Axion-like Dark Matter

[kadrlica]

This is an issue to track progress on the axion dark matter hack. Our plan is to do some reading tonight on 4 different astrophysical axion constraints:

• Tip of the red giant branch
• Horizontal branch population ratios
• White dwarf luminosity function
• Neutron star constraints.

After reading, we are going to come back together and choose one of these topics that we are most interested in diving into deeply. We plan to spend at least a morning (and possibly longer) exploring one of these topics (hopefully the one deemed most exciting for LSST). Our proposed product is a 1-page summary of the existing constraints (both theory motivation and observation) and the potential for LSST to improve these constraints.

Some interested parties are @cray0n, @kadrlica, Tim Tait, @aismail3, and @davidmckeen.

[aismail3]

Some general references on astrophysical axion bounds to start:

• https://arxiv.org/abs/hep-ph/0611350
• https://arxiv.org/abs/1708.02111 (more recent)

[davidmckeen]

Hints of additional cooling mechanism in white dwarfs:

• https://arxiv.org/abs/0806.2807
• https://arxiv.org/abs/0812.3043
• https://arxiv.org/abs/1204.3565

[kadrlica]

@tmptait here is our thread. Follow the link at the bottom of the email that gets sent to you.

[kadrlica]

Overview

• Raffelt's "bible" on astrophysical constraints of axions

Axions in globular clusters/massive stars:

• https://arxiv.org/abs/1210.1271
• https://arxiv.org/abs/1311.1669
• https://arxiv.org/abs/1406.6053
• https://arxiv.org/abs/1802.10357

Axion brems in dense stars:

• http://adsabs.harvard.edu/abs/1987ApJ...322..291N
• http://adsabs.harvard.edu/abs/1988ApJ...326..241N

Adding @andrew-zentner to this thread

[aismail3]

And I think @cray0n was referring to this for neutron stars? https://arxiv.org/abs/1512.07828

I would suggest focusing on the HB/RGB ratio, which gives a limit on the coupling of an axion-like particle to photons. The white dwarf and RGB tip constraints depend primarily on the coupling to electrons, which is also interesting but somewhat less connected to being an "axion," e.g. there are axion models with no tree-level fermion couplings.

The neutron stars are interesting too, but it seems like part of the HB/RGB ratio uncertainty comes from the statistics of counting O(10^2) stars in each of 15 globular clusters (Figure 2.21 and Equation 2.37 of the Raffelt book linked by @kadrlica) in 1983. To whatever extent this can be improved, perhaps a better limit could be obtained.

[kadrlica]

I think more recent references (also listed above) on the HB/RGB ratio (aka, the "R-parameter") are:

• https://arxiv.org/abs/1406.6053
• http://inspirehep.net/record/1511517/files/fulltext.pdf

I'll try to read the first paper in more detail.

[cray0n]

Axion cooling of neutron stars by Sedrakian: https://arxiv.org/abs/1512.07828

[cray0n]

Kilonova detection with LSST (via Lucianne Walkowicz): https://arxiv.org/pdf/1611.09822.pdf

[kadrlica]

Some comments on 1406.6053:

• I need to look at 0403600 to learn more about how the R-parameter is measured (1406.6053 has very sparse details).
• The RGB and HB stellar sequences are bright in Galactic GCs, so this is not the regime that LSST is going to make large improvements. We probably want to extend this type of analysis to larger distances and possibly other types of stellar systems (i.e., galaxies). There will be complications from multiple stellar populations...
• Populate the HB of GCs is a complicated question. The metallicity [Fe/H] is expected to be the primary parameter. However, there are continued discussions of infamous "second" and "third" parameters for determining the population of HB stars (i.e., 1004.3862).
• The classic "second" parameter is cluster age, while the dependence on the initial He fraction (the "Y" parameter) is proposed as the "third" parameter. I think that from the observational side we probably want to pay more attention to the dependence of R on the second and third parameters.
• Specifically, I'm a bit confused about the discussion of the current values of Y (i.e., the solar abundance or the value measured in blue galaxies). My understanding is that the GC stellar population is dictated by the initial value of Y, not the current value.

I think for the purpose of the hack we can follow 1406.6053 and sweep the second and third parameter under the rug, but I wanted to document some of these concerns (read: interesting astrophysics) for later...

[cray0n]

@soares-santos: hi, Chanda here! I am wondering if you have a reference for connections between your work and LSST for kilonova observations?

[kadrlica]

I think that the determination of R = 1.39 +/- 0.03 is coming from Figure 1 of astro-ph/0403600 after applying a cut of [Fe/H] < -1.1 in the scale of Carretta & Gratton. This is shown in the lower panel of the figure below:

I am attempting to pseudo-quantitatively confirm this now...

The original data for these observations come from a set of 74 GC observations with Hubble (HST/WFPC2) astro-ph/0207124. In the future, we might consider improving/augmenting these observations with more recent (HST/ACS observations)[https://archive.stsci.edu/prepds/acsggct/].

I can reproduce the above figure and recalculate the weighted average and uncertainty on the weighted average by selecting the 39 clusters with [Fe/H] < -1.1 (CG97-scale).

Estimating the weights:

w_i = 1/sigma_Ri**2
wavg =  np.sum(Ri*w_i)/np.sum(w_i)
sigma_wavg = 1/np.sqrt(np.sum(w_i))

yields

wavg: 1.3906
sigma_wavg: 0.029

[davidmckeen]

SDSS White Dwarf luminosity curves:

• https://arxiv.org/abs/astro-ph/0510820
• https://arxiv.org/abs/0709.2190

[kadrlica]

Updated WDLF from a similar author set:

• https://arxiv.org/abs/1611.06275

[andrew-zentner]

Today's progress - Limited to figuring out how to add anomalous heating and cooling mechanisms to a MESA stellar evolution model.

[aismail3]

[esrabulbul]

Axion cooling of neutron stars:
1512.07828.pdf

[esrabulbul]

axioncooling.pdf

[aismail3]

@andrew-zentner How much additional cooling were you using in your plot, again (5%?)? As a benchmark, the axion luminosity expected from the Sun is ~ 2 * 10^(-3) * (axion-photon coupling * 10^10 GeV)^2 * solar luminosity. The current CAST limit on the axion-photon coupling is around 10^-10 GeV^-1.

There are more details in section 5.2 of Raffelt (http://wwwth.mpp.mpg.de/members/raffelt/mypapers/199613.pdf) about how this is calculated. For what it's worth, the energy loss per unit volume goes as (axion-photon coupling)^2 * T^7 * form factor, where the difference in the form factor for the Sun and an HB star is only a factor of 2.

[kadrlica]

Here's an ipython notebook for my previous calculation:
https://github.com/lsstdarkmatter/axions/blob/master/hb_rgb_ratio.ipynb

[andrew-zentner]

Here is the other bible for reference: http://wwwth.mpp.mpg.de/members/raffelt/mypapers/199613.pdf

[andrew-zentner]

@aismail3 @davidmckeen The MESA code works in cgs units. Is the following the correct conversion to cgs? This is Raffelt's equation 5.9 that we discussed this morning.
latex-image-1.pdf

[aismail3]

@andrew-zentner The result of my conversion differs from you by an order-1 factor, i.e. I get 0.067 rather than 0.087. But at least the overall order of magnitude is right! @davidmckeen is checking now too

[andrew-zentner]

I was able to put axion cooling into the MESA software and run some simulations. Not surprisingly, the helioscope bounds preclude any interesting effect on cooling in the Sun. Even in very low mass stars near M=0.1Msun, a coupling of g_a,gamma ~ 10^-8 GeV^-1 is necessary in order to get significant alterations to stellar evolution. Alas this is 2 orders of magnitude larger than helioscope constraints. So, this seems as though it will not lead to anything. I will refocus my efforts on simulating red giant and horizontal branch evolution for more sun-like stars.

[davidmckeen]

I agree with @andrew-zentner on the prefactor.

[andrew-zentner]

@kadrlica @aismail3 @davidmckeen
Well, I seem to have had some success. In the plot showing luminosity as a function of time, you can see that I can reproduce the (already known) shift in the HB lifetime for a reasonable value of the axion coupling (g = 10^{-10} GeV^{-1}). The RGB phase is the first peak in luminosity, the HB phase is the valley, and the AGB phase is the second peak in luminosity.

You'll notice that there is also a small shift in the maximum luminosity of the giant branches (e.g., tip of the RGB and so on).

So, that's good. There is also some strange behavior of the star as it transitions from the AGB to WD phases. This phase is very uncertain in the standard model because it depends upon many complicated things including the stellar mass loss, so I'm not sure that we can place any importance on this. I'll ask some stellar astrophysicists if they can help with this. Here is the relevant plot.

[kadrlica]

@andrew-zentner very cool! My understanding is that stars spend so little time in the post-AGB phase that it's very difficult to set constraints on population statistics. I think the next step would be to see what MESA predicts for the HB/RGB ratio. Ayala et al. 2014 quote

R(g_a,, Y ) = 6.26 Y − 0.41 g_a − 0.12

which yields a predicted value of R = 1.45 with Y = 0.25.

On a slightly unrelated topic, here is the results of my MCMC fit to the HB/RGB ratio from Salaris et al. (2004):

The best-fit parameters slope and intercept for the line R = m * [Fe/H] + b are

m = -0.24 [+ 0.14, -0.15]
b = 1.06 [+0.20, -0.21]

As we could tell by eye, the fit yields a slight preference (~1.7sigma) for a slope in the ratio as a function of [Fe/H]. The full analysis can be found here in an ipython notebook here:
https://github.com/lsstdarkmatter/axions/blob/master/hb_rgb_ratio.ipynb

[kadrlica]

I've been thinking about what it would take to really do this analysis rigorously. I think that the rigorous way to do this would be to fit the observed CMDs of the globular clusters using a MESA isochrone where the axion cooling was left as a free parameter (along with the age, metallicity, distance modulus, and Y-parameter). This would be very similar to the MCMC analysis of Wagner-Kaiser et al.
(2017), but adding the axion cooling as another free parameter in the fit.

I realize that generating a full set of isochrones with different axion cooling parameters, ages, metallicities, and primordial He abundances may be too computationally intensive. As an alternative, one could fit age and metallicity using the existing MESA isochrone set from Dotter and then re-run the best-fit isochrone with additional axion cooling to estimate the change in the HB/RGB ratio. The nice thing about having the best-fit MESA isochrone is that you can self-consistently define the color-magnitude selection region for the HB and RGB stars in the data and simulation.

Both of these analyses may be more involved than we want to get, and I'm not actually pushing them. I think it would already be a useful contribution to just point out how dependent the R parameter is on the choice of synthetic isochrone modeling code (i.e., MESA vs PARSEC vs FUNS) and the other assumptions that go into the predicted R value. That said, if we do want to do something more rigorous we do have a lot of tools for doing CMD fitting of dwarf galaxies that could be applied to globular clusters.

[andrew-zentner]

@kadrlica - Actually, I think the MESA isochrone thing would be the best thing to do and not be too computationally intensive. The reason is that isochrones of arbitrary age can be generated using a single run of MESA. So, we only need to probe axion cooling, Y, and [Fe/H]. Moreover, the isochrones vary very smoothly as a function of these parameters, so I think we can sample quite sparsely. I'll try to set up a large run of MESA models this week and use that to estimate the computational cost of doing so.