Three LIGOs make a Banana Slicer

Ponder for a moment what Space throws at you.  Photons of all sizes, of course —  infra-red ones that warm your skin, visible ones that show you the beach, ultra-violet ones that give you tan and sunburn.  Neutrinos and maybe dark matter particles that pass right through you without even pausing.  All of those act upon you in little bits at little places — gravity pervades you.  You can put up a parasol or step into a cave, but there’s no shielding yourself from gravity.

Gravity’s special character has implications for LIGOs.  A word first about words.  LIGO as a generic noun unwinds to Laser Interferometer Gravitational-Wave Observatory, a class of astronomical instruments. LIGO as a proper noun denotes a project that culminated in the construction of a specific pair of devices that went live in 2002.

That hardware wasn’t sensitive enough to detect the gravitational waves it was created to seek.  To improve the initial LIGO’s power and sensitivity, the LIGO infrastructure and organization morphed into the Advanced LIGO (aLIGO) project.  Concurrently, the LIGO instrument was upgraded and renamed.  No surprise, the instrument’s new name is aLIGO.  An early phase of aLIGO bore uncannily fortunate fruit with the Sept 14 gravitational wave detection.

Four other LIGOs are proposed, under construction or in operation around the world — KARGA in Japan, INDIGO in India, GEO600 in Germany and VIRGO in Italy.  Why so many, and why even consider space-borne LIGOs like LISA Pathfinder and eLISA?

Astronomers ask a series of questions of the Universe:

  • What objects are out there?
  • Where are they?
  • What are they doing?
  • Why are they doing that?

September’s aLIGO incident gave us a gratifyingly unexpected answer to the first question.  To the surprise of theoreticians, the detected event was the collision of two black holes, each of which was in a size range that current theory says shouldn’t be populated.  Even more surprising, such objects are apparently common enough to meet up, form binary pairs and eventually merge.

1 LIGO localizationThe second question is harder.  The best the aLIGO team could do was point to a “banana-shaped region” (their words, not mine) that covers about 1% of the sky.  The team marshaled a world-wide collaboration of observatories to scan that area (a huge search field by astronomical standards), looking for electromagnetic activities concurrent with  the event they’d seen.  Nobody saw any.  That was part of the evidence that this collision involved two black holes.  (If one or both of the objects had been something other than a black hole, the collision would have given off all kinds of photons.)

Why such poor localization?  Blame gravity’s pervasive character and Geometry.  With a telescope, any kind of telescope, you know which direction you’re looking.  Telescopes work only with photons that enter through the front; photons aimed at the back of the instrument stop there.

2 LIGO localizationIn contrast, a LIGO facility is (roughly speaking) omni-directional.  When a LIGO installation senses a gravitational pulse, it could be coming down from the visible sky or up through the Earth from the other hemisphere — one signal doesn’t carry the “which way?” information.  The diagram above shows that situation.  (The “chevron” is an image of the LIGO in Hanford WA.)  Models based on the signal from that pair of 4-km arms can narrow the source field to a “banana-shaped region,” but there’s still that 180o ambiguity.

The good news is that the LIGO project built not one but two installations, 2500 miles apart.  With two LIGOs (the second diagram) there’s enough information to resolve the ambiguity.  The two also serve as checks on each other — if one sees a signal that doesn’t show up at the other that’s probably a red herring that can be discarded.

3 LIGO localizationThe great “if only” is that the VIRGO installation in Italy was not recording data when the Hanford WA and Livingston LA saw that September signal.  With three recordings to reconcile, the aLIGO+VIRGO combination would have had enough information to slice that banana and localize the event precisely.

When the European Space Agency puts Evolved LISA (eLISA) in orbit (watch the animation, it’s cool) in 2034, there’ll be a million-kilometer triangle of spacecraft up there, slicing bananas all over the sky.

~~ Rich Olcott

aLIGO and eLISA: Tuning The Instrument

Oh, it’s good to see Big News in hard science get big attention in Big Media.  The LIGO story and Columbia’s Dr Brian Greene even made it to the Stephen Colbert Late Show.  Everyone chuckled at the final “boowee-POP” audio recording (simulation at 7:30 into this clip; get for-real traces and audio from this one).

There’s some serious science in those chirps, not to mention serious trouble for any alien civilization that happened to be too close to the astronomical event giving rise to them.

LIGO trace 3
Adapted from the announcement paper by Abbot et al

The peaks and valleys in the top LIGO traces represent successive spatial compression cycles generated by two massive bodies orbiting each other.  There’s one trace for each of the two LIGO installations.  The spectrograms beneath show relative intensity at each frequency.  Peaks arrived more rapidly in the last 100 milliseconds and the simulated sound rose in pitch because the orbits grew smaller and faster.  The audio’s final POP is what you get from a brief but big disturbance, like the one you hear when you plug a speaker into a live sound system.  This POP announced two black holes merging into one, converting the mass-energy of three suns into a gravitational jolt to the Universe.

Scientists have mentioned in interviews that LIGO has given us “an ear to the Universe.”  That’s true in several different <ahem> senses.  First, we’ve seen in earlier posts that gravitational physics is completely different from the electromagnetism that illuminates every kind of telescope that astronomers have ever used.  Second, black hole collisions generate signals in frequencies that are within our auditory range.  Finally, LIGO was purposely constructed to have peak sensitivity in just that frequency range.

Virtually every kind of phenomenon that physicists study has a characteristic size range and a characteristic frequency/duration range.  Sound waves, for instance, are in the audiophile’s beloved “20 to 20,000” cycles per second (Hz).  Put another way, one cycle of a sound wave will last something between 1/20 and 1/20,000 second (0.05-0.000 05 second).  The speed of sound is roughly 340 meters per second which puts sound’s characteristic wavelength range between 17 meters and 17 millimeters.

No physicist would be surprised to learn that humans evolved to be sensitive to sound-making things in that size range.  We can locate an oncoming predator by its roar or by the snapping twig it stepped on but we have to look around to spot a pesky but tiny mosquito.

So the greenish box in the chart below is all about sound waves.  The yellowish box gathers together the classes of phenomena scientists study using the electromagnetic spectrum.  For instance, we use infra-red light (characteristic time range 10-15-10-12 second) to look at (or cause) molecular vibrations.

RegimesWe can investigate things that take longer than an instrument’s characteristic time by making repeated measurements, but we can’t use the instrument to resolve successive events that happen more quickly than that.  We also can’t resolve events that take place much closer together than the instrument’s characteristic length.

The electromagnetic spectrum serves us well, but it has its limitations.  The most important is that there are classes of objects out there that neither emit nor absorb light in any of its forms.  Black holes, for one.  They’re potentially crucial to the birth and development of galaxies.  However, we have little hard data on them against which to test the plethora of ideas the theoreticians have come up with.

Dark matter is another.  We know it’s subject to gravity, but to our knowledge the only way it interacts with light is by gravitational lensing.  Most scientists working on dark matter wield Occam’s Razor to conclude it’s pretty simple stuff.  Harvard cosmologist Dr Lisa Randall has suggested that there may be two kinds, one of which collects in disks that clothe themselves in galaxies.

That’s where LIGO and its successors in the gray box will help.  Their sensitivity to gravitational effects will be crucial to our understanding of dark objects.  Characteristic times in tens and thousands of seconds are no problem nor are event sizes measured in kilometers, because astronomical bodies are big.

GrWave Detectors
Gravitational instrumentation, from Christopher Berry’s blog and Web page

This is only the beginning, folks, we ain’t seen nothin’ yet.

~~ Rich Olcott

Would the CIA want a LIGO?

So I was telling a friend about the LIGO announcement, going on about how this new “device” will lead to a whole new kind of astronomy.  He suddenly got a far-away look in his eyes and said, “I wonder how many of these the CIA has.”

The CIA has a forest of antennas, but none of them can do what LIGO does.  That’s because of the physics of how it works, and what it can and cannot detect.  (If you’re new to this topic, please read last week’s post so you’ll be up to speed on what follows.  Oh, and then come back here.)

There are remarkable parallels between electromagnetism and gravity.  The ancients knew about electrostatics — amber rubbed by a piece of cat fur will attract shreds of dry grass.  They certainly knew about gravity, too.  But it wasn’t until 100 years after Newton wrote his Principia that Priestly and then Coulomb found that the electrostatic force law, F = ke·q1·q2 / r2, has the same form as Newton’s Law of Gravity, F = G·m1·m2 / r2. (F is the force between two bodies whose centers are distance r apart, the q‘s are their charges and the m‘s are their masses.)

Jim and AlAlmost a century later, James Clerk Maxwell (the bearded fellow at left) wrote down his electromagnetism equations that explain how light works.  Half a century later, Einstein did the same for gravity.

But interesting as the parallels may be, there are some fundamental differences between the two forces — fundamental enough that not even Einstein was able to tie the two together.

One difference is in their magnitudes.  Consider, for instance, two protons.  Running the numbers, I found that the gravitational force pulling them together is a factor of 1036 smaller than the electrostatic force pushing them apart.  If a physicist wanted to add up all the forces affecting a particular proton, he’d have to get everything else (nuclear strong force, nuclear weak force, electromagnetic, etc.) nailed down to better than one part in 1036 before he could even detect gravity.

But it’s worse — electromagnetism and gravity don’t even have the same shape.

Electric (red) and magnetic (blue) fields in a linearly polarized light wave
(graphic from WikiMedia Commons, posted by Lookang and Fu-Kwun Hwang)

A word first about words.  Electrostatics is about pure straight-line-between-centers (longitudinal) attraction and repulsion — that’s Coulomb’s Law.  Electrodynamics is about the cross-wise (transverse) forces exerted by one moving charged particle on the motion of another one.  Those forces are summarized by combining Maxwell’s Equations with the Lorenz Force Law.  A moving charge gives rise to two distinct forces, electric and magnetic, that operate at right angles to each other.  The combined effect is called electromagnetism.

The effect of the electric force is to vibrate a charge along one direction transverse to the wave.  The magnetic force only affects moving charges; it acts to twist their transverse motion to be perpendicular to the wave.  An EM antenna system works by sensing charge flow as electrons move back and forth under the influence of the electric field.

Gravitostatics uses Newton’s Law to calculate longitudinal gravitational interaction between masses.  That works despite gravity’s relative weakness because all the astronomical bodies we know of appear to be electrically neutral — no electrostatic forces get in the way.  A gravimeter senses the strength of the local gravitostatic field.

Maxwell and EinsteinGravitodynamics is completely unlike electrodynamics.  Gravity’s transverse “force” doesn’t act to move a whole mass up and down like Maxwell’s picture at left.  Instead, as shown by Einstein’s picture, gravitational waves stretch and compress while leaving the center of mass in place. I put “force” in quotes because what’s being stretched and compressed is space itself.  See this video for a helpful visualization of a gravitational wave.

LIGO is neither a telescope nor an electromagnetic antenna.  It operates by detecting sudden drastic changes in the disposition of matter within a “small” region.  In LIGO’s Sept 14 observation, 1031 kilograms of black hole suddenly ceased to exist, converted to gravitational waves that spread throughout the Universe.  By comparison, the Hiroshima explosion released the energy of 10-6 kilograms.

Seismometers do a fine job of detecting nuclear explosions.  Hey, CIA, they’re a lot cheaper than LIGO.

~~ Rich Olcott