Research spotlight: Quentin Parker

Sulfur should be one of the easier elements to count. It is forged in massive stars alongside oxygen, neon and argon, and it holds the same proportional ratios everywhere astronomers point their spectrographs: in star-forming regions, in blue compact galaxies, in the diffuse gas between stars. Then dying Sun-like stars entered the picture, and for twenty years sulfur refused to behave.

New observations from the European Southern Observatory's 8-metre Very Large Telescope cut that problem down to size. Shuyu Tan and Quentin Parker, both at the Laboratory for Space Research at the University of Hong Kong, measured roughly 130 planetary nebulae in a 10-degree by 10-degree window at the centre of the Milky Way and found sulfur tracking argon almost exactly, with a best-fit slope of 0.98 against the one-to-one relationship theory predicts. The paper, "Whither or Wither the Sulfur Anomaly in Planetary Nebulae?", appeared in The Astrophysical Journal Letters in February 2024.

Planetary nebulae are the glowing shells of gas shed by stars of roughly one to eight times the Sun's mass as they collapse toward white dwarfs. They live for tens of thousands of years, a blink against the billions their progenitors took to get there. That brevity is what makes them useful. Each nebula is an almost instantaneous photograph of a dying star, and its emission lines record which elements were present in the cloud the star was born from.

Which is why the sulfur deficit mattered. If planetary nebulae systematically under-report sulfur, then a standard tool for reading the chemical history of the Galaxy has a calibration error baked into it, and every model built on those abundances inherits the error. Tan and Parker's finding is that most of the shortfall was produced by the measuring apparatus rather than by the nebulae. A smaller, genuine deficit survives, and it appears to track something interesting: the mass and age of the stars that made the nebulae.

Counting ions you cannot see

An optical spectrum does not hand you an element. It hands you emission lines from particular ions, atoms that have lost one, two or three electrons, and each ion glows at its own wavelengths under its own conditions.

For sulfur, the optical window catches the S+ ion and, when the nebula is hot enough, S2+. Higher stages such as S3+ radiate mostly in the infrared, out of reach of the optical spectrographs that produced most of the historical data. So astronomers estimate the total sulfur by measuring what they can see and multiplying by an "ionization correction factor," or ICF: a calculated number meant to account for the sulfur locked in stages the telescope missed.

The ICF is a bit like estimating an iceberg's mass from the tip you can see, using a formula that assumes a typical shape. Get the shape wrong and the estimate drifts. Two competing schemes dominate the literature. One, dating to the 1990s and used in the largest prior sulfur survey, was the version applied by Richard Henry and collaborators in their 2012 analysis. The other, published by Gloria Delgado-Inglada and colleagues in 2014, is the one Tan and Parker adopted. Which scheme you pick had never been tested against a decisive dataset.

Argon as the yardstick

The comparison element in most prior work was oxygen, and that turns out to be part of the problem. Oxygen can be altered inside a planetary nebula's progenitor star during its final stages of nuclear burning, so a nebula's oxygen abundance may not faithfully record the birth cloud. Delgado-Inglada's group had already suggested argon and chlorine as cleaner metallicity indicators for exactly this reason. Chlorine lines are faint and awkward to measure, so argon wins by default.

Against argon, the picture changed. In the older 162-nebula disk sample, plotting sulfur against oxygen produced two families: a sparse upper track, about 13 percent of objects, that sat where theory wanted it, and a heavily populated lower locus, 87 percent, that carried the anomaly. The slope of that fit was 0.66 instead of 1, a clear failure of lockstep. Swapping oxygen for argon collapsed the two families into one broad band sitting close to the expected line.

Tan and Parker's own VLT sample, drawn from the Galactic bulge and reduced to 124 objects with abundance uncertainties below 0.2 dex, did better again. Sulfur against oxygen gave a slope of 1.05 with a correlation coefficient of 0.84. Sulfur against argon gave 0.98 with a correlation coefficient of 0.83. Both are lockstep within the errors, and both are a first for planetary nebulae. The analysis is described in full in the published letter.

One number puts the size of the old problem in perspective. In the cleaned-up 2012 disk sample, the median sulfur deficit was about 0.4 dex against the expected trend, meaning nebulae appeared to hold roughly two and a half times less sulfur than they should. In the new bulge sample the deficit distribution is narrower and peaks near 0.3 dex, with a tail of young objects reaching zero.

Photo by NASA on Unsplash

A random forest audits the arithmetic

To test whether the correction factors themselves were to blame, the pair trained a machine-learning model to predict the sulfur ICF directly from other observed ion ratios, including helium, oxygen, argon and chlorine ratios, without assuming any analytic formula. The training set came from a grid of more than 700,000 photoionization models computed with the CLOUDY code, of which about 120,000 met realistic criteria for planetary nebulae.

The result split cleanly. For the new VLT sample, the 2014 correction scheme and the machine-learning predictions agreed almost exactly. For the older 2012 sample, the differences were skewed, indicating that the older scheme had been systematically underestimating sulfur by around 0.07 dex on average.

That is real, and it is not the whole story. The authors are explicit that a bias of that size cannot account for an anomaly that routinely exceeds 0.1 dex. Bad correction factors were a contributor, not the culprit.

Infrared check: the sulfur isn't hiding in higher ions

The other leading explanation was that the missing sulfur was sitting in high ionization stages that optical spectra miss, so the correction factors were simply too small. Infrared spectra can settle that, because the S3+ stage radiates at mid-infrared wavelengths that the Spitzer Space Telescope could observe.

Eight bulge nebulae overlap between the new sample and Spitzer measurements published by Pottasch and Bernard-Salas in 2015. For six of the eight, the infrared-derived sulfur abundances fall on the expected trend. Where the two datasets disagree, the infrared sulfur abundances run higher than the optical ones by a median of 0.17 dex, and their S2+ values from infrared lines exceed the optical equivalent by 0.16 dex.

The authors read this as a partial win for the older suspicion and a loss for the specific mechanism proposed to explain it. Higher ionization stages are being underestimated somewhat, but correcting for that does not close the gap. Two of the eight objects are also known oddballs. An eight-nebula sample is small, the paper concedes, and that particular test should be treated as suggestive rather than final.

Age, dust, and the deficit that remains

What is left after the measurement artefacts are stripped away is not noise. It correlates with the kind of star that made the nebula.

Using age classifications from earlier papers in their VLT bulge series, Tan and Parker divided nebulae into young and old progenitor groups. A two-sample Kolmogorov-Smirnov test, which asks whether two distributions could plausibly come from the same population, returned p-values of 8×10⁻⁴ for the disk sample and 1×10⁻⁵ for the bulge sample. At their stated threshold of 0.001, the young and old sulfur deficits are drawn from different populations.

Young, massive progenitors show little or no deficit. Older, lower-mass progenitors show more. There is a spatial echo of this: among young disk nebulae with reliable Gaia parallax distances, 62 percent sit within 0.25 kiloparsec of the Galactic mid-plane, which is where the thin disk's younger stars concentrate.

Dust chemistry sharpens the pattern. Grouping nebulae by the infrared dust features seen by Spitzer, those with carbon-rich dust carry a median deficit of 0.51 dex, those with oxygen-rich dust 0.34 dex, and those with mixed chemistry just 0.07 dex. Sulfur-bearing solids such as magnesium sulfide and iron sulfide are expected to form in carbon-rich environments, and sulfur also locks into molecules including hydrogen sulfide, carbon monosulfide and sulfur monoxide. Chemistry that traps sulfur in grains or molecules removes it from the gas phase, where the emission lines are made.

"The sulfur deficit is almost absent for PNs from higher mass, younger progenitors, and those with oxygen or dual dust chemistry related to progenitor mass," the authors write in their summary of findings. Carbon-rich nebulae of intermediate progenitor mass remain the hard case.

Photo by Marek Pavlík on Unsplash

What the result does not settle

The caveats are the authors' own, and they are worth taking seriously.

• Age classifications for individual nebulae are coarse. The paper describes the age-based results as "indicative" rather than definitive, because the bins are broad and the boundary cases uncertain.
• The mid-infrared cross-check rests on eight objects, however well measured.
• Central star identifications from Gaia data carry an error rate the team puts at up to 12 percent, which propagates into the distance and Galactic height calculations.
• Choices of extinction law, by contrast, turn out not to matter: swapping between prescriptions left the anomaly essentially unchanged.

There is also history to weigh. Henry and colleagues tested the deficit against 19 nebular properties in 2012 and found no strong correlations with any of them, concluding that an unrecognised feature of the nebular gas was probably distorting the correction factor. The new work partly vindicates that instinct about correction factors while rejecting the higher-ionization mechanism they favoured.

A skeptic could reasonably note that a result built on a single instrument, a single telescope and one patch of sky needs replication elsewhere, particularly in nebulae of known, independently determined progenitor mass. The University of Hong Kong's own announcement of the work is available here.

Reading a galaxy's age from its nebulae

The most speculative part of the paper is also the most interesting. If the residual sulfur deficit tracks progenitor mass, and progenitor mass tracks age across a stellar population, then the deficit becomes a clock of sorts. Measure sulfur and argon across a galaxy's planetary nebulae, and you get a rough read on how weighted that population is toward young or old stars, without resolving individual stars at all.

That is a proposal, not a demonstrated technique, and the authors present it as such. But it points somewhere useful. Distance is the perennial bottleneck in astronomy, and any abundance ratio that encodes stellar age implicitly encodes something about the population being observed. The same VLT bulge programme has already turned up related oddities, including a population of bipolar nebulae in a region long assumed to be dominated by ancient stars.

The immediate takeaway is narrower and more practical. Anyone deriving sulfur abundances from optical spectra should be using argon rather than oxygen as the metallicity reference, and should be using a modern ionization correction scheme. A preprint of the paper is freely readable on arXiv, which matters for groups working without journal subscriptions. The larger lesson is about data quality: two decades of theoretical contortions were needed to explain a discrepancy that a sharper spectrum and a better-chosen comparison element largely dissolved. Sometimes the anomaly is in the instrument, and the way to find out is to build a better one and look again.