An analytic post-Newtonian method for detecting general relativistic effects in the S stars

The motions of stars in the inner 0.1 pc of the Galactic Center, known as S stars, have played a crucial role in identifying and characterizing the supermassive black hole (SMBH) at the center of the Milky Way (Sgr A*) and have even opened a pathway for probing general relativity (GR) itself. With the 2018 periapsis of the S0-2 star, groups studying the dynamics of the Galactic Center reported the first detections of GR effects (gravitational redshift and periapsis precession) in any S star orbit. The discovery of more S stars with potentially shorter periods and closer periapsis distances are anticipated with the debut of extremely large telescopes (ELTs) on the horizon. However, current methods of modeling the S stars are relatively slow and computationally expensive due to the numerical nature of the calculations. We have developed an analytic, first-order post-Newtonian (PN) method for modeling astrometric and spectroscopic observations of the S stars. Our model is extremely fast compared to existing numerical methods and does not accumulate integration errors. For the first time, our model will enable simultaneous, multi-star fitting of S star orbits to observations. Furthermore, the PN formalism allows for straightforward identification and modeling of the signatures of GR effects, which is important in both data analysis and observational planning. Our research suggests that the Shapiro effect – an additional GR effect not yet detected in S star orbits – could be detectable with ELTs during S0-2’s next periapsis passage in 2034. If a star with a shorter period than S0-2 is discovered, its Shapiro effect might be observable with current facilities. In addition to S star observations, our model also opens possible avenues for observing similar effects and/or searching for SMBHs in external galaxies.