Sunday, July 27, 2014

The Case for keV Dark Matter

As I've mentioned before in previous posts, the case for GeV Cold Dark Matter is becoming weaker and weaker every day. However, that doesn't seem to stop people who work in this field from defending their theories and attacking Warm Dark Matter.
That's fine, but for those of you who actually care about understanding how the universe works. We need to move on and actually analyze what the data is suggesting.
So, here's a list of what we know:

(1) Dark matter is real, and it's roughly 25% (+/-3%) of the universe. We can detect it "directly" through gravitational lensing and "indirectly" from the CMB spectra. Dark Matter is not an artifact due to Modified Newtonian Dynamics (i.e. MOND) because the location of dark matter is not 100% correlated with the location of normal matter. The Bullet Cluster is an excellent example of this, but there are many many more examples of this phenomena. When galaxies collide, the normal matter of doesn't always follow the dark matter and the dark matter doesn't immediately clump together. This is one of many signs that dark matter is not GeV rest mass particles, but rather is quantum degenerate fermions with rest mass in the low keV range.

(2) Dark Matter particles can't have a rest mass less than 1 eV (or else they would be relativistic when universe first de-ionized.) Because a keV dark matter particle is non-relativistic when electrons and protons recombine, a keV dark matter particle only affects the "effective number of Relativistic Particles" (i.e the Neff in the CMB) with a contribution of roughly 0.03. This is well within the error bars for Neff, which was measured by Planck+BAO to be 3.30+/-0.27. When you include data from Big Bang Nucleosynthesis, the allowed range for Neff remains pretty much the same. This means that a keV sterile neutrino is completely compatible with data from the Planck satellite to within 1 sigma uncertainty on Neff.

(3) If Dark Matter particles are Fermions, then their rest mass can't be less than ~ 2 keV because the mass density would be too low to explain experimental data on dark matter density in dwarf galaxies. (de Vega and Sanchez 2013)

(4) Using the Lyman Alpha Forest data in the early universe, there are constraints on the rest mass of dark matter particles. The exact cut-off depends on the allowed uncertainty (i.e. 1 sigma, 2 sigma, 3 sigma, 5 sigma) and on the model assumptions about the particle. The most recent best-fit-value I found for dark matter using Lyman Alpha Forest data was listed as 33 keV in Table II of Viel et al. 2013. The 1 sigma range was 8 keV to infinite rest mass (i.e. no constraint on the high end), and the 2 sigma range was 3.3 keV to infinite rest mass. What's interesting is that the best fit through the data was a keV rest mass dark matter particle...not a GeV rest mass dark matter particle. One way of explaining this is that a GeV dark matter particle would over-predict the Density Perturbations, whereas a 10-100 keV particle is a better fit through the data. For example, in the plot below of the Power Spectrum P(k) vs. wavenumber (k)  (where larger wavenumber means smaller length scales), the Cold Dark Matter line is well above the data points for the Lyman Alpha Forest (and this was known even back in 2002.) More recent data confirms that the data is better fit with a 33 keV particle than with a GeV scale particle.

The reason I find this funny is that the Lyman Alpha Forest had been used by proponents of GeV Dark Matter to fend off proponents of Warm Dark Matter. Ah, how the tides turn. While Lyman Alpha Forest Data can't rule out GeV Dark Matter, it is now suggesting that Dark Matter is Warm  (i.e. in the keV scale.)

(5) If a GeV Dark Matter particle obtains its mass from the Higgs Boson (like it appears that the tau lepton and the bottom quark do), then we can rule out the mass of the particle from ~ GeV to half the rest mass of the Higgs Boson. The reason is that the branching ratios of the Higgs Boson are proportional to the rest mass of the Fermion. In other words, we would have indirectly detected Dark Matter particles at CERN if they had rest masses on the order of ~1-62 GeV. In addition, if the dark matter particle were 10-1000 GeV we would have likely detected it in detectors looking for WIMPS. As such, the range 1-1000 GeV is effectively ruled out for dark matter particles. (See plot from Aad et al. in PRL 23 May 2014)

(6) GeV Dark Matter would clump together in the center of galaxies. There is nothing to stop GeV Dark Matter from clumping together. This is the well known "Cuspy Core Problem" of GeV dark matter, and it also shows up as a problem with estimating the number and size of dwarf galaxies.
What solves these problems and keeps dark matter from clumping is the Fermi Exclusion Principle, which states that only 1 Fermi particle can fill any position-momentum level. As mentioned above, the Fermi exclusion principle sets a lower limit of ~1-2 keV for dark matter in order to explain the actual density of dark matter in dward galaxies. But the principle also helps to explain why the density of dark matter is not cuspy in the center of galaxies, provided that the mass of the dark matter particle is in the range of 1-10 keV. Below is a comparison (from de Vega et al. 2014 that compares observational data for the density of dark matter in galaxies vs. theory for quantum degenerate dark matter with a rest mass around 2 keV.) Notice that the theory matches the observational data quite well at small radius. GeV dark matter would tend to clump up at the center and could in no way match the data. However, it should be noted that I was unable to determine after reading the entire paper what rest mass was actually used in the simulations. This is a major oversight on their part, and I hope that it gets corrected shortly. The point is that a ~2 keV dark matter particle does a pretty good job of reproducing the actual distribution of dark matter in a wide variety of different types of galaxies.

So, let me summary the points above:

Tuesday, July 1, 2014

Rosencrantz and Guildenstern Are Alive: The case for Edward de Vere

I've been taking a break from energy and physics, and delving into the topic that caused me to pick the pen name that I did for this blog: Eddie Devere.
Yes, this is a play off of the names  Eddie Vedder and Edward de Vere, two artists I admire greatly.
I was caused to delve into the Shake-Spear authorship question by a friendly email from Alan Tarica, who sent me a link to a website (Forgotten Secrets) he created in which all 154 of William Shake-Speare's Sonnets are available to read, along with Alan's comments. While there's a lot to read, Alan makes a very convincing case that the Sonnets are written by Edward de Vere, and that the sonnets are written to Queen Elizabeth and the Earl of Southhamption, who is likely the son of Edward de Vere and Queen Elizabeth.  While personally think that there's still some debate as to whether the Earl of Southhamption was the bastard child of Edward de Vere and Queen Elizabeth, I have virtually no doubt that  Edward de Vere used the pen name William Shake-Speare. The goal of this blog is to give a summary of the main arguments why Edward de Vere is the actual author of the sonnets, narrative poems, and plays that were written under the pen name William Shake-Spear.

Trying to determine who is the author of these sonnets, narrative poems, and plays is like going down the rabbit hole or getting stuck in the Matrix. It's easy to get lost in a world of Elizabethian politics, paranoia, and conspiracy theories. But let's not get stuck down in the rabbit's hole.
Let's ask ourselves one simple question: what do famous authors write about?  Answer: they write about what they know best.

What did James Joyce write about? what about Faulkner? Virginia Woolf? They wrote about what they knew best. Ireland, the South, and depressed women.

So, let's look at a few of the many possible authors of the Shake-spear collection:  Francis Bacon, William Shakspear, Edward de Vere, Queen Elizebeth, Christopher Marlowe, and Ben Johnson.

Now let's ask the question: what did Francis Bacon write about? He wrote about science and religion. His most famous text (Novum Organum) is a philosophical text about the methods of science, that is written in bullet format. It's pretty dry, just like Aristotle's lecture notes "The Organum", of which this text is based. Francis Bacon just didn't have the literary skills to write the Shake-spear collection, even though he might have had the education to have done so. 

Now what about William Shakspear? We don't know much about William Shakpeare of Stratford-upon-Avon. But one thing is abundantly clear. William Shakpeare of Stratford-upon-Avon was not capable of writing poems, let alone sign his name. William Shakpeare's will makes it abundantly clear that William Shakpeare is not a world famous playwright. Likely, what happened is that, after the death of William Shakpeare of Stratford-upon-Avon, the local church in  Stratford-upon-Avon tried to make it look like William Shakpeare of Stratford-upon-Avon was William Shake-speare, due to the similarity of the names and the fact that nobody else had stepped forward as the author of the poems and plays.

So, let's once again ask the question: what did Edward de Vere write about? Guess what!  Edward de Vere wrote poems about love and melancholy, and with a lot of references to Greek&Roman mythology. Here's a link to some of the poems. But that's not all. As detailed in a Front Line documentary make in 1989 of the Shake-spear question, it was well known at the time that Edward de Vere wrote under a pen name. (See the end of the following website for quotes from famous writers who list Edward de Vere as an excellent poem and playwright.)

A lot of authors write under pen names. Here's a wiki list of some of the famous ones. Some of the most famous include: Ben Franklin (Richard Saunders of the Poor Richard's Almanac), Mark Twain (Samual Langhorne Clemens), Pablo Neruda, Moliere, Lewis, Carroll, Mary Ann Evans (George Elliot), George Orwell (Eric Arthur Blair), Leslie McFarlane (of HardyBoys fame), J.K. Rowling, O. Henry, Isaac Asimov, V. Nabokov, Sylvia Plath, Soren Kierkegaard, Lemony Snicket, Woody Allen, and many, many more.

The assumption should be that the name on a book or play is a pen name, unless there is some direct proof that it's not a pen name. As such, there's no direct proof that William Shakspeare wrote the poems and plays of William Shake-speare. For example, we have no evidence that William Shakspeare could even write; we have no evidence in his will that he wrote poems/plays; and we have virtually no evidence from his original gravestone monument that he wrote plays/poems. (See image below.)