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A recent paper on Oumuamua claims the following:

'Oumuamua (1I/2017 U1) is the first object of interstellar origin observed in the Solar system. Recently, Micheli et al. (2018) reported that 'Oumuamua showed deviations from a Keplerian orbit at a high statistical significance. The observed trajectory is best explained by an excess radial acceleration Δa∝r−2, where r is the distance of 'Oumuamua from the Sun. Such an acceleration is naturally expected for comets, driven by the evaporating material. However, recent observational and theoretical studies imply that 'Oumuamua is not an active comet. We explore the possibility that the excess acceleration results from Solar radiation pressure. The required mass-to-area ratio is m/A≈0.1 g cm−2. For a thin sheet, this requires a width of w≈0.3−0.9 mm. We find that although extremely thin, such an object would survive an interstellar travel over Galactic distances of ∼5 kpc , withstanding collisions with gas and dust-grains as well as stresses from rotation and tidal forces. We discuss the possible origins of such an object including the possibility that it might be a lightsail of artificial origin. Our general results apply to any light probes designed for interstellar travel

This assumes the impulse is merely due to radiation pressure, so assuming that the outgassing is zero or below some upper bound. Is not clear how tight is the upper bound in outgassing thanks to lack of gas activity during perihelion.

But the more interesting aspect is that acceleration excess decreases with inverse square law. Outgassing pressure has dependency with temperature as well as pressure, is not clear to me that one would expect outgassing pressure to follow inverse square law just like radiation pressure, but something that depends on the thermodynamic sublimation properties of the hypothetical surface solid

Is outgassing a viable explanation to acceleration dependence with inverse square law of distance? how tight is the upper bound on undetectable outgassing?

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    $\begingroup$ This may be a better fit for the astronomy stack exchange. $\endgroup$ – Organic Marble Nov 3 '18 at 20:57
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    $\begingroup$ @OrganicMarble I've left an answer, but people in Astronomy could have more to say as well. $\endgroup$ – uhoh Nov 3 '18 at 23:23
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tl;dr: The paper only explores the possibility that Δa doesn't come from outgassing and asks what are the implications if it were only radiation pressure. It shows that something hard and very thin could have survived the trip and exhibited the Δa due to radiation pressure alone. It doesn't say that that's what did happen. This leads to some interesting possibilities:

E.T. lost her kite!

We discuss the possible origins of such an object including the possibility that it might be a lightsail of artificial origin. Our general results apply to any light probes designed for interstellar travel.

enter image description here

Source: Washington Post's Harvard’s top astronomer says an alien ship may be among us — and he doesn’t care what his colleagues think

Avi Loeb poses in the observatory near his office in Cambridge, Mass. His theory about an alien spaceship has made the rounds in the media and caused controversy in the academic community. (Adam Glanzman/For The Washington Post)


This is a good question, and the OP is right. While the solar illumination on a solar-system body will scale as r-2, the various resulting propulsive effects may have more complex behavior.

Let's start with the linked paper there.

The ArXiv paper Could Solar Radiation Pressure Explain ‘Oumuamua's Peculiar Acceleration?'s abstract says:

The observed trajectory is best explained by an excess radial acceleration Δa∝r−2, where r is the distance of 'Oumuamua from the Sun. Such an acceleration is naturally expected for comets, driven by the evaporating material.

One key to the OP's question lies in what the phrase "...is best explained by..." means, or at least how it is often used in science. In cases like this it really just means "can be fit by" or "is consistent with".

  1. ACCELERATION BY RADIATION PRESSURE

Micheli et al. (2018) had shown that Oumuamua’s experiences an excess radial acceleration, with their best fit model

$$\Delta a = a_0\left( \frac{r}{AU}\right)^n$$

with n = -2 and a_0 = (4.92±0.16)×10−4 cm s−2

That's Micheli, M., Farnocchia, D., Meech, K. J., et al. 2018, Nature, 559, 223: Non-gravitational acceleration in the trajectory of 1I/2017 U1 (‘Oumuamua) Non-paywalled draft and downloadable researchgate

That's pretty small, the paper postulates that if 'Oumuamua were only a few millimeters thick, then the deviation from Keplerian could be explained by the weak solar pressure.


The OP mentions:

Outgassing pressure has dependency with temperature as well as pressure, is not clear to me that one would expect outgassing pressure to follow inverse square law just like radiation pressure, but something that depends on the thermodynamic sublimation properties of the hypothetical surface solid

That's certainly right. But with such a small amount of data from an object so far away with so little known about it, astronomers will reach for the simplest functions to start, and in cases like this (and others) those are usually power laws.

In my question Did Rosetta improve on models of non-gravitational effects on comet 67P's orbit? I outline the Marsden parameterization for non-Keplerian effects on solar-system bodies.

Using the following convention: $\hat{\mathbf{e}}_R, \ \hat{\mathbf{e}}_T, \ \hat{\mathbf{e}}_N$ are unit vectors at the location of the comet in the radial, transverse, and normal directions where $\hat{\mathbf{e}}_R$ points away from the sun, $\hat{\mathbf{e}}_N$ is the direction of the angular momentum vector (perpendicular to the orbit plane) and $\hat{\mathbf{e}}_T$ is perpendicular to the first two and approximately in the direction of motion, non-gravitational accelerations can be parameterized using the empirical equations:

$$\mathbf{a}_{NG} = ( A_1\hat{\mathbf{e}}_R \ + \ A_2\hat{\mathbf{e}}_T \ + \ A_3\hat{\mathbf{e}}_N) \ g(r), $$

where:

$$g(r)= 0.111262\left(\frac{r}{2.808}\right)^{-2.15} \left(1+\left(\frac{r}{2.808}\right)^{5.093}\right)^{-4.6142}, $$

and the acceleration coeficients $A_1,A_2,A_3$ commonly have units of $AU / day^2$.

That's a parameterization and the exponents of those two power-law terms are just optimized somehow. They are meant to capture some effects of outgassing without getting into the gory details.

More about Brian G. Marsden: Wikipedia, and New York TImes and Columbia University.


Enough with the background already! What's the point?

The linked ArXiv paper Bialy and Loeb 2018 would like to explore the possibility that the acceleration deviation might be only due to radiation pressure without outgassing. Not that it doesn't, this is only a "what if". This "what if" is consistent with the data, (which itself is consistent with inverse-square), if 'Oumuamua were a few millimeters thick.

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    $\begingroup$ so basically this paper is not tackling the issue of minimal outgassing that is consistent with non-observation, it is just assuming it is zero or much less than the radiation pressure $\endgroup$ – lurscher Nov 4 '18 at 15:09
  • $\begingroup$ @lurscher that's my understanding, yep. Really not so much assuming as just "what if-ing." $\endgroup$ – uhoh Nov 4 '18 at 15:14
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According to Drahus et al, the non-gravitational acceleration is "remarkably strong"... https://ui.adsabs.harvard.edu/#abs/2018DPS....5030102D

The above article provides upper bounds on any remnant outgassing. While another answer suggests that a non-gravitational $r^{-2}$ acceleration of (4.92±0.16)×10−4 cm s−2 at 1 AU is "pretty small", from the perspective of scientists who've looked at this carefully, that discrepancy is not at all small, and in fact quite puzzling and the subject of active research.

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  • $\begingroup$ If we're not supposed to respond to other answers then why do you do just that? Either make this a comment (read this and this) or edit this into a decent answer (read this). $\endgroup$ – Jan Doggen Nov 8 '18 at 21:43
  • $\begingroup$ thanks! I was wondering about that too, if they are getting such a thin sail from the calculation it means that this is going rather strong. This is why I was wondering about the upper limit of outgassing, because in reality even a little bit of outgassing can result in a lot of thrust, at least when you compare with solar pressure $\endgroup$ – lurscher Nov 8 '18 at 21:51
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    $\begingroup$ actually @MarkOmo, I think it provides information that was not on the accepted answer. Perhaps with a reformatting, it could be a good complementary answer, and avoid leaving this extra information at risk of being potentially lost when comments are moved into chats $\endgroup$ – lurscher Nov 8 '18 at 22:45
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    $\begingroup$ yes, indeed this paper provides upper bounds of outgassing, which was the second part of my question $\endgroup$ – lurscher Nov 8 '18 at 22:49
  • $\begingroup$ The last sentence of the abstract in your link: "'Oumuamua's tumbling is consistent with an ancient collision in the body's home planetary system, but might have also been caused by the mysterious non-gravitational forces during 'Oumuamua's passage through the Solar System." might be a bit sensationalizing. Astronomical observation yields data that can't be easily explained all the time. Just because we can't explain the motion of a dot tens or hundreds of millions of miles away to the last arcsecond doesn't necessarily mean there are "mysterious forces" at work. $\endgroup$ – uhoh Nov 9 '18 at 0:41

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