References

References and short summaries from selected morning discussions... (those for which the discussion leader acted and provided some material here...). Direct Links to Anchors: March 20, Dynamical Evidence for IMBHs in Globular Clusters March 18, Multiple Populations tutorial (The Observations) March 16, GC Fundamental Plane March 11, GC Orbits and Disruption March 6, Tidal Tails of Globular Clusters March 5, Globular Cluster Formation February 25, Post-Newtonian Effects February 20, Spectral Modeling and Ages of Star Clusters



Friday, Mar 20, 11:00 a.m.: //Discussion: Dynamical Evidence for IMBHs in Globular Clusters (Discussion Leader: Eva Noyola)//
Observational ingredients for dynamical modeling: 1. Density profile: can come from star counts, integrated light, or a combination of both. Caveat: M/L estimations are always necessary to convert the observations into a light profile. 2. Kinematics: can come from proper motions or from radial velocities, both individual and integrated.

Types of dynamical models: 1. Based on solving the Jeans equation: can be done with a parametric or a non-parametric approach. 2. N-body, Fokker-Planck: can test the evolution of individual stars and test for stability of the system. 3. Schwarzschild models: based on orbital distribution. Good for testing anisotropy.

Individual objects discussed in detail: G1, omega Cen, M54, NGC 6752 (see for more details and references).



Wednesday, Mar 18, 11 am: //Discussion: Tutorial on Multiple Populations (Discussion leader: Alison Sills)//
Let's concentrate on the observations and see where they lead us.

And remember, we're ignoring w Cen.

Two lines of observations have pointed to multiple populations

1. Spectroscopic

(good overview: [|Gratton et al ARA&A 2004])

"Abundance anomalies" have been known in GCs since the 80's. These are star-to-star variations in light elements seen in basically all globular clusters that have been looked at carefully (e.g. [|Carretta et al 2008]). The variations are seen in giant branch stars, but also down to turnoff stars, so they cannot be the result of internal processes in the current stars: must be the result of stars being created from material with a variety of initial compositions

There is no star-to-star variation in iron & iron-peak elements (except w Cen, and we're ignoring that one, and possibly in M22).

Na is anti-correlated with O, in the sense that higher Na means lower oxygen. This is not seen in the field -- only high O, low Na stars are seen. Globular cluster stars show the full range. All clusters observed to date show some of this trend.

Al is anti-correlated with Mg. These elements are harder to observe than Na & O, so this is seen in fewer clusters.

C & N are also anti-correlated, in the sense of high N, low C in clusters. However, these elements get complicated, because a number of things are going on. First, we do see a trend of abundances with luminosity on the giant branch, pointing to evidence for internal mixing in the giants themselves bringing CNO-processed material to the surface (and this mixing must be more than just the traditional convection, which doesn't go deep enough). But we also see C-N variations down to the turnoff as well, meaning that pre-formation pollution is also present as well.

What does this mean? Because we have the CNO, NaNe, and AlMg cycles, these trends point to hot hydrogen burning. According to [|Prantzos et al 2007], it means that the most extreme material must have been subjected to hydrogen burning at temperatures of ~70-80 MK.

That's hot.

But you can get there in a) cores of massive main sequence stars (> 20 Msun) or b) hydrogen burning shells in AGB stars (5-10 Msun)

Then you need to get the processed material out before it undergoes He burning, since C+N+O is (basically) constant in these stars. Winds of AGB stars will do that for you. If your massive stars are rotating rapidly, they'll both mix well, and shed their outer layers as they rotate at or near break-up.

There is one measurement ([|Yong et al 2009]), in NGC 1851, of 4 very bright giants, in which the C+N+O content varies by a factor of 4, and that content correlates with increased s-process elements. This points strongly to an AGB star pollution source.

Two other points about spectroscopy -- Carretta et al 2008 point out that the extent of the spread in the Na-O anti-correlation is itself correlated with the maximum temperature of the HB stars in the cluster.

Also, they find a nice correlation between the spread and a combination of cluster mass and cluster galactic orbit, in the sense that more massive clusters which interact with the galaxy less strongly have a larger Na-O spread. While the errors on this correlation are probably large, this result makes me happy. Remember that the field halo stars do NOT show any Na-O anti-correlation, so if you believe that disrupted clusters formed the halo, they must be the clusters which did not have this second generation phenomenon.

2. Photometric

(see the talk by Giampaolo Piotto at the KITP conference for the largest collection of recent CMDs)

A few clusters have clearly-separated multiple main sequences (w Cen and 2808 each have 3 sequences, M54 seems to have more than one, 47 Tuc is claimed to have a wider main sequence than can be explained with photometric errors). The bluest sequence in w Cen has been shown to be the most metal-rich population (spectroscopically) leading to the conclusion that its blue colour comes from a high helium content. NGC 2808 in particular has a clear single turnoff, subgiant branch and giant branch (although there are indications that it may have fewer bright giants than one would expect, [|Sandquist 2007]). w Cen and M54 have very messy CMDs with multiples of almost all their sequences.

A larger number of clusters show no spread or split in their main sequence, but do show a clear split on their subgiant branch. The first of these was NGC 1851, which has a very clean main sequence with absolutely no width to speak of; the others (NGC 6388, NGC 5286, M22) don't have such excellent photometry down the main sequence yet but there's no evidence for split MSs here.

Interestingly, [| Pietrinferni et al 2009] claim that these two kinds of CMDs can be explained in the following way -- high Y produces a split MS, but constant Y with high C+N+O produces the split on the SGB only. They don't comment on the effect of these differences on the horizontal branch (see below).

One cluster, NGC 6397, has an incredibly good CMD, proper-motion-cleaned etc -- and a single sequence everywhere. It does, however, show a (small) spread in Na-O, and some claim that this cluster is a pure second-generation population.

Let us now turn our attention to the horizontal branch. It is important to remember that the HB can be thought of as a locus of constant core mass (M=0.48 Msun, pretty much independent of mass, metallicity, helium content, etc) and varying envelope mass. If the envelope is large, it shields the hot helium-burning core, and the star stays red; if the envelope is very thin, it can't do much to keep the energy produced in the core, and out it all comes at very high temperatures (i.e. blue stars). Therefore, the position of the star on the HB is dependent on the amount of mass lost on the RGB, and also the metallicity and helium content of the envelope (they essentially control how well the envelope can keep the energy of the He-burning core contained).

Understanding HB morphology has been a mess for 40 years or more, but it is quite conceivable that helium is the (or 'a') "second parameter". Francesca D'Antona has been working quite hard to understand the HB morphologies of clusters in the context of two or more helium contents in clusters, and I encourage you to see her talk for a more complete understanding.



Monday, Mar 16, 11:00 a.m.: //Open discussion: The Fundamental Plane of GCs (Self proclaimed discussion leader: Mario Pasquato)//
Results contained in [|Pasquato & Bertin 2008, A&A, 489, 1079] and related issues were discussed, in particular the physical meaning of GC Fundamental Plane in relation to virial equilibrium, the present day quality of the data used to build a GC FP, the correlation of residuals to the FP to the central surface brightness profile slopes measured by [| Noyola & Gebhardt 2006].



Wednesday, Mar 11, 11:00 a.m.: //Discussion: GC Orbits and Disruption (Discussion Leader: Aaron Romanovsky//
Link to [|Paper by Toshio Tsuchiya (2000)] on Orbital Deformation of Satellites by Dynamical Friction in Spherical Halos with Anisotropic Velocity Dispersion. Anybody please post conflicting or other papers following up our discussion on that topic.
 * //See detailed notes and references on Schedule page...//**



Tuesday, Mar 10, 11:00 a.m.: //Discussion: Measuring Density Profiles for Globular Clusters (Discussion Leader: Eva Noyola)//
We discussed the benefits and limitations of measuring density profiles from star counts and from integrated light. We also discussed the effect of measuring radii (r_c, r_h) using parametric fits to the measured profiles or using non-parametric analysis.

We focused on the results coming from measuring profiles from HST data. The details of the method and results for a sample of 38 Galactic globular clusters measured with integrated light can be found in [|Noyola & Gebhardt, 2006]. Profiles obtained using star counts have been obtained for a few clusters: M15 ([|Sosin & King, 1997]); [|Guhathakurta et al., 1996]), NGC 6752 ([|Ferraro et al., 2003]), omega Centauri ([|Ferraro et al., 2006]), NGC 6388 ([|Lanzoni et al., 2007])

Friday, Mar 6, 11:00 a.m.: //Discussion: Tidal Tails of Globular Clusters (Discussion Leader: Simone Zaggia)//
Discussion of tidal tails of Pal 5 - knots in tidal tails, detected by [|Odenkirchen et al. 2001]. [|Capuzzo-Dolcetta, Di Matteo and Miocchi 2005] simulate the generation of tails in a cluster encounter with the central regions of the galaxy and find clumps. [|Küpper, McLeod & Heggie (2008)] and [|Just et al. (2009)] examine in detail how such clumps can form through epicylclic motion even if the cluster is on a circular orbit.

Modelling of the tidal tails of NGC5466, paper of [|Fellhauer et al. 2007] mentioned by Simone Zaggia, these and similar simulations were done with the nice moving-multi-grid particle-mesh code Superbox, developed at the ARI in Heidelberg [|(Fellhauer et al. 2000)]. As a little advertisement (by R.S.) - this nice code has also been successfully used to model growth and saturation of global modes in numerical disks [|(Khoperskov et al. 2007).]



Thursday, Mar 5, 11:00 a.m.: //Discussion: Globular Cluster Formation (Discussion Leader: Jay Strader)//
A summary of the observational constraints and comments on scenarios for globular cluster formation can be found in the review of [|Brodie & Strader (2006)].

The slightly older review of [|Harris (2001]; from his 1998 Saas-fee lectures) is highly recommended, especially for the Milky Way globular cluster system. In fact, I don't think there is a better review, even though this one is now ~ 10 years old.

Here's a partial bibliography of papers on cosmological metal-poor GC formation:

[|Peebles (1984)] The original paper on GCs forming in little halos. [|Fall & Rees (1985)] GCs formed in thermal instabilities in hot halos. [|Rosenblatt et al (1988)]The first paper to tie radial distribution to initial overdensity. [|Bromm & Clarke (2002)] GCs form in minihalos that get erased (maybe). [|Cen (2001)] GCs formed in minihalos shocked by reionization. [|Diemand et al (2005)] Radial distribution gives formation at z >~ 12 in halos >~ 10^8 M_sun. [|Kravtsov & Gnedin (2005)] / [|Prieto & Gnedin (2008)] There are issues but this is close to my mental model. [|Mashchenko & Sills (2005)] Why DM halos in GCs are hard to see, even if they were there (why Ben Moore is wrong). [|Moore (1996)] Low M/L -> no DM. [|Scannapieco et al (2004)] Evan's model---GCs form in minihalos shocked by galactic winds.



Wednesday, Feb. 25, 11:00 a.m.: Discussion: Post-Newtonian Effects (Discussion leader: Rainer Spurzem)
Several recent astrophysical papers have used Post-Newtonian PN Dynamics as an approximation to describe the relativistic motion of two tightly bound bodies (typically: black holes) in a stellar dynamical cluster simulation. Pioneering models of [|Man-Hoi Lee (1993)] and on Black Hole Binaries in Galactic Nuclei [|(Aarseth 2003)] were followed by [|Kupi et al. (2006)] (runaway merger of black holes in dense cluster), and another paper on compact object binaries in star clusters [|(Aarseth 2007)]. A recent paper on the last parsec problem in binary black hole mergers [|(Berentzen et al. 2009)] leads from a 1kpc separation down to relativistic coalescence in one simulation. In the latter paper (and also in Kupi et al. 2006) the PN dynamics is used down to the actual coalescence of two black holes. //(Note that the recent citations in this paragraph are subjectively selected, the use of PN dynamics is quite widespread. Anybody is welcome to add further citations here).//

A discussion started about the validity of PN dynamics as compared to full numerical solutions of general relativity. Many talks from both sides can be found in the KITP program [|AGN06 on Active Galactic Nuclei in 2006.] A PN critical paper of the Cornell group is e.g. [|Mroue et al. (2008).] A consensus was reached that PN dynamics and PN waveforms break down at different stages near the last stable orbit, but that the astrophysical error in using PN dynamics till the last moment is very small due to the extremely short time scale involved for the last inspiral phases.

To derive Post-Newtonian Dynamics of two comparable masses from first principles (Einstein's Field Equations) is mathematically and conceptually very complex (at least for the discussion leader...). See excellent and detailed living review by [|Blanchet (2006)].[|Blanchet et al. 2006] and [|Faye et al. 2006] provide expressions for Spin-Spin and higher order Spin-Orbit Interactions in the framework of Post-Newtonian Dynamics, which also allow to follow the evolution of black hole spins. For a better physical understanding and motivation I presented here, however, the approach of [|Kannan & Saha (2009)], who consider test particle motion in a Kerr metric. See more details here.



Friday, Feb. 20, 11:00 a.m.: //Discussion: Spectral Modeling & Ages of Star Clusters (//Discussion leader: Peter Anders).
[|Analysing observed star cluster SEDs with evolutionary synthesis models: systematic uncertainties] (by Peter Anders, Nicolai Bissantz, Uta Fritze-v. Alvensleben, Richard de Grijs): describes the analysis tool I use to derive physical parameters from integrated cluster photometry, and tests of its reliability and accuracy under a range of assumptions Some plots from today's discussions:

[|NBODY meets stellar population - the HYDE-PARC Project] //(by Andrea Borch, Rainer Spurzem & Jarrod Hurley)//, paper re-submitted to Astron. & Astroph. after referee's report, preliminary working copy, since not yet accepted, copy 'as is', no warranty :-) . Present E-Mail Address of first author: borch@iiap.res.in