Constraining DM substructures in the Galactic halo with microlensing

[smurgia]

Goal: constraints on the DM sub halo mass function in the Galactic halo using photometric microlensing. DM subhalos are diffuse, and the microlensing signal depends on the slope of the DM density distribution, in addition to the subhalo mass. However, the slope of the DM profile is not known or constrained by simulations for DM subhalo masses below ~ dwarf spheroidal galaxies. In addition, there is an indication that primordial subhalos have significantly steeper inner profiles. I propose to probe a broad range in DM subhalo inner slope, extension (consider effect of tidal stripping), and mass using current constraints and to determine prospects for LSST.

[bechtol]

There was a paper on this topic by Erickcek and Law 2011, https://arxiv.org/abs/1007.4228 , with the concept to search for astrometric anomalies induced by a nearby DM substructure (e.g., within 200 pc) crossing the line of sight to a background star. The signal amplitude is highly dependent on the slope of the inner profile, and for standard NFW, the expected signal is very small. Even for a steeper profile, the signal amplitude is at the microarcsecond level, and one would need to monitor billions of stars to have a chance of detecting the signal. Its too bad the amplitude is so small, because it is a beautiful signature. In principle, we could constrain the inner profile shape and the mass for an individual halo, so there would be a lot of physics to be learned. The astrometric distortion would be coherent over a few arcseconds, so maybe one could stare at a field with very high stellar density to improve the odds of detection by analyzing multiple stars together. In any case, the astrometric signal would require something like WFIRST rather than LSST based on what I've read on the subject.

[kadrlica]

@smurgia Does it make sense to combine this issue with #12?

[smurgia]

@bechtol What I've been mostly thinking about is primordial sub halos, and what that looks like is going to depend on things like the underlying particle nature of DM. I've been talking to @chuckkeeton and Manoj Kaplinghat about this. The question is how much the microlensing signal for such an object with a mass below M_Sun and a very steep profile (1/r^2, which is pretty extreme according to the literature) differs from a point lens. In addition to mass and inner profile, the signal is going to also depend on the tidal cutoff radius. Scanning a broad range of parameters in this parameter space, being as open minded as possible on what these sub halos look like is what I have in mind. The paper you refer to is focusing on much more massive halos which addresses the same underlying question, but the approach would be different.

[chuckkeeton]

I think this and #12 are both interesting but somewhat distinct. The observables are different: here we are still thinking about seeing full, time variable light curves; one of the science questions is whether the time scales would actually be detectable, given expectations for low-mass, primordial subhalos.

[kadrlica]

@chuckkeeton @smurgia sounds good, I'm happy to keep them separate.

How low mass are we talking about? What is the crossing time?

[chuckkeeton]

I can compute light curves for different assumptions about the density profile. @smurgia and I have looked at some examples in dimensionless units. Now we are checking numbers to determine the physical scales.

[smurgia]

As a start, we are focusing on Earth-mass micro halos.

[wadawson]

The work in issue #8 is relevant here.

[chuckkeeton]

The numbers for CDM microhalos look terrible. I take M200 = 2.6e-7 Msun, r200 = 7.0e-3 pc, and alpha = 1.4 from Table 1 of https://arxiv.org/pdf/1302.0003.pdf. I consider a source at 50 kpc and a lens halfway. A point mass with that mass would have an Einstein radius of 8e8 m or 2e-7 arcsec. But an extended microhalo with a power law slope of 1.4 would have an Einstein radius of 2e-12 m (!!!), if I've done the numbers right. Of course, on that scale the power law assumption is horrible. But I can't see any way around the conclusion that these microhalos are simply too puffy to act as lenses.

[smurgia]

@chuckkeeton Thanks for the numbers! It does look pretty hopeless for these simulated CDM microhalos, perhaps unsurprisingly. My question would be how puffy can the microhalos be in order to be within reach of microlensing constraints. In other words, how much should they be "un-puffed" to produce an observable signal (from current or future experiments), and what parameters should be considered in "reshaping" them. I initially focused on the inner slope, but thats not the whole story. The bottom line is that we don't really know what these microhalos look like (or if any are around!) but we might be able to set constraints. How interesting those constraints would be then is a relevant question. E.g., some particle physics scenarios predict halos that could be very compact (I will send some references)