Galaxy cluster constraints of dark matter

[wadawson]

The basic idea is to write up some material on the galaxy cluster constraints of dark matter. In particular what LSST can do in conjunction with other facilities (e.g. X-ray telescopes, and spectroscopic facilities). The could include probes such as: wobbling BCG’s, merging galaxy clusters, and halo density profiles.

[wadawson]

Also mentioned was the use case of stacking LSST identified (and mass measured) clusters with X-ray spectroscopy to look for annhilation line features.

[wadawson]

We had a quasi-detailed discussion working out a potential project to use an X-ray selected sample of clusters and compare their X-ray centers with the location of the BCG's. Kim et al. showed that the BCG can slosh in a spring like fashion about the center of the potential in a SIDM relaxed cluster on the order of 10-100 kpc. The probability density of it's location should be something like beta distribution with a cos(theta) spherical cap effects.

Ng et al 2017 showed that the intrinsic variability in BCG and center of potential is ~+/-30 kpc. Although there are some large outliers in the remaining 5 percent of cases.

Stacy is working on simulations with non-equal mass mergers. Esra will provide a list of relaxed clusters. Nate will work on BCG locations of the systems. Will will work on the statistics of the measurement.

Questions that remain: can you use velocity offsets as well. Seems doubtful given the ~1000 km/s velocity dispersion.

[sazabi4]

I would also be interested in knowing how spectroscopy can help on merging cluster and halo density profile, and, whether a signal of wobbling BCG is detectable in velocity with a large sample...

[nrgolovich]

Pulling in everyone: @esrabulbul is helping us find relaxed clusters by looking at X-ray images in the Chandra archive and fitting X-ray profiles to determine the X-ray center. Also, @stacykim and @ahgpeter's simulations of merging galaxy clusters were providing much of the impetus for this. One keep prediction is the wobbling of BCGs, which have a tunable prediction with the SIDM cross section. Furthermore, there is a cored dark matter density in SIDM clusters which allow multi-cored BCGs to exist. This provides another prediction and pulls in interest from @mkapling, with whom I have been talking about this concept for at least a year.

[nrgolovich]

Furthermore, @sazabi4, the spectroscopic angle on the wobbling BCG will depend on the cross section. sigma_DM = 1 cm^2/g gives 100 kpc/1 Gyr = 100 km/s, which I think would be very detectable; however, sigma_DM = 1cm^2/g gives 10 kpc/1 Gyr = 10 km/s, which I think would be hard to detect. You could argue that a factor of 100 more clusters would be able to push the constraint down.

I guess this is where we need a realistic count of relaxed clusters that LSST will find. I suspect someone is DESC has this number.

[wadawson]

@sazabi4 asked the question about what fraction of galaxy clusters have undergone a major merger in the past that might result in the wobbling of the BCG. @nrgolovich noted that some of the UC Davis group has been exploring large n-body simulations looking for analogs of existing mergers and some of this might be useful for answering the distribution of merger ratios for clusters of a given mass.

@stacykim noted that they have already repeated their earlier work but with unequal mass mergers; the simulation results just need to be analyzed.

@mkapling also expressed interest in this topic.

[nrgolovich]

These show the ability to recover the true redshift of a cluster of redshift z=0.1 and velocity dispersion vdisp=1000 km/s with varying numbers of measured redshifts. In order to measure the velocity difference between the BCG and cluster. We'd like to get to within 10 km/s for sigma_DM = 0.1 cm^2/g and to within 100 km/s for sigma_DM=1 cm^2/g.

[nrgolovich]

@stacykim: Following up all of this just so we are working toward something... in your simulations, you have the BCGs as more massive particles that are trackable. When there is a zero impact parameter, the motion of the BCG a long time after the merger occurred and has started to settle down is sort of like a mass-spring situation where it oscillates back and forth along a line segment collinear with the merger axis and with amplitude the scales with the cross section. In this simplest case, I'd like to know how the amplitude scales with cross section, but also how this motion evolves over time. That is, where are we most likely to observe the BCG? Furthermore, how does this change with mass ratio, and finally, how does it change with impact parameter? I presume that the orbit becomes elliptical in that case.

One question I have about initialization of the simulations. You smash together two clusters that are "relaxed" in their initial state. Does this mean there is no wobbling? How hard would it be to have to clusters that are the end product of a previous merger? This would help capture some of the hierarchical nature of the mergers? What I'm getting at is that if the BCG isn't wobbling before the merger from it's (presumable) previous merger, how much is the wobbling affected by this over simplification?

Final question: with equal mass mergers you made your two BCGs the same size. In SIDM simulations, what happened to the two of them? Did they merge together? Or is that not allowed? Did they both oscillate along the merger axis in a similar manner? Following on that, if you have unequal mass mergers, how do you pick the BCG masses? I think there has been work done to look for BCG mass -- cluster mass connections, but that may be with stellar masses. I'm not sure. I think in the most realistic cases, the impact parameter is non-zero (probably small though -- < 100 kpc), so there should be some sort of elliptical orbit of the BCGs in our observations. How do the two BCGs survive this experience? Do they merge together ever? How long can they live orbiting around the cored-profile? Is this dependent on the cross section? @mkapling is particularly interested in this question.

I hope this helps summarize some of the open questions at this point. Sorry for the large dump of questions.

[nrgolovich]

@esrabulbul: Just reconnecting here about selecting good relaxed systems. We had already agreed upon looking at the Chandra-Planck massive cluster catalog here. That should be a good starting point, but I'll leave it to you to come up with other relaxed systems since I'm sure you can do much better than me with that.

Now for the technical side: if we want to do this to constrain SIDM, @stacykim has simulations that show about 10 kpc wobbling with sigma_DM = 0.1 cm^2/g. We'll want to be able to measure the offset to this level. It'll be interesting to see how precisely fitting beta models to the X-ray profiles will predict the X-ray center as that will be our largest systematic.

To get to ~ 10 kpc, we shouldn't go too high in redshift. As a concrete example, MACS J1149 has a redshift of 0.55, and 1" = 6.4 kpc. What is your gut feeling of how precisely (in arc seconds) we can estimate the X-ray peak via fitting beta models to the X-ray surface brightness? This answer will inform our redshift cut.

[nrgolovich]

One issue is optical imaging. X-ray clusters could be anyway, so what will be the best available imaging for clusters? SDSS and DES should be sufficient when the overlap takes place. After that...? We can check the Subaru archive where necessary and also perhaps resort to DSS plates, which is not ideal but might be good enough to locate the BCG in low redshift clusters at least. I've used it for targeting DEIMOS slitmasks for clusters up to redshift 0.3 in the past.

@stacykim mentioned that @rhw may be interested in the DES angle. I'd be happy to involve her for this aspect.

@esrabulbul, a list of relaxed clusters is first priority, but the first order cut we can make is to search within those survey footprints.

[stacykim]

No worries---thanks for getting the post-workshop discussion started, Nate! As for the scaling of the BCG oscillation amplitudes with cross section under zero impact parameter, I've attached a figure that shows the BCG orbits (keep in mind that two BCGs are oscillating in the core, so if you followed one of them, it'd generate every other arc on the plot). You can see that the oscillation amplitude is roughly 300 kpc for 10 cm^2/g and 100 kpc for 1 cm^2/g. That's roughly the size of the constant-density cores at the centers of the merger remnants. We haven't run any 0.1 cm^2/g sims (though I can do this easily enough to check), but the core sizes you'd expect would be around 10 kpc.

[nrgolovich]

@stacykim This is great. It's way more direct of a signal right at sidm than merger offsets which have a ton of systematics and other issues like the one you pointed out in your paper, the dark matter tails that form rather than all of the momentum going into a bulk offset.

Thanks for this

[esrabulbul]

@nrgolovich I think the precision on X-ray locations will be quite high. The systematics we should worry are due to point spread function and astrometry. Both are below arcsec for Chandra. To avoid poissonian systematics to dominate the results, we should avoid high-z clusters and focus on nearby well-exposed clusters instead. @stacykim @nrgolovich One things I worry is to distinguish this BCG displacement from other astrophysical effects. For example, sloshing of the core would create a (perhaps) similar displacement (see http://adsabs.harvard.edu/abs/2013ApJ...762...78Z). Any insights on this?

[stacykim]

@esrabulbul That's a good point. Based on a quick skim of the paper, it sounds like the gas sloshing is induced by mergers. My first thoughts are that in the specific case of equal mass mergers, there should be no sloshing due to the symmetry of the merger---the momenta of the colliding gas clouds are equal and opposite, so they'd cancel without sloshing. For unequal mass mergers though, where there is no such symmetry, I could see it becoming important, and the relevant question becomes how quickly the sloshing would damp. By any chance, do you know what that timescale might be? I'm not very familiar with the gas sloshing literature, so if anyone has other thoughts, please jump in! In any case, @ahgpeter and I are planning to think about this more... thanks for pointing it out!

To all---spring break has started at OSU, and I'll be traveling all week. I'll try to keep pushing on this project when I have time, but my responses might be a little slow (including more answers to your questions, @nrgolovich!). Apologies in advance! I should be back in full contact the week after.