Coronal response to magnetically-suppressed CME events in M-dwarf stars

We report the results of the first state-of-the-art numerical simulations of Coronal Mass Ejections (CMEs) taking place in realistic magnetic field configurations of moderately active M-dwarf stars. Our analysis indicates that a clear, novel, and observable, coronal response is generated due to the collapse of the eruption and its eventual release into the stellar wind. Escaping CME events, weakly suppressed by the large-scale field, induce a flare-like signature in the emission from coronal material at different temperatures due to compression and associated heating. Such flare-like profiles display a distinctive temporal evolution in their Doppler shift signal (from red to blue), as the eruption first collapses towards the star and then perturbs the ambient magnetized plasma on its way outwards. For stellar fields providing partial confinement, CME fragmentation takes place, leading to rise and fall flow patterns which resemble the solar coronal rain cycle. In strongly suppressed events, the response is better described as a gradual brightening, in which the failed CME is deposited in the form of a coronal rain cloud leading to a much slower rise in the ambient high-energy flux by relatively small factors ($\sim2-3$). In all the considered cases (escaping/confined) a fractional decrease in the emission from mid-range coronal temperature plasma occurs, similar to the coronal dimming events observed on the Sun. Detection of the observational signatures of these CME-induced features requires a sensitive next generation X-ray space telescope.


Introduction
Of the different manifestations of solar/stellar magnetic activity, flares, and coronal mass ejections (CMEs) are the most dramatic in terms of energetics and temporal evolution. It is widely accepted that they are interlinked phenomena, sharing a common origin in the energy transformation from magnetic into kinetic (particles and plasma) and radiative power (Chen 2011;Webb & Howard 2012;Benz 2017). These transient events are expected to play an important role in the evolution of stellar rotation and activity (Drake et al. 2013;Cranmer 2017), as well as in the conditions for retention of exoplanet atmospheres and habitability (Micela 2018;Tilley et al. 2019). Most of our knowledge of their origins, properties, and evolution comes from observations of the Sun, which indicate that large solar flares are typically accompanied by a CME (Gopalswamy et al. 2009;Compagnino et al. 2017).
While strong flares are routinely detected in active stars, particularly M-dwarfs (see Schmidt et al. 2019 and references therein), recent studies have shown that the solar flare-CME paradigm might be different in the stellar regime, such that the occurrence rate of CMEs and their associated kinetic energies are reduced dramatically (Moschou et al. 2019;Vida et al. 2019). The recent direct detection of a stellar CME by Argiroffi et al. (2019) follows the same trend. In Alvarado-Gómez et al. (2018) we showed that these properties are expected due to the interaction between the escaping eruption and the suppressing effect imposed by the large-scale magnetic fields present in these stars.
The growing interest in close-in, habitable zone planets orbiting M-dwarfs motivates a better understanding of the CME magnetic confinement process, especially given the relatively strong magnetic fields reported for these stars (e.g., Morin et al. 2010;Shulyak et al. 2017). This Letter contains the results of the first three-dimensional numerical simulations of CMEs developing within surface magnetic field values representative of moderately active M-dwarf stars. Our state-of-the-art models explore the response of the high-energy stellar corona to the different regimes of the CME confinement spectrum, analyzing specific observables in the context of previous solar and stellar studies, and their possible detection with future instrumentation.

Numerical Models
We proceed in a similar manner to Alvarado-Gómez et al. (2018), first obtaining a steady-state description of the corona and stellar wind, and then using this solution as an initial condition of a time-dependent flux-rope CME simulation. The models employed here are incorporated in the latest version of the Space Weather Modeling Framework 6 (SWMF; see Gombosi et al. 2018).

Corona and Stellar Wind
Our M-dwarf corona and stellar wind simulations are constructed with the aid of the Alfvén Wave Solar Model (AWSoM; van der Holst et al. 2014), and the 3D MHD code BATS-R-US (Tóth et al. 2012). This model, originally developed for solar system studies and adapted for the stellar regime, considers the distribution of the radial magnetic field on the surface of the star as a boundary condition. The field strength and polarity are used to construct an Alfvén wave turbulent dissipation spectrum that provides self-consistent heating of the corona and acceleration of the stellar wind. These Alfvén wave-driven contributions are incorporated as sources in the energy and momentum equations which, combined with the magnetic induction and mass conservation equations, complete the set of nonideal MHD equations solved by the code. Effects of radiative losses and electron heat conduction are also included in the simulation (see van der Holst et al. 2014 for additional details). The numerical scheme evolves until a steady-state solution is obtained in the domain, described by a spherical grid extending from ∼1.0 R * to 85 R * for the simulations discussed in this work.

Stellar Magnetic Field
We have previously used surface magnetic field maps reconstructed with the technique of Zeeman-Doppler Imaging (ZDI; Donati et al. 1997;Kochukhov & Piskunov 2002) to simulate the corona and stellar wind environment around specific systems (Alvarado-Gómez et al. 2016a, 2016bPognan et al. 2018), or as magnetic proxies for objects without observations Alvarado-Gómez et al. 2019). Unfortunately, ZDI is not sensitive to the small-scale field expected to power CME activity and instead we drive models using the field topology, down to active region lengthscales, resulting from a self-consistent dynamo simulation of a slowly rotating fully convective star (Yadav et al. 2016). This dynamo model not only has been tailored to match the mass, radius, and rotation period of Proxima Centauri (hereafter, Prox Cen), but also yields a long-term cyclic magnetic field evolution that roughly captures the observed timescale of the activity cycle in this star (P cyc ∼7 yr, see Suárez Mascareño et al. 2016;Wargelin et al. 2017). Cohen et al. (2017) followed a similar approach to study the coronal structure of rapidly rotating M-dwarf stars.
To ensure that the simulated magnetic field geometry is a robust representation of Prox Cen and other moderately active M-dwarfs, the field distribution is extracted at a time in which the dynamo solution is well within a cyclic regime. 7 As described by Yadav et al. (2016), the outer boundary for the dynamo simulation was set at 95% of the stellar radius, which for the purposes of this study will be considered as the effective photosphere of the star. We apply five different scalings (preserving the field topology) to adjust the maximum surface radial field strength, ranging from ±600 G to ±1400 G in 200 G increments. These values are consistent with magnetic field measurements in low to medium activity M-dwarf stars (Reiners 2014

Flux-rope Eruption
To initialize our CME simulations, we consider the analytical Titov & Démoulin (1999, TD) flux-rope eruption model. This model is based on the magnetic pressure/tension imbalance acting on a twisted arc-like structure (sustained by a force-free field), which is embedded in the background magnetic field obtained in the steady-state stellar wind solution. The numerical implementation used here has been widely applied in detailed comparative studies in the solar context (e.g., Manchester et al. 2008;Jin et al. 2013).
Eight parameters are required to determine the starting state of the TD model, including the position, orientation, and geometrical properties of the flux tube, together with the electric current (used to compute the flux-rope magnetic free energy, E B FR ) and mass loaded into the structure. As illustrated in Figure 1, we anchor and align the flux-rope foot points to the strongest mixed-polarity region on the stellar surface, fixing in this way the location (longitude: 270°, latitude: 36°, orientation: 28°), and size of the TD flux tube (length: ∼150 Mm, radius: 20 Mm).
The eruption is initialized with a magnetic free energy  sweep off in the CME evolution is expected to be larger (by ∼1-2 orders of magnitude), particularly due to the relatively denser corona and stellar wind compared to typical solar conditions. For each surface magnetic field scaling (see Section 2.1.1), we follow the evolution of the eruption for 1.5 hr of real time, which is sufficient to cover the travel time of a very slow (∼25 km s −1 ) coronal perturbation through the inner corona (up to R2.0 R * ). We extract the MHD properties in the entire 3D domain at a cadence of 1 minute.

Results and Discussion
Figures 2-4 contain a summary of the results obtained for three of the magnetic field scalings considered (Section 2.1.1). We include simulated line-of-sight images of the stellar corona, synthesized following response functions of three EUV channels of AIA 8 /SDO, 9 as well as contours of the X-ray emission traced by the Ti-Poly filter of XRT 10 Hinode. 11 Light curves of the mean flux (F M ) normalized to the pre-CME quiescent level (F Q ) in each filter, and different 3D visualizations of the events are also included for all cases. 12 These results are representative of different regimes in the CME confinement spectrum: weak ( =  B 600 r,max range G, Figure 2), partial ( =  B 1000 r,max range G, Figure 3), and strong ( = B r,max range 1200 G, Figure 4). The status of each eruption is determined by visual inspection of the evolution in density contrast at n(t)/n SS = 3.0 (with n SS representing the steady-state pre-CME solution, see Figure 5), and comparing the speed of the perturbation front with the local escape velocity ( = v esc GM H 2 * , where H indicates the front position and G is the gravitational constant).

Weaker Field Case (±600 G)
As presented in the top panels of Figure 2, a clear coronal response in all channels is obtained in this case. In the first frames of evolution (4 minutes), it is possible to observe the collapse of the inserted flux rope toward the stellar surface, reaching in-falling radial speeds 400 km s −1 . This collapse is not radial but follows the overarching field configuration, bringing the perturbation equatorwards from the initial launching latitude. During this process the ambient plasma of the underlying canopy is strongly compressed, rapidly increasing the local coronal density and temperature (by factors of ∼5-10), leading to a flare-like signature as registered by the high-temperature sensitive filters (94 Å and Ti-Poly). Correspondingly, the mean X-ray flux increases by more than an order of magnitude compared to the quiescent level before the flux-rope insertion (Figure 2, middle panel). A smaller increase is obtained in the 94 Åchannel, as the average pre-CME emission in this band is higher. The maximum flux in these two filters appears 6-7 minutes after the flux-rope eruption. Observations indicate that similar processes could occur in the solar corona on much smaller scales (e.g., Hong et al. 2014;Sterling et al. 2015), in line with expectations given the relatively weak solar large-scale field. We stress here that our simulation does not include a magnetic reconnection flaring component and only considers the eruption of the flux rope in the corona.
The collapse continues, reaching lower and cooler layers of the corona, generating an excess in the 304 Åchannel (visible also in the mean flux; middle panel in Figure 2) until the perturbation bounces back due to the strong local magnetic tension. At this stage, surrounding material lifts off with speeds on the order of 50 km s −1 , while the core of the eruption reaches a radial velocity exceeding the local escape value (∼200 km s −1 for Prox Cen). Taking into account the initial range of speeds in this region, the resulting coronal Doppler shift average velocities associated with the final eruption would lie in the range of 90-150 km s −1 . Snapshots of the Doppler shift evolution can be seen in the bottom panels of Figure 2.

Medium Field Cases (±800-1000 G)
The evolution in the =  B 1000 r,max range G case (Figure 3) globally follows the previous description, although important differences are clearly visible. The average speeds for the collapse and escape are significantly reduced (by ∼40% and 30%, respectively), which leads to a broader (longer duration) flare-like profile, with a weaker peak that develops at a later time (16-18 minutes after the flux-rope insertion; see Figure 3, middle and bottom-left panels). The stronger stellar field also induces the fragmentation of the perturbation preceding the CME escape (Figure 3, bottom-right panel). A fraction of the eruption remains confined in the corona, displaying rise and fall patterns (with | | DU r up to 100 km s −1 ), similar to plasma flows observed during solar coronal rain (Antolin & Rouppe van der Voort 2012) or condensations (Li et al. 2018).
After the escape of the eruption, the corona relaxes to a quasisteady state with slightly higher levels of emission in some of the analyzed bands (compared to the pre-CME configuration; Figures 2 and 3, middle panel). This was expected due to the permanent modification of the surface magnetic field (required for the flux-rope initiation), and the time-accurate nature of the simulation. Throughout the entire evolution, the mean flux from the 171 Åchannel remains on average ∼15% below the quiescent level, with a transient dark sector visible in the corresponding synthetic images (Figures 2, top-center). This feature clearly resembles the mid-temperature coronal dimmings observed on the Sun, which have been shown to occur consistently during CMErelated flaring events (Harra et al. 2016;Mason et al. 2016). However, note that the dimming in this band is also visible during fully confined CME events (Figure 4). Given that this flux deficit can occur due to thermodynamic changes in local plasma instead of evacuation and ejecta, this feature alone is probably insufficient to discriminate unambiguously CMEs in stellar observations.
The results for the =  B 800 r,max range G scaling (not shown) fall in between the ±600 G and ±1000 G scenarios, as expected for a smooth transformation between the regimes of weak and partial CME confinement. This change in global behavior takes place over a relatively large range of surface field values (D = B 400 r,max range G).

Strong Field Cases (±1200-1400 G)
In the remaining two cases ( =   B 1200, 1400 r,max range G), the erupting flux rope is not able to escape, so no CME is generated. This indicates that the transition to a strong CME confinement regime is more abrupt in terms of magnetic field increment than the changes between the weaker and moderate field cases, and that the suppression threshold for this particular eruption (Section 2.2) is close to the ±1200-1400 G background field values.
In Figure 4 we present the fully confined eruption in the =  B 1200 r,max range G case. The response of the corona is more gradual (i.e., less transient), with a much slower rise in the high-energy emission (by factors of ∼2-3), peaking after ∼50-60 minutes. As mentioned before, the behavior in the 171 Åfilter shows little difference with respect to its counterpart in the escaping events. In the remaining channels it is possible to observe a small dip (∼10%-15%) in the mean flux during the first few minutes of evolution (Figure 4, middle panel). For a shorter duration, this feature is also visible in the weakly and partially confined CME cases (Figures 2 and 3). Similar pre-flare dips in optical wavelengths have been reported, which, among other possibilities, could be interpreted as possible tracers of CMEs in stars (Giampapa et al. 1982). For the coronal emission studied here, they are related to the decrement in the emitting volume during the collapse of the flux rope (common among all cases).
The bottom panels of Figure 4 show two views late in the evolution in this event (80 minutes), focused on a density perturbation induced by the failed CME. During its evolution, the disturbance grows until a large fraction of the stellar disk is covered, moving pole-and east-ward with respect to the fluxrope launching site. The structure displays a spatial distribution in Doppler shift velocities within a ±50 km s −1 range. However, over the course of the simulation, the integrated values for ΔU r are actually negative (i.e., net in-falling material), with a mean time-average of ∼−2.5 km s −1 . As such, we identify this structure as a coronal rain cloud, which also shows a clear spatial correspondence with signatures visible in lower (and cooler) regions of the corona, captured in the 304 Åimages (Figure 4, top-right panel). Interestingly, an extensive observational analysis shows that similar processes might be taking place in the corona of the young solar-analog EK Draconis (see Ayres & France 2010;Ayres 2015).
The system is still dynamically evolving after the 90 minutes of evolution captured in our simulation. Nevertheless, a relaxation of the corona into a new quasi-steady state is expected (as observed in the previous cases), with an associated decline in the high-energy emission following standard radiative cooling timescales of optically thin plasmas (incorporated in AWSoM; see van der Holst et al. 2014).

Observational Prospects and Conclusions
The recondite nature of CMEs on stars contrasts with their importance, both from the perspectives of stellar physics and their impacts on planetary environments. Here we investigated numerically the coronal response during a flux-rope eruption event, under the suppressing influence of magnetic field values expected for moderately active M-dwarfs. Depending on the strength of the stellar field, we obtained a distinctive set of observational signatures of this CME-suppression process: 1. Weakly and partially suppressed CME events lead to increases-by factors between ∼5 and more than 10-in the integrated X-ray coronal emission (0.2-2.5 keV) lasting from tens of minutes up to an hour. These brightenings resemble a normal stellar flare, but are instead powered by strong compression of the coronal material rather than by magnetic reconnection. 2. The induced flare-like events display a rapid (<1 hr) evolution of Doppler shift signals (from red to blue), with velocities up to 200 km s −1 , transitioning from hotter (log (T)6.8) to cooler (log(T)6.0) coronal lines. Lower