Evidence for a gravitational wave background from a galaxy-sized detector
astrobites.org
astrobites.org
How does this play into our understanding of the size and expansion of the universe?
> So when we say that a star is N light years away and therefore it would take N years to reach at the speed of light, is that not true?
Sort of, sort of not. The distance distortion caused by gravitational waves is way too small to make a difference. You're talking maybe nanoseconds sooner or later you'd arrive compared to prediction. But this is true within gravitationally bound regions of space, that is, regions with sufficient mass density to prevent expansion. It's the regions between galaxies and especially between galactic clusters that is expanding rapidly, because insufficient mass density exists in these regions to slow it or stop it. So if you set out for Proxima Centauri, you'll get there in about the amount of time you'd expect. But if you set out to leave the local supercluster to some destination in a different supercluster that is megaparsecs outside of the Milky Way, you may never get there at all, even at the speed of light, because the best cosmological model we currently have predicts the expansion rate between superclusters will eventually exceed the speed of light.
[Future of an expanding universe](https://en.wikipedia.org/wiki/Future_of_an_expanding_univers...) seems to suggest this will happen in about 150 billion years. Earth won't exist by then, but any signal sent from within any location in the local group outside of it will never arrive anywhere else if its sent past that time.
Note the other comment's point that some astronomical features are actually moving toward us is only true within the local group. All supercluster-sized mass regions are receding from all others.
There's also a lot of electromagnetic radiation around, and you can't calculate a proper time for that. Likewise gravitational waves and gluons.
Surely the causal structure depends in part on matter? Future null cones of time-orientable flat Minkowski spacetime narrow in the presence of mass; matter is also relevant in null cones on general curved Lorentzian spacetimes.
The speed of light through space is constant. But the space itself can stretch and contract.
You can also “slow light down” by just making it go further: a few clever mirrors will do this easily. This is even more of a cheat, as the light itself isn’t any slower, it just gets where it was going a little later because it went further.
In a sense that’s what’s happening here: the spacetime is being stretched on one axis and squeezed on another, as gravitational waves pass through it. It isn’t by much, which is why we need a whole galaxy to measure it.
The nearest millisecond pulsar is about 500 light years away. There are closer "classical" pulsars. Most of the millisecond pulsars used by PTA collaborations are a few thousand light years away.
Maybe a better way of thinking about the gravitational wave is that it alters a form of gravitational potential along a fraction of the worldline of an element representing a pulse, causing light to run a little uphill (redshifting) or downhill (blueshifting). cf. the Harvard tower experiment (Pound-Rebka). This doesn't seem very geleneral-relativistic but hey looking for a Poisson equation in the Newtonian approximation goes back to Einstein. The Earth and the array pulsars are moving sufficiently slowly with respect to each other, and low-redshift SMBHBs are OK where (handwave handwave) linearized gravity is OK, so we could work likek Einstein in the Newtonian limit with some care. A more modern approach to calculating a Poisson-equation gravity potential analogue is a technically annoying trip through the spacetime decomposition formalism, but once it's there it's conceptually useful, and for gravitation physicists it can be related to the g-induction and g-field in gravitoelectromagnetism.
There are other ways to describe the elephant <https://en.wikipedia.org/wiki/Blind_men_and_an_elephant> though; an equivalence to acceleration (one can change the direction component of the velocity vector for electromagnetic waves); calculating time-dependent (and here that means depends on the orbital phase of the supermassive black hole binary) null geodesics; and so forth. This is the gift of general covariance: we can choose practically whatever coordinates we want, which highlights different components of the covariant tensors used in relativistic theories (e.g. the electromagnetic field tensor F_{\mu\nu} or the Einstein curvature tensor G_{\mu\nu}).
Finally, the concept of https://en.wikipedia.org/wiki/Retarded_time would probably be useful in this thread and others like it that try to understand how what we see here-and-now arose in the past there-and-then. "Perhaps surprisingly - electromagnetic fields and forces acting on charges depend on their history, not their mutual separation" -- the same is true for gravitational fields and forces acting on masses, and this is what drives some of the above Poisson-equation thinking and the GEM formal analogy to the electromagnetic Heaviside-Maxwell equations.
PS: for experts, re my handwave and GEM, see Ruggiero 2022, https://link.springer.com/article/10.1007/s10714-022-02983-8 (open access).
> when we say that a star is N light years away and therefore it would take N years to reach at the speed of light, is that not true?
That is not what "N light years away" means. It means that the light we're right now seeing from that star was emitted N years ago. But stars don't stay put. If you point a rocket at the star and fly N light years of distance, you won't end up inside the star -- it'll have moved on.
This seems pedantic (and it is), but consider the expansion of the universe. You're seeing light from N years ago - when the universe was smaller. Suppose expansion is more or less uniform, i.e. something like "every 1000 years, each meter becomes 0.1% longer" (it isn't, but reasonable approximation). Then: the greater the original distance was, the faster the star is moving away due to expansion of the universe. After all, each meter in between expands x% per second, so more meters in between is greater increase in distance every second.
If the distance is great enough, then each year, the universe expands that distance so much, it increases by more than 1 light year. That means that light from that star can nerve reach us again (unless the universe starts contracting). This phenomenon is called the Cosmological Horizon.
> If the distance is great enough
It's not, in this context.
> Stars don't stay put
Close enough, in this context. The uncertainties ("red noise") in PTA timing residuals from scattering in the interstellar medium and local properties (mostly internal structure) of the pulsars dwarf the uncertainties in relative motion.
PTAs also care about the pulse timing not the carrier of the pulse. That is, the beam points at us with a predictable period and that period evolves (in parts per million) in the presence of nanohertz gravitational waves. The beam itself is broadband (radio to gamma rays) and any spectral line structure could be anything (most likely the interstellar medium).
Detailed redshift studies look at the spread of spectral lines, particulary the Lyman and Balmer series, and pulsars are what you get when there's no hydrogen left to fuse. ("Finally, pulsars have broadband continuum spectra, so if there are gas clouds along our line of sight, pulsars can be used to probe the ISM via absorption by spectral lines of Hi or molecules. Such absorption spectra can be used to estimate pulsar distances" -- end of §6.2 of Condon & Ransom's Essential Radio Astronomy advanced undergraduate one-semester-course textbook (2016 ed.), web version at https://www.cv.nrao.edu/~sransom/web/Ch6.html )
I have a related comment in this thread if you're interested.
What's being tracked on Earth is not the speed of light or the radial distance to each pulsar (which is in any case not known to good precision) but rather the rotation rate of each pulsar. That's known to very good precision for each of the selection of pulsars by each pulsar timing array (PTA) collaboration. Each collaboration selects a number of pulsars with very stable rotation rates.
The PTA antennae listen to the beam from the pulsar in convenient radio frequencies; they're not especially interested in the spectral structure of the pulsar signal, and are not deliberately looking for a gravitational redshift of the beam's radio frequencies as opposed to a gravitational redshift of the beam's amplitude.
The amplitude modulation of the listened-to frequencies is driven by the very much slower than light rotation of the pulsar which drags a beam around so that we see it very strongly once or twice per rotation.
At the top of this page <https://www.astron.nl/pulsars/animations/> there is an animation of a pulsar; we're interested interested in the bright flashes when the beam fills the video window. The evolution of timing of those bright flashes are what PTAs track. Notice that the flash is sharp rather than smeared out, waxing and waning slowly over the course of a rotation. This is a useful property and distinguishes a pulsar from ordinary astronomical radio soruces (and the essentially constant light from ordinary stars). Here's a typical "chirp" from eight different millsecond pulsars observed at Arecibo <https://scx2.b-cdn.net/gfx/news/2019/palfasurveyr.jpg>. The first line in each box is the name of the pulsar; the lines below the names are the rotation rate (the other two lines are details about the observation and processing rather than the pulsar).
Another useful property is that the "chirp" is seen in an enormous range of frequencies, so two immediately adjacent radiotelescopes listening to the pulsar in two very different radio frequencies will notice the pulse essentially simultaneously. Some millisecond pulsars even flash at high frequencies (up to gamma rays) although in practice PTAs aren't particularly interested in that part of the spectrum (although it is certainly watched by other astronomers!).
In many millisecond pulsars the interval between bright flashes is very very very stable (they don't have "starquakes" and don't have significant amounts of matter accreting on them) and thus predictable. That means (with a good frequency standard on our side) we can tell if the gap between a pair of pulses is short or long compared to the long term average.
The gravitational waves the pulsar timing array (PTA) experimentalists are interested in will induce a gradual (over the course of months to years) increase and decrease of the gap between pulses. The change is quite small; if we have a "true" millisecond pulsar where the long term average has us seeing one pulse every millisecond exactly, a nanohertz (say, a cycle time of one year and of moderate amplitude) gravitational wave over the course of the year will stretch the millisecond timing to a maximum of one millisecond plus low tens of nanoseconds and a minimum of one milliecond minus low tens of nanoseconds. Most of the time it's between those outer bounds and close to the long term once-per-millisecond-exactly average.
The hard work for the experimentalists is in signal processing and spotting sources of noise in the pulse timings.
However, depending on their nature, there is a possibility that this is still a pretty significant event. When we observed the cosmic microwave background, because this is light emanating from everywhere at the very first time photons decoupled from ionized matter and the mean free path exceeded the particle horizon (the universe "became transparent" as they say), this is the furthest back you ever see using light. A much earlier event can possibly be observed via the cosmic neutrino background. The universe would have been transparent to neutrinos much earlier, when the electroweak force first decayed into the weak and electromagnetic forces. This is a big difference, fractional seconds after the Big Bang compared to I think 379,000 years or so for light.
However, the very earliest event that could ever be observed by any means at all would be the cosmic gravitational background expected to exist when gravity first decoupled from strong and electroweak forces. If that's what this is, we're not seeing the literal beginning, but it's the closest we can ever get by any sensor we currently have the ability to conceive of.
No, this is about the nanohertz gravitational wave "background", which comes from massive binaries with orbital periods of on the order of months to years. Sources are expected to be be randomly arranged in spherical coordinates (up to an unfortunately low radial distance cutoff), like the (low-redshift) galaxies they likely live in the middle of.
Primordially, most still-viable types of inflation produce gravitational waves on all length scales, so some very short wavelength primordial GWs are in principle accessible to us despite the large cosmological redshift (z >> 10^10; 10^10 is about the redshift at neutrino decoupling, a good guess is that z ~ 10^25 is the ballpark for the latest high-amplitude-peak (~ 10^-17 Hz) inflation-produced gravitational radiation[1]). If multimessenger and other techniques can help subtract the "foreground" of binary black holes and the like, then perhaps we will see them as redshifted-to-light-year-wavelengths not traceable to a hard SMBH binary or foreground mimicers.
The CMB, particularly in its B-mode polarization, is already a useful probe of primordial gravitational radiation as was anticipated at least as early as BOOMERanG's 2003 flight. A better measurement of (dust and gas, and also some gravitational lensing) foregrounds is important there too.
[1] Grischchuk 2005 §3, most easily obtained at https://arxiv.org/abs/gr-qc/0504018v4 (see Comments section below abstract for its provenance).
PS: Bécsy, Cornish & Kelley 2022 (open access at The Astrophysical Journal, but easiest to grab the arxiv version which matches the published paper) https://arxiv.org/abs/2207.01607 is a very good overview of the nanohertz GW background(s) and how they're accessible to pulsar timing arrays. A couple of the recent coordinated-release papers by the various intl PTA members are also good overviews https:///www.ipta4gw.org/
Lenses, and the telescope and microscope, both advanced astronomy and biology tremendously. Interferometry grows out of optics, spectroscopy, and the ability to detect interference at scales. Chemical tests, electromagnetic principles, radiation, and the ability to detect electromagnetic radiation outside the visible spectrum (infrared, radio, ultraviolet, x-ray, gamma ray) had similarly large influences. Another area of progress is increased precision in measuring both space and time, which this discovery addresses.
I've also done some fairly casual eyeball-assessments of trends in Nobel-awarded research in physics and chemistry since roughly 1960, which is a convenient demarcation between the period of profound discovery through the earlier part of the 20th century, with fundamental laws and particles making frequent mention, to the past 60 or so years in which it's often been measurement or emission capabilities (think LIGO and blue LEDs) which have been the subject of awards. In one sense, these seem less significant than the earlier work, and that's been my own tendency in ascribing heft. But if this does in fact represent a gestation period in which new observational tools and techniques are being cultivated, there might well be more impact than appears initially.
We're in what may well be the early stages of gravitational wave measurement and detection, and we're figuring out how to "build" galactic-- and intergalactic-scale measurement "devices" which are necessary to detect this pervasive but very low-energy effect. It is exciting, and I'm thinking over the past record of sensing technologies to think how these might inform us. My initial read is that gravitational waves are very low frequency, which is to say, low resolution, but because they have extraordinarily high upper bounds on magnitude (unlike, say, magnetic or electromagnetic events associated with stars, galaxies, and even black-hole and neutron-star interactions, though the latter play a strong role in gravitational wave phenomena), what I suspect we'll find is a general sensing capability which can "see through" cosmic structures that are otherwise opaque to us (gravity isn't bothered by dust and other matter), and also provides a mechanism for directly observing dark matter, which is defined by the fact that it does interact gravitationally but does not with the electromagnetic spectrum.
That's a lay view, no specific expertise, but informed by a model of technologies and capabilities afforded, one element of which is information, itself comprised of sensing, processing, storage and recall, and transmission.
If I'm not mistaken, they would be indistinguishable at our current level of tech because you'd have to do a sort of tomographic analysis by taking the same measurement at multiple points that are very distant from each other
There are a lot of binary sources across the sky whose orbits differ in duration and orientation (and likely ellipticity and mass-ratio) and distance from the Milky Way, so the idea is to spot one oscillating volume in between us and multiple pulsars, or one wave inducing ~identical oscillations (including their amplitude) in between us and several pulsars. Alternatively, one can see how well interferometry measurements of time-of-flight match the Hellings and Downs curve, which predicts timing residuals for a pulsar timing array in the presence of a a background from random binary sources all over the sky.
I'll be unusually speculative. I usually try to avoid that on HN. One could perhaps contrive a flow of dark matter which slightly delays a pulsar signal given enough time-of-flight, and with some effort could work out how that might mimic one gravitational wave source. It's much harder to do it for the sources all over the sky and at various orientations. Also, the dark matter density between us and the pulsar will have to avoid disturbing the orbits through the Milky Way of objects between us and the pulsars (e.g. gas clouds, stars), while remaining overdense enough to delay the beam path the requisite amount. I'd start with the idea of a wrought iron fence, where the bars are exactly aligned along our view of a pulsar, and then realize that the bars have to smear along their (cylindrical) radius. I'd need a smeared-bar/gap/differently-smeared-bar/gap cycle over the course of months to years, and I'd need that cycle to continue for decades. I'd also need to realign the long axis of the cylinders (harder to do than spherical regions) as Earth and the pulsar move with respect to each other; among other things I have to control the gravitational redshift of large background things (galactic star clusters and molecular clouds up to background galaxies with predictable light curves - supernovae, active galactic nuclei etc) at some angular separation from the pulsar. I'd end with realizing that nothing like this could be physical with cold dark matter for even one source, and because of the Hellings-Downs approach I'd have to do this for multiple pulsars.
On reflection it's easier to think about a density distribution of dark matter that is precisely -- conspiratorially even -- arranged to induce changes in the local proper motion of all the pulsars in the PTA. If the pulsars are drawn to an overdensity of dark matter behind them (from our point of view) and beside them periodically, one could mimic the effect of dim nanohertz sources. I think bright sources kill this idea though, because the requisite overdensity would affect orbits of objects near the pulsars. It's also easier to think of how these pockets of extra DM could smear out over experimental time than to keep them precisely overdense and precisely located with respect to the pulsars for many years.
[1] handy animated gif https://d18l82el6cdm1i.cloudfront.net/uploads/FP84etZqf6-pmo... where we see a ring of test particles at the margin of a slice through our spherical volume, the left is the + polarization the right is x. The change from circular to elliptical cross section is HUGELY exaggerated. The gravitational waves in question would not even change a pixel if we drew two oscillating-to-scale circles instead.
BTW don't shy away from being speculative. This was an effective explanation.
Take a child's mobile or a pair of differently-coloured tennis balls (say red and green) glued to the end of a paper tube and suspend that from the ceiling at about shoulder height. Set the thing spinning in the plane parallel to the ceiling. Step back a bit and choose one hand's index finger to point at one of the tennis balls and the other hand's to the other. Left index to red, right index to green. Extend and retract each arm to try to maintain a constant distance from each fingertip to the ball it's pointing at. Play with parallax so that you notice your arms crossing during part of the orbit (red ball on right at same distance to you as green ball on left) and uncrossing half an orbit later. You'll also notice the other phase where both fingers/arms point practically parallel but with one hand closer to you, then half an orbit later further from you.
Your fingers are basically indicating the masses in their circular orbit. For gravitational radiation from the orbiting binary tennis balls a ~cylinder of space where index fingers lie on the axis lengthens axially and contracts radially. (A really tiny amount). This is encoded in the Weyl tensor, which is the traceless part of the Riemann curvature tensor (for more on that, see Baez's stab at this, <https://math.ucr.edu/home/baez/gr/ricci.weyl.html>). In a linearization of the Einstein Field Equations, which is how most people are taught gravitational radiation, we get the h+ and hx polarizations; hx is maximal when your arms are crossed and half an orbit later, h+ maximizes when your arms are parallel. Most people also think about their mass-detector (fingertips) pointing at the nearest mass rather than always at one of the binary, and so miss the thinking behind "cross" and this edge-on vs a face-on view of the tennis ball binary.
The GW spectrum and in particular the brighter sources makes it really hard to come up with something astrophysical that isn't an essentially isotropic set of shells of inspiralling supermassive black hole binaries (~billions of solar masses, orbital periods of about a third of a year to a couple of years) with scattering and orientation statistics similar to the observed distribution of galaxies (including nonspirals) and our view of spirals as edge-on vs face-on.
> Why not have periodically distributed dark matter
Big warning: I don't do galactic dynamics! That will colour my approach to answering your question. It's a neat question though.
Second big warning: in no way is this rigorous, and I won't feel bad if someone blows me up with math.
Think Lorentzian rather than Euclidean. The dark matter (DM) blobs have to move around the pulsar timing array (PTA) members in order to induce longitudinal redshift and blueshift, and also (because the beamline is dragged by the other polarization) brightening and dimming. DM is famously bad at dimming background objects...
DM is also really hard to compactify (you need it to couple with gravitationally collapsing hot baryons and get the latter to cool fast) and has tiny bulk viscosity. So you're going to need really weird initial conditions to get the overdensities you want in place.
Cold DM is also really hard to lift to a higher gravitational potential. Around the PTA pulsars its even hard to lift baryonic clouds since our galaxy is super-quiet (no AGN outflow or feedback) and the PTA millisecond pulsars are well out of the central bulge. That ties your hands a bit on Lorentzian periodicity, and my bet is that from generic initial values you end up with a pulsar with a sparse but fat ~spherical "atmosphere" of DM.
Euclidean v Lorentzian in a nutshell. Euclid: take an equilateral tetrahedron (to keep things nice and simple), spatial lengths in lightseconds (and setting c=1). You and three friends at the vertices stay put with respect to each other. Lorentz equilateral tetrahedron: put one vertex a second in the future, and its opposite side in the present. You and two friends at the vertices of that past side move at c to the future vertex. We can take you and your two friends' movement timelike and to the non-relativistic limit through rescaling. We can rotate the E vs L tetrahedra or change the areas of one or more sides so that the points trace out the worldlines of some DM masses. Thinking E-style you arrange four blobs of dark matter at the vertices of a tetrahedron around the pulsar enclosed by a (not necessarily equilateral and not necessarily unchanging in edge length or face area or volume) tetrahedron. Invites Kepler thinking. But we don't have Euclidean symmetries in our universe, we have Lorentzian ones. Thinking L-style you arrange three blobs of dark matter around the pulsar enclosed by the L-tetrahdron, and blobs and the pulsar eventually collide (that's basically Raychaudhuri's focusing theorem). Evading eventual Raychaudhuri collision is hard because there's basically no contact forces within the DM blobs or between them and the pulsar (so no outward acceleration), therefore you need to rely on vorticity to oppose collapse. And the point of the exercise is to introduce or at least mimic nonzero shear (sphere->ellipsoid), which acts against vorticity.
It's not quite "CRUNCH" because the DM blobs will sail through each other and the pulsar, but the pulsar won't move the way you want and dynamical drag effects will settle the DM blobs into an atmosphere around (and through!) the pulsar. Thanks to the pulsar spin, high frequency multipole gravitational radiation from bumps on the crust and interior quakes and things (yay, pulsar glitches) will dominate the GW spectrum.
Lots of wiggling, and not obviously the wiggling you want. I'm inclined to demand a description of initial conditions that leads to the wiggling you want (in-flight frequency and brightness evolution of the emitted beam), because in all honesty I don't trust my intuition that the IVs would be really non-generic in angular momentum but I'd think it's really really cool if I were wrong on the "there's no way that would work" reaction to the DM blobs mimicking nHz GW background idea.
Final two things: I kept editing in and out dissipation and viscosity, because I don't do and don't want to do galactic dynamics. However, subgalactic DM overdensity blobs are unlikely to stay blobs.