Friday, July 17, 2015

Comparison of the Wealth of Nations: The 2015 Update

Yup, it’s that time of year again. A few weeks ago, BP released their latest updates for the production and consumption of energy throughout the world. (These links go to the previous posts on this subject made in 2011,  in 2012, in 2013, and in 2014 on the Wealth of Nations.) One thing to note is that, this year, I've added five countries to the list of countries analyzed: Saudi Arabia, South Korea, Indonesia, Mexico, and Italy. This now means that all 15 countries with the largest GDP PPP (as of 2015) are included in this analysis. (The next 3 largest countries would be Iran, Turkey, and Spain, which I would like to add next year to the analysis.)

Here are some conclusions before I get into a detailed breakdown of the analysis for this year.

(1) The US economy (as measured in [TW-hrs] of useful electrical and mechanical work produced) increased by 1.0% in 2014. 
(2) Many countries had negative growth rates in 2014: Mexico (-1.5%), Canada (-1.8%), Germany (-2.3%), France (-2.7%), Japan (-3.0%), Italy (-4.0%) and the UK (-4.8%). This was a particularly bad year for the UK as far as generating useful work. There were two countries with near-zero growth rates: South Korea (0.0%) and Russia (0.5%.) The major countries with the highest growth rates were: China (3.3%), Indonesia (3.6%), Brazil (3.7%), Saudi Arabia (7.4%), and India (7.8%.) This was a particularly good year for India and Saudi Arabia, which is one reason that Saudi Arabia is now on my list of countries to analyze. (Another reason is that it's economy is very different than other countries I analyze, so it'll be good to see how their useful work generation compares with their GDP PPP.)

(3) The purchasing power parity GDP (i.e. PPP GDP) remains a pretty good reflection of a country's capability to do mechanical and electrical work. However, there are still some countries who generate a lot more useful work [TW-hr] than they are given credit in their GDP PPP. These countries are: Canada, South Korea, and Saudi Arabia. However, there are a number of countries whose GDP PPP is significantly higher than their generation of useful work: Indonesia, Italy, UK, Germany, and India. Of these, Indonesia has the widest gap between their GDP PPP and their generation of electrical+mechanical work. It's not clear to me why there is such a difference between Canada and Indonesia. As I'v mentioned before, if I were a Canadian representative for the IMF, I would voice my concern that the IMF is underestimating the size of the Canadian economy by at least two fold.

So, now I'm going to present a more detailed breakdown of the analysis and present the data in graphical form. 

Sunday, July 5, 2015

Updates on 3.55 keV line

Well, it looks like the emission peak around 3.55 keV may not actually be from a decaying sterile neutrino. In a previous post, I wrote about the news of a possible sterile neutrino with a rest mass of 7.1 keV. However, recent experimental data does not appear to back up this claim.

For example, see the following papers:

Where do the 3.5 keV photons come from? A morphological study of the Galactic Center and of Perseus
Carlson et al. Jan 2015

Constraints on 3.55 keV line emission from stacked observations of dwarf spheroidal
Malyshev et al. Aug 2014

Discovery of a 3.5 keV line in the Galactic Centre and a critical look at the origin of the line across astronomical targets
by Jeltema and Profumo Aug 2014

The main evidence (as it seems to me) against the claim for the 7.1 keV particle with a sin squared 2 theta of ~10^-10 is that there is essentially no signal from dwarf spheroidal galaxies.

But all is not lost for sterile neutrinos as warm dark matter. It is still possible to have a sterile neutrino with a smaller value of sin squared 2 theta. A smaller value of theta is possible if there is a larger lepton asymmetry in the universe. The constraints on lepton asymmetry in the universe is extremely weak because N_eff is very loosely constrained. Lepton asymemtry of +/- 0.1 is still entirely possible, whereas only a value of 0.001 would be needed to stay below the constraints set by X-rays emission from dwarf spheroidal galaxies.

As such, it's possible that the sterile neutrino could have a smaller value of theta and still be consistent with cosmological constrains on N_eff.

Finally, I'd like to point out that most of the papers that analyze X-ray emission in order to put constraints on dark matter are pretty ad hoc (the same applies to papers using Gamma-ray emission to detect Cold Dark Matter.) There is dark matter all over the place. Everywhere you look, there's dark matter. It's fairly evenly distributed through the universe. True, it's slightly lumpy here and here, but there would be X-ray signal from every direction (with some redshift depending on how far away the source is.)
As such, researchers in this area needs to be a much systematic about searching for X-ray (or gamma-ray) emissions from possible dark matter. This means doing a correlation analysis against dark matter lensing maps (after subtracting off known sources of X-rays or gamma-rays.)
(Such as detailed by Fornengo and Regis or Zandanel et al. on how to do these correlations, though not actually done by them.)
This is not easy to do because you need to know the density of dark matter as function of the distance from us across the whole sky. But we know have maps of dark matter density vs. z and we have X-ray emissions as a function of energy. It should be possible to do a full-sky analysis of decaying dark matter (rather than just this silly looking at few galaxies with known, unknown sources of X-rays.)

This means that, in order to claim a 'detection' of a decaying dark matter particle, researchers need to match their signal with actual data on the 3D density of dark matter (i.e. two spatial dimension plus distance, z.)

If anybody is aware of such a detailed, full-sky correlation analysis between dark matter and X-ray emission, please provide me a link in the comment section below.

Saturday, July 4, 2015

A New Cosmological Simulation that models Warm Dark Matter as Quantum Degenerate Fermions & Calcs to Estimate Dark Matter Mass and Temperature

(Updated: 7/14/2015)
In previous comment section of a post, I had written that I had not seen an article that conducted a Cosmological Simulation of Structure formation when including the quantum degenerate nature of fermionic, warm dark matter.
I'm happy to say that an article has recently been submitted to arxiv that does just this.

"Structure formation in warm dark matter cosmologiesTop-Bottom Upside-Down"
by Sinziana Paduroiu, Yves Revaz, and Daniel Pfenniger

Basically, the gist of the paper is the following:  everybody who has modeled warm dark matter previously has had to make assumptions that (a) are not valid, and (b) simplify the simulations too much. As such, Paduroiu et al. argue that modeling warm dark matter is extremely complicated, and nobody is doing it correctly.

They have posted a YouTube site with videos of their simulations.

One problem with the manuscript is that there is no comparison to actual data.

One thing that I want to add to the discussion (which I've mentioned previously) is that non-thermal warm dark matter does not act exactly the same as a thermal warm dark matter, but with a rest mass lower than the rest mass of the actual rest mass. Too many times, proponents of Cold Dark Matter make simplification of how warm dark matter interacts (such as assuming that non-thermal WDM acts like a thermal WDM particle of lower rest mass), and then show that the rest mass of the particle that explains the "small-scale crisis" is in compatible with the rest mass required to explain the Lyman-alpha forest data. And therefore this CDM proponents claim that WDM fails, and therefore CDM is still king.
The logic here is silly. In particular, I'll thinking of the paper by Schneider et al. "Warm dark matter does not do better than cold darkmatter in solving small-scale inconsistencies."
The logic in this paper is absurd.
(1) We acknowledge that CDM has a small scale crisis
(2) So we poorly model WDM, and find that it can't solve both the small-scale crisis and fit with data from Lyman-Alpha Forest
(3) "Hence, from an astrophysical perspective, there is no convincing reason to favour WDM from thermal or thermal-like production (i.e. neutrinos oscillations) over the standard CDM scenario."

Let's not ignore the small-scale crisis (as was done by all but one of the spearkers that the recent CMB@50 event at Princeton a few weeks ago.) There is a real problem with CDM, and it won't be solved by Self-interacting Cold Dark matter. The plots below from the  Schneider et al. paper and from the Weinberg et al. paper are two ways of visualizing that there is a small-scale crisis for CDM.

There's also the too high reionization optical depth problem and the core/cusp problem of cold dark matter. There is no "Dark Matter" crisis. It's just a question of what is the rest mass and thermal distribution of dark matter. 
Basically, the small-scale crisis is best solved by having a thermal rest mass of ~2 keV and the  Lyman-Alpha forest is best fit with a thermal particle with rest mass of 32 keV. (Though, it should be noted that this best fit was done before the Planck 2015 data release. It will be interesting to see how this "best-fit" changes with updated data from Planck, as well as updated BAO, SZ, & lensing data.)
Because it's the velocity (i.e. v =   (4/11)^(1/3) 3kTo/mc * (1 + z) ≈ 151 (1 + z) / m (in eV)
km/s  ) that's important for the Lyman-Alpha Forest, this means that the Lyman-Alpha Forest can also be equally explained by a 16 keV rest mass particle that is born with a thermal energy one half as large as a 32 keV thermally-born particle. Or a 8 keV rest mass particle that is born with a thermal energy one fourth as large as a 32 keV thermally-born particle.
(For more information on calculating the temperature/velocity of fermi particles vs. z,  that transition between being relativistic to being non-relativistic at time z=z_critical, is given by equations (10)-(15) in Pfenniger and Muccione 2008.)

Because it's the number density times deBroglie wavelength cubed that's important for quantum degeneracy at the small-scale, i.e. lambdaDM * hbar^3 / (m^4*v^3) ~ lambdaDM / (m*T^3), then quantum degeneracy remains the same provided that m*T^3 = constant = (2 keV)*(T_thermal)^3
Note that the fact that a resonant sterile neutrino can be born with a temperature less than the temperature of the photons/neutrinos in the surrounding thermal bath means that the sterile neutrinos become non-relativistic sooner than you would expect, and hence their temperature starts dropping as (1+z)^2 sooner than for a thermal particle. The net effect is that, quantum mechanically, a sterile neutrino born with half of the thermal energy and 8 times the rest mass has the same degeneracy parameter as a thermal sterile neutrino. In other words, the number density times deBroglie wavelength cubed is the same for a 2 keV, thermal sterile neutrino as it is for a 16 keV sterile neutrino born with half of the thermal energy.

And as emntioned above, the Lyman Alpha forest suggests that (T_thermal) / (32 keV) = (T/m)

Solving the two equations, you get the following answers:
Rest Mass = 16 keV
Temperature at birth = 0.5 * Global thermal Temperature at the time of birth

So, this means that a fermion dark matter particle with a rest mass of ~16 keV that is born with half of the thermal energy of the photons and neutrinos (and which can't interact with other particles after decoupling) should be able to explain the small-scale crisis, the missing satellite, and the Lyman-Alpha forest. It should be noted that there are large error bar on the numbers listed above because of the uncertainty of the best fit for Lyman Alpha and uncertainty on the best fit for a quantum particle to explain dwarf galaxies. So, the rest mass of dark matter is likely between 10-20 keV with temperatures of 0.4-0.6 compared with the surrounding media.

Sterile neutrinos generated by the Shi-Fuller mechanism often have distribution function such that they are effectively colder than the surrounding photons/active-neutrinos by a factor of 0.6.

The main point here is that a non-thermal sterile neutrino can explain both the Lyman Alpha forest and the small-scale crisis, the missing satellite, as well as the Lyman-Alpha forest. What we are looking for is a non-thermal particle with a rest mass ~10-20 keV.