THE FIRST MILLIMETER DETECTION OF A NON-ACCRETING ULTRACOOL DWARF

TVLM 513 was observed with ALMA on UT date 2015 April 03 (proposal 2013.1.00293.S, PI: Casewell) using the "band 3" receivers (∼100 GHz observing frequency) in the standard wideband continuum mode. The correlator recorded data for two sidebands centered on 91.46 GHz (lower sideband, LSB) and 103.49 GHz (upper sideband, USB), each having a total bandwidth of 4 GHz. The observations lasted just under 4 hr, with the total on-source integration time being 2.15 hr. Full Stokes correlations were not obtained, precluding a polarimetric analysis.

Calibrated visibilities and a preliminary image were provided to us by the European ALMA Regional Center (EARC) after reduction by their staff. We examined the data and identified no lingering problems. Figure 1 shows the result of our re-imaging of the full data set, using a somewhat larger field of view than the EARC analysis.

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Using the astrometric parameters reported by Forbrich et al. (2013), the expected position of TVLM 513 at the time of the ALMA observations was R.A. = 15:01:08.1463, decl. = +22:50:01.224, with an approximate uncertainty of 1 mas. In the ALMA image we find a source that is 6.2σ above the background noise at a position of R.A. = 15:01:08.139, decl. = +22:50:01.14. Fitting a source model to the image, we measure a flux density of 56 ± 12 μJy and a positional uncertainty of 0.5 arcsec, where the uncertainty on the flux density is higher than the image rms (9 μJy) because it includes covariances with the source positions. The positions are consistent to 0.2σ, and we identify this source with TVLM 513.

We imaged the two ALMA sidebands separately to assess the spectral index of TVLM 513 at millimeter wavelengths. Our results are summarized in Table 1. In the LSB image, with an effective frequency of 91.46 GHz, the flux density of the source is 66 ± 8 μJy. In the USB image, with an effective frequency of 103.49 GHz, it is 31 ± 18 μJy. The rms of the latter image is ∼12 μJy, so that the signal is at the 2.6σ level. The spectral index inferred from the ALMA data alone is ${\alpha }_{\mathrm{mm}}\approx -5\pm 4,$ largely unconstrained but inconsistent at the 97% confidence level with thermal emission, defined here as α ≥ 1.5 (Andrews & Williams 2005).

We extracted light curves from the calibrated LSB, USB, and band-averaged ALMA visibilities using the technique described in Williams et al. (2013), subtracting the lone additional source visible in the image from the visibilities. The resulting raw light curves have a sampling cadence of 2 s. The top panel of Figure 2 shows the LSB light curve after averaging to a bin size of 102 s, splitting bins across individual scans. We are unable to find conclusive evidence for variability, although there is a possible flux density increase around BMJD 57115.265 that we discuss below.

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We also analyzed unpublished archival observations of TVLM 513 performed with the Karl G. Jansky Very Large Array (VLA). TVLM 513 was observed at three frequencies on UT date 2010 December 16 while the VLA upgrade was being performed (project ID TRSR0033, PI: Hallinan). Three sequential observations were performed in K band (∼20 GHz), C band (∼6 GHz), and L band (∼1.5 GHz) over the course of 1 hr. In the K band observation, data were taken in two basebands with center frequencies of 19.0 and 20.5 GHz and bandwidths of 1.024 GHz each. The C band observation used the same configuration with center frequencies of 4.8 and 7.4 GHz. The L band observation had two basebands of 0.512 MHz bandwidth configured contiguously, resulting in an effective spectral window of width 1.024 GHz centered at 1.58 GHz. In all cases individual spectral channels were 2 kHz wide. 3C 286 was the bandpass and flux density calibrator and 4C 23.41 was the complex gain calibrator.

We calibrated the data using standard procedures in the CASA software system (McMullin et al. 2007). We used the aoflagger tool to automatically flag radio-frequency interference (Offringa et al. 2010, 2012) and set the flux density scale using the preliminary, 2010 version of the scale defined by Perley & Butler (2013). From fitting a point-source model to images generated from data in the three bands, we obtain the flux densities reported in Table 1. The flux density measurement in L band is marginal but consistent with prior observations (Osten et al. 2006).

We observed TVLM 513 using IO:O on the fully robotic 2-m Liverpool Telescope (LT) on La Palma, on the night of 2015 August 5th (UT). We used the Sloan Digital Sky Survey (SDSS) i' filter with exposure times of 60 s. We bias-subtracted the images using the CCD overscan region and used twilight sky flats for flat field correction.

We extracted fluxes for TVLM 513 and four nearby comparison stars using apertures whose sizes were scaled to 1.6 times the measured seeing in each image. Average seeing was 2'', and the seeing ranged between 16 and 4''. Conditions were photometric and all data were taken below an airmass of 1.15. We used the brightest two comparison stars to correct the data for transparency variations. We plot the LT optical light curve in the lower panel of Figure 2.

We measured the time of optical maximum in the LT light curve to be BMJD = 57150.049 ± 0.001 by fitting a sinusoid to the data, constraining the period to match the value determined by Wolszczan & Route (2014). The combined radio/optical ephemeris described in that work predicts an optical maximum at BMJD = 57150.028 (A. Wolszczan 2015, private communication), ∼90° out of phase with our observations.

The ≳100 Myr age implied by the lack of Li absorption in TVLM 513 (Martín et al. 1994; Reid et al. 2002) is significantly longer than typical disk dissipation timescales of ∼10 Myr (although there is evidence that disk lifetimes are inversely correlated with [sub]stellar mass; e.g., Williams & Cieza 2011). Furthermore, TVLM 513 does not have reported IR excesses, and the spectral index of the ALMA data is not consistent with the α ≈ 2 expected from thermal (photospheric or disk) emission (Reid & Menten 1997; Andrews & Williams 2005). We therefore reject this origin for the ALMA emission.

Topka & Marsh (1982) consider the relationship between X-ray emission and free–free radio emission from the active M4+M5 binary EQ Peg. Assuming parameters appropriate for active low-mass stars, they find that ${S}_{\nu ,\mathrm{ff}}=({10}^{6}\ \mathrm{Jy}){f}_{X},$ where f_X is measured over the 0.2–4 keV band in units of erg s⁻¹ cm⁻². Applying TVLM 513's measured X-ray flux of ∼6 × 10⁻¹⁶ erg s⁻¹ cm⁻² (Berger et al. 2008) and ignoring minor factors such as the chosen X-ray band, we estimate a negligible free–free contribution of S_ν,ff ≈ 1 nJy. While this value is calculated for centimeter wavelength emission, the flat spectrum associated with optically thin free–free emission implies that it holds at mm wavelengths as well.

ECMI emission occurs predominantly at the cyclotron frequency ${\nu }_{c}={eB}/2\pi {m}_{e}c,$ requiring the presence of a magnetic field of ≳34 kG strength to explain the millimeter detections. This would be an order of magnitude stronger than any directly measured magnetic fields in low-mass stars (Reiners & Basri 2007, 2010; Morin et al. 2010) and exceeds theoretical limits on the surface field strengths associated with fully convective dynamos of ∼3 kG (from energy equipartition with convective motions; Feiden & Chaboyer 2014). Therefore we reject an ECMI origin for this emission.

Having eliminated these other options, we conclude that the observed ALMA emission is synchrotron emission associated with TVLM 513's magnetic activity, as detailed below. Our results represent one of a handful of detections of such emission from single dwarfs at ALMA frequencies (84–950 GHz), ultracool or not (Bower et al. 2003). If additional observations constrain the brightness temperature of the millimeter emission to be implausibly large for the gyrosynchrotron process (e.g., detection of a rapid, bright burst), the previous paragraph implies that non-ECMI coherent processes such as the antenna mechanism (e.g., Komesaroff 1970) or plasma emission (e.g., Ginzburg & Zhelezniakov 1958) should be considered.

In Figure 3 we assemble a composite centimeter-to-millimeter spectrum of TVLM 513 from available simultaneous and quasi-simultaneous data. All published radio observations of TVLM 513 lie within this frequency range, with the exception of a 2.5σ upper limit of S_ν < 795 μJy at 325 MHz (Jaeger et al. 2011). TVLM 513 is variable at the ∼30% level over long (≳month) timescales (Antonova et al. 2010), so that inferences about the radio spectrum made by combining non-contemporaneous observations should be treated cautiously. The results of Osten et al. (2006) and the VLA analysis we present both suggest a spectrum peaking between 2 and 4 GHz with α ≈ −0.4 at higher frequencies. In constrast, Hallinan et al. (2007) report quasi-simultaneous observations at 4.88 and 8.44 GHz indicating a rising spectrum. However, their observations were made one day apart, so that variability may play a role in this finding. Furthermore, the flux densities they report average over several bright, polarized flares that are significantly brighter at the higher frequency. Using their Figure 3 to estimate the bias caused by these flares, we infer that the non-flaring spectrum in their observations has α ≈ −0.1.

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In Figure 3 we show two possible models for the broadband spectrum of TVLM 513. We emphasize that these examples connect observations made years apart and so should not be used for quantitative analysis. In orange, we show a standard gyrosynchrotron model based on the equations of Dulk (1985), fit to our ALMA data and the measurements of Osten et al. (2006). Here we fixed B = 100 G and the electron energy spectral index δ = 2, where ${dN}/{dE}\propto {E}^{-\delta },$ which leads to α = −0.5 in the optically thin limit. Our ALMA data are consistent with a model in which the optically thin portion of spectrum extends all the way to the ALMA band. In this picture there is a hint of a spectral cutoff in the ALMA band. From the ALMA measurements, however, we calculate a ∼12% chance that ${\alpha }_{\mathrm{mm}}\gt -0.5,$ i.e., that the millimeter spectrum is at least as flat as that observed at centimeter wavelengths. Fixing the known distance of TVLM 513 and the properties of our LSB detection, we infer a brightness temperature ${T}_{{\rm{B}}}\sim {({10}^{6.4}\;{\rm{K}})(r/{R}_{{\rm{J}}})}^{-2},$ where r is the characteristic length of the emitting region (Dulk 1985). This is consistent with gyrosynchrotron emission in the optically thin regime unless r ≲ 0.003 ${R}_{{\rm{J}}}$.

Hallinan et al. (2006, 2008) have suggested that the broadband, non-flaring radio emission of ultracool dwarfs may be due to the ECMI rather than the gyrosynchrotron process, if there is continuous particle acceleration across a range of magnetic field strengths and propagation effects depolarize the emission. Osten et al. (2009) have used the plasma properties inferred from multi-band observations to argue against this interpretation for the binary LP 349–25 AB, and Ravi et al. (2011) analyze the broadband (5–24 GHz) radio spectrum of DENIS-P J104814.9–395604 to argue similarly. As argued above, our detection challenges this interpretation for TVLM 513 as well. To represent the sort of spectrum that might result from such an emission mechanism, in Figure 3 we show a version of the spectrum of Uranus' kilometric radiation (UKR) as shown by Zarka (1998), where both the emission frequencies and luminosities have been scaled arbitrarily to overlap the VLA measurements reported in Table 1. While this is just one possible example, it is representative of solar system observations (Zarka 1998). Although the preexisting data could have been consistent with such a spectral shape, the ALMA data exclude it.

We do not find statistically significant evidence for variability in the millimeter emission. While the data show a ∼15-minute period of elevated emission around BMJD = 57115.265, we cannot exclude the possibility that this elevated period is a noise fluctuation, given the duration of the observation and measurement scatter. A simple likelihood ratio test comparing a constant model and one with an exponentially fading flare yields an empirical p-value of ∼7% (∼1.8σ); i.e., in about 7% of simulated realizations of the constant model, the likelihood ratio of the best-fit flaring and constant models is least as high as that observed. Therefore the constant model cannot be rejected with confidence. An alternative Bayes factor analysis yields compatible results. The best-fit flare model achieves a peak flux density ∼220 μJy above the quiescent level.

Confidence in this possible signal could be increased if it were periodic and observed multiple times, but the ALMA observation spanned only ∼1.3 rotations of TVLM 513 and the timing of the putative event prevents this check. If the flare is real, it phases up with the maxima of TVLM 513's optical variability as revealed by our LT observations (Figure 2). Additional ALMA observations covering multiple rotation periods, paired with contemporaneous optical monitoring, could easily resolve whether the millimeter emission is periodically variable and how it might phase relative to the optical emission. If the possible variation is real and periodic, it would be out of phase with the polarized cm bursts, which differ in phase from the optical maxima by 0.41 ± 0.02 of a period (Wolszczan & Route 2014).