An Adaptive Scheduling Tool to Optimize Measurements to Reach a Scientific Objective: Methodology and Application to Measurements of Stellar Orbits in the Galactic Center

Abstract

In various fields of physics and astronomy, access to experimental facilities or to telescopes is becoming more and more competitive and limited. It becomes therefore important to optimize the type of measurements and their scheduling to reach a given scientific objective and to increase the chances of success of a scientific project. In this communication, extending the work of Ford (2008) and of Loredo et al. (2012), we present an efficient adaptive scheduling tool aimed at prioritzing measurements in order to reach a scientific goal. The algorithm, based on the Fisher matrix, can be applied to a wide class of measurements. We present this algorithm in detail and discuss some practicalities such as systematic errors or measurements losses due to contigencies (such as weather, experimental failure, . . . ). As an illustration, we consider measurements of the short-period star S0-2 in our Galactic Center. We show that the radial velocity measurements at the two turning points of the radial velocity curve are more powerful for detecting the gravitational redshift than measurements at the maximal relativistic signal. We also explicitly present the methodology that was used to plan measurements in order to detect the relativistic redshift considering systematics and possible measurements losses. For the future, we identify the astrometric turning points to be highly sensitive to the relativistic advance of the periastron. Finally, we also identify measurements particularly sensitive to the distance to our Galactic Center: the radial velocities around periastron and the astrometric measurements just before closest approach and at the maximal right ascension astrometric turning point.

First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric

“…Nearinfrared (NIR) observation with 8-10 m class telescopes supported by adaptive optics (AO) revealed the orbits of individual stars in the innermost arcsec (the so-called S stars), in particular the star S0-2. 149 For this star, the combined fit for orbital elements and black hole parameters (mass, distance, projected position in the sky, proper motions, and radial velocity) has provided the most precise estimates for Sgr A * 's mass and distance so far (Schödel et al 2003;Eisenhauer et al 2005;Ghez et al 2005bGhez et al , 2008Gillessen et al 2009aGillessen et al , 2009bGillessen et al , 2017Meyer et al 2012;Boehle et al 2016;Chu et al 2018;Hees et al 2019;O'Neil et al 2019;Gravity Collaboration et al 2021a).…”

Probing Modified Gravity Theories with Scalar Fields Using Black-Hole Images

“…Two different instruments, the Keck Observatory and the Very Large Telescope, together with the interferometer GRAVITY (VLTI), were used to study the orbits of individual stars around Sagittarius A * . The brightest star observed, S0-2, with a period of 16 years, has helped scientists test relativistic effects, such as gravitational redshift and the Schwarzschild precession [133][134][135][136], and to constrain alternative theories of gravity [137][138][139]. Its observation has also provided the most accurate measurements so far of the mass and distance of Sagittarius A * .…”

Constraining modified gravity theories with scalar fields using black-hole images

“…Two different instruments, the Keck Observatory and the Very Large Telescope together with the interferometer GRAVITY (VLTI), were used to study the orbits of individual stars around Sagittarius A * . The brightest star observed, S0-2, with a period of 16 years, has helped scientists to test relativistic effects such as gravitational redshift and the Schwarzschild precession [102][103][104][105] and to constrain alternative theories of gravity [106][107][108]. Its observation has also provided the most accurate so far measurements of the mass and distance of Sagittarius A * .…”