Dark Matter halo fits – today’s cut

I said I would occasionally talk about scientific papers. Today’s post is about the new paper Testing Feedback-Modified Dark Matter Haloes with Galaxy Rotation Curves: Estimation of Halo Parameters and Consistency with ΛCDM by Harley Katz et al.

I’ve spent a fair portion of my career fitting dark matter halos to rotation curves, and trying to make sense of the results.  It is a tricky business plagued on the one hand by degeneracies in the fitting (there is often room to trade off between stellar and dark mass) and on the other by a world of confirmation bias (many of us would really like to get the “right” answer – the NFW halo that emerges from numerical structure formation simulations).

No doubt these issues will come up again. For now, I’d just like to say what a great job Harley did. The MCMC has become the gold standard for parameter estimation, but it is no silver bullet to be applied naively. Harley avoided this trap and did a masterful job with the statistics.

The basic result is that primordial (NFW) halos do not fit the data as well as those modified by baryonic processes (we specifically fit the DC14 halo model). On the one hand, this is not surprising – it has been clear for many years that NFW doesn’t provide a satisfactory description of the data. On the other hand, it was not clear that feedback models would provide something better.

What is new is that fits of the DC14 halo profile to rotation curve data not only fit better than NFW (in terms of χ2), they also return the stellar mass-halo mass relation expected from abundance matching and are also consistent with the predicted concentration-halo mass relation.


The stellar mass-halo mass relation (top) and concentration-halo mass relation (bottom) for NFW (left) and DC14 (right) halos. The data are from fits to rotation curves in the SPARC database, which provides homogeneous near-IR mass models for ~150 galaxies. The grey bands are the expectation from abundance matching (top) and simulations (bottom).

The relations shown in grey in  the figure have to be true in ΛCDM. Indeed, SCDM had predicted much higher concentrations – this was one of the many reasons for finally rejecting it. The non-linear relation between stellar mass and halo mass was not expected, but is imposed on us by the mismatch between the steep predicted halo mass function and the flat observed luminosity function. (This is related to the missing satellite problem – a misnomer, since it is true everywhere in the field.)

It is not at all obvious that fitting rotation curves would return the same relation found in abundance matching. With NFW halos, it does not. Many galaxies fall off the relation if we force fits with this profile. (Note also the many galaxies pegged to the lower right edge of the concentration-mass panel at lower left. This is the usual cusp-core problem.)

In contrast, the vast majority of galaxies are in agreement with the stellar mass-halo mass relation when we fit the DC14 halo. The data are also broadly consistent with the concentration-halo mass relation. This happens without imposing strong priors: it just falls out. Dark matter halos with cores have long been considered anathema to ΛCDM, but now they appear essential to it.

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