KINEMATICS AND FINE STRUCTURE OF AN UNWINDING POLAR JET OBSERVED BY THE SOLAR DYNAMIC OBSERVATORY/ATMOSPHERIC IMAGING ASSEMBLY

Coronal jets are heated plasmas along open or large-scale magnetic field lines. They often have a linear or slightly bent structure. In general, magnetic reconnection is regarded as the basic driving mechanism for them (e.g., Shibata et al. 1996; Chen et al. 2008). The detailed observational characteristics could be found in Shimojo et al. (1996). On the other hand, Hα surges, which are cold plasma flows and are observed as emission in Hα or absorption at other wavelengths, are usually considered to be cool counterparts of coronal jets in the chromosphere owing to the close relationship between them in space and time (Liu & Kurokawa 2004; Jiang et al. 2007). It should be noted that sometimes surges can trigger large-scale coronal mass ejections (Liu et al. 2005; Liu 2008).

Jets or surges (hereafter, we will refer to both as "jets") with rotary motion have been reported in numerous studies (e.g., Xu et al. 1984; Ökten & Cakmak 1990; Canfield et al. 1996; Pike & Mason 1998; Alexander & Fletcher 1999; Harrison et al. 2001; Jibben & Canfield 2004; Patsourakos et al. 2008; Liu et al. 2009; Moore et al. 2010). However, the exact physical causes remain unclear due to the limitation of our observations. Xu et al. (1984) proposed that the double-pole diffusion of plasmas, which results from the sharp density gradient between the ejecting plasmas and their surrounding open field, could help to interpret the jet's rotary motion. Others have explained such phenomena as the product of magnetic reconnection between a small bipole with a twisted closed field and a large-scale background open field (Canfield et al. 1996). Jibben & Canfield (2004) adopted such a scenario to explain the twist propagation from the twisted closed field of the bipole to the ambient open field. They found that the direction of the observed spin of jets is in agreement with the relaxation of the twist stored in the closed field of the bipole. A 2.5-dimensional simulation proposed by Shibata & Uchida (1986) showed that the mass and twist stored in the twisted closed field of the bipole could be driven out into the ambient open field. In addition, they further pointed out that there should be a helical velocity field in the jet consisting of a hot core and a cool sheath. Three-dimensional simulations also indicated that the releasing of stored twist does produce massive, high-speed jets driven by nonlinear Alfv$\rm \acute{e}$n waves in the solar corona (Pariat et al. 2009, 2010). However, before the launching of the Solar Dynamic Observatory (SDO), very few observations could provide enough information to confirm the close relationship between the plasma motions and the non-potential magnetic field energy released for the jets.

In this paper, we study the fine structure and kinematics of an unwinding coronal jet occurring in the north polar coronal hole on 2010 August 21. In addition, the energy relationship between the jet and its non-potential magnetic field are investigated. Observations and instruments are described in Section 2, results are presented in Section 3, discussions and conclusions are summarized in Section 4.

The observations used in this paper are taken by the SDO/Atmospheric Imaging Assembly (AIA; Title et al. 2006) and the Solar Magnetic Activity Research Telescope (SMART; Ueno et al. 2004) instruments. Full-disk EUV images supplied by the AIA telescope on board the recently launched SDO satellite have a cadence of 12 s and a spatial resolution of 12. SMART can simultaneously provide full-disk images in five channels: Hα line center and four off-bands (±0.5, ±0.8 Å). The images are taken with 1 minute cadence and 12 spatial resolution. All the images are differentially rotated to a reference time (06:40:00 UT). Meanwhile, they are rotated such that north (east) is up (left).

The jet started at about 06:07 UT and ended around 07:08 UT. It ejected along a straight trajectory resembling a cylinder with clear helical structures on the surface. In addition, obvious unwinding motions around the jet's main axis were observed during the rising period.

Figure 1 is a time sequence of Hα images. At 06:07 UT, the jet appeared and displayed as a cuspate bright structure in Hα observations near the northeast of the disk limb (see Figure 1(a)). About 10 minutes later, it evolved into a collimated structure consisting of separate dense points (see the jointed white arrows in Figures 1(b) and (c)). According to Ökten & Cakmak (1990), these dense points represent the appearance of the rotary motion of the moving plasmas in a jet. The rising speed of the jet front is measured to be 68 km s⁻¹ from the Hα images, and the maximum height traced is up to 5 × 10⁴ km. It is worthwhile to note that various speeds discussed in this paper are the apparent speeds of propagating bright structures in the sky plane.

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Figure 2 shows the time evolution of the jet in the 304 Å and 193 Å images. The jet first displayed a cuspate structure (see the white arrow in Figure 2), then it developed into a long cylindrical shape with many helical bright structures on the surface (see Figure 2(c)). During this period, rotary motion around the jet's main axis and radial expansion of the jet at its western side are remarkable (refer to Figure 2 and the associated animation in the online version of the journal). It is interesting to find that both the rising and the radial expansion periods of the jet stopped as the rotary motion drew to an end, which seems to imply that these coupled motions were caused by a single physical mechanism. At 06:43 UT, the jet reached the maximum height (∼1.7 × 10⁵ km), then it began to fall back along two distinct straight paths, no longer exhibiting a helical signal (see the two parallel black arrows in Figure 2(d)). We notice that a narrow cavity with a length of about 9 × 10⁴ km between the two paths was conspicuous in 304 Å images around 06:43 UT but unidentifiable at other wavelengths. Since the 304 Å line is not only out of local thermodynamic equilibrium and optically thick but also sensitive to the material motion (Labrosse et al. 2007, 2010), the peculiar cavity in the 304 Å images was possibly due to the longer integration length along the line of sight when observing the dynamic cylinder structure from the side. Based on this result, we propose that the mass of the jet should mainly be distributed on the shell of a cylinder. In addition, a pre-existing bright point, which represents a small bipole with a closed field, is observed near the footpoint of the jet in the 193 Å images (Figure 2(f)). It became larger and brighter just before the start of the jet and then disappeared several minutes later, which suggests that the jet was the result from the interaction between the bipole and its surrounding background open field.

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The kinematics of the jet are displayed in the time–distance diagrams along (Figure 3) and across (Figure 4) the jet's main axis. In Figure 3, by applying a linear (least-squares polynomial) fit to the data, the rising (falling) speed of the jet front along the eastern cut is estimated to be ∼86 (161) km s⁻¹, while the acceleration of the downward flows along the western cut is 0.026 km s⁻², which is far less than the solar gravitational acceleration (∼0.27 km s⁻²). Also, the cavity is obvious in the 304 Å time–distance diagram (Figure 3(b)) but undetectable in 193 Å at the same position (Figure 3(d)). In Figure 4, an intriguing characteristic is the radial expansion of the jet along its western side, which underwent three distinct phases, each of which lasted for about 12 minutes. For the convenience, we call them the gradually expanding phase, the fast expanding phase, and the steady phase, respectively. The gradually expanding phase can only be traced at low heights (cuts 1–3), while the fast expanding and steady phases can be distinguished at all heights (cuts 1–5). The expanding speeds for the gradually and fast expanding phases are 10 and 24 km s⁻¹, respectively. We note that the transition from the gradually expanding phase to the fast expanding phase was very quick, which is possibly due to a sudden acceleration of the magnetic reconnection between the closed field of the bipole and its ambient open field. During the steady phase, the jet kept its width to be about 4.0 × 10⁴ km for 12 minutes before falling back to the solar surface. Furthermore, these phases are observable in other wave bands unlike the cavity mentioned above (see Figure 4(f)), which indicates that they indeed resulted from the mass motion rather than temperature change.

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When the highly twisted closed field lines of the bipole reconnected with the untwisted open field lines, nonlinear torsional Alfv$\rm \acute{e}$n waves propagating along the reconnected field lines would be produced. These waves can not only drive the jet but also locally compress the plasma in the jet, so the apparent speeds of the helical bright structures in the jet would be different from the actual plasma motion (Pariat et al. 2009). However, to estimate the rotary speeds of these helical structures, we simply suppose that these helical structures are the results of the rotating plasmas. Consequently, the speeds can be obtained by tracing the bright stripes on the time–distance diagrams and making a linear fit to the data. The results are listed in Table 1. The axial (transverse) speed component (v_ax (v_tr)) is obtained from time–distance diagrams along (Figure 3) and across (Figure 4) the jet's main axis, while the resultant (angular) speed (v_re (ω)) is calculated based on the relation $v_{{\rm re}} = \sqrt{v_{{\rm ax}}^2 + v_{{\rm tr}}^2}$ ($\omega = \frac{v_{{\rm tr}}}{r}$, here r is the radius of the jet). The average axial and transverse speeds and the resultant speed of the rotating plasmas are 171, 123, and 211 km s⁻¹, respectively. When considering the speeds in different height ranges and different expanding phases, we find that the values above 3.5 × 10⁴ km from the jet base are obviously higher than those below this height. Therefore, the rotating plasmas were accelerated during the rising period, and the progressing pinch front, the J × B force (Shibata & Uchida 1986), and the torsional Alfv$\rm \acute{e}$n waves (Pariat et al. 2009) in the unwinding helices are considered to be the possible drivers. The mean angular speeds (ω) of the rotating plasmas are 11.1 × 10⁻³ rad s⁻¹ (period = 564 s), and there is little difference between the values for the gradually and fast expanding phases. Furthermore, we estimate the twist shed into the outer corona in the eruption. The upper boundary value of the twist stored could be obtained by multiplying ω by the unwinding time of the jet (∼24 minutes), while the lower boundary is estimated by multiplying ω by the mean untwisting time of some individual helical structures (∼11 minutes), since the reconnection occurs sequentially over different field lines and the new reconnected open lines will untwist orderly at a different moment. So the twist stored is between 1.17 and 2.55 turns, or 2.34–5.1π. Since magnetic helicity is conserved under reconnection, the released twist should be equal to the twist stored in the twisted closed field of the bipole. In addition, by dividing the turns of the released twist by the jet's maximum length, it yields the force-free factor (α) of the jet's magnetic field, which is between 0.7–1.5 × 10⁻⁸ m⁻¹, in agreement with a typical α value of active regions (Pevtsov et al. 2003).

It has been widely accepted that the energy source of solar eruptions is mostly transferred from magnetic free energy storing in non-potential magnetic field systems and releasing through magnetic reconnection. To investigate the energy relationship between the jet and its magnetic field, we calculate the jet's total energy and compare it with the free energy stored in the jet's non-potential magnetic field. With the formula $\Phi (R) = \frac{LB_\phi (R)}{RB_z(R)}$, here Φ(R), L, and R are the twist, length, and radius of the jet, respectively, B_ϕ and B_z are the azimuthal and the longitudinal components of the jet's magnetic field, respectively (Priest 1984), the azimuthal component (B_ϕ) can be obtained by setting the local vertical components (B_z) as 5 G (Smith & Balogh 1995). Thus B_ϕ is between 3.8 and 8.3 G. Moreover, assuming the jet's shape to be a cylinder, the free energy storing in the non-potential magnetic field of the jet is estimated to be (1.0–4.5) × 10³⁰ erg. On the other hand, the total energy (including the kinetic energy and the gravitational potential energy of the jet, and the thermal energy of a microflare associated with the jet) of the jet is about 2.0 × 10²⁹ erg if the electron density is set as 4 × 10⁹ cm⁻³ and the thermal energy of the associated microflare is 10²⁸ erg (Shimojo & Shibata 2000). The results indicate that the free energy in the jet's non-potential magnetic field is one order of magnitude higher than the total energy of the jet. That is to say, the non-potential magnetic field of the jet can be the energy source for the jet.

With the high temporal and spatial observations, we study the kinematics and fine structure of an unwinding polar jet, which can be interpreted by using the reconnection models invoking magnetic untwisting as the driving mechanism (Shibata & Uchida 1986; Pariat et al. 2009, 2010). The main results are summarized as follows. (1) The jet showed separate dense points along its body in Hα observations. It represents the appearance of helical motions in the jet. (2) The shape of the jet resembled a cylinder with helical structures on the surface. Since the cavity can only be observed in the 304 Å line, we propose that the mass of the jet should mainly be distributed on a cylindrical shell. (3) The erupting plasmas fell back to the solar surface along two distinct paths. The acceleration of the downward flows along the western path was far less than the solar gravitational acceleration, which possibly results from the projection and the damping effects of the background magnetized plasmas. (4) The jet's radial expansion mainly occurred at its western side and underwent three distinct phases: the gradually expanding phase, the fast expanding phase, and the steady phase. Each phase lasted for about 12 minutes. (5) The rising, radial expansion, and unwinding motions of the jet are identified to stop approximately at the same time. We conjecture that these coupled motions are driven by a single physical mechanism. (6) The mean angular speed of the rotating plasmas around the jet's main axis is about 11.1 × 10⁻³ rad s⁻¹ (period = 564 s), while the twist shed into the outer corona in the eruption is estimated to be 1.17–2.55 turns (or 2.34–5.1π). In addition, the α of the jet's magnetic field ((0.7–1.5) × 10⁻⁸ m⁻¹) is consistent with the α of active regions. (7) Based on the observational results, we calculate the jet's total energy and the free energy stored in the non-potential magnetic field of the jet. It suggests that the non-potential magnetic field of the jet is enough to supply the total energy for the jet.

In terms of theory, a twisted, force-free, cylindrical flux tube will become unstable to kink instability if the twist of the tube reaches up to 1.3 turns, or 2.6π (Priest 1984). In the numerical simulation presented by Pariat et al. (2009), the authors found that the threshold for producing a coronal jet is 1.4 turns (2.8π) of twist. In our case, the twist of the closed field not only agrees with the theoretical result but also confirms that it indeed affects the tube's stability. It seems incompatible that the falling speed of the jet at the eastern side is higher than the rising speed. This is possible given that the heated erupting plasma has cooled down and therefore diminished the emission from the 304 Å images during the falling period (Labrosse et al. 2007). Since the jet is driven by magnetic twist through the reconnection process, we propose that the rising, radial expanding, and unwinding of the jet are the different manifestations of the reconnection. In addition, the expanding phases are thought to be closely associated with the reconnection between the closed field of the bipole and its ambient open field, and the transition from the gradually expanding phase to the fast expanding phase is possibly owning to a sudden acceleration of the reconnection process. In the energy calculation, the jet's shape is considered to be a cylinder. However, our observation indicates that the mass of the jet is mainly distributed on a cylindrical shell (viz., a hollow cylinder). If the thickness of the shell is assumed to be half of the jet's radius, the free energy stored in the jet's non-potential magnetic field is estimated to be (0.7–3.4) × 10³⁰ erg, while the jet's total energy is about 1.7 × 10²⁹ erg. This result is consistent with the conclusion summarized above. To fully understand the jet phenomenon, more observational and theoretical investigations with high temporal and spatial observations are needed in future work.

The AIA data are courtesy of SDO (NASA) and the AIA consortium, and we thank the SMART team for the Hα data support. We thank the referee for many helpful comments and valuable suggestions. This work is supported by the NSFC under Grants 10933003, 11078004, and 11073050, MOST (2011CB811400), and the Open Research Program of the Key Laboratory of Solar Activity of the National Astronomical Observatories of the Chinese Academy of Sciences (KLSA2011–14).