New Way to Date Globular Clusters: Brown Dwarf Cooling Sequences

Abstract

As the oldest building blocks of our Galaxy, globular clusters retain the archaeological footprint of the early stellar environments. Accurate absolute ages of globular clusters are required to interpret this ancient record. Existing dating techniques often produce precise but discordant ages, suggestive of systematic errors in excess of 1 Gyr. The James Webb Space Telescope (JWST) has unlocked a new dating method that leverages the cooling behavior of previously unobservable brown dwarf members. With a largely independent set of systematic errors, this new method provides a new consistency test for more established methodologies. I present a likelihood-based histogram-free method to derive globular cluster ages from multi-band JWST photometry of cluster members near and below the hydrogen-burning limit. By applying the method to a large set of simulated observations, I establish that formal age errors (i.e. errors based on measurement uncertainties alone) under 0.2 Gyr are attainable for nearby globular clusters. I also evaluate the significance of associated systematic effects, including the chemical heterogeneity of globular clusters (multiple populations), unresolved binary systems and uncertainties in brown dwarf cooling rates. As with other methods of age determination, systematic effects dominate the error budget (in selected cases, by over an order of magnitude), but may be reduced with more sophisticated analysis. Finally, I provide a lookup table for determining the number of observations, exposure times and temporal baselines required to estimate the age of a given cluster to a prescribed precision.

Figures (9)

• Figure 1: Simulated luminosity function of a globular cluster with the metallicity and distance similar to those of 47 Tuc. Individual subplots show the evolution of the luminosity function with cluster age (age increases from left to right). The horizontal axis displays the apparent magnitude in the F322W2 band of the Near Infrared Camera on JWST. In the legend, "BDs" refers to brown dwarfs. The vertical axis is scaled linearly with an arbitrary scaling factor.
• Figure 2: Theoretical mass-luminosity relationships (left) and color-magnitude diagrams (right), extracted from the SANDee stellar models for the average chemical composition of 47 Tuc. The "true" hydrogen-burning limit (HBL) of $0.077\ \mathrm{M}_\odot$ is shown for reference, as defined in SANDee.
• Figure 3: Top left: expected errors in the inferred proper motion (PM) of cluster members from NIRCam images as functions of the F322W2 magnitude, for different observing strategies. The intrinsic scatter in proper motion among cluster members ($0.5\ \mathrm{mas\ yr}^{-1}$) is shown with a horizontal line. Bottom left: expected errors in photometry for the two photometric bands considered in this study. Note that the expected errors in photometry (but not proper motion) are shown after the membership selection, as described in Section \ref{['sec:completeness']}. Estimates are not available for the faintest test stars, since none of those stars passed the selection criteria. Right: example of a simulated F322W2 observation of a $20$th magnitude star with NIRCam. In the legends, times in hours refer to exposure times, and baseline refers to the temporal baseline between the two observation epochs (ep).
• Figure 4: Left: estimated completeness of the observed luminosity function of 47 Tuc for different observing strategies. In the legend, observing strategies are denoted in the same way as in Figure \ref{['fig:errors']}. The magnitude of the hydrogen-burning limit (HBL) is shown for reference. Right: simulated color-magnitude diagram (left subplot) and luminosity function (right subplot) for $2\times1\ \mathrm{hr}$ exposures taken $5$ years apart. The theoretical luminosity function refers to the simulated luminosity function without measurement errors and completeness effects. The simulations in the right panel are shown for the age of $11.5\ \mathrm{Gyr}$. The luminosity function is shown on a linear scale with an arbitrary scaling factor.
• Figure 5: Model luminosity functions for 47 Tuc in F322W2 (left) and F150W2 (right) JWST NIRCam bands. The top, middle and bottom subplots show the effect of cluster age, high-mass power law slope and low-mass power law slope (see Equation \ref{['eq:powerlaw']}) on the luminosity function, respectively. The vertical axis is linear and has arbitrary normalization.