Colliding Magnetospheres in The Young High-Eccentricity Binary DQ Tau: Discussion

Table of Links

• Abstract and Intro
• X-ray Observations and Data Extraction
• Flare Analyses
• Comparison with X-ray Flares from Young Stars
• Discussion
• Conclusions
• Acknowledgments and References

5. DISCUSSION

5.1. X-ray Flares Produced by DQ Tau

5.1.1. Flaring Near Periastron

Conceptually, flare-related events triggered by magnetosphere collision may proceed in a manner described by the classical non-thermal thick-target model, potentially involving larger-scale coronal structures. According to the classical non-thermal thick-target model, which applies to solar and stellar flares (Brown 1971; Lin & Hudson 1976), electrons are accelerated to high energies through coronal magnetic reconnection processes. These energetic electrons spiral along the coronal magnetic field lines, emitting radio and microwave radiation (detected in DQ Tau by Salter et al. (2008, 2010)), and subsequently collide with the underlying atmosphere. These collisions result in the production of non-thermal hard X-rays, which may be detectable in the NuSTAR energy band. Furthermore, this electron-atmosphere interaction leads to heating of the surrounding transition region, chromosphere, and photosphere plasma, giving rise to the production of optical/ultraviolet (observed by Swift-UVOT), and infrared radiation. Additionally, the interaction drives chromospheric evaporation, causing the filling of coronal loop(s) with hot plasma that emits thermal X-rays in the soft bands observed by Chandra/Swift-XRT.

The Neupert effect, which establishes a correlation between the time-integrated radio or microwave (or hard non-thermal X-ray) light curve and the rising portion of the soft X-ray light curve (Neupert 1968), serves as compelling observational evidence supporting the classical non-thermal thick-target model. This effect has been observed in numerous solar flares (e.g., Dennis & Zarro 1993) and certain stellar flares (G¨udel et al. 2002). Remarkably, Getman et al. (2011) discovered the presence of the Neupert effect in the context of the January 11-12, 2010 periastron passage of DQ Tau, where they observed correlations between the IRAM microwave and Chandra X-ray flares. Furthermore, Salter et al. (2010) and Getman et al. (2011) found that the heights of the coronal structures associated with these flares reached several stellar radii.

The analytic model proposed by Adams et al. (2011) provides a comprehensive description of the magnetic energy release process in eccentric binary systems, specifically addressing the stored magnetic energy within the large-scale, dipole magnetic fields of the stellar components. This release is achieved through the magnetic interaction of the binary stellar components’ magnetospheres. Additionally, the authors discuss the replenishment of this magnetic energy through the combined effects of the orbital and spin motions of the binary components. Adams et al. (2011) and Das et al. (2023) have determined that this magnetic model yields reasonable estimates of the magnetic reconnection energy responsible for powering the radio and Xray flares observed near the periastrons of the V773 Tau and ϵ Lupi eccentric binaries, respectively.

Within the context of the basic equation (17) and Figure 5 in Adams et al. (2011), as well as Figure 9 presented here, it’s worth noting that during the orbital phase range of (0.5−1), the two stars draw closer to each other. This proximity leads to the compression of their magnetic fields, resulting in an excess of magnetic energy becoming available to fuel flare events. Conversely, it’s not expected for there to be a significant release of magnetic energy during the orbital phase range of (0 − 0.5) when the stars move away from each other. During this phase, it is anticipated that the two magnetospheres will replenish their energies through a combination of orbital and stellar spin motions, as well as through internal stellar dynamos.

According to this simplified model, the peak of the available excess magnetic energy occurs 2 days before reaching the periastron point (as shown in Figure 9). Equation (17) and Figure 5 in Adams et al. (2011) assume that the magnetic configuration can instantaneously adjust to magnetic stresses and immediately dissipate excess energy. However, in reality, magnetic accumulation and reconnection do not occur instantaneously. Therefore, related flare events may be observed near and after the periastron point (Fred Adams, private communication).

While it is plausible that the presence of general uncertainties surrounding all flare energetics and stellar properties, as derived in the current study or obtained from the literature, might account for part of this discrepancy, we propose two main sources of this inconsistency. The first is related to the partial inclusion of accretion-related optical/NUV emission (Tofflemire et al. 2017; K´osp´al et al. 2018; Muzerolle et al. 2019; Fiorellino et al. 2022). The second is associated with the potential overestimation of temperatures and bolometric luminosities in our simplistic modeling of the optical/NUV periastron flaring (see § 3.3.2). Specifically, previous research has reported the presence of optically thin line and Balmer continuum emissions in the U-band radiation of stellar flares (Figure 3 in Kowalski et al. 2013). Since our model fitting does not account for such “additional” emission, it may lead to an overestimation of the temperature and luminosity of the true black body component.

The temperatures around T ∼ 10000 K, which are obtained from our optical SED analyses, are relevant in both cases: stellar magnetic reconnection flares and accretion hot spots. Unfortunately, neither temperatures nor colors4 (used as observational proxies for temperatures) can distinguish between flare and accretion events. The morphology of large optical flares, as observed in young stars of NGC 2264 (Flaccomio et al. 2018, their Appendix B), often differs from the ’fast-rise and slow-decay’ morphology, and their durations frequently align with those of concurrent soft X-ray flares. Similar optical-X-ray behavior is observed for both the main and second DQ Tau flares (see Figure 2). The high durations of the optical, NUV, and X-ray flares during periastron in DQ Tau can be explained by the sustained heating resulting from the magnetic energy release due to colliding magnetospheres. The presence of two distinct optical/NUV peaks, particularly evident in the V , W1, and M2 bands (Figure 2), occurring before the peaks of the primary and secondary X-ray flares, is indicative of an observational feature associated with the solar/stellar flare Neupert effect. Overall, we identify observational indications suggesting the presence of 4 The U, B, V UVOT colors (and magnitudes) across the entire (0.9 − 1.25) orbital phase range covered by the Swift observations are consistent with Figure 1 of Tofflemire et al. (2017) and indicate that DQ Tau is bluer when brighter and redder when fainter. magnetic reconnection-related optical/NUV flares, but it is not possible to differentiate their energetics from those of the underlying accretion events based solely on the optical/NUV data.

In summary, distinguishing between the energetics of magnetic reconnection-related and accretion-related periastron events based on the optical/NUV data alone is challenging. Nevertheless, we have observed the Neupert effect between millimeter and X-ray flares, and identified consistent rates of magnetic energy release and non-thermal electron injection. The optical-to-Xray energy ratios of DQ Tau and large solar/stellar flares align when we adjust the observed optical energy of DQ Tau to match the energy levels predicted by the Adams et al. (2011) model. Furthermore, two distinct optical/NUV peaks precede the corresponding X-ray peaks, and the optical and X-ray events powered by sustained heating from colliding magnetospheres have similar durations. These findings collectively support the idea that the millimeter/X-ray periastron flares, and tentatively, the magnetic reconnection-related components of the optical/NUV emissions, conform to the classical solar/stellar non-thermal thick-target model.

5.1.2. Non-Periastron Flaring

According to the magnetic model proposed by Adams et al. (2011), it is plausible that the release of magnetic energy from the large-scale magnetic fields can occur at orbital phases away from periastron, albeit with a lower energy release rate. Moreover, the interaction between the magnetospheres of the two stars could disrupt the small-scale surface magnetic fields, potentially leading to additional flaring events. However, the occurrence of an extended magnetically calm phase detected by Chandra lasting over 7 days, devoid of significant flares (corresponding to the orbital phase range of (1.1 − 1.55) in Figure 3), suggests a more intricate nature underlying non-periastron X-ray flaring.

Given the predictable occurrence of X-ray super-flares and accretion outbursts in close proximity to periastron passage, DQ Tau stands as an exceptional laboratory for examining the impact of stellar radiation on the gasphase ion chemistry within its disk. Nevertheless, the system also displays sporadic and frequent super-flaring events away from periastron, thereby rendering a comprehensive multi-wavelength investigation into the influence of DQ Tau’s radiation on its disk a more formidable undertaking than initially envisioned.

5.2. Non-detection of Hard Non-thermal X-rays

In this study, we performed NuSTAR observations in the vicinity of DQ Tau’s periastron in order to investigate the presence of the non-thermal flaring X-ray component, as predicted by the classical non-thermal thicktarget model. Our NuSTAR observation did not reveal any significant hard X-ray emission (> 10 keV) from DQ Tau near periastron (§§ 2.1, 3.2).

To the best of our knowledge, only a few flares from young stellar objects, all within the nearby ρ Oph region, have been observed by NuSTAR thus far (Vievering et al. 2019; Pillitteri et al. 2019). Vievering et al. detected several bright flares from IRS43, WL19, and Elias 29 young stellar objects, but no evidence of non-thermal X-ray emission was found. In the case of another two detected X-ray flares from the Elias 29 object, Pillitteri et al. reported a tentative power-law excess of hard X-ray emission in the (20 − 50) keV band, as deduced from its NuSTAR spectrum

Isola et al. (2007) conducted an analysis of soft X-ray GOES and hard X-ray RHESSI data for 45 bright Solar flares, revealing a strong correlation between the GOES fluxes in the (1.6 − 12.4) keV band and RHESSI fluxes in two bands, (20 − 40) keV and (60 − 80) keV. These findings align with the expectations derived from the thick-target model. Isola et al. further demonstrated that the same scaling law observed for solar flares between the (1.6 − 12.4) keV and (20 − 40) keV fluxes also holds true for more powerful stellar flares.

To predict NuSTAR count rates we utilize the Portable, Interactive Multi-Mission Simulator (PIMMS). Considering a purely non-thermal nature for the (20 − 40) keV X-ray photons, we employ the powerlaw model in PIMMS, setting the expected unabsorbed flux to FX,20−40 and choosing a photon index range of δ = (2.5 − 3) (Pillitteri et al. 2019). PIMMS predicts a source count rate in the (20 − 40) keV band of 10−5 counts s−1 for both FPMA and FPMB modules when applying a 50% PSF extraction. Isola et al. (2007) suggest that in powerful flares, the thermal contribution to the (20 − 40) keV X-ray emission can be significant. However, similar count rates are predicted if we instead assume a purely thermal nature for the (20−40) keV Xray emission, employing the apec model with a possible flare temperature range of kT = (4 − 8) keV (Getman et al. 2011). In the (20 − 40) keV band, our NuSTAR data reveal a background count rate of 0.002 counts s−1 . Consequently, not only does the background overwhelms the predicted signal from DQ Tau in the (20 − 40) keV band, but it also dominates in any other > 10 keV band, as clearly demonstrated in Figure 1b. But the absence of observed hard (> 10 keV) X-ray emission from DQ Tau should not be interpreted as evidence against the applicability of the thick-target model to DQ Tau’s flares.

5.3. Characteristic X-ray Emission

There have been numerous observations of magnetic dynamo cycles in stars, analogous to the 11-year solar cycle observed on the Sun. These cycles, often referred to as stellar activity cycles, are characterized by longterm periodic variations in magnetic activity indicators, including starspots, photometric variability, chromospheric emission lines, and coronal X-ray emission. Various X-ray studies on stars of different ages have suggested that activity cycles on younger stars may be shorter and less pronounced, if present at all.

For example, Wargelin et al. (2017) conducted X-ray analyses on several mature stars and observed a decrease in the amplitude of quiescent variability as X-ray activity increased. Coffaro et al. (2020, 2022) discovered that ϵ Eri, a star approximately 440 million years old, and Kepler-63, a star approximately 210 million years old, exhibited the shortest X-ray cycles and smallest X-ray amplitudes when compared to several older solar-mass stars known to have X-ray cycles. Additionally, their findings suggested that the surfaces of these stars may be extensively (around 60%-100%) covered by solar-type X-ray emitting magnetic structures, such as active region cores and flares. Furthermore, Marino et al. (2006) reported no substantial evidence of long-term X-ray variability in the stellar members of the approximately 100 million-year-old open cluster NGC 2516. Similarly, Maggio et al. (2023) reported only a small long-term Xray variability with an amplitude of approximately ∼ 2 for the 12 million-year-old young star V1298 Tau.

The absence of evidence for long-term variability in the X-ray characteristic emission of the one million-yearold DQ Tau aligns with the notion that younger stars possess larger active regions and more extended X-ray coronal structures (Coffaro et al. 2022; Getman et al. 2022b, 2023), which may mitigate the appearance of magnetic dynamo cycling.

[3] The 2.4-day window encompasses the first two X-ray flares and the optical/NUV flare, while the 3.5-day and 4.0-day windows additionally include the third and fourth X-ray flare.

[4] The U, B, V UVOT colors (and magnitudes) across the entire (0.9 − 1.25) orbital phase range covered by the Swift observations are consistent with Figure 1 of Tofflemire et al. (2017) and indicate that DQ Tau is bluer when brighter and redder when fainter.