Why missing radio signals do not rule out black holes in dwarf galaxies

A relationship that needs the right signals

Dwarf galaxies offer a way to investigate the population of relatively low-mass black holes, which could help constrain ideas about how the first black holes formed and grew. But identifying an accreting black hole—one drawing in surrounding material—is difficult. Star formation, stellar systems emitting X-rays and unrelated background galaxies can confuse the picture.

The study examines the radio/X-ray Fundamental Plane, an empirical relationship connecting compact radio luminosity, hard-X-ray luminosity and black-hole mass. Luminosity describes how much energy a source emits; hard X-rays are the higher-energy X-rays used here in the 2–10 kiloelectronvolt band.

The relationship is most directly motivated for black holes in a low-rate accretion state with a compact jet. It is not a precise weighing scale. Its substantial intrinsic scatter means that sources with the same assumed mass and X-ray luminosity can have very different radio luminosities.

The radio and X-ray measurements must also describe the same accreting object. Mixing extended radio emission with unrelated X-rays, or assigning a background source to a foreground dwarf galaxy, would undermine the test.

What the existing observations show

The authors used published measurements and classifications from the Very Large Array, or VLA; the Very Long Baseline Array, or VLBA; the Chandra X-ray Observatory; and the Hubble Space Telescope. They did not newly reduce or reanalyse the original telescope observations.

The starting sample contained 13 compact radio sources whose radio luminosities exceeded expectations from star formation. VLBA follow-up detected four. All four were also the sources with the largest separations between their radio positions and the optical positions of the target galaxies.

Their high radio brightness temperatures support compact, nonthermal emission rather than ordinary star formation. But compactness does not establish that a source belongs to the intended dwarf galaxy. Some could be unrelated background objects.

Under a specific comparison in which four detections are randomly assigned among the 13 sources ranked by offset, the probability that they occupy exactly the four largest offsets is about 0.14%. The paper explicitly treats this as a sample-level result, not a background-source probability for any individual object.

Published optical and X-ray follow-up leaves three objects—IDs 26, 82 and 83—as the strongest nuclear accreting massive-black-hole candidates. Their black-hole masses remain unestablished. None was detected by the VLBA.

Forecasting detection instead of inferring a mass

Rather than turning a radio upper limit into a mass estimate, the authors ask a forward question: if a candidate contained a black hole of a specified mass, how likely would the observation be to detect its compact radio emission?

Their calculation includes scatter in the Fundamental Plane, X-ray measurement uncertainties, uncertainty in how radio brightness changes with frequency, image noise and the source’s size relative to the telescope’s resolution.

For the paper’s adopted intermediate-mass interval of 100,000 to one million solar masses, existing observations generally have low detection probabilities. At one million solar masses, assuming an unresolved radio source and a detection threshold five times the image noise, the reported probabilities are:

• ID 26: approximately 0.005%–2.9%.
• ID 82: approximately 3%–6%.
• ID 83: approximately 8%–17%.

These ranges reflect alternative model choices, including a check using another Fundamental Plane regression and, for ID 26, two estimates of the hard-X-ray component. They are not statistical confidence intervals.

With detection probabilities this low, a missing radio signal is unsurprising even under the assumed black-hole scenario. The authors therefore conclude that the existing limits do not provide useful mass upper bounds within the adopted interval.

Sharper images are not always more informative

The observations leave an important gap in spatial coverage. The VLA beams sample roughly 116–221 parsecs, while the VLBA beams probe about 0.6–1.8 parsecs. A parsec is approximately 3.26 light-years.

Very high resolution can spread an extended source’s emission across multiple image elements, reducing its peak brightness. An interferometer can also fail to recover structures larger than the angular scales sampled by its antenna separations.

For an illustrative five-parsec-wide source with a smooth Gaussian brightness profile, the model predicts peak-brightness reductions of approximately 13, 33 and 29 in the existing VLBA beams for IDs 26, 82 and 83. These are assumed source-size scenarios, not measured sizes.

Longer observing time cannot recover structure that the array configuration filters out. The authors recommend combining compact-core imaging with observations sensitive to intermediate structures on roughly 10–100 parsec scales.

What a stronger test would require

For a 50% probability of detecting an unresolved, one-million-solar-mass source at a five-times-noise threshold, the forecast requires 9-gigahertz image noise of 0.10–0.76 microjanskys per beam for ID 26, 0.77–1.67 for ID 82 and 3.37–8.31 for ID 83. These units describe radio-image sensitivity; lower noise means a deeper observation.

ID 83 has the most favourable forecast. Under the point-source assumption, the paper estimates that sufficiently deep present-generation very-long-baseline observations could reach about 50% completeness—the probability of detecting a source under the model. Its approximate VLBA-equivalent observing time is 7–50 hours, not a guaranteed detection.

ID 26 first needs a more secure separation of its hard-X-ray emission from thermal emission. For ID 82, the paper identifies future long-baseline observations with the proposed next-generation VLA as a plausible option. Facility times are thermal-noise estimates, not complete observing plans; calibration, source structure and other practical requirements can increase them.

Conditional forecasts, not confirmed masses

The forecasts assume that the Fundamental Plane applies and that the compact radio and hard-X-ray components arise from the same accretor. The authors adopt emission below 3% of the Eddington luminosity—a mass-dependent reference luminosity—as an operational accretion-state criterion, not a universal boundary or sufficient proof that the relationship applies.

The radio and X-ray observations also need coordination because source brightness can change. The existing VLA and VLBA measurements were taken about six years apart, so their differences cannot be attributed solely to spatial structure.

Reaching 90% detection completeness would demand much deeper observations because the model allows a substantial population of radio-faint sources. The authors present the most extreme depths as a limitation of individual-object tests, not routine observing recommendations.

The preprint’s main contribution is therefore an observing framework. Applied to larger samples, it could quantify which black holes a survey was capable of detecting. Inferring how many dwarf galaxies contain black holes would still require additional assumptions about activity, contamination and source association.