Project Background

My research interest in stars is broadly catagorized into Galatic Archeology (GA). This field is concerned with understanding the formation and evolution of galaxies. We often use the Milky Way as a local analog for interpreting more distant galaxies. This is a consequence of convenience because the Milky Way is the easiest to observe stellar popullations. In some repsect, stars are the bedrock of how we do observational astronomy . They are photon generating engines which we use to understand the Universe.

Galactic Archeology is divided into simulations and observations. These two approaches mutually beneifical to each other and have complementary pros and cons. My current research focuses on observational GA (hereafter GA will refer to observational GA unless noted otherwise).

A key challenge in GA is the timescale over which information must be preserved. If our current age estimates are correct, the Milky Way is ~12 Gyo. The other problem is mixing, as the Galaxy evolves stars move around either from secullar processes (e.g. tidal forces, settling) or more violent events like mergers with other galaxies.

In the context of GA, we require properties of stars which change very slowly, on Gyr timescales. Presently, I am aware of only two traits which could change on this timescale i) the kinemtatics of the star (often thought of in phase space) and ii) the chemical composition of the stars (by this I mean the composition of the photosphere). There are numerous caveats with both. I will probably detail some of these in later posts.

Intuitively, we expect stars formed from the same gas at the same time and evolving under the same environmental conditions to be similar. Differences can arise from the stars having different masses (and therefore having different evolutionary tracks on the HR diagram and lifetimes), difficulties with measuring chemical abundances, and so on. Freeman et al 2002 hypothesize that if the chemical make up of all stars in some group are identical and the abundance pattern for each group is unique, then we could undo the mixing of stellar populations within the Galaxy and reconstruct the progenitor groups. This hypothesis is called chemical tagging.

My research involves testing the first requirement in chemical tagging. Stars which are born together (meaning from the same giant molecular cloud) are conatal and star which are the same age are coeval. In the Solar neighborhood (which extends out to roughly 200 pc), from some simulations of the Milky Way, we expect stars which are co-moving (i.e. they have similar 3D velocities) are likely conatal even if they have large 3D separations (e.g. less than 40 pc). My work is investigating how similar these supposedly conatal stars are in chemical abundances.

We have observations of 37 co-moving pairs of F and G dwarfs. A large majority of these stars are stellar twins. We are seeking to measure precise differential abundances between these stars to see how chemically homogenous these co-moving stars are at different separations. I think of this work as an extension of the wide binary work done by other recent studies (e.g. Andrews et al 2019, Ramirez et al 2019, Hawkins et al 2020).

Plot specific background

We suspect there is a jump in the spread of the metalicity difference between the components of the co-moving pairs at ~10^6 AU or ~5pc. If we were to see a change in the spread in the metalicity difference at different separations it would mean that tagging might need additional position information to work at the same level provided we are actually using conatal stars(this violates the idea that we can do tagging solely with abundances). This is shown in the top panel of the visualization results 1 and 2 (the 2nd and 3rd images from the top of the page). Our working hypothesis is the jump arises from a change in the intrinsic scatter of metalicity as a function of separation. This post details some of my work to quantify this intrinsic scatter.

Each comoving pair has a 3D separation and Delta[Fe/H] with errors. The errors in metalicity are easy to account for during maximum likelihood estimation if they are gaussian since this coincides with the weighted least squares problem which yields an elegant analytic solution. The addition of errors on the independent variable (i.e. the separation) makes this problem essentially intractable analytically.

To overcome this barrier I used monte carlo sampling of the separation errors to generate many realizations of the observations. The premise of this method is performing the fit to many different version of the data can essentially allow us to envoke some form of the central limit theorem bypassing the analytic issues of this problem.

I described the errors of the separations as truncated normal distributions to ensure I could not draw negative separations. I also performed the fitting process with the logirthm of the separation because fitting over numerous orders of magnitude can be challenging for numeric methods. I expressed the intrinsic scatter as a quadratic function of the separation, this intrinsic scatter sigma was added in quadrature with the measurement errors in the measurement error for the difference in metalicity. I use Powell’s method during the mimization because the other minimization methods have trouble converging to a solution. I suspect arises from the numerical differentiation because the main difference with Powell’s method is the absence of derivatives.

Plot 1 Information

The function I fit was sigma(sep) = (a_1*sep + b_1)^2 + (a_2*sep + b_2)^2. All fits on this page use the same 10k realizations for the co-moving pairs. The first image on the page is a corner diagram of the fit coefficients. The input to this plot were a set of the optimial coefficients for each realization. The diagram shows the joint and marginal distributions of the coefficients. There is a clear bimodality in the marginal distributions for a_1, b_1, b_2. I beleive these arise from the two linear polynomials trading values in sigma intrinsic. With this in mind, I have attempted a constrained fit, imposing an ordering on the b_1, b_2 terms however the minimization algorithm does not seem able to move from the starting point at the moment. Perhaps this is from not using Powell’s method.

Plots 2 and 3

Both images display sanity checks on the fitting process, with the data being fit shown in the top panels of both images. The bottom panel of image 2 is a quick and dirty way to inspect the quality of the fit. In blue are the measurement errors on Delta[Fe/H], the orange is a windowed standard deviation of the Delta[Fe/H] which in some sense tries to imetate what our eyes are doing in picking out the spread. There are problems with this naive windowing, namely that it does not handle separations gracefully. It is likely flawed because it is mixing apples and oranges but remains a good starting point. The black, magneta, and green markers are found as follows: i) we take the sigma intrinsic fits for all realizations and evaluate the sigma function at each separation, ii) for each separation we take the 50th, 84th, and 16th percetile of the sigma intrinsic functions generated. This approximates the best value +/- 1 sigma of the sigma intrinsic fit. The third visualization plots the median sigma intinsic values from the bottom panel of image 2 over the data we are fitting. I thought it would look too cluttered with the three intervals all superimposed so I have not included all of them here.

Interpretation of Plots

Provided the analysis is correct, we see a small increase in the spread function between the closest and furthest separations, going from ~0.077 dex to ~ 0.09 dex. The increase is more muted for the 16th percentile changing by ~0.005 dex over the 2 orders of magnitude. The 84th percentiles show a more pronouced change of ~0.03 dex over the separations probed. Visually, it looks like the ~5pc separation is where the slopes start to increase perhaps incidating different processes driving the differences in the less than 5pc and greater than 5pc regime.

Future questions

If there’s a good chance of stars being conatal out to 40pc why do we see this uptick at 5 pc. What is the significance of this separation? How depended are these results on the position of the first pair with Delta[Fe/H] greater than or equal to ~0.2 dex?