Orbits of bright stars near the Galactic Centeras a tool to test gravity theories

А.Ф. Захаров (Alexander F. Zakharov)E-mail: zakharov@itep.ru
Bogoliubov Laboratory of Theoretical Physics
Joint Institute for Nuclear Research, Dubna, Russia

23.08.2021
Twentieth Lomonosov Conference on Elementary
Particle Physics
MSU, Moscow, Russia• Ya. B. Zeldovich: I dislike the no hair theorem

The Royal Swedish Academy of Sciences has decided to award the Nobel Prize inPhysics 2020 to Roger Penrose, University of Oxford, UK, Reinhard Genzel, Max
Planck Institute for Extraterrestrial Physics, Garching, Germany and University ofCalifornia, Berkeley, USA, and Andrea Ghez, University of California, Los Angeles,USA.
With one half to Roger Penrose, University of Oxford, UK“for the discovery that black hole formation is a robust prediction of the general
theory of relativity”
and the other half jointly toReinhard Genzel, Max Pla nck Institute for Extraterrestrial Physics, Garching,
Germany and University of California, Berkeley, USA, and Andrea Ghez, Universityof California, Los Angeles, USA“for the discovery of a supermassive compact object at the centre of our galaxy”
Black holes and the Milky Way’s darkest secretThree Laureates share this year’s Nobel Prize in Physics for their discoveries about oneof the most exotic phenomena in the universe, the black hole. Roger Penrose showedthat the general theory of relativity leads to the formation of black holes. Reinhard
Genzel and Andrea Ghez discovered that an invisible and extremely heavy object
governs the orbits of stars at the centre of our galaxy. A supermassive black hole is theonly currently known explanation.

“The discoveries of this year’s Laureates have broken
new ground in the study of compact and supermassiveobjects. But these exotic objects still pose manyquestions that beg for answers and motivate future
research. Not only questions about their inner structure,
but also questions about how to test our theory ofgravity under the extreme conditions in theimmediate vicinity of a black hole”, says David
Haviland, chair of the Nobel Committee for Physics.

Outline of my talk
• Nobel prize in Physics in 2020
• Introduction• Bright star trajectories around BH at GC as a toolto evaluate BH parameters and DM cluster• Constraints on massive graviton theories• Forecasts for graviton mass improvements• Constraints on tidal charge• Applications for current and forthcoming
observations• Conclusions

References•
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AFZ, F. De Paolis, G. Ingrosso, and A. A. Nucita, New Astronomy Reviews,
56, 64 (2012).
D. Borka, P. Jovanovic, V. Borka Jovanovic and AFZ, Physical Reviews D,
85, 124004 (2012).
D. Borka, P. Jovanovic, V. Borka Jovanovic and AFZ, JCAP 11, 050 (2013).
AFZ, Physical Reviews D 90, 062007 (2014).
AFZ, D. Borka, P. Jovanovic, V. Borka Jovanovic, Advances in Space
Research 54, 1108 (2014).
AFZ, J Astrophys. Astron. 36, 539 (2015)
AFZ , P. Jovanovic, D. Borka, V. Borka Jovanovic, gr-qc: 1605.00913v;
JCAP (2016)
AFZ, P.Jovanovic, D. Borka, and V. Borka Jovanovic, JCAP (2018).
AFZ, EPJ C (2018)
AFZ, IJMPD (2019)
P. Jovanovic, D. Borka, V. Borka Jovanovic, AFZ, EJPD (2021)

Three Nobel prizes in last four years (2017, 2019,2020)• LIGO-Virgo: BBHs, BNS (kilonova) GW 170817;• GRAVITY, Keck and new tests of GR (gravitational
redshift for S2 near its periapsis passage)• EHT and M87* images• The confirmation of relativistic precession for S2(GRAVITY)Reinhard Genzel, Prof. Dr.
Max Planck Institute for Extraterrestrial Physics, Garching
Curriculum Vitae
Born on March 24, 1952 in Bad Homburg v.d.H. Study of physics Bonn Univ.,
doctorate Max Planck Institute for Radioastronomy Bonn (1978), Postdoctoral
Fellow, Harvard-Smithsonian Center for Astrophysics (1978-1980), Cambridge, MA,
Associate Professor of Physics and Associate Research Astronomer, Space Sciences
Laboratory, University of California, Berkeley (1981- 1985), Full Professor ofPhysics, University of California, Berkeley (1985-1986), Director and Scientific
Member at the Max Planck Institute for Extraterrestrial Physics (since 1986),
Honorary Professor Munich Univ. (since 1988), Full Professor of Physics Universityof California Berkeley (since 1999).

American citizen. Born 1965 in
New York City, NY, USA. Ph.D.
1992 at California Institute ofTechnology, Pasadena, CA, USA.
Professor at University ofCalifornia, Los Angeles, CA, USA.

Four woman against more than 200 men• Ho1• Ho2

Black holes in centers of galaxies(L.Ho,ApJ 564,120 (2002))

R. Hooke’s “proof” that F ~1/r2
could explain Kepler’s laws, German Aerospace Center(Robert Hooke Strasse, 7)

A. N. Kolmogorov, A.M. Obukhov, V. I. Tatarskii developed
mathematical foundations of AO (based on conversations withPaul Hickson (University of British Columbia))

P. L. Kapitsa (1946): "A large number of the largest
engineering initiatives were born in our country. We
have almost never been able to develop themourselves... Often the reason for not using innovation isthat we usually underestimated our own andoverestimated foreign ones. Usually, organizational
shortcomings prevented our technical pioneer workfrom developing and influencing the world technology.
Many of these shortcomings exist to this day, and one of
the main ones is the underestimation of their own andoverestimation of foreign forces.”In 2003, Nobel laureate Reinhard Genzel, right, posed with his mentor, Charles Townes, who won
a Nobel Prize in Physics for invention of the laser. Townes, who died in 2015, and Genzel
collaborated on some of the first observations of the galactic center, later shown by Genzel andNobel co-winner Andrea Ghez to host a supermassive black hole. (2003 UC Berkeley photo)“Charlie Townes’ dream was to do this experiment we have done, already in the 1970s,” he said.
“And he, in fact, did these fantastic, pioneering experiments. But (when he saw) the results, heknew he would never get to the galactic center, which was a real disappointment to him.”

Ch. H. Townes

Large telescopes, AO and brightstars in IR

Keck TelecopesThe VLT, Very Large Telescope
4 european 8 m telescopes at Cerro Paranal in Chili

l/D @ 2 µm = 60 mas (600 a.u. or 0.003 pc)

Going beyond boundaries thanks to accurate
spatial information•••

Bring the ultimate evidence that Sgr A* is a black hole: the mass is
contained in the Schwarzschild radius.
Understand the nature of flares.
Use the black hole as a tool to study general relativity in the strong fieldregime10 µasScale ~ 1 Rs••

Study relativistic effects on nearby stars
Understand the nature of S stars and their distribution

Scale ~ 100 Rs

1 mas

AFZ, A.A. Nucita, F. De Paolis, G. Ingrosso, PRD 76, 062001(2007)

D. Borka, P. Jovanovic, V. Borka Jovanovic and AFZ, PRD, 85,124004 (2012).

D. Borka, V. Borka Jovanovic, P. Jovanovic, AFZ
From an analysis of S2 orbit one can find signaturesof Yukawa gravity (JCAP, 2013)Massive graviton theories• M. Fierz and W.Pauli-1939• Zakharov; Veltman, van Dam – 1970
• Vainshtein - 1972
• Boulware, Deser -- 1972
• Logunov, Mestvirishvili, Gershtein et al.
• Visser – 1998 (review on such theories)• Rubakov, Tinyakov – 2008
• DeRham --2016Constraints on graviton mass fromS2 trajectory• AFZ, D. Borka, P. Jovanovic, V. Borka Jovanovic grqc: 1605.00913v; JCAP (2016) :• λg > 2900 AU = 4.3 x 1011 km with P=0.9 or• mg < 2.9 x 10-21 eV =5.17 x 10-54 g• Hees et al. PRL (2017) slightly improved ourestimates with their new data mg < 1.6 x 10-21 eV(see discussion below)

Impact of our studies
Claudia de Rham, J. Tate Deskins, Andrew J. Tolley, ShuangYong Zhou, Graviton Mass Bounds, Reviews in Modern
Physics 89, 0250004 (2017).
A. Hees, T. Do, A. M. Ghez, G. D. Martinez, S. Naoz, E. E.
Becklin, A. Boehle, S. Chappell, D. Chu, A. Dehghanfar, K.
Kosmo, J. R. Lu, K. Matthews, M. R. Morris, S. Sakai, R.
Schodel, and G. Witze, Testing General Relativity with stellar
orbits around the supermassive black hole in our Galactic
center, arXiv:1705.07902v1 [astro-ph.GA], PRL 118,211101.
A couple of our papers have been quoted in the second paper.

Graviton mass estimate improvement forecastGRAVITY result about PN(1) correction
for gravitational redshift• For orbital precession f=0.94 ± 0.09 (2018)• R = 8178 ± 13stat. ± 22sys. parsecs• Mass = 4.154 ± 0.014*10^6 solar masses
f = 1.04±0.05• Gravity Collaboration 2019, A&A, 625, L10•

Keck group: Do et al., Science 365, 664–668 (2019) 16 August 2019
• f= 0.88 ± 0.17, is consistent with generalrelativity (f = 1) and excludes a Newtonianmodel (f = 0) with a statistical significance of 5 σ.

Results from nine (!) our papers were used

Relativistic precession of S2 (see the cover
page of the Bergman’s book)An alternative potential for ellipticaltrajectoriesBertrand’s theorem
There are only two central potentials where allbounded orbits are closed and elliptical (L&L,Mechanics; Arnold, 1989)
UOH (r) = a r2 (a>0) (harmonic oscillator
potential)
andUN(r) = - k/r (Newtonian potential)

The smallest angle between apocenter andpericenter• ΦOH=π/2• ΦN=πIf astronomers monitor quasi-elliptical trajectories of stars with higheccentricities it is very easy to distinguish UOH (r) and UN(r)potentials since in the case of the RAR potential stars centers of ellipses
should coincide with the Galactic Center while in the case of theNewtonian potential stars foci of the ellipses coincide with the Center.
Orbital periods of stars moving in the harmonic oscillator potential areconstant and they do not depend on semi-major axis. Even in the case if theGalactic Center position is not accurately known in respect to quasielliptical trajectories, a set of trajectories with high eccentricity clearly
showed that the Newtonian potential is preferable and stars are movingaround a common focus but not around a common center (Zakharov, 2021)

The most important conclusions• C. Will (1986,1993): “Was Einstein right?”• T. Damour (1994): “Was Einstein 100% right?”• C. Will(2020): “Is Einstein still right?”• Taking into account all experiments and observations• (including observations of bright stars near
BH@GC) at the moment one could say “Einsteinwas 100% right”• It has been proven that 4*106 M☉ is located inside 40
A.U. (Solar system size)• We put several small bricks in the Great Wall ofknowledge about BH @ GC• 2019: Observers operating largest telescopeswith AO use our ideas to constrain parametersof alternative theories of gravity• 2020: GRAVITY showed that precession of S2star follows GR predictions• 2020: Keck constraints on fine structure
constant

Main conclusions• The gravity law near the BH @ GC has to follow GR (at leastat the first PN-approximation). It leads from S2 precession andgravitational redshift the near pericenter passage• We found graviton mass constraints which are comparablewith LIGO’s ones
• The observers working with largest telescopes with AO (Keck,VLT, GRAVITY, TMT, E-ELT) follow our ideas to improvecurrent graviton mass constraints with current and forthcoming
facilities. The current graviton mass LIGO constraint will beoutperformed with current GRAVITY observation (privatecomm.)• The observers use our ideas to constrain parameters ofalternative theories of gravity with observations of bright stars
near GC• Conclusions• Studies of great mathematicians (Kolmogorov, Penrose…) could
have a giant practical impact in physics and technology• Trajectories of bright stars or bright spots around massive BHs
are very important tool for an evaluation of BH parameters• Trajectories of bright stars or bright spots around massive BHs
can be used to obtain constraints on alternative theories ofgravity (f(R) theory, for instance)• Constraints on Yukawa potential has been found• Constraints of graviton mass have been obtained (they areconsistent with LIGO ones)• Perspectives to improve the current graviton mass estimateswith future observations (VLT, Keck, GRAVITY, E-ELT, TMT)
are discussed• If an accuracy of the observations will be improved one should
not need to observe entire quasi-elliptical orbit to test
gravitational potential• Constraints of tidal charge have been obtained• The harmonic oscillator potential UOH (r) is not suitable for GC• Thanks for your kind attention!

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