Would a nearby "Orphan planet" be detectable?

Question

I understand that there may be large numbers of "orphan" planets not circling any star.

If there were such a planet, say the size of Jupiter, in the vicinity of the Sun, about how close would it have to be in order for telescopes to detect it?

Answer 1

The infrared satellite WISE did an all sky survey at near and mid-infrared wavelengths.

A nearby "rogue planet" would likely be moving quickly on the sky and if the size of Jupiter would emit substantial infrared radiation.

Close examination of the WISE survey data (in the context of looking for planet X) concluded there was unlikely to be Jupiter-sized planet within 26,000 au.

Answer 2

All sky surveys tend to be at optical or radio wavelengths and more rarely at infra-red or x-ray wavelengths using space-based telescopes. The exposure times are short, so the chances of finding a cold dark quiet object in deep space are very slim. You might get very lucky a catch an occultation.

However, assuming you know exactly where to look ...

Hubble can detect objects down to about magnitude +30 albeit with very long observation times. Jupiter shines in reflected light from the Sun at magnitude -2.7. Since reflected brightness falls as the 4th power of distance, its magnitude will drop as 2.5.log10(distance^4), so Jupiter would not be visible if it were more than 10^(32.7/2.5/4) = 1860 times further away. That would put it at a distance of about 10,000 AU. That distance would vary with the square root of the object's diameter and the fourth root of its albedo.

Jupiter also emits in the infra-red. Some that energy comes from the Sun, but most of it comes from inside Jupiter. Assuming a temperature of 150K for a wandering Jupiter, that corresponds to a wavelength of 20 microns. This is in the range that JWST can sense (0.6 - 28.3 microns) though it is much less sensitive than at optical wavelengths. With many hours of observation, it might get down to magnitude 23. Assuming black body radiation, the Sun provides a good reference point at 6000K, 1.4E6 km diameter, 1AU with magnitude -27. So we could reduce its brightness by 50 magnitudes before it disappears. That is a factor of 10^(50/2.5) = 10^20 in absolute brightness. Brightness goes as the fourth power of temperature, the square of diameter and the inverse square of distance. So a Jupiter sized object at 150K would become invisible to JWST at sqrt(10^20 * (150/6000)^4 * (143,000/1.4E6)^2) = 640,000 AU. Remarkably, that's more than twice as far away as the nearest star. But again, you would have to know exactly where to look and spend many many hours looking.

Answer 3

Rogue Planets are Discovered Mainly Through Micro-Lensing

We have alreqdy discovered a number of rogue exoplanets, but we don't do it by directly imaging them. Rather, we detect them by watching their gravity distort the light of a star they pass across.

Data from the Kepler mission has been used to identify 27 rogue planet candidates, including four that may be earth-sized:

Candidate short-duration events from the first space-based survey for planetary microlensing

The upcoming Nancy Roman Grace Telescope will survey the sky in the direction of the galactic bulge looking for micro-lensing events. It will use a wide-field camera to look at the same region of the galaxy repeatedly for transient events. It will be able to discover rogue planets down to the size of Mars.

I don't think the distance to us really matters much - it's more about the geometry between the rogue planet and the star it is lensing. This technique will also be used to detect Earth-sized exoplanets around other stars.

Nancy Roman Grace Galactic Bulge Time Domain Survey