Detection of a 20 minute time lag observed from Sgr A* between 8 and 10
  GHz with the VLA
  We report the detection and analysis of a radio flare observed on 17 April
2014 from Sgr A* at $9$ GHz using the VLA in its A-array configuration. This is
the first reported simultaneous radio observation of Sgr A* across $16$
frequency windows between $8$ and $10$ GHz. We cross correlate the lowest and
highest spectral windows centered at $8.0$ and $9.9$ GHz, respectively, and
find the $8.0$ GHz light curve lagging $18.37^{+2.17}_{-2.18}$ minutes behind
the $9.9$ GHz light curve. This is the first time lag found in Sgr A*'s light
curve across a narrow radio frequency bandwidth. We separate the quiescent and
flaring components of Sgr A* via flux offsets at each spectral window. The
emission is consistent with an adiabatically-expanding synchrotron plasma,
which we fit to the light curves to characterize the two components. The
flaring emission has an equipartition magnetic field strength of $2.2$ Gauss,
size of $14$ Schwarzschild radii, average speed of $12000$ km s$^{-1}$, and
electron energy spectrum index ($N(E)\propto E^{-p}$), $p = 0.18$. The peak
flare flux at $10$ GHz is approximately $25$% of the quiescent emission. This
flare is abnormal as the inferred magnetic field strength and size are
typically about $10$ Gauss and few Schwarzschild radii. The properties of this
flare are consistent with a transient warm spot in the accretion flow at a
distance of $10$-$100$ Schwarzschild radii from Sgr A*. Our analysis allows for
independent characterization of the variable and quiescent components, which is
significant for studying temporal variations in these components.
