# What wavelength to best detect the “9th planet”?

We know that the reflected sunlight will make detecting the 9th planet very difficult in the visible light. Is there another band that will be more likely to detect it? What is the surface temperature of this object likely to be, and what would that mean about its optimal detection wavelength?

• If it exists. – David Hammen Jan 22 '16 at 12:16
• Even if it doesn't exist, asking a question like this helps to decide if in fact it does exist. – PearsonArtPhoto Jan 22 '16 at 12:17
• That's really a separate question, I would suggest that you ask why WISE didn't detect this object, which could lead to some interesting discussion. – PearsonArtPhoto Jan 22 '16 at 12:39
• All bets are off if this supposed ninth planet is a magically captured rogue planet that is much older than the solar system. In that case, it will have cooled to the state of near invisibility. – David Hammen Jan 22 '16 at 12:44
• @DavidHammen Yes, there is no "Saturn" within 10,000 au. But this possible planet 9 is probably not a gas giant. Unless it were significantly heated by radioactivity or tides in some way (see answers below), it could not possibly be seen by WISE at 1000 au (its equilibrium temperature would be too low). Perhaps this is the reason (I have not seen any paper yet), why the authors say it is likely not a gas giant. Do you have a reference/URL for where a calculation for a Neptune-sized object in WISE is done? I can only find limits for Jupiters/Saturns. – ProfRob Jan 22 '16 at 16:54

Direct reflection of sunlight is the most likely scenario for a ninth planet discovery, however that does not hold if the object has a very low albedo. I assume you are interested in what wavelengths the planet would radiate.

For the surface temperature, the rotation of the planet is important. If it is locked with one side facing the sun, or rotates very slowly, the centre of the sun facing hemisphere radiates as much energy as it gets from the Sun. At 60 AU, the solar flux is about 0.38 W/m². Using the Stefan-Boltzmann law, we obtain a equilibrium surface temperature of 51 K (that is the highest possible surface temperature, assuming it does not have an atmosphere). Wien's displacement law tells us that radiation from a 51 k object peaks at a wavelength of 57 µm (infra-red).

For a rotating body, the equator temperature is 38 K, with radiation peaking at 78 µm (still infra-red).

Using an albedo of 0.5, the peaks are 68 µm and 90 µm for a non-rotating and a rotating body respectively. Note that this is for the equator region only, the actual peak-wavelength is going to be a little bit higher, belonging in the far infra-red spectrum. Also, the high uncertainty of rotation, albedo and mass (mass is important for internal heat), makes it impossible to get a higher accuracy than that

60 au is a very optimistic perihelion distance for the ninth planet, so for a more realistic distance of say 200 au, it is not possible to observe it in the IR spectrum, if it does not have a significant internal heat source.

• Interesting, although I believe radioactive decay, among other factors, would also be a significant influencer in the surface heat. – PearsonArtPhoto Jan 22 '16 at 14:59
• You have to factor in how difficult it is to measure anything at those wavelengths. You would need a working cryogenic IR space telescope for one thing. – ProfRob Jan 22 '16 at 16:14
• The possible planet 9 is a lot further away than 60 au ? It will only be detectable in the IR if it has some sort of internal heat generation. – ProfRob Jan 22 '16 at 16:27
• 60 au is best case – SE - stop firing the good guys Jan 23 '16 at 10:01
• I have to say, I have yet to hear of 60 AU being used, even as a perihelion distance. The figures I've seen are easily in the hundreds of AU. I'm curious to know your source for that. This is just a minor point, though - maybe. – HDE 226868 Jan 24 '16 at 22:03

The possible planet 9 is thought to be about 10 Earth masses and is unlikely to be a gas giant (it may be the core of an "interrupted" gas giant). As such, it will not be generating significant luminosity itself and would be rocky, or more likely, icy in character. It would thus only be seen by reflected light.

The considerations for what wavelength to search in balance the sensitivity of the instruments at hand with the likely spectrum of the object. This in turn depends on the solar spectrum and the wavelength dependence of the reflectivity (albedo).

For most icy objects, including Pluto and Trans-Neptunian objects, the reflectance increases to the red and near-infrared, whilst the solar spectrum peaks at shorter wavelengths. This suggests that searches are best carried out with wide field optical instruments in the R or r' bands at around 600 nm.

A further factor in finding a candidate is that you are going to have to cover a large area. This is only feasible at optical and NIR wavelengths unless the object was bright enough in the mid-IR to show up in WISE (which I'm sure is being thoroughly checked). A press release I saw said SUBARU is being used for the search. I would bet they are using the half degree field of Suprime-Cam at optical wavelengths and not pursuing COMICS mid-IR imaging with it 42x32 arcsecond field!

Confirming a candidate should be easy, given the enormous parallax and proper motion expected.

• I'm not sure that kbo observations would be valid. This object is predicted to be much larger that a typical kbo... – PearsonArtPhoto Jan 22 '16 at 14:22
• @PearsonArtPhoto Feel free to make up your own reflectance spectrum. Even if it were flat that might only shift the search range to the V or g' bands. – ProfRob Jan 22 '16 at 14:24
• The reflectance spectrum is probably close, I will give you that, but I'm somewhat more skeptical of the thermal IR detection possibilities. See my answer. – PearsonArtPhoto Jan 22 '16 at 15:10

There are two basic ways to detect such an object. First is to detect it through reflected sunlight. Second is from the heat that it produces. We already know that the reflected light of such an object likely would be around a 16.5 magnitude. To determine the infrared, we have to estimate the temperature

The temperature very much depends on the composition. For simplicity, let's assume a composition similar to Earth, and was created about the same time as the rest of the Solar System. These assumptions may not prove to be valid, but they are among the possibilities discussed. Earth's internal heat, in fact, is at least 50% from radioactive decay, according to Scientific America. Of course, that's the internal heat only, not all of that will make it to the surface.

This proposed planet is somewhat akin to a "Rogue Planet", where a small disk of gas collapsed into a planet without a star, or were ejected from their host system. A fair bit also depends on if there is a sizable moon of the object. If so, then tidal heating would dramatically increase the temperature of the object. Any such determination can't be made without observation, but it is possible. An atmosphere would also help to keep the planet from freezing. A paper for detecting rogue planets comes from Abbott and Switzer. They hypothesis that a 3.5 Earth Mass object could be detected if it comes within 1000 AU, specifically in the far infrared, with a surface temperature of about 50 K.

Bottom line, it would probably be wise to try to detect both in the far infrared, as well as the visible, although it might be difficult to detect, even then. Given parallax as the primary means of motion, the detection should be done at several points in Earth's orbit, probably the same spot should be searched about 90 days apart to give the maximum opportunity to move, as parallax would only be visible if the motion of the Earth was perpendicular to the location of the object.

• A third method would be to discover several more comets (or TNOs or KBOs) who have had their orbits shaped by this Ninth guy. Even if directly unobserved, a planet like this will become more real if the evidence stacks up. And IR survey space telescopes, and maybe other survey telescopes, in the pipeline should improve the detectability of its "victims" by alot. – LocalFluff Jan 22 '16 at 15:06
• True enough, but no one is really going to consider it solved until they have detection of it. All that further evidence really does is to shrink the part of the sky to look for it. – PearsonArtPhoto Jan 22 '16 at 15:09
• I do not think there are any far-IR survey-type facilities and this has to be factored in. Sure, look for it in the far-IR after it has been found. The search is taking place with Subaru according to the press release. My guess is they are using the half degree field of the optical SuprimeCam and not the 42x32 arcsec of the COMICS near and mid-IR camera ! – ProfRob Jan 22 '16 at 16:19
• I'm not sure how realistic this approach is, but in theory wouldn't you be able to find Planet9 by looking for objects that are hidden? By that I mean, make comparisons of the sky and find objects that are missing that normally should be visible. – TryHarder Jan 23 '16 at 11:20