Galaxy Rotation Curves Collapse onto One Curve Twice as Far Out as Before

Astronomers have long known that the rotation speeds of spiral galaxies, when properly rescaled, trace out a single universal curve. A new analysis of the SPARC catalog now pushes that result twice as far from the galactic centers as before, into territory where dark matter overwhelmingly dominates. The study, published in the journal Discover Space, builds the Universal Rotation Curve out to twice the optical radius of the stellar disk, doubling the radial range over which this curve has been established directly from observations rather than extrapolated from models.

The team, led by Esha Bhatia and including Paolo Salucci, Tiziano Schiavone and Sandeep Haridasu, exploited the extended neutral hydrogen, or HI, rotation curves available in the SPARC catalog. Previous constructions of the Universal Rotation Curve relied on optical rotation curves that reached only the optical radius, defined as the radius enclosing 83 percent of a galaxy’s total luminosity and equal to 3.2 times the disk scale length. Beyond that boundary, the curve had to be extrapolated using galaxy mass models. The new work instead measures what happens in the region between one and two optical radii, a zone where the declining contribution of the stellar disk makes it significantly easier to disentangle dark and luminous matter.

The SPARC catalog comprises 175 rotationally supported galaxies spanning spirals and irregulars, most located within about 10 megaparsecs of the Milky Way. Its HI rotation curves come from multiple radio interferometers, including the Very Large Array, the Westerbork Synthesis Radio Telescope, the Australian Telescope Compact Array and the Giant Metrewave Radio Telescope, with beam sizes ranging from 13 to 45 arcseconds. For the stellar component, the catalog provides fluxes and magnitudes in the Spitzer 3.6-micrometer band, an excellent estimator of stellar disk masses, spanning from 10^7 to 10^12 solar luminosities.

Not every galaxy made the cut. Of the 175 SPARC galaxies, 22 were rejected because they are face-on systems or have very low-quality rotation curves, following the original catalog analysis. The researchers then applied two further criteria: a rotation curve was included only if it contributed data points to at least three of the six radial bins used in the analysis, or to two bins provided the outermost measurement fell within the fourth or fifth bin. These requirements excluded 48 curves that, despite good quality inside the optical radius, lacked the necessary measurements in the outer region or showed pronounced non-axisymmetric motions there. The final sample comprised 105 rotation curves.

The key step is double normalization. Each rotation curve’s radius is divided by the galaxy’s optical radius, and its velocity is divided by the velocity at that optical radius. In physical units of kilometers per second and kiloparsecs, the 105 curves look like a chaotic ensemble with a low statistical correlation with the optical velocity. After double normalization, all of them collapse into a single family, with the optical velocity acting merely as a label identifying each curve. The researchers grouped the normalized curves into eight velocity bins, with mean optical velocities ranging from about 43 kilometers per second to 295 kilometers per second, covering both spirals and dwarf irregulars, and then averaged the data within six radial bins in each velocity bin, producing 48 coadded measurements.

From those 48 coadded points, the team fitted an empirical analytical expression valid between one and two optical radii, in which the slope of the curve depends on the logarithm of the optical velocity through a low-order polynomial. They deliberately avoided adding a cubic term to prevent overfitting and non-monotonic behavior in the velocity profiles. The fit reproduces the coadded measurements with a reduced chi-squared of 2.64 and a root-mean-square scatter of 0.0229 dex, which the authors describe as an excellent fit. The small uncertainties on the coefficients and the very low scatter indicate that the mass distribution information of these galaxies is efficiently captured by a universal function, with the optical velocity and optical radius serving as the free observational parameters tagging each system.

A crucial test came from comparison with an entirely independent route to the same region. Earlier work had constructed the Universal Rotation Curve out to the virial radius, the size of the dark halo, but only by extrapolating from data inside the optical radius using halo-disk mass decomposition and the abundance-matching relationship between virial and disk mass. The new, directly measured curve agrees very well with that extrapolated prediction, even though the data, their location in the galaxies and the analysis methods are completely independent. The team also built a zoomed curve around the optical radius itself using the PROBES catalog, the largest available collection of disk galaxy rotation curves with surface brightness measurements, drawing on 3677 independent measurements from 1118 galaxies. This buffer region, spanning 0.95 to 1.2 optical radii, marks the edge of the stellar disk and the rise of the HI disk as the main baryonic component. All three curves agree, providing a strong consistency check that rules out the possibility that the universal curve arises from survey-specific biases.

The result carries weight for dark matter research because the outer region probed here is dominated by the dark halo in all objects, and the shape of the curve there constrains the halo’s density profile. Notably, the researchers report that the range between one and two optical radii contains several cases of distinctly rising or declining profiles, which they state is inconsistent with the predictions of both MOND, a modified-gravity alternative to dark matter, and the scenario of an NFW dark matter halo combined with a Freeman stellar disk, both of which envisage rather flat rotation curves in this radial range. They caution that blindly adopting a density profile without direct reference to observational data is likely to be unsuccessful, since dark matter halos have a complicated general profile that can probably be determined only by reverse engineering the available observations. They also note that roughly one third of the sample’s rotation curves should be excluded when rigorously testing specific halo profiles or gravity modifications, as they are not usable or do not yield reliable mass modeling results.

As a second strand, the team investigated the Radial Tully-Fisher relation, a family of relationships between galaxy luminosity and circular velocity measured at fixed normalized radii, rather than at a single reference velocity as in the classical Tully-Fisher relation. Using 129 SPARC rotation curves and about 600 velocity measurements, they fitted six independent linear relations between infrared luminosity at 3.6 micrometers and velocity at radii from 1.05 to 1.9 optical radii. The relations emerge clearly, and their slopes increase with radius, continuing the trend established inside the optical disk by earlier work. The SPARC slope values connect smoothly at the optical radius to those of the inner-region relations, which the authors say confirms that the Radial Tully-Fisher relationship extends beyond the luminous-mass-dominated optical region into the dark-matter-dominated outskirts, reflecting the intertwined distribution of dark and luminous matter.

The broader significance is methodological as much as physical. Co-adding many individual rotation curves averages out observational errors and kinematical disturbances unrelated to the galaxy mass distribution, allowing the intrinsic systematics to emerge, while a sample of about 100 objects with very extended, high-resolution curves allows every galaxy to be probed separately. The authors argue the two approaches are complementary and converge on a single scenario: the slopes and amplitudes of rotation curves in the inner regions can reliably predict those in the outer regions. Because the Universal Rotation Curve is not constrained by any specific theoretical model, the team views it as a portal toward the new physics that the dark matter phenomenon entails, now with direct observational support twice as far out as ever before.

Subject of Research: Construction of an extended universal rotation curve for spiral galaxies out to twice the optical radius using SPARC HI rotation curves

Article Title: Extended universal rotational curve of spiral galaxies

Article References: Bhatia, E., Salucci, P., Schiavone, T., & Haridasu, S. (2026). Extended universal rotational curve of spiral galaxies. Discover Space, 130(1), Article 14. https://doi.org/10.1007/s11038-026-09594-2

Image Credits: AI Generated

DOI: 10.1007/s11038-026-09594-2

Keywords: universal rotation curve, spiral galaxies, dark matter, SPARC catalog, HI rotation curves, galaxy mass models, radial Tully-Fisher relation, PROBES catalog, double normalization, dark matter halos, MOND, NFW profile