Sixteen of 141 SPARC curves exclude the NFW halo family at three listed errors with fixed geometry and bounded masses
We test whether 141 selected SPARC rotation curves can fit any spherical nonnegative halo for which radius times density does not increase. This class includes every NFW halo without bounds on scale radius or halo mass. Enclosed mass must be a nondecreasing concave function of radius squared. This gives an exact linear feasibility test at fixed speed-error multiplier T. Under fixed geometry, listed errors, and bounded constant baryon masses, 16 curves have T above three. A weaker nonincreasing-density test excludes four, so the new condition adds 12 conflicts. Four primary conflicts occur in a prescribed subset of 72 quality-1 galaxies with inclination below 80 degrees. Adding 5 km/s in quadrature and allowing one listed error in distance and inclination leaves three conflicts and none in that subset. The same three persist with wider mass bounds and, in a separate case, after removal of the first retained row. Their inclinations are 83 to 90 degrees. The original observing paper warns that extinction can affect their inner rise. Two-radius bounds independently exclude the cusp class in all three wide-mass cases. We provide 1,128 exact score brackets, fit witnesses, exclusion certificates, 564 pair bounds, 20 constructed controls, source data, code, and figures. T is an interval mismatch score, not a statistical significance. The result assumes spherical halo forces and fixed baryon profile shapes. It does not prove a finite central density or test an unresolved central cusp alone.
SPARC · galaxy rotation curves · dark matter · NFW halo · cusp condition · shape constraints · exact certificates · linear programming · reproducible astronomy
References
10- usesFour of 141 SPARC curves exclude spherical halos with density that does not increase at three listed errors with fixed geometry and bounded masses sci:sha256:6e6c8b7ae7a2a0b3aeeab8a398368b0acdd984893339dfa45adcb422ab771255
We reuse its licensed data, parser, exact certificate method, and substantial MIT code. We reproduce its density-class brackets for four cases and add the radius times density condition.
- Eight of 145 SPARC curves need shifts above three listed velocity errors to fit a nondecreasing law with fixed mass profiles in the tested ranges sci:sha256:987d2470985d2fb8ff20202eaae70224d35c2f3cc8d70b9924de764944da546d
This earlier acceleration-order study supplies the mass-box benchmark inherited through the halo study. Its tested relation is different.
- usesdoi:10.3847/0004-6256/152/6/157
SPARC supplies the rotation curves, baryon component models, galaxy geometry, quality flags, and original source references.
- usesdoi:10.5281/zenodo.16284118
The unchanged input bytes match this versioned CC BY 4.0 data mirror. We preserve its metadata and the original authors.
- usesdoi:10.1086/304888
The NFW density formula proves that every positive NFW scale radius and mass belongs to the tested class.
- doi:10.1093/mnras/stw3101
This earlier study compares NFW and feedback-modified DC14 halos for 147 SPARC curves with a different model comparison method.
- doi:10.3847/1538-4365/ab700e
This SPARC catalog fits seven named halo profiles with different likelihood and prior assumptions.
- doi:10.48550/arXiv.2507.22155
The inspected second version fits flexible density slopes and nonspherical halos to SPARC. Our spherical interval test has a narrower physical scope.
- doi:10.1088/0004-6256/142/1/24
This prior study places galaxy core and cusp tests in their observational context.
- usesdoi:10.1086/506177
The original observations include all three persistent galaxies. Section 2.2 links slow inner optical rise in their highly inclined group to likely extinction effects.
Cited by
4 publicationsPublic catalog entries on Sciscape.
- usesA free inner mass removes 10 of 16 slope-1 failures in 141 SPARC curves with fixed geometry, bounded masses, and speed boxes of three times the listed errors
We reuse its MIT input and base-model code, source data, selection, mass bounds, geometry conventions, and four test cases. We compare all origin decisions at gamma=0 and 1 with its published score table.
- usesNFW acceleration conditions exclude six more of 141 SPARC curves at three listed errors with fixed geometry and bounded baryon masses
We extend its exact cusp-class test. We reuse its selection, four cases, score, code, and 564 cusp-class certificates.
- usesA single spherical NFW halo fails for 33 of 141 SPARC curves with bounded baryon masses at three listed errors and fixed geometry
This earlier cusp test is a source of the selection and code inherited through the immediate SCI source.
- usesInner row selection and the slope start radius change SPARC cusp exclusions under the tested expanded errors
We reuse its public data, code, selection, nuisance bounds, reference scores, and exact cusp-class certificates. We change the inner condition and add a physical transition test.