1. Calculating Escape Velocities on 75,000 Double Star Systems Using Gaia Data Release 2
By Tol Wassman, Zachary Haarz, Morgan Watts, Jake North, and Kalée Tock

2. Double Stars Close together Confirm orbits & find mass
Washington Double Star catalogue (WDS) tracks these stars
Gaia improves our ability to tell binaries from optical doubles

3. Binary Stars Same distance from Earth: parallax (Plx)
Moving together in space: Proper Motion (PM), radial velocity (RV)
Relative motion less than escape velocity (vesc)

4. Richard Harshaw’s Data
Previous paper, also using Gaia data
Used parallax data, relative radial velocity, fit to R^2, and proper motion
Many stars did not have Gaia data
Created a spreadsheet with the scores

5. Matching WDS and Gaia Query Gaia around WDS coordinates
Guess and check:
Magnitude within 2
PA within 3o
Sep within 1’’
Algorithm:
Closer to WDS, better
Also PM, Dist to precise search coordinates wherever possible
Ideally obtain PMs, RVs, Lum/Mag, and Plxs

6. Separation

7. Velocities
Escape velocity needs mass, which needs luminosity, sometimes needs mag and plx
R is pythagorean theorem with tangential and radial separation
Relative velocity needs speeds which need Plx, PM, and RV

8. Z factor Z = Escape velocity/relative velocity
Z > 1.5 will be binary, Z < 0.5 will be optical
Simple range of 1.5 to 0.5 is nuanced range - looks best as Z - 0.5

9. Results Harshaw sorts stars without parallax, Z-Factor ignores them
68.5% optical doubles using Z-factor, and 16% using Harshaw’s method
Large difference in stars considered physical, considering omissions

10. Notes For Future Research
Small percent in between, binaries grow harsher over time?
Use orbital state vectors to determine theoretical orbits for binaries
Identify a more general stellar mass formula or refine the current one

11. Categories