The next round of WTF star papers continues. Brian Metzger (whom I know from grad school), Ken Shen, and Nicholas Stone have submitted a paper to MNRAS exploring in detail the idea that that Boyajian’s Star is dimming secularly because it recently “ate” a companion, and it’s still processing the energy from the merger, which is slowly “dribbling” out as an excess of luminosity.

Steinn and I explored this in our rundown of possible explanations. It appeared as hypothesis 13 in my blog post as “post-merger return to normal” and in our paper in section 11.3.

We had two primary objetctions: it would not really explain the dips, and the timescales are all wrong. We wrote:

One issue here is that the dimming is too fast. When confronted with big changes in energy content or flux, stars evolve on the Kelvin-Helmholz timescale, roughly the time it takes for all of the energy in the star at a given moment to finally escape the surface (while being constantly replenished by the fusion in the star’s core). For Boyajian’s Star this timescale is about 1 million years. This means that if the entire star is processing a big change in internal energy or luminosity, it takes around 1 million years to complete the adjustment. Changing by 15% in 100 years is therefore about 10,000 times too fast. But, the star’s radiative envelope is not very massive, so perhaps the energy never made it deep into the star? In that case the Kelvin-Helmholz timescale is a bit shorter, so maybe we’re off by only 1,000 times. It’s an order of magnitude argument, so maybe we’re being too pessimistic by a factor of 10, so we’re only off by 100 times. It’s possible that a detailed simulation of such a merger will reveal shorter timescale events, perhaps even things that might produce the dips. So, I’m intrigued, and I like the idea despite the timescale argument not working out. It’s possible that there are other ways to temporarily brighten a star we haven’t thought of. I’d like to hear from people who model these things before I commit to a plausibility level, so I’ll say: Subjective verdict: unclear.

Well, Brian Metzger and company have come through. In their paper, they look at the same mechanism Neslušan and Budaj explored to put material on highly eccentric, “cometary” orbits around the Boyajian’s Star. The idea is that the close companion (which is presumably bound to Boyajian’s Star) interacts with material (anything from comets, planets, brown dwarfs to other stars) and slowly perturbs it into a highly eccentric orbit. Then, if it’s comets, it outgasses when it gets close and you get the big dusty comae that might cause the dips.

Metgter et al. invoke the same mechanism to put a heavier object on an eccentric orbit, then have that object merge with Boyajian’s Star. They deposit the energy into the envelope of the star, then run a stellar structure and evolution code called MESA to see how the energy is processed.

Their key result is their Figure 2:

It shows, on the top, the total brightness of Boyajian’s star after merging with four fiducial objects of very different sizes. The extra energy here is coming from the object’s orbital kinetic energy, which gets dissipated as heat when the two objects merge and eventually comes out as starlight. Bigger objects have more energy to deposit, and deposit it at different levels.

The bottom plot shows the fractional change in the star’s luminosity with time (it’s the time derivative of the top plot divided by the top plot). Zero means the star is not changing brightness, -0.01 means that the star changes its brightness by one e-folding (a factor of 2.7) in about 1/0.01 = 100 years. The grey bands are the long-term dimmings seen by the DASCH plates over the last 100 years (top) and by Kepler over 4 years(bottom).

Steinn and I argued that the values you get in this scenario are more like -10-6, so way too small to notice. What Metzger et al. have shown is that most of the energy does indeed end up in the envelope—the top millionth of the star’s mass—so time timescales are correspondingly shorter. Our order of magnitude estimate was way way off, and so the hypothesis may be plausible after all (we recognized this could be the case in our paper, which is why we declined to give this scenario a plausibility).

So there are regions of the graph where all four curves cross the secular dimming levels seen. This means that the model does not have to commit to what merged with Boyajian’s Star to explain the dimming.

So where does this scenario rank now? There are still several details to be worked out:

First, there’s the dips. Metzger et al. point out that the same mechanism that sent the object into the star could also send other material there — a big planet could have lost its moons during a merger, or a planet could have been ripped apart, or something similar. This is essentially Boyajian et al.’s original hypothesis of material on a cometary orbit due to a single disruption event. The big difference is that there was originally a lot more material in the form of something that fell into the star.

Then, there’s the lack of infrared flux. Again, the highly eccentric orbits save the hypothesis, and Metzger et al. point out that stellar radiation will blow sufficiently small dust out of the system, where it would no longer be warm and radiate.

The next is the details of the Montet & Simon light curve. It changes slope pretty dramatically, and overall is steeper than the Schaefer dimming. What does this imply? I don’t see similar changes in slope in the Metzger et al. models, but presumably they’re invoking multiple ingestion events. Is this a problem for the model, or does it perhaps tell us the timings and masses of the mergings?

The next is the luminosity. The European Gaia spacecraft will measure the distance to the WTF star very precisely. This, combined with its apparent brightness, will give us the total luminosity of the star quite precisely. This should give constraints on the merger history of the star. Combined with the various secular dimmings, this should constrain the model—or prove inexplicable. It would be nice to know what Gaia weill tell us, if anything, about this model. It would be especially nice if this model turned out to make a falsifiable prediction for the parallax.

Finally—and Metzger et al. acknowledge this is a major flaw in the model—there’s the issue of how likely this is to happen. Steinn and I have argued that whatever the explanation for Boyajian’s Star, it’s got to be an unlikely one because it’s unique among 200,000+ stars Kepler has observed. But this scenario turns out to be really unlikely—like Kepler had all but zero chance of seeing such a thing happen. The effects of these merging events don’t last very long, so you need to stare a long time to have any chance of catching it happen. You would need practically every F star to have planetary material ready to go on eccentric orbits and merge, and even then you need a lot of planetary material.

I’m glad to see this scenario fleshed out so well. I suspect that there are ways to save the model by finding ways to make sort of event occur more frequently—perhaps by making the merging/dips more frequent by getting a chain of material from a single massive object—so I’m optimistic there’s more to this. I’d say this paper has moved the “post-merger return to normal” scenario from “unclear” plausibility to something like “less plausable,” or even higher.

As I wrote last time: