where [M.sub.planet] is the planet mass, i is the orbital plane inclination, [M.sub.star] is the stellar mass, [M.sub.Jupiter] is the Jupiter mass
, a is the semi-major axis, and [M.sub.Sun] is the mass of the Sun.
"Over the last 12 years or so nearly 400 planets have been found, and the vast majority of them have been very large - Jupiter mass
or even larger," said researcher Paul Butler of the Carnegie Institution's Department of Terrestrial Magnetism.
First, some argue that lone brown dwarfs having just a Jupiter mass
or two might form the same way that heavier brown dwarfs and stars do: directly from collapsing clouds of interstellar gas and dust.
The structure contains less than a Jupiter mass
right now, but it could collect 3 to 5 Jupiters of material over time, which gives it the potential to someday form planets.
His calculations show that the normal star-formation process can give birth to objects with less than 1 Jupiter mass
The team estimates that about 9 percent of massive stars have gas giants between 5 and 13 Jupiter masses
beyond a distance of 10 AU, and fewer than 1 percent have brown dwarfs between 10 and 100 AU.
The astronomers estimate the object to have an upper limit of 5-14 Jupiter masses
. Revisiting observations taken in 2012 with the Gemini South telescope's Near-Infrared Coronagraphic Imager, the team concludes that PDS 70b orbits its star every 120 years.
According to theoretical calculations about how stars work, objects must be 80 Jupiter masses
or more to fuse hydrogen nuclei (protons) into helium.
After two-months of observations and extensive data analysis, Carnegie's Yuri Beletsky's team, led by Henri Boffin of the European Southern Observatory (ESO), found that both objects have a mass between 30 and 50 Jupiter masses
. By comparison, the Sun has a mass of about 1,000 Jupiter masses
Careful analysis and theoretical modeling determined that Fomalhaut b could not be more massive than three Jupiter masses
. The gravity of anything more than that would destroy the vast dust belt encircling the star.
The difference between a gas giant planet and a brown dwarf remains hotly debated among astronomers, but one rule of thumb that astronomers use is the mass below which deuterium fusion ceases, known as the "deuterium-burning limit," around 13 Jupiter masses
Indeed, Schlaufman found that, in 146 carefully selected planetary systems, objects with masses less than 4 to 10 Jupiters tend to form around stars rich with heavy elements, while objects with more than 10 Jupiter masses
form around all kinds of stars.