The Occurrence Rate of Quiescent Radio Emission for Ultracool Dwarfs using a Generalized Semi-Analytical Bayesian Framework

Abstract

We present a generalized analytical Bayesian framework for calculating the occurrence rate of steady emission (or absorption) in astrophysical objects. As a proof-of-concept, we apply this framework to non-flaring quiescent radio emission in ultracool ($\le$ M7) dwarfs. Using simulations, we show that our framework recovers the simulated radio occurrence rate to within 1-5% for sample sizes of 10-100 objects when averaged over an ensemble of trials and simulated occurrence rates for our assumed luminosity distribution models. In contrast, existing detection rate studies may under-predict the simulated rate by 51-66% because of sensitivity limits. Using all available literature results for samples of 82 ultracool M dwarfs, 74 L dwarfs, and 23 T/Y dwarfs, we find that the maximum-likelihood quiescent radio occurrence rate is between $15_{-4}^{+4}$ - $20_{-5}^{+6}$%, depending on the luminosity prior that we assume. Comparing each spectral type, we find occurrence rates of $17_{-7}^{+9}$ - $25_{-10}^{+13}$% for M dwarfs, $10_{-4}^{+5}$ - $13_{-5}^{+7}$% for L dwarfs, and $23_{-9}^{+11}$ - $29_{-11}^{+13}$% for T/Y dwarfs. We rule out potential selection effects and speculate that age and/or rotation may account for tentative evidence that the quiescent radio occurrence rate of L dwarfs may be suppressed compared to M and T/Y dwarfs and phenomenon. Finally, we discuss how we can harness our occurrence rate framework to carefully assess the possible physics that may be contributing to observed occurrence rate trends.

References in corpus (54)

• The NumPy array: a structure for efficient numerical computation
• Stellar magnetism: empirical trends with age and rotation
• Confirmation of the Electron Cyclotron Maser Instability as the Dominant Source of Radio Emission from Very Low Mass Stars and Brown Dwarfs
• The Hawaii Infrared Parallax Program. II. Young Ultracool Field Dwarfs
• Radio Observations of a Large Sample of Late-M, L, and T Dwarfs: The Distribution of Magentic Field Strengths
• Periodic Bursts of Coherent Radio Emission from an Ultracool Dwarf
• Strong Brightness Variations Signal Cloudy-to-Clear Transition of Brown Dwarfs
• Activity and Kinematics of Ultracool Dwarfs Including An Amazing Flare Observation
• Discovery of a young planetary mass companion to the nearby M dwarf VHS J125601.92-125723.9
• Rotational Modulation of the Radio Emission from the M9 Dwarf TVLM 513-46546: Broadband Coherent Emission at the Substellar Boundary?
• A Cross-Match of 2MASS and SDSS: Newly-Found L and T Dwarfs and an Estimate of the Space Densitfy of T Dwarfs
• SpeX Spectroscopy of Unresolved Very Low Mass Binaries. II. Identification of Fourteen Candidate Binaries with Late-M/Early-L and T Dwarf Components
• BOSS Ultracool Dwarfs I: Colors and Magnetic Activity of M and L dwarfs
• The Arecibo Detection of the Coolest Radio-flaring Brown Dwarf
• The population of M dwarfs observed at low radio frequencies
• A large spectroscopic sample of L and T dwarfs from UKIDSS LAS: peculiar objects, binaries, and space density
• Estimating the magnetic field strength in hot Jupiters
• Near-infrared photometry of Y dwarfs: low ammonia abundance and the onset of water clouds
• Simultaneous Multi-Wavelength Observations of Magnetic Activity in Ultracool Dwarfs. II. Mixed Trends in VB10 and LSR1835+32 and the Possible Role of Rotation
• Simultaneous Multi-Wavelength Observations of Magnetic Activity in Ultracool Dwarfs. I. The Complex Behavior of the M8.5 Dwarf TVLM513-46546
• A Panchromatic View of Brown Dwarf Aurorae
• BANYAN. IX. The Initial Mass Function and Planetary-Mass Object Space Density of the TW Hya Association
• The Hawaii Infrared Parallax Program. IV. A Comprehensive Parallax Survey of L0-T8 dwarfs with UKIRT
• The Luminosities of the Coldest Brown Dwarfs
• A scaling relationship for non-thermal radio emission from ordered magnetospheres: from the top of the Main Sequence to planets
• Dynamical parallax of sigma Ori AB: mass, distance and age
• An Improved Age-Activity Relationship for Cool Stars older than a Gigayear
• Sporadic Long-term Variability in Radio Activity from a Brown Dwarf
• A 3D Search for Companions to 12 Nearby M-Dwarfs
• Discovery of Radio Emission from the Tight M8 Binary: LP 349-25
• A New Brown Dwarf Desert? A Scarcity of Wide Ultracool Binaries
• Variable and polarized radio emission from the T6 brown dwarf WISEP J112254.73+255021.5
• A Mini-survey of Ultracool Dwarfs at 4.9 GHz
• Resolved imaging of an extrasolar radiation belt around an ultracool dwarf
• Quasi-Quiescent Radio Emission from the First Radio-Emitting T Dwarf
• Direct radio discovery of a cold brown dwarf
• Centrifugal breakout reconnection as the electron acceleration mechanism powering the radio magnetospheres of early-type stars
• The Second Arecibo Search for 5 GHz Radio Flares from Ultracool Dwarfs
• CCD Parallaxes for 309 Late-type Dwarfs and Subdwarfs
• Steady and Transient Radio Emission from Ultracool Dwarfs
• Auroral Radio Emission from Ultracool Dwarfs: a Jovian Model
• Evidence for a radiation belt around a brown dwarf
• Brown dwarfs as ideal candidates for detecting UV aurora outside the Solar System: Hubble Space Telescope observations of 2MASS J1237+6526
• $K2$ Ultracool Dwarfs Survey. VI. White light superflares observed on an L5 dwarf and flare rates of L dwarfs
• No Detectable H3+ Emission from the Atmospheres of Hot Jupiters
• Detection of a giant white-light flare on an L2.5 dwarf with the Next Generation Transit Survey
• Radio Constraints on Activity in Young Brown Dwarfs
• Polarised radio pulsations from a new T dwarf binary
• Radio-flaring Ultracool Dwarf Population Synthesis
• On the Correlation between L Dwarf Optical and Infrared Variability and Radio Aurorae
• WISEP J060738.65+242953.4: A Nearby. Pole-On L8 Brown Dwarf with Radio Emission
• Low-resolution optical spectra of ultracool dwarfs with OSIRIS/GTC
• Optical Spectra of Ultracool Dwarfs with the Southern African Large Telescope
• Physical properties and astrometry of radio-emitting brown dwarf TVLM513-46546 revisited

Cited by in corpus (4)

• Hints of auroral and magnetospheric polarized radio emission from the scallop-shell star 2MASS J05082729$-$2101444
• Radio Emission from a Nearby M dwarf Binary
• Simulations of Electron Beam Interactions in Brown Dwarf Atmospheres
• A scaling relationship for non-thermal radio emission from ordered magnetospheres - II. Investigating the efficiency of relativistic electron production in magnetospheres of BA-type stars