Dark matter has eluded us for many decades.

Even our most advanced particle colliders   and sophisticated underground detectors  have come up short.

But it may be that   we can finally solve this mystery  with a much simpler experiment,   involving a ray of light, a  good clock, and the planet Mars.

Over 80% of the mass in the universe is in the  form of some mysterious, invisible, unseeable   substance that, for want of any idea whatsoever  what it is, we call dark matter.

At first, many of   us thought that it was just some sort of regular  stuff that wasn’t easy to see—maybe lots of small,   dense, non-shining bodies like brown dwarfs  or neutron stars or even black holes.

But as   we ruled out most of the possible mass ranges  for these, more and more of the dark matter   hunting has been about finding some kind of exotic  particle—Neutrinos, axions, etc.

But, again, after years and years of looking for the dark matter particle, we’re in the  same place with this hypothesis—there’s   just no credible evidence in favor of any  hypothesis for what dark matter really is.

It’s like when you look for your keys in the usual  spots, don’t find them so check under the couch,   under the cat, inside the refrigerator.

But when you still don’t find them you   double check your pockets.

Maybe it was  in one of the obvious places all along.

And there are indeed a couple of pockets still to  check, where “pockets” means range of masses for compact bodies.

The most promising under-explored range is 10^17 to  10^23 g, roughly the mass range of asteroids.

Now,   dark matter can’t be asteroids because there’s  no conceivable way to make 5 times the mass in   asteroids than there is in stars—after all,  asteroid material is made inside stars.

There aren’t that many stars, and also dark  matter had to be around before the first stars.

But there is an option for a truly invisible  object in that mass range, and one that would have been   around since near the beginning and that's the primordial  black hole (PBH).

These days, black holes are formed in   the deaths of massive stars and their masses start at around 3 times the Sun’s mass.

But, as we’ve seen before on   this show, there is a way to produce asteroid-mass  black holes, and that’s right after the Big Bang.

Back then, there were tiny variations in the  density of the hyper-dense sea of matter and   energy that filled the universe.

Some of these  would later collapse under gravity into galaxies   and galaxy clusters, but right at the beginning  the most dense such regions could have collapsed   directly into black holes.

These primordial black  holes could have a range of masses depending on   yet-unknown details about the very early universe.

But if we tune our Big Bang parameters just right,   we can get enough PHBs in the right mass  range to account for all of dark matter.

Not only have we talked about PBHs before,  we’ve talked about PBHs as dark matter,   AND we’ve talked about the possibility of  detecting PBHs from the scars they might   leave as they pass through the Earth, or even the  Moon.

But such a detection is going to take quite   a bit of luck—the Earth and Moon make pretty  small targets on the scale of the solar system,   and distinguishing the scars from old  PBH impacts isn’t necessarily so easy.

But it turns out that we may not even  need PBHs to hit planets in order to   detect them.

Recent studies have shown  that our entire solar system may serve   as a gigantic PBH detector, with these  little black holes leaving their faint   but very possibly detectable gravitational  signature on the orbits of the planets.

Let’s run some numbers to see if this can really make this work.

And by “we” I mean the scientists who are   actively figuring this out as we speak.

One paper  I’ll focus on in particular Tung Tran, Sarah   Geller, Benjamin Lehmann and David Kaiser and it was  published just this September and I think does the   best job at assessing the plausibility of turning  the solar system into a black hole detector.

Let’s start with dark matter.

Based on the orbits  of stars in the Milky Way, we have a pretty good   idea of the distribution of dark matter in our  galaxy.

The density of dark matter at our solar   system’s position in the galaxy is about 7x10^-25  g/cm^-3 or about the equivalent of the mass of a   proton in every sugar cube of volume.

So, if dark  matter is a proton-mass particle, something like   10 million of them pass through you every second.

Experiments trying to detect dark matter particles   assume that they stream through our detectors in  enormous numbers, so that even if there’s a very   low probability of interaction, we’ll eventually  catch some.

Although apparently not yet.

The more massive the dark matter particle,  the lower the number density.

If dark matter   is a compact object like a black hole, then they’d be  pretty spread out.

For example, if all dark matter   consists of Sun-mass black holes, there’d need  to be one per 15 cubic light year volume to do the job.

So what mass range might these PBHs have if  they really do account for all of dark matter?

Astronomer’s favourite way to constrain has been  with gravitational lensing.

Although black holes   are invisible, their gravitational fields warp  the paths of light rays passing close by.

If a   black hole passes between us an a more distant  star, that star will briefly brighten as its   light gets focused towards us in an effect called  microlensing.

The OGLE survey recently published   new results from their decades-long effort to  count compact objects in the Magellanic clouds   this way.

They rule out huge mass ranges  of primordial black holes as dark matter,   everything from half the mass of the moon up  to about 1% of the mass of the sun, roughly   the boundary between brown dwarfs and proper  stars- that’s a factor of a million in mass.

And in fact the only remaining mass window that’s still wide  open to potentially account for all of dark matter   is the so-called “asteroid mass range”, from  around 10^17 grams to 10^23 grams, or less than   0.1% of the moon's mass.

If such small black holes make  up all dark matter we’re going to need a lot of   them.

If PBHs are at the bottom of range—10^17  grams—then we’d expect there to be one somewhere   in the inner solar system right now.

At the upper  end of this range of asteroid-mass black holes, we   might expect one to pass through the  solar system every century.

In between   these extremes we have them passing through  the solar system on timescales of months to   decades.

And that is frequent enough that we should  think about how to detect one when it comes.

So we’re not going to see a primordial black hole  with a telescope.

In the asteroid mass range,   our PBHs have event horizons that range from the  subatomic to the microscopic.

So even if they were   visible they wouldn’t be visible.

Instead, we’d  spot a PBH passing through our solar system in   the same way we discovered dark matter in the  first place—from its gravitational influence.

When an interstellar object enters  the solar system it almost always   exits again—the speed it gathers falling  into the Sun’s gravitational field is,   by definition, exactly what it needs  to escape.

Add to this the fact that   an interstellar object is on a different  orbit to the solar system, so it’s already   coming in hot—with some appreciable fraction  of the galactic orbital speed of 220 km/s.

The result is that a black hole fly-through  is going to be pretty quick, with a passage   through the inner solar system lasting a few  months at most.

If this is the sort of black   hole produced by the death of a star—a  stellar black hole—then its effect on the   planetary system would be devastating.

Orbits may be significantly altered,   planets ejected, and the black hole may even  capture planets into its own orbit.

However,   the effect of an asteroid-mass primordial black  hole would be no more significant than an actual   interstellar asteroid passing through the  solar system—which means almost no effect.

Planets are many millions to trillions  of times more massive than any such PBH,   and so the acceleration a planet experiences due  to that passage will be commensurately tiny.

But   tiny isn’t zero.

Think about it this way:  imagine you and another car are side by side   on the highway both going exactly 100.00 km/hr.

Your cruise control glitches and you speed up to   100.01 km/hr.

You don't notice that right away, but  an hour later your car will be 10 meters ahead,   that’s an entire car length, which you’ll  definitely notice.

In the same way, a tiny,   parts-per-trillion change in a planet’s  position will be visible over years.

Let’s say a PBH in the upper-middlish of  our asteroid-mass range—10^21 grams—passes   through our solar system a little way outside  the orbit of Mars.

The red planet’s change in   speed would be pretty much unmeasurable at the time.

But after a decade it would add up to a   difference in position of about 1m compared  to the expected location.

That also sounds   pretty hard to measure, given the 10s of  millions of km distance between Earth and   Mars.

But there are two factors that  make this actually possible.

The first is that the motion of the  planets is predictable.

With   clockwork precision, the planets are slaves to the law   of gravity—whether Newton’s or Einstein’s.

If we  know the positions and velocities of a system of   gravitating bodies at one point in time, we can  trace their motion far into the future.

Neptune   was discovered based on a small discrepancy in  the motion of Uranus, and that was calculated   with pen and paper back in the middle 1800s.

Modern  computers can compute the future motion of the   planets with incredible precision, although  including the gravitational influence of the   many smaller residents of the solar system starts  to make it complicated, and I’ll come back to that.

Knowing precisely where a planet is, even down  to the centimeter, isn’t helpful if we can’t actually measure the distance to the planet with that same precision.

But fortunately, that’s also within humanity’s skill set.

We don’t   measure distances to planets directly.

Instead,  we measure the travel time of light.

Conveniently,   the speed of light in the near vacuum  of interplanetary space is constant and   extremely well known—so timing its round trip  from Earth and back gives us a distance that’s   as precise as the stopwatch we use to time  that trip.

And we do have some exceedingly   precise atomic stopwatches these days.

One of the most precisely measured   distances in the solar system is the Earth-Moon  separation.

It’s known to about 1 mm precision   thanks to the retroreflectors—fancy mirrors—placed  on the lunar surface by the US, the Soviets,   and now India.

The precision of our measurement  of the Earth-Moon distance makes the moon sound   like a good option for a good black hole  detector.

But it’s actually not our best   option.

The fact that the moon is so close means we can't really treat it as a single point.

But the Earth and Moon are big, slightly irregular balls that squish and stretch in each others gravity.

Although we can measure the distance to those retroreflectors with amazing precision it's hard to convert that to a well defined distance to the moon.

The trick then is to look farther, to Mars.

While Mars  doesn’t yet have a retroreflector big enough this,   we have something that may be even better--our  own satellites orbiting Mars.

At any one time   over the past 20 years, we have had at least three  different functioning spacecraft in Martian orbit.

It's straightforward enough to get an exact  distance to any one of these based on the   signal travel time, and the satellites can use  complex triangulation to get their own altitude   above the Martian surface.

By collecting these  distances over time and for multiple spacecraft,   we can now define and keep track  of a robust "distance to Mars",   and have been able to do so for 20 years.

We can likely spot the 1 meter offset caused   by the 10^21g PBH we saw earlier, and perhaps  even the 10cm-ish offset caused by a PBH 10   times smaller.

That covers half of  the possible range for PBH masses.

OK, so apparently we can both predict  and measure the location of Mars with   the precision needed to tell if it  strayed by a foot or two from where   it was supposed to be.

How do we know  that was caused by a passing black hole?

The solar system is a busy place, packed  with planets, moons, dwarf planets,   asteroids, and comets.

The mini-tweaks that the  Earth and Mars might get from a PBH is one of   millions, all of which must be accounted  for if the signal from the black hole is   to be separated from the noise.

In fact, any  asteroid in the inner solar system with a mass   comparable to our PBH would need to be included  in calculations, otherwise its gravitational   effects will completely wash out the effect  we’re searching for.

The good news is that,   while 10^20 grams or so makes a black hole  as small as an atom, it makes an asteroid  of that mass about a 100 km across, and all asteroids  that big are all pretty well tracked.

Also, a PBH flyby will have a very different  trajectory to a solar system asteroid.

Objects   in the solar system orbit pretty close to  the same plane that the planets orbit in,   and all at speeds low enough to keep  them bound in the Sun’s gravitational   field.

A passing PBH will be moving quite a bit  faster, and could come in at any angle relative   to the plane of the solar system.

In-plane  flybys will tend to tweak a planet’s speed,   but keep it in the same plane.

Steeper flybys will  tend to tug a planet slightly out of that plane,   altering its orbital inclination.

Because of  this, the change in a planet’s position due   to an extrasolar object versus a solar  system object may be quite distinct.

Let’s talk about the two experiments  we can do.

One we can do right now,   and one is for the future.

We currently have around 20 years of  precision data on the position of Mars,   and in principle we could find the signs of past  PBH passes in these data.

Some preliminary efforts   have been made to analyze this, but not with  conclusive results because it’s going to require   some very sophisticated simulations to analyze  the data properly.

The proper way to do this is   by running many, many computer simulations  to map the space of possible ways in which   the orbit of Mars could evolve in response to the  gravitational influence of known and unknown solar   system objects.

That will tell us whether, at some  time in the past 30 years, Mars strayed from this   space of probable orbits in a way consistent  with an interaction with a massive flyby.

Then we add potential extrasolar  visitors to our simulation and see   how well Mars’ trajectory is explained by  different flyby masses and trajectories.

There’s no direct way to tell if such a flyby  was really a PBH or just an extra-solar asteroid   of the same mass.

If we find it in this  old data then by now it’ll be long gone,   so we can’t look for it with our telescopes.

We do know that there are such asteroids living   between the stars—for example, Oumuamua, although  it’s way below our desired mass range.

However,   if dark matter is made of primordial black  holes at these masses then those PBHs need to be way,   way more abundant that extra-solar asteroids.

So  if we find way too many such kicks to the Martian   orbit in those 20 years of data, it’s good evidence  that they’re coming from PHBs and not asteroids.

OK, so that’s the experiment we can do now, and  astronomers are indeed working on this.

But what   we’d really want is to get more direct evidence.

Monitoring future data from Mars can allow us to   notice a change in its motion within a few years  if we’re lucky, and then it might be possible to   track the offending source of gravity as it coasts  away from the solar system.

If it’s an asteroid   then it’ll be visible to a sufficiently  giant telescope.

If it’s a black hole   it will not be.

So maybe we’ll discover  what dark matter is by observing nothing.

It may be that to find the next level of  action in particle physics we'll need to   build a particle collider the size of the solar  system.

Well, we already have a solar system   sized particle detector that could discover dark  matter.

Assuming dark matter is made of countless   subatomic-sized black holes with the masses of  asteroids.

In which case we can solve dark matter   from miniscule shifts they cause in  planetary paths through spacetime.