We present 1.3 millimeter observations of the debris disk surrounding the HR 8799 multi-planet system from the Submillimeter Array to complement archival ALMA observations that spatially filtered away the bulk of the emission .
The image morphology at 3 \farcs 8 ( 150 AU ) resolution indicates an optically thin circumstellar belt , which we associate with a population of dust-producing planetesimals within the debris disk .
The interferometric visibilities are fit well by an axisymmetric radial power-law model characterized by a broad width , \Delta R / R \gtrsim 1 .
The belt inclination and orientation parameters are consistent with the planet orbital parameters within the mutual uncertainties .
The models constrain the radial location of the inner edge of the belt to R _ { \text { in } } = 104 _ { -12 } ^ { +8 } AU .
In a simple scenario where the chaotic zone of the outermost planet b truncates the planetesimal distribution , this inner edge location translates into a constraint on the planet b mass of M _ { \text { pl } } = 5.8 _ { -3.1 } ^ { +7.9 } M _ { Jup } .
This mass estimate is consistent with infrared observations of the planet luminosity and standard hot-start evolutionary models , with the uncertainties allowing for a range of initial conditions .
We also present new 9 millimeter observations of the debris disk from the Very Large Array and determine a millimeter spectral index of 2.41 \pm 0.17 .
This value is typical of debris disks and indicates a power-law index of the grain size distribution q = 3.27 \pm 0.10 , close to predictions for a classical collisional cascade .