Valeri,

(fascinating question)

Photometric variation, or Doppler broadening are the only methods I can think of off the top of my head.

Both require an intrinsically radiant object, and without a star to illuminate the vagrant world it'll be a challenge to get enough photons to do either.

If the object has a magnetic field, the frequency and periodicity of radio emission can give a handle on the spin rate.

Perfect answers :-)

The deep interior and maybe near the surface as well should be conductive due to pressure ionization and degeneracy.  With a primordial magnetic field as a seed there is probably dynamo action. Consequently there may be output of energetic particles and radiation so looking for emission and variability in microwave and radio wavelengths is one way to probe the processes in these objects.  If there is variability then that would provide a means of determining the rotation rates.  You may need to use the highest sensitivity so systems like ALMA, the VLA and Arecibo would be good bets.  You need to pick the targets that are closest.

I have never heard of the term Solivagant before. I like it better than "rogue." 

If you can see it in the Far-IR, you should be able to see the effects of surface albedo fluctuations and thus get a rotation period as you would for an asteroid or Kuiper belt object. Of course, for the magnetized bodies, the radio emissions will also vary with the rotational period. 

These methods are indeed probably tho only possibilities. Though, they imply to have a significant amount of time on these objects, knowing that the facilities to reach these goals are very requested. How fast is a "rapid rotation" ?

How fast is a "rapid rotation" ?

At one level, anything significantly faster than Jupiter. 

Given that the fastest known brown dwarf rotation is 1.96 hours*, and there is a general increase in rotation rate with mass,  and that we by no means have complete statistics here, I would say that we should be prepared to see planetary rotations as fast as 1 hour. 

* see http://arxiv.org/pdf/1210.1864v1.pdf

It seems to me that the Doppler broadening of the spectral photometric changes brightness is the only method.

But this requires a significant flow of light. And if the body have no stars, then it must be observed in the infrared spectrum.

I agree with D. Spiegel answer. As an example of how radio emissions can be used to get information about an exoplanet rotation, you can have a look at this paper:

http://www.aanda.org/articles/aa/abs/2011/07/aa16510-11/aa16510-11.html

β Pictoris b spins with a period of 8.1 hours - see http://www.eso.org/public/archives/releases/sciencepapers/eso1414/eso1414a.pdf

Note that this was determined using absorption spectroscopy, which is not likely to be available for nomads. For nomads, I think the choices are only IR or CMI radio. 

My main concern regarding the photometric method (in the infrared) is the availability of photons. Realistically, we can expect rather small amplitudes of variation from surface features. Given the intrinsically faint signal, and a small periodic change we would need to detect, single photons would need to be counted resulting in extremely long integration times to accumulate a decent, confident SNR. Are there any estimates for the hypothetical nearby solivagants with JWST, for example?

The radio detection looks promising to me, but may be because I do not know much about this kind of radiation. Thanks for the references. There is a call for ALMA proposals, if I am not mistaken -- could that make a reasonable project? Can accurate astrometry be obtained in the radio as well?

On the issue of how fast is a fast rotation, in the framework of potential habitability, a rotation period significantly shorter than the orbital period of the exomoon is fast enough to generate a substantial amount of internal heating. Such systems may also have tidally boosted eccentricities, even if the exomoon is synchronized. As M. Eubanks suggested, Jupiter's rotation can be a useful benchmark, but even periods as long as 1-2 days are of interest.

Clearly, there are going to be troubles with collecting enough photons, even in the far-IR. In fact, my paper shows that a nearby "dark Earth" will likely be undetectable with near-term technology, unless one is either unexpectedly close or unexpectedly young. I think that finding such bodies will take a substantial space effort - very large IR telescopes in space, full sky deep transit instruments, or large low frequency radio arrays on the Moon. That will likely put such discoveries 20 - 30 years _or more_ into the future. 

If there is a push to improve spacecraft velocities by roughly an order of magnitude every 10 to 20 years, and if 10-15 years remains an acceptable duration for a single mission, then by the 2060 or so we could be sending fast flyby missions to examine the nearest nomadic planets in situ. By that time, the technology to find such bodies should be well advanced, and there would hopefully be no shortage of possible targets for such missions. 

Valeri,

I'm struggling a little to imagine what processes might be at work that yield a radio signature and can come up only with a Jupiter-Io magnetospheric flux tube - that would do the job - a nice strong decametric source. That's an interesting question - don't recall off-hand what the total power is in RF emission, but it's bound to be higher by a handful of orders of magnitude than the reflected starlight from a vagabond world.

(what a wonderful question!)

Valeri;

What I was thinking of possibly proposing to ALMA would be a parasitic survey mode - to look for moving nomadic planets in their data. Note that a dark Jupiter at 3 ly could easily move 20 mas / day, or ~ 1 mas / hour, due to parallax and proper motion. As ALMA is supposed to reach ~ 0.1 mas accuracy in 8 hours, ALMA would observe nomadic planets as streaks in a long observation (exactly as a deep optical image would see a KBO as a streak). A single 8 hour integration could lead to a 10 sigma detection; what would be needed would be the infrastructure to routinely search for moving sources in each ALMA image.

A couple of thoughts on this interesting question which subdivides into two somewhat separate issues: 1) How do you find the candidate nomadic planets and 2) How do you determine that it is rapidly rotating.  The ALMA approach gets both parts at once so that is good.  Another way is to pick out single dip events from the Kepler data base.  These might be from a nearby nomadic planet that happens to wander in front of a background star.  After a bit of time, the planet would be far enough away from the background star that you could find the microwave emission with ALMA as a separate object then follow it as the separation increases.  Such a detection could only be successful for those nomadic planets that are also rapidly rotating.

Roger, Kepler is looking at rather too few stars to have much of an expectation to see a _nearby_ nomadic planet, although it does have the right cadence (integration time, in its case). (This is briefly covered in the paper, BTW.) 

Note that a "transit"* instrument with multiple telescopes would be very useful, both in weeding out false positives AND in determining the angular velocity of the transiting body. Something like the TAOS array would probably be best

* Most nomadic planet transits, down to Earth mass and below, would actually cause microlensing and thus would amplify the background flux, not reduce it. 

Marshall,

This is an excellent idea to use ALMA for a serendipitous search of nearby solivagants en masse. Alexey Goldin and I wrote a high-efficiency algorithm to automatically detect streaking objects in Pan-STARRS detection data and successfully tested it a year ago on preliminary MDS 10 data. Now we are waiting for the public release to run this algorithm for the entire 3\pi of the sky.  

I agree that catching a random planet as a transit across a stellar disk may be rather improbable, but more distant passes should result in microlensing spikes in the light curves.

Dear Valeri

There is a lot of interest in the microlensing community to move to shorter cadences - this survey http://arxiv.org/abs/1406.2316 should certainly be able to detect nomadic planets from the ground. Now, if you could just do that all sky and from space...

There is a strong need for these high cadence microlensing surveys - we need them to determine whether or not the nomadic planet number density increases or decreases as the mass decreases, That will reduce the uncertainty in the distance to the nearest "dark Earth's" - of course, it would be convenient if these are located 1 ly away rather than 5. 

You could model how the rotation rate of a rogue planet affects the microlensing signal it produces as a function of planet mass and radius and re-analyze microlensing events in the literature.  Not sure if this has been done yet.

Valeri, you may know that I have long thought that the USNO should become a spacefaring entity (my biggest beef with KJ / FAME was that he was trying to run it purely with beltway bandit consultants). So, in that light, consider the Whipple telescope proposal : 

http://www.lpi.usra.edu/decadal/sbag/topical_wp/CharlesRAlcock.pdf

http://www.tiara.sinica.edu.tw/activities/workshop/20081208/lecture/Alcock_Whipple_TIARA.pdf

There are strong overlaps here, with the same technology being able to discover Oort cloud objects, with occultations, and nomadic planets, with microlensing (and much else besides). One difference is that nomadic planets are big enough that an event would benefit from a rapid response on the ground (i.e., looking at the star in question say 10 seconds later from a ground based telescope). 

Just something to think about...

Dear Lauren; 

Excellent idea, but I fear that is going to be tough. These are not black holes (fortunately), their gravitomagnetism will be tiny. Now, if they spin fast, they should have a large J2 / oblateness, which will affect their lensing (in a static field fashion, not via frame dragging), but in a second order way (as its effect on lensing goes as 1/R^3 IIRC). A quick search reveals 

http://iopscience.iop.org/0004-637X/572/1/540

I'll have to take a look at it. This would, BTW, argue for a TAOS type approach - more telescopes to sample the light curve at different latitudes. 

Hi Marshall,

The above paper by Hui & Seager is about how oblate planets affect transit light curves (i.e. when they have a host star), not microlensing light curves (which are used to detect rogue planets).  The effect on a microlensing light curve will be totally different.

L

You are of course correct. 

I suspect no one has done this - there is a little work on oblateness for gravitational lens  _sources_ http://www.astronomy.ohio-state.edu/~gaudi/structures.pdf but we are interested in lens structures. As I said, I think it will be hard to see for realistic oblatenesses. 

Dear Lauren,

Determining the spin rate of close-in exoplanet with a host star is an interesting, open issue too, although perhaps separate from the original question, because the technical approach may be different. How do tidally interacting exoplanets rotate, are they synchronized, pseudo-synchronized, or perhaps captured in higher spin-orbit resonances? We do not really know. Thelatter possibility is especially intriguing as the signatures in Kepler transit curves can be discernible.

This new paper shows the power of terrestrial parallax, 

http://arxiv.org/abs/1412.1546

If the spin can be measured at all, I think terrestrial parallax will be involved. 

Most galaxies, projected on the sky, are elliptical, and so there are a number of papers dealing with lens ellipticity (oblateness) for strong lensing (see below). I  do not think there will be much difficulty in introducing this into the microlensing formalism. Whether or not the data will be good enough to actually determine nomad rotation oblateness is, of course, another question. 

http://iopscience.iop.org/0004-637X/482/2/604/pdf/0004-637X_482_2_604.pdf