Month: May 2016

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.

Figure_3

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.

And then there were six

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

– John von Neumann

The simple and elegant cosmology encapsulated by the search for two numbers has been replaced by ΛCDM. This is neither simple nor elegant. In addition to the Hubble constant and density parameter, we now also require distinct density parameters for baryonic mass, non-baryonic cold dark matter, and dark energy. There is an implicit (seventh) parameter for the density of neutrinos.

Now we also include the power spectrum as cosmological parameters (σ8, n). These did not use to be considered on the same level as the Big Two. They aren’t: they concern structure formation within the world model, not the nature of the world model. But I guess they seem more important once the Big Numbers are settled.

Here is a quick list of what we believed, then and now:

 

Paramater SCDM ΛCDM
H0 50 70
Ωm 1.0 0.3
Ωbh2 0.0125 0.02225
ΩΛ 0.7
σ8 0.5 0.8
n 1.0 0.96

 

There are a number of “lesser” parameters, like the optical depth to reionization. Plus, the index n can run, one can invoke scale dependent non-linear biasing (a rolling fudge factor for σ8), and people talk seriously about the time evolution of antigravity the dark energy equation of state.

From the late ’80s to the early ’00s, all of these parameters (excepting only n) changed by much more than their formal uncertainty or theoretical expectation. Even big bang nucleosynthesis – by far the most robustly constrained – suffered a doubling in the mass density of baryons. This should be embarrassing, but most cosmologists assert it as a great success while quietly sweeping the lithium problem under the carpet.

The only thing that hasn’t really changed is our belief in Cold Dark Matter. That’s not because it is more robust. It is because it is much harder to detect, let alone measure.

Two Numbers

Cosmology used to be called the hunt for two numbers. It was simple and elegant. Nowadays we need at least six. It is neither simple nor elegant. So how did we get here?

The two Big Numbers are, or at least up till the early-90s were, the Hubble constant H0 and the density parameter Ω. These told us Everything. Or so we thought.

The Hubble constant is the expansion rate of the universe. Not only does it tell us how fast the universe is expanding, it sets the size scale through the Hubble distance-velocity relation. Moreover, its inverse is the Hubble time – essentially the age of the universe. A Useful and Important Number. To seek to measure it was a noble endeavor into which much toil and treasure was invested. Getting this right was what the Hubble Space Telescope was built for.

The density parameter measures the amount of stuff in the universe. Until relatively recently, it was used exclusively to refer to the mass density – the amount of gravitating stuff normalized to the critical density. The critical density is the over/under point where there is enough gravity to counteract the expansion of the universe. If Ω < 1, there isn’t enough, and the universe will expand forever. If Ω > 1, there’s more than enough, and the universe will eventually stop expanding and collapse. It controls the fate of the universe.

Just two numbers controlled the size, age, and ultimate fate of the universe. The hunt was on.

Of course, the hunt had been on for a long time, ever since Hubble discovered that the universe was expanding. For the first fifty years it largely shrank, then settled into a double valued rut between two entrenched camps. Sandage and collaborators found H0 = 50 km/s/Mpc while de Vaucoulers found a value closer to 100 km/s/Mpc.

The exact age of the universe depends a little on Ω as well as the Hubble constant. If the universe is empty, there is no gravity to retard its expansion. The age of such a `coasting’ universe is just the inverse of the Hubble constant – about 10 Gyr (10 billion years) for H0 = 100 and 20 Gyr for H0 = 50. If instead the universe has the critical density Ω = 1, the age is just 2/3 of the coasting value.

The difference in age between empty and critical ages is not huge by cosmic standards, but it nevertheless played an important role in guiding our thinking. Stellar evolution places a constraint on the ages of the oldest stars. These are all around a Hubble time old. That’s good – it looks like the first stars formed near the beginning of the universe. But we can’t have stars that are older than the universe they live in.

In the 80s, a commonly quoted age for the oldest stars was about 18 Gyr. That’s too old for de Vaucoulers’s H0 = 100 – even if the universe is completely empty. Worse, Ω = 1 is the only natural scale in cosmology; it seemed to many like the most likely case – a case bolstered by the advent of Inflation. In that case, the universe could be at most 13 Gyr old, even adopting Sandage’s H0 = 50. It was easy to imagine that the ages of the oldest stars were off by that much (indeed, the modern number is closer to 12 Gyr) but not by a lot more: Ages < 10 Gyr with H0 = 100 were right out.

Hence we fell into a double trap. First, there was confirmation bias: the ages of stars led to a clear preference for who must be right about the Hubble constant. Then Inflation made a compelling (but entirely theoretical) case the Ω had to be exactly 1 – entirely in mass. (There was no cosmological constant in those days.  You were stupid to even consider that.) This put further pressure on the age problem. A paradigm emerged with Ω = 1 and H0 = 50.

There was a very strong current of opinion in the 80s that this had to be the case. Inflation demanded Ω = 1, in which case H0 = 50 was the only sensible possibility. You were stupid to think otherwise.

That was the attitude into which I was indoctrinated. I wouldn’t blame any particular person for this indoctrination; it was more of a communal group-think. But that is absolutely the attitude that reigned supreme in the physics departments of MIT and Princeton in the mid-80s.

I switched grad schools, having decided I wanted data. Actual observational data; hands on telescopes. When I arrived at the University of Michigan in 1987, I found a very different culture among the astronomers there. It was more open minded. Based on measurements that were current at the time, H0 was maybe 80 or so.

At first I rejected this heresy as obviously insane. But the approach was much more empirical. It would be wrong to say that it was uninformed by theoretical considerations. But it was also informed by a long tradition of things that must be so turning out to be just plain wrong.

Between 1987 and 1995, the value of the Big Numbers changed by amounts that were inconceivable. None of the things that must be so turned out to be correct. And yet now, two decades later, we are back to the new old status quo, where all the parameters are Known and Cannot Conceivably Change.

Feels like I’ve been here before.