Brown dwarfs are objects whose masses fall below the limit required for stable hydrogen fusion to occur in their cores. A brown dwarf cools continuously from the gradual release of gravitational potential energy. The timescale over which a brown dwarf cools depends on its mass, with more massive brown dwarfs taking longer to cool. There is good evidence to suggest that terrestrial-mass planets can form around brown dwarfs. One compelling discovery is the object Kepler-42, a very low mass star with a trio of planets measuring 0.7, 0.8 and 0.6 Earth-radii respectively. These planets orbit Kepler-42 with periods no longer than 2 Earth days. The Kepler-42 system very much resembles a scaled up version of Jupiter and its 4 large moons - Io, Europa, Ganymede and Callisto. Since brown dwarfs cover the mass domain between Jupiter-like planets and the lowest mass stars, it is reasonable to expect that the process of forming planets around brown dwarfs is somewhat robust.
Figure 1: This artist’s concept compares the Kepler-42 (KOI-961) planetary system to Jupiter and the largest four of its many moons. The planet and moon orbits are drawn to the same scale. The relative sizes of the stars, planets and moons have been increased for visibility. Credit: NASA/JPL-Caltech.
Because a brown dwarf is so much fainter than the Sun, a terrestrial-mass planet has to orbit much closer in to receive as much warmth as the Earth gets from the Sun. In fact, a habitable planet around a brown dwarf is likely to have an orbital period of not more than a few Earth days. The habitable zone of a brown dwarf is a region of space around a brown dwarf where temperatures are neither too high nor too low for liquid water to exist on the surface of a terrestrial-mass planet. As a brown dwarf cools and fades over time, its habitable zone will likewise shrink inwards. A planet around a brown dwarf may start out too hot to support life. But as the habitable zone shrinks around a cooling brown dwarf, the planet will subsequently find itself within the habitable zone where temperatures are just right. As the habitable zone continues to shrink, the planet will eventually find itself exterior to the habitable zone where temperatures become too cold for surface life.
The development of life or even complex life on a terrestrial-mass planet around a brown dwarf is expected to depend a lot on the amount of time the planet spends within the habitable zone or the "Goldilocks zone". On Earth, it appears that the development of life required at least 0.5 billion years, while the development of complex multicellular life took perhaps ~3 billion years. As a result, a planet has to reside long enough in the shrinking habitable zone of a brown dwarf in order for life or even advanced lifeforms to develop. Andreeshchev and Scalo (2002) show that a planet in a close-in orbit around a 0.07 solar-mass brown dwarf can reside within the habitable zone for a duration of up to 10 billion years. The duration of habitability decreases for a brown dwarf of lower mass. For instance, a planet around a 0.04 solar-mass brown dwarf can remain habitable for no longer than 4 billion years.
Nevertheless, a planet outside the habitable zone of a brown dwarf does not necessarily mean that it cannot support life. One can imagine, in a close-in orbit around a brown dwarf, a hot Venus-like planet with a think and steaming atmosphere of water vapour. Although the planet's surface is too hot for life, it may be possible for life to develop in the cool layers of the planet's upper atmosphere. Over time, the brown dwarf cools, causing the habitable zone to shrink inwards until the planet eventually finds itself within it. Temperatures now become cool enough for the atmosphere to rain out, forming oceans on the planet's surface and creating a planet that more resembles the Earth. The planet can remain in this state for billions of years.
Slowly but surely, as the brown dwarf continues to cool, the planet will finally find itself exterior to the habitable zone. Temperatures now become sufficiently low for the oceans to freeze. Although the ocean surface freezes, deeper down, the ocean can still be kept liquid due to the feeble input of geothermal heat from the decay of radioisotopes in the planet's interior. Eventually, even the deep ocean will start to freeze as the geothermal heat flux from the decay of radioisotopes dwindles. However, if other planets exist around the brown dwarf, they can provide sufficient perturbation to keep the freezing planet in a slight non-circular orbit around the brown dwarf. This will allow tidal heating to operate for eons, pumping energy into the planet's interior and keeping the oceans liquid under a surface layer of ice. The planet now more resembles Jupiter's moon Europa.
Andreeshchev and Scalo, "Habitability of Brown Dwarf Planets", Bioastronomy 2002: Life Among the Stars. IAU Symposium, Vol. 213, 2004