HIGH-MASS, FOUR-PLANET CONFIGURATIONS FOR HR 8799: CONSTRAINING THE ORBITAL INCLINATION AND AGE OF THE SYSTEM

Abstract

Debates regarding the age and inclination of the planetary system orbiting HR\n8799, and the release of additional astrometric data following the discovery of\nthe fourth planet prompted us to examine the possibility of constraining these\ntwo quantities by studying the long-term stability of this system at different\norbital inclinations and in its high-mass configuration (7-10-10-10 MJup). We\ncarried out ~1.5 million N-body integrations for different combinations of\norbital elements of the four planets. The most dynamically stable combinations\nsurvived less than ~5 Myr at inclinations of 0{\\deg} and 13{\\deg}, and 41, 46,\nand 31 Myr at 18{\\deg}, 23{\\deg}, and 30{\\deg}, respectively. Given such short\nlifetimes and the location of the system on the age-luminosity diagram for\nlow-mass objects, the most reasonable conclusion of our study is that the\nplanetary masses are less than 7-10-10-10 MJup and the system is quite young.\nTwo trends to note from our work are as follows. (1) In the most stable\nsystems, the higher the inclination, the more the coordinates for planets b and\nc diverge from the oldest archival astrometric data (released after we\ncompleted our N-body integrations), suggesting that either these planets are in\neccentric orbits or have lower orbital inclinations than that of planet d. (2)\nThe most stable systems place planet e closer to the central star than is\nobserved, supporting the conclusion that the planets are more massive and the\nsystem is young. We present the details of our simulations and discuss the\nimplications of the results.\n