# Lucky planets: how circum-binary planets survive the supernova in one of the inner-binary components

### Submission summary

 As Contributors: Simon Portegies Zwart Arxiv Link: https://arxiv.org/abs/2101.08033v1 (pdf) Code repository: http://amusecode.org Date submitted: 2021-01-21 14:26 Submitted by: Portegies Zwart, Simon Submitted to: SciPost Astronomy Academic field: Astronomy Specialties: Solar and Stellar Astrophysics Approaches: Theoretical, Computational

### Abstract

Since the discovery of exoplanets around pulsars, there has been a debate on their origin. Popular scenarios include in situ formation or the dynamical capture of a planet in a dense stellar system. The possibility of a planet surviving its host star's supernova is often neglected, because a planet in orbit around a single exploding star is not expected to survive the supernova. A circum-binary planet, however, may stand a chance in staying bound when one of the binary components explodes. We investigate the latter and constrain the distribution of post-supernova orbital parameters of circum-binary planets. This is done by performing population synthesis calculations of binary stars until the first supernova. Just before the supernova, we add a planet in orbit around the binary to study its survivability. In our supernova model, the exploding star's mass is assumed to change instantaneously, and we apply a velocity kick to the newly formed remnant. The mass loss and velocity kick affect the orbits of the two stars and the planet. Only $2 \cdot 10^{-3}$ of systems survive the supernova while keeping the circum-binary planet bound. The surviving planetary orbits are wide ($a \apgt 10$ au) and eccentric ($e \apgt 0.3$). It turns out much more likely ($3\cdot 10^{-2}$ system fraction) that the newly formed compact object is ejected from the system, leaving the planet bound to its companion star in a highly eccentric orbit (typically $\apgt 0.9$). We expect that the Milky way Galaxy hosts at most $10$ x-ray binaries that are still orbited by a planet, and $\aplt 150$ planets that survived in orbit around the compact object's companion. These numbers should be convolved with the fraction of massive binaries that is orbited by a planet.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 2101.08033v2 on 17 June 2021

Submission 2101.08033v1 on 21 January 2021

## Reports on this Submission

### Strengths

1- In this work, the authors tackle the novel idea of (circumbinary) planet survivability beyond the main sequence.
2-Heuristic or semi-quantitative arguments about "second generation" planets or "Phoenix" planets around stellar remnants have been proposed on-and-off for the past ~30 years. However, detailed Monte Carlo experiments are less numerous, and thus such degree of novelty makes this paper worthy of publication

### Weaknesses

1- The paper is verbose and its main message is muddled with extraneous arguments and caveats.
2- It reads to me like a null result, but without directly presenting itself as such.
3- Some figures seem unnecessary.

### Report

Dear Scientific Editor:

I have carefully read the Scipost manuscript 2101.08033v1 entitled "Lucky planets: how circumbinary planets survive the supernova in one of the inner-binary components". In this work, the authors tackle the novel idea of (circumbinary) planet survivability beyond the main sequence. In particular, the authors study the fates of planets around massive binaries that undergo supernova explosion. Via simple analytic arguments and Monte Carlo simulations, the authors compute the fraction of systems that could harbor a planet after the supernova and discuss the potential observational signposts of such processes.

MAIN IMPRESSION:
While certainly publishable, this paper could benefit from further streamlining its message: ideally, it should be direct and concise, and not weakened by its own counterpoints/caveats, or diluted by open ended speculations and pessimistic takes on how observable the theoretical predictions are.

Heuristic or semi-quantitative arguments about "second generation" planets or "Phoenix" planets around stellar remnants have been proposed on-and-off for the past ~30 years. However, detailed Monte Carlo experiments are less numerous, and thus such degree of novelty makes this paper worthy of publication.

However, the tone and purpose of this paper is ambiguous. The Introduction opens with a discussion on the pulsar planets, making the reader think that this paper is about mechanisms of producing such systems. If "pulsar planet production from pre-existing circumbinary planets" is indeed the hypothesis being tested here, then this paper is reporting a null result. And null results are fine. But neither in the abstract, the conclusion, nor anywhere in the narrative of the paper is categorically stated that the inferred hypothesis (perhaps I misunderstood the intended one) has been proven inadequate.

Thus, for good writing's sake, the authors need to decide if this is a null result (which is welcome) or something else, but the disconnect between the Introduction and the rest of the text is too striking not to be addressed. It appears as if the Introduction was written before the results came in.

Just to reiterate: this is careful, quantitative work, and is deserving of a more effective (and ideally shorter) delivery than is currently being given. Moreover, the readership of this journal (and other researchers working on related topics) will benefit from a straightforward description of the results, even if they seem less exciting that originally expected. In summary, directly saying "pulsar planets CANNOT form this way", is an informative result.

- Section 2.2, Second paragraph:
Much like in Brandt & Podsiadlowski (1994), it would be useful to the reader to clarify that the semi-major axis a in the definition of E' is the *old* semi-major axis and distinct from the post-explosion semi-major axis a'.

- Section 2.2, Second paragraph:
At the time of mass loss, why is the true anomaly nu_i chosen to be zero at all times? Should not the *mean anomaly* (i.e., time) be sampled randomly from 0 to 2pi? For eccentric binaries, choosing nu_0=0 is certainly not "without loss of generality" and might affect some of the results. Case in point: in Section 3.3, Sixth paragraph, the authors state that for the A,C pair to remain bound,"the remnant must receive a kick in the right direction and with the proper magnitude to either pass close-by the planet C, [...]". If a kick "in the right direction" is needed, how can this scenario not depend on the choice of nu_i at the time of mass loss and velocity kick?

-Section 3.3, First paragraph
Care to comment on how the Mardling+Aarset stability criterion compares to the Holman+Wiegert stability criterion (https://ui.adsabs.harvard.edu/abs/1999AJ....117..621H/abstract) which was especially derived for circumbinary systems?

- Section 3.3, Second paragraph:
The bullet point list of this section is very helpful to visualize the potential outcomes the authors are studying. However, the second category "dynamically unstable" could use further clarification. According to the caption of figure 5 (the explanation should be in the main text as well), these are "[...]systems which remain fully bound but become dynamically unstable." If the Mardling & Aarseth triple stability criterion was used to flag these systems, then that citation should be made explicit when this category is introduced (the paper is cited elsewhere in the manuscript).

Also, I would suggest careful wording here. If the post-explosion triple has total negative energy (i.e., remains bound on energetic grounds), and then becomes dynamically unstable with one object being kick out to infinity, there must be a left-over binary with negative energy. So, one cannot go from bound triple to fully dissolved triple from dynamical interactions alone (I am certain the authors know this basic fact, but the text is a bit ambiguous).

Finally, "and undergoes a three-body interaction" seems an unnecessary addition to "becomes dynamically unstable", especially since all triples, in a strict sense, are undergoing three-body interactions.

- Section 3.3, Fifth paragraph:
The sentence: "[...] attribute the decrease in the fraction of (A,B) systems that stay bound for ao > 10^3 au to the systematically larger measure of ai in this region[...]" is difficult to parse. But it also difficult to see why it is worth pointing out why the purple curve decreases slightly for a_o > 1e3...

- Section 3.3, Eighth paragraph:
The authors state that the "probability for stable triples quickly drops for ao > 1e3 au [...]". Is this independent of the initial distribution of planetary semi-major axes? It is clear that distant planets, being weakly bound to begin with, should be more susceptible to being unbound when the central object loses mass. But what is not so clear is whether this 1000 au boundary scales with the initial outer tail of the planet semi-major axis distribution.

- Section 3.3, Ninth paragraph:
How are the authors defining a negative inclination? Relative inclinations are formally defined as arccos(n_i.n_o) where
n_i, n_o are the normal vectors of the inner (binary) and outer (planet) orbits, respectively. Thus, relative inclination is always a positive quantity (0-90 is prograde and 90-180 is retrograde). This finding and the discussion around it are very confusing.

-Section 4:
This overall Section reads more like a Discussion than a Conclusion. What are the actual findings of this work?
Paragraphs 1,2,3 contain raw findings, but they could be *significantly* condensed. Paragraph 4 and 5 are definitely Discussion material. Paragraph 6 is a conclusion. Paragraph 7 is mostly meandering caveats than bring down the momentum of the paper and end on a slightly negative tone (caveats are good, but ending with caveats is just weird).

-Section 4, Fourth paragraph:
The authors skim over a very intriguing possibility (in my humble opinion): a second SN explosion in the triples that survived. In this case, the BC scenario could very well repeat itself and leave us with a pulsar planet. Even more intriguingly, the authors suggest that "the planet sticks to the inner compact-object binary until they merge due to the emission of gravitational waves". This scenario would circle back to some of my objections with the Introduction, i.e., the formation of pulsar planets. Alas, the authors conclude that the probability of this happening is small. Yet, I could not find where the numbers they use came from (except for 0.14).

- Section 1, First paragraph:
If the authors do keep their initial discussion on pulsar planets, I recommend reading/referencing a fascinating early take on this systems by Phinney & Hansen 1993 (https://ui.adsabs.harvard.edu/abs/1993ASPC...36..371P/abstract) in which the survivabilty of planets beyond the main sequence is discussed.

- Section 1, Second paragraph:
I am well aware that the term "ionize a binary" is widely used in the binary evolution community (despite my own preference for simply "unbind"). However, the expression "ionizes the planet" can be easily misinterpreted. Please change to "ionizes the planetary orbit" and make sure that either "ionize" or "unbind" is consistently used throughout the paper for the sake of clarity: e.g., Figure 5 refers to "unbound" binaries. There is even a "dissociate" in Section 3.1

- Section 3.1 Second paragraph.
What is the real purpose of training a smooth kernel on an empirical distribution? Bootstrap the number of systems? Benefit from the sample of a continuous (and differentiable) function? The benefit of this technique over simply resampling from an empirical histogram should be clearly stated, otherwise it seems like an unnecessary over-sophistication.

TYPOS:
The manuscript contains several typos and a few punctuation errors. Here are a few:
- Section 1, second paragraph: might works -> might work
- Section 1, third paragraph: larger then -> larger than
- Section 3.2, first paragraph: zero binaries-> zero eccentricity binaries?
- Section 3.3, last paragraph: neutral star -> neutron star

I hope that the authors find these comments constructive

Best regards,

### Requested changes

1- Streamline the paper. At the very least reword the Introduction and shorten /strengthen the Conclusions (or move part of the Conclusions to a Discussion section)
2 - Explain/fix the issue of negative inclinations
3- Justify/fix the choice of true anomaly nu_i=0 in their calculations
4 - Explain the category "unstable triple" better

• validity: good
• significance: ok
• originality: good
• clarity: ok
• formatting: acceptable
• grammar: good