astronomy - What parameters control the amount of thermal energy an object must possess for it to be detectable in space?

What parameters control the amount of thermal energy a space object must possess for it to be detectable by a sensor also in space (i.e. one that does not have to deal with interference from a planet's atmosphere)?

Answer

It's not the heat that matters, but the brightness. Sedna, discovered in 2003, has an apparent magnitude of 21.3. Wikipedia lists an apparent magnitude of 27 as the faintest object observable from an eight-meter ground-based telescope, and magnitude 36 as the faintest observable with a 40-meter telescope under construction.

These objects are not seen by their thermal radiation, like stars, but because they have nonzero albedo and reflect sunlight. Both incident and reflected sunlight fall off like the square of the distance. When Sedna moves from perihelion (now) to aphelion (in 11,000 years) its distance will increase by about a factor of ten; the sunlight incident on the surface will decrease by a factor of 100 (which is five magnitudes) and the brightness at Earth of the reflected light will decrease by another factor of 100. At aphelion, then, Sedna will have an apparent magnitude of around 37 and might or might not be visible from Earth's surface using a telescope the size of a baseball diamond. That's at a distance of 0.015 light-year.

So we don't have to worry about seeing Oort cloud objects by their reflected light at a light-year. For blackbodies (like stars) there is a straightforward relationship between absolute magnitude, distance, and size: a big, cold object can emit more light and be more luminous than a small, hot object. Absolute magnitudes are based on brightness at a distance of 10 parsecs or 32 light-years, so our barely-detectable magnitude-37 blackbody at one light-year would have an absolute magnitude of 42.5 or so. Such an object would either be a stray planet (of which, apparently, there are many) or a black dwarf. I'm not certain whether a brown dwarf could be that cool and still retain its atmosphere, and a brown dwarf that lost its atmosphere would just be a rocky stray planet. (I may come back later and edit in a calculation, hmmmm.)