UR: Blue stars that should not exist

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Yanbo Pan

University of Michigan

Yanbo Pan is a third-year undergraduate studying astrophysics and statistics at the University of Michigan. This post describes research he completed during the summer at the University of Wisconsin-Madison under the supervision of Professor Robert Mathieu and graduate student Evan Linck. He plans to present these results at AAS244. You can check out Yanbo’s Homepage here.


When astronomers peek at open star clusters, they spot bright blue stars that should not exist based on the standard model of stellar evolution. Despite having high masses, blue stars are believed to have short lifetimes since these stars burn their fuel much more quickly than red stars. Explaining these “blue stragglers” in old stellar systems is a challenge for astronomers. The popular idea is these blue straggler stars (BSS) originated from interactions between two stars orbiting each other, known as binary stars, such as colliding, merging, and exchanging mass.

Fig 1: Artistic Rendering of a Blue Straggler under Mass Transfer. The red giant star is losing its outer envelope, which forms an accretion disk around its blue companion. Eventually, the envelope of the red giant star will be shed, leaving only its white dwarf core behind, while its companion becomes a blue straggler star. Image credit: Aaron M. Geller

Therefore, modeling binary orbits is crucial for understanding BSS formation and evolutionary processes. In this study, we applied The Joker¹ (a customized Monte Carlo rejection sampler² for the two-body problem) to model binary orbits in the WIYN Open Cluster Survey (WOCS).

Our objective was to test The Joker’s prediction efficacy on binary orbits with limited radial-velocity data (RVD). Radial-velocity tells us how fast the stars are moving about their center of mass along our line of sight. Thus, it is an important physical quantity for understanding motions in binary systems. In many cases, the bright star will outshine the faint star in the binary system, so astronomers only have access to the velocities of the bright star. This is also known as a single-lined binary system, and the single-lined binary system is the focus of our study.

Exploring the potential usage of The Joker, designed for sparsely measured radial-velocity data, we applied it to known single-lined binary orbits in the open star clusters M67 and NGC 188. Analyzing 70+ binary systems, we compared our Joker orbital parameters (period, eccentricities, inclinations, and more) among binary systems with diverse combinations of period, eccentricity, and number of RVDs.

Fig 2: Example of a well-fit orbital solution with only 7 radial-velocity data (RVD). The solution is phase-folded, aligning data from multiple cycles of a periodic event. Previous studies usually require 10-12 RVD to estimate orbital solutions. The x-axis (orbital phase) describes the position of the star around the center of mass of the binary system, calculated as a portion of its complete orbit. The legend gives the period and eccentricity estimate and the dashed line marks the center of mass radial velocity.

Despite requiring more data, previous findings using the direct integrator provide more precise estimates of orbital parameters, while The Joker provides useful orbit solution estimates even when there are only a few radial-velocity measurements present.  So, we are interested in whether our method agrees with previous results done on the same stellar population. We found 5-7 RVD start to meaningfully constrain orbital parameters, and 8-10 RVD are required for unimodal period solutions (catch the biggest catfish in the pond) with eccentricities converging to previous studies’ solutions.

Additionally, we explored the possibility of devising plans to observe binaries that have limited prior measurements using The Joker to predict possible periastron approach times (when the measured star is moving fastest in its orbit) to constrain eccentricity and hint at the underlying physics of the binary stars. This work enables us to estimate binary orbital solutions with fewer RVD and to enhance our understanding of the alternative evolutionary tracks of binary systems.

Fig 3: The Color-Magnitude Diagram of the open cluster M67 in the WOCS survey with a limiting magnitude of V=16.5. This diagram shows different classes of stars present in M67. Stars that have taken alternative evolutionary pathways (blue stragglers, yellow stragglers, and sub-subgiants) are labeled. From the classical stellar evolution theory, blue straggler stars are too old to exist. However, binary star interactions allow these cluster members to exist. Image credit: Emily Leiner

¹Fun fact: The Joker is short for Johannes Kepler and pronounced accordingly [YO-ker] /’joʊkər/

²Rejection sampling works like catching catfish in a lake. We cast a wide net to catch 10 million fish at once and only keep the catfish we are looking for and let the rest go. In this research, we are catching the orbits that fit our data the best.

Featured Image Credit: Aaron Geller

Astrobite edited by: Emma Clarke

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