Coronal Mass Ejections and Dimmings: A Comparative Study using MHD Simulations and SDO Observations

“Coronal dimming” refers to the reduction in intensity on or near the solar disk across a large area during solar eruptive events. It was first observed in white light corona and described as a “depletion” (Hansen et al., 1974) and later was found in solar X-ray observations as “transient coronal holes” (Rust & Hildner, 1976). Interest in coronal dimmings increased after they were identified in images from multiple EUV channels with different emission temperatures (Thompson et al., 1998) by Solar and Heliospheric Observatory (SOHO)/Extreme-ultraviolet Imaging (EIT) observations (Delaboudinière et al., 1995). Coronal dimmings were often found to be associated with coronal EUV waves (also called “EIT waves”, Thompson et al. 1999). EUV observations at higher temporal ($\sim$12 s) and spatial resolution ($\sim$1.2 arcsec) in seven channels from the Solar Dynamics Observatory (SDO; Pesnell et al. 2012)/Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) as well as the high spectral resolution data from SDO/Extreme Ultraviolet Variability Experiment (EVE; Woods et al. 2012) provided unprecedented opportunities to study coronal dimmings (Mason et al., 2014, 2016).

Two decades of solar observations suggest that the majority of coronal dimmings are associated with coronal mass ejections (CMEs; e.g., Sterling & Hudson 1997; Reinard & Biesecker 2008). Furthermore, since observations show simultaneous and co-spatial dimming in multiple coronal lines (e.g., Zarro et al. 1999; Sterling et al. 2000) and the spectroscopic observations show that the dimming region has up-flowing expanding plasma (e.g., Harra & Sterling 2001; Harra et al. 2007; Imada et al. 2007; Jin et al. 2009; Attrill et al. 2010; Tian et al. 2012), it is widely accepted that coronal dimmings are due to plasma evacuation during the launch of CMEs. Specifically, dimming areas are believed to correspond to the footprint of the erupting flux rope. This physical picture is also supported by magnetohydrodynamics (MHD) modeling results (e.g., Cohen et al. 2009; Downs et al. 2012).

In addition, coronal dimmings are closely correlated with the observed physical properties of the associated CMEs, including mass, speed, and energy (e.g., Hudson et al. 1996; Sterling & Hudson 1997; Harrison et al. 2003; Zhukov & Auchère 2004; Aschwanden et al. 2009; Cheng & Qiu 2016; Krista & Reinard 2017). In this regard, coronal dimmings provide useful information for space weather forecasts. For example, Krista & Reinard (2013) found correlations between the magnitudes of dimmings/flares and CME masses by studying the variations between the recurring eruptions and dimmings. Recently, by using SDO/EVE observations, Mason et al. (2016) found linear relationships between the speeds and masses of CMEs and coronal dimming properties (e.g., dimming depth and dimming slope), and suggested their relationships could be used for space weather operations of estimating CME mass and speed. Using logarithmic base-ratio images of SDO/AIA to measure the time-integrated coronal dimming parameters (e.g., the size of dimming region, total unsigned magnetic flux, total brightness) in 62 events during 2010-2012, Dissauer et al. (2018, 2019) found that CME mass is strongly correlated with coronal dimming parameters. In addition, as the core dimming is believed to be the footpoints of the erupting flux rope, the enclosed magnetic flux in the dimming region provides an estimate of the total magnetic flux in the erupting flux rope, which has been shown to be consistent with the in-situ flux rope measurements at 1 AU in multiple Earth-directing events (Webb et al., 2000; Qiu et al., 2007). Since routine remote sensing measurements of the magnetic field strength and geometry of coronal flux ropes remain unavailable, coronal dimmings provide much needed diagnostics that are critical for space weather prediction. Furthermore, by exploring the characteristics of 42 X-class solar flares, Harra et al. (2016) found that coronal dimmings are the only signature that could differentiate powerful flares that have CMEs from those that do not. Therefore, dimmings might be one of the best candidate proxies for detection of stellar CMEs from distant Sun-like stars. To gain a better understanding about solar coronal dimmings would provide important reference for solar-stellar connection studies as well as for planning future missions to detect stellar CMEs.

By modeling a realistic CME event on 2011 February 15 (Schrijver et al., 2011; Jin et al., 2016), we investigate the coronal dimming phenomenon in a global perspective by combining observational and simulation efforts, in which both the core dimmings and secondary/remote dimmings (e.g., Thompson et al. 2000) are studied. Also, the relationship between coronal dimmings and CMEs in the simulations is investigated and compared with observational results. In §2 we briefly introduce the global MHD model utilized in this study. In §3 we present the dimming observations for the 2011 February 15 event. The main results are presented in §4, followed by discussion and conclusions in §5.

In this study, Alfvén Wave Solar Model (van der Holst et al., 2014) developed within the Space Weather Modeling Framework (SWMF; Tóth et al. 2012) is used to reconstruct the global corona and solar wind environment. With inner boundary condition specified by observed magnetic maps, AWSoM’s simulation domain starts from the upper chromosphere, and extends to the corona and heliosphere. The global magnetic map at the inner boundary is taken from the surface-flux transport model of Schrijver & De Rosa (2003), into which SDO/HMI magnetogram data within 60^∘ from disk center are assimilated. The global magentic map is used as input without any scaling factor applied. Physical processes included in the AWSoM model are multi-species thermodynamics, electron heat conduction (both collisional and collisionless formulations), optically thin radiative cooling, and Alfvén-wave turbulence that accelerates and heats the solar wind. The Alfvén-wave description is physically self-consistent, including non-Wentzel-Kramers-Brillouin (non-WKB) reflection and physics-based apportioning of turbulent dissipative heating to both electrons and protons. AWSoM has demonstrated the capability to reproduce high-fidelity solar corona and wind conditions (Sokolov et al., 2013; van der Holst et al., 2014; Oran et al., 2013, 2015; Jin et al., 2016, 2017a). We also acknowledge one limitation of the model, specifically that, due to the fixed density and temperature at the inner boundary, the chromospheric evaporation process could not be correctly captured that impacts the post-flare emission in the model, which we discuss in more detail in §4.2.

The CME is initiated by inserting an analytical Gibson-Low (GL) flux rope (Gibson & Low, 1998) into the steady-state global corona and solar wind solution. The GL flux rope has been successfully used before to model CMEs (e.g., Manchester et al. 2004a, b; Lugaz et al. 2005; Manchester et al. 2014; Jin et al. 2016, 2017a). Jin et al. (2017b) developed a module (EEGGL) to calculate the GL flux rope parameters based on near-Sun observations to automate the flux rope initiation process in the model. The mathematical form of GL flux rope is derived by solving the magnetohydrostatic equation $(\nabla\times{\bf B})\times{\bf B}-\nabla p-\rho{\bf g}=0$ under solenoidal condition $\nabla\cdot{\bf B}=0$. After inserting the flux rope into the steady-state solar corona solution: i.e. $\rho=\rho_{0}+\rho_{\rm GL}$, ${\bf B=B_{0}+B_{\rm GL}}$, $p=p_{0}+p_{\rm GL}$, and starting the simulation forward in time, the flux rope erupts immediately due to the force imbalance of the combined background–flux-rope system. The simulation setup in this study is similar to that in our previous work (Jin et al., 2016), to which the reader may refer for further details about the model setup.

The coronal dimming we will focus on is associated with an X2.2-class flare that occurred on 2011 February 15 01:46:50 UT from AR 11158 (see Schrijver et al. 2011 for a detailed study about the event). In Figure 1, we show the coronal dimming observation in 2011 February 15 event at two different times and in two of the AIA channels (171 Å and 211 Å). The two channels are selected to represent the coronal plasma both at transition region ($\log_{10}T/K\sim 5.8$) and coronal ($\log_{10}T/K\sim 6.3$) temperatures. To better identify the dimming signature across the disk, we process the images by the percentage base-difference method, in which base images at 2011 February 15 01:50:15 UT (171 Å) and 01:50:02 UT (211 Å) are subtracted. We also correct the solar rotational effect before subtracting. Figures 1(a) and 1(c) show the early-stage evolution ($\sim$20 minutes after flare onset) of the waves and dimmings associated with the eruption. The EUV waves in AIA 171 Å show a “darkening” feature while in AIA 211 Å they are “brightenings”. This suggests a typical plasma warming process (Schrijver et al., 2011; Nitta et al., 2013; Liu et al., 2018), in which the lower temperature plasmas are heated up to higher temperature by processes like adiabatic compression. For the source region, both channels show evident dimmings that we ascribe to plasma depletion due to the CME. Figures 1(b) and 1(d) show the evolution at a later phase ($\sim$60 minutes after flare onset), at which time the waves have traversed the visible disk and more dimming features are evident. Compared with the early-stage phase, the core-dimming is more prominent in both channels and the dimmings at more distant locations are stating to occur.

In addition to AIA observations, we plot the EVE light curves of Fe IX 171 Å and Fe XIV 211 Å for the event in Figure 2. The EVE Fe IX 171 Å intensity profile contains a significant dimming feature starting at $\sim$02:30:00 UT and has not recovered to its pre-event value even after 4 hours following CME onset has elapsed. For EVE Fe XIV 211 Å, the intensity profile shows no dimming feature. This behavior arises because the post-flare loop emissions at high coronal temperatures $\sim$2 MK dominate during the recovery phase (Mason et al., 2014).

In the following analysis, we will also find it helpful to screen out the brightening due to post-flare loops in the EVE light curves, and so we make use of a scheme to synthesize the EVE light curves from differential emission measure (DEM) inversion techniques applied to the set of corresponding AIA images. The sparse inversion technique developed by Cheung et al. (2015) is employed to infer the coronal DEM distribution from 6 AIA channels (94 Å, 131 Å, 171 Å, 193 Å, 211 Å, 335 Å). Synthesized light curves are achieved by convolving the DEM with the contribution function $G(T)$ of EVE lines obtained from CHIANTI database (Landi et al., 2013) to get the synthetic EVE line irradiance. The synthesized curves for the full disk are shown in red in Figure 2, which match the EVE line intensity profiles from the 2011 February 15 event reasonably well. For the DEM analysis, we only use AIA images with the automatic exposure control enabled (AEC_TYPE=2) and the exposure time longer than 0.01 seconds. The AIA instrumental degradation is not considered in this study because this event occurred in early phase of the mission when the degradation was minimal. In Figure 2, the integrated EM in specific temperature bins, as derived from the AIA DEM inversion around the peak emission temperatures of Fe IX 171 Å ($\log T/K$ = 5.85 to 5.95) and Fe XIV 211 Å ($\log T/K$ = 6.25 to 6.35), are plotted in blue. Both EM evolution profiles show a trend similar to the observed major emission lines in those temperature ranges. After the impulsive phase of the flare, the total plasma content in $\log T/K$ = 5.85 to 5.95 decreases to a lower value than the pre-eruption state, while the plasma content increases in $\log T/K$ = 6.25 to 6.35. We also noticed an increase in EM of $\log T/K$ = 5.85 to 5.95 after reaching the minimum around $\sim$2:30 UT, which could be attributable to plasma cooling shifting emission measure to a lower temperature. This increase is also visible in the EVE Fe IX 171 Å irradiance but not as evident as in the EM profile, which could be ascribed to a wider temperature range of plasma that contributes to the Fe IX 171 Å irradiance.

To better understand the coronal dimming evolution, we simulate CME eruptions with different initial flux rope parameters, which lead to a variety of flux rope energies and configurations. This series of cases not only enable us to investigate the coronal dimming characteristics under different CME eruptions but also help to account for the uncertainties of flux rope parameters that are not well constrained from observations. The simulation cases used in this study are summarized in Table 1. Note that 5 out of 7 cases in this study are from our previous study (Jin et al., 2016) and we add two new cases (Run 2 and Run 4) in this study. We also calculate the magnetic energy of the inserted flux rope for different cases, which ranges from 4.1$\times$10³¹ erg to 4.2$\times$10³² erg. All the simulations are advanced for at least 2 hours when the CMEs are well into the interplanetary space and the global corona has begun to relax. We then synthesize EUV emissions for AIA optically-thin channels and process the synthetic data using the same method as for the observational data (see §3). In the following, we summarize the results into three main findings.

In this study, by combining SDO observations and advanced MHD modeling, we conducted a comparative study of the coronal dimming induced by the CME on 2011 February 15. The results show that our model could reproduce many observed features of the coronal dimming after the CME eruption. By varying the flux rope properties, the ensemble of models possess a close relationship between the CME and dimming characteristics, similar to the trends found from observations of coronal dimming events (Mason et al., 2016; Dissauer et al., 2018, 2019). Our result suggests that coronal dimmings encode important information about CME energetics, CME mass, and the magnetic configuration of erupting flux ropes. Moreover, with the help of DEM and column density analysis of the simulation data, we found that the transient dimming / brightening patterns are related to plasma heating processes (either by adiabatic compression or reconnection), while the long-lasting “core” and “remote” dimmings are caused by mass loss process induced by the CME eruption. We illustrate the relationship between the CME, dimmings, and EUV waves in Figure 9.

We found that when relating the long-lasting dimming patterns across the solar disk with the global coronal field configuration (as shown in Figure 3d), the dimming areas are always associated with open or quasi-open field lines. We found that most of these open/quasi-open field lines are pre-existing, i.e., they are present in the steady-state solution before the CME eruption (see Figure 5 in Jin et al. 2016). But some of the open field in the CME source region is formed after the eruption due to the magnetic reconnection between the flux rope and surrounding coronal field as it propagates out into the heliosphere. This is consistent with the view that the core dimmings correspond to the footpoints of the erupting flux rope system but how the remote area far away from the CME source region loses mass that eventually leads to long-last dimmings? By further comparing the remote dimming areas with the global topological structures of the corona (see Figure 13 in Jin et al. 2016), we found that all the remote dimming areas are connected to the source region by some topological structures (e.g., separatrix surfaces) so that the plasma evacuation in the source region could directly influence these remote areas. On the other hand, it is the open/quasi-open field in these regions that provides a pathway for the plasma to leave the Sun, and as a result these remote dimming patterns can exist for hours after the CME eruption. In sum, both connection to the source region and the open/quasi-open field are required for getting the remote dimmings.

Furthermore, the CME-dimming relationship could also be important for space weather forecasting purposes because the CME-induced coronal dimming (especially the core dimming) occurs much earlier than other observable CME disturbances. Currently, we are able to estimate the CME speed only when it is observed in the white light coronagraph at least 20-30 minutes after the CME onset. With a reliable CME-dimming relationship, it is possible to estimate the CME speed at an earlier phase of the eruption. This information is important for most space weather forecasting models, especially those forecasting the propagation solar energetic particle models as the SEP can arrive at Earth in minutes to hours after CME onset. Additionally, for the type of modeling presented here, the EEGGL model (Jin et al., 2017b) requires an estimate of the CME speed in setting the flux rope parameters, and consequently early estimates of the CME speed will better constrain EEGGL and improve the model performance.

As mentioned §1, Schrijver et al. (2011) studied the same 2011 February 15 event with detailed observation and MHD modeling efforts. Therefore, it would be interesting to compare the results from the two individual studies about the same event. There are many aspects that the two studies agree on for the event. For example, the adiabatic nature of the expansion front as discussed in §4.1, as well as the non-adiabatic process that is needed to explain the northward-propagating segment of the front. In Jin et al. (2016), we found that this non-adiabatic process is caused by the magnetic reconnection between the expanding flux rope and the active region field to the north of the CME source region. Also, in both MHD models presented in the studies, the wave-like warming compression front moves significantly ahead of the erupting flux rope, which is also shown in other recent MHD simulations of EUV waves (e.g., Mei et al. 2020; Downs et al. 2021). However, there are also differences found in the two models. In this study, we found two distinct wave-like structures (as shown in Figure 10 of Jin et al. 2016): first, the outmost one (i.e., warming compression front) demonstrates more features like a fast-mode wave as it does not stop at the topology boundaries (e.g., the helmet structures mentioned in Schrijver et al. 2011). However, it is evidently weakened passing these boundaries likely due to the wave reflection. The second structure is related to the expanding flux rope volume. As discussed in Jin et al. (2016), the erupting flux rope does not easily break out from the topological structures therefore stopped by the streamer structures. Note that the flux rope and background coronal field settings are quite different in these two simulations, which could largely contribute to the differences mentioned above. We will leave the more detailed comparison for future study as we concentrate more on the coronal dimmings induced by the CME in this study.

Finally, we discuss the possibility of using coronal dimming to detect stellar CMEs. Even though the stellar flares are frequently observed, it remains challenging to associate stellar CMEs with any of these flares. The ability to distinguish between stellar flares and CME events is important since the two phenomena affect exoplanet habitability through very different physical processes (as is true in our own solar system). CMEs have a much larger influence than flares on stellar evolution through mass loss and angular-momentum loss (e.g., Benz & Güdel 2010), and can significantly impact the habitability of exoplanets due to their ability to erode their atmospheres (e.g., Lammer et al. 2007; Airapetian et al. 2020). Argiroffi et al. (2019) detected a stellar flare with blue-shifted O VIII line with 90$\pm$30 km s^-1 on the active star HR 9024 using data from Chandra X-ray Observatory space telescope, which might indicate a CME eruption in place. However, this kind of observation is still very close to the star surface and therefore reflects the very early-stage of the eruption. It is hard to obtain signals at greater heights, and as a result we do not know whether the eruption propagated into the astrosphere, and, if so, what its speed and mass are. Indeed, MHD modeling suggests that confined eruptions could be common for stellar case due to the stronger magnetic confinement (Alvarado-Gómez et al., 2018). Additionally, Type II radio bursts caused by accelerated electrons associated with CME-driven shocks seem to be conspicuously absent (Crosley & Osten, 2018a, b). More recently, using H_α spectroscopic observations, Namekata et al. (2021) detected a strong blueshifted absorption component with a velocity of $\sim$510 km s^-1 associated with a TESS white-light flare on the young solar-type star EK Draconis, which presents a probable detection of an eruptive filament. A comparative study with the solar events further suggests that this filament likely leads to a CME into the interplanetary space.

The ability to use coronal dimming signatures as a proxy for detecting stellar CMEs seems promising, and has been recently explored in more detail by Veronig et al. (2021) using historical data from XMM, HST, and EUVE, from which they identified 21 stellar dimming events (i.e., CME candidates) on 13 different stars. The statistics of these dimming events suggest stronger dimming compared with the solar case, with the strongest stellar dimming event corresponding to a depletion of half of the stellar corona. In another study, Jin et al. (2020) modeled the stellar dimming with enhanced magnetic flux density for M dwarf and young Sun-like stars and found that, due to the stronger magnetic field and coronal heating, the spectral lines showing stellar dimmings are shifted to higher temperature range. Although it remains possible that stellar dimming patterns may differ in significant ways from the solar case, coronal dimming phenomena are likely ubiquitous phenomenon for all G-M type stars. And for the stars with a similar mass, temperature, and magnetic field strength as the Sun, solar coronal dimming events, such as the one shown in this article, serve as good references for comparative studies of stellar coronal dimming. In addition, by applying the instrument performance estimates from the Extreme-ultraviolet Stellar Characterization for Atmospheric Physics and Evolution (ESCAPE; France et al. 2022), which will provide extreme- and far-ultraviolet spectroscopy (70 - 1800 Å), the study demonstrates that, with instrumentation optimized for these measurements, we would be able to detect the stellar coronal dimming in UV/EUV range. Meanwhile, current and further solar observations (e.g., MUSE: Multi-slit Solar Explorer; De Pontieu et al. 2020, 2021; Cheung et al. 2021) will keep facilitating our understanding about solar coronal dimming events, their relationship to CME, and their applications to solar-stellar connection studies.