Coronal Response to Magnetically Suppressed CME Events in M-dwarf Stars

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.

2.1.1. Stellar Magnetic Field

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, ${E}_{{\rm{B}}}^{\mathrm{FR}}$) 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).

Zoom In Zoom Out Reset image size

The eruption is initialized with a magnetic free energy ${E}_{{\rm{B}}}^{\mathrm{FR}}\simeq 6.57\times {10}^{34}$ erg (associated with an electric current I₀ = 8.0 × 10¹² A), carrying a mass of M^FR = 4.0 × 10¹⁴ g. Our selection of ${E}_{{\rm{B}}}^{\mathrm{FR}}$ lies slightly above the high-end values observed in eruptive solar active regions and CMEs (Gopalswamy et al. 2009; Webb & Howard 2012; Toriumi et al. 2017), and should be easily achievable during typical flaring—and presumably CME—events in Prox Cen and other M-dwarf stars (see Osten & Wolk 2015; Howard et al. 2018). A nominal solar value is assumed for M^FR (Chen 2011), as the final mass 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.

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.

The evolution in the ${B}_{{\rm{r}},\max }^{\mathrm{range}}=\pm 1000$ 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 $| {\rm{\Delta }}{U}_{{\rm{r}}}|$ 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 quasi-steady 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 CME-related 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 ${B}_{{\rm{r}},\max }^{\mathrm{range}}=\pm 800$ 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 (${\rm{\Delta }}{B}_{{\rm{r}},\max }^{\mathrm{range}}=400$ G).

In the remaining two cases (${B}_{{\rm{r}},\max }^{\mathrm{range}}=\pm 1200,\pm 1400$ 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 ${B}_{{\rm{r}},\max }^{\mathrm{range}}=\pm 1200$ 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 flux-rope 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).

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 velocities (<100 km s⁻¹), and longer durations (≳1 hr), are expected for more strongly confined eruptions.
• 3.  
  Fully suppressed CME events result in a gradual brightening of the soft X-ray corona (by factors of ∼2–3) over the course of several hours. This emission is redshifted (<−50 km s⁻¹), indicative of in-falling material (designated here as a coronal rain cloud).

None of these phenomena are likely to be observable with current instrumentation, which is generally sensitive to only the most extreme CME candidates and events (Argiroffi et al. 2019; Moschou et al. 2019). While velocities revealed in our simulations—90–150 km s⁻¹ in the case of the weakly suppressed escaping CME—can in principle be discerned by Chandra (see, e.g., Argiroffi et al. 2019), the problem for observability lies in the short time over which the shifts occur and the low comparative brightness of these less extreme events. The intensity of the induced X-ray emission would be expected to rapidly decline due to its density squared dependence and expansion as the CME is accelerated outward.

However, the coronal response to all of the events simulated here could in principle be observed by more sensitive next generation X-ray missions, such as the ARCUS and Lynx concepts (see Drake et al. 2019). Requirements would be a resolving power λ/Δλ ≥ 5000 to see the relatively small Doppler shifts in the coronal vicinity, and a larger effective area than the Chandra HETG by at least an order of magnitude, in order to perform X-ray spectroscopy with the required temporal resolution.