TY - JOUR

T1 - Test of the equivalence principle for galaxy’s dark matter by lunar laser ranging

AU - Zhang, Mingyue

AU - Müller, Jürgen

AU - Biskupek, Liliane

N1 - Funding Information: Current LLR data are collected, archived and distributed under the auspices of the International Laser Ranging Service (ILRS) (Pearlman et al. ). We acknowledge with thanks that 50 years of processed LLR data have been obtained under the efforts of the personnel at the Observatoire de la Côte dAzur in France, the LURE Observatory in Maui, Hawaii, the McDonald Observatory in Texas, the Apache Point Observatory in New Mexico, the Matera Laser Ranging station in Italy, the Wettzell Laser Ranging System in Germany. This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2123 QuantumFrontiers, Project-ID 390837967. Further financial supports were from the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB23030100 and XDA15017700) and the National Natural Science Foundation of China (Projects No. 41704013). We are very thankful to Franz Hofmann who calculated the LLR residuals used in this paper and to Hu Wu who gave many precious advices. Sergei Kopeikin provided valuable hints for improving the final manuscript.

PY - 2020/5/14

Y1 - 2020/5/14

N2 - Having 50 years of unique observations, lunar laser ranging (LLR) is used to test central elements of Einstein’s theory of relativity, like a possible temporal variation of the gravitational constant or metric parameters. Here, we focused on a possible violation of the equivalence principle (EP) due to assumed dark matter in the galactic center. According to the EP, Earth and Moon experience the same acceleration in the gravitational field of any matter including the galactic dark matter. In the latter case, a violation of the EP would cause an Earth–Moon range oscillation with a sidereal-month period. Recent LLR measurements with high accuracy give us the opportunity to carry out high-precision EP tests for dark matter. We estimated the amplitude of a possible sidereal range oscillation from LLR post-fit residuals. First, we analyzed the characteristics of the residuals for each station and selected a subset of best LLR data. Using this dataset, we obtained 0.6 ± 1.0 mm (realistic error) as a final result for the sidereal amplitude in the direction of the galactic center. It strongly limits a possible violation of the EP for galaxy’s dark matter. Our investigations also show that, for the EP test, a good orbit coverage with good data is more relevant than the number of data or a long time span. As verification, a spectral analysis of the non-uniform LLR residuals has been performed. There again, no significant sidereal signal was found, confirming our previous result.

AB - Having 50 years of unique observations, lunar laser ranging (LLR) is used to test central elements of Einstein’s theory of relativity, like a possible temporal variation of the gravitational constant or metric parameters. Here, we focused on a possible violation of the equivalence principle (EP) due to assumed dark matter in the galactic center. According to the EP, Earth and Moon experience the same acceleration in the gravitational field of any matter including the galactic dark matter. In the latter case, a violation of the EP would cause an Earth–Moon range oscillation with a sidereal-month period. Recent LLR measurements with high accuracy give us the opportunity to carry out high-precision EP tests for dark matter. We estimated the amplitude of a possible sidereal range oscillation from LLR post-fit residuals. First, we analyzed the characteristics of the residuals for each station and selected a subset of best LLR data. Using this dataset, we obtained 0.6 ± 1.0 mm (realistic error) as a final result for the sidereal amplitude in the direction of the galactic center. It strongly limits a possible violation of the EP for galaxy’s dark matter. Our investigations also show that, for the EP test, a good orbit coverage with good data is more relevant than the number of data or a long time span. As verification, a spectral analysis of the non-uniform LLR residuals has been performed. There again, no significant sidereal signal was found, confirming our previous result.

KW - Dark matter

KW - Earth–Moon range oscillation

KW - Equivalence principle

KW - Lunar laser ranging

UR - http://www.scopus.com/inward/record.url?scp=85084660006&partnerID=8YFLogxK

U2 - 10.1007/s10569-020-09964-6

DO - 10.1007/s10569-020-09964-6

M3 - Article

AN - SCOPUS:85084660006

VL - 132

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 4

M1 - 25

ER -