High speed magnetized flows in the quiet Sun

With the selection criteria described in Section 2, we have found 398 strongly blue-shifted Stokes $V$ profiles belonging to 64 different events and 158 highly red-shifted Stokes $V$ profiles corresponding to 46 events. Hereafter, we will refer to these events as blue and red cases, respectively. Although not demanded by our selection criteria, all the selected circular polarization profiles happen to be highly asymmetric, $\delta A\rightarrow 1$, featuring one single lobe. In addition, the intensity profiles (Stokes $I$) also possess some common features. For instance, Stokes $I$ in the blue cases, present a mean continuum signal above one, indicating that they are located over bright regions on the continuum map (granular edges). The red cases, however, show the opposite behavior and display a mean continuum intensity below one, thus appearing preferably over dark regions on the continuum map (intergranular lanes). We have also found that the outer-blue wing of Stokes $I$ is strongly pushed toward shorter wavelengths in the blue cases. Likewise, the outer red wing of Stokes $I$, in the red cases, presents a strong shift toward larger wavelengths. This produces strongly asymmetric intensity profiles that are indicative of large depth variations in the LOS component of the velocity.

In addition, we have searched for blue- or red-shifted circular polarization signals inside a $2\times 2\arcsec$ region centered in every detected event, and we found that 73% of the blue cases are related to a red event. The rest of the blue cases, 27% of the total, seem to be isolated events. Interestingly, red cases never appear isolated. The distance between blue and the associated red cases varies but, whenever both events are close enough, they are connected by pixels that present strong linear polarization. In those in-between regions with large levels of linear polarization, Stokes $V$ is also highly asymmetric ($\delta A\rightarrow 1$), but in this case the profiles are not single lobed. Instead, they present two lobes of the same sign. Figure 1 shows a typical example of the spatial distribution of the Stokes $V$ profiles whenever a blue event appears related to a red event. This figure is composed of $6\times 6$ panels representing adjacent pixels. Each panel displays the Stokes $V$ profiles of both iron lines, Fe i 6301.5 and 6302.5 Å. Dotted vertical lines represent the rest center wavelength. In every panel, the vertical scale goes from -4% to +2% of I_c. We plotted in blue the Stokes $V$ profiles that we classify as belonging to a blue event, while red indicates the profiles with Stokes $V$ belonging to a nearby red event. Green profiles in between the blue and red profiles correspond to the Stokes $V$ profiles where the linear polarization is above 1% of I_c. We note that the closest pixels to the green profiles that display Stokes $V$ blue- or red-shifted signals, also show a non-negligible amount of linear polarization, albeit below the 1% level. The rest of the pixels in blue or red (e.g., panels on the top leftmost, $[1,1]$, and bottom rightmost, $[6,6]$, part in Fig. 1) do not possess a significant amount of linear polarization. We emphasize that the polarization signals in these observations, with circular and linear polarization levels higher than $0.03\leavevmode\nobreak\ I_{c}$ and $0.01\leavevmode\nobreak\ I_{c}$, respectively, are much stronger than those in the quiet-Sun internetwork (cf. Fig. 4 in Borrero & Kobel 2013).

An interesting property of the events in this configuration (Fig. 1) is that the sign of the single lobe in Stokes $V$ is the same for the red and blue cases: if one of the patches displays negative single-lobed profiles, then the associated event will also show negative Stokes $V$ profiles but with the opposite wavelength shift, and vice-versa (e.g., compare panels $[2,2]$ and $[5,5]$). We also see that the missing lobe is always the one closer to the rest wavelength (vertical dotted lines in each panel). These two facts seem to indicate that the circular polarization profiles in the blue and red cases are produced by magnetic fields of opposite polarity that harbor plasma flows along opposite directions. This can be realized by picturing circular polarization profiles where the missing lobe, in both red and blue cases, would be present close to the rest wavelength (vertical dotted lines). In addition, we observe that the Stokes $V$ profiles in the region that connects the red and blue events (green profiles in Fig. 1) are also highly asymmetric. Unlike the blue and red Stokes $V$ profiles, these profiles are not single-lobed, but rather they possess two lobes of the same sign (i.e., panel $[3,3]$).

The properties described above point to a configuration of the magnetic field in the form of a magnetic loop, where the footpoints possess a magnetic field of opposite polarities and velocities of opposite signs. The detection of linear polarization signals between footpoints further supports this picture. Interestingly, this scenario could also explain the observed asymmetries in Stokes $V$. The circular polarization profiles at the footpoints would have single-lobed shapes because the observer sees two different atmospheres along the line of sight: one with magnetic field and the other without it (Viticchié 2012). On the other hand, the Stokes $V$ profiles in the region with large linear polarization signals (green colors in Fig. 1) can be ascribed to the limited spatial resolution of the telescope, either produced by the contamination of the point spread function the telescope introduces in each pixel (van Noort 2012) or by the presence of two magnetic fields with opposite polarities on the same resolution element (Sigwarth 2001). For instance, Stokes $V$ in panel $[3,3]$ can be thought as being produced by a mixture of the Stokes $V$ profiles from panels $[2,2]$ and $[4,4]$. In spite of all the information gathered by the visual inspection of the profiles, it is so far not possible to establish whether the magnetic loop corresponds to a $\Omega$-loop or a U-loop. We will answer this question in the following sections.

Finally, Figure 2 illustrates an example of the remaining 27% of detected blue-shifted events, where no red-shifted counterpart could be identified within a $2\times 2\arcsec$ region around it. It was not possible to detect any significant linear polarization signals there either. In this figure, the vertical scale ranges from -3% to +8% of I_c. The blue-shifted single-lobed Stokes $V$ profiles in Figure 2 are very similar to those displayed in Figure 1. The only discernible difference is that the amplitude of the blue-shifted Stokes $V$ lobe in the isolated events is generally larger than the amplitude of the blue-shifted Stokes $V$ lobe when the blue event is accompanied by a red event.

To analyze the spatial distribution of the detected events we have plotted in Figure 3 the locations of all blue and red cases on a magnetogram constructed by integrating the signed circular polarization signals across the Fe i 6302.5 Å spectral line. Blue squares mark the position of the blue cases, while red squares correspond to the red cases. In order to make them visible, the size of each square has been magnified with respect to the real area occupied by each event. The locations of these events seem to be related to regions where the magnetic field is concentrated. They are close to network areas and rarely appear on the internetwork.

These events appear in patches of different sizes over the entire map. The mean areas are 6.2$\pm$3.1 and 3.5$\pm$2.1 pixels, for blue and red cases respectively. The smaller area of the latter could explain why we detect fewer of them, 46 red events compared to 64 detected blue events. To obtain the rate of occurrence of these events we divide the number of detected cases, 64 blue cases and 46 red cases, by the total area of the map ($328^{\prime\prime}\times 154^{\prime\prime}$). This provides a rate of occurrence of $1.2\times 10^{-3}$ blue cases per arcsec² and $9.1\times 10^{-4}$ red cases per arcsec². These values indicate that we would find nearly 12 different blue events, or nine red cases, in a FOV of $100\times 100$ arcsec².

We complement the information presented in Sections 3.1, and  3.2 using the time series from Hinode/SP described in Section 2. In the three hours of observations available we found five cases that are analogous to those found in the normal map (see Fig. 3)¹¹1Considering the total area spanned by the time series and the rate of occurrence determined in Sect. 3.2 a total of about 40 events should have been detected. The fact that we see ten times fewer might indicate that the slit of the raster scan probably sit on an internetwork region, where many fewer events are usually seen (see Fig. 3). Because of the small FOV ($2.9^{\prime\prime}\times 38^{\prime\prime}$) it is difficult to detect any blue case, along with its associated red event, that falls into the small scanned region during the entire lifetime of the event. Out of five detected events, only one of them remains within the field of view throughout its evolution. In Figure 4, we analyze the time evolution of this particular event using Hinode/SP scans as well as CN and Ca ii h broadband images from Hinode/BFI. The event lasts nearly ten minutes. From top to bottom each row displays the continuum intensity from Hinode/SP, CN broadband images, Fe i 6302.5 Å magnetogram (obtained in the same way as Fig. 3), and Ca ii h broadband images. Each of the four columns correspond to a different time step in the event’s evolution: $\Delta t=0$, 72, 144 and 216 seconds. Following the same convention used in Fig. 1, we have also marked in blue the pixels harboring blue-shifted single-lobed Stokes $V$, in red the pixels displaying red-shifted single-lobed Stokes $V$, and in green the pixels with a linear polarization above 1% of $I_{c}$.

The left most column in Fig. 4 corresponds to the initial detection of the event. At this time, the event displays only a patch of large linear polarization signals and almost no blue- or red-shifted Stokes $V$ profiles. The pixels where the linear polarization is above 1% of $I_{c}$ exhibit $Q$-like circular polarization profiles characterized by two lobes of the same sign (similar to those in Fig. 3; panel $[3,3]$). After 72 seconds (second column) two patches of blue- and red-shifted single-lobed Stokes $V$ profiles developed and they appear connected through the region of enhanced linear polarization. The third and fourth columns show that the patches of blue- and red-shifted single-lobed circular polarization profiles separate, while the pixels with high linear polarization signals vanish. The footpoints keep moving away from each other for the remaining of the event’s lifetime (10 min). According to the Fe i continuum and CN broadband images (first and second rows), the blue- and red-shifted patches lie over bright and dark regions, respectively. The Fe i 6302.5 Å magnetogram (third column in Fig. 4) further demonstrates (see Sect. 3.1) that these two patches appear over magnetic fields of opposite polarities. Finally, we do not find any traces of these events higher up in the atmosphere (Ca ii h images on the bottom row in Fig. 4) at any time in their evolution.

As already mentioned in Sect. 3.1 (where we studied instantaneous images of these events) the observed configuration, as seen from its temporal evolution, is also compatible with a magnetic loop where the linear polarization connects two footpoints with opposite velocities and magnetic fields of opposite polarity. Since the linear polarization precedes the appearance of the footpoints of the loops, the time evolution could correspond to either an emerging $\Omega$-loop or to a submerging U-loop. These kinds of events have been previously reported in Martínez González et al. (2007); Centeno et al. (2007); Martínez González & Bellot Rubio (2009); Ishikawa et al. (2010); Viticchié (2012). All of them describe the structure as two footpoints of opposite Stokes $V$ signals connected by linear polarization, but only (Ishikawa et al. 2010) found opposite velocities, and only Viticchié (2012) detected single-lobed Stokes $V$ profiles.

The SIR code (Stokes inversion based on Response Functions; Ruiz Cobo & del Toro Iniesta 1992) allows us to infer the optical-depth dependence of the atmospheric parameters at each pixel through the inversion of the observed Stokes profiles. In our inversions we employ a single magnetic component parametrized by: seven nodes in the temperature $T(\tau_{500})$²²2The parameter $\tau_{500}$ refers to the optical depth evaluated at a wavelength where there are no spectral lines (continuum). In our case this wavelength is 500 nm., three in the line of sight (LOS) component of the velocity ${\rm v}_{\rm LOS}(\tau_{500})$, three in the magnetic intensity $B(\tau_{500})$, two for the inclination of the magnetic field with respect to the observer’s LOS $\gamma(\tau_{500})$, and one for the azimuthal angle of the magnetic field in the plane perpendicular to the observer’s LOS $\phi(\tau_{500})$. Variables such as micro- and macro-turbulence are fixed to zero and not inverted. At each iteration step the synthetic profiles are convolved with the spectral transmission profile of Hinode/SP (Lites et al. 2013). Since each node corresponds to a free parameter during the inversion, our model includes a total of 16 free parameters. The total number of data points is 448 distributed across 112 wavelength positions for each of the four Stokes profiles.

The nodes in $B(\tau_{500})$, $\gamma(\tau_{500})$, and ${\rm v}_{\rm LOS}(\tau_{500})$ are necessary to reproduce the extreme area asymmetries ($\delta A\rightarrow 1$) in the observed (see Figs. 1 and 2) circular polarization profiles (Landolfi & Landi Degl’Innocenti 1996). Additionally, the inferred physical parameters could be reliant on the initial atmosphere. To avoid this dependence, we have decided to invert each individual pixel with 25 different initial atmospheric models. These models were determined by randomly perturbing the temperature stratification of the Harvard-Smithonian Reference Atmosphere (HSRA) model (Gingerich et al. 1971). The rest of the physical parameters of the initial model ($B$, $\gamma$ and ${\rm v}_{\rm LOS}$) were determined via a uniform probability distribution and considered to be independent of the optical-depth. Out of the 25 solutions obtained for a given pixel, we retain the one that yields the smallest value of $\chi^{2}$.

We have inverted all 556 selected pixels in Hinode/SP normal map (398 blue- and 158 red-shifted; Sect. 3.1) employing the configuration described in Sect. 4.1. Figure 5 presents the averaged physical parameters as a function of the optical-depth evaluated at a wavelength of 500 nm ($\log\tau_{500}$) for the blue (upper row) and red cases (bottom row). The shaded-grey areas in this figure indicate the standard deviation obtained from the ensemble of pixels belonging to each of the two cases.

The mean temperature stratification (left most panels) is very similar in both blue and red cases. In the deep photosphere, $\log\tau_{500}\geq 0$, both kinds of events follow the stratification from the HSRA model (dashed lines) very closely. Above this region, $\log\tau_{500}\leq 0$, the inferred temperature in both cases is larger than that of the HSRA model. However, there are two particular layers ($\log\tau_{500}\approx-3.5$ and $\log\tau_{500}\approx-2$) where the temperature in these events is the same as in the aforementioned model. The only minor difference between the inferred temperature stratifications appears close to the continuum, $\log\tau_{500}=0$, where we obtain that the blue cases are slightly hotter (on average) than HSRA, whereas the red cases are slightly cooler. This was foreseeable because the former tend to appear at bright regions as seen on the continuum intensity, while the latter occur at dark regions (see Sect. 3.1 and upper row in Fig. 4).

Unlike the temperature, the inferred LOS velocities (second column in Fig. 5) are very different in the blue and red cases. In the former, the LOS velocity changes from large blue-shifts in the deep photosphere, ${\rm v}_{\rm LOS}=-5$ km s^-1 at $\log\tau_{500}=0$, to red-shifts in the higher photospheric layers: ${\rm v}_{\rm LOS}=3$ km s^-1 at $\log\tau_{500}=-3$. In the red cases, however, the velocity stratification is exactly opposite, with large red-shifts in the deep photosphere, ${\rm v}_{\rm LOS}=5$ km s^-1 at $\log\tau_{500}=0$, which become blue-shifts at higher photospheric layers: ${\rm v}_{\rm LOS}=-3$ km s^-1 at $\log\tau_{500}=-3$. The LOS velocities inferred from the inversion close to $\log\tau_{500}=0$ correspond to what should have been expected from the visual inspection of the profiles (see Fig. 1), since the blue cases featured highly blue-shifted Stokes $V$ profiles and enhanced absorption on the blue wing of Stokes $I$, and vice versa for the red cases (see Sect. 3.1).

As far as the magnetic properties of these events are concerned, the inversion returns a magnetic field strength $B$ that, despite being rather large (about 1 kG) in the deep photosphere, quickly decreases toward higher photospheric layers and becomes negligible above $\log\tau_{500}=-2$. This behavior is observed in both blue and red cases (see third column in Fig. 5). Meanwhile, the inclination of the magnetic field indicates that the field lines are nearly vertical close to $\log\tau_{500}=0$, and they gradually become horizontal as we move upward in the photosphere. The value of the inclination, $\gamma$, at $\log\tau_{500}=0$ follows the polarity of the magnetic field already seen in Fig. 4 (third row) and is the opposite for blue and red cases. The inferred inclination for $\log\tau_{500}\leq-2$ carries no significance because of the large scatter (see shaded areas) and because the magnetic field strength vanishes above this layer ($B\rightarrow 0$ when $\log\tau_{500}\leq-2$).

Besides the data from the Hinode/SP normal map (Sect. 4.2), we have also inverted the Stokes profiles from the time series described in Sect. 3.3. This allows us to follow the evolution of the physical parameters in the example presented in Fig. 4. Inferring the magnetic field vector $B$, $\gamma$, and $\phi$ from noisy data is a difficult task (Borrero & Kobel 2011) and therefore, we have decided to invert only for the temperature $T(\tau_{500})$, and LOS velocity ${\rm v}_{\rm LOS}(\tau_{500})$ in those pixels in Fig. 4 where the total polarization is below 2 % of $I_{c}$. In this case, we use three nodes for the temperature and the LOS velocity. Pixels with polarization values above this threshold were treated in the way described in Sect. 4.2. The inversion of all pixels in Figure 4 yields the physical parameters ($T$, $B$, $\gamma$, $\phi$, and ${\rm v}_{\rm LOS}$) as a function of $(x,y,\log\tau_{500},t)$. To visualize the results, we present in Figures 6 and 7 maps of the physical parameters at two different optical depths in the photosphere: $\log\tau_{500}=0,-2$, respectively. Each of these two figures display, from the top to bottom, the temperature $T(x,y)$, LOS velocity ${\rm v}_{\rm LOS}(x,y)$, and finally the LOS magnetic field $B_{\rm LOS}(x,y)$ obtained as the product between $B$ and $\cos\gamma$. Each column presents a different time in the event’s evolution: $\Delta t=0,72,144,216$ s.

We note that the temperature $T(x,y)$ at $\log\tau_{500}=0$ (upper panels in Fig. 6) closely follows the intensity pattern (i.e., granulation) outside the strong magnetic field regions (see first and second rows in Fig. 4). The Wilson depression inside the magnetic element causes the $\tau_{500}=1$ level to shift with respect to its surroundings. This effect, in combination with the existence of vertical gradients in the temperature, produces the apparent discontinuities in the temperature between the magnetic and non magnetic region. The color palette for ${\rm v}_{\rm LOS}(x,y)$ in the second row in Figures 6 and 7 has been chosen such that positive velocities are in red (red-shifts or downflows) and negative velocities are in blue (blue-shifts or upflows). In addition, $B_{\rm LOS}(x,y)$ (third row in Figs. 6 and 7) shows positive polarity magnetic fields (pointing toward the observer) in red, while negative polarity magnetic fields (pointing away from the observer) are indicated in blue.

Figure 6 demonstrates that, in the two regions with strong magnetic fields, the polarities and LOS velocities are inverted. As mentioned in Sects. 3.1 and 3.3, these two regions correspond to the footpoints of the magnetic loop that separate from each other as time passes. Higher up in the photosphere, $\log\tau_{500}=-2$ (see Figure 7), we can see that the temperature in the regions with strong magnetic fields are close to those of the HSRA model, where T_HSRA(log $\tau_{500}$=-2)=4660 K. This is in agreement with the previous section (see also Fig. 5). We also observe that the LOS magnetic field and velocity above the location of the footpoints have vanished (see also the third column in Fig. 5). The fact that ${\rm v}_{\rm LOS}$ and $B_{\rm LOS}$ are only present at the bottom of the photosphere lead us to identify this structure as an $\Omega$-loop structure rising through the atmosphere. A more detailed analysis of the loop structure will be performed in the next section.

In this section, we will analyze the vertical structure of the loop in Figures 6 and 7 as seen from the side. To that end we employ the results from the inversion presented in Section 4.3. Here we focus only on the time step $\Delta t=72$ seconds. At this time the loop is completely developed. In addition, the footpoints and the linear polarization signal that connects them are clearly discernible. To determine the physical properties of the loop as seen from the side we average, at each optical depth, the physical quantities temperature, LOS velocity, and magnetic field vector along the direction perpendicular to the line that connects both footpoints. This connecting line, or bisector, is denoted by the inclined solid black line in Figure 8. In this fashion, we can transform all relevant physical parameters from the $(x,y,\tau_{500})$ coordinate system into $(L,\tau_{500})$, where $L$ refers to the direction along the bisector in Figure 8.

Once in this new reference frame $(L,\tau_{500})$, we need to translate the physical parameters into a frame where the vertical axis corresponds to the geometrical height $z$ instead of the optical depth scale $\tau_{500}$. To achieve this, we employ a simplified version of the method described in Puschmann et al. (2010b, a). The idea is to determine a $z(\tau_{500})$ conversion for each pixel along the $L$ direction. This can be done by integrating the relation $dz=-d\tau_{500}/[\rho(\tau_{500})\kappa(\tau_{500})]$. Here, $\kappa$ and $\rho$ correspond to the opacity and density, respectively, of the averaged ($L$-direction) atmosphere, with the latter being obtained through the assumption of hydrostatic equilibrium along the vertical $z$-axis. The solution to this equation requires an integration constant. In our case, this constant is taken as the Wilson depression $z_{w}=z(\tau_{500}=1)$. With this procedure, a different $z(\tau_{500})$ conversion can be established for every point $L$ along the loop. In order to establish a common $z$-scale for all pixels, we allow the aforementioned integration constant to vary along the bisector, $z_{w}(L)$, such that the divergence of the magnetic field, $\nabla\cdot{\rm\bf B}$, is minimized along the loop.

Before this minimization is performed, we need to solve the 180^∘ ambiguity in the azimuth ($\phi$) of the magnetic field. This ambiguity makes it impossible to distinguish between the following two solutions: ${\rm\bf B}=(B_{x},B_{y},B_{z})$ and ${\rm\bf B}^{\dagger}=(-B_{x},-B_{y},B_{z})$. If left unattended, the terms corresponding to the horizontal derivatives in $\nabla\cdot{\rm\bf B}$ ($\partial B_{x}/\partial x$ and $\partial B_{y}/\partial y$) will dominate over the vertical derivative ($\partial B_{z}/\partial z$), thereby hindering the minimization of the divergence of the magnetic field by changing the boundary condition $z_{w}(L)$. The ambiguity is solved by choosing, at each pixel along the bisector in Fig. 8, either ${\rm\bf B}$ or ${\rm\bf B}^{\dagger}$, such that the magnetic field in the $XY$-plane always points along the same quadrant. The red headless arrows in Fig. 8 show the direction of the magnetic field on the horizontal plane after the correction for the 180^∘-ambiguity, illustrating that the field lines connect both footpoints of the structure.

After a common $z$ scale has been established for all pixels along the bisector in Fig. 8, we can study the behavior of the physical parameters as a function of the common vertical $z$-coordinate and the distance $L$ along the loop. This is equivalent to looking at the structure from the side, hence the title of Section 5. Figure 9 displays: magnetic field $B(L,z)$ (upper left panel), inclination of the magnetic field $\gamma(L,z)$ (upper right panel), gas pressure $P_{g}(L,z)$ (lower left panel; logarithmic scale), and LOS velocity ${\rm v}_{\rm LOS}(L,z)$ (lower right panel). Each panel indicates the magnetic field lines of the loop displayed in white or black. We can see that the minimization of $\nabla\cdot{\rm\bf B}$ (which shifts up or down the vertical scale at each pixel along the bisector; see Sect. 5.1) forces the central sections of the loop to be located higher in the photosphere than the footpoints. This behavior produces a clear $\Omega$-loop shape: the footpoints (formed deep in the photosphere) are characterized by somewhat vertical fields with opposite polarities: $\gamma\approx 45^{\circ}$ on the left footpoint ($L\approx 700$ km), but $\gamma\approx 120^{\circ}$ on the right footpoint ($L\approx 1600$ km). Meanwhile, the apex of the loop ($L\approx 1200$ km) possesses a more horizontal magnetic field ($\gamma\approx 90^{\circ}$). In addition, the LOS velocity ${\rm v}_{\rm LOS}$ at each footpoint has the opposite sign (bottom-right panel), thus indicating that the plasma flows from the right footpoint (upflow; ${\rm v}_{\rm LOS}<0$) toward the left footpoint (downflow; ${\rm v}_{\rm LOS}>0$). We emphasize that the values of ${\rm v}_{\rm LOS}$ at the footpoints are of the order of $3-4$ km s^-1, but if we project these velocities along the loop’s axis, assuming that the velocity and magnetic field vectors are parallel, we obtain absolute values of $5-6$ km s^-1 at the footpoints. These velocities are significantly faster than the typical convective velocities seen in the granulation.

The bottom left panel in Fig. 9 allows us to detect gas pressure imbalances $\Delta P_{g}$ between two points along the loop at a fixed height. This panel should be treated with caution however, because of the exponential dependence of $P_{g}$ with height. This dependence means that small errors in the determination of the Wilson depression at each point along the loop, $z_{w}(L)$, greatly increase the uncertainty in the gas pressure difference between any two given points.

During the inversion, only one node was given to the azimuthal angle of the magnetic field $\phi$ (see Sect. 4.1). Because of this, $\phi$ does not depend on $z$ (or $\tau$). However, the azimuth angle does feature an interesting behavior along the loop. This behavior, $\phi(L)$, is indicated in Figure 10, where we observe that the average magnetic field is not completely aligned with the structure. In the upflowing footpoint (${\rm v}_{\rm LOS}<0$; $L\approx 1600$ km), the azimuth of the field closely follows the inclination of the bisector ($-57^{\circ}$ in Fig. 8), but it gradually deviates from this value as we approach the downflowing footpoint (${\rm v}_{\rm LOS}>0$; $L\approx 700$ km). We conclude, therefore, that the magnetic field shows a certain degree of twist along the loop. This can be produced by a structure with magnetic helicity. The torsion of the magnetic field lines is also visible in the relative orientation between the bisector and the red headless arrows in Figure 8.