If you track the motion of individual stars in the ultra-dense star cluster at the very center
of the Milky Way you’ll see that they swing in sharp orbits around some vast but invisible
mass—that’s the Sagittarius A* supermassive black hole. These are perilous orbits,
and sometimes a star wanders just a little too close to that lurking monster, leading to its
utter destruction in the spectacular phenomenon known as a tidal disruption event. Now we’ve never
seen a TDE in the Milky Way, but we’ve seen them in other galaxies—and we now know how to spot
stellar destructions so extreme that they reveal properties of the black hole itself.
What happens when a star gets a little too close to a galaxy’s central supermassive black hole? Well as
it approaches, the gravitational force on the side of the star closer to the black hole gets stronger
than the pull on the far side. This gravitational differential results in a tidal force that,
from the star’s perspective, feels like it’s being stretched in the direction of the black hole and
compressed in the perpendicular direction. If the star gets within a certain critical distance to
the black hole—the tidal radius—the tidal force becomes greater than the force of gravity binding
the star together. The star is smeared out in a fluid-like, noodley mess in a process called
spaghettification. Some of this material gets ejected outwards, while more spirals rapidly into
the black hole, heating to incredible temperatures before disappearing into the black hole.
These tidal disruption events or TDEs are so rare that we’ve never seen one in our own Sag A* black
hole. But we’ve seen around 100 candidate TDEs in distant galaxies. Even from Sag A*, and certainly
from other galaxies, a TDE appear to us as just a flash of light from the galactic center. But fear
not! There is a way to get as close as we want to one of these stellar trainwrecks: by recreating
them in supercomputer simulations. By tuning those simulations to our observations we're able to
study matter moving in the strange, warped spacetime around a black hole. And recently, we’ve
even predicted a type of extreme tidal disruption never before seen, but we may see very soon.
Throwing virtual stars at virtual black holes is actually enormously challenging,
and we’ve only just pretty good at it. To understand how we do this and why it’s so hard,
let’s start with some of the gravitational physics behind these tidal disruption events.
We’ve been able to simulate motion under gravity for some time now. The
Apollo program did the orbital mechanics of its spacecraft on
“supercomputers” with the computing power of a hand-held calculator… from the 90s.
These simulations used Isaac Newton’s theory of gravity—calculating the gravitational force
between all pairs of objects, seeing how those forces change velocities
and how those velocities change positions over small time steps, and then repeating
over and over. The calculations are quick enough that modern computers can calculate
the interactions of millions of objects to simulate entire galaxies, or even universes.
But Newtonian gravity is only an approximation of how gravity really
works—an approximation valid when gravity is weak. That’s fine for most of the universe,
and even for mild tidal disruption events like the one that may have torn apart a moon to form
Saturn’s rings. But to properly describe a TDE near a black hole we need the full theory—and
that’s Einstein’s general theory of relativity. Rather than describing gravity as a force,
general relativity, or GR describes the warping of space and time by massive objects,
and explains gravity as the effect of that warping on the motion of objects.
Although general relativity is incredibly well-tested and certainly “correct”,
it’s also notoriously complicated. For one thing, the nice symmetries that lead to clean circular
or elliptical orbits in Newtonian gravity no longer apply in regions of space where GR becomes
important. As a result, orbits around a black hole can be twisted and tangle over themselves,
especially around rotating black holes. Within a certain distance from the black hole,
there are no stable orbits whatsoever. This gravitational messiness has implications both
for a disrupted star and for the complexity of simulating these disruptions on our computers.
For the star itself it means that, within a certain distance,
all material must either fall into the black hole or be flung back out.
We can’t have nice ring systems of stellar material in the region close to a black hole
And the complexity of these orbits makes our simulations much more computationally
challenging. In GR we describe the motion of objects under gravity in terms of geodesics—paths
taken under pure gravity. To calculate the motion of an object in such a region, it’s not enough
to calculate the force at every point—you need to plot out the geodesics—in fact,
you need to build a map of the warped spacetime. It gets much harder if you have to consider the
star’s own effect on that spacetime curvature, but fortunately for these TDEs the star’s mass is so
piddling compared to the black hole that the star can be neglected. But we have a different challenge.
Once the star is disrupted, it’s no longer a single object; it’s a smeared-out fluid.
To simulate this we need relativistic hydrodynamics. We need to employ the equations
of fluid motion for material traveling at close to the speed of light in a warped spacetime. We
need to consider a variety of complex effects like friction and the bath of intense radiation
produced by that superheater material which can drive out the infalling material outwards. Oh,
and we also need to simulate how that light escapes the vicinity of the black
hole to make its way to us. The same warped spacetime that destroyed the star also twists
the paths of departing light rays in the phenomenon known as gravitational lensing.
Until relatively recently, we’ve only been able to simulate piecemeal parts of this phenomenon,
like the early time disruption of a star, or the formation of a disk. But these days,
modern state of the art codes can follow a tidal disruption event from the incoming star,
all the way through its destruction to the observable flashes of light we see.
Cool, so what do these simulated TDEs actually look like? Well,
there are different types. The most important factor in determining what
happens is just how close the star gets to the black hole—whether its orbit takes it
within certain critical distances. The most well-known such distance is the
event horizon—the surface of no escape. For a non-rotating black hole this is at
the Schwarzschild radius—around 3 km for black hole with the Sun’s mass.
If the star’s orbit would take it across that surface, it is possible for it to drop directly
into the black hole without any part of it escaping. This is called a direct capture event. Now,
depending on the size of the black hole, it may be tidally disrupted before entering—that’s the
case if the tidal radius is larger than the event horizon … true for any black hole smaller than a
few million solar masses. Then the black hole slurps up the entire spaghettified
stellar noodle. Larger than that and the star is still a star as it submerges. These direct
capture events are typically not produce much of an electromagnetic signature—the star just isn’t
ravaged enough to shine brightly before vanishing forever. These should also be quite rare due to the
relatively small target of the black hole event horizon, so we’ll leave these aside for now.
But the other end of the spectrum is the partial TDE. If the star passes close
enough to be significantly stretched but not enough to be disrupted—so outside the star’s
tidal radius—then the star may shed significant material from its outer layers, but enough remains
intact that it remains a star—fusion continues in its core and it settles down upon escape.
But the real fireworks begin with the full tidal disruption event—also
called the common TDE—because these are the ones we most commonly observe
due to their brightness. This is when the star crosses the tidal
radius but its orbit doesn’t carry it directly through the event horizon.
Let’s take a look at a relativistic hydrodynamic simulation of a common TDE to see what should
happen. This is a simulation of a star three times the Sun’s mass passing within the tidal
radius of a 100,000 solar mass black hole. That’s where the tidal forces are now large enough that
they overcome the star’s self gravity. Over about a day, the star completes its flyby,
but it keeps expanding, producing a giant plume of plasma- the core of the star loses pressure,
and fusion cuts off. But that giant stream doesn’t just keep going, not all of it anyway. That tail
starts to fall back toward the black hole and then begins to loop back in on itself. The material
that hasn’t escaped ends up on an elliptical orbit that can clearly be seen as the snake biting
its tail, and much of the material that didn’t escape finds stable orbits around the black hole,
forming the start of an accretion disk. An important feature of this orbit is this violent choke-point at the
closest point of the orbit. This choke point is called a “nozzle shock” caused by the tremendous
speeds that the stellar material attains. It’s at this point that friction and turbulence and
other forces in the stream of debris cause potentially observable flares of photons.
A common TDE can be bright enough to outshine the entire surrounding galax. But it seems that that
universe is capable of doing even better—even if we haven’t seen this yet. Simulations have
revealed the possibility of something that astrophysicists are calling an
extreme tidal disruption event—an eTDE. This should happen when a star’s orbit
takes it within the tidal radius of a black hole and very close to the event horizon,
say 2 to 3 Schwarzchild radii for a non-rotating black hole. The result is a vastly more energetic
phenomenon than the common TDE. We don’t yet have a confirmed observation of an eTDE,
but recent simulations are helping us to understand exactly what to look for and how
to look. Let’s take a look at the relativistic hydrodynamic simulation of this event. by Dr.
Taeho Ryu at the Max Planck Institute and JILA at CU Boulder. This was just published,
and is the first to follow the eTDE from a star with realistic stellar structure to the hot
mess that it gets shredded into. And by the way, the earlier simulations we saw are also by Dr. Ryu.
This time we’re throwing a 1 solar mass star at a million solar mass black hole, aiming to
skim just outside the event horizon. It begins somewhat similarly to the common TDE. However,
within seconds we see direct capture of some of the star, with an emphasis on “some”. The
rest of it is dragged out into a tail that whips around the black hole multiple times,
leaving a spiral trail that was not seen at with the elliptical orbit of the
fallback that made the common TDE. Very soon an entirely new phase emerges – within tens of
minutes the windings of the tail merge together, leaving behind a circularized ring made up of the
last bits that narrowly escaped their demise. These remaining bits now sit in an expanding,
circular cloud. Though stable for quite some time, the innermost portions of the ring nevertheless
begin to fall back toward the central black hole. As the inside of the ring fills in the
previously empty cavity, the black hole accretes the material and a long lived accretion disk is
formed until eventually all of the surrounding material is ultimately either consumed or ejected.
As the matter gets accreted by the black hole, much of that gravitational potential energy
is converted to radiation energy, making a bright burst of light. In the extreme TDE,
this “luminosity” increases very rapidly until it reaches what is called the Eddington luminosity. This is
a sort of upper limit on the radiative output for a given black hole mass,
where the outward radiative force directly balances the inward force of gravity;
any more radiation, and the material is blown outward by the radiative winds. Being at this
Eddington limit puts the system in a state of temporary equilibrium, with outward radiation
balancing gravity. But after a while, the outgoing radiation drops off and the
black hole’s gravity dominates again, enabling it to finish gobbling up the stellar material.
These extreme TDEs should be rare because the star has to make a very close approach. But
it turns out that for larger supermassive black holes, these are the only tidal disruption events
that can happen. That’s because, as the mass of a black hole grows, both the event horizon and tidal
radius grow. But the event horizon grows faster, so that at a few tens of millions of solar masses
the tidal radius is very near or even inside the event horizon. Approaching these masses, if the
star gets close enough to be disrupted at all, it’s also close enough to undergo an extreme TDE.
So we now know what tidal disruption events should look like if you’re actually close to
one. But the real value of these simulations is to predict what they look like from Earth
so we can actually test our ideas. And potentially identify our first extreme TDE.
So what do TDEs look like to us? Because they’re too far away to resolve the spatial details,
we really just see a point of light growing in the center of a distant galaxy where we expect
the supermassive black hole to lie. That point brightens as the star disrupts and
spreads out and then fades away as the stellar material either falls into the black hole or
disperses. The timescale depends on the black hole mass. For a million solar mass black hole,
the rise time is around a month and then, typically, it will have faded away within
a year. For a common TDE, most of that light is emitted at visible wavelengths. Flashes of
light that grow over about a month and then fade over several months. We can also see radio flares
as ejected material slams into the diffuse stuff in the surrounding galaxy, producing shockwaves.
Extreme TDEs are expected to be quite a bit more extreme, as one would hope. They should
rise in brightness much more quickly. An eTDE around a million solar mass black hole should
brighten over only a few hours instead of a month and then maintain a more consistent
brightness than a common TDE for up to a year before finally fading out. This
is something that the new study revealed because the simulations found this temporary equilibrium
as outgoing radiation helps resist gravity. Those simulations also predicted super compact
accretion with a temperature peaking at around a million Kelvin. This results in a broad spectrum
of light with most photons being X-rays, and is around 10 times brighter than a common TDE.
We find common TDEs in our visible-light surveys of the sky. They don’t happen very often—every
several thousand years in a given galaxy, and most commonly around smaller supermassive black
holes. We’ve never seen one directly in the Milky Way, but there are observed remnants such as radio
lobes in the galactic center that would indicate that one occurred a few thousand years ago.
ETDEs should be rarer than common TDEs because they require a closer approach tend to happen
around larger black holes, which are rarer than smaller ones. But Dr. Ryu and team estimate one
per 15,000 years for a 20 million solar mass black hole. To spot such a thing we need to
monitor a lot of galaxies, which is something new large field surveys can do—but we also
need to do it at X-ray wavelengths, which is much harder than visible light wavelengths.
Fortunately, we already have an instrument that may be up to the task. eROSITA is an X-ray
detector on Spektr-RG space observatory and it's created an X-ray survey of the entire sky—but unfortunately
operation was suspended in 2022 before covering the X-ray energies needed to
detect an eTDEs. But eROSITA will soon resume its operations and finish its
survey in the next couple of years. And then our first eTDEs will hopefully shine out.
And this will be a rare chance to witness the motion of matter in the region very close to
a black hole event horizon. Comparing what we see with our simulations will let us test
our models of these violent events—how stars get ripped apart by black holes,
and also our understanding of how gravity really works in the most extreme regions of spacetime.