# Unlocking the Origins of Ultracool Dwarf Radio Emission

A. G. Hughes  Department of Physics and Astronomy, University of British
Columbia, 6224 Agricultural Rd., Vancouver, BC V6T 1Z1, Canada  A. C. Boley
Department of Physics and Astronomy, University of British Columbia, 6224
Agricultural Rd., Vancouver, BC V6T 1Z1, Canada  R. A. Osten  Space Telescope
Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Center for
Astrophysical Sciences, Johns Hopkins University, Baltimore, MD 21218, USA  J.
A. White National Radio Astronomy Observatory, 520 Edgemont Rd.,
Charlottesville, VA, 22903, USA  Jansky Fellow of the National Radio Astronomy
Observatory  M. Leacock  Department of Physics and Astronomy, University of
British Columbia, 6224 Agricultural Rd., Vancouver, BC V6T 1Z1, Canada

###### Abstract

Empirical trends in stellar X-ray and radio luminosities suggest that low mass
ultracool dwarfs (UCDs) should not produce significant radio emission. Defying
these expectations, strong non-thermal emission has been observed in a few
UCDs in the $1{-}10$ GHz range, with a variable component often attributed to
global aurorae and a steady component attributed to other processes such as
gyrosynchrotron emission. While both auroral and gyrosynchrotron emission peak
near the critical frequency, only the latter radiation is expected to extend
into millimeter wavelengths. We present ALMA 97.5 GHz and VLA 33 GHz
observations of a small survey of 5 UCDs. LP 349-25, LSR J1835+3259, and NLTT
33370 were detected at 97.5 GHz, while LP 423-31 and LP 415-20 resulted in
non-detections at 33 GHz. A significant flare was observed in NLTT 33370 that
reached a peak flux of $4880\pm 360\,\mu Jy$, exceeding the quiescent flux by
nearly an order of magnitude, and lasting 20 seconds. These ALMA observations
show bright 97.5 GHz emission with spectral indices ranging from
$\alpha=–0.76$ to $\alpha=–0.29$, suggestive of optically thin gyrosynchrotron
emission. If such emission traces magnetic reconnection events, then this
could have consequences for both UCD magnetic models and the atmospheric
stability of planets in orbit around them. Overall, our results provide
confirmation that gyrosynchrotron radiation in radio loud UCDs can remain
detectable into the millimeter regime.

##  1 Introduction

Ultracool dwarfs (UCDs) are brown dwarfs and low-mass M stars of spectral type
later than M7. M dwarfs are the most common stellar objects in the Milky Way
(Henry et al., 2006), yet because they are so faint, UCDs are difficult to
study. They are also not expected to behave in the same way as more massive
M-type stars, which are notorious for their flaring and variability (Davenport
et al., 2012). Unlike more massive stars, UCDs are fully convective and lack a
tachocline, or shearing layer between convective and radiative regions
(Chabrier & Baraffe, 2000). Since the tachocline is thought to play a crucial
role in the solar dynamo, it was long assumed that UCDs would be unable to
generate solar strength magnetic fields and corresponding radio emission
(Mohanty et al., 2002).

Observations of magnetically active F through early-M stars show a clear trend
known as the Güdel-Benz relation (GBR), a tight correlation between the X-ray
and radio luminosities (Guedel & Benz, 1993). The relation is described well
by a single power law and extends through 10 orders of magnitude, suggesting a
common emission mechanism. If UCDs were to follow the GBR, most would have no
detectable radio emission whatsoever. This makes the detection of some UCDs at
radio frequencies particularly mysterious. Highly sensitive observatories such
as the NSF’s Karl G. Jansky Very Large Array (VLA) and Arecibo have revealed
that about 10% of UCDs are bright at radio frequencies, with $1{-}10$ GHz
emission exceeding the GBR by up to four orders of magnitude (Berger, 2006;
Antonova et al., 2013; Route & Wolszczan, 2016; Lynch et al., 2016). Strong
magnetic fields up to kG strength have been measured in UCDs (Reiners & Basri,
2006; Reiners, 2009; Reiners & Basri, 2010a), and inferred from radio emission
(e.g. Kao et al., 2018). The overall radio detection rate of $10\%$ curiously
increases to nearly $50\%$ for objects with
$\textit{v}\,sin\textit{i}>20~{}km\,s^{-1}$. The reason for this switch is
unclear and the $50\%$ detection rate is determined from a sample of ${<}\,20$
targets (McLean et al., 2012).

UCDs occupy the mass range in the transition between giant planets and stars,
and observations indicate that radio active UCDs are capable of behaving like
either one (Berger et al., 2001; Berger, 2006; Hallinan et al., 2006; McLean
et al., 2012; Williams et al., 2015). Auroral emission prompted by the
electron cyclotron maser instability (ECMI) (Williams et al., 2014; Hallinan
et al., 2015; Kao et al., 2016; Pineda et al., 2017) is akin to what is
observed in all Solar System planets possessing a magnetic field (Zarka et
al., 2001), whereas synchrotron and gyrosynchrotron radiation are responsible
for incoherent millimeter emission from the Sun and other stars (Dulk, 1985;
Güdel, 2002; Bastian et al., 1998; Osten, 2008; Osten et al., 2009).

Bright, pulsed emission is more characteristic of aurorae, although Hallinan
et al. (2006) suggest that auroral emission could become depolarized during
propagation through the magnetosphere. In contrast, quasi-quiescent emission
(i.e. steady emission with small variations in magnitude) is largely
consistent with gyrosynchrotron radiation (Berger, 2002, 2006). Early radio
detections of UCDs were in the $1-10\,\,GHz$ range, where both emission
mechanisms are expected to peak for most UCD magnetic field strengths. These
first detections often showed both a quiescent component, attributed to
synchrotron or gyrosynchrotron emission, and a bursting component, usually
attributed to ECMI (Liebert et al., 1999; Burgasser & Putman, 2005; Berger,
2006; Hallinan et al., 2008a; Williams & Berger, 2015). It was unclear from
these detections alone whether the presumed gyrosynchrotron component would
extend to higher radio frequencies. However, the first detection of a UCD by
Williams et al. (2015) at millimeter wavelengths confirms the presence of
optically thin gyrosynchrotron radiation and measures the spectral index of
the emission in this regime.

While auroral emission and gyrosynchrotron radiation can both be present in
the same object, gyrosynchrotron radiation in the optically thin regime can
most effectively be characterized using observations at high radio
frequencies. In particular, gyrosynchrotron radiation will dominate between
$20-100$ GHz for typical UCD magnetic field strengths, while ECMI emission
becomes unlikely for frequencies above the fundamental frequency (Melrose &
Dulk, 1982; Treumann, 2006). For lower magnetic field strengths, this
frequency range will be shifted to lower frequencies as well. The first
detection of the non-accreting UCD TVLM 513-46546 in this range could
consequently not be attributed to ECMI, leaving optically thin gyrosynchrotron
radiation as the presumed emission mechanism (Williams et al., 2015).

Each emission mechanism traces different underlying magnetic processes and
field configurations. The presence of auroral emission could suggest a global
largely dipolar magnetic field (Kao et al., 2016; Pineda et al., 2017;
Berdyugina et al., 2017), in which the co-rotation breakdown between
magnetosphere plasma and the UCD magnetic field enables electrons to drift
along electromagnetic currents (Cowley & Bunce, 2001). Gyrosynchrotron
emission, per Williams et al. (2014), could be produced by reconnection events
resulting from a non-axisymmetric field topology at higher-order field
components. Both situations can occur simultaneously, with a global dipolar
magnetic field producing auroral emission and localized reconnection events
producing gyrosynchrotron radiation, potentially explaining the apparent
concurrence of both mechanisms in radio bright UCDs.

UCDs are likely to have a high occurrence rate of terrestrial planets
(Dressing & Charbonneau, 2015). This presents a different possibility; planets
in orbit around UCDs may be capable of inducing auroral radio emission in an
analogous way to Io around Jupiter (Turnpenney et al., 2018). However, should
gyrosynchrotron emission and the corresponding reconnection events also be
present, then the stability of planetary atmospheres could be threatened by
the outgoing energetic particle flux (Segura et al., 2010; Tilley et al.,
2017).

In this paper, we present high radio frequency observations ($30-100$ GHz) of
five UCDs. Prior to this work, the only non-accreting UCD to be detected in
this frequency range was TVLM 513-46546, which Williams et al. (2015) found to
have 95 GHz emission consistent with gyrosynchrotron radiation. We find that
two of our five targets are radio quiet over the course of the observations,
and place upper flux limits on their emission. The detected UCDs represent the
second through fourth non-accreting UCDs found to emit at millimeter
wavelengths.

Property | LP 349-25 AB | LSR J1835$+$3259 | NLTT 33370 | LP 415-20 | LP 423-31
---|---|---|---|---|---
Spectral Type | M8[1] | M8.5[5] | M7[7] | M9.5[10] | M711
$M_{tot}$ ($M_{\odot}$) | $0.120^{+0.008[2]}_{-0.007}$ | $0.05\pm 0.0038^{[6]}$ | $0.179^{+0.055[8]}_{-0.062}$ | $0.09\pm 0.06$ | $0.01\pm 0.003^{[12]}$
Distance (pc) | 10.3$\pm 1.70^{[3]}$ | $5.67\pm 0.02^{[5]}$ | $16.39\pm 0.75^{[7]}$ | $21\pm 5^{[10]}$ | $10.7\pm 0.3^{[12]}$
Age (Myr) | - | $22\pm 4^{[6]}$ | $\sim 30-200^{[8]}$ | - | -
$T_{eff}$ (K) | - | $2800\pm 30^{[6]}$ | $3200\pm 500^{[8]}$ | $2600\pm 100^{[10]}$ | -
$3100\pm 500^{[8]}$ | $2400\pm 100^{[10]}$
$\textit{v}\,sin\textit{i}$ $(km~{}s^{-1})$ | $55\pm 2^{[4]}$ | $50\pm 5^{[6]}$ | $45\pm 5^{[9]}$ | $44\pm 4^{[4]}$ | $9.0\pm 2^{[11]}$
$83\pm 3^{[4]}$ | $36\pm 4^{[4]}$
Obs Frequency (GHz) | 97.5 | 97.5 | 97.5 | 97.5 | 33.0
Flux (mJy) | $70\pm 15$ | $114\pm 21$ | $604\pm 61$ | $<20$ | $<30$
Table 1: Properties of ultracool dwarfs presented in this work, including
combined spectral type, total mass ($M_{tot}$), stellar distance, stellar age,
effective temperature ($T_{eff}$), $\textit{v}\,sin\textit{i}$, frequency of
the observations (GHz), and observed flux (mJy).
References: [1] Gizis et al. (2000) [2] Konopacky et al. (2010) [3] Schmidt et
al. (2007) [4] Konopacky et al. (2012) [5] Reid et al. (2003) [6] Berdyugina
et al. (2017) [7] Lépine et al. (2009) [8] Schlieder et al. (2014) [9] McLean
et al. (2011) [10] Siegler et al. (2003) [11] Reiners & Basri (2010b) [12]
Cruz et al. (2003).

##  2 Observations and Results

In this section, we discuss each of the five targets used in this study along
with the corresponding observations. The results and target list are reported
in Table 1.

LP 349-25, LSR J1835$+$3259, and NLTT 33370 are detected and exhibit bright
radio emission at 97.5 GHz. All three of these targets were also detected at
lower radio frequencies in previous studies (e.g., Phan-Bao et al., 2007;
Hallinan et al., 2008b; McLean et al., 2011). The images of the detected
sources are given in Figure 1. In contrast, the observations of LP 423-31 and
LP 415-20 yield null detections at 97.5 GHz and 33 GHz, respectively. LP
423-31 had been previously observed at 8.46 GHz, which also resulted in a null
detection, while there are no previous radio observations of LP 415-20. For
both targets, we use the non-detections to place upper limits on the radio
fluxes.

Figure 1: All detected UCDs. The visibilities are phase-shifted to account for
the proper motion. LP 349-25 has peak flux of 70 $\mu Jy$ with RMS of 9 $\mu
Jy$, LSR J1835+3259 has a peak flux of 114 $\mu Jy$ with RMS 18 $\mu Jy$, and
NLTT 33370 has a peak quiescent flux of 604 $\mu Jy$ with RMS 7.3 $\mu Jy$.
The synthesized beam is denoted by the black ellipse in the bottom left of
each image.

###  2.1 LP 349-25

LP 349-25 is a spectroscopic binary of spectral types M8 and M9, with rapid
rotation speeds of $55\pm 2$ and $83\pm 3~{}\rm km~{}s^{-1}$, respectively
(Konopacky et al., 2012). It was previously detected at 8.46 GHz by Phan-Bao
et al. (2007) at a flux density of $365\pm 16~{}\mu Jy$, at $8.3$ and $5$ GHz
at flux densities of $365\pm 16~{}\mu Jy$ and $329\pm 38~{}\mu Jy$,
respecively by Osten et al. (2009) and by McLean et al. (2012) at $323\pm
14\,\mu Jy$, also at 8.46 GHz.

The archival Atacama Large
Millimetre/Submillimeter Array (ALMA) Cycle 4 observations
(ID 2016.1.00817.S, PI Williams) were centered on J2000 coordinates RA = 00h
27m 55.99s $\delta$ = +22d 19’ 32.80”. The data were taken in 3 execution
blocks (EBs) from 2016 October 22 to 2016 November 6 for a total of 2 hr on-
source (2.9 hr including overhead). There were 45 antennas used with baselines
ranging from 15 m to 500 m.

The Band 3 observations have a total bandwidth of 8 GHz split among 4 spectral
windows (SPW). Each SPW has $128\times 15.625$ MHz channels. The SPWs are
centred at 90.4 GHz, 92.4 GHz, 102.5 GHz, and 104.5 GHz, giving an effective
continuum frequency of 97.5 GHz. The data were reduced using CASA 5.4.1
(McMullin et al., 2007), which included water vapor radiometer (WVR)
calibration; system temperature corrections; flux and bandpass calibration
with quasar J0423-0120; and phase calibration with quasar J0431$+$1731\. The
average precipitable water vapor (PWV) was 2.08 mm throughout the
observations.

We generated CLEANed images using the CASA task tclean, natural weighting down
to a threshold of the RMS noise, and a cell size of $\frac{1}{10}$ the beam
size. These ALMA 97.5 GHz observations achieve an RMS sensitivity of
$9~{}\upmu\textrm{Jy}~{}\textrm{beam}^{-1}$ as measured from the CLEANed image
away from the source. The size of the resulting synthesized beam is $0\farcs
82\times 0\farcs 62$ at a position angle of $28.3^{\circ}$, corresponding to
$7$ au at the system distance of $10.3\pm 1.70$ pc (Schmidt et al., 2007). We
use the CASA task uvmodelfit to fit a point source to the visibilities, we
find a best fit flux of $70\pm 9\,\mu Jy$. The data were subsequently split by
observing scan, and both the flux density and RMS of each scan were taken
using uvmodelfit to generate a time series. No flaring activity was seen over
the course of the observations.

###  2.2 LSR J1835$+$3259

LSR J1835$+$3259 is a brown dwarf of spectral type M8.5 (Reid et al., 2003)
with a rapid rotation speed of $\textit{v}\,sin\textit{i}=50\pm
5\rm~{}km~{}s^{-1}$ known to be variable across multiple wavelengths. It has
been detected at 8.44 GHz with both quiescent, largely unpolarized emission
and $100\%$ circularly polarized bursting emission, with an average flux
density of $722\pm 15\,\mu Jy$ and variable emission reaching up to $2500\,\mu
Jy$ (Hallinan et al., 2008b).

The archival ALMA Cycle 4 observations
(ID 2016.1.00817.S, PI Williams were centered on J2000 coordinates RA = 18h
35m 37.88s $\delta$ = +32d 59’ 53.31”. The data were taken in 2 EBs from 2016
November 6 to 2016 December 1 for a total of 1 hr on-source (2 hr including
overhead). There were 40 antennas used with baselines ranging from 15 m to 460
m.

The Band 3 observations have a total bandwidth of 8 GHz split among 4 SPWs.
Each SPW has $128\times 15.625$ MHz channels. The SPWs are centered at 91.5
GHz, 93.4 GHz, 101.5 GHz, and 103.5 GHz, giving an effective continuum
frequency of 97.5 GHz. The data were reduced using CASA 4.7.2, which included
WVR calibration; system temperature corrections; flux and bandpass calibration
with quasar J2025$+$3343; and phase calibration with quasar 3 J1848$+$3219\.
The average PWV was 2.53 mm throughout the observations.

We generated CLEANed images using the CASA task tclean, natural weighting down
to a threshold of the RMS noise, and a cell size of $\frac{1}{10}$ the beam
size. These ALMA 97.5 GHz observations achieve an RMS sensitivity of
$18~{}\upmu\textrm{Jy}~{}\textrm{beam}^{-1}$ as measured from the CLEANed
image away from the source. The size of the resulting synthesized beam is
$2\farcs 85\times 1\farcs 18$ at a position angle of $-41.8^{\circ}$,
corresponding to $12$ au at the system distance of $5.6875\pm 0.0005\,pc$
(Gaia Collaboration et al., 2018). We use the CASA task uvmodelfit to fit a
point source to the visibilities, we find a best-fit flux of $114\pm 18\,\mu
Jy$. The data were subsequently split by observing scan, and both the flux
density and RMS of each scan were taken using uvmodelfit to generate a time
series. No flaring activity was seen over the course of the observations.

###  2.3 NLTT 33370

NLTT 33370AB (originally LPSM J1314+1320) is a resolved binary of combined
spectral type M7.0e (Law et al., 2006; Lépine et al., 2009; Forbrich et al.,
2016). This magnetically active system has been well-studied relative to other
UCDs due to its brightness. Although the system is binary, we refer to it as
NLTT 33370 for ease of reading.

NLTT 33370 has been detected with short, polarized bursts and quiescent,
largely unpolarized radio emission, both of which are brighter than that
observed in any other UCD. Quasi-quiescent emission was detected with the VLA
at 8.46 GHz with a flux density of $1156\pm 15\,\,\mu Jy$ and at 22.5 GHz with
a flux density of $763\pm 84\,\,\mu Jy$ (McLean et al., 2011). It was
subsequently detected in a multi-wavelength study by Williams et al. (2015),
exhibiting both quasi-periodic steady emission and flaring radio emission.
These studies found that the steady emission was circularly polarized and
modulated sinusoidally with a period of $3.89\pm 0.05\,hr$. Williams et al.
(2015) further found an additional unpolarized component in one of their two
VLA monitoring campaigns. The observations are interpreted to include a
combination of flaring due to the ECMI and stable emission due to
gyrosynchrotron radiation.

The archival ALMA Cycle 2 observations
(ID 2013.1.00976.S, (PI Williams) were centered on J2000 coordinates RA = 13h
14m 20.38s $\delta$ = +13d 18’ 58.34”. The data were taken in 4 EBs from 2015
June 10 to 2015 June 12 for a total of 2.7 hr on-source (4.8 hr including
overhead). There were 38 antennas used with baselines ranging from 25 m to 820
m.

The Band 3 observations have a total bandwidth of 8 GHz split among 4 SPWs,
each with $64\times 31.25$ MHz channels. The SPWs are centred at 90.5 GHz,
92.4 GHz, 102.5 GHz, and 104.5 GHz, giving an effective continuum frequency of
97.5 GHz. The data were reduced using CASA 4.7.0, which included WVR
calibration; system temperature corrections; flux and bandpass calibration
with quasar J1229$+$0203; and phase calibration with quasar J1347$+$1217\. The
average PWV was 0.71 mm throughout the observations.

We generated CLEANed images using the CASA task tclean, natural weighting down
to a threshold of the RMS noise, and a cell size of $\frac{1}{10}$ the beam
size. These ALMA 97.5 GHz observations achieve an RMS sensitivity of
$9~{}\upmu\textrm{Jy}~{}\textrm{beam}^{-1}$ as measured from the CLEANed image
away from the source. The size of the resulting synthesized beam is $1\farcs
58\times 1\farcs 04$ at a position angle of $-44.8^{\circ}$, corresponding to
$22$ au at the system distance of $16.39\pm 0.75$ pc (Lépine et al., 2009). A
10-second flare (Fig. 4) was also captured during these observations, with a
peak flux of $4880\pm 360\,\mu Jy$ from the CLEANed image of the flare only.
We use the CASA task uvmodelfit to fit a point source to the visibilities, we
find a best-fit flux of $604\pm 7.3\,\mu Jy$ for the quiescent emission.

###  2.4 LP 415-20AB

LP 415-20AB is a resolved binary with spectral types M7(A) and M9.5(B) and
high $\textit{v}\,sin\textit{i}$ of $40\pm 5$ and $37\pm
4\rm~{}km\,~{}s^{-1}$, respectively (Konopacky et al., 2012). The presence of
two UCDs with rapid rotation suggests that this system should be a radio
emitter; however, we see no evidence of emission throughout the duration of
our observations.

The ALMA Cycle 6 observations (ID 2018.1.01088.S, PI Hughes) presented here
were taken in 3 EBs from 2019 January 8 to 2019 January 21 for a total of 2 hr
on-source (2.7 hr including overhead). There were 58 antennas used with
baselines ranging from 15 m to 500 m.

These Band 3 observations have a total bandwidth of 8 GHz split among 4 SPWs,
each with $128\times 15.625$ MHz channels. The SPWs are centred at 90.5 GHz,
92.4 GHz, 102.5 GHz, and 104.5 GHz, giving an effective continuum frequency of
97.50 GHz. The data were reduced using CASA 5.4.1, which included WVR
calibration; system temperature corrections; flux and bandpass calibration
with quasar J0423-0120; and phase calibration with quasar J0431$+$1731\. The
PWV ranged from 2.9 mm to 5.9 mm throughout the observations.

We generated CLEANed images using the CASA task tclean, natural weighting down
to a threshold of the RMS noise, and a cell size of $\frac{1}{10}$ the beam
size. These ALMA 97.5 GHz observations achieve an RMS sensitivity of
$6.7~{}\upmu\textrm{Jy}~{}\textrm{beam}^{-1}$ as measured from the CLEANed
image away from the source. The size of the resulting synthesized beam is
$3\farcs 26\times 2\farcs 91$ at a position angle of $30.1^{\circ}$,
corresponding to $65$ au at the system distance of 21 pc. We report a 97.5 GHz
non-detection of LP 415-20AB with a $3{\sigma}$ upper level flux limit of 20
$\mu Jy$ measured from the CLEANed image.

###  2.5 LP 423-31

LP 423-31 is an M7 star with a relatively low rotation rate of
$9\,\,km~{}s^{-1}$ and strong magnetic field of $3500^{+400}_{-600}$ G
(Reiners & Basri, 2010b; McLean et al., 2011). Berger (2006) placed an upper
flux limit of $<39~{}\mu Jy$ using VLA observations at 8.46 GHz. This star is
expected to be radio silent given the existing trends and models in UCD radio
emission, but confirmation is needed.

The observations were taken during the VLA Semester 18B (ID VLA-18B-241, PI
Hughes) over 2 scheduling blocks (SBs) on 2018 December 12 for a total of 12.8
minutes on-source (35.5 min including overhead). Data were acquired with the
array in the C antenna configuration, with 26 antennas and baselines ranging
from 35 m to 3400 m.

The instrument configuration uses the Ka band receiver with a correlator setup
consisting of $7808\times 1$ MHz channels for a total bandwidth of 7.8 GHz.
Four separate basebands are included with rest frequency centres at 30 GHz, 32
GHz, 34 GHz, and 36 GHz giving an effective continuum frequency of 33.0 GHz.
The quasar J0750$+$1231 was used for gain and phase calibration and quasar
3C286 was used as a bandpass and flux calibrator. Data were reduced using the
CASA 4.7.2 pipeline, which included bandpass, flux, and phase calibrations.

We generated CLEANed images using the CASA task tclean, natural weighting down
to a threshold of the RMS noise, and a cell size of $\frac{1}{10}$ the beam
size. These VLA 33 GHz observations achieve an RMS sensitivity of
$10~{}\upmu\textrm{Jy}~{}\textrm{beam}^{-1}$ as measured from the CLEANed
image away from the source. The size of the synthesized beam is $0\farcs
86\times 0\farcs 72$ at a position angle of 40.7∘. The beam size corresponds
to $8$ au at the system’s distance of $10.3\pm 1.70$ pc (Konopacky et al.,
2012). We report a 33 GHz non-detection of LP 423-31 with a $3\sigma$ upper
level flux limit of $30~{}\mu Jy$ measured from the CLEANed image.

The lack of emission at high radio frequencies of a slowly rotating UCD
observed to be radio-quiet at lower frequencies is consistent with emerging
trends in UCD radio emission that indicate rapid rotators are more likely to
be radio bright (McLean et al., 2011; Pineda et al., 2017). Our results show
that UCDs active at 1-8 GHz may be likely to be bright at millimetre
wavelengths as well.

##  3 Discussion

The five UCDs presented in this work have a range of properties, including
low/high $\textit{v}\,sin\textit{i}$ value, binarity, and detection/non-
detection at low radio frequencies, making them a good selection for probing
trends in high radio frequency emission. LP 349-25, LSR J1835$+$3259, NLTT
33370, and LP 423-31 have all been observed at lower radio frequencies. LSR
J1835$+$3259, LP 349-45 and NLTT 33370 have been observed multiple times in
the $1-10$ GHz range. In all cases the flux densities were consistent between
observations. LP 423-31, however, has been detected in some 8.46 GHz
observations (Stelzer et al. in prep) and not detected in others (Berger,
2006). We find that all three UCDs that are consistently active at low radio
frequencies are also active at high radio frequencies, where ECMI emission is
cut off. Furthermore, if the emission is largely due to ECMI, then there could
be some level of circular polarization present in the ALMA data. In principle,
this would provide an additional metric to disentangle the emission
mechanisms. Unfortunately, these data were taken in earlier ALMA cycles when
polarization calibration was unreliable so no conclusive determination on the
presence of polarization during the observations can be made. However, the
inferred spectral indices, discussed below, and strength of emission at these
high frequencies suggest that optically thin gyrosynchrotron radiation is
active in all the detected UCDs. A larger sample of UCDs must be observed in
this range to determine whether this small sample is representative of radio
emitting UCDs as a whole.

The measurements at different frequencies can be used to estimate a spectral
index $\alpha$ such that $F_{\nu}\,\propto\,\nu^{\alpha}$ for flux density
$F_{\nu}$ (Fig 2). Moreover, if gyrosynchrotron radiation is responsible for
the detections, then the spectral indices can be related to an electron energy
distribution following Dulk & Marsh (1982). LSR J1835-46546 and LP 349-25 have
spectral indices of $\alpha=-0.76\pm 0.07$ and $\alpha=-0.52\pm 0.06$,
respectively, which are consistent with optically thin gyrosynchrotron
radiation. NLTT 33370 is best fit by a spectral index of $\alpha=-0.29\pm
0.04$, slightly more shallow than what would be expected for gyrosynchrotron
or synchrotron radiation. Using the relation between $\alpha$ and $\delta$, we
calculate a common electron index of $\delta\approx 2$, with individual values
ranging from $2.20\pm 0.08$ to $1.68\pm 0.05$. Also plotted in Figure 2 are
ECMI profiles of Jupiter and Saturn, shifted to the peak flux and frequency of
NLTT 33370, which illustrate the sharp cutoff of ECMI with increasing
frequency compared with gyrosynchrotron radiation.

The three detected UCDs share two key characteristics: reliably detectable
emission at 8.46 GHz and rotation speeds far in excess of the ad hoc $40~{}\rm
km~{}s^{-1}$ cutoff, where radio emission becomes much more likely (McLean et
al., 2011; Pineda et al., 2017). Previous detections of radio emission from
UCDs have predominantly been in the $1-10$ GHz frequency range, where both
ECMI and gyrosynchrotron emission are generally present. The brightness
temperatures implied by the flux densities of observations presented in this
work range from $\sim 10^{6}-10^{8}$ K. Incoherent processes are limited to
brightness temperatures below approximately $10^{12}$ K (Readhead, 1994),
whereas coherent processes such as ECMI can reach much higher brightness
temperatures typically of order $10^{12}$ K and above (Melrose, 1991). The
inferred brightness temperatures indicate that the detected millimeter
emission is likely produced by gyrosynchrotron radiation. The emission from
LSR J1835+3259 and LP 349-25 AB was quiescent over the respective 1-hour and
2-hour observations, with no evidence of flaring or variability. While the
emission of NLTT 33370 was mostly quasi-quiescent, the June 12 observations
included a massive 20-second burst, with emission over 5 times brighter than
the quiescent flux.

The origin of the NLTT 33370 burst is unclear, but consistent with previous
observations of the system at lower frequencies. NLTT 33370 was found by
Williams et al. (2015) to have both bursts and quiescent flux modulated with
two distinct periodicities of $3.7859\pm 0.0001$ and $3.7130\pm 0.0002$ hours,
slightly less than the stellar rotation period of 3.9 hours (McLean et al.,
2011). The flare presented in this work did not recur with either of these
periods. ECMI bursts due to auroral emission are expected to occur with the
stellar rotation period. Unfortunately, none of the on-source observing blocks
corresponded to a 3.9 hour interval from the time of the burst. Given the
presence of quiescent emission at 97.5 GHz, the burst could be associated with
gyrosynchrotron radiation released during a major flare. Long-term monitoring
of NLTT 33370 at high radio frequencies is necessary to determine if such
emission is quasi-periodic or stochastic.

The other UCDs in the sample, LP 415-20 and LP 423-31 were not detected. We
place $3\sigma$ upper flux density limits of 21 $\mu Jy$ and 30 $\mu Jy$,
respectively. LP 415-20 has not been previously observed at low radio
frequencies, but its high $\textit{v}\,sin\textit{i}$ makes the non-detection
surprising compared with the other targets and is an important target for
follow up. While we did not detect emission at 33 GHz, the slowly rotating LP
423-31 has been observed to have variable and highly polarized emission at 8
GHz (Stelzer et al. in prep). The lack of 33 GHz emission, in conjunction with
the prior 8 GHz detection, might suggest that ECMI is present in this object
and quiescent gyrosynchrotron is weak, not present at all, or does not extend
to millimeter wavelengths. However, because previous observations by Berger
(2006) at 8.46 GHz have also reported non-detections, additional observations
of this target are required to confirm whether it is also variable at high
radio frequencies and possibly inactive over the course of the 35 minute
observations presented in this work.

Figure 2: Radio emission profiles of all three detected UCDs are shown. The
kilometric radiation profiles of Jupiter and Saturn adapted from Zarka (1998)
are plotted in blue and green, scaled and shifted to the peak flux and
frequency of NLTT 33370, whereas the dotted lines correspond to fitted
gyrosynchrotron models. The spectral indices of LP 349-25 and LSR J1835-46546
were determined by connecting the two existing data points for each UCD, and
were $\alpha=-0.52$ and $\alpha=-0.76$, respectively.

The measured flux can be used to estimate the size of the emitting region.
Assuming the low frequency limit of $h\nu<<k_{B}T_{b}$, which is valid for the
frequency of observation, the Rayleigh-Jeans law can be rearranged to give,

$X_{R_{J}}\approx 1400\frac{d_{\rm pc}}{\nu_{\rm GHz}}\sqrt{\frac{S_{\rm\mu
Jy}}{T_{b}}},$ (1)

where $d_{\rm pc}$ is the stellar distance, $\nu_{\rm GHz}$ is the observing
frequency, $S_{\rm\mu Jy}$ is the flux density, $T_{b}$ is the brightness
temperature, and $X_{R_{J}}$ is the size of the emitting region in units of
Jupiter radii. In the case of an isolated source with constant non-thermal
effective temperature, the brightness temperature can be related to the non-
thermal effective temperature by $T_{b}=(1-e^{-\tau(\nu)})T_{\textrm{eff}}$,
where $\tau(\nu)$ is the optical depth. This gives the size of the emitting
region in the optically thin regime,

$X_{R_{J}}\approx 1400\frac{d_{\rm pc}}{\nu_{\rm GHz}}\sqrt{\frac{S_{\mu
Jy}}{(1-\exp^{-\tau(\nu)})T_{\textrm{eff}}}}.$ (2)

The precise value of the optical depth for gyrosynchrotron emission depends
critically on the angle between the magnetic field, the line-of-sight to the
observer (Zheleznyakov, 1970), and the frequency of observations.

The size of the emitting region is plotted against magnetic field strength for
all three UCDs in Figure 3. The solid lines are determined from the previously
published ${\sim}8.5$ GHz flux densities of all UCDs. The emitting region is
calculated by following Equation 1, where we are assuming the observations are
at approximately the peak emission frequency where $\tau\approx 1$ and $T_{b}$
approaches $2/3T_{\textrm{eff}}$ following the non-thermal Dulk & Marsh (1982)
relations. Taking the average UCD radius to be that of Jupiter (Sorahana et
al., 2013), these results show that LP 349-25 and LSR J1835$+$3259 have
emitting regions ranging between the full stellar disk at large magnetic field
strengths (${\sim}2000$ G) to a fraction of the stellar disk for low magnetic
field strengths. If the 97.5 GHz flux densities originate from the same
emitting region, then we expect an optical depth of $\tau\approx 0.0001$.

Figure 3: The size of the emitting region for a given magnetic field strength
for all detected UCDs. The solid curves show the size of the emitting region
given $\sim 8.5$ GHz flux density of each UCD, assuming this is in the
transition region where $\tau\approx 1$. The size of the emitting region is
given in Jupiter radii $R_{\rm J}$, characteristic of UCD sizes, while the
magnetic field range is chosen to be representative of Solar to typical UCD
values.

The values spanned by this range are consistent with observations of M stars
that show significant portions of the disk covered with magnetically active
regions (Johns-Krull & Valenti, 1996; Alekseev & Kozlova, 2002), showing a
magnetic filling factor - the fraction of surface covered by magnetically
active area - significantly higher than Solar values (which are typically
${<}1\%$). The emitting region for NLTT 33370 is larger than the stellar disk
for magnetic field strengths $>100$ G. This enhanced emitting region is
possibly owing in part to the binarity of the system. If both NLTT 33370 A and
NLTT 33370 B are radio loud, then the inferred size of the emitting region
includes contributions from both stellar disks and accounts for an additional
factor of up to $\sqrt{2}$. However, this cannot explain the predicted
emitting region of NLTT 33370 for magnetic field strengths $>$170 G. If the
magnetic field strength exceeds this value, the size of the emitting region
could be enhanced by the effect of a companion.

Figure 4: Time series of all NLTT 33370 observations presented in this work,
including time on June 10th and June 12th, 2015. The data set was split into
30-second bins, and the peak flux and RMS were taken using the CASA task
uvmodelfit. The two panels show the light curves of each day, while the
overlayed plot shows the June 12 flare that reached a peak flux of $4880\pm
360~{}\mu Jy$. Due to the gaps in the data, it is unclear whether this flare
repeats with the stellar rotation.

As detailed by Williams et al. (2014), gyrosynchrotron radiation could
originate in frequent small-scale magnetic reconnection events. These events
accelerate a population of downward-directed electrons to near-relativistic
energies, prompting detectable radio emission, while also injecting highly
energetic particles into the stellar environment. The outgoing energetic
particles cannot be detected directly, but gyrosynchrotron emission produced
by the mildly relativistic electrons can be used as a tracer for such events
(Bastian et al., 1998; Osten et al., 2016; Hughes et al., 2019). While several
studies have shown that stellar UV emission alone may not be catastrophic for
planets and could even be beneficial (Ranjan & Sasselov, 2016), simulations
ran by Segura et al. (2010) and Tilley et al. (2017) suggest that it is
energetic particles, not UV emission alone, that is the most damaging to
planetary atmospheres. If gyrosynchrotron radiation is indeed produced by
reconnection events and is commonplace around the 10% of UCDs that are radio
active, then its presence might be an important consideration for modeling of
exoplanet atmospheres in orbit around such UCDs.

##  4 Summary

In this work we presented ALMA and VLA observations of five UCDs with a range
of properties and radio behavior. Of these targets, three were found to be
active at 97.5 GHz, whereas two were not detected at 33 GHz (LP 423-31) or
97.5 GHz (LP 415-20). Thus far, all UCDs that have been reliably detected near
8 GHz and within $30-100$ GHz exhibit emission in both of these frequency
ranges. The observations presented here give spectral indices ranging from
$\alpha=-0.76$ to $\alpha=-0.29$, suggestive of optically thin gyrosynchrotron
emission. The data for all detected UCDs were split into smaller time bins,
with the peak flux and RMS taken from each chunk using the CASA task
uvmodelfit. Each peak flux was then used to generate a time series of the
stellar brightness. Two of the detections (LP 349-25 and LSR J1835) show
little time variation throughout the observations (2 hr and 1 hr on source,
respectively), while NLTT 33370 shows minor temporal variability and a strong
flare that exceeded the average quiescent flux by a factor of 20. Of the non-
detections, LP 415-20 is a very rapid rotator that has not previously been
observed at radio frequencies. Our observations at 33 GHz show it to be radio
quiet, consistent with most UCDs but at odds with other rapidly rotating UCDs.
LP 423-31 exhibits no detectable high radio frequency emission during the
observations. This particular source has been observed twice previously, one
of which resulted in a detection (Stelzer et al. in prep) and the other in a
non-detection (Berger, 2006) at low radio frequencies. The presence of
variable emission at low radio frequencies and the lack of detectable
quiescent emission at high radio frequencies is suggestive of ECMI. However,
the low $\textit{v}\,sin\textit{i}$ of this source muddles this picture.
Overall, these results provide further evidence for the presence of millimeter
emission radio loud UCDs, although additional observations are necessary to
determine how common such emission might be. If the gyrosynchrotron radiation
is produced by reconnection events, then a high resulting energetic particle
flux can threaten the stability of planetary atmospheres (e.g. Hughes et al.,
2019).

This work is part of an ongoing project to characterize the high radio
frequency emission of UCDs. As of yet, very few observations of UCDs have been
made in the $20-100\,GHz$ range where the emission mechanism could be more
readily distinguished through the emission’s spectral index. With additional
observations of a larger sample, we will gain a better understanding of UCD
radio behavior.

## Acknowledgements

We thank the referee for the valuable feedback that improved the manuscript.
This work was supported in part by an NSERC Discovery Grant, The University of
British Columbia, The Canadian Foundation for Innovation, the BC Knowledge
Development Fund and the Canada Research Chairs program. This paper makes use
of the following ALMA data: ADS/JAO.ALMA#2016.1.00817.S, ADS/JAO.ALMA
#2013.1.00976.S, ADS/JAO.ALMA#018.1.01088.S. ALMA is a partnership of ESO
(representing its member states), NSF (USA) and NINS (Japan), together with
NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in
cooperation with the Republic of Chile. The Joint ALMA Observatory is operated
by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a
facility of the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc.

## References

  * Alekseev & Kozlova (2002) Alekseev, I. Y., & Kozlova, O. V. 2002, A&A, 396, 203
  * Antonova et al. (2013) Antonova, A., Hallinan, G., Doyle, J. G., et al. 2013, A&A, 549, A131
  * Bastian et al. (1998) Bastian, T. S., Benz, A. O., & Gary, D. E. 1998, ARA&A, 36, 131
  * Berdyugina et al. (2017) Berdyugina, S. V., Harrington, D. M., Kuzmychov, O., et al. 2017, ApJ, 847, 61
  * Berger (2002) Berger, E. 2002, ApJ, 572, 503
  * Berger (2006) —. 2006, ApJ, 648, 629
  * Berger et al. (2001) Berger, E., Ball, S., Becker, K. M., et al. 2001, Nature, 410, 338
  * Burgasser & Putman (2005) Burgasser, A. J., & Putman, M. E. 2005, ApJ, 626, 486
  * Chabrier & Baraffe (2000) Chabrier, G., & Baraffe, I. 2000, ARA&A, 38, 337
  * Cowley & Bunce (2001) Cowley, S. W. H., & Bunce, E. J. 2001, Planet. Space Sci., 49, 1067
  * Cruz et al. (2003) Cruz, K. L., Reid, I. N., Liebert, J., Kirkpatrick, J. D., & Lowrance, P. J. 2003, AJ, 126, 2421
  * Davenport et al. (2012) Davenport, J. R. A., Becker, A. C., Kowalski, A. F., et al. 2012, ApJ, 748, 58
  * Dressing & Charbonneau (2015) Dressing, C. D., & Charbonneau, D. 2015, ApJ, 807, 45
  * Dulk (1985) Dulk, G. A. 1985, ARA&A, 23, 169
  * Dulk & Marsh (1982) Dulk, G. A., & Marsh, K. A. 1982, ApJ, 259, 350
  * Forbrich et al. (2016) Forbrich, J., Dupuy, T. J., Reid, M. J., et al. 2016, ApJ, 827, 22
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * Gizis et al. (2000) Gizis, J. E., Monet, D. G., Reid, I. N., et al. 2000, AJ, 120, 1085
  * Güdel (2002) Güdel, M. 2002, ARA&A, 40, 217
  * Guedel & Benz (1993) Guedel, M., & Benz, A. O. 1993, ApJ, 405, L63
  * Hallinan et al. (2006) Hallinan, G., Antonova, A., Doyle, J. G., et al. 2006, ApJ, 653, 690
  * Hallinan et al. (2008a) —. 2008a, ApJ, 684, 644
  * Hallinan et al. (2008b) —. 2008b, ApJ, 684, 644
  * Hallinan et al. (2015) Hallinan, G., Littlefair, S. P., Cotter, G., et al. 2015, Nature, 523, 568
  * Henry et al. (2006) Henry, T. J., Jao, W.-C., Subasavage, J. P., et al. 2006, AJ, 132, 2360
  * Hughes et al. (2019) Hughes, A. G., Boley, A. C., Osten, R. A., & White, J. A. 2019, ApJ, 881, 33
  * Johns-Krull & Valenti (1996) Johns-Krull, C. M., & Valenti, J. A. 1996, ApJ, 459, L95
  * Kao et al. (2016) Kao, M. M., Hallinan, G., Pineda, J. S., et al. 2016, ApJ, 818, 24
  * Kao et al. (2018) Kao, M. M., Hallinan, G., Pineda, J. S., Stevenson, D., & Burgasser, A. 2018, The Astrophysical Journal Supplement Series, 237, 25.  http://dx.doi.org/10.3847/1538-4365/aac2d5
  * Konopacky et al. (2010) Konopacky, Q. M., Ghez, A. M., Barman, T. S., et al. 2010, The Astrophysical Journal, 711, 1087–1122.  http://dx.doi.org/10.1088/0004-637X/711/2/1087
  * Konopacky et al. (2012) Konopacky, Q. M., Ghez, A. M., Fabrycky, D. C., et al. 2012, ApJ, 750, 79
  * Law et al. (2006) Law, N. M., Hodgkin, S. T., & Mackay, C. D. 2006, MNRAS, 368, 1917
  * Lépine et al. (2009) Lépine, S., Thorstensen, J. R., Shara, M. M., & Rich, R. M. 2009, AJ, 137, 4109
  * Liebert et al. (1999) Liebert, J., Kirkpatrick, J. D., Reid, I. N., & Fisher, M. D. 1999, ApJ, 519, 345
  * Lynch et al. (2016) Lynch, C., Murphy, T., Ravi, V., et al. 2016, MNRAS, 457, 1224
  * McLean et al. (2011) McLean, M., Berger, E., Irwin, J., Forbrich, J., & Reiners, A. 2011, ApJ, 741, 27
  * McLean et al. (2012) McLean, M., Berger, E., & Reiners, A. 2012, ApJ, 746, 23
  * McMullin et al. (2007) McMullin, J., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical data analysis software and systems XVI, Vol. 376, 127
  * Melrose (1991) Melrose, D. B. 1991, ARA&A, 29, 31
  * Melrose & Dulk (1982) Melrose, D. B., & Dulk, G. A. 1982, ApJ, 259, 844
  * Mohanty et al. (2002) Mohanty, S., Basri, G., Shu, F., Allard, F., & Chabrier, G. 2002, ApJ, 571, 469
  * Osten (2008) Osten, R. A. 2008, arXiv e-prints, arXiv:0801.2573
  * Osten et al. (2009) Osten, R. A., Phan-Bao, N., Hawley, S. L., Reid, I. N., & Ojha, R. 2009, ApJ, 700, 1750
  * Osten et al. (2016) Osten, R. A., Kowalski, A., Drake, S. A., et al. 2016, ApJ, 832, 174
  * Phan-Bao et al. (2007) Phan-Bao, N., Osten, R. A., Lim, J., Martín, E. L., & Ho, P. T. P. 2007, ApJ, 658, 553
  * Pineda et al. (2017) Pineda, J. S., Hallinan, G., & Kao, M. M. 2017, ApJ, 846, 75
  * Ranjan & Sasselov (2016) Ranjan, S., & Sasselov, D. D. 2016, Astrobiology, 16, 68
  * Readhead (1994) Readhead, A. C. S. 1994, ApJ, 426, 51
  * Reid et al. (2003) Reid, I. N., Cruz, K. L., Laurie, S. P., et al. 2003, AJ, 125, 354
  * Reiners (2009) Reiners, A. 2009, in Cosmic Magnetic Fields: From Planets, to Stars and Galaxies, ed. K. G. Strassmeier, A. G. Kosovichev, & J. E. Beckman, Vol. 259, 339–344
  * Reiners & Basri (2006) Reiners, A., & Basri, G. 2006, ApJ, 644, 497
  * Reiners & Basri (2010a) —. 2010a, ApJ, 710, 924
  * Reiners & Basri (2010b) —. 2010b, ApJ, 710, 924
  * Route & Wolszczan (2016) Route, M., & Wolszczan, A. 2016, ApJ, 830, 85
  * Schlieder et al. (2014) Schlieder, J. E., Bonnefoy, M., Herbst, T. M., et al. 2014, ApJ, 783, 27
  * Schmidt et al. (2007) Schmidt, S. J., Cruz, K. L., Bongiorno, B. J., Liebert, J., & Reid, I. N. 2007, The Astronomical Journal, 133, 2258–2273.  http://dx.doi.org/10.1086/512158
  * Segura et al. (2010) Segura, A., Walkowicz, L. M., Meadows, V., Kasting, J., & Hawley, S. 2010, Astrobiology, 10, 751
  * Siegler et al. (2003) Siegler, N., Close, L. M., Mamajek, E. E., & Freed, M. 2003, ApJ, 598, 1265
  * Sorahana et al. (2013) Sorahana, S., Yamamura, I., & Murakami, H. 2013, ApJ, 767, 77
  * Tilley et al. (2017) Tilley, M. A., Segura, A., Meadows, V. S., Hawley, S., & Davenport, J. 2017, arXiv e-prints, arXiv:1711.08484
  * Treumann (2006) Treumann, R. A. 2006, A&A Rev., 13, 229
  * Turnpenney et al. (2018) Turnpenney, S., Nichols, J. D., Wynn, G. A., & Burleigh, M. R. 2018, ApJ, 854, 72
  * Williams & Berger (2015) Williams, P. K. G., & Berger, E. 2015, ApJ, 808, 189
  * Williams et al. (2015) Williams, P. K. G., Berger, E., Irwin, J., Berta-Thompson, Z. K., & Charbonneau, D. 2015, The Astrophysical Journal, 799, 192.  http://dx.doi.org/10.1088/0004-637X/799/2/192
  * Williams et al. (2015) Williams, P. K. G., Casewell, S. L., Stark, C. R., et al. 2015, ApJ, 815, 64
  * Williams et al. (2014) Williams, P. K. G., Cook, B. A., & Berger, E. 2014, ApJ, 785, 9
  * Zarka (1998) Zarka, P. 1998, J. Geophys. Res., 103, 20159
  * Zarka et al. (2001) Zarka, P., Treumann, R. A., Ryabov, B. P., & Ryabov, V. B. 2001, Ap&SS, 277, 293
  * Zheleznyakov (1970) Zheleznyakov, V. V. 1970, Radio emission of the sun and planets