Deep divefrom Episode 6Cosmology14 October 202629 min

Thirty-Thousand-Year Waves, Quasars and Pulsars Together

A deep dive into one paper: what was known before, what the researchers did, what the numbers say and what they don't.

The paper: Combining astrometry with pulsar timing: the first joint analysis of very low frequency gravitational waves (arXiv preprint)

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Transcript

The script the two AI voices read from. The times are worked out from the script, not heard, so a line can start a few seconds early or late.

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Cold open

Host 1You heard the trailer — this is the whole story. Welcome to the Hastrup Review of Science — where artificial intelligence reads real science, so you don't have to pretend you understood the paper. Today, one paper, and gravitational waves so slow that a single ripple can take longer to pass than human civilisation has existed.

Host 2The paper is called Combining astrometry with pulsar timing: the first joint analysis of very low frequency gravitational waves. It is by Lorenzo Filipello and colleagues Beordo, Akhmetov, Crosta and Lattanzi, all at the Italian National Institute for Astrophysics observatory in Turin, with affiliations in Kyiv and Kharkiv. It was posted to arXiv in September twenty twenty-six as a manuscript for Astronomy and Astrophysics.

Host 1Posted, so not yet through peer review?

Host 2Treat it as a preprint. Every number today comes from the version dated the twenty-first of September.

Host 1The claim, in two sentences.

Host 2They combined the slow drift of one and a half million quasars measured by the Gaia space telescope with the slowly changing orbits of eleven binary pulsars, and searched both together for a single giant black hole pair. They found nothing, and turned that nothing into the tightest limit so far on such signals in this extremely low frequency range.

Host 1So this is a null result.

Host 2It is a null result, and the authors say so plainly. The interesting part is the method, and how much bookkeeping it takes to avoid fooling yourself.

Why this field exists

Host 1Start with the basics. What is a gravitational wave, in one breath?

Host 2This is background, not the paper. A gravitational wave is a ripple in spacetime itself, predicted by Einstein, that briefly stretches distances in one direction and squeezes them in the other as it passes. The size of that stretch is called the strain, written h, and it is tiny.

Host 1How tiny?

Host 2The LIGO detectors, which first caught colliding black holes in twenty fifteen, measure strains around ten to the minus twenty-one. That is a change in length of about one part in a thousand billion billion.

Host 1And these waves come in different frequencies, like sound.

Host 2Exactly like sound, and each frequency band needs a different instrument. LIGO hears hundreds of cycles per second, from stellar-mass black holes in their final moments; a planned space mission called LISA will listen around millihertz.

Host 1And pulsar timing arrays?

Host 2Also background. Pulsar timing arrays such as NANOGrav watch dozens of millisecond pulsars, spinning neutron stars that tick with clock-like regularity, and look for tiny shared delays in their pulses. They are sensitive around nanohertz, meaning waves with periods of years to decades.

Host 1And this paper goes lower than that.

Host 2Much lower. The paper targets frequencies from one picohertz, ten to the minus twelve hertz, up to about one nanohertz, ten to the minus nine.

Host 1Translate that into periods.

Host 2One nanohertz is a wave period of about thirty years. One picohertz is a period of roughly thirty thousand years.

Host 1Who makes a wave that takes thirty thousand years to go up and down once?

Host 2According to the paper, two main candidates. Pairs of supermassive black holes, each millions to billions of times the mass of the Sun, that are still early in their slow spiral towards each other, with orbits of years to millennia.

Host 1And the second?

Host 2A background hum of cosmological origin, left over from the early universe. The paper lists cosmic strings, phase transitions and primordial fluctuations from inflation or primordial black hole formation as possible sources.

Host 1Why do the authors care about this band in particular?

Host 2Because it is largely unexplored. Pulsar timing arrays cover the nanohertz band, and the Planck satellite set limits on primordial waves at around ten to the minus eighteen hertz, but between those, the picohertz region has very few measurements.

What was known before

Host 1What did we know before this paper?

Host 2From the paper's introduction: pulsar timing collaborations reported evidence for a gravitational wave background at about three standard deviations in twenty twenty-three, approaching four by the time of writing. That is near the nanohertz band, not the band this paper targets.

Host 1And in the picohertz band specifically?

Host 2Two separate lines of work. One uses astrometry, the precise measurement of where things sit on the sky, and the other uses slow changes in binary pulsar orbits.

Host 1Start with astrometry. How does a gravitational wave move a star?

Host 2A gravitational wave passing through the space between us and a distant object bends the incoming light very slightly, so the object appears displaced on the sky. That was worked out by Pyne and colleagues in nineteen ninety-six, and the displacement follows a specific pattern across the whole sky.

Host 1And Gaia measures where things are.

Host 2Background: Gaia is a European Space Agency mission launched in twenty thirteen that maps the positions and motions of more than a billion stars. The paper notes Gaia was not designed to deliver time series, so its positions at individual epochs will only be published in the fourth data release.

Host 1So what can you do without time series?

Host 2You use proper motions, which is how fast each object appears to drift across the sky. If a gravitational wave's period is much longer than the observing window, its effect shows up as a slow, steady apparent drift rather than a wobble.

Host 1Clever. A wave too slow to wiggle looks like a drift.

Host 2Exactly, and the paper calls these secular effects. The earlier constraints from real astrometric data, cited in the paper, all come from proper motions.

Host 1And the pulsar side?

Host 2Same trick, different direction. Several groups proposed using the slow drift in the orbital period of binary pulsars as a picohertz detector, and the paper cites a twenty twenty-six analysis by Zheng and colleagues as its closest pulsar-only comparison.

Host 1Had anyone combined the two?

Host 2Not on real data. The paper cites theoretical forecasts suggesting a joint analysis could improve sensitivity by as much as fifty percent over pulsar timing alone, but this is the first time anyone has actually run it on real data.

The open question

Host 1So what is the open question?

Host 2Can you fold two completely different kinds of measurement, made by different instruments and with different noise, into one consistent search? And if you do, does it actually beat either one alone?

Host 1Why would they help each other?

Host 2Because they see different components of the same wave. That is the core idea, so let me take it slowly.

The one idea

Host 1Go ahead. Slowly.

Host 2A pulsar binary acts like a clock whose ticking we watch along the line of sight, so a passing wave shows up as an apparent acceleration towards or away from us. The paper calls this the radial effect.

Host 1And the quasars?

Host 2Quasars show the opposite component: apparent motion sideways across the sky, perpendicular to our line of sight. The paper calls this the tangential effect.

Host 1So one sees forward and back, the other sees side to side.

Host 2Yes. The authors describe them as orthogonal, and the point is that each method alone has blind spots and ambiguities about where a wave is coming from, which the other can partly fill.

Host 1Like two security cameras at right angles.

Host 2A reasonable picture. One camera alone cannot tell how far away something is along its line of sight; two cameras at an angle can.

Host 1What exactly are they looking for?

Host 2A continuous wave from a single supermassive black hole binary. Because the wave period is so long, it is effectively one steady sine wave across the whole observation, described by seven numbers.

Host 1Which seven?

Host 2The strain, the frequency, two sky coordinates for where it comes from, two angles for how the binary is tilted and oriented, and a phase. Strain is the headline number.

Ingredient one: quasars

Host 1Walk me through the data. Quasars first.

Host 2They use the Gaia Celestial Reference Frame from the third data release, about one point six million quasars observed over thirty-four months, from July twenty fourteen to May twenty seventeen. Most of these quasars sit at redshifts around one and a half to two, meaning billions of light-years away.

Host 1Why quasars and not ordinary stars?

Host 2Because quasars are so distant they should not move at all on the sky; their real sideways motion is far below what Gaia can measure. So any drift Gaia sees in a quasar comes from something else: our own motion, the reference frame, instrument quirks, or a gravitational wave.

Host 1There are cleaner quasar catalogues, aren't there?

Host 2The paper mentions one called Quaia with higher purity. They chose Gaia's own catalogue because it reports how the errors in the two motion directions are correlated, and ignoring that, they argue, would underestimate errors and could bias the search towards a preferred wave direction.

Host 1Did they throw out any quasars?

Host 2They kept sources with a good astrometric fit and dropped those drifting faster than one milliarcsecond per year, as likely stars or artefacts. That leaves one million five hundred five thousand four hundred twenty-seven quasars.

Host 1How noisy is each one?

Host 2Very. The typical uncertainty on each quasar's motion is around six hundred microarcseconds per year, and the spread of measured motions is about seven to eight hundred. Individually, almost every quasar is pure noise; the signal can only emerge from the pattern across the whole sky.

Host 1And a million and a half quasars is a lot to fit.

Host 2So they compress. They divide the sky into equal-area pixels, take an error-weighted average motion in each pixel with a combined covariance, and discard pixels holding fewer than ten quasars.

Ingredient two: binary pulsars

Host 1Now the pulsars.

Host 2They start from the ATNF pulsar catalogue, a public catalogue maintained by Australia's national science agency, and look at the orbital period of pulsars in binary systems and how fast that period is changing. Gravitational wave effects show up in that rate of change.

Host 1Why orbital period rather than the spin?

Host 2The paper says orbital periods are measured with high precision and stability across all pulsar timing collaborations. The spin could be used too, and they list spin-based observables as future work.

Host 1How many pulsars survive?

Host 2Eleven. They required a distance measurement from parallax with better than ten percent uncertainty, and a distance closer than one kiloparsec, about three thousand three hundred light-years.

Host 1Why is distance so important?

Host 2Because nearly every other effect on the orbital period scales with distance, and so does part of the gravitational wave response. If you get the distance wrong, you get every correction wrong.

Host 1What are those other effects?

Host 2Three main ones. First, the Shklovskii effect: a pulsar moving across the sky appears to accelerate away from us purely by geometry, an apparent Doppler drift that grows with speed squared times distance.

Host 1Second?

Host 2The Milky Way's own gravity pulls on both the pulsar and the Sun differently, and we only measure the difference along the line of sight. Third, the binary itself loses energy by emitting gravitational waves, so its orbit genuinely shrinks.

Host 1The famous Hulse-Taylor effect.

Host 2Exactly, that is background, and it earned a Nobel Prize in nineteen ninety-three. In this paper, for most of the eleven pulsars the Shklovskii term dominates; the exception is a pulsar called B fifteen thirty-four plus twelve, where orbital decay from gravitational wave emission dominates because it has a massive neutron star companion and a short, eccentric orbit.

Host 1Where are these pulsars on the sky?

Host 2Mostly away from the Galactic disk, because dust and gas in the disk hide pulsars there. So adding pulsars does not fill the quasar gaps as much as you might hope, which the authors say openly.

Host 1Any assumptions about the stars themselves?

Host 2Where masses are not measured well enough, they assume the standard pulsar mass of one point four solar masses and use the median inferred companion mass.

Under the hood

Host 1Now the machinery. How do you fit both at once?

Host 2They build a Bayesian model with one likelihood for pulsars and one for quasars, and multiply them. Free parameters are the seven wave parameters, the pulsar distances, and a set of terms describing the quasar sky's systematic patterns.

Host 1Bayesian in practice meaning what?

Host 2They write down what each measurement should look like with and without a wave, and ask how much better the wave hypothesis explains the data. They use a technique called nested sampling to compare models, and a Markov chain Monte Carlo sampler to map the range of allowed wave strengths.

Host 1You said the bookkeeping was the interesting part.

Host 2It is. The authors put it bluntly: without careful noise modelling, both datasets produce spurious detections.

Host 1Start with the pulsars.

Host 2The Galaxy's gravitational pull is not well known, and recent studies disagree about the Milky Way's mass. They take a standard model of the Galaxy from twenty seventeen, by McMillan, and shake its parameters.

Host 1Shake them how?

Host 2They draw ten thousand random sets of six model parameters from their published uncertainties, compute the Galactic acceleration on each pulsar for every set, and use the spread as an extra error bar. That model uncertainty is added to each pulsar's total error.

Host 1And without that?

Host 2The paper says the residuals differ significantly from zero, consistent with an earlier study that needed an extra jitter term. After adding the Galactic model uncertainty, the spurious detection goes away.

Host 1Which means either the timing errors are underestimated or we do not understand the Galaxy well enough.

Host 2Those are exactly the two explanations the authors give. They lean towards the Galactic model, but they cannot say which.

Host 1Now the quasars.

Host 2Two known effects make every quasar appear to drift. One is called the glide: the Solar System is falling around the Galactic centre, and that acceleration causes a small apparent drift of all distant objects towards that direction.

Host 1And the other?

Host 2A possible slow rotation of the reference frame itself. Both make a simple sky-wide pattern called a dipole, one side flowing towards a point and away from the opposite point.

Host 1And the gravitational wave makes a different pattern.

Host 2Yes, mostly a quadrupole, a four-lobed pattern, with weaker contributions at finer scales. The paper decomposes the sky into what are called vector spherical harmonics, essentially a set of standard patterns at increasing levels of detail.

Host 1Like breaking a sound into notes.

Host 2A fair analogy for a sphere. Dipole is the lowest note that matters here, quadrupole the next, octupole the one above that.

Host 1What went wrong when they only modelled the dipole?

Host 2Gaia's quasar motions have known systematic patterns at medium and small scales, so the fit forced the gravitational wave to absorb that leftover power and produced unphysical strain values. So they added free quadrupole and octupole terms alongside the wave.

Host 1But wait. If the main wave signature is a quadrupole, and you add a free quadrupole, couldn't that soak up a real wave?

Host 2That is the obvious worry, and they address it. Their argument is that a single wave is described by only seven parameters, while the free terms need a very specific arrangement of many coefficients to mimic it, so in the presence of a real wave the simpler wave model should win.

Host 1Is that argument tested?

Host 2Partly, by injection tests we will come to. It is a reasonable argument, but listeners should hold it as an argument, not a proof.

Host 1And the priors on the glide?

Host 2To avoid using Gaia's own glide estimate on Gaia's own data, they centred the glide on an independent radio measurement of five point two microarcseconds per year towards the Galactic centre. Rotation was centred on zero, both with a loose width of five microarcseconds per year.

Host 1Did the glide come out sensibly?

Host 2Yes. In the appendix they report a glide magnitude consistent with Gaia's own value within one standard deviation, pointing towards the Galactic centre within the errors, which is a useful sanity check that the machinery works.

Results: any signal?

Host 1Results. Did they find a wave?

Host 2No. The joint analysis gives a log Bayes factor of minus zero point four two, plus or minus zero point zero three.

Host 1Explain a Bayes factor without the maths.

Host 2It is the betting odds between two hypotheses after seeing the data. A log Bayes factor near zero means the data cannot tell the difference; negative means the no-wave model is slightly favoured.

Host 1What about each dataset alone?

Host 2The pulsar-only search strongly preferred no wave, similar to the earlier pulsar result by Zheng and colleagues. The quasar-only search is a little messier.

Host 1Messier how?

Host 2First, the data strongly preferred adding the quadrupole and octupole terms over a dipole-only model, which tells you Gaia's quasars have patterns that glide and rotation alone cannot explain, as the Gaia team already reported. Then, adding a wave on top gave a weak preference for the wave, a log Bayes factor above one.

Host 1That sounds like a hint.

Host 2The authors say not to read it that way. That value is within three standard deviations of zero, and they attribute it to the sampler weakly overfitting leftover systematic power at finer scales than the octupole.

Host 1How do they back that up?

Host 2They used a second, simpler method called the Savage-Dickey density ratio, which tests whether the wave strength is consistent with zero without fitting extra models. That gave minus zero point seven one, no evidence for a wave, and they used the same method for the joint result.

Host 1How do they know the pipeline won't cry wolf?

Host 2Sky scrambling. They kept every measured value but shuffled the sky positions of all the objects fifty times, which destroys any real wave pattern, and none of the fifty shuffles exceeded a log Bayes factor of minus zero point two.

Host 1So noise alone does not produce false detections.

Host 2Not in those fifty trials. Fifty is a modest number for estimating rare false alarms, so it is a reassurance rather than a precise false alarm rate.

A word from our sponsor

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Results: the limits

Host 1Back to the paper. No detection, so what can they say?

Host 2How loud a wave could be and still have escaped notice. At a reference frequency of four times ten to the minus ten hertz, a wave period of about eighty years, the strain must be below six point four times ten to the minus eleven, with ninety-five percent confidence.

Host 1That number seems enormous compared to LIGO.

Host 2It is, and that is expected. A slower wave produces a smaller apparent drift for the same strain, since these observables scale with strain times frequency, so at very low frequencies you can only rule out very loud waves.

Host 1How did they get a limit across frequencies?

Host 2They fixed the frequency at a grid of values and ran the fit at each one, taking the ninety-fifth percentile of the strain distribution as the limit. They stopped at a frequency of one over four times the observing time, to keep the slow-wave approximation valid.

Host 1And the gain from combining?

Host 2The joint limit is twenty to thirty percent tighter than the pulsar limit alone. The paper says Gaia's third data release is still two to three times less sensitive than the pulsars on their own.

Host 1So the pulsars do most of the work.

Host 2Right now, yes. The quasars add a meaningful but modest improvement, which is less than the fifty percent some earlier forecasts had suggested.

Host 1And the claim of tightest limits?

Host 2The authors state these are the tightest constraints to date on continuous waves in the picohertz band. We have not independently checked that comparison; it is their claim, made against the work they cite.

Host 1Does it matter which direction the wave comes from?

Host 2A lot. At a fixed frequency of two point five times ten to the minus ten hertz, a period of roughly a hundred and thirty years, the limit ranges from two point nine four times ten to the minus eleven in the best direction to two point six five times ten to the minus ten in the worst.

Host 1That is close to a factor of ten.

Host 2About nine. It follows where the pulsars sit and where Gaia sees the most quasars, and the authors say the combination also reduces that spread compared with either dataset alone.

Host 1Can they say anything about where a wave might come from?

Host 2No. The direction, orientation and phase all came back looking exactly like the starting assumptions, which is what you expect when there is no signal.

Results: the Gaia DR4 forecast

Host 1The abstract mentions Gaia's fourth data release. What do they forecast?

Host 2The fourth data release extends Gaia's observing span from thirty-four months to five and a half years. Positional precision improves with the square root of time, but proper motion precision improves faster, roughly as time to the power of three halves, because you also gain a longer lever arm.

Host 1So doubling the time does more than double the precision.

Host 2For proper motions, yes, about two point eight times better, in the idealised case. More quasars also pass the one milliarcsecond per year cut.

Host 1How did they test this?

Host 2They built mock catalogues using the real quasar positions with expected new error bars, plus mock pulsar data, injected simulated black hole binaries, and ran the full pipeline. In what they call a fairly realistic scenario, the joint limit could fall below ten to the minus eleven.

Host 1And can it actually detect something if it is there?

Host 2They injected one hundred mock signals per strain level at two point five times ten to the minus ten hertz. Below a strain of ten to the minus eleven, no injection produced a positive log Bayes factor; above ten to the minus ten, every injection gave very strong evidence for a signal.

Host 1So a grey zone between those two.

Host 2A factor of ten between invisible and clearly detected. They set ten to the minus ten as the level where ninety-five percent of real signals would be caught, and show that in that range the recovered strain matches the injected one well.

Host 1Any caveats to the forecast in the paper?

Host 2Two, stated by the authors. They only modelled random white noise, while Gaia has a known systematic floor, and the extra quasars that pass the cut may be fainter and noisier, which would pull sensitivity back down.

Why it matters

Host 1So what is the principle here?

Host 2Two instruments that see the same wave from orthogonal angles can be combined into one search, and the combination is better than either alone. That is now demonstrated on real data rather than only in forecasts.

Host 1What changes, and for whom?

Host 2For gravitational wave researchers, it is a working pipeline, with the systematics problems identified and handled. For the Gaia community, it is a concrete use for the fourth data release beyond its original goals.

Host 1And astrophysically?

Host 2Background, framed carefully: waves in this band would come from the heaviest black hole pairs, early in their spiral, so these limits start to constrain how many such extreme pairs exist nearby. The paper itself does not translate its limits into black hole masses or numbers, so we will not either.

Host 1What does it not mean?

Host 2It does not mean anyone detected a gravitational wave at these frequencies. It does not say anything about the nanohertz background that pulsar timing arrays have reported, which is at higher frequencies and a different kind of signal.

Host 1And it is not a full cross-correlation either.

Host 2Right. It combines slow drifts, not time series. True cross-correlation of periodic signals between astrometry and pulsar timing would need Gaia's epoch data, which the authors list as a future step.

Honest caveats

Host 1Caveats. Start with the biggest.

Host 2The noise model drives the result. On both sides, the authors found spurious detections until they added extra terms, so the limits depend on choices about how much unexplained noise to allow.

Host 1Is that a problem or just honesty?

Host 2Mostly honesty, and it is the right direction to err. But it means the limits are as good as the Galactic model and the systematic model, and the authors acknowledge that remaining power at finer scales than the octupole was not modelled.

Host 1Second caveat.

Host 2The pulsar sample is small, eleven binaries, with no raw timing data, only catalogue values. The authors say themselves that without raw data they infer, rather than demonstrate, where the extra noise comes from.

Host 1Anything odd in the tables?

Host 2One thing a careful listener might spot. The paper states a cut of ten percent parallax uncertainty, but one listed pulsar, J zero six one three minus zero two zero zero, has a parallax of one point zero plus or minus zero point five milliarcseconds, which is fifty percent; the paper does not explain that discrepancy.

Host 1Third.

Host 2The quasar systematic terms could in principle absorb part of a real wave. The authors argue the wave model would be preferred, and the injection tests are encouraging, but those injections were run on mock data with simple white noise, not with Gaia's real systematic patterns.

Host 1Fourth.

Host 2The false alarm check used fifty sky scrambles, and the injection tests used one hundred signals per level at one frequency. Those are sensible checks, but modest in size.

Host 1And the comparison to other work?

Host 2The improvement is twenty to thirty percent over pulsars alone, below the fifty percent some forecasts suggested. The authors frame it as a first step, and that is the fair way to read it.

Host 1One more. Is it the only possible Galactic model?

Host 2No. They use one standard model and propagate its uncertainties, while noting that other recent studies suggest a lighter Milky Way. A different model could shift the pulsar corrections in ways the error bars do not capture.

What to watch next

Host 1What should listeners watch for?

Host 2Gaia's fourth data release, with five and a half years of data and individual epoch positions. That is when the authors expect the joint limit to break ten to the minus eleven, and when real periodic searches become possible.

Host 1And on the pulsar side?

Host 2The Square Kilometre Array radio telescope, which should find many more millisecond pulsars, especially towards the Galactic bulge. That would fill the sky gaps that currently make the joint sensitivity so uneven.

Host 1Anything else they plan?

Host 2Using the second time derivative of pulsar spin, called the jerk, to separate strain from frequency. And extending the method from a single black hole pair to a background hum, which could probe early-universe physics.

Host 1What would change your mind either way?

Host 2If the analysis on the fourth data release with richer systematics modelling still finds nothing, the limits tighten and this becomes a standard tool. If a signal appears only in the quasars and tracks a known Gaia systematic pattern, that would be a warning that the noise model is doing the work.

Sign-off

Host 1That is the deep dive: Combining astrometry with pulsar timing, by Filipello, Beordo, Akhmetov, Crosta and Lattanzi. The link is in the show notes.

Host 2Short version: a million and a half quasars plus eleven pulsars, searched together for the slowest gravitational waves, found nothing, and set limits twenty to thirty percent tighter than pulsars alone. A careful first step, with the real test coming in Gaia's next data release.

Host 1Every Friday this same feed carries the roundup episode: five new papers as trailers, and you pick which become deep dives. This has been the Hastrup Review of Science.