Formation of Cool and Warm Jets by Magnetic Flux ... - IOPscience

The Astrophysical Journal, 852:16 (15pp), 2018 January 1

https://doi.org/10.3847/1538-4357/aa9996

© 2017. The American Astronomical Society. All rights reserved.

Formation of Cool and Warm Jets by Magnetic Flux Emerging from the Solar Chromosphere to Transition Region 1

Liping Yang1,2,3, Hardi Peter4, Jiansen He2,3

, Chuanyi Tu2

, Linghua Wang2

, Lei Zhang1

, and Limei Yan2

SIGMA Weather Group, State Key Laboratory for Space Weather, National Space Science Center, Chinese Academy of Sciences, 100190, Beijing, China 2 School of Earth and Space Sciences, Peking University, 100871 Beijing, China; [email protected] 3 HIT Institute of Space Science and Applied Technology, 518055, Shenzhen, China 4 Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Strasse, D-37191 Katlenburg-Lindau, Germany Received 2015 December 7; revised 2017 October 31; accepted 2017 October 31; published 2017 December 28

Abstract In the solar atmosphere, jets are ubiquitous at various spatial-temporal scales. They are important for understanding the energy and mass transports in the solar atmosphere. According to recent observational studies, the high-speed network jets are likely to be intermittent but continual sources of mass and energy for the solar wind. Here, we conduct a 2D magnetohydrodynamics simulation to investigate the mechanism of these network jets. A combination of magnetic flux emergence and horizontal advection is used to drive the magnetic reconnection in the transition region between a strong magnetic loop and a background open flux. The simulation results show that not only a fast warm jet, much similar to the network jets, is found, but also an adjacent slow cool jet, mostly like classical spicules, is launched. Differing from the fast warm jet driven by magnetic reconnection, the slow cool jet is mainly accelerated by gradients of both thermal pressure and magnetic pressure near the outer border of the mass-concentrated region compressed by the emerging loop. These results provide a different perspective on our understanding of the formation of both the slow cool jets from the solar chromosphere and the fast warm jets from the solar transition region. Key words: methods: numerical – Sun: chromosphere – Sun: corona Schmieder et al. 1984, 1995; Jiang et al. 2007; Uddin et al. 2012; Yang et al. 2014; Li et al. 2016). They move upward at speeds of 20–200 km s−1 along either a straight trajectory or a slightly curved one, reach heights of 10–100 Mm, and then fall along the same trajectory. Their lifetimes range from 10 to 20 minutes, and the diameters are usually several megameters. Cool surges often occur around emerging bipolar regions and are usually associated with hot, high-speed EUV or X-ray jets, which indicates that the interaction of emerging flux with the ambient field is a possible driver (Shibata et al. 1992; Vargas Domínguez et al. 2014). Classical spicules are jet-like phenomena with fine scale at the chromospheric limb (Sterling 2000; Tsiropoula et al. 2012). They thrust at speeds of tens of kilometers per second, reach as high as 2–10 Mm above the photosphere, and finally either disappear or fall onto the photosphere. They are short-lived (2–12 minutes) moving structures, with diameters from 200 to more than 1000 km. These thin jets form in the vicinity of photospheric magnetic field concentrations and have a temperature of about 104 K, as well as a number density of around 1011 cm−3. To explain the observed properties of classical spicules, various models have been proposed by employing different drivers, such as shocks (Hollweg 1982), Alfvén waves (Haerendel 1992), p-mode leakage (De Pontieu et al. 2004), magnetic forces from reconnection (Uchida 1969; MartínezSykora et al. 2009), and a low-pressure region above the chromosphere (Hammer & Nesis 2003). However, it seems that none of the proposed drivers are sufficient to simultaneously explain all the observed properties of classical spicules. Numerical simulations have been employed to understand the formation of other types of jets in the solar atmosphere (Sterling 2000; Tsiropoula et al. 2012; Raouafi et al. 2016, and references therein). Many authors modeled hot jets (e.g., coronal jets) as a consequence of magnetic reconnection in the

1. Introduction Solar jets are typical transient ejecta at various spatio-temporal scales. They provide some crucial clues to understanding the energy and mass transports in the solar atmosphere. Based on the spatial sizes, lifetimes, morphology, and physical properties, solar jets are variously categorized as, e.g., spicules (Beckers 1968), chromospheric anemone jets (Shibata et al. 2007), penumbral jets (Katsukawa et al. 2007), extreme-ultraviolet (EUV) jets (Innes et al. 1997), and X-ray jets (Shibata et al. 1992). The occurrence of a chromospheric spicule jet is found to be associated with the propagation of kink/Alfvén waves (transverse oscillation) along the spicule structure, which indicates the dual channels of energy release during the magnetic reconnection in the chromosphere (He et al. 2009; He et al. 2010a; Liu et al. 2014). Moreover, the magnetic reconnection is demonstrated to be intermittent with the observation of intermittent spicule jets along locally open structure, which is squeezed by horizontally moving magnetic field structure (Yan et al. 2015). Using high-resolution observations from the Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014), Tian et al. (2014) reported network jets with speeds of 80–250 km s−1 from the solar transition region. These jets have lifetimes from 20 to 80 s, and can recur at roughly the same locations at timescales of 2–15 minutes. They have a width of around 300 km, a temperature of about 105 K, and a height beyond 15 Mm. The network jets originate from bright regions, and often display typical inverted Y-shape morphology, suggesting magnetic reconnection between small loops and open fluxes as a possible driver. Narang et al. (2016) found that these network jets appeared not only in coronal holes but also in quiet-Sun regions. Cool surges are large-scale plasma ejecta rooted in the chromosphere, and reach coronal heights (Roy 1973; 1


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solar corona due to flux emergence or quasi-static footpoint motions. In these simulations, the hot jets are accelerated by the magnetic tension of the newly reconnected field lines, and/or by nonlinear Alfvén waves induced by the release of shearing or twist of magnetic field lines. As for cool jets, various simulations with different mechanisms have been performed. Shibata et al. (1982) presented a 1D hydrodynamic simulation of solar surges, which were considered to be jets owing to a sudden thermal pressure enhancement at the base of the atmosphere. To model fibrils nonlinearly, Sterling & Hollweg (1989) applied a single, quasi-impulsive force at the base of a flux tube, which generated a series of rebound shocks propagating upward. Directly driven by the observed photospheric velocities, a simulation by De Pontieu et al. (2004) showed that the acoustic shocks, developed by the leakage of photospheric flows and oscillations, could reproduce the observed occurrence and properties of individual spicules. In realistic 3D simulations of the outer solar atmosphere, Martínez-Sykora et al. (2011) reported the features of a Type-II spicule, which was driven by a strong Lorentz force that squeezed chromospheric materials. To explain chromospheric anemone jets, Yang et al. (2013b) performed a numerical experiment, and found that anemone jets accompanied by slow-mode shocks could be explained by chromospheric magnetic reconnection. Meanwhile, many simulations have been devoted to investigating the simultaneous ejection of hot and cool plasmas associated with magnetic flux emergence through the low atmosphere to the corona. By exploiting a 2D magnetohydrodynamics (MHD) simulation of the reconnection between emerging flux and uniform coronal fields, Yokoyama & Shibata (1995) showed that hot jet-like plasmas and a cool blob could be ejected simultaneously from microflares. In their model, the hot jet-like plasmas were accelerated by the reconnection between the emerging flux and the nearby coronal fields, while the cool blob was accelerated by the tension from the disconnected field lines. With the help of a 2.5D MHD model, Jiang et al. (2012) found that coronal microflares, induced by magnetic flux emergence into a canopy-type background magnetic field, could lead to an ejection of both hot and cool plasma. A 3D numerical experiment by MorenoInsertis & Galsgaard (2013) showed that magnetic flux emergence yielded both a hot fast coronal jet, similar to the observed EUV/X-ray jets, and a cool dense region surrounding the emerged magnetic loop. Using a realistic treatment of radiation transfer and material properties, Nóbrega-Siverio et al. (2016) carried out a 2.5D simulation to study the formation and evolution of a cool ejection when magnetized plasmas emerged through (meso) granular convection cells into the corona, and found that entropy sources were key factors. Their study gave a new perspective on cool ejections associated with magnetic flux emergence. Here, we present a 2D MHD numerical simulation to investigate the formation of the network jets reported by Tian et al. (2014). To carry this out, we simulate the effects of the magnetic reconnection between the emerging magnetic loop and background funnel fields. The loop first emerges from the solar chromosphere into the transition region, and then is propelled by a horizontal flow toward the center of the background funnel fields. The paper is organized as follows. Section 2 gives a general description of the numerical MHD model. In Section 3, we present the results of the numerical

simulation and display the features and formation processes of the driven jets. Section 4 provides a summary and discussion. 2. Numerical MHD Model 2.1. Governing Equations We utilize the scheme developed by Feng et al. (2014) to solve MHD equations in spherical coordinates. In the scheme, the MHD equations are split into fluid and magnetic induction parts. A Godunov-type finite volume method is applied for the fluid part, and a constrained-transport (CT) method is used for the magnetic induction part (Ziegler 2011). We adopt a secondorder accurate linear ansatz reconstruction as well as the Harten–Lax–van Leer approximate Riemann solver to compute numerical fluxes (Feng et al. 2011). The governing equations are as follows: ¶r +  · ru = 0, ¶t

(1 )

⎤ ⎡ ⎛ ¶ru 1 2⎞ 1 +  · ⎢ruu + I ⎜ p + B ⎟BB⎥ = rg , ¶t 2m 0 ⎠ m 0 ⎥⎦ ⎝ ⎣⎢

(2 )

⎤ ⎡ ⎛ ¶e 1 2⎞ 1 (u · B) B⎥ B ⎟+  · ⎢u ⎜e + p + ⎥⎦ ⎢⎣ ⎝ ¶t m0 2m 0 ⎠ = ru · g +  · (B ´ hj ) - L r +  · q + H + CN , ¶B =  ´ E, ¶t

(3 ) (4 )

where e = (1 2) ru2 + p (g - 1) + (1 2m0 ) B2 , j =

1  m0

´

B, and E = u ´ B - hj correspond to the total energy density, the current density, and the electric field, respectively. Here, ρ is the mass density; u is the velocity; p is the thermal pressure; B denotes the magnetic field; t is time; g is the solar gravitational acceleration; m0 is magnetic permeability; and g (=5 3) is the adiabatic index. A simple ideal gas with a constant specific heat ratio is assumed. The anomalous magnetic resistivity η (Yokoyama & Shibata 1995; Yang et al. 2013a) has the following form: ⎧ 0, ud  uc h=⎨ 2 a ( u u ⎩ d c - 1) ,

ud > uc

(5 )

where α is the resistivity parameter, and ud = J r is the current-carrier velocity. J is the total current density and uc is the threshold above which the anomalous resistivity is switched on. In this paper, α and uc are 0.01 and 500, respectively. Due to the spatial distribution of ud, the anomalous resistivity is non-zero only close to the reconnection region, and is zero elsewhere. In Equation (3), L r = N 2 L(T ) is the radiation loss, with N being number density and the radiative loss function L(T ) having the form given by Cook et al. (1989);  · q is the anisotropic thermal conduction, and q is the heat flux vector parallel to the magnetic field; CN is the Newton cooling term applied to the lowermost part of the model. For more details on these terms, please refer to Yang et al. (2013a). The parameterized heating function H consists of two terms: H = Hexp + Hloop.

2

(6 )


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Following Yang et al. (2013a), the first term Hexp is to maintain a background corona against conductive, radiative, and solar wind losses, and the second one, Hloop , designed to maintain hot loops, has the following form: Hloop = C ´ f1 ´ r ,

boundary condition as done by Yokoyama & Shibata (1995) and Yang et al. (2013a, 2013b): r (i , jmax + 1) = r (i , jmax ) + r 0 (i , jmax + 1) - r 0 (i , jmax ) ,

(7 )

(8 )

p (i , jmax + 1) = p (i , jmax )

−2

+ p0 (i , jmax + 1) - p0 (i , jmax ) ,

where C is a constant with the value 1000 W m , and f1 works like a switch, with its value being 1 in the loop region, and 0 elsewhere. To discern the loop region as heated, we trace magnetic field lines according to the following criteria: (1) both ends of the traced field lines should be located at the bottom boundary; (2) the left end has a positive polarity. During the computation, the loop plasmas are continuously heated to sustain the high temperature. As soon as one closed field line reconnects with the open field, we stop heating in the region through which the newly formed open field line passes. It should be mentioned that despite the importance of the loop heating, there is no final solution to the real mechanism of the problem, which may be associated with wave dissipation, direct current dissipation, or Alfvén wave turbulence dissipation. Here, we set a heating function proportional to the local density, following Forbes & Malherbe (1991), just because of its simplicity. In this work, we adopt a 2D MHD system as described above, i.e., all physical quantities are dependent on the heliocentric distance and the latitude. The computational region extends from 696 to 724 Mm in the radial (r-)direction, and from 1.545 to p 2 in the latitudinal (θ-)direction. The spherical coordinate system is usedjust for future consideration of a larger domain. The computational domain is covered by a uniform grid space in the θ-direction with dq = 1.43 ´ 10-4 , and a non-uniform grid space in the r-direction with dr = 25 km for 696 Mm  r  700 Mm, dr = 50 km for 700 Mm  r  702 Mm, and dr = 100 km for r  702 Mm. The bottom boundary of r=696 Mm is set at the top of the chromosphere, and the right boundary of q = p 2 corresponds to the center of the magnetic funnel. Note that we display the numerical results in x−z coordinates, with x denoting the distance from the center of the funnel and z denoting the height from the top of the chromosphere.

u (i , jmax + 1) = u (i , jmax ) ,

(9 ) (10)

B (i , jmax + 1) = B (i , jmax ) + B 0 (i , jmax + 1) - B 0 (i , jmax ).

(11)

Here, the values at guard cells are extrapolated using linear functions from the boundary values, and r0, p0 , B0 denote the values at t=0. Note that when a high-density jet arrives at the top boundary, these treatments cannot guarantee the hydrostatic equilibrium there, but slow down the jet. From the numerical results shown below, there are almost no artificial reflections of waves or large perturbations originating from the top boundary. At the bottom boundary of r=696 Mm, an emerging loop is first introduced into the computational domain by an upward flow (Vup ) of 2 km s−1 for 2 minutes, and then advected by a horizontal flow of 3 km s−1. The duration and upward speed of the emerging loop are comparable to the observations (Centeno et al. 2007; Gömöry et al. 2010, 2013; van Driel-Gesztelyi & Green 2015). In the first stage, we identify the region where the emerging loop intersects the bottom boundary (ELIBB), marked as red 2 - h (t )2 , dimension lines in Figure 3,using (x - xc )2  rloop where xc (=12 Mm), r loop (=2 Mm), and h(t) are the center of the loop, the radius of the loop, and the vertical distance between the center of the loop and the bottom boundary, respectively. Here, h (t ) = 0 - r loop + Vup ´ t . In the ELIBB region, we set the magnetic field and the thermal pressure to be equal to those of the loop, assign an upflow velocity of 2 km s−1, and fix the density to be the initial value. Outside of the ELIBB region, all variables are set to be the initial values. After t=2 minutes, we switch to the second stage, set up the horizontal flow as Yang et al. (2013a) did, and fix both the density and the thermal pressure. As for the vertical flow at the bottom boundary vr (i, 0), the settings depend on the vertical flow speed, vr (i, 1), at the grid point directly above the point under consideration. If vr (i, 1) > 0, we set the boundary condition vr (i, 0) = 0; otherwise, a linear extrapolation is applied. This is based on the consideration that we must keep the boundary open for downflow from reconnection; if we stop it, it may bounce and “pollute” the solution. To check the influence of the zero vertical flow at the boundary, we have conducted another case, in which we employ  · rV = 0 to obtain vr (i, 0). In this case, vr (i, 0) is found to be very small. The evolution of the reconnection and the stratification show no significant differences from the case in which vr (i, 0) = 0 is adopted if vr (i, 1) > 0. It should be noted that two layers of guard cells along all the boundaries are utilized. According to the boundary settings as illustrated above, we first determine the values of guard cells at the first layer, which is the one nearest the boundaries, and then apply the same methods to find the values of the guard cell at the second layer. This way of introducing the emerging loop through the bottom boundary differs from the approaches of Stein & Nordlund (2006) and Martínez-Sykora et al. (2008). We

2.2. Initial and Boundary Conditions The initial state of the plasma is assumed to be in a hydrostatic equilibrium, i.e., p = rg and u = 0 (Yang et al. 2013a). For the initial magnetic field, we use the same potential form as that from Hackenberg et al. (2000), with the following parameters: L=30 Mm, d=0.34 Mm, B0 = 11.8 G, and Bmax = 1.15 kG. In comparison with Hackenberg et al. (2000), our choice for the small Bmax can give a small region of closed fields, which is located below z=0 in Figure 1. Our computational region expands from the top of the chromosphere, rather than from the photosphere, and we achieve a completely open field configuration as shown in Figure 1. Along q = p 2, a symmetric boundary condition is employed. At the side boundary of q = 1.545, we apply an open boundary condition, i.e., the normal gradients of the density, the thermal pressure, and the velocity are set to zero and the magnetic field is linearly extrapolated. At the top boundary of r=724 Mm ( j = jmax ), we implement a free 3


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Figure 2. Assigned distribution of the magnetic field strength Bloop in the local coordinates. The black streamlines denote the magnetic field lines.

field in the chromosphere decreases to about 10% of that in the photosphere. Considering that the strength of the observed emerging loops is about hundreds of Gauss in the photosphere, we thus set the strength of the emerging loop in the chromosphere to be about 50 G as shown above. The magnetic field distribution of the emerging loop in the local coordinates is shown in Figure 2. As the plasmas in the ELIBB region are imparted the upward speed of 2 km s−1 with a duration of 2 minutes, there is also a mass flux through the ELIBB region. The relative increase of the mass in the computational domain can be estimated as

Figure 1. Initial distribution of the vertical magnetic field Bz. The black streamlines denote the magnetic field lines, and the white lines are the contours of the initial Alfvén speed (unit: km s−1). The markers of “chromo” and “photo” denote the tops of the chromosphere and the photosphere, respectively. The abscissa stands for the distance from the center of the funnel and the vertical coordinates represents the height from the top of the chromosphere.

directly prescribe the magnetic field in the ELIBB region to be that of the emerging loop. This may introduce divergence of the magnetic field at the first grid layer in the radial direction. We check the distribution of  · B, and find that it is small at the first grid layer in the radial direction as compared to the maximum of the derivatives of the magnetic field in radial and latitudinal directions. The divergence of the magnetic field approaches zero at the other grid cells as the employed CT method guarantees.

2 minutes

dm =

The emerging loop satisfies the equations p loop = jloop ´ Bloop and jloop = 1 m0  ´ Bloop , where p loop , jloop and Bloop are the thermal pressure, the current density, and the magnetic field of the emerging loop (Wu et al. 1995). Assuming an axisymmetrical cylinder containing a volumetric current represented in the local cylindrical coordinates (r ¢, q ¢, z ¢) by jloop = j0 (r loop - r ¢) eˆz , we obtain

ploop = p0 +

m 0 j02 18

4 rloop

,

(14)

In this section, we present the results of the simulation, including the global scenario and the evolution of the fast warm jet and the slow cool jet. 3.1. Global Scenario

(13)

Figure 3 shows the calculated distributions of temperature T, number density N, and vertical velocity Vz at t=3.6 minutes with magnetic field lines in black. It can be seen that both a warm jet and a cool jet appear at t=3.6 minutes, when the horizontal advection is being exerted on the bottom boundary and the loop ceases to emerge. In the figure, we mark the regions of the jets with two big arrowheads. The warm jet is almost directly above the ELIBB region, while the cool jet is on the right side of the ELIBB region. The figure also reveals that magnetic reconnection occurs between the loop

Here, the thermal pressure at the interface between the loop and the surrounding medium is continuous, i.e., p loop = p0 at r ¢ = r loop , where p0 is the thermal pressure of the surrounding medium. By setting p loop (r ¢)∣r ¢= 0 = mp0 , we get j0 = 18 (m - 1) P0 . 4 m0 rloop

∬W rdxdz

3. Numerical Results

(12)

m 0 j02

2 ⎛1 2 ⎞ 1 5 ´ ⎜ rloop r ¢ 2 + r ¢ 4 - r loop r ¢ 3⎟. ⎝2 ⎠ 6 9

dt ò r 0 Vup dx ∣z = 0

with r0 being the bottom density and Ω being the computational domain. In practice, we find that dm is around 0.01. To explore the influences of this mass increase, we consider another case in which only Vup at the bottom boundary is artificially set to be zero, and the other variables at the bottom boundary are prescribed in the same way as implemented above. That is to say, the center of the magnetic loop goes upward at a fixed speed of 2 km s−1, and the magnetic field in the ELIBB region is also fixed to be that of the magnetic loop. We still observe a loop emerging from the bottom boundary, without any significant changes that could be attributed to the upflow in the computational domain. However, in this case, the plasma motion and the magnetic field do not couple at the bottom boundary.

2.3. Definition of the Emerging Loop

⎛1 1 ⎞ Bloop = m 0 j0 ⎜ r loop r ¢ - r ¢ 2⎟ eq , ⎝2 3 ⎠

ò0

The strength of the magnetic field of the loop

increases when m becomes large. Here, we set m=10 to get the magnetic field strength of the loop to be about 50 G in the chromosphere. Verth et al. (2011) showed that the magnetic 4


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Figure 3. Calculated distributions of temperature T, number density N, and vertical velocity Vz at t=3.6 minutes. The black streamlines denote the magnetic field lines, and red dimension lines mark the region where the emerging loop intersects the bottom boundary.

Figure 4. Calculated distributions of temperature T, number density N, and vertical velocity Vz at t=3.6 minutes, which are zoomed-in to display the region of both jets. The black streamlines denote the magnetic field lines, with numbers marking each line.

5


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and the background magnetic fields of the transition region. The warm jet is probably driven from the transition region by the reconnection, and the cool jet, next to the warm jet, is shot up from the chromosphere. At this moment, the warm jet has arrived at about 10 Mm, and the cool jet reaches around 8 Mm. In order to clearly exhibit the features of the warm and cool jets, we present an enlarged view of Figure 3 with x from 6.5 to 16.5 Mm and z between 0 and 10.5 Mm, which is displayed in Figure 4. Magnetic field lines are denoted as black lines and numbered 1–8 in each subfigure. In the region between Lines 4 and 6 above 3 Mm, the temperature is about 105 K; the number density changes from about 7 ´ 1010 cm−3 at 3 Mm to about 1010 cm−3 at 9 Mm; the upward velocity is about 85 km s−1. Thus, the fast warm jet is identified as lying between Lines 4 and 6. Meanwhile, in the region between Lines 6 and 7 above 2 Mm, the temperature is about 104 K; the number density changes from about 2.5 ´ 1011 cm−3 at 2 Mm to about 1011 cm−3 at 7 Mm; the velocity varies from about −20 km s−1 to 20 km s−1. Thus, we can recognize this region as the slow cool jet.

We compute the values of A (x, z ) by integrating the equation first from (0, 0) to (0, zmax ), then from (0, zmax ) to (x, zmax ), and finally from (x, zmax ) to (x,z). The magnetic diffusion only becomes substantial near the reconnection sites, so the integrated path selected above can minimize the effects of the diffusion. With these settings, we can assert that the magnetic diffusion cannot significantly influence the computation of the value of A for the selected field line above z=6 Mm after t=2.3 minutes. The solid purple lines in Figure 5 are the contours of A at the corresponding times, with its value equal to that of the solid purple line at t=2.3 minutes. Obviously, these solid purple lines above 6 Mm after t=2.3 minutes correspond to the same magnetic field line. Figure 6 presents the variations of temperature T, number density N, and vertical velocity Vz along the solid purple lines in Figure 5 with t from 3.0 to 14.0 minutes and z between 6 and 28 Mm. Tian et al. (2014) and Narang et al. (2016) pointed out that network jets can be identified in the spectra of Si IV lines (around 105 K). So, we plot the contour of T = 10 5 K in the t−z plane as dashed white lines in Figure 6 to represent the top end of the warm jet on the selected field line. Considering that the parameterized heating functions balance the energy loss due to radiation and heat conduction when achieving a quasi-static stratified atmosphere, we roughly reckon that the top end of the warm jet in the selected field line is the same parcel of jet plasmas from t=3.0 to 14.0 minutes. This figure shows that at t=4.0 minutes, the fast warm jet along the selected field line arrives at about 6 Mm, with a temperature of about 105 K, a number density of about 2.0 ´ 1010 cm−3 , and an upward speed of about 80 km s−1. At t=6.0 minutes, the number density of the top end becomes around 1010 cm−3 at a height of 16 Mm, and the velocity is still about 80 km s−1. At t=10.0 minutes, the top end of the warm jet begins to fall down with a number density of about 3.0 ´ 109 cm−3. In addition, we apply a linear fit to the top end of the warm jet on the temperature profile from t=5.0 to 6.5 minutes, which is shown as the solid black lines in Figure 6. We can obtain the propagation speed of the top end of the warm jet by calculating the slope of the solid black lines, which is about 83 km s−1. This value coincides with the typical observational speed of about 80 km s−1, which demonstrates that the plasma at the top end of the warm jet travels upward at a speed of about 80 km s−1. It should be noted that the bright yellow inclined line from (t , z ) = (3.5, 6) to (4.5, 28) in the panel of Vz is just a consequence of the selection of the color bar, and does not correspond to any physical signal because we cannot find any coherent structures on the panels of T and N.

3.2. Fast Warm Jet To clearly demonstrate the evolution of the fast warm jet driven by the magnetic reconnection, we present four snapshots of the calculated distributions of temperature T, number density N, and vertical velocity Vz at t=2.3 minutes, 3.6 minutes, 4.9 minutes, and 6.2 minutes in Figure 5, with different color bars from those in Figure 3. At t=2.3 minutes, the loop has stopped emerging, and moves leftward due to the horizontal flow at the bottom boundary, which compresses the open fields and triggers the magnetic reconnection. At t=3.6 minutes, the ongoing reconnection drives the warm jet of about 105 K, which goes upward at a speed of about 80 km s−1 along the reconnected field lines. The width of this driven warm jet is several hundreds of kilometers. At t=4.9 minutes, the reconnection site goes down in height, and the magnetic reconnection tends to abate gradually. As a result, the base of the warm jet slows down, while its top end reaches around 15 Mm. In addition, the loop shrinks due to the erosion of the magnetic reconnection. At t=6.2 minutes, the magnetic reconnection almost dies out and the warm jet rises to about 20 Mm. The motion of the warm jet plasmas after the magnetic reconnection basically follows the law of magnetic freezing. Thus, we can investigate the characteristics of the warm jet by tracing the magnetic field lines to which the jet plasmas cling. To trace the magnetic field lines passing through the warm jet at different times, we introduce the vector potential Aŷ defined by B =  ´ Aŷ. The contours of A represent the magnetic field lines. In practice, we fix the value of A (0, 0) at the lower left corner, and obtain the values of A (x, z ) at other places by integrating the above equation. We note that the velocity at the lower left corner is fixed to be zero, and thus at this point dA (0, 0) ¶A = 0 . Wherever there is + u · A = 0 , that is, dt ¶t negligible ohmic diffusion, it can be proved that dA (x, z ) dA (0, 0) = dt = 0 . Therefore, if a field line is frozen into dt the plasma, it keeps the same value of A at all times. In order to trace field lines frozen to the plasma in the jet region, we must follow constant values of A in regions well above the reconnection site. We choose the magnetic field line newly formed at t=2.3 minutes, which is denoted by the solid purple line in the leftmost panels of Figure 5. We focus our attention on the evolution of the warm jet through the selected magnetic field line during the interval from t=3 to 14 minutes.

3.3. Slow Cool Jet In addition to the fast warm jet, the emerging loop also launches the slow cool jet in the neighborhood of the loop. In this subsection, we discuss the evolution and acceleration of the slow cool jet. 3.3.1. General Evolution of the Slow Cool Jet

To see the features of the driven slow cool jet, we show the corresponding distributions of temperature T, number density N, and vertical velocity Vz at different moments in Figure 7. It can be seen that at t=1.0 minutes, the loop has entered the domain, and becomes hot due to the heating being introduced in Equation (3). At the same time, the cool jet (about 104 K) 6


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Figure 5. Calculated distributions of temperature T, number density N, and vertical velocity Vz at different moments, with the black streamlines denoting the magnetic field lines and the solid purple lines showing the traced field lines in the fast warm jet. Note that the color bars shown here differ from those in Figure 3.

on the right side of the loop starts to rise into the corona. At t=1.7 minutes, the loop continues to emerge, and thus becomes large. The cool jet with a number density of around 3 ´ 1011 cm−3 has shot up to around 4 Mm. At t= 3.0 minutes, carried by the horizontal flow, the loop moves leftward, and reconnects with the coronal fields, while the slow cool jet has reached a height of about 7 Mm. At t= 5.6 minutes, the slow cool jet starts to fall, and it completely falls back to the lower atmosphere, and disappears from the computational domain at t=8.2 minutes. Following the method used in Figure 6, we investigate the features of the cool jet over z=3 Mm along the solid purple lines shown in Figure 7. From this figure, we find that the magnetic reconnection has almost no influence on the selected field line over z=3 Mm. In Figure 8, we display the calculated

time–distance diagrams of temperature T, number density N, and vertical velocity Vz along the selected field line passing through the slow cool jet. This figure reveals that the slow cool jet travels upward from about t=1.0 to 4.5 minutes, and downward after t=4.5 minutes. At t=2.0 minutes, the slow cool jet along the selected field line moves at a speed of about 25 km s−1 and reaches around z=4 Mm. At t=4.5 minutes, it comes to the maximum height of around 7 Mm. At t= 6.0 minutes, the slow cool jet along the selected field line falls to about 5 Mm, with a speed of about −30 km s−1. At t= 7.0 minutes, it completely falls to the chromosphere. 3.3.2. The Forces Controlling the Cool Jet’s Vertical Motion

To investigate the roles that different forces play in the motion of the cool jet, we plot in Figure 9 the time evolution of 7


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Figure 6. Calculated time–distance diagrams of temperature T, number density N, and vertical velocity Vz along the selected field line passing through the fast warm jet, which is shown as the solid purple lines in Figure 5. The solid black lines denote a linear fit on the temperature profile, and the dashed white lines are determined as the contour of T = 10 5 K.

Figure 7. Calculated distributions of temperature T, number density N, and vertical velocity Vz at different moments, with the black streamlines denoting the magnetic field lines. Note that the color bars shown here differ from those in Figures 3 and 5.

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Figure 8. Calculated time–distance diagrams of temperature T, number density N, and vertical velocity Vz along the selected field line passing through the slow cool jet, which is shown as the solid purple lines in Figure 7. Note that the color bars shown here differ significantly from those in Figure 6 for the fast warm jet.

Figure 9. Time evolution of the vertical component of the Lorentz force FLz , the vertical thermal pressure gradient force Fpthz , gravity force Fgz , and temperature T (in units of K) at different heights (z=6.0 Mm, z=4.5 Mm, z=3.0 Mm, and z=0.6 Mm ) of the field lines passing through the slow cool jet, marked with solid yellow dots in Figure 7. The unit of force is 3.3 ´ 10-9 dyn cm−3 for all forces, and the unit of temperature is K.

yellow dots in Figure 7, and are sampled along the field lines passing through the slow cool jet. It should be noted that only the vertical components of the forces are calculated as the jet is

the vertical component of the Lorentz force FLz , the vertical thermal pressure gradient force Fpthz , gravity force Fgz , and temperature T at four points, which are indicated with large 9


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Figure 10. Calculated distributions of number density N, the acceleration a tot due to the total force, the acceleration a pth due to the thermal pressure gradient force, the acceleration aL due to the Lorentz force, the acceleration a pB due to the magnetic pressure gradient force, and the acceleration a ten due to the magnetic tension force, which are zoomed-in to show the region where the emerging loop lies at t = 0.26 minutes. In this figure, the black streamlines denote the magnetic field lines, the green lines (in the distribution of number density only), represent the contours of the plasma β, and the thick solid red arrows show the velocity vector in the top left panel and the thick solid purple arrows display the accelerations in the other panels. Note that the density of magnetic field lines does not denote the strength of the magnetic field.

a quasi-vertical structure. The first three rows of Figure 9 show the time evolution of the forces at z=6.0 Mm, z=4.5 Mm, and z=3.0 Mm after the slow cool jet is triggered, while the fourth row exhibits the time evolution of the forces at z=0.6 Mm, which can demonstrate the forces during the launching of the slow cool jet. To distinguish the plasmas of the slow cool jet from the background, we plot the temporal profiles of the temperature for reference. In our model, the gravity acceleration is constant and points to -z , producing a constant acceleration -g, thus Fgz = -gr . Basically speaking, the first three panels in Figure 9 show a two-phase evolution for the three forces. The transition from the first phase to the second one occurs roughly at t=4.2 minutes. In the first phase, the profiles of Fgz fall gradually, although there are some small fluctuations in the curves. As a result, the gravitational forces reach the maximum absolute values at the end of the first phase. Meanwhile, the vertical components of

Lorentz force FLz are negative most of the time, while the vertical thermal pressure gradient forces Fpthz are often directed upward. In the second phase, the profiles of Fgz rise and the absolute value of Fgz decreases to about 10−9 dyn cm−3 at t = 8.0 minutes. Compared with Fgz , the FLz and Fpthz are very small and can be neglected. According to the above analysis, we can find that the gravity force is dominant over the other two forces during the whole evolution. The temporal evolution of the forces at z=0.6 Mm shows that the slow cool jet experiences an acceleration before t=1.0 minutes by both the vertical thermal pressure gradient force Fpthz and the vertical component of Lorentz force FLz , with the former greater than the latter. The acceleration ends at about t = 0.5 minutes. 3.3.3. The Acceleration at the Nascent Phase

To see clearly how the slow cool jet is launched, in Figures 10 and 11 we display the calculated distributions of 10


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number density, the resultant acceleration, and components caused by all the forces in the region containing the emerging loops at t = 0.26 minutes and t = 0.78 minutes, respectively. In the top left panels of these figures, the color maps correspond to the number density and the thick solid red arrows correspond to the velocity vector. In the other panels of these figures, the color maps correspond to the module of the acceleration and the thick solid purple arrows indicate the actual acceleration vector. At an earlier time (t=0.26 minutes), compressed by the emerging loop, the mass is concentrated in the loop-shaped region adjacent to the loop, which is shown as the red band in the top left panel of Figure 10. The concentration results in a thermal pressure enhancement, which produces an upward thermal pressure gradient near the outer border of the loopshaped mass-concentrated (LSMC) region. The panels of a pth and a pB in Figure 10 reveal that the upward gradient forces of the thermal pressure and magnetic pressure contribute to the acceleration of the cool plasma. Figure 10 also shows that the acceleration, a ten , caused by the magnetic tension, is basically directed horizontally in the interior of the LSMC region, while it has an upward component at the left side and downward component at the right side, respectively. Although the field lines are more strongly bent on the left side of the LSMC region than on the right side, a ten is much larger on the right side because of the much stronger magnetic field there. Note that the density of the magnetic field lines shown in Figure 10 does not denote the total strength of magnetic fields. Both a ten and a pB are significantly larger on the right side of the LSMC region than on the left side,thus the acceleration due to the Lorentz force, aL , is also the largest on the right side, as revealed in this figure. In addition, aL is relatively small in the interior of the emerging loop because the downward acceleration a ten is nearly balanced by the upward acceleration a pB. At t=0.78 minutes, the LSMC region disintegrates due to the mass depletion centered around at x=12.5 and z=1.5, and the accelerated cool plasmas in the upper right panel of Figure 11 rise upward at a speed of tens of kilometers per second, and reach a height of about 2.5 Mm. In the interior of the emerging loop, a ten is still nearly balanced by a pB, while near the outer border of the emerging loop, the dominant acceleration becomes aL in most regions. The thermal pressure enhancement in the LSMC region naturally excites some perturbation in the overlying top chromosphere. In order to illustrate how the perturbation propagates upward, we present the calculated distributions of temperature T, number density N, and vertical velocity Vz at different moments in Figure 12. The bottom panel of the first column in Figure 12 shows that at t=0.26 minutes, the plasmas near the thermal pressure enhancement have a speed of around 40 km s−1, which is much larger than the sonic speed in the local medium (less than 20 km s−1). Therefore, the highspeed plasmas at this time should excite a shock, which will invariably penetrate into the low corona and evolve into a coronal shock as pointed out by Shibata et al. (1982) and De Pontieu et al. (2005). At t=1.04 minutes, the front of the shock arrives at a height of about 7.61 Mm, and at t= 1.30 minutes, it reaches about 11.90 Mm. We can estimate the propagation speed (vper ) along the shock’s normal direction shown as the dashed yellow line in this figure using (11.90 - 7.61) ´ 103 , where θ is the angle between the shock’s (1.30 - 1.04) ´ 60 ´ cos q normal direction and the vertical direction. As a result, vper is

about 282 km s . The propagation speed is greater than the upstream undisturbed sonic speed (cs) of about 234 km s−1. Figure 13 displays the calculated profiles of number density N, temperature T, vertical velocity Vz, and thermal pressure P along the normal direction at t=1.04 minutes. Across the front of the shock, there is a jump for number density, temperature, vertical velocity, and thermal pressure, although it appears that the jump is rather weak. At the reference frame moving with the shock, the upstream normal speed of the local plasma is about −292 km s−1, greater than the local sonic speed, and the downstream normal speed is about −223 km s−1, less than the local sonic speed. The amplitude of the velocity jump at the shock front is calculated as the difference between the incoming and the outgoing speeds, and is about 69 km s−1. This value is approximately equal to the velocity variation vamp (about 66 km s−1) derived from the local Rankine–Hugoniot 3 M2 - 1 relation, vamp = 4 M 2 vper , with M being Mach number (M = vper cs ~ 1.22) (e.g., Shibata et al. 1982). On the other hand, the ratio of the number densities between the downstream and upstream of the shock is about 1.38, while the ratio of the normal velocities is 1.31. The error of 5% between the two ratios, which is basically acceptable, can probably be attributed to the uncertainty of the shock normal direction and the inaccuracy of the shock propagation velocity used in the calculation. It may be also due to the fact that the shock being considered is at a non-stationary phase as shown in Figure 12. 4. Conclusion and Discussion In this work we conduct a 2D MHD simulation to investigate the formation and evolution of the network jet triggered by magnetic reconnection between a loop and open fluxes in the transition region. The simulation results show that not only a fast warm jet, but a slow cool jet, are ejected. The cool jet is ejected first, and later the warm and cool jets coexist. Finally, the cool jet falls down, while the warm jet continues traveling upward and then falls back after the driver stops. From Section 3, we can also obtain the properties of the fast warm and slow cool jets. The fast warm jet, triggered by the magnetic reconnection, has a temperature of about 105 K, a number density of about 1010 cm−3, a maximal speed of about 85 km s−1, and a maximal height beyond 20 Mm, which match the network jets reported by Tian et al. (2014) and Narang et al. (2016). The slow cool jet, launched by the thermal pressure enhancement in the LSMC region, has a temperature of around 104 K, a number density of around 1011 cm−3, an up–down path with an upward speed of around 25 km s−1, a maximal height beyond 5 Mm, and a lifetime of about 6 minutes, which are similar to those of classical spicules (Sterling 2000; Tsiropoula et al. 2012). As analyzed in Section 3, it is the upward thermal pressure gradient force and the upward magnetic pressure gradient force of the LSMS region that accelerate the local plasmas to generate the slow cool jet. The temporal profiles of the vertical component of the forces reveal that the gravity dominates the motion of the slow cool jet after it is launched. Note that the cool jet is not launched by the heating effect of Hloop in Equation (7). In fact, we find that there is little difference among the accelerations of the slow cool jet, whether Hloop is put into effect or not. Therefore, the thermal pressure enhancement near the outer border of the LSMC region, which drives the slow cool jet, results from the strong ram pressure of 11


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Figure 11. Same as Figure 10 but at t = 0.78 minutes. Note that arrows are re-scaled.

a driver. Some studies employed magnetic flux emergence to drive the simulations and attained both hot and cool jets (Yokoyama & Shibata 1995; Nishizuka et al. 2008; Jiang et al. 2012; Nóbrega-Siverio et al. 2016). The hot jets were similar to X-ray or EUV jets and the cool ones were similar to cool surges. Nóbrega-Siverio et al. (2016) exploited the technique of 2D Lagrange tracing of the mass elements in the driven surge and showed that the Lorentz force and gas pressure gradients at and near the current sheet could easily accelerate the surges. They also found that the plasma populations with temperatures higher than 105 K experienced cooling processes and achieved the classical surge temperatures of the order of 104 K. Particularly, the model by Nóbrega-Siverio et al. (2016)

the emerging loop, rather than from the heating of the loop that is introduced in Equation (7). In addition, the emerging loop has not been heated when the slow cool jet is just launched. In this work, the emerging loop plays an important role in the generation of the cool jet, which emanates from unipolar magnetic regions, as shown in Figure 7. This scenario is consistent with several observational studies (Christopoulou et al. 2001; Tavabi et al. 2011; Koutchmy et al. 2012). In addition, the simulated warm and cool jets give some different results from previous modeling studies. Using horizontal advection to propel the magnetic flux, an isolated warm jet was achieved by Yang et al. (2013a) and a single cool jet was obtained by Yang et al. (2013b), with magnetic reconnection as 12


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Figure 12. Calculated distributions of temperature T, number density N and vertical velocity Vz at different moments, with the black streamlines denoting the magnetic field lines. In this figure, the dashed yellow line is along the normal direction to the perturbation front.

constitutes a large step forward for studying the evolution of the surge, because it took many realistic effects into account. Furthermore, more observational studies should be performed to deeply investigate the possible connection between the network jets and spicules that are revealed in our simulation. Recently, Jiao et al. (2015) and Samanta et al. (2015) found that the start of coronal propagating disturbances is almost coincident with the time of the spicule envelope, and proposed that they share a common origin. The propagating disturbances might be heating signals and continuation of the fast network jet in the corona (see the supporting online materials of Tian et al. 2014). The compressional propagating disturbances in the solar corona are damped due to Landau resonance with the semi-collisional coronal plasmas in kinetic simulations, causing weak asymmetry of velocity distribution and emission line profile (Ruan et al. 2016). Our current model is comparable to the observation. In our simulation, the process of flux emergence in the solar

atmosphere simultaneously triggers both a fast warm jet and a spicule, as shown in Figure 4. According to the analyses of Figure 6, the fast warm jet travels into the solar corona at a speed of 80 km s−1, which coincides with the observational speed of the network jets (Tian et al. 2014). Further,pre, the model provides another interpretation of the observational fact that spicules often continue their evolution in hotter passbands (De Pontieu et al. 2011). In our simulation, the warm plasma adjacent to the spicule corresponds to the warm jet. Of course, more detailed observational and numerical studies are needed to understand the complete scenarios of the network jets and spicules (Tsiropoula et al. 2012; Raouafi et al. 2016). Finally, in order to achieve more realistic pictures infuture studies, we should constrain our model more by employing observational diagnostics of the transition region with high spatial resolution and temporal cadence from IRIS, which can help us to enrich our understandings of the nascent release and 13


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Figure 13. Calculated profiles of number density N, temperature T, normal velocity Vn, and thermal pressure P along the dashed yellow line in Figure 12 at t=1.04 minutes.

evolution in the solar wind region. The mass supply of the intermittent jets to the nascent solar wind may also be responsible for the observed alternation of plasma draining and replenishing near the edge of the solar active region (He et al. 2010b; Zhang et al. 2015). Additionally, considering the importance of the network jets to the formation of the solar wind, we should extend our model to three dimensions in the future in order for us to achieve some understandings that 2D simulations cannot provide, and if possible, incorporate the results from the improved models into the solar wind models (Feng et al. 2010; Yang et al. 2012, 2013a).

invaluable suggestions and comments that were provided by the anonymous reviewer. Special thanks go to Dr. Xiang in our laboratory for the instructive discussions and helpful suggestions to amend the paper. ORCID iDs Jiansen He https://orcid.org/0000-0001-8179-417X Chuanyi Tu https://orcid.org/0000-0002-9571-6911 Linghua Wang https://orcid.org/0000-0001-7309-4325 Lei Zhang https://orcid.org/0000-0003-2562-0698

This work is supported by NSFC grants under contracts 41774157, 41231069, 41231068, 41474147, 41574168, and 41421003, and the Specialized Research Fund for State Key Laboratories. The work was carried out at National Supercomputer Center in Tianjin, China and the calculations were performed on TianHe-1 (A). The authors appreciate the

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