On the importance of the nonequilibrium ionization of Si IV and O IV and the line-of-sight in solar surges

TL;DR

This study uses advanced simulations to show that nonequilibrium ionization and line-of-sight effects are crucial for understanding the enhanced emission of Si IV and O IV lines in solar surges, challenging traditional equilibrium assumptions.

Contribution

It introduces 2.5D radiative-MHD simulations including nonequilibrium ionization to explain surge emissions and highlights the significance of line-of-sight effects in spectral observations.

Findings

Surges exhibit enhanced Si IV and O IV emission due to nonequilibrium ionization.

Line-of-sight effects cause intermittent brightenings in spectral lines.

Statistical equilibrium assumptions underestimate ion presence in surges.

Abstract

Surges are ubiquitous cool ejections in the solar atmosphere that often appear associated with transient phenomena like UV bursts or coronal jets. Recent observations from the Interface Region Imaging Spectrograph (IRIS) show that surges, although traditionally related to chromospheric lines, can exhibit enhanced emission in Si IV with brighter spectral profiles than for the average transition region (TR). In this paper, we explain why surges are natural sites to show enhanced emissivity in TR lines. We performed 2.5D radiative-MHD numerical experiments using the Bifrost code including the nonequilibrium ionization of silicon and oxygen. A surge is obtained as a by-product of magnetic flux emergence; the TR enveloping the emerged domain is strongly affected by nonequilibrium effects: assuming statistical equilibrium would produce an absence of Si IV and O IV ions in most of the region. Studying the properties of the surge plasma emitting in the Si IV 1402.77 {\AA} and O IV 1401.16 {\AA} lines, we find that a) the timescales for the optically-thin losses and heat conduction are very short, leading to departures from statistical equilibrium, and b) the surge emits in Si IV more and has an emissivity ratio of Si IV to O IV larger than a standard TR. Using synthetic spectra, we conclude the importance of line-of-sight effects: given the involved geometry of the surge, the line-of-sight can cut the emitting layer at small angles and/or cross it multiple times, causing prominent, spatially intermittent brightenings both in Si IV and O IV.

Figures

Tables

Table 1. Table 1: Relevant parameters for the studied emission lines

Line	$T_{{}_{SE}}$ (K)	$g_u$	$g_l$	$f_{lu}$	$n_u/{ϵ}_{\lambda }$
Si IV 1402.77 Å	${10}^{4.9}$	$2$	$2$	$2.7\times {10}^{-1}$	$974$
O IV 1401.16 Å	${10}^{5.2}$	$6$	$4$	$5.1\times {10}^{-7}$	$7.62\times {10}^8$

Table 2. Table 2: Parameters of the initial twisted magnetic tube for both experiments

$x_0$ (Mm)	$z_0$ (Mm)	$R_0$ (Mm)	$q$ (Mm-1)	$B_0$ (kG)
15.0	-2.8	0.10	2.4	20

Equations

$${ϵ}_{\lambda }$$

$$A_{ul}$$

$$r$$

$$H$$

$$I_{ϵ}(x)$$

Full text

Sun: atmosphere $-$ Sun: chromosphere $-$ Sun: transition region $-$ magnetohydrodynamics (MHD) $-$ methods: numerical

1 Introduction

The solar atmosphere contains a wide variety of chromospheric ejections that cover a large range of scales: from the smallest ones with maximum size of a few megameters, such as penumbral microjets (e.g., Katsukawa et al., 2007; Drews & Rouppe van der Voort, 2017), or spicules (Hansteen et al., 2006; De Pontieu et al., 2007; Pereira et al., 2012, among others); up to ejections that can reach, in extreme cases, several tens of megameters, like surges (e.g., Canfield et al., 1996; Kurokawa et al., 2007; Guglielmino et al., 2010; Yang et al., 2014) and macrospicules (Bohlin et al., 1975; Georgakilas et al., 1999; Murawski et al., 2011; Kayshap et al., 2013). Surges, in particular, are often associated with magnetic flux emergence from the solar interior. They are typically observed as darkenings in images taken in the H$\alpha$ blue/red wings with line-of-sight (LOS) velocities of a few to several tens of km s*-1*, and are usually related to other explosive phenomena like EUV and X-ray jets, UV bursts and Ellerman bombs (see Nóbrega-Siverio et al., 2017, hereafter NS2017, and references therein). Although observationally known for several decades now, the understanding of surges has progressed slowly and various aspects like, e.g., their impact on the transition region (TR) and corona concerning the mass and energy budget, are still poorly known.

From the theoretical point of view, the first explanation of the surge phenomenon came through 2.5D numerical models (Shibata et al., 1992; Yokoyama & Shibata, 1995, 1996), where a cold ejection was identified next to a hot jet as a consequence of a magnetic reconnection process between the magnetic field in plasma emerged from the interior and the preexisting coronal field. Nishizuka et al. (2008) used a similar numerical setup to associate the surge with jet-like features seen in Ca II H+K observations by means of morphological image comparisons. Further 2.5D models that include the formation of a cool chromospheric ejection are those of Jiang et al. (2012) (canopy-type coronal magnetic field), and Yang et al. (2013, 2018), who study the cool jets resulting from the interaction between moving magnetic features at the base of their experiment and the preexisting ambient field in the atmosphere. Turning to three dimensional models, in the magnetic flux emergence experiment of Moreno-Insertis & Galsgaard (2013), a dense wall-like surge appeared surrounding the emerged region with temperatures from $10^{4}$ K to a few times $10^{5}$ K and speeds around $50$ km s*-1*. MacTaggart et al. (2015) found similar velocities for the surges in their 3D model of flux emergence in small-scale active regions. The availability of a radiation-MHD code like Bifrost (Gudiksen et al., 2011) has opened up the possibility of much more detailed modeling of the cool ejections than before. Bifrost has a realistic treatment of the material properties of the plasma, calculates the radiative transfer in the photosphere and chromosphere and includes the radiative and heat conduction entropy sources in the corona. Using that code, Nóbrega-Siverio et al. (2016), hereafter NS2016, argued that entropy sources play an important role during the surge formation and showed that a relevant fraction of the surge could not be obtained in previous and more idealized experiments.

The realistic treatment of surges may require an even larger degree of complication. The solar atmosphere is a highly dynamical environment; the evolution sometimes occurs on short timescales that bring different atomic species out of equilibrium ionization, thus complicating both the modeling and the observational diagnostics (e.g., Griem, 1964; Raymond & Dupree, 1978; Joselyn et al., 1979; Hansteen, 1993). For hydrogen, for instance, using 2D numerical experiments, Leenaarts et al. (2007, 2011) found that the temperature variations in the chromosphere can be much larger than for statistical equilibrium (SE), which has an impact on, e.g., its coolest regions (the so-called cool pockets). For helium, Golding et al. (2014, 2016) described how nonequilibrium (NEQ) ionization leads to higher temperatures in wavefronts and lower temperatures in the gas between shocks. For heavy elements, Bradshaw & Mason (2003); Bradshaw & Cargill (2006); Bradshaw & Klimchuk (2011); Reep et al. (2016) showed, through 1D hydrodynamic simulations, that there are large departures from SE balance in cooling coronal loops, nanoflares and other impulsive heating events that affects the EUV emissivity. Through 3D experiments, Olluri et al. (2013a) found that deduced electron densities for O IV can be up to an order of magnitude higher when NEQ effects are taken into account. Also in 3D, Olluri et al. (2015) discussed the importance of the NEQ ionization of coronal and TR lines to reproduce absolute intensities, line widths, ratios, among others, observed by, e.g., Chae et al. (1998); Doschek (2006); Doschek et al. (2008). De Pontieu et al. (2015) were able to explain the correlation between non-thermal line broadening and intensity of TR lines only when including NEQ ionization in their 2.5D numerical experiments. Martínez-Sykora et al. (2016) studied the statistical properties of the ionization of silicon and oxygen in different solar contexts: quiet Sun, coronal hole, plage, quiescent active region, and flaring active region, finding similarities with the observed intensity ratios only if NEQ effects are taken into account. Given their highly time-dependent nature and the relevance of the heating and cooling mechanisms in their evolution, surges are likely to be affected by NEQ ionization. Motivated by this fact, NS2017 included the NEQ ionization of silicon to compare synthetic Si IV spectra of two 2.5D numerical experiments with surge observations obtained by the Interface Region Imaging Spectrograph (IRIS, De Pontieu et al., 2014) and the Swedish 1-m Solar Telescope (SST, Scharmer et al., 2003). The results showed that the experiments were able to reproduce major features of the observed surge; nonetheless, the theoretical aspects to understand the enhanced Si IV emissivity within the numerical surge and its properties were not addressed in that publication.

The aim of the present paper is to provide theoretical explanations concerning the relevance of the NEQ ionization for surges and the corresponding impact on the emissivity of TR lines. We use 2.5D numerical experiments carried out with the Bifrost code (Gudiksen et al., 2011) including the module developed by Olluri et al. (2013b) that solves the time-dependent rate equations to calculate the ionization states of different elements, thus allowing for departures from SE. Here we apply this module to determine the ionization levels of silicon and oxygen. We conclude that consideration of NEQ is necessary to get the proper population levels of the ions and, consequently, the right emissivity to interpret observations. A statistical analysis of temperature is provided to constrain the plasma properties involved in the emissivity of relevant lines of Si IV and O IV within the surges. Through detailed Lagrange tracing, we are able to determine the origin of the emitting plasma and the role of the optically thin radiation and thermal conduction to explain the departure of SE of the relevant ions. Furthermore, we compute synthetic profiles to understand previous observational results and predict future ones, highlighting the surge regions that are more likely to be detected and addressing the importance of the angle of LOS.

The layout of the paper is as follows. Section 2 describes the physical and numerical models. Section 3 explains the general features of the time evolution of the experiments. In Section 4, we show the main results of the paper splitting the section in a) the relevance of the NEQ ionization of Si IV , and also O IV, in surges (Section 4.1); b) the consequences of the NEQ ionization for the surge plasma emitting in those TR lines, analyzing its properties and compare them with a generic quiet TR (Section 4.2); and c) the origin of the NEQ plasma, addressing the role of the entropy sources (Section 4.3). In Section 5, we have calculated absolute intensities and synthetic spectral profiles for diagnostic purposes and comparison with observations, emphasizing also the importance of the surge geometry and LOS. Finally, Section 6 contains a summary and conclusions.

2 The physical and numerical model

We have run two 2.5D numerical flux emergence experiments in which surges are a natural consequence of magnetic reconnection processes. Those two experiments were also used by NS2017 and Rouppe van der Voort et al. (2017) to compare the synthetic profiles with the complex profiles observed with IRIS and SST.

This section is divided into two parts: (1) the numerical code, and (2) the description of the model underlying our experiments.

2.1 The numerical code

The two experiments have been carried out with the 3D radiation-MHD (R-MHD) Bifrost code (Gudiksen et al., 2011; Carlsson & Leenaarts, 2012; Hayek et al., 2010), which treats the radiative transfer from the photosphere to the corona and thermal conduction in a self-consistent manner (see also NS2016 for further details of this code applied to surge experiments). Furthermore, we have enabled in the code a module developed by (Olluri et al., 2013b) to follow the NEQ ionization states of elements with atomic number greater than 2. This module solves the rate equations for those elements using the temperature, mass density, electronic number density $n_{e}$ and velocity values of the simulation without modifying the results of the R-MHD calculation, so there is no feedback, e.g., on the energy equation terms such as the optically thin losses (see the discussion in Section 6.1). In particular, we have employed it to calculate the NEQ ionization fraction for silicon and oxygen, using abundances from Asplund et al. (2009), 7.52 and 8.69, respectively, in the customary astronomical scale where 12 corresponds to hydrogen.

2.2 Description of the models

2.2.1 Physical domain and initial condition

In the two experiments, we began with a statistically stationary 2D snapshot that spans from the uppermost layers of the solar interior to the corona, and whose physical domain is $0.0$ Mm $\leq x\leq$ $32.0$ Mm and $-2.6$ Mm $\leq z\leq$ $30.0$ Mm, where $z=0$ Mm corresponds to the solar surface. The grid is uniform in the $x$-direction with $\Delta x=31$ km, but it is nonuniform in the vertical direction in order to better resolve the photosphere and chromosphere: the vertical grid spacing is $20$ km from the photosphere to the transition region, and increases gradually in the corona up to $147$ km at the top of the domain.

The left panel in Figure 1 contains the horizontal averages for the initial density, $\rho$, gas pressure, $P_{g}$, and temperature, $T$, for both experiments normalized to photospheric values, namely, $\rho_{ph}=3.1\times 10^{-7}$ g cm*-3*, $P_{g_{ph}}=1.1\times 10^{5}$ erg cm*-3* and $T_{ph}=5.7\times 10^{3}$  K. The corona has a temperature around $1$ MK and a magnetic field with a strength of $10$ G, with the difference that one of the experiments (hereafter the vertical experiment) has a vertical magnetic field in the corona while in the other (the slanted experiment), the magnetic field in the corona is inclined $30$° with respect to the vertical direction (see magnetic field lines superimposed in black in the 2D temperature maps for the initial snapshot in Figure 1).

2.2.2 Chemical elements calculated in NEQ and their spectral lines

We have used the NEQ module of Olluri et al. (2013b) mentioned in the Introduction to compute the nonequilibrium ionization of silicon in both numerical experiments. Furthermore, in the vertical experiment we also calculate the NEQ ionization of oxygen, with the goal of predicting future observational results. Once the NEQ populations are obtained, we are able to compute the emissivity using

[TABLE]

where $h$ is the Planck’s constant, $c$ the light speed, $\lambda$ is the wavelength of the spectral line, $n_{u}$ the population density of the upper level of the transition (i.e., the number density of emitters), and $A_{ul}$ the Einstein coefficient for spontaneous de-excitation given by

[TABLE]

where $e$ is the electron charge, $m_{e}$ the electron mass, $g_{l}$ and $g_{u}$ the statistical weights of the lower and upper states respectively, and $f_{lu}$ the oscillator strength. The units used in this paper for the emissivity $\epsilon$ are erg cm*-3* sr*-1* s*-1*. For the sake of compactness, we will refer to it in the following as $\epsilon_{{}_{CGS}}$.

Since we are interested in understanding the response of the TR to chromospheric phenomena like surges, we have chosen the following IRIS lines: Si IV 1402.77 Å, which is the weakest of the two silicon resonance lines; and O IV 1401.16 Å, the strongest of the forbidden oxygen lines that IRIS is able to observe. The corresponding formation temperature peaks in statistical equilibrium, $T_{{}_{SE}}$, and other relevant parameters to calculate the Einstein coefficient (Equation 2) and the corresponding emissivity (Equation 1) of these lines are shown in Table 1. Under optically thin conditions, Si IV 1393.76 Å is twice stronger than 1402.77 Å, so the results we obtain in this paper can also be applied to Si IV 1393.76 Å. Furthermore, the study of Si IV 1402.77 Å can provide theoretical support to our previous paper NS2017. In turn, the choice of the 1401.16 Å line for oxygen is because the O IV lines are faint and require longer exposure times to be observed (De Pontieu et al., 2014). Thus, in order to make any prediction that could be corroborated in future IRIS analysis, we focus on the strongest of the oxygen lines, which has a better chance to be detected. For simplicity, hereafter we refer to the Si IV 1402.77 Å and O IV 1401.16 Å emissivities as the Si IV and O IV emissivities, respectively.

2.2.3 Boundary conditions

We are imposing periodicity at the side boundaries; for the vertical direction, characteristic conditions are implemented at the top, whereas an open boundary is maintained at the bottom keeping a fixed value of the entropy of the incoming plasma. Additionally, in order to produce flux emergence, we inject a twisted magnetic tube through the bottom boundary following the method described by Martínez-Sykora et al. (2008). The parameters of the tube (specifically, the initial location of the axis, $x_{0}$ and $z_{0}$; the field strength there, $B_{0}$; the tube radius $R_{0}$; and the amount of field line twist $q$) are identical in both experiments and given in Table 2.2.3. The total axial magnetic flux is $\Phi_{0}=6.3\times 10^{18}$ Mx, which is in the range of an ephemeral active region (Zwaan, 1987). Details about this kind of setup are provided in the paper by NS2016.