  Debates regarding the age and inclination of the planetary system orbiting HR
8799, and the release of additional astrometric data following the discovery of
the fourth planet prompted us to examine the possibility of constraining these
two quantities by studying the long-term stability of this system at different
orbital inclinations and in its high-mass configuration (7-10-10-10 MJup). We
carried out ~1.5 million N-body integrations for different combinations of
orbital elements of the four planets. The most dynamically stable combinations
survived less than ~5 Myr at inclinations of 0{\deg} and 13{\deg}, and 41, 46,
and 31 Myr at 18{\deg}, 23{\deg}, and 30{\deg}, respectively. Given such short
lifetimes and the location of the system on the age-luminosity diagram for
low-mass objects, the most reasonable conclusion of our study is that the
planetary masses are less than 7-10-10-10 MJup and the system is quite young.
Two trends to note from our work are as follows. (1) In the most stable
systems, the higher the inclination, the more the coordinates for planets b and
c diverge from the oldest archival astrometric data (released after we
completed our N-body integrations), suggesting that either these planets are in
eccentric orbits or have lower orbital inclinations than that of planet d. (2)
The most stable systems place planet e closer to the central star than is
observed, supporting the conclusion that the planets are more massive and the
system is young. We present the details of our simulations and discuss the
implications of the results.
