled features. Column (4) shows the two cancelling features, their dilated masks, and PIL (green outline). Each row of images represents a different ROI. The color of the square beside the right-most image corresponds to the color of the ROI in the full field of view magnetogram in Figure 1.
away from the strong field regions belonging to the network patches. In this section, we first present our results for one example cancellation event ( §4.1) and then the statistical analysis for all 38 events ( §4.2). The evolution of an additional four exemplary regions is provided in Appendix A.

Example of individual cancellation event, ROI 03
Figure 3 (top row) shows evolution of the magnetic field in one example event, region of interest 3 (ROI 03). We chose to give this event special attention since it showed a marked flux cancellation, allowing us to compare the Doppler velocity in the PIL region before and during the cancellation. Furthermore, the polarities in this region were easy to identify by eye and there was very noticeable flux cancellation in both regions.
From the beginning of its detection, ROI 03 contained positive and negative polarities with relatively equal magnetic flux. Around 10 minutes into the tracking run, the two polarities became entangled (see PIL region in Figure 3 panel 2a). Around six minutes after the PIL is defined, or at around 08:11:11 UTC, the polarities began cancelling, losing flux at an average rate of 4.9×10 14 Mx s −1 . V LOS in the PIL region shows a small submergence of 0.1 km s −1 when the PIL was first defined (Figure 3, panel 2c) but then increased to over 1 km s −1 after the cancellation intensifies (Figure 3, panel 4c). The event lasted ten minutes before the negative polarity decreased below the instrument noise level as seen in Figure 3, panel 7a. During the cancellation the positive and negative polarities lost 1.87 × 10 17 Mx and 2.48 × 10 17 Mx, respectively, i.e. around 54.7% of the unsigned initial magnetic flux of the bipole. The cancellation took place in an intergranular lane as seen in the continuum and Doppler velocity images. As illustrated in Figure 4, before cancellation, the Doppler velocity of the PIL was ≈0.1 km s −1 . As both polarities started cancelling, with the peak cancellation rate of 4.4×10 15 Mx s −1 occurring at 08:16:35 UTC, the downlflows at the PIL increased up to ≈1 km s −1 , persisting for approximately five minutes.

Results: Statistical Analysis of 38 Cancellation Events
We repeat the analysis described in the previous section for 38 events in our dataset. In Table 1 we present a summary of all events and major indices. In Table 2 we summarize our results showing cancellation parameters for 38 cancellations events.
Duration: We found an average cancellation duration of ≈ 39.2 minutes. Cancellation lifetimes of 9 minutes were reported by de Wijn et al. (2008) and Gošić (2015) with a range of 1 to 22 minutes found by Gošić et al. (2018).
Initial magnetic flux: The distribution of initial fluxes, φ B,i , of the features is seen in Table 2. and we see a distribution clustered around [1 − 3] × 10 17 Mx. The observed magnetic flux is [0.7 − 8.2] × 10 17 Mx. This wide range of values shows that our dataset reflects the diversity of internetwork magnetic field strengths. The average value ofΦ B,i = 3.3 ± 0.3 × 10 17 Mx, and is lower than the value of 5.5 × 10 17 Mx reported by Kaithakkal & Solanki (2019b) and 6 × 10 17 Mx reported by Guglielmino et al. (2012) but is nearly identical to the 3 × 10 17 Mx reported by Gosic et al. (2012).
Cancelled magnetic flux: Values of the magnetic flux change, ∆Φ B , show a clustering below 10 17 Mx ranging from 0.2×10 17 Mx to 3.1×10 17 Mx. We find the average cancelled magnetic flux to be ∆Φ B = [1.6 ± 0.16] × 10 17 Mx. Comparing with the initial flux, this change corresponds to [44.9 ± 2.3]% of the initial flux being cancelled.
Cancellation rates: We found cancellation rates ranging from 0.3 × 10 14 Mx s −1 to 7.4 × 10 14 Mx s −1 with a mean cancellation rate of 3.8 ± 0.5 × 10 14 Mx s −1 . Kaithakkal & Solanki (2019a) found similar results for small magnetic elements with fluxes around 10 17 Mx and the flux decay rates of 4 × 10 14 Mx s −1 . Our values were slightly larger than the 2.6 × 10 14 Mx s −1 found by Guglielmino et al. (2012) and the 3.6 × 10 14 Mx s −1 reported by Chae et al. (2002). For all events we found the mean of the peak flux cancellation rate to be R peak = 2.9 ± 0.2 × 10 15 Mx s −1 , i.e. around one order of magnitude higher than the average rate, R avg .
Convergence speeds: For 38 cancellation events we find mean convergence speed v conv = 0.6 ± 0.07 km s −1 with values ranging from 0.2 km s −1 to 2.1 km s −1 . Kaithakkal & Solanki (2019a) reported a range of 0.3 km s −1 to 1.8 km s −1 . These convergence speeds are similar to supergranular flow velocities found by Litvinenko et al. (2007); Chae et al. (2002); Iida et al. (2012). Still, we agree with Kaithakkal & Solanki (2019a) that the wide distribution of convergence speeds as seen in individual cancellation events (see Figure 5) are evidence of the more chaotic flows found on granular-scales. Using the average convergence speed to deduce whether cancellations are driven by   supergranular motions or convective behavior is not entirely appropriate. According to Eq. 7, polarities moving away would have a negative convergence speed. Averaging the unsigned speeds (v proper = |v conv |) produces a result that more accurately depicts the internetwork environment. Using an approach similar to Kaithakkal & Solanki (2019a) we derived the proper motion speeds of the cancellations to be 0.9 ± 0.05 km s −1 , which is markedly higher than the convergence speeds. These proper motion speeds are more consistent with the rms velocity of magnetic elements in internetwork areas found by Nisenson et al. (2003). Our results are also consistent with other studies of magnetic cancellations, e.g. Yang et al. (2009) reporting proper motion speeds around 1 km s −1 while Kaithakkal & Solanki (2019a) observed proper motion speeds higher than convergence speeds calculated using the traditional COG method (as seen in Figure 5). Keys et al. (2011) also noted that the horizontal velocity of merging bright points is ≈ 1 km s −1 and higher than the speed of isolated bright points.
Downflow speeds: Across 38 cancellations we observed average downflows of V LOS,avg = 0.5±0.03 km s −1 and mean peak downflow speeds of V LOS,peak = 0.6±0.1 km s −1 . These high downflow speeds observed at flux cancellation sites are consistent with results from Chae et al. (2004). Harvey et al. (1999) found that emission structures from IN magnetic cancellations lasted longer in the photosphere than the chromosphere and corona, concluding that magnetic flux is retracting below the surface. Analyzing the magnetic elements overlaid on the continuum images (i.e. Figure 3 panels 1-7b), we noticed that many magnetic bipoles began cancellation in upflow regions and ended in downflow lanes, most likely due to convective motions. This was also observed in Kaithakkal & Solanki (2019a).
To explore this phenomenon we compared the ∆V LOS to the V LOS,avg , shown in Figure 6. This would indicate whether small outlier values of V LOS,avg simply resulted from a greater downflow shift from local upflow convection. We see that although the mean V LOS,avg = 0.5 ± 0.03, the ∆V LOS = 1.1 ± 0.07. There is no statistically significant relationship between ∆V LOS and V LOS,avg (The Pearson Correlation Coefficient, ρ = 0.07).  Investigating further correlations between V LOS and other statistical parameters, we first addressed the hypothesis that more magnetic flux cancellation may lead to a higher downflow signature. We plotted V LOS,peak vs. ∆Φ B in Figure 7 and no correlation was found. Relationships between ∆ V LOS and ∆Φ B , and V LOS,avg vs. ∆Φ B were also plotted but are not shown in the manuscript; analysis found no correlation. R 2 values were 0.04, 0.004, and 0.03 for the data sets, respectively. The notion that downflows may be limited by cancelled flux, as if by a threshold, is not supported by these data. This finding may also suggest that the magnitude of downflows is more dependent on the magnitude of decay than its amount. To investigate this notion, we plotted all V LOS parameters against the average and peak flux cancellation rates, R avg and R peak , respectively. We find that while there is statistical evidence to support cancellation events drive submergence, whether or not the submergences are a result of the magnetic cancellation or the typical downflows found in intergranular lanes where many polarities eventually coalesce and cancel is indeterminable from this initial analysis. As opposed to studying the effects of ∆Φ B on V LOS , R avg and R peak provide the best insight into how the physical process of magnetic cancellation relates to submergences, since timescales vary with differing amounts of ∆Φ B . Compared to typical submergence speeds in intergranular lanes, which have been reported as 0.30 to 0.50 km s −1 by Oba et al. (2017), the downflows associated with the cancellation events are much faster.
For V LOS vs. r, the specific cancellation rate, we find no correlation (Figure 9).
Analyzing single event-performance we found a stronger correlation between peak Doppler velocity and specific cancellation rate than analysis of the entire cancellation set. In ROI 03 (see Figure 3) we directly plotted R(t) vs. V LOS , finding weak correlation. We hypothesize that this might be caused by the definition of magnetic cancellation stating that only one feature in the cancelling pair is required to lose magnetic flux; the other participant may gain magnetic flux concurrently, therefore R, which we define as R(t)=R(t) + +R(t) − , the net decay of the bipole, is not entirely appropriate for these cases. Secondly, the measurement variability is so great that its effect can directly confound results. Given these postulates, from the first time step where cancellation occurred we averaged every 84 seconds, essentially time-binning the values of R and V LOS by 3. We find a weak correlation of unbinned values (R 2 = 0.1558) yet a moderate correlation with the binned values (R 2 = 0.3779). This is seen more clearly in Figure 10. As stated earlier, during cancellation events we see magnetic fields frequently below the instrument noise level, so it is possible a correlation between V LOS and R would be more apparent with a more sensitive dataset. We also analyzed the correlation between V LOS and R for the 15, 10, and 5 strongest flux patches but found no correlation. It is possible that some undiscovered mechanism is creating a positive time separation between submergences and magnetic cancellation such that when the features dip below the instrument threshold even more of the downflows are lost due to background noise. We calculated error by taking the standard deviation divided by the square root of the number of frames in the sequence relevant to the cancellation event. Ultimately, the standard error represents the standard deviation of the mean within the dataset.
Finally, we find that specific cancellation rate, r, was correlated with R avg (R 2 =0.707). This indicates that the primary transport mechanism of magnetic flux out of the bipole is through the polarity inversion line.

DISCUSSION AND CONCLUSION
In this study we used spectropolarimetric measurements from the SST to investigate the physical properties of magnetic cancellations in the quiet Sun photosphere. Examining an LOS magnetogram we visually identified 38 cancellations, and using the YAFTA program suite (Welsch et al. 2004), we tracked the magnetic elements involved in the cancellation and extracted their time-dependent physical parameters. We found that cancellations and downflows occur simultaneously, with an average relative speed of ∆V LOS = 1.1 km s −1 . We found no increase of the linear polarization signal in our data, corresponding to the horizontal component of magnetic field B t probably because it was below the noise level of the observations. This means that we can not comment on whether the flux retracts below the photosphere and forms structures which could lead to reconnection. Our findings are consistent with the study from Kubo et al. (2010) which also did not find horizontal magnetic fields. A snapshot ΦB,i is the initial flux of the bipole, ∆ΦB is the amount of cancelled flux, Ravg is the average rate of cancellation, R peak is the peak rate of cancellation, r is the specific cancellation rate, T is the duration of the event, VLOS,avg is the average Doppler velocity at the PIL, V LOS,peak is the peak Doppler velocity at the PIL, ∆VLOS is the total change in Doppler velocity at the PIL, vconv is the convergence velocity of the polarities, and a represents the percent of initial flux cancelled; many cancellations ended below the noise floor.
of the data is included in Sec. A. We expect that with more sensitive data these magnetic cancellations would be observed with enhanced B t signals, providing stronger evidence of possible magnetic reconnection. While establishing the link between downflows and cancellations is an important discovery in this study, we also calculated other statistical parameters that characterize these events: Φ B,i , ∆Φ B , R avg , R peak , r, T, and v conv (see Table 1).
Aside from v conv , we estimated the proper motion of the magnetic elements by using the unsigned average of their speeds, v proper = |v conv |. While this is not the same method used by others such as Kaithakkal & Solanki (2019a), we found v proper to be on average 1 km s −1 . This was significantly higher than the average speed of v conv = 0.6±0.06. Because the v conv for individual events was highly variable (see Figure 5) and our new value of v proper agreed with the rms velocity for magnetic internetwork elements (Nisenson et al. 2003), we assume that magnetic cancellations are driven by granular motions that force the magnetic elements into intergranular lanes where they cancel. In future studies, we would like to analyze the contribution of supergranular flows to the movement of the magnetic elements. Our exact value of v proper is likely an underestimate since it is still a relative measurement.
Although our study identified many cancellations, their lifetimes were noise-limited. In Section 5 we theorized that because of the instrument noise level some weak fields may not have been detected and tracked by the YAFTA program. This is evident by only around 45% of initial flux being cancelled in an average magnetic bipole. Given the YAFTA parameters outlined in Section 2, we were unable to track polarities below the noise floor of the dataset (Lamb et al. 2008). Because many of the events ended below the noise floor, this limited our analysis into the direct correlation between magnetic flux cancellation and plasma downflows.
Limiting our study to same-sized opposite-polarity elements and avoiding elements where same-signed flux recombined prevented us from detecting more events and thus led to an underestimation of magnetic flux evolution. In Figure 2 of Gošić et al. (2016) the authors present a methodology to track differently sized features. We may employ a similar method in future studies of IN magnetic elements.
Although we determined the optimal threshold to detect features in YAFTA, more in-depth understanding of QS magnetism would be achieved by observations with larger-aperture telescopes, and more advanced tracking algorithms.
In the YAFTA program we empirically determined both a minimum size and magnetic threshold that determined whether features were tracked. We did this by simply observing the point at which noise patterns were no longer detected as features by YAFTA, then used that threshold in the analysis of all the ROIs. As stated before, we excluded pixels below 40 G and magnetic elements under 4 pixels in size from our analysis. It is possible that algorithmically determining the exact thresholds for each ROI would yield better detection of the events near the end of their lifetimes.
Magnetic reconnection also may occur with U-loop emergences which cause brightenings in the local chromosphere (Gošić et al. (2018), Kontogiannis et al. (2020), and others). In order to investigate the effects of small-scale reconnection events on the higher layers of the atmosphere, we plan to combine observations in photospheric (as those employed in this study) and chromospheric lines. In particular, we plan to acquire spectropolarimetric observations in Ca II 854.2 nm to investigate the evolution of the chromospheric magnetic field and broad-band images in Ca II UV lines (e.g. the Ca II-H filter at the SST) to estimate the amount of energy released in the chromosphere during reconnection. The statistical parameters found in our study are important for implicating magnetic cancellations in future studies of the quiet Sun and complement existing literature. Lastly, it would be interesting to re-examine QS magnetic fields using higher-aperture telescopes. Higher-aperture telescopes naturally have higher spatial resolution which is required to resolve the PIL; better spectropolarimetric sensitivity is necessary to track features for longer times, and will increase the detectability of features and therefore increase the quality of the derived statistics. Spectropolarimetric measurements from existing and upcoming installments such the Big Bear Solar Observatory, the European Solar Telescope (EST) and the Daniel K. Inouye Solar Telescope (DKIST, Rast et al. 2021), respectively, will allow for more detailed study of the evolution of the magnetic field components.
In this section we describe the evolution of four more cancellations in detail -ROI 07, ROI 08, ROI 11, and ROI 23. These events are shown in context with the dataset in Figures 1 and 2. A.1. Analysis of ROI 07 ROI 07 involves a larger negative polarity and smaller positive polarity cancelling in an intergranular lane, as illustrated in Figure 11. Φ − B,i was 4.1×10 17 Mx and Φ + B,i was 1.1×10 17 Mx. As shown in Figure 12, after approximately 13 minutes the bipole lost 49.7% of its initial magnetic flux, or 2.6×10 17 Mx. During the cancellation the positive and negative polarities lose 0.7×10 17 Mx and 1.9×10 17 Mx, respectively. The average cancellation rate was 3.7×10 14 Mx s −1 . Within about 2 minutes of cancelling there was a 0.6 km s −1 increase in submergence speed, then a gradual oscillation and decrease to around 0 km s −1 .

A.2. Analysis of ROI 08
In ROI 08 we see cancellation occurring by examining the top row of Figure 13. Examining continuum imagery, we see the cancellation occurred in an intergranular lane. Positive polarity labeled 87 and negative polarity labeled 92, seen in Figure 13 begin cancelling at 08:21:27 UTC and the event lasts until 08:41:03 UTC. Φ − B,i was 2.1×10 17 Mx and Φ + B,i was 4.02×10 17 Mx and during the cancellation the positive and negative polarities lose 1.2×10 17 Mx and 1.8×10 17 Mx, respectively. About 50% of the initial bipole magnetic flux was lost during the cancellation event. The average cancellation rate through the event was 2.5×10 14 Mx s −1 . Visual inspection of the magnetograms in Figure 13, reveals that both the positive and negative polarities lose apparent size as they cancel, with the negative polarity falling below the instrument noise level in panel a7. Figure 14 shows that within roughly 2 minutes after first cancelling the Doppler velocity at the PIL jumps from -0.2 km s −1 to 0.8 km s −1 . Following that initial increase the Doppler velocity is relatively variable but still higher than the initial -0.2 km s −1 detected.

A.3. Analysis of ROI 11
ROI 11 involved a small positive polarity (0.9 × 10 17 Mx) and a large negative polarity (7.4 × 10 17 Mx) that cancelled over the course of around 18 minutes. The cancellation began in a downflow of 0.3 km s −1 and the submergence speed peaked at around 0.8 km s −1 , the same time as the cancellation rate peaked (R peak = 27 × 10 14 Mx        Figure 14. Evolution of LOS magnetic flux and PIL mean Doppler velocity, ΦB and VLOS, in ROI 08. Refer to the caption of Figure 4 for an explanation of the legend and other graphical details from most in that it begins in an upflow of roughly 0.3 km s −1 and ends in a downflow of roughly 1.1 km −1 meaning that the ∆V LOS of this event is large, ≈ 1.4 km s −1 . Both Figure 17 and the plot in Figure 18 show that this is a very clear case of cancellation ending in a downflow region in an intergranular lane.     Figure 16. Evolution of LOS magnetic flux and PIL mean Doppler velocity, ΦB and VLOS, in ROI 11. Refer to the caption of Figure 4 for an explanation of the legend and other graphical details.