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‘Oumuamua: Some More Strangeness

So is ‘Oumuamua natural or artificial?

First it should be understood that a clear and unequivocal answer to this can only be achieved by an in-situ examination.

The artist impressions of ‘Oumuamua which have become memes on the internet generally depict ‘Oumuamua as an elongated cigar-shaped rock. This meme may have done a great deal of damage to scientific objectivity because it seems often to be implicitly assumed that they are the best images science can come up with, or alternatively even that they are true pictures of ‘Oumuamua and that the nature of ‘Oumuamua is completely understood.

In fact neither of these is true and indeed we know that a flat-pancake would be a more likely shape to explain the changes in brightness with time – the light curve – for ‘Oumuamua.

So the true nature of ‘Oumuamua remains unresolved but nevertheless one can still look for more oddities which might make ‘Oumuamua even more special.

There is a whole list of unusual traits together betray ‘Oumuamua’s weirdness, some of these are listed below:

  1. Its unusual shape – either elongated or flat
  2. A strange force which could be outgassing or solar radiation pressure
  3. Its high reflectivity
  4. Its speed w.r.t. the sun is close to our solar system’s local speed through interstellar space
  5. It came from around the Solar Apex, the direction in which the solar system is heading through interstellar space

As far as (4) & (5) are concerned, these combined facts suggest that ‘Oumuamua was almost fixed in interstellar space when our solar system ploughed straight into it (this observation has been made by many scientists including Avi Loeb [1] by the way).

So let us assume that ‘Oumuamua’s motion relative to interstellar space was close to static whilst its motion relative to our sun was almost entirely a consequence of the sun travelling through interstellar space. Thus as we Earth observers are concerned, ‘Oumuamua’s orbit started a) close to the Solar Apex and b) at an initial speed of 26.4km/s with respect to the sun.

Do these two constraints (a) & (b) completely specify all the orbital parameters for ‘Oumuamua?

Just as a reminder the orbital parameters of a celestial body are a set of 5 numbers which completely define the shape, orientation and plane of the body’s motion. Furthermore if we also throw in an epoch, like for example a time of perihelion (closest approach to the sun), then that makes 6 orbital parameters altogether. Are all these parameters defined when we specify (a) & (b)?

The answer is no. Firstly let’s take the epoch – the time and date of perihelion. This could have taken any value, and varying it would have increased or reduced the perigee distance (that’s the closest approach to Earth which for ‘Oumuamua was only 0.16 au) accordingly.

Furthermore there are two additional parameters which would be required to completely specify ‘Oumuamua’s orbit. These are the impact parameter, b, and the β (Beta) angle, defined below and in Figure 1.

Figure 1 Diagram illustrating the Beta Angle, β, and the Impact Parameter, b

For the definition of b and β, let’s take the direction from which ‘Oumuamua arrived in the solar system (the arrival asymptote), this would be in a direction approximately parallel to the Solar Apex. If we extend this approach direction forwards toward the sun it would pass by the sun at a ‘closest approach’ vector, b, the magnitude of which is the impact parameter, b. This vector b lies in a plane normal to the approach direction. The parameter β is the angle between a line in this plane and parallel to the ecliptic plane, iβ, and the vector b . This is all illustrated in Figure 1.

So what we shall assume in the following analysis is that ‘Oumuamua came from approximately the Solar Apex with speed 26.4km/s, but there was a degree of ‘randomness’ in the following values:

  1. The time of perihelion
  2. The impact parameter, b
  3. The Beta angle, β

When we use the word ‘randomness’ we must be more specific as to the exact nature of this, because ‘randomness’ comes in many guises - many shapes and sizes.

For (1) we shall assume that the time is uniformly distributed in the year 2017, ‘Oumuamua’s arrival year

For (3) the β value can take any value between 0° and 360°, again uniformly distributed

As for (2) this is the difficult one.

When b = 0au, then the approach direction is aligned with the centre of the sun and we get an orbital singularity, this needs to be avoided so that the computations are not faced with any annoying infinities. For information, I chose b in the range 0.1au < b < 2.0au corresponding to minimum perihelia intersecting the sphere of the sun (for b = 0.1au) to maximum perihelia at approx. 1.0au (for b = 2.0au). (Also note here that the results don’t vary too much with the chosen minimum value of b – in this case 0.1 au.) As for the uniform distribution (and unless you are technically savvy, you might want to skip the following bit), this does not strictly apply for b, because if we assume that there is an even distribution of interstellar objects intersecting any given plane at any point in time, we would thus expect that the likelihood of b would increase proportionally with b as it increases. However I have again assumed a flat, uniform distribution of b, which we shall bear in mind as being an approximation in what follows.

So what happens when we try lots and lots of different combination of (1), (2) & (3), distributed in the manner described above, what is the resulting distribution of perigee distances? Note that this problem can be resolved by a Monte Carlo Simulation, where many parameters which are known and are subject to a known level of uncertainty are randomly selected many times over and the resulting distribution of an unknown parameter can then be established. Figure 2 shows the results of the solution to 1000 such simulations.

Figure 2 Probability Histogram for Perigee Based on 1000 Solutions

To put numbers to this, we have a probability of ‘Oumuamua coming within 0.16au of Earth (on the far left of Figure 2) as about 2.3%. We could compare this with other research which has been conducted in this field. Refer to [2], wherein we find distributions of various orbital parameters for ISOs encountering our solar system. Note [2] makes no assumption as to the incoming velocity vector that we have made here, though does make the point that most ISOs will come from the Solar Apex. If we refer to Figure 9 in this paper, we see the distribution of Perigee distances for putative ISOs. Observe there is a similarity in the profile, the chief difference being the number of solutions in [2] is much larger allowing more resolution and a higher number of bins.

We can now address the issue as to what the traditional orbital parameters of ‘Oumuamua would have looked like for different values of (1), (2) & (3), again keeping ‘Oumuamua’s initial approach speed and direction (approx. Solar Apex) constant.

I have performed this analysis and have discovered nothing extraordinary stands out apart possibly from inclination.

To understand inclination, think about a spinning top. Imagine a massive spinning top whose disc lies in the plane of the solar system (the ecliptic) and its handle sticking up vertically at right angles. ‘Oumuamua’s orbit also can be considered as a plane, in this case the handle is at an angle to that of the solar system’s. This angle is equivalent to the orbital inclination.

For ‘Oumuamua its inclination was about as high as it could possible get, just about the yellowest and brightest area in Figure 3, at around 123°.

Referring this time to Figure 6 of reference [2], which provides the inclination distribution of ISOs, we see no cut-off of inclination at around 123°, instead where ‘Oumuamua’s inclination is provided, there is a gradual downward slope to the right of the probability histogram. One must suppose therefore that their ISO model must have included a significant fraction of ISOs originating from elsewhere and not from the Solar Apex.

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Figure 3 Possible Orbital Inclinations of 'Oumuamua

Conclusion

We have discovered two further peculiarities to ‘Oumuamua’s orbital path on top of the other unusual characteristics already known and listed above. To be precise, the close perigee has already been identified as being unusually low, here I have quantified the probability as around 2.3%, given the aforementioned assumptions.

In addition the inclination of ‘Oumuamua’s orbit reached about its highest possibility value. I have yet to assess the full implications of the latter, however observe that this means that ‘Oumuamua’s orbit was just about as retrograde as it could possibly be, remember an inclination fully retrograde (at 180°) would be impossible due to the assumption that ‘Oumuamua came from around the Solar Apex, and so initially had a considerable latitude.

Adam Hibberd

July 2022

Bibliography

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1.LOEB, A. 6 Strange Facts about Interstellar Visitor 'Oumuamua. Scienitific American, November 2018. Disponivel em: <https://blogs.scientificamerican.com/observations/6-strange-facts-about-the-interstellar-visitor-oumuamua/>.
2.HOOVER, ; SELIGMAN , Z.; PAYNE. The Population of Interstellar Objects Detectable with the LSST and Accessible for In Situ Rendezvous with Various Mission Designs. arXiv. Disponivel em: <https://arxiv.org/abs/2109.10406>.

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