The habitable planet of Gaia BH1

 tl;dr - ... does most likely not exist.

As every year in March, I attended the Mathematik Modellierungswoche last week, held at the Rechtenthal Castle in the small village of Tramin, South Tyrol. Along with four other STEM teachers, I brought an assignment for five of the most talented students from various schools across the province. Their task was to work on it and get as close to a solution as possible. As usual, my assignment this year came from the wide and never disappointing field of astronomy.

Over the past year, I was 'commander-in-chief' of a nice 16-inch remote rental telescope in Australia and used it to image the southern night sky. During the bright moon phases, galaxies and nebulae weren't ideal targets, so I focused on finding interesting star-like objects to point my telescope toward. I can't recall exactly where or when I first read about Gaia BH1, the first stellar black hole discovered by the prolific astrometry satellite Gaia in 2022, but it surely caught my attention.

The star field I took with my Australian remote telescope.
Gaia BH1 is the bright star-like object in the centre.

Now, usually, a black hole wouldn't qualify as a target at all, since, being what it is, it does not emit light. Even worse, Gaia BH1 is an inactive black hole, so it has no accretion disk from which it feeds - so no light coming from there either. But if so, how did Gaia find this elusive, 10-solar-masses monster in the first place? 

Gaia BH1 has a companion - a main-sequence star with almost the same spec sheet as our Sun. Its mass, radius, surface temperature, and luminosity, are all nearly identical. The star orbits the black hole on a somewhat eccentric orbit with an apoapsis (farthest distance) of about 2 AU and a periapsis (closest distance) of 3/4 AU. These values are in the same magnitude as Earth's orbit and suddenly my little Homer Simpson cymbal monkey froze.

What if there's an Earth-like planet orbiting close to the black hole? Would it have a surface temperature suitable to support life? Could there be, at least occasionally, liquid water? And are such orbits even stable? 

A gentle smile slowly spread across my face.

What if a Renaissance-like civilization were living on that planet? Would their alien Galileo Galilei advocate for the geocentric model?

I realized that these hypotheses were worth exploring in detail. I had just found the perfect problem to pose next year at the Mathematik Modellierungswoche.

The participants of the last edition of the Mathematik-Modellierungswoche.

Several months later, I found myself surrounded by five young astronomy aficionados, supported by a fellow physics teacher, all eager to pour their very souls into the quest. During the next four days, we explored a bunch of different approaches. We quickly decided to use the REBOUND library from Hanno Rein to get the orbit simulation part done, assigning Oswald the task of implementing it.

Initially, our models for the surface temperature were rudimentary, relying on plain empirical relations for the habitable zone of a star. Later on, we shifted to more sophisticated energy balance models, with and without an atmospheric greenhouse effect. Ultimately, we dropped the assumption of thermal equilibrium completely, calculated a mean heat capacity for the planet's upper layer, and allowed it to store and release heat.

Screenshot from the Python script we developed. 

Theo dove into the topic of tidal heating and tidal locking. We quickly discovered that our planet would almost certainly become tidally locked to the black hole. Furthermore, for close, eccentric orbits, the energy input from tidal heating would surpass the energy received from the star. By this point, the status of our relationship with the potential sister planet had undoubtedly shifted to "it’s complicated," especially since Oswald’s findings revealed that only orbits close to the black hole were stable over reasonable timescales.

Short video with one of our unstable orbits:

A video I shot during the Mathematik-Modellierungswoche 2022:

Altogether, we invested a total of 266 man-hours (Wait, we had one female student in our group. Do woman-hours exist? 🤔) into the task. However, we are still far from a final conclusion. To get the job done we would certainly need more expertise in the field (we buildt most of our knowledge base from scratch) and much more time. But as the week came to a close, the students dispersed, each moving on their own "orbits," which will soon carry them away from their hometowns to university and beyond.

For Gaia, too, the winds of change have come. After measuring positions and velocities for 1.8 billion objects and creating a catalog that could aptly be called Google Maps of the stars during its mission, the satellite will leave its stable orbit and Earth's sphere of influence in the next few days. 👋😢

My orbit is way more predictable. Yesterday I slept for 12 hours straight (and 10 today) to recover from the strain this week has put on poor me 🙈. Tomorrow, I will head back to my school, return to my classroom, check on my students, and see if they missed me as much as I missed them ❤️.

Christof Wiedemair