ASYMMETRY OF HELICITY INJECTION FLUX IN EMERGING ACTIVE REGIONS

NOAA 8214 is observed as a newly emerging AR as it appears at the eastern limb. Its area increases rapidly from 40 area units (area units = 10⁻⁶ hemispheres of the solar disk) at N26E47 on April 30 to the largest area of 650 area units at N26W23 on May 5.² It develops to be a well defined bipolar AR with an evident center of positive (negative) magnetic field as its leading (following) polarity. It rotated around the western limb on May 10, and then reappeared on the eastern limb on May 24, and was named as a new AR, NOAA 8227. We believe AR 8227 is a recurrence of NOAA 8214 based on the location of AR 8227 at N26L96 on June 1, which is very close to AR 8214 at N26L95 on May 4, (see also Bentley et al. 2000).

Figure 1 displays MDI 96 minute magnetograms of ARs 8214 (left) and 8227 (right). It is evident for AR 8214 that the magnetic field emerges very quickly and that the two opposite polarities separate rapidly. The leading polarity with positive flux (white patches) is more compact, while the following polarity with negative flux (black patches) is more dispersed and fragmented. Its recurrent AR, NOAA 8227, was observed as a decaying region. However, we can again note that the leading polarity with positive flux decayed more slowly and still contained a significant distribution of compact flux, while the following polarity with negative flux decayed and fragmented very quickly and dispersed over a large area.

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The development of the magnetic flux of the AR 8214 is shown in Figure 2(a), where the increase of the positive and negative fluxes is seen to be roughly similar. The correlation coefficient of the positive and negative fluxes is very high, C_r = 0.997, for 75 data points (see Figure 2(b)). A slope of the best linear fit, k, is 1.69, indicating that the increase of the positive flux is significantly faster than that of the negative flux.

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This emerging AR is a good example with which to study helicity injection and related topics because we can follow its development from almost the beginning of its emergence to several days later including the passage across the central meridian (i.e., over a longitudinal change from 40E to 40W). We employ the same method and LCT technique as used in Tian & Alexander (2008) to calculate the radial magnetic flux, helicity injection rate, and total helicity flux over 5 days spanning central meridian passage. Here, we distinguish the contribution from positive and negative polarities to the overall coronal helicity. Because the AR possesses a well defined bipolar magnetic structure, the contribution of positive (negative) flux to the coronal helicity can be considered to be that of the leading (following) polarity. The helicity injection rate and helicity flux injected by the leading (positive) and following (negative) polarities are separately shown in Figures 2(c) and 2(d), where "◊" (P) and "*" (N) denote values related to positive and negative fluxes, respectively. From the figure, we find that the positive leading polarity contributes at least seven times more helicity flux than that of the negative following polarity.

We can find from Figure 2(e) that the magnetic flux of the leading positive polarity and the following negative polarity is not balanced for the bulk of AR evolution over most of the time of observation. However, there is a transient balance at time "T1," i.e., magnetic flux of the leading polarity is equal to the magnetic flux of the following polarity. Comparing with Figure 2(c), the helicity injection rate of the positive leading polarity is much larger than that of the negative following polarity at all times. This indicates that the significant imbalance in the helicity injection rate and total helicity flux (see Figures 2(c) and 2(d)) is not directly related to the imbalance of the magnetic flux, though we show later that the magnetic flux imbalance is likely to result in the helicity flux imbalance.

We also see in Figure 2(c) that the measured helicity injection rate shows significant fluctuations in time, with the following polarity markedly varying in sign throughout the AR evolution. This is consistent with the recent simulation results of Y. Fan (2009, in preparation) where the fragmentation of the following leg of an emerging flux rope produces an untangling array of individual field lines with a mix of both positive and negative values of twist helicity. The distribution of helicities varies with length along the flux rope legs. A narrower distribution of helicity values, and all predominantly of the same sign, is seen for the leading polarity. If we assume that the structure simulated by Fan emerges to produce a bipolar AR, we would expect to see a picture similar to that shown in Figure 2(c), namely, an imbalance, coupled to strong fluctuations, in the helicity injection rate with the sign of the following polarity varying with time.

Considering that the tilt of the axis of the whole AR to the equator and its clockwise rotation are very small, the writhe helicity (related to the tilt angle), and the writhe helicity flux (related to the change of the tilt angle) injected into the corona should also be small, since the total helicity is a sum of twist helicity and writhe helicity. Combining conclusions from Jeong & Chae (2007) and Tian & Alexander (2008), that the coronal helicity originates predominantly from the emergence of magnetic field in the solar interior, and the result from this paper, that the leading polarity injects much more helicity flux into the corona, we argue that significantly larger twist helicity in the leading leg of the emerging flux tube can maintain the cohesion of the leading polarity field against possible sources of distortion (e.g., turbulence in the upper levels of the convection zone).

NOAA 0656 (S13L83) is also a fast-emerging bipolar AR when it appears around the eastern disk. Its area increases quickly from an initial 250 area units at S13E58 on August 7 to its largest value of 1360 area units at S13W22 on August 13. It rotated around the western limb on August 18, and then reappeared on September 1, and was named NOAA 0667 (S13L93) with 0670 (S13L83), having split into two separate regions. The recurrent ARs are located using the X- and Y-coordinates associated with AR 0656 but one rotation later. MDI 96 minute magnetograms of ARs 0656 (left) and 0667 + 0670 (right) are shown in Figure 3. From the figure it is evident for AR 0656 that the leading polarity with negative flux is more compact, emerges strongly, and moves fast, while the following polarity, with positive flux, is dispersed and fragmented. Its recurrent AR, NOAA 0667+0670, is decaying, with the leading polarity decaying more slowly and remaining more compact than the following polarity. This AR maintains its leading polarity (see Figure 3) better than that of NOAA 8214 to NOAA 8227 (see Figure 1), while the fragmentation of the following polarity is similar, i.e., very dispersed.

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Figure 4 displays the evolution of the positive and negative radial fluxes (Figure 4(a)), the ratio of magnetic flux increase of the leading and following polarities (Figure 4(b)), helicity injection rate (Figure 4(c)), and helicity injection flux (Figure 4(d)) over a period of 5 days spanning central meridian passage. The result of the helicity flux (Figure 4(d)) indicates that the leading (negative) polarity injects a large amount of negative helicity flux into the corona, while the following (positive) polarity injects a much smaller amount of positive helicity. Once again we see significant fluctuations in the helicity injection rate (see Figure 4(c)) with the rate for the following positive polarity varying in sign over the observation period. For this AR, these fluctuations result in a cumulative helicity injection in the fragmented following polarity that is of opposite sign to that of the compact leading polarity (see discussion). It is evident that the magnetic flux increase of the leading polarity is much larger than that of following polarity (see Figure 4(b)), a ratio of 2.90. Moreover, the magnetic flux of the leading polarity is larger than that of the following polarity after the time "T1," i.e., for most of time during the 5 days of observation (see Figure 4(e)). However, the leading negative polarity still has a higher helicity injection rate (see Figure 4(c)), even before the time "T1," when the magnetic flux of the leading polarity is lower than that of the following polarity. This again reflects the weak relationship between the imbalance of helicity injection flux and magnetic flux imbalance. During the 5 days spanning the central disk, the imbalance of the leading and following magnetic flux has an average value 1.23 ± 0.19, as shown in Figure 2(e). Even taking into account the magnetic flux difference, we still find that helicity flux injected by the leading polarity is at least 12 times (H ∼ Φ²) larger than that of the following polarity. This implies significantly faster emerging motions of the leading polarity (see Equations (1) and (2)). Similar to the results for AR 8214 we suggest that the 7–20 times larger twist helicity in the leading leg of the flux tube is related to much better flux coherence in the leading magnetic field.

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We use the same analysis described in Sections 3.1 and 3.2 to calculate the total magnetic flux, helicity injection rate and helicity flux of eight emerging ARs. Figure 5 displays the results of four ARs located in the southern hemisphere, that the injection rate and helicity flux over 5 days of the negative (leading) polarity tend to be much larger than that of the positive (following) polarity. Figure 6 displays the results of four ARs in the northern hemisphere, that the helicity injection rate and the helicity flux of the positive (leading) polarity tend to be much larger than the negative (following) polarity. The corresponding MDI 96 minute line-of-sight magnetograms of the eight ARs are shown in Figure 7, when the ARs were crossing the central meridian. From the Figure, we find that the following polarity in these strongly emerging bipolar ARs tends to be more dispersed and fragmented than the more compact leading polarity. Comparing results obtained in Figures 5 and 6, we find that the more compact leading polarity tends to have a much higher helicity injection rate and total helicity flux over 5 days than the more dispersed and fragmented following polarity. The result is same to that found in ARs 8214 and 0656 (see Figures 2(c) and 4(c)).

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The study of the above 10 emerging ARs signifies that in the bipolar strongly emerging ARs considered the leading polarity injects much more helicity flux into the corona than the following polarity. This is associated with the general magnetic configuration for such ARs that the leading magnetic field remains more compact and maintains a coherent structure for longer, while the following polarity is easily dispersed and fragmented. We summarize the statistical results of the sample of 15 ARs in Table 2, all of which show strong emergence, with both the positive and negative magnetic fluxes developing almost synchronously, and significant helicity flux injection over 5 days. A more detailed description for the full sample can be found in Section 2.

In Table 2, Φ_L/Φ_F and ΔΦ_L/ΔΦ_F denote ratios of the magnetic flux and the magnetic flux increase of the leading and following polarities. It is found in most of the ARs that the mean magnetic flux of the leading polarity is, in general, larger than that of the following polarity (i.e., Φ_L/Φ_F > 1.0). However, for part of their evolution some ARs show a leading flux that is smaller than the following polarity (i.e., Φ_L/Φ_F < 1.0, reflected in the standard deviation "σ" in Table 2). The ratio may reflect real magnetic flux imbalance between the leading and following polarities, though there is some uncertainty in the flux measurements, for regions with very weak field (|B| < 20 G) and very strong field (|B|>3500 G). In the former, the sensitivity of MDI means that significant flux, if distributed across a large number of small flux elements, may not be accounted for, while for the latter, saturation in the MDI leads to an underestimate of the leading polarity flux. Moreover, for most of the ARs the increase of the leading flux is faster than that of the following flux (i.e., ΔΦ_L/ΔΦ_F > 1.0, see also Figures 2(b) and 4(b)), typically over 1.5 times. This ratio may suggest that the leading polarity generally emerges faster than the following polarity. Consequently, the fast emergence results in fast horizontal motions, which have been measured by the LCT technique and taken into account in the calculation of helicity flux (see Equations (1) and (2)). The limitations of the LCT technique will be discussed in detail in last discussion section below. In the seventh column of Table 2, ΔH_L (ΔH_F) denotes the helicity flux injected by the leading (following) polarities, respectively. It is found that ΔH_L for eight of the ARs is over five times larger than ΔH_F, while about two to four times larger for the other six ARs. Only one AR, NOAA 0050, has lower ΔH_L than ΔH_F. In order to "remove" the gross effects of the flux imbalance, we produce a flux-weighted helicity flux, $T_L/T_F=[\frac {\Delta H_{L}} {\Phi_{L}^2}]/[\frac {\Delta H_{F}}{\Phi_{F}^2}]$, which is shown in the last column of Table 2. This value denotes the ratio of turn numbers of the twist in the leading and following magnetic field, and shows a smaller but still large helicity asymmetry. This result strongly signifies a predominant contribution of the leading polarity to the coronal helicity, which we believe is responsible for the leading polarity remaining compact and dispersing slowly.

The source of the energy released in solar flares is believed to be free magnetic energy stored in ARs. In particular, the energy is thought to derive from the nonpotential component (e.g., twist) of the magnetic field, which generates a current system that flows along the axis from one footpoint of a flux tube crossing the corona back to the other footpoint. It has been found that the emergence of electrical currents with magnetic flux, rather than surface shear flows or other purely atmospheric effects, appears to be key in driving AR flaring (e.g., Melrose 1995; Wheatland 2000; Schrijver et al. 2005).

Wheatland (2000) used vector magnetograms in the photosphere and found that nonneutralized current exists in most (13/21) of the ARs he studied, i.e., one polarity of an AR possesses a positive vertical current while the opposite polarity possesses a negative vertical current. The current can cause a line-of-sight flux imbalance because of the directionality of the magnetic field they produce (see Gary & Rabin 1995). Moreover, Moore (2008) has also shown recently that the currents in the two polarities may not be balanced with the current being stronger in the leading polarity. We use Huairou vector magnetograms to calculate the vertical current for AR 8214, and find that the total vertical current is also imbalanced in this AR: 0.23 ± 0.02 × 10¹²A for the leading polarity and −0.16 ± 0.01 × 10¹²A for the following polarity. This result implies that the current helicity (∫∫B_zJ_zdxdy) could also not be balanced since the magnetic flux of the leading polarity tends to be larger than that of the following polarity. Thus, both the current and twist helicity in the leading polarity tends to be stronger than in the following one. However, modern vector magnetograms are not good enough to be used quantitatively, due to considerable uncertainties such as reliability of the transverse field, resolution of the 180° ambiguity, effect of Faraday rotation, and large noise in transverse field. We can expect to get good vector data from SDO/HMI, together with Hinode, to investigate the imbalance of the vertical current, current helicity, helicity flux, and/or other twist parameters, for an AR at the same time in the future. The significant imbalance of the helicity flux observed in this paper may provide evidence supporting the current imbalance, since both reflect the same physical character.

The main result of this paper is that the leading polarity injects a much larger component of the total helicity flux than the following one. Although the study could be affected by the limitations of the use of MDI line-of-sight magnetograms in both very weak (|B| < 20 G) and very strong (|B|>3500 G) field regions due to the observational noise and flux saturation, respectively, and the immaturity of the LCT techniques, the large observed difference of the helicity flux, over a factor of 10 in some ARs (8760, 8910, 9139, 9574, and 0656; see Table 2), between the leading and following polarities, should be physical in origin (see above). Magnetic flux imbalance will contribute somewhat to this, but should not be the major source, because we find, in some ARs, that even when the leading flux is smaller than the following flux, the helicity injection rate is still much higher in the leading polarity (see Figures 2(c) and 2(e), 4(c) and 4(e), the last column in Table 2, and the analysis in Section 3).

This result implies that the leading leg of a presumed Ω-shaped flux tube possesses more twist than that of the following leg prior to its emergence from the interior. If the twist of the magnetic field is produced by dynamo action in the solar interior, what processes generate the twist asymmetry? Longcope & Welsch (2000) predicted a particular behavior of twist depending on the rate of the flux tube emergence, i.e., the level of rotation of the footpoint of the flux tube will depend upon the rapidity of flux emergence. This would imply, from the ratio of ΔΦ_L and ΔΦ_F shown in Table 2, that the leading polarity emerges faster than the following one, over 1.5 times as fast. Though present observations do not supply enough data to investigate if the leading sunspot rotates more strongly than the following sunspot, a number of observations (Brown et al., 2003; Longcope & Ravindra, 2007; Tian et al. 2008; Yan et al. 2008) clearly show this implication. Based on the work of Longcope & Welsch (2000), the results shown in Table 2 imply that the leading polarity should rotate faster and thereby produce more helicity. Therefore, the leading polarity possesses more helicity so that the leading flux is maintained to be compact and cohesive, due to a stronger tension of the magnetic field, and consequently, is less affected by the convective motions. The opposite situation occurs in the following polarity: slow flux emergence related to slow rotation and so less helicity, due to which the following field is seriously affected by the convective motions, resulting in dispersal and fragmentation with the helicity injection flux characterized by having large fluctuations. Y. Fan's (2009, in preparation) simulation does find that there is a systematically greater magnitude of helicity injection rate compared to the following at all depths when a flux tube rises in the solar interior.

The magnetic flux of the leading polarity increases faster than that of the following flux, which is characterized by the ratio ΔΦ_L/ΔΦ_F shown in Table 2. Faster emergence in the leading polarity can result in more rapid horizontal motions in the photosphere. Such asymmetric proper motions have previously been observed in young ARs and sunspot groups (see Chou & Wang, 1987; van Driel-Gesztelyi & Petrovay, 1990; Petrovay et al., 1990), supporting the observations reported in this paper. Fan et al. (1993) explained that as the field strength in the leading leg becomes proportionately stronger, it becomes more buoyant. Moreno-Insertis et al. (1994) and Caligari et al. (1995) argued that the asymmetric proper motions are due to geometrical asymmetry of the Ω-shaped flux tube, with the leading leg being inclined more horizontally than the following leg. This field strength asymmetry may explain the observed more compact morphology of the leading polarity compared to its following polarity.

The overall movement of the magnetic field elements can be roughly estimated based on Equation (1), which indicates ΔH ∝ U · ΔΦ², where ΔH, U, and ΔΦ denote helicity flux injected, overall speed, and the increase of the magnetic flux, respectively. Thus, ratios related to the leading and following polarities are of the form

$$\begin{eqnarray*} &&{\frac{\Delta H_L}{\Delta H_F}}\propto {\frac{U_L}{U_F}}\cdot {\frac{\Delta \Phi _L^2}{\Delta \Phi _F^2}}, \end{eqnarray*}$$

and

$$\begin{equation} {\frac{U_L}{U_F}}\propto {\frac{\Delta H_L}{\Delta H_F}}\div \left({\frac{\Delta \Phi _L}{\Delta \Phi _F}}\right)^2, \end{equation} \tag{ 5 }$$

where subscripts "L" and "F" denote associated parameters of leading and following polarities. Figure 8(a) shows that the helicity flux imbalance (${\frac{|\Delta H_L|}{|\Delta H_L|+|\Delta H_F|}}$) of 14 ARs is over 65%, except NOAA 0050; the imbalance in nine ARs is over 80%. Figure 8(b) shows that the asymmetry of helicity flux (${\frac{|\Delta H_L|}{|\Delta H_F|}}$) injected by the leading and following polarities has little relationship with the square of the ratio of the magnetic flux increase; a small correlation coefficient of 0.049. However, the asymmetry of helicity flux is highly correlated to the speed asymmetry (${\frac{U_L}{U_F}}$); a much larger correlation coefficient of 0.916 with a confidence level >99.9%. These rough relationships suggest that the leading polarity with more helicity emerges and also moves horizontally faster than the following polarity, which is same to that obtained previously (see Chou & Wang 1987; van Driel-Gesztelyi & Petrovay 1990; Petrovay et al. 1990), and supports the prediction of Longcope & Welsch (2000) discussed above. Consequently, the leading leg of the presumed Ω-shaped flux tube rotates faster than the following leg, producing more helicity that can maintain its magnetic field lines more cohesively due to the stronger magnetic tension force. The result reported here supports the ideas that the asymmetry of helicity flux indeed exists between the leading and following magnetic field, and is related to the difference of the emerging speed of the two legs of the inclined Ω-shaped flux tube. Moreover, Murray & Hood (2008) found that magnetic tubes with higher degree of twist (and therefore greater magnetic tension) have higher rates of emergence into the atmosphere, which is also supported by a model result of Cheung et al. (2008). Our observational conclusions are consistent with that of these models.

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