Title: Time-Resolved High Spectral Resolution Observation of 2MASSW J0746425+200032AB,
Abstract: Many brown dwarfs exhibit photometric variability at levels from tenths to
tens of percents. The photometric variability is related to magnetic activity
or patchy cloud coverage, characteristic of brown dwarfs near the L-T
transition. Time-resolved spectral monitoring of brown dwarfs provides
diagnostics of cloud distribution and condensate properties. However, current
time-resolved spectral studies of brown dwarfs are limited to low spectral
resolution (R$\sim$100) with the exception of the study of Luhman 16 AB at
resolution of 100,000 using the VLT$+$CRIRES. This work yielded the first map
of brown dwarf surface inhomogeneity, highlighting the importance and unique
contribution of high spectral resolution observations. Here, we report on the
time-resolved high spectral resolution observations of a nearby brown dwarf
binary, 2MASSW J0746425+200032AB. We find no coherent spectral variability that
is modulated with rotation. Based on simulations we conclude that the coverage
of a single spot on 2MASSW J0746425+200032AB is smaller than 1\% or 6.25\% if
spot contrast is 50\% or 80\% of its surrounding flux, respectively. Future
high spectral resolution observations aided by adaptive optics systems can put
tighter constraints on the spectral variability of 2MASSW J0746425+200032AB and
other nearby brown dwarfs.