Reading feedback, halo and MOND comparisons

Record the version and the 147-galaxy selection

The source is Amy Smith and colleagues’ “Dark Matter and MOND successes and degeneracies in reproducing SPARC rotation curves and weak lensing data”, arXiv:2610.33157v1. Its watermark is dated 23 October 2026. The abstract page says MNRAS Accepted; this guide follows the actual 26-page preprint. The PDF’s 2025 typesetting year is not used as a publication year.

Section 2 selects $147$ late-type SPARC galaxies, explaining quality 3, low-inclination and small-sample exclusions, plus choices where total speed squared becomes invalid. Those conditions define which population enters the comparison. Read them before interpreting a distribution of fit scores.

Our fixed NGC 2403 branch retains its own 73 points and does not import the paper’s multi-galaxy cuts. One named object’s NFW/core analysis and a population-level model comparison ask different questions.

Reading: Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1 · Lelli, McGaugh & Schombert (2016), SPARC, AJ152,157

Figure 1 shows density; feedback enters through a simulation-based profile

Figure 1 plots radius in kiloparsecs against halo density on logarithmic axes. Identify curves by model name in the legend and note the illustrative halo mass/luminosity in the caption. A density core, cusp or transition is not already a speed-curve shape: enclosed mass must first be integrated.

Section 3.1 contrasts the NFW family fitted to collisionless simulations with DC14, calibrated on hydrodynamic simulations including baryonic feedback. Feedback involves star formation, explosions and gas flows changing the gravitational potential. Collisionless matter can change its orbit in that changing field; gas winds need not directly collide with it.

DC14 relates profile shape to stellar-to-halo mass ratio. The figure displays model predictions; the changing density profiles belong to the simulations used to calibrate that family.

Reading: Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1

Read Figure 5’s inner residuals alongside Tables 1 and 3

Figure 5 compares NFW above and DC14 below for UGC01281, with speed and residual panels for each. Locate the departures at the same radii, then examine how stars, gas and halo share the force. The example shows how the feedback-motivated family alleviates this object’s inner mismatch.

Table 3 extends the comparison to sample medians. At fixed distance/inclination the NFW and DC14 working reduced chi-square medians are $1.387$ and $0.934$. The varying-geometry columns give $1.485$ and $1.157$, with parameter counts changing from 3 to 5. These are not just improvements of one unchanged fitted curve: conditions and degrees of freedom also change.

Return to Table 1 for parameter ranges and priors. A prior assigns weight to parameter choices before applying the likelihood. A width in dex for a lognormal mass-to-light distribution differs from a linear standard deviation. Recomputing the comparison requires the complete distribution definitions, width conventions and parameter ranges in the fitting code.

Reading: Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1

Figure 6 uses different reference models in its panels

Section 4.1.6 uses $\mathrm{BIC}=-2\ln L+p\ln N$, where $p$ is parameter count and $N$ the measurements in one galaxy. BIC approximately balances likelihood improvement against complexity under its sample/model conditions. It is not a probability for a dark-matter particle.

The horizontal axis is $\Delta\mathrm{BIC}=\mathrm{BIC}_X-\mathrm{BIC}_{\rm ref}$; the vertical axis is the fraction of galaxies whose comparison lies at or below a given horizontal value. Positive values mean the reference has smaller BIC. The upper reference is DC14. The lower comparisons use the appropriate fixed-acceleration Standard/Simple MOND counterpart. Subtracting curve positions across rows would mix reference models. This reading follows the separate reference for each function stated in section 4.1.6. The lower-right caption of Figure 6 names only Simple MOND; these two descriptions are not identical. Without the implementation, we leave that wording discrepancy unresolved.

Modified Newtonian Dynamics, MOND, changes the low-acceleration relation between motion and baryonic gravity. Here it is the authors’ modified-inertia realization, with functions connecting the high/low-acceleration behaviour and a one-dimensional approximation for environmental fields acting on internal motion. It is not a solution of every modified-gravity field equation. Letting the acceleration scale vary per galaxy is also used as a degeneracy experiment; that freedom should not silently become part of a universal-constant theory.

A small example makes the complexity term tangible. With the same $73$ data points and error coordinate, one extra parameter that reduces $\chi^2$ by only $2$ changes BIC by $-2+\ln73\simeq2.29$. The older model has smaller BIC. A real cross-theory comparison additionally needs common data definitions, defensible priors and model checks. Different physical parameter names alone do not mathematically prohibit statistical comparison.

Reading: Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1 · Independent saved-observation rotation-curve calculation

Figure 10’s megaparsec curve comes from stacked lensing

The horizontal unit now becomes $\mathrm{Mpc}$. The inner blue curve averages HI rotation curves in baryonic-mass bins. Outer points come from stacked weak-lensing surface-density signals, deprojected to acceleration and expressed as equivalent circular speed. They are not gas tracers directly followed at those outer radii.

Section 4.3 and the caption describe mass bins, at least three contributors to each HI radial mean, exclusion of the inner two lensing points and the isolation limit beyond one megaparsec. The halo curves also use different mass–concentration prescriptions. Each choice belongs to this particular comparison.

Separate the full-range and outer-only scores. In Table 6 a small full reduced score can accompany a large outer score; numerous inner points can conceal an outskirts mismatch. Figure 14 then checks the fitted halo parameters against the selected scaling relations.

The authors find that their MOND cases sustain the extended flat curves more naturally, and discuss further effects such as material outside bound haloes. We read this fixed version in full, but did not acquire its privately supplied full lensing covariance or rerun its 147-galaxy MCMC/deprojection. Read the reported comparison together with those conditions.

Reading: Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1

Worked example: changing baryonic gravity changes a collisionless orbit

A small model explains why feedback can influence dark matter. Start a test particle on a circular orbit about a central mass, then remove one tenth of that mass instantaneously. Its velocity and angular momentum are unchanged at that instant. Its potential becomes shallower, and the orbit becomes more elongated.

For initial central mass $M$ and circular radius $r_0$, $v_0^2=GM/r_0$. Removing fraction $f$ changes specific energy to $E'=(f-\tfrac12)GM/r_0$. The specific angular momentum is $h=r_0v_0$. At an apocentre, radial speed is zero, so $E'=h^2/(2r_a^2)-G(1-f)M/r_a$. Substitution gives the original turning point $r_0$ and, for $0<f<1/2$, the outer one $r_a=r_0/(1-2f)$. Thus $f=0.1$ gives $r_a=1.25r_0$.

The independent material checks three removed fractions by solving the turning-point energy equation numerically. This illustrates an orbit responding to a time-dependent potential. Real feedback also requires the gas-loss/return history, repeated cycles and self-gravity. This point-mass example does not produce a DC14 halo.

Reading: Independent saved-observation rotation-curve calculation · Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1

Keep the conditions beside the conclusion

After reading, state whether the evidence concerns individual rotation or stacked lensing; how cusp/core structure enters; whether geometry is fixed; which reference defines each score; and how outer material and covariance are handled. Those details preserve the question the study actually answers.

They also identify useful next measurements. Better spatial resolution probes the inner curve, independent geometry and stellar-mass information narrows compensating choices, and lensing extends the radial scale. Combined evidence can help separate physical explanations that give similar local curves.

Reading: Smith et al., Dark Matter and MOND successes and degeneracies, arXiv:2610.33157v1 · Independent saved-observation rotation-curve calculation