Wednesday, March 22, 2017

A star orbitally skimming a black hole

Centauri Dreams had a post yesterday describing the unusual system 47 Tuc X9 which is 14,800 light years from Earth. It appears to be a white dwarf star in a very close orbit (radius about a million kilometres) around a black hole, with orbital period 28 minutes (!).

The post is illustrated by an artist's impression of the system:

and a statement of the curious orbital dynamics:
"This white dwarf is so close to the black hole that material is being pulled away from the star and dumped onto a disk of matter around the black hole before falling in,” says lead author Arash Bahramian (University of Alberta and Michigan State University). “Luckily for this star, we don’t think it will follow this path into oblivion, but instead will stay in orbit. ...

"We think the star may have been losing gas to the black hole for tens of millions of years and by now has now lost the majority of its mass. Over time, we think that the star’s orbit will get wider and wider as even more mass is lost, eventually turning into an exotic object similar to the famous diamond planet discovered a few years ago."
It isn't obvious why the star is winding its way out from the black hole and several commentators get confused (hint: it's not frame-dragging).

From the star's period and orbital radius we can work out the mass of the black hole: 94 solar masses. From this, we can calculate the black hole's schwarzschild radius - an event horizon of 277 km, just under 100 times larger than the event horizon of a solar mass black hole (3 km).

The black hole's gravity at the orbital radius of the star is 13.4 km/sec2, or just under 1,400g. You can see why it's whipping around so fast (c. 3,300 km/sec or 1% of the speed of light).

Try to imagine it. If this black hole were placed at the centre of the Earth, it would be an unimaginably tiny object (277 km!) in the middle of the core. The star, meanwhile, is two and a half times the distance of the Moon. The star's experience of the black hole comes down to some pretty crazy tidal forces.

We know about tidal forces: they try to tear the star apart and rearrange its material into an orbital ring. None of this would explain material infalling into the black hole or the star spiralling outwards. We don't see such phenomena at Saturn for example.

The secret is explained by the authors in this remark:
"Low mass X-ray binaries (LMXBs) are systems in which a compact object [neutron star (NS) or black hole (BH)] accretes matter from a low mass companion (typically a main sequence star) through Roche-lobe overflow or wind-fed accretion (from a red giant). ...

"In the most likely scenario, this particular star would have first started losing mass to the suspected black hole several tens of millions of years ago when it was much closer, in an orbit with a period of just minutes.

"Over time, as that star has lost most of its mass, the size of the orbit would have increased, and the rate at which mass has been lost to the black hole would have decreased. The rate of mass loss would once have been a billion times higher. So yes, the star would initially have been much closer to the black hole.

"How close a star can get to a black hole before starting to lose mass to the black hole depends on the kind of star it is. Big, fluffy giant stars can lose gas to a black hole when they are much further away than small, compact stellar remnants like this white dwarf, whose gravity is strong enough that they are able to hold onto their mass more tightly, so need to get much closer before mass can be torn away.

"We also think that this star will have been gradually losing mass over tens to hundreds of millions of years; in this case it is not being torn apart in a single cataclysmic event that results in it being shredded into streams of debris, as we have seen in spectacular outbursts from the centres of some external galaxies (known as tidal disruption events).

"Rather, in this case, we have a steady loss of mass to the black hole over time."
The Roche-lobe overflow effect is an interesting one (Wikipedia article). If debris from the star can reach the L1 Lagrange point (between the star and the black hole) it can migrate to the black hole itself. The remaining stellar material has higher than before angular momentum and its orbital radius increases. [Note: but apparently not - see comments.]

Roche Lobe potential: from the Wikipedia article

There are few things more counter-intuitive than orbital mechanics.


  1. There are several parts to the physics of Black Hole Accretion Disks!

    The basic Roche theory seems to be Newtonian. In that framework we then ask why the angular momentum of the remaining star is increasing. I suppose we can say L = mr^2 w and Angular Momentum conservation gives: L = L_star + L_material. So if L_star > L we need L_material < 0 which means (m.r^2w) <0 which requires the material to be rotating counter to the star direction.

    The BH is probably also rotating and so is described by a Kerr solution: it will have an Ergosphere and so some gas will undergo frame-dragging. But the Ergosphere will be some distance from L1. This might produce a Jet or some other odd effect.

    Also that artist's impression might not be complete, in that on one side the gas radiation is blue shifted and on the other side red shifted and the whole thing is to be pictured with some local gravitational lensing.

    Once the Chatbot is ready it will deal with these BH questions easily, I assume.

    1. Yep, it's still a problem as to why the orbital radius increases. The chatbot is unlikely to inform us and the reasons you suggest so satirically are, of course, not too plausible; although some of those Roche orbits are pretty weird (horseshoe?).

      So why does it spiral out?

    2. Another possibility is that the originating events in this binary system caused the WD to be in too high an energy orbit for its initial radius around the (pre-)BH object. This might happen, for example, if the preBH object itself lost mass before becoming a BH. So now the WD is stuck in the wrong orbit and slowly escapes.

      Earth has a horseshoe companion.


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