Multiwavelength Observations of Ultracool Dwarfs IV

# Simultaneous Multiwavelength Observations of Magnetic Activity in Ultracool Dwarfs. IV. The Active, Young Binary Nltt 33370 Ab (= 2mass J13142039+1320011)

P. K. G. Williams11affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , E. Berger11affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , J. Irwin11affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA , Z. K. Berta-Thompson22affiliation: MIT Kavli Institute, 77 Massachusetts Avenue, Cambridge, MA 02139, USA , D. Charbonneau11affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
###### Abstract

We present multi-epoch simultaneous radio, optical, , UV, and X-ray observations of the active, young, low-mass binary NLTT 33370 AB (blended spectral type M7e). This system is remarkable for its extreme levels of magnetic activity: it is the most radio-luminous ultracool dwarf (UCD) known, and here we show that it is also one of the most X-ray luminous UCDs known. We detect the system in all bands and find a complex phenomenology of both flaring and periodic variability. Analysis of the optical light curve reveals the simultaneous presence of two periodicities, and  hr. While these differ by only 2%, studies of differential rotation in the UCD regime suggest that it cannot be responsible for the two signals. The system’s radio emission consists of at least three components: rapid 100% polarized flares, bright emission modulating periodically in phase with the optical emission, and an additional periodic component that appears only in the 2013 observational campaign. We interpret the last of these as a gyrosynchrotron feature associated with large-scale magnetic fields and a cool, equatorial plasma torus. However, the persistent rapid flares at all rotational phases imply that small-scale magnetic loops are also present and reconnect nearly continuously. We present an SED of the blended system spanning more than 9 orders of magnitude in wavelength. The significant magnetism present in NLTT 33370 AB will affect its fundamental parameters, with the components’ radii and temperatures potentially altered by % and %, respectively. Finally, we suggest spatially resolved observations that could clarify many aspects of this system’s nature.

stars: activity — stars: individual: NLTT 33370 — stars: low-mass
slugcomment: Draft: July 25, 2019

## 1. Introduction

Low-mass stars are the most common stars in the Universe (Reid & Gizis, 1997), dominating the solar neighborhood in particular (Kirkpatrick et al., 2012). The ultracool dwarfs (UCDs) are those very low-mass stars and brown dwarfs (BDs) with spectral types of M7 and later (Kirkpatrick et al., 1999; Martín et al., 1999), and they comprise some of our closest neighbors (e.g., Luhman, 2013, 2014). Despite this prevalence and proximity, there are significant gaps in our understanding of the nature of these objects, including their formation and multiplicity (Luhman, 2012), internal structure (Baraffe et al., 2002), radiative output (Dupuy et al., 2009, 2014), atmospheric chemistry (Marley et al., 2013), magnetism (Williams et al., 2014; Cook et al., 2014), and rotational evolution (Irwin & Bouvier, 2008; Reiners & Mohanty, 2012; Gallet & Bouvier, 2013).

Besides their intrinsic interest, these topics have received increased attention because low-mass stars are appealing host candidates for exoplanets (Scalo et al., 2007; Tarter et al., 2007), in particular Earth-like planets in the habitable zone (Bonfils et al., 2013; Kopparapu, 2013). The inferred properties of such planets depend sensitively on those of their host stars, making accurate knowledge of the fundamental properties of the hosts a topic of paramount importance. Simultaneously, searches for the coolest UCDs are penetrating into regions of parameter space occupied by giant exoplanets amenable to direct imaging (e.g., Chauvin et al., 2005; Bowler et al., 2010; Patience et al., 2010; Barman et al., 2011; Delorme et al., 2012; Dupuy & Kraus, 2013; Liu et al., 2013; Luhman, 2014), driving interest in understanding the physical properties of these analogous populations.

The presence of magnetic activity in the UCD regime has important implications for both the fundamental physics of these objects and their role as exoplanet hosts and analogs. Magnetic fields alter their internal structures, affecting estimates of radii, temperatures, and mass by 5–30% (Stassun et al., 2012), likely playing a role in explaining the frequent measurement of UCD radii that are significantly larger than those predicted by models (e.g., López-Morales, 2007; Ribas et al., 2008; McLean et al., 2011; MacDonald & Mullan, 2013). High flare rates and strong stellar winds will dramatically impact the location or existence of habitable zones around low-mass stars, prompting a significant amount of work investigating the magnetic (McIvor et al., 2006; Khodachenko et al., 2007; Lanza, 2013; Llama et al., 2013; Cohen et al., 2011, 2014) and radiative (Segura et al., 2005; Lammer, 2007; Lecavelier des Etangs, 2007; Tian, 2009; Poppenhaeger et al., 2013; Linsky et al., 2014; Shkolnik & Barman, 2014) interactions between stars and planets.

The generation of magnetic fields in UCDs, however, is not clearly understood. UCDs are fully convective (Chabrier & Baraffe, 2000) and thus lack a tachocline, the shearing interface between stellar radiative and convective zones that is understood to play a vital role in the generation of magnetic fields in Sun-like stars (Ossendrijver, 2003). Early theoretical work supported the idea that these objects would therefore not be able to generate large-scale magnetic fields via dynamo action (Durney et al., 1993). The detection of radio bursts from the young BD (catalog LP 944-20), however, demonstrated that large-scale fields could in fact be present (Berger et al., 2001), and subsequent observations have established this using a wide range of techniques (Berger, 2002, 2006; Burgasser & Putman, 2005; Hallinan et al., 2006; Reiners & Basri, 2006, 2007, 2010; Morin et al., 2010; Route & Wolszczan, 2012). More recent simulations have also demonstrated the generation of large-scale magnetic fields in fully-convective systems (Chabrier & Küker, 2006; Dobler et al., 2006; Browning, 2008; Brown et al., 2010a).

Observational tracers of UCD magnetism also present puzzles. The radio detection of (catalog LP 944-20), for instance, was a surprise, because it exceeded predictions based on the empirical Güdel-Benz relation (GBR; Güdel & Benz, 1993; Benz & Güdel, 1994) between the radio and X-ray luminosities of magnetically active stellar systems by more than four orders of magnitude (Berger et al., 2001). Subsequent observations have revealed that 5–10% of UCDs are similar outliers, and the origin of this divergence remains unclear (Stelzer et al., 2012; Williams et al., 2014). Other observational tracers of magnetic activity, on the other hand, fade away dramatically in UCDs. Chromospheric activity as traced by  emission is generally “saturated” at luminosities of in dMe flare stars, but this ratio decreases rapidly in the UCD regime (Gizis et al., 2000; West et al., 2004; Berger et al., 2010). X-ray emission follows a similar pattern, with typical luminosities decreasing from a saturation value of (Vilhu, 1984; Pizzolato et al., 2003) to virtually undetectable levels in L dwarfs (Stelzer et al., 2006a; Berger et al., 2008a, 2010; Williams et al., 2014); (catalog Kelu-1 AB) is the only such object to be detected, with 3–4 photons from Chandra (Audard et al., 2007). In each of these bands, the relationship between rotation and magnetic activity evolves significantly from what is found for earlier-type dMe stars, showing no saturation in the radio, the appearance of weakly emitting rapid rotators in , and an anti-correlated “super-saturation” relationship in X-rays (Mohanty & Basri, 2003; Berger et al., 2008a, 2010; Reiners & Basri, 2010; McLean et al., 2012; Cook et al., 2014). Possible physical underpinnings of these trends include the increasing neutralization of the outer layers of the (sub)stellar atmosphere (Mohanty et al., 2002) or a shift in the topology of the large-scale magnetic field (Donati et al., 2008; Morin et al., 2008a, 2010). An understanding of the dynamo in the lowest-mass stars and BDs should lead to insight into the magnetic properties of massive exoplanets themselves.

Simultaneous multi-wavelength observations of activity tracers yield insight into a wide range of topics such as the chromospheric heating mechanism (Berger et al., 2008b), the magnetic field topology (Berger et al., 2008a), and role of variability in biasing empirical relationships between activity tracers (Berger et al., 2010). Here we present a detailed study of the active, young binary NLTT 33370 AB (= 2MASS J131420391320011) using simultaneous observations in the radio, optical, , UV, and X-ray bands. NLTT 33370 ABis a unique system in terms of both its fundamental physical parameters and its magnetic properties. It is a tight, low-mass binary ( AU,  M; Schlieder et al., 2014) resolvable with adaptive optics, so that it promises to become one of a small sample of benchmark UCD systems with dynamically measured component masses (Bouy et al., 2008; Dupuy et al., 2010; Konopacky et al., 2010). Unlike most other such systems, NLTT 33370 AB is young, with an estimated age of 30–200 Myr (Schlieder et al., 2014). This youth may be related to another dramatic characteristic: it is phenomenally magnetically active. It the most radio-luminous UCD system known (McLean et al., 2011), and, as we demonstrate in this work, it is also one of the brightest in X-ray and  emission, with frequent flaring across the electromagnetic spectrum.

We proceed by reviewing the observed and inferred properties of NLTT 33370 AB (Section 2). We then describe the observations (Section 3) and their analysis (Section 4), which yield a rich multi-wavelength data set with complex phenomenology that we summarize in Section 5. We discuss the implications of the data for the system’s physical configuration and emission processes in Section 6. Finally, we summarize our findings and present our conclusions in Section 7.

Throughout this work, we use the notation , with being measured in cgs units unless specified otherwise. Bolometric luminosities () are measured in units of L. Parentheses following numbers indicate uncertainties in the final digits; for instance, is shorthand for . To avoid linguistic contortions we will sometimes refer to NLTT 33370 AB as a single object; depending on the context, such references should be taken to mean either the blended system, or a single but unspecified component of the binary.

## 2. Nltt 33370 Ab

NLTT 33370 AB was originally identified as a high-proper-motion object in the New Luyten Two-Tenths catalogue (Luyten, 1979). It was subsequently recovered by Lépine & Shara (2005), who gave it the identifier (catalog LSPM J1314$+$1320). Further followup assigned a blended spectral type of M7.0e, a tangential velocity of  km s, and a distance of  pc via trigonometric parallax (Lépine et al., 2009). Lépine et al. (2009) also measured an  equivalent width111Throughout this work, we report  as a positive number; some authors, including Schlieder et al. (2014), choose to use negative values for spectral lines in emission. This work involves no discussion of absorption lines so there is no ambiguity. () of 54.1 Å. Lucky imaging of NLTT 33370 AB resolved it into a binary with a separation of  arcsec (2.1 AU; 2500 R) and a companion 1 mag fainter than the primary in the band (Law et al., 2006). Although continued monitoring has refined the binary orbit, showing evolution in position angle (PA) and separations of 0.07 arcsec, the system parameters are still uncertain (Schlieder et al., 2014). A recent detailed analysis of the available astrometry, blended spectroscopy, and resolved photometry by Schlieder et al. (2014) has yielded estimates of and  K for the two components, masses of and  M, a system bolometric luminosity ( erg s), and a young system age of 30–200 Myr. NLTT 33370 AB may be a member of the nearby, young AB Dor moving group (Schlieder et al., 2012), but such an assignment is still tentative (Schlieder et al., 2014).

McLean et al. (2011) detected NLTT 33370 AB in the radio as part of a large VLA survey of UCDs (McLean et al., 2012). The emission was bright ( mJy at 4.86 GHz) and broadband ( mJy at 22.5 GHz). Furthermore, NLTT 33370 AB was detected at a similar flux density in the Faint Images of the Radio Sky at Twenty Centimeters survey (FIRST; Becker et al., 1995), indicating that the emission was stable over a 10-yr timescale. The radio emission varied sinusoidally with a period of  hr and amplitudes of 30% (20%) at 4.86 (8.46) GHz. At 4.86 GHz the periodicity was also detected in circular polarization (CP), with the polarization helicity alternating between left- and right-handed in phase with the total intensity. McLean et al. (2011) also obtained broadband optical photometry of NLTT 33370 AB from the MEarth survey (Nutzman & Charbonneau, 2008; Berta et al., 2012) using the Monitor pipeline (Irwin et al., 2007), finding periodic modulation with a period of  hr and an amplitude of 15 mmag (1.4%). The optical periodicity is thus marginally shorter than the radio periodicity, differing by  min. Finally, McLean et al. (2011) obtained optical spectroscopy and measured  km s and, on two observing sessions separated by 100 days,  EWs of 9.9 and 14.6 Å.

NLTT 33370 AB has also been observed in the radio using very long baseline interferometry (VLBI), a technique that can easily resolve the binary and could potentially resolve the radio emission from each binary component. McLean et al. (2011) report a detection of one unresolved source with a synthesized beam of size 21 mas, indicating that the emission originates from a region 50 R in size. Additional sources brighter than 0.2 mJy are excluded. Subsequent VLBI observations continue to reveal only a single radio source (J. Forbrich, 2014, priv. comm.). The system’s astrometric parameters are not sufficiently well-known to identify whether the primary or the secondary is the radio source. Upcoming observations will measure these parameters more precisely (cf. Schlieder et al., 2014), resolving this question and allowing much more stringent constraints to be placed on the radio luminosity of the undetected source.

## 3. Observations and Data Reduction

We observed NLTT 33370 AB in two simultaneous multiwavelength campaigns in March, 2012 and April, 2013. In

provide a graphical overview of the observations. The centerpiece of Campaign 1 (2012) was two consecutive ten-hour nights of intensive optical and radio observations, with additional optical spectroscopic observations on the second night. We performed additional optical monitoring observations over 20 days on either side of the intensive observations. The centerpiece of Campaign 2 (2013) was a ten-hour session of simultaneous broadband optical, radio, X-ray, and UV observations, again with additional broadband optical observations surrounding the period of intensive observing. Below, we describe the observations and data reduction in more detail.

The calibrated photometric data from the intensive observing sessions are shown in Figures 5 (Campaign 1) and 6 (Campaign 2). We have converted all timestamps to modified, barycentric Julian dates (MBJDs) in the barycentric dynamical time (TDB) timescale, which is the most appropriate system for long-term timing applications (Eastman et al., 2010). The integration times of the measurements presented in this work are all well above the 5 ms uncertainties in our conversion routines.

### 3.1. MEarth

We obtained long-term photometric monitoring of NLTT 33370 AB with telescopes in the MEarth array (Nutzman & Charbonneau, 2008; Berta et al., 2012). The observations of Campaign 1 span from 2012 March 1 to April 10, covering 27 nights. Those of Campaign 2 span from 2013 April 22 to April 30, covering 6 nights. The observations were made with a long-pass RG715 Schott glass filter. This is the same configuration as used in the observations reported by McLean et al. (2011), but the instruments and filters were reconfigured in the interval between the two studies, so the bandpasses are likely slightly different. All observations were made with an exposure time of 42 s. The median FWHM in the Campaign 1 observations is 3.1 (4.1 pixels); in Campaign 2, it is 2.6 (3.4 pixels). This is somewhat smaller than in the observations of McLean et al. (2011) because MEarth operated with a slight defocus in the 2008–2009 observing season.

Most of the MEarth observations occurred with a cadence of 20 min over the course of each night. However, during two “intensive” nights in each campaign (indicated with filled boxes in

observations were essentially continuous, with a cadence of 71 s. These nights were the ones in which the simultaneous monitoring at other bands occurred. The beginning of the first intensive night of Campaign 1 was affected by significant cloud cover, as is discernable in

he other observations were generally performed in clear conditions.

We also used previous MEarth observations of NLTT 33370 AB, taken between 2010 February 13 and February 19 and described by McLean et al. (2011). These data were reprocessed with a newer version of the MEarth reduction pipeline than used in that work, but the changes in the outputs are minor. We refer to these measurements as originating in Campaign 0.

The raw MEarth images are processed automatically using the Monitor project pipeline (Irwin et al., 2007) with facility-specific improvements as described in the processing documentation for MEarth Data Release 2 (DR2). The resulting tables of differential photometry are affected by three lingering systematic effects that can be described with the equation:

 mtrue=mobs+∑ikZP,iδ(S−i)+kCMCM+kFWHM(FWHM−FWHM0). (1)

Here is the true differential magnitude, is the observed value reported by the pipeline, the CM term refers to a “common mode” effect due to color-dependent extinction, and the FWHM term refers to seeing-dependent offsets in the photometry. The sum is a zero-point term: each MEarth instrument configuration or “segment” is assigned a unique integer identifier (denoted above) and has its own zero point. The MEarth DR2 release notes contain much more detailed information on these effects.

The variables , , CM, and FWHM are output by the pipeline for each photometric measurement. In our data, . The variables are calibration terms that must be determined for each source by simultaneously modeling their values as well as the underlying source magnitudes . FWHM is an arbitrary constant that can aid the numerical stability of the modeling; it is degenerate with the . The FWHM-dependent term is only significant for crowded fields, and we found in practice that the parameter was not well-constrained in our modeling. We therefore fixed it to zero, leaving five calibration parameters when modeling the three campaigns.

We discarded individual photometric measurements based on data quality metrics. Measurements in which the fitted source position was offset from its expected location by more than 12 pixels in either the or direction (table columns Delta_X, Delta_Y) were rejected, as were those in which the estimated cloud extinction exceeded 1 mag (table column DMag). The locations of these cutoffs were determined empirically, and they eliminate 9% of the measurements. Cuts on other quantities (source ellipticity, FWHM, etc.) were investigated but were not found to be beneficial.

### 3.2. Vla

We monitored NLTT 33370 AB in the radio with the Karl G. Jansky Very Large Array (VLA) on the nights of 2012 March 26, 2012 March 27, and 2013 April 28 (projects VLA/12A-090 and SE0124; PI: Berger). The VLA was in the C configuration for first two nights (Campaign 1) and the D configuration for the third (Campaign 2). Each observing session lasted 10 hr and consisted of integrations on the target with periodic visits to a phase calibrator, (catalog J1309$+$1154), at a 9-min cadence. In all cases, (catalog 3C286) was used as a bandpass, flux density, and polarization calibrator, with multiple visits over the course of the night allowing full polarimetric calibration. The integration time was 5 s and the C band receivers were used, with 2048 MHz of total bandwidth divided into two basebands centered at 5.0 and 7.1 GHz, each containing 512 spectral channels. In each night, the total integration time on the target was 496 min, or 83% of the session.

We additionally obtained multi-band radio photometry of NLTT 33370 AB with the VLA on the night of 2012 March 24 (project VLA/12A-090), just before the intensive monitoring observations of Campaign 1. The details of these observations and their outcome will be described in a forthcoming publication.

We calibrated the VLA data using standard procedures in the CASA software system (McMullin et al., 2007). Radio-frequency interference was flagged automatically using the aoflagger tool, which provides post-correlation (Offringa et al., 2010) and morphological (Offringa et al., 2012) algorithms for identifying interference. Each observation included four visits to the calibrator (catalog 3C 286), allowing full polarimetric calibration. The flux density scale was referenced to (catalog 3C 286) using the preliminary, 2010 version of the scale defined by Perley & Butler (2013). After calibration, the data sets were time-averaged to a uniform cadence of 10 s.

To check data quality and develop a model of the radio emission from unrelated sources in the NLTT 33370 AB field, we imaged the data. For each night we made an image of 20482048 pixels, each 11. The imaging process used multi-frequency synthesis (Sault & Wieringa, 1994) and CASA’s multi-frequency CLEAN algorithm with 2250 iterations. Because of the wide bandwidth of the data, we used two spectral Taylor series terms for each CLEAN component, i.e. modeling both the flux and spectral index of each source. The reference frequency for these images is 6.05 GHz. We detected NLTT 33370 AB robustly at all times.

We then extracted photometry for NLTT 33370 AB from the visibility-domain data following the procedure described in Williams et al. (2013), using the deep images to establish a precise source position and model the radio emission in the field. The Stokes  and  light curves are plotted in Figures 5 and 6. Values of greater (less) than zero denote right (left) circular polarization (RCP, LCP). We denote the fractional circular polarization . Stokes parameters are defined such that for any given emission component, and . The Stokes parameters for the superposition of two components are simply sums: , . The radio data are all consistent with zero linear polarization.

ows the Stokes  photometry of NLTT 33370 AB for the two VLA basebands separately. The common vertical scale of the three panels makes clear the different variation patterns seen in Campaigns 1 and 2. The flat spectrum reported by McLean et al. (2011) is evident in the fact that in most cases the flux densities in the two basebands are virtually identical. The rapid flares, however, are generally brighter at lower frequencies. Conversely, the rising periods of the slow variation in Campaign 2 are associated with brighter emission in the 7.1 GHz baseband.

### 3.3. Chandra

The Chandra observations were performed on 2013 April 28 (proposal 14200124; Chandra observation ID 14530; PI: Berger) using the S3 backside-illuminated chip of the ACIS imager. The total exposure was 35.6 ks, ranging from MBJD 56410.019–56410.457. No grating was used, the data mode was VFAINT, and the exposure mode was “timed” (TE).

We analyzed the Chandra data in CIAO version 4.6.1 (Fruscione et al., 2006) using CalDB version 4.5.9. Following VFAINT reprocessing to eliminate a substantial fraction of background events, we estimated the residual background in the data by extracting events in an energy range of 0.3–7 keV in a large annulus around the astrometrically predicted position of NLTT 33370 AB. The mean whole-chip background rate is 0.39 s, which is consistent with typical nonflaring behavior. We performed a Bayesian blocks analysis (Scargle, 1998; Scargle et al., 2013) to search for background flares as manifested by significant changes in the background count rate, using the implementation described in Williams et al. (2014). No such changes were found.

Based on the astrometric parameters given by Schlieder et al. (2014), the predicted location of NLTT 33370 AB at the time of the Chandra observation is 13:14:20.17, 13:19:58.4, with an uncertainty of 1. The Chandra data contain an X-ray source of 909 counts (0.3–7 keV) within a 5 aperture at 13:14:20.14, 13:19:58.5 (separation of 0.5). This aperture is expected to contain 4.2 background counts. We identify this source with NLTT 33370 AB.

### 3.4. Swift

NLTT 33370 AB was observed by Swift on 2013 April 28 (target of opportunity ID 4717) with the X-ray Telescope (XRT), UV/Optical Telescope (UVOT), and -ray Burst Alert Telescope (BAT). No sources were detected with the BAT. The UVOT had the UVW1 filter (2280–2930 Å) in place and the XRT was in photon-counting (PC) mode. A total of 5.0 ks were spent on-source, divided among 8 visits of durations varying between 384 and 975 s. As can be seen in

he total time spanned by the observations was 13 hr, with the final two visits occurring after the end of the simultaneous VLA, MEarth, and Chandra observations.

We analyzed the Swift XRT data using HEAsoft version 6.15.1 with CalDB version 20140120. We calibrated and cleaned the low-level data with the xrtpipeline task. We then extracted source events from a region coincident with NLTT 33370 AB having a radius of 20 pixels. Over the duration of the observation, 59 events were detected in the region, with an expectation of 7 of those coming from the background. The bottom panel of

ows the resulting Swift XRT light curve. Here the event rates have been converted into fluxes using an energy conversion factor (ECF) of  erg cm ct, which was derived using PIMMS for a 0.7 keV APEC plasma. This is the temperature obtained in a fit to the Chandra data (Section 4).

We analyzed the Swift UVOT data using the same software stack as for the XRT. We used the uvotmaghist task to derive the light curve data shown in

he uncertainties shown are sums in quadrature of the pipeline-reported systematic and statistical uncertainties, which are dominated by the latter. The UVW1 filter of the UVOT is susceptible to a “red leak” of optical light with wavelengths 4500 Å (e.g., Brown et al., 2010b). While these wavelengths qualify as “red” compared to the UV band, they are still quite blue compared to the photosphere of NLTT 33370 AB. Based on the UVW1B color of NLTT 33370 AB, the estimates of Brown et al. (2010b) suggest that the contribution of the photosphere is 0.2 mag, and a convolution of the UVW1 bandpass with the representative photospheric model described in Section 5.1 yields a contribution of  erg s cm Å, 10% of the observed value in the UVW1 band.

### 3.5. Mmt

We obtained optical spectroscopic observations of NLTT 33370 AB on 2013 March 27 UT with the Blue Channel spectrograph mounted on the MMT 6.5-m telescope. Six 300-s exposures were obtained at regular intervals between 05:05 and 11:42 UT, in conjunction with day 2 of Campaign 1. The observations were obtained with the 1200 l/mm grating leading to a wavelength coverage of  Å at a resolution of about 1.5 Å.

We processed and analyzed the data using standard routines in IRAF, and measured H EWs using the task splot. The resulting values are plotted in

he errors on each measurement are  Å.

## 4. Analysis

We detected variable emission from NLTT 33370 AB in every observed band. We find both ubiquitous flaring and periodic, non-flaring modulations.

### 4.1. MEarth

The intensive MEarth observations in all three campaigns reveal sinusoidal variability. While the MEarth data do not show flares, examination of Figures 5 and 6 shows that there is variability on the 5 mmag level from one cycle to the next. Here we investigate the periodicities present in the MEarth data without attempting to model these low-level variations.

A single sine curve with a period of  hr can reproduce the phasing of the observations very well over the full 3.4-yr time baseline of the data. A standard weighted nonlinear least-squares fit to the data yields a large reduced () of 6.89, however, with periodic structure in the residuals of the intensive observations. Comparison of Figures 5 and 6 suggests that, at a minumum, the oscillation amplitude evolves from one campaign to another. We performed this fit (and all others in this section) with a Python implementation of the Levenberg-Marquardt algorithm based on the classic MINPACK version (Moré, 1978).

A sine curve model with a single period but different amplitudes and phases for each campaign achieves an improved but still shows periodic residuals. Adding a second sine term yields with much less marked structure in the residuals. The derived periods in this model are and  hr. The former value is consistent with the period of  hr derived by McLean et al. (2011) from the Campaign 0 data alone. A third sine term yields with the new period being  hr. This is close to the sidereal period ( hr), suggesting that this component represents a systematic effect. The addition of a fourth term yields a marginal improvement (). We use the 3-sine model to guide our interpretation of the data, treating the first two periodicities as astrophysical and the third as a systematic. The longer-period astrophysical term always has the higher amplitude and we refer to it as the “primary” component, while the shorter-period term is the “secondary.” The 3-sine model and residuals are shown in

d the derived parameters are listed in Table 1, where the sinusoidal components are given by

 mtrue=Aisin(2π(t−Ti)Pi). (2)

Parameter uncertainties are derived from the covariance matrix determined by the Levenberg-Marquardt minimization. Because this model is defined in terms of magnitudes, maxima in luminosity correspond to minima in . All plots of MEarth data in this work use axes such that brighter emission is closer to the top of the plot.

A more flexible model in which the periods of the sine curves may also vary between each campaign yields an indistinguishable . In this model, the best-fit periods are all consistent with those obtained above. We conclude that there is no evidence for year-timescale evolution in the periodicities present in the data, but cannot rule out changes at the 0.5% level.

The phase offsets between the Campaign 1 and 2 signals are  deg for the primary periodicity and  deg for the secondary. Between Campaign 0 and 1 they are and  deg, respectively. A model with constant phasing between the three epochs achieves an inferior , with large residuals outside of the regions of intensive observations, suggesting that the least-squares optimizer converged on a solution that worked unusually well for the densely-sampled points, rather than a solution that fairly represented the overall system light curve.

We investigated whether the dual period results might be due to variations that are not strictly periodic (and hence are broadened in Fourier space) rather than two discrete components. In particular, we explored an alternative “quasi-sine” model in which and in Equation 2 wander randomly in time (i.e., possibly corresponding to a long-lived photospheric feature with evolving size and longitude). We realized 512 such models by drawing the amplitude and phase curves from squared-exponential Gaussian processes, in which the covariance between measurements separated by an interval is

 C(Δt)=aexp(Δt2s)2. (3)

We drew uniformly in log-space between and for the amplitude variation and between and  rad for the phase variation. We drew uniformly in log-space between and  hr. The characteristic excursions were in scale. We evaluated these models with the sampling of Campaign 1, which has the longest time baseline and most measurements of the three campaigns.

mpares Lomb-Scargle periodograms for the Campaign 1 data, the 3-sine model, and the quasi-sine realizations. The 3-sine model reproduces the observed periodogram well, while the quasi-sine realizations do not: they cannot recreate the asymmetry of the data periodogram.

The sum of two oscillations with frequencies and can be expressed as the product of two oscillations with frequencies and . In this case the corresponding periods are  hr and  d. Detailed investigation of the raw data does not reveal any evidence that the proximity of the long beat period to an integral number of days is due to a systematic. This periodicity is not prominent in the MEarth sampling pattern or any of the systematics parameters such as the CM “common mode” term. Efforts to model the data with a 16 d modulation term do not perform as well as the 3-sine fit (generally ) and leave a persistent residual periodicity of 3.71 hr. We therefore conclude that the data require two periods separated by min.

### 4.2. Vla

As previously found by McLean et al. (2011), the VLA photometry shows clear variability with a period comparable to that seen in the optical bands. At most times the emission has moderate RCP, with average values of and  mJy outside of flares in Campaigns 1 and 2, respectively. Unlike the observations of McLean et al. (2011), however, rapid (5 min), 100% left circular polarized (LCP) flares are observed superposed on the steadier emission in both Campaigns 1 and 2. Previous observations of the radio-active ultracool dwarf TVLM 513–46546 have revealed similar behavior: bright polarized bursts are sometimes observed (e.g., Hallinan et al., 2007) and sometimes excluded to high significance (e.g., Hallinan et al., 2006). One such flare, at MBJD , reaches a peak flux density of 8 mJy, which would have been clearly detectable in the data of McLean et al. (2011). We show this flare’s dynamic spectrum in

d a zoom-in of its light curve in

he flare is completely absent from the upper baseband, with a cutoff frequency of 5.8 GHz suggested by extrapolation of the available data.

Such flares are generally interpreted as coherent radio emission (Hallinan et al., 2006, 2008; Berger et al., 2009; Route & Wolszczan, 2012) arising from the electron cyclotron maser instability (ECMI; Wu & Lee, 1979; Treumann, 2006). In the ECMI paradigm, emission cuts off at approximately the cyclotron frequency  GHz. Given the results shown in

his suggests  kG, in line with measurements of M dwarfs made through observations of Zeeman broadening of the magnetically sensitive FeH molecule (Reiners & Basri, 2006, 2007, 2010). Taking a representative bandwidth of  GHz and flux density of 7 mJy, the flare luminosities reach , where Schlieder et al. (2014). Using a duration of 3 min (0.002 d), the flare energy output is  erg.

To better understand the non-flaring emission, we subtracted the rapid LCP flares from the data as follows. First, we manually identified flare events by looking for abrupt simultaneous excursions in Stokes  and . For each flare, we modeled the underlying non-flaring emission in both Stokes  and  with cubic polynomials and fitted to the surrounding flare-free measurements. For each in-flare measurement, we computed the flare intensity as the weighted mean of and , then subtracted this quantity to obtain the non-flare residual. Although not required by our method, the modeled flare intensity is always consistent with being nonnegative. We investigated modeling of the flares with fractional circular polarizations that were high, but not 100%. The fits with 100% LCP were qualitatively the best, and are further justified by the near-perfect agreement between and seen in

n Campaign 1, the 100% LCP flare duty cycle is %, while it is % in Campaign 2. The event rates are 0.9 hr and 0.5 hr, respectively.

The non-flaring component of the radio data shows quasi-periodic variations. We used phase dispersion minimization (PDM; Stellingwerf, 1978) to identify a period of  hr in the Campaign 1 Stokes  data, consistent with the primary MEarth periodicity, but different from the secondary periodicity at 70. The PDM periodicity of the Campaign 2 Stokes  radio data is  hr; because the observation covered only 2.6 rotations, the precision is insufficient to make informative comparisons against the Campaign 1 or the MEarth results.

ows the VLA light curves after removal of the 100% LCP flares, along with indicators showing the phasing of the data with regard to the primary MEarth periodicity. We derived mean phase profiles for the Campaign 1 data by separately fitting smoothed cubic splines to the Stokes , Stokes , and measurements after phasing them to this periodicity.

ows both these mean profiles and the smoothed un-phased data. Disagreements between these curves indicate deviations from purely periodic variation. Disagreements are common even in the Campaign 1 Stokes  light curves: NLTT 33370 AB’s radio emission modulates periodically but varies stochastically as well. We show the Campaign 1 mean phase profiles alongside the Campaign 2 data to aid comparison despite the time gap between the observations and the clear change in nature of the Campaign 2 Stokes  emission.

The non-flaring Stokes  radio emission in both campaigns is similar: it varies periodically in a sawtoothed pattern with a rapid rise and slow decay. In both campaigns the midpoint of the Stokes  decay phases with the maximum of the primary MEarth component, while the phasing with regards to the secondary MEarth component is not stable. There is a zero-point offset between the emission in the two campaigns, and the amplitude of the Campaign 2 variation is somewhat smaller: the smoothed flux density ranges between –0.36 mJy in Campaign 1 and 0.02–0.33 mJy in Campaign 2. The Stokes  flux density and do not differ significantly between the two VLA basebands at 5.0 and 7.1 GHz. The range of variation we observe is similar to that found at 8.5 GHz by McLean et al. (2011), although those authors were unable to detect a periodicity in that emission. At 4.9 GHz McLean et al. (2011) found periodic variation with  mJy, i.e. extending to significantly more net LCP than we observe. This difference may be due to the presence of low-level LCP flares in their data comparable to the ones we have removed, but the sensitivity of the pre-upgrade VLA is insufficient to determine this; we note that these flares are more significant at lower frequencies (Figures 3.2, LABEL:f.vladynspec). In the non-flaring data %, also consistent with the 8.5 GHz results of McLean et al. (2011).

The non-flaring Stokes  radio emission of Campaign 2, on the other hand, differs substantially from that of Campaign 1. Although the minimal non-flaring Stokes  flux densities in both campaigns are 1.0 mJy, the maximum in Campaign 2 is 2.2 mJy, against 1.6 mJy in Campaign 1. While the Campaign 1 emission shows a sawtoothed, double-humped light curve structure that mirrors the Stokes  variation, in Campaign 2 the variation is more uniform. As judged by the locations of the light curve minima, the phasing of the Stokes  emission relative to MEarth shifts by 180° between the two campaigns. McLean et al. (2011) measured flux densities somewhat lower than we do, finding  mJy and  mJy at 4.9 and 8.5 GHz, respectively. The emission maxima (minima) in that study are decreased (increased) compared to this work because of the longer averaging interval used (25 m vs. 8 m). The modulation amplitudes are therefore also attenuated. The observed amplitudes are consistent with our Campaign 1 results but not those of Campaign 2.

Along with the phase shift relative to the optical emission, in Campaign 2 the rising portions of the non-flaring Stokes  light curve are associated with a rising spectrum, an effect not seen at any time in the Campaign 1 data (

Meanwhile, as discussed, the Campaign 2 Stokes  light curve has a shape and phasing consistent with that of Campaign 1. These facts suggest the Campaign 2 radio emission may be the sum of a “Campaign 1” term and an additional component with . The phasing and evolution of this additional component imply that it arises from a distinct region and has a lifetime of at least a few rotations. As shown in

owever, the Campaign 2 Stokes  minima fall below what would be expected from Campaign 1. This could be due to the presence of an absorber, as discussed in Section 6.2.

The general phenomenology of the Campaign 2 Stokes  emission (temporary increase in flux density, rising spectrum) is suggestive of optically thick gyrosynchrotron flares. We applied standard gyrosynchrotron models and analysis (Dulk, 1985; Osten et al., 2005) to these periods in Campaign 2, assuming that the observed emission was the sum of a spectrally flat oscillating component and a rising-spectrum flare component. We find  G, a brightness temperature  K, and a length scale of 1.7  for the emitting region. These results are in line with previous studies of similar objects (Berger, 2002, 2006; Osten et al., 2002, 2005; Burgasser et al., 2013) and earlier work on NLTT 33370 AB (McLean et al., 2011). The length scale is compatible with spatially resolved VLBI observations of M dwarfs (Alef et al., 1997; Benz et al., 1998). We derive a number density of nonthermal ( keV) electrons  cm, with substantial uncertainties because the location of gyrosynchrotron spectral peak is weakly constrained. This value is consistent with the results of Osten et al. (2005) and several orders of magnitude smaller than typical estimates of overall (thermal and nonthermal) cool star coronal electron densities, generally found to be  cm (Ness et al., 2002, 2004).

The non-flaring Stokes  spectral luminosity in Campaign 1 ranges between and , where the uncertainties are due to the source distance and thus are correlated between the two measurements. In Campaign 2  ranges between and . Taking as a representative value we find .

To summarize, the complex radio light curve of NLTT 33370 AB appears to combine emission from at least three separate components: rapid 100% LCP flares, periodically modulated emission with moderate RCP, and an additional unpolarized component seen only in Campaign 2. The complex morphology of the moderate RCP component implies that it further represents the combined emission of multiple regions or components. For instance, if the fact that the total intensity never drops below 1.0 mJy is taken as evidence for the presence of a constant component of that intensity, the periodic modulation in Campaign 1 would represent the emission of a component with  mJy. Furthermore, the mathematics of Stokes parameters (Section 3.2: within each component) and anti-correlated variability in and then imply that the constant term has % while the modulating term has %.

### 4.3. Chandra

Grouping the X-ray events into forty 15-min bins suggests a largely steady source with at least one rapid flare (Figures 6 and 37).

ows a 90% confidence region for the binned count rates assuming a steady source and Poisson statistics. The measurement at MBJD is a outlier. The second-most outlying bin, at MBJD , contains 36 events and is a 2.9 outlier. In 39 measurements there is a 7% chance of obtaining at least one value that large.

The red curve in the top panel of

dels the emission of NLTT 33370 AB as a constant (“quasi-quiescent”) term plus a Gaussian flare. We determined the parameters for this model using a maximum-likelihood technique considering the arrival time of each observed photon. In particular, using a similar approach as the Bayesian Blocks technique, we performed a one-dimensional Voronoi tesselation of the photon arrival times and chose parameters to maximize the likelihood function of detecting one photon in each bin, evaluating the instantaneous rate function at each photon’s observed arrival time. The fitted peak flux of the flare (above the quasi-quiescent level) is 0.11 ct s. This is significantly above the corresponding 15-min bin (

ecause the modeled flare timescale is  min.

oms in on the flare, showing a finer (90 s) binning as well as the arrival times and energies of the individual X-ray events.

The lower panel of

ows the median photon energy in five time bins. This quantity provides a more robust quantification of the spectral shape than a traditional hardness ratio (Hong et al., 2004). The second bin encompasses the region of the flare, while the final three bins are uniform in size. Uncertainties on the medians are calculated using the method of Maritz & Jarrett (1978). The higher median photon energy in the flare bin is consistent with the general finding of elevated temperatures during such events (e.g., Robrade & Schmitt, 2005). Strikingly, the median energy of the quasi-quiescent emission increases over the course of the observation. This may be a precursor to the slowly-evolving flare captured by Swift after the end of the Chandra observations (

We modeled the overall X-ray spectrum of NLTT 33370 AB with Sherpa version 1 (Freeman et al., 2001). We used the Sherpa implementation of the Nelder & Mead (1965) simplex algorithm to optimize the statistic of Cash (1979). We did not group the data in energy or subtract the (negligible) background. Photons with energies outside of the range 0.3–2.5 keV were ignored. We used the solar abundances of Lodders (2003). A two-temperature solar-abundance APEC (Astrophysical Plasma Emission Code; Smith et al., 2001) model yields a satisfactory fit, achieving a reduced statistic with 146 degrees of freedom. We show the data and best-fit model in

he temperatures of the two components are  keV and  keV, consistent with results seen in other active mid-to-late M dwarfs (e.g., Robrade & Schmitt, 2005; Williams et al., 2014). We note that, although there is evidence that the rapid flare has a hotter spectrum than the quasi-quiescent emission, it comprises 5% of the total number of observed events, and thus does not significantly affect the modeling. We have verified this by modeling only the events from the quasi-quiescent time periods. Table 2 reports the mean and peak X-ray fluxes based on our spectral modeling. The peak flux is derived assuming the same energy conversion factor (ECF; ratio of energy flux to count rate) as the mean emission, and thus may be slightly underestimated if the flaring spectrum is indeed hotter than the mean emission.

We investigated alternative models for the X-ray spectrum. In particular, high-S/N observations of active M dwarfs often reveal non-solar elemental abundances, usually in the form of an inverse first ionization potential (IFIP) effect, in which elements with higher FIPs have elevated abundances (e.g., Robrade & Schmitt, 2005). No single-temperature model with adjustable elemental abundances yields a superior fit to the data compared to the two-temperature solar-abundance model. Two-temperature models with adjustable elemental abundances show hints of an IFIP effect in NLTT 33370 AB, but the results are not statistically significant.

We also searched for periodicity in the non-flaring X-ray emission. As may be judged from

ny periodicity in the data must be weak, and requires statistical analysis to uncover. Unfortunately, the small number of observated rotations (2.6) means that statistical approaches have low sensitivity in this dataset. Calculations of the Rayleigh test statistic (Kruger et al., 2002) showed that it simply correlated with the candidate rotation period in the parameter region of interest. The same outcome was found with the Kuiper statistic (Kuiper, 1960), a variant of the Kolmogorov-Smirnov test more suited for data on a circle. The available data do not provide significant evidence for periodicity in the X-ray emission.

We find and , where the and subscripts denote quiescent and flaring states. (Here we consider the rapid X-ray flare observed by Chandra, and not the more poorly-characterized event in the Swift data; both appear to have similar luminosities.) Unlike what is presented in Table 2, the flaring luminosity used here includes the contribution from the quiescent emission, for consistency with other studies. We find and , comparable to the saturated X-ray emission seen in early-M dwarfs.

The total energy output of the flare is  erg. No counterpart is apparent in the radio data, while the MEarth and Swift data do not overlap this event. There is a suggestion of a rapid decrease in optical luminosity just after the flare in the MEarth photometry, but these points were observed in partially cloudy conditions and are not reliable enough to be conclusive. A similar rapid X-ray flare, with a timescale  min, was observed in the dM4.5e dwarf (catalog EV~Lac) (Osten et al., 2005), and some X-ray flares initially evolve on a similarly rapid timescale before shifting to slower decay (e.g., as seen on (catalog LP 412-31); Stelzer et al., 2006b). Assuming  keV and thermal bremsstrahlung emission, the emission measure () corresponding to the peak luminosity is  cm, in line with previous observations of flare stars (e.g., Schmitt & Liefke, 2002; Robrade & Schmitt, 2005; Stelzer et al., 2006b).

### 4.4. Swift Xrt

The simultaneous Swift and Chandra data generally agree, with the exception of the Swift flux measurement at MBJD , which is substantially below that of Chandra. In particular, only one source event is detected in 380 s of observing. Its energy is 1.03 keV. During the precise Swift good-time interval () the Chandra count rate is consistent with the wider bin shown in

s are the photon energies. We suspect an unidentified instrumental phenomenon during this Swift observation.

The two Swift observations occurring past the end of the VLA and Chandra monitoring suggest a substantial, slowly-evolving (timescale 3 hr) flare. The median photon energies in these bins are and  keV, suggesting a continuation of the hardening trend seen in the bottom panel of

he observed X-ray luminosity in this event is compatible with that observed in the rapid Chandra X-ray flare, but the overall energy output would be larger by 2 orders of magnitude if the apparent timescale is accurate.

### 4.5. Swift Uvot

Similar to the XRT data, the UVOT measurements past the end of the simultaneous Chandra/VLA monitoring suggest a slowly-evolving flare. Assuming a UVW1 filter bandwidth of 795 Å and pivot wavelength of 2517 Å (Breeveld et al., 2011), the flare luminosity peaks at . It is tempting to infer a slow rise in UV luminosity in the period , but we caution that the sparse sampling may mask more complicated variation. There is a 30% decline in the UV flux between the first and second samples of the flare light curve (MBJD  56410.48 and 56410.62, respectively). At this time, the X-ray light curve appears flat, although the measurement uncertainty is nonnegligible. X-ray and UV variability often track each other fairly closely, with inter-band delays small compared to the timescales probed here (Osten et al., 2002, 2004; Mitra-Kraev et al., 2005; Berger et al., 2008a). The luminosity ratio between the two bands in this event is consistent with scaling relations found in simultaneous observations of flare stars (Mitra-Kraev et al., 2005).

The mean non-flaring luminosity is , or . Assuming a radius of  R (Schlieder et al., 2014), the surface flux is (erg s cm Å), lying between typical values obtained for main-sequence and classical T Tauri stars (Johns-Krull et al., 2000) in a study performed at somewhat shorter wavelengths (1958 Å) and higher  (3500–4500 K). While the non-flaring UVOT data are consistent with a constant flux (), their variations are suggestive of an oscillation with a periodicity similar to that of the MEarth data. Assuming a periodicity fixed to that of the primary MEarth component (3.7859 hr), we fit a sine curve to the UVOT data. The oscillation amplitude is %, the phase relative to the primary MEarth component is  deg, and (2 degrees of freedom).

### 4.6. Mmt

The sparse time sampling of the MMT observations preclude a detailed analysis of the time variability of . We interpret the first measurement as a flare and the subsequent four as quiescent activity. In quiescence,  Å, an unusually high value compared to typical mid-to-late M dwarfs (e.g., Lee et al., 2010). This is consistent with the average value of  Å reported by McLean et al. (2011). Lépine et al. (2009) and Schlieder et al. (2014) find and 50 Å, respectively, in single observations, suggesting frequent flares of luminosities a factor of 2 above what is contained in our observations.

We derive  from  using a “ factor” approach, using the relation (Walkowicz et al., 2004)

 LHαLbol=χEW(Hα)1 \AA. (4)

Reiners & Basri (2008) determine as a polynomial function of  in the mid-to-late M dwarf regime. Taking  K, we find . This is compatible with the value found using the polynomial fit to as a function of color given by West & Hawley (2008). It does not agree well with the value of reported by the latter authors for objects of spectral type M7 (); however, there is large scatter to their relation precisely at this spectral type, and it coincides with an inflection in their -vs-SpT data. We therefore prefer the Reiners & Basri (2008) computation. We find in quiescence that and that . As may be expected from the large quiescent , the derived value of  is also unusually large compared to most M7 dwarfs, which typically have (West et al., 2004, 2011). McLean et al. (2011) find a lower but compatible value of for the quiescent emission from equivalent values of , indicating different values for and/or .

Previous studies suggest that the  flare timescale is likely 10–100 min (Hilton et al., 2010; Lee et al., 2010). The observed magnitude of the flare can be assessed as , consistent with observations of flare stars (Lee et al., 2010). There is no clear correlation with any variations in the radio band. While a 100% LCP flare occurs 20 min before the high  measurement, the radio events are sufficiently frequent that there is plausibly happenstance. It is somewhat surprising that the  event appears to take place around the maximum of the optical light curve: in a model in which the optical light curve is modulated by dark spots, presumed to be associated with enhanced magnetic activity,  would be expected to be correlated with optical minima, a trend that has been observed (Frasca et al., 2000).

The non-flaring  data suggest an oscillation with a periodicity similar to that of the MEarth data. Here, a fit at the secondary MEarth periodicity gives a better (1 degree of freedom) compared to that at the primary periodicity, . We find an amplitude of % and a phase relative to the secondary MEarth component of  deg. The relatively large values of and small parameter errors are driven by the small ( Å) statistical error bars on the measurements of .

## 5. Summary of the Phenomenology

### 5.1. Spectral Energy Distribution

Table 3 summarizes several key parameters regarding the emission of NLTT 33370 AB in the radio, broadband optical, , UV, and X-ray bands. The optical luminosity is computed for the band assuming the -corrections of Blanton & Roweis (2007). The non-flaring radio parameters are derived for the Stokes  emission and the flare parameters refer to the rapid 100% LCP events. The UV and X-ray flare parameters refer to the slowly-evolving event detected by Swift. The parameters for the flares outside of the radio band are uncertain because only portions of single events were observed.

NLTT 33370 AB is the brightest UCD in terms of radio flux density (with the nearest rival being (catalog LSPM J1835+3259) at  Jy in quiescence; Berger, 2006) and radio spectral luminosity (significantly outshining the next most luminous source, (catalog 2MASS J05181131-3101529) at ; McLean et al., 2012). It is also one of the brightest UCDs in X-rays, whether quantified in terms of flux, luminosity, or bolometrically-normalized luminosity. Only the serendipitously-discovered object (catalog 2XMM~J043527.2-144301) may be more X-ray luminous; however, this object is not well-studied, and in particular has an uncertain spectrophotometric distance of  pc (Gupta et al., 2011). In quiescence, . The (non-contemporaneous) quiescent luminosities between the bands fall on the scaling relations determined by Stelzer et al. (2013).

Figures 51 and 54 show the SED of the blended components of NLTT 33370 AB.

ows details in the optical/infrared (OIR) bands. Included in these plots is a representative BT-Settl model photospheric spectrum (Allard et al., 2012) with  K, , and solar metallicity, computed with the CIFIST2011 version of the code, which uses the solar abundances of Caffau et al. (2011). The parameters of this model match those used by Schlieder et al. (2014) to model the individual components of the binary, except for , for which we find that a lower value provides a better match on the blue end of the OIR SED. The value used here is within 1 of the values found by Schlieder et al. (2014), which are and  K for the A and B components, respectively. The normalization of this model was set by weighted least-squares optimization of the synthetic photometry against the measurements shown in

he reduced of this fit is 5.29; similar fits with other values of , stepped in 100 K increments, yield inferior results (, for ,  K). We emphasize that this model should not be expected to precisely match the observations because the data considered here blend the emission of two distinct objects.

aces the OIR photometry in a broader context using our radio and X-ray observations as well as archival photometry from GALEX (Martin et al., 2005). Magnetic phenomena dominate the photospheric contribution outside of the comparatively narrow OIR window. The radio component has a strikingly broad and flat spectrum (in terms of flux density), and our data show only suggestions of a turnover in the spectrum around 40 GHz ( Å). The radio component is nonetheless energetically insignificant compared to the X-ray component, as is generally the case in comparable systems (Güdel & Benz, 1993; Williams et al., 2014).

### 5.2. Variability

Our data show flares and/or non-flaring modulation in every band. They are consistent with findings from other detailed multiwavelength studies of cool flare stars: there is striking variation in the flaring phenomenology, both within the same band and in multi-band correlations (Osten et al., 2004, 2005). It is clear that there is no one single observational manifestation of flaring activity, and the underlying physical phenomena are plausibly as variegated as their resulting emission.

The only data in which we do not observe flares are the broadband optical MEarth observations. This is not surprising: white-light flares are expected to be relatively blue, while both the MEarth filter and the photospheric emission of NLTT 33370 AB are red. Using the model spectrum of Davenport et al. (2012), we find that such flares would need to reach 4% of  to be detectable.

esents all of the light curves in compact form, with vertical scalings chosen to emphasize the nature and relative phasing of the variability in each band. The MEarth data are shown in light blue. The upper light curves show the data and full emission model, while the lower curves plot the primary and secondary sine components. The rapid, 100% LCP radio flares are shown in dark blue. Double-peaked LCP flares are seen during all 7 observed minima of the primary MEarth component. These flares may also preferentially occur around the midpoints of the rising portions of both the primary and secondary MEarth components.

ows the non-flaring radio data in red. The upper (lower) light curves show Stokes  (Stokes ) averaged across the two basebands. In Campaign 1, the Stokes  variations mirror those in Stokes  to a good approximation. In Campaign 2, the Stokes  variations are of about twice the amplitude, and the phasing of the light curve minima is shifted by 180° relative to the primary MEarth component, which we interpret as being due to the presence of an additional emission and absorption component (Section 4.2). The Campaign 2 Stokes  variations are approximately in phase with the secondary MEarth component.

The middle panel of

ows the  data in dark green. The  flare occurs around the time of a maximum in the MEarth light curve, although the sparse sampling makes timing analysis difficult. At the time of the  flare there is a noticeable dip in the Stokes  radio emission, but no 100% LCP flaring component.  modulates 180° out of phase with the optical emission.

The lower panel of

ows the X-ray data in light green. There is no evidence for periodic variations in the Chandra data. A rapid X-ray flare occurs around the predicted time of a maximum in the primary MEarth light curve, although no MEarth data were obtained at that time. The X-ray flare occurs of a rotation after the second-largest radio flare in the data set. The UV data are in purple; the last measurement appears to be associated with the rising phase of the slowly-evolving X-ray/UV flare (

The best sinusoidal fit to the UV data is approximately 180° out of phase with the primary MEarth component.

## 6. Discussion

### 6.1. Interpreting the MEarth Periodicities

We find two similar but distinct periodicities in the MEarth light curves: a primary component at  hr with amplitude 14 mmag and a secondary at  hr with amplitude 7 mmag. Modeling of the individual campaigns indicates that the periods are stable to levels of % across the 3.4-yr time baseline of the observations. Below we discuss what we consider to be the most plausible explanations for the data: either there are multiple spots on one object with differential rotation (DR), or both components of the binary rotate with very similar periodicities.

#### 6.1.1 Differential rotation

The similarity of the periodicities might be taken to suggest the presence of two spots on one differentially-rotating photosphere. The implied level of DR, however, is not expected to occur in stars in this mass range. The inferred absolute shear is  rad d and the relative shear is , where both quantities are lower bounds because they are generally expressed in terms of pole-to-equator variation, and latitudes of the putative spots are unknown. These values are well within bounds for partially convective rapid rotators ( K; Reinhold et al., 2013), but not fully convective ones. In the coolest stars in the sample of Reinhold et al. (2013),  rad d. Zeeman Doppler imaging (ZDI) observations of mid-M dwarfs find very low levels of DR in moderately rapid rotators ( hr), with  rad d (Morin et al., 2008b, a; Donati et al., 2008). In (catalog V374 Peg) (M4), (Morin et al., 2008b). These findings are supported by some magnetohydrodynamic simulations that find that Maxwell stresses virtually arrest DR in fully-convective objects (Browning, 2008).

A single night of spatially resolved photometric monitoring of the binary could determine if the optical variability is confined to one object. If so, the inferred presence of DR would be extremely surprising for such a cool dwarf. We speculate that in this scenario some cool dwarfs may indeed have high DR, and that this may lead to large radio luminosities; in this case, the discovery of unusual DR in NLTT 33370 AB would be a consequence of its selection in the radio survey of McLean et al. (2011, 2012).

#### 6.1.2 Similar rotation periods

Alternatively, it is possible that the two periodicities correspond to separate signals from the two components of the binary. Although the similarity of the rotation periods seems implausible, magnetic coupling to the protostellar disk might synchronize the components’ rotation (Königl, 1991; Edwards et al., 1993; Scholz, 2013, and references therein), and subsequent spin-up due to contraction (which dominates the rotational evolution of a system this age; Reiners & Mohanty, 2012; Gallet & Bouvier, 2013) would only alter the period ratio by 5% (assuming the evolutionary models of Baraffe et al., 1998). However, resolved measurements of  in low-mass binaries suggest that 50% of them have significantly different projected rotational velocities, and it is improbable that the differences are entirely due to the term (Konopacky et al., 2012).

If both components of NLTT 33370 AB truly have similar masses, ages, and rotation rates, one might expect them to have similar levels of magnetic activity. However, VLBI observations indicate that the system’s steady radio emission is dominated by only one of the components, with the nondetected component being 5 times fainter than the detected one (McLean et al., 2011). NLTT 33370 AB may therefore be an excellent laboratory for understanding the apparent bimodality in the radio and X-ray emission levels of otherwise-similar UCDs reported by several authors (McLean et al., 2012; Stelzer et al., 2012; Williams et al., 2014; Cook et al., 2014), which may stem from a bistability in the underlying dynamo (Morin et al., 2010; Gastine et al., 2013)444Another reference point is the binary (catalog BL/UV Cet) (dM5.5e+dM5.5e; often referred to as UV Cet AB), in which the components have indistinguishable projected rotational velocities ( km s; Jones et al., 2005) but the secondary (catalog UV~Cet) is far more active than the primary (e.g., Audard et al., 2003). VLBI observations detected spatially extended gyrosynchrotron emission from (catalog UV~Cet) but not (catalog BL~Cet) (Benz et al., 1998). Intriguingly, in the same observation (catalog BL~Cet) was seen to emit rapid polarized pulses, while (catalog UV~Cet) was not.. Because NLTT 33370 AB is a visual binary and its components have such similar masses and (possibly) rotation rates, many potential confounding factors in the effort to understand the radio/X-ray bimodality could be eliminated.

### 6.2. Non-flaring variability

The data presented in this work are consistent with the model proposed by McLean et al. (2011), in which the stellar magnetic field is dominated by a dipole that is misaligned with the rotation axis. While McLean et al. (2011) were unable to phase-align their optical and radio data, the Campaign 2 results suggesting anti-phased radio and optical maxima would be consistent with the regions of maximal field strength hosting cool spots. Extrapolation of our MEarth model to the VLA data of McLean et al. (2011) using the Campaign 0 phasing suggests that a phase difference of 100° between the two modulations, although the 330-day gap between the observations is comparable to the time scale on which the modulation phase drifts in our data.

The model of a magnetized cool spot is supported by the fact that the  modulation, the possible UV modulation, and the Campaign 2 Stokes  radio emission all peak around the time of optical minimum. Furthermore, we observed Stokes  radio flares during all 7 optical minima. However, the rapid X-ray and  flares occur around optical maximum, the Stokes  flares occur at all phases, and the Campaign 1 Stokes  radio emission modulates approximately in phase with the optical data. The double-humped shape of the Campaign 1 emission may indeed indicate the presence of two separate emitters. While magnetic phenomena appear to be enhanced during optical minimum, they clearly occur at all phases.

A model developed for higher-mass magnetic chemically peculiar (MCP) stars ascribes radio modulation to the presence of a torus of cold, absorbing plasma around the magnetic equator (Trigilio et al., 2004, 2011). Such tori are also found encircling Jupiter and Saturn (e.g., Kivelson, 2005, and references therein) and thus may plausibly occur in NLTT 33370 AB as well. Simulated radio light curves, spectra, and radio/X-ray luminosity ratios are broadly in line with the observations of NLTT 33370 AB (Trigilio et al., 2004), and periodic auroral bursts are predicted that could be consistent with the LCP flares at optical minima (Trigilio et al., 2011).

We argue in Section 4.2 that the Campaign 2 emission includes an additional component that may be due to optically thick gyrosynchrotron flaring, explaining the apparent phase shift of the radio Stokes  relative to the optical maxima. However, the decrease of Stokes  in Campaign 2 relative to the expected Campaign 1 emission (

equires the presence of an absorber. The additional emission component may thus be associated with the creation or expansion of an absorbing plasma torus as suggested by the MCP model. The component associated with the Stokes  modulation may be confined to the magnetic poles, where the expanded torus would not alter the observed signal.

Models with large polar spots may seem difficult to reconcile with the presence of two periodic signals in the MEarth data. However, we note that magnetic phenomena in the two hemispheres of Saturn are associated with rotation periods that differ at the 1% level (Gurnett et al., 2009). We speculate that one of the components of NLTT 33370 AB may host two large polar spots that similarly rotate at slightly different rates. One caveat is that in Saturn, this effect may be driven by the Sun (Gurnett et al., 2009); NLTT 33370 AB does not have a similar driver.

### 6.3. Flaring conditions

Although the non-flaring modulation suggests the presence of large-scale magnetic fields, the rapid flares we observe imply the presence of significant magnetic energy in small-scale fields as well, as is expected for low-mass stars in general on both observational (Reiners & Basri, 2009) and theoretical grounds (Lang et al., 2014). The frequent (30% duty cycle) LCP radio flares suggest the nearly continuous occurrence of magnetic reconnection, especially since such coherent emission is expected to be strongly beamed. Reconnection dominated by large-scale (R) magnetic fields, on the other hand, would lead to less frequent, larger flares, as observed in some UCDs in X-rays (Stelzer et al., 2006b; Robrade et al., 2010); the slow-evolving X-ray/UV flare observed by Swift may be an instance of one of these. Hydrodynamic modeling of flaring loops suggests a length scale of  R from the 150 s decay timescale of the rapid Chandra flare (Serio et al., 1991). Frequent small-scale reconnection events, as suggested by the radio LCP and X-ray flares, may be related to radio emission above that predicted by the Güdel-Benz relation (Güdel & Benz, 1993) both specifically in NLTT 33370 AB and more generally (Williams et al., 2014).

Applying the Güdel-Benz relation to the rapid X-ray flare, the expected radio luminosity is , equivalent to a flux density of 0.03 mJy. Such an enhancement would not be discernible in the radio light curves. Assuming that  luminosity represents 10% of the white-light component of a flare (Neidig, 1989) and that flare soft X-ray luminosity is 20% of that of the white light (Woods et al., 2004), the flaring  measurement would correspond to a nearly identical value of , and have a similarly insignificant radio component. Combined with the energetic insignificance of the coherent radio emission (Table 3), the overall lack of correlation among rapid flare events at multiple bands is striking, but potentially not surprising (e.g., Osten et al., 2004, 2005).

### 6.4. Effect of activity on fundamental measurements

The high levels of activity in NLTT 33370 AB have significant implications for its status as benchmark system for young, low-mass objects. The results of Stassun et al. (2012) suggest that mass estimates will not be strongly affected because  is approximately conserved; however, this particular system will yield dynamical mass measurements regardless. On the other hand, their relations predict that magnetism may alter  by % and by +20%. (Our estimates are 2 times larger than those of Schlieder et al. (2014), likely due to the use of a different factor, since we use their  and equivalent  values.) The detection of only a single component in VLBI (McLean et al., 2011) suggests that these effects may be concentrated in only one component of the binary. However, Stassun et al. (2012) rely on  rather than radio emission as a metric of magnetic activity, and it remains to be conclusively determined what the most physically relevant tracer truly is.

## 7. Summary & Conclusions

We have presented a detailed simultaneous study of the magnetic activity of the young UCD binary NLTT 33370 AB from two observational campaigns in the radio, optical, , UV, and X-ray bands. Some of the key phenomena are:

• Extreme magnetic activity, with the highest radio luminosity of any known UCD, one of the highest X-ray luminosities, and a large  luminosity as well (Table 3).

• Periodic modulation of emission in at least the radio and optical bands, and plausible UV and  modulation. The long-term MEarth data set reveals two distinct periodicities of and  hr, with 50% evolution in the modulation amplitude and phase from year to year.

• Significant evolution in the Stokes  radio modulation between the two campaigns, with the amplitude increasing by a factor of 2 and the phase shifting by 180°. However, Stokes  is stable and phases consistently with the primary MEarth periodicity in both campaigns.

• A very bright Stokes  flare with a spectral cutoff suggesting a magnetic field strength of 2.1 kG in the ECMI interpretation.

• A typical X-ray spectrum adequately fit by two temperature components of and  keV. However, the hardness gradually increases before a large X-ray/UV flare lasting 0.1 d.

• A general lack of correlation between flares in any band. The exceptions are the slow X-ray/UV flare observed by Swift, and the consistent detection of Stokes  flares at optical minima.

Our analysis leads us to conclude that:

• The explanation for the two MEarth periodicities is unclear. Although they differ by only 2%, even this level of differential rotation is not expected in stars this cool. If NLTT 33370 AB indeed shows unusual differential rotation, it may possibly be a consequence of its selection as an unusually magnetically active system.

• The periodic modulation of the non-flaring emission of NLTT 33370 AB may be understood in a model with a large-scale magnetic field misaligned with the rotation axis. The change in the relative phasing of the radio Stokes  and optical modulation between Campaigns 1 and 2 is the most difficult to explain in such a context. The stability of the radio Stokes  signal, however, suggests that the Campaign 2 radio emission is the sum of that seen in Campaign 1 and an additional component that is furthermore associated with an absorbing equatorial torus of cold plasma (Trigilio et al., 2004, 2011).

• The presence of frequent, rapid flares at all rotational phases implies the additional presence of significant magnetic energy in small scales that is being dissipated in reconnection events nearly continuously. This may be related to the excessive radio luminosity of NLTT 33370 AB relative to the Güdel-Benz relation (Williams et al., 2014).

• The high levels of magnetic activity in this system may alter  by % and by +20%.

Significant progress can be made with currently-available resources. Not only will spatially resolved astrometric monitoring improve constraints on the fundamental parameters of the binary components, it will allow much tighter constraints on the radio emission of the more radio-faint component by providing knowledge of its position in existing VLBI data sets. Such monitoring is in progress, as are continued VLBI observations. Spatially resolved spectroscopy of this system is achievable with state-of-the-art facilities (e.g., Konopacky et al., 2012) and would yield both resolved radial velocity measurements, diagnosing the inclination of the binary orbit, and resolved  measurements, providing key insight into the rotation rates of the two components. Spatially resolved photometric monitoring would be resource-intensive but could resolve the ambiguity in spectroscopic rotation measurements. With a separation of 0.1, NLTT 33370 AB is unfortunately not spatially resolvable by Chandra or any planned X-ray observatories — unless its orbit turns out to be highly eccentric.

New spatially-resolved observations of NLTT 33370 AB will advance the understanding of habitable exoplanets around low-mass stars because of this system’s twofold importance: it is a benchmark for measurements of both fundamental stellar properties and magnetic activity at the bottom of main sequence. The former affect the derived properties of exoplanets themselves, and the latter may strip the atmospheres of close-in planets or otherwise render them inhospitable to life.

We thank Jan Forbrich for sharing preliminary VLBI results and helpful suggestions. P. K. G. W and E. B. acknowledge support for this work from the National Science Foundation through Grant AST-1008361. Z. K. B.-T. acknowledges support from the Torres Fellowship for Exoplanetary Research. The VLA is operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and NASA’s Astrophysics Data System. This research has made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASI Science Data Center (ASDC), Italy. This paper makes use of data from the MEarth Project, which is a collaboration between Harvard University and the Smithsonian Astrophysical Observatory. The MEarth Project acknowledges funding from the David and Lucile Packard Fellowship for Science and Engineering and the National Science Foundation under grants AST-0807690, AST-1109468, and AST-1004488 (Alan T. Waterman Award), and a grant from the John Templeton Foundation. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Facilities: Chandra, Karl G. Jansky Very Large Array, MEarth, MMT, Swift.

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