More Trouble For Dark Matter

An analysis of ambient radio wave activity at particular frequencies provides a window into the nature and temperature of the universe very early in its existence. What does it show?

The profile is largely consistent with expectations for the 21-centimetre signal induced by early stars; however, the best-fitting amplitude of the profile is more than a factor of two greater than the largest predictions. 

This discrepancy suggests that either the primordial gas was much colder than expected or the background radiation temperature was hotter than expected. Astrophysical phenomena (such as radiation from stars and stellar remnants) are unlikely to account for this discrepancy; of the proposed extensions to the standard model of cosmology and particle physics, only cooling of the gas as a result of interactions between dark matter and baryons seems to explain the observed amplitude. The low-frequency edge of the observed profile indicates that stars existed and had produced a background of Lyman-α photons by 180 million years after the Big Bang. The high-frequency edge indicates that the gas was heated to above the radiation temperature less than 100 million years later.

Of course, the (literally) defining property of dark matter in the standard model of cosmology (called ΛCDM for a cosmological constant with "cold dark matter") is that dark matter is completely or almost collisionless with respect to ordinary baryonic matter . . . . dots that this abstract refrains from connecting.

What correctly predicts what is observed?

A universe with no dark matter where the matter in the universe is entirely made up of baryonic matter (i.e. a modified gravity hypothesis), as explained in a readable two page (exclusive of references) paper supplementing the paper in the journal Nature linked above, that accepts virtually all of its data, theoretical framework and equations. It merely connects the dots that the paper in Nature didn't. They money language:

Equation 1 then predicts a maximum absorption of  

T21, max = −0.24 K for fb = 0.16; (2)  

T21, max = −0.60 K for fb = 1. (3)  

The observed value is T21 ≈ −0.5 K (Bowman et al. 2018), and appears from their Fig. 2 to be closer to −0.55 K. Such a strong signal is expected in a baryonic universe, but is unobtainable in ΛCDM. 

Figure 1 of the supplemental paper shows that a naive, unmodified ΛCDM prediction (as opposed to the maximal possible variation of it) is T21 ≈ −0.05 K, about 9% of the observed value, as opposed to 92% of the value predicted in a purely baryonic scenario (the exact margin of error isn't stated).

Once again, modified gravity theorists have correctly predicted the results of future experimental observations and dark matter theories made the wrong prediction, on a matter independent of previous predictions that have been confirmed.

McGaugh's linked supplement paper also makes some further predictions that new data can test:

1. Strong 21cm absorption will also be observed during the dark ages (z > 30).  

2. The 21cm power spectrum will show pronounced baryonic features.  

3. Large galaxies and the cosmic web emerge earlier than anticipated in ΛCDM (Sanders 1998; McGaugh 2015).  

The first two predictions stem simply from a universe made of baryons. Only the third prediction is model-specific; some hints of large early structures already exist (e.g., Steinhardt et al. 2016; Franck & McGaugh 2016). This implies that structure grows nonlinearly, erasing baryonic features at late times through mode mixing (McGaugh 1999).

UPDATE March 16, 2018: A completely separate paper constrains dark matter models via metal enrichment in very old galaxies.

UPDATE: March 20, 2018: Virtually all of the scatter in the radial acceleration relation observed in galaxies can be explained by measurement error - the residual scatter after estimating the effects of various forms of measurement error is about 3%.

These tweets from Federico Lelli explain the paper's significance:

In https://arxiv.org/abs/1609.05917 and https://arxiv.org/abs/1610.08981 we show that baryons and dynamics are tightly linked in galaxies at a *local* level: the observed acceleration (from the gas rotation curve) correlates with that expected from the distribution of baryons (using Newton's law).

At high accelerations gobs=gbar because baryons fully dominate the dynamics. These data come from the central parts of massive galaxies where there is no need for dark matter. At low accelerations, the data deviates from the 1:1 line. That's the classic indication of dark matter! 

We were expecting something like this! @DudeDarkmatter did a similar work back in 2004: https://arxiv.org/abs/astro-ph/0403610 … What really shocked us was the tightness of the relation! The deviations from the mean relation (aka "scatter") are of the order of 30%! 

This scatter is absurdly small for the (poor) standards of galactic astronomy. So we did a simple math exercise: let's propagate the errors on the measurements and compare the resulting expected scatter from errors (black) with the observed scatter (red). The two are consistent!

This means that the relation is consistent with NO intrinsic scatter. The width of the relation can be fully explained by observational errors. In general this happens only when you deal with Laws of Nature, like Kepler's laws. This is a big deal, so we further looked into it. 

The problem is that errors in Astronomy are a mess. We don't have complete control on them as Physicists can have with their experiments in their labs. Our lab is the Universe and the Universe doesn't care about what we wanna do. And here comes Pengfei's paper. 

There are three main sources of error on gobs and gbar: the galaxy distance, the galaxy inclination, and the conversion from stellar light to stellar mass. If you got them a bit wrong, the galaxy will shift perpendicularly or horizontally from the mean relation, adding scatter. 

The fact that the observed scatter is only 30% means that we did a pretty good job in estimating these quantities. But now we want to know whether this 30% can completely disappear when the errors are taken into account. 

To do this, Pengfei used Bayesian statistics and a technique called Markov Chain Monte Carlo (MCMC). Essentially you can fit the mean relation to individual galaxies, allowing the light-to-mass conversion, distance, and inclination to vary a little, within the observed errors. 

This is an example of how good the fits can be. They are not all this good. But if we measure the mean deviation from the fits for all galaxies, the resulting number is ridiculously small: 13%. We have a recipe that explains rotation curves better than 13% using only baryons!

When we optimize distance, inclination, and mass-to-light conversion, the radial acceleration relation becomes extremely tight. This didn't necessarily have to happen because we are varying *global* quantities while looking at a *local* relation, connecting different galaxy radii. 

If you are still following me, you may wonder what drives the remaining 13% scatter. Well, part of it could be intrinsic, but most of it must surely come from errors on the rotation velocities (due to non-circular motions and other nuisances) which are indeed of the order of 10%. 

To summarize: we have a relation which is very tight for astronomical standards. The deviations from the mean can all be explained by measurement errors. The relation is consistent with no intrinsic scatter. So is this a Law of Nature? Or just another galaxy scaling relation? 

Ops! I forgot to add the key plot. Here you see the radial acceleration relation using best-fit distance, inclination, and mass-to-light ratio. The tiny residuals need two tiny Gaussians, but we think we understand why this happens. It's likely how velocity errors are estimated.

The paper's abstract and citation are as follows:

Galaxies follow a tight radial acceleration relation (RAR): the acceleration observed at every radius correlates with that expected from the distribution of baryons. We use the Markov Chain Monte Carlo method to fit the mean RAR to 175 individual galaxies in the SPARC database, marginalizing over stellar mass-to-light ratio (Υ⋆), galaxy distance, and disk inclination. Acceptable fits with astrophysically reasonable parameters are found for the vast majority of galaxies. 

The residuals around these fits have an rms scatter of only 0.057 dex (∼13%). This is in agreement with the predictions of modified Newtonian dynamics (MOND). 

We further consider a generalized version of the RAR that, unlike MOND, permits galaxy-to-galaxy variation in the critical acceleration scale. The fits are not improved with this additional freedom: there is no credible indication of variation in the critical acceleration scale. The data are consistent with the action of a single effective force law. The apparent universality of the acceleration scale and the small residual scatter are key to understanding galaxies.

Pengfei Li, Federico Lelli, Stacy McGaugh, James Schormbert, "Fitting the Radial Acceleration Relation to Individual SPARC Galaxies" arXiv (February 28, 2018).

This successfully replicates and improves upon a finding from a December 14, 2015 paper.

And, don't forget the stunning case of the Crater II galaxy where MOND accurately predicted an outlier result that could not be obtained with a dark matter model.

Crater II isn't completely independent of the low scatter result but tests the same thing in very different domains of applicability in different ways. And the other empirical datasets discussed above are completely independent of these results.

A 2016 paper with overlapping authorship with this one shows that observation is not consistent with dark matter that does not interact with baryonic matter is not consistent with observation, a finding that another independent study has replicated.

Cosmological N-body simulations predict dark matter (DM) haloes with steep central cusps (e.g. NFW, Navarro et al. 1996). This contradicts observations of gas kinematics in low-mass galaxies that imply the existence of shallow DM cores. 

Baryonic processes such as adiabatic contraction and gas outflows can, in principle, alter the initial DM density profile, yet their relative contributions to the halo transformation remain uncertain. 

Recent high resolution, cosmological hydrodynamic simulations (Di Cintio et al. 2014, DC14) predict that inner density profiles depend systematically on the ratio of stellar to DM mass (M∗/Mhalo). Using a Markov Chain Monte Carlo approach, we test the NFW and the M∗/Mhalo-dependent DC14 halo models against a sample of 147 galaxy rotation curves from the new Spitzer Photometry and Accurate Rotation Curves (SPARC) data set. These galaxies all have extended H{\small I} rotation curves from radio interferometry as well as accurate stellar mass density profiles from near-infrared photometry. 

The DC14 halo profile provides markedly better fits to the data compared to the NFW profile. Unlike NFW, the DC14 halo parameters found in our rotation curve fits naturally fall within two standard deviations of the mass-concentration relation predicted by ΛCDM and the stellar mass-halo mass relation inferred from abundance matching with few outliers. 

Halo profiles modified by baryonic processes are therefore more consistent with expectations from Λ cold dark matter (ΛCDM) cosmology and provide better fits to galaxy rotation curves across a wide range of galaxy properties than do halo models that neglect baryonic physics. Our results offer a solution to the decade long cusp-core discrepancy.