The strong equivalence principle (SEP) distinguishes general relativity (GR) from other viable theories of gravity.
The SEP demands that the internal dynamics of a self-gravitating system under freefall in an external gravitational field should not depend on the external field strength. We test the SEP by investigating the external field effect (EFE) in Milgromian dynamics (MOND), proposed as an alternative to dark matter in interpreting galactic kinematics.
We report a detection of this EFE using galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog.
Our detection is threefold: (1) the EFE is individually detected at 8σ to 11σ in “golden” galaxies subjected to exceptionally strong external fields, while it is not detected in exceptionally isolated galaxies, (2) the EFE is statistically detected at more than 4σ from a blind test of 153 SPARC rotating galaxies, giving a mean value of the external field consistent with an independent estimate from the galaxies’ environments, and (3) we detect a systematic downward trend in the weak gravity part of the radial acceleration relation at the right acceleration predicted by the EFE of the MOND modified gravity.
Tidal effects from neighboring galaxies in the Λ cold dark matter (CDM) context are not strong enough to explain these phenomena. They are not predicted by existing ΛCDM models of galaxy formation and evolution, adding a new small-scale challenge to the ΛCDM paradigm. Our results point to a breakdown of the SEP, supporting modified gravity theories beyond GR.
Galaxies of similar properties but subjected to different external gravitational fields show noticeably different rotation-curve behaviors at large radii (i.e., at very low accelerations). Two galaxies in the strongest environmental fields show declining RCs in the outer parts, while two similar galaxies in the weakest environmental fields have flat RCs. The connection between internal dynamics and large-scale environment is corroborated by a statistical analysis of the entire SPARC sample.
At accelerations 10 times lower than g†, the RAR is not fully described by a simple function of gbar/g† (Equation (1)) but requires an EFE-incorporated generalized function with an additional free parameter e (Equation (6)). Moreover, rotation-curve fits with Equation (6) give a mean value of e that is indistinguishable from the mean environmental gravitational field at the location of SPARC galaxies, computed in a fully independent fashion from the average distribution of mass in the nearby universe.
These results are summarized in Figures 3 and 5. Note that these results of fitting Equation (6) to RCs are fully empirical, independent of any theoretical interpretation.
Can these results be explained in the standard ΛCDM framework? For the two golden massive galaxies subjected to strong large-scale gravitational field genv, declining RCs are observed over a radial range of about 30–50 kpc, which are less than ∼15% of the virial radius of the DM halo. Clearly, this is not the decline that should occur in the outer parts of ΛCDM halos, where the density profile decreases as r−3, since we are probing the inner parts of the halo where the density profile goes approximately as r−2, leading to flat RCs.
Thus, the only remaining option is represented by tidal forces. We calculated the expected tidal radii in ΛCDM using the formalism of King (1962), taking the source of the tidal field to be the nearest 2M++ galaxy to the SPARC galaxy in question. We assume the source and test galaxies to have Navarro–Frenk–White (Navarro et al. 1997) halos following the M⋆–Mvir relation of Kravtsov et al. (2018) and the Mvir−concentration relation of Diemer & Kravtsov (2015).
We find the tidal radii to be much larger than the last measured points of the RCs, so the galaxies themselves are effectively shielded against large-scale tides.
The agreement between the MOND fitting parameter e (Equation (6)) and the environmental gravitational field eenv is an unpredicted result from the ΛCDM point of view. In principle, the baryon plus DM combination can combine to produce a declining rotation curve within tens of kiloparsecs as found here (i.e., e > 0). For that matter, however, there is no a priori reason that the degree of declining must agree with the strength of the environmental gravitational field.
There could have been an order-of-magnitude difference between e and eenv. Yet, we are seeing an interesting coincidence between the two.
Moreover, a downward deviation in the RAR near a tenth of g† is not predicted by current ΛCDM state-of-the-art simulations or semianalytical models (Di Cintio & Lelli 2016; Desmond 2017; Keller & Wadsley 2017; Navarro et al. 2017; Tenneti et al. 2018) with some predicting the opposite trend (Ludlow et al. 2017; Fattahi et al. 2018; Garaldi et al. 2019). To the best of our knowledge, there is no reported scenario in which the DM–baryon coupling in the outskirts of the disks depends on the external gravitational field from the large-scale galaxy environment in the manner found here.
The empirical evidence is fully consistent with the EFE predicted by MOND modified gravity (Bekenstein & Milgrom 1984). More generally, our results suggest a violation of the SEP in rotationally supported galaxies. While in GR the internal dynamics of a gravitationally bound system is not affected by a uniform external field, our analysis indicates that external fields do impact the internal dynamics.
Our results are encouraging for modified gravity as an alternative (or modification) to the DM hypothesis and the standard ΛCDM cosmological model. They also highlight the path for future theoretical investigations of relativistic theories of gravity beyond GR (see, e.g., Skordis & Zlośnik 2020), possibly leading to a new cosmological model.
In this paper we provide observational evidence for the existence of the EFE (or a phenomenon akin to it) predicted by MOND modified gravity (Bekenstein & Milgrom 1984). We use accurate rotation curves and mass models from the SPARC database (Lelli et al. 2016) and detect the EFE in three separate ways:
1.
The EFE is individually detected in “golden” galaxies subjected to exceptionally strong external gravitational fields. The detection is highly significant (11σ in NGC 5055 and 8σ in NGC 5033) and the best-fit values of the external gravitational fields are fully consistent with the independent estimates from the large-scale distribution of mass at the galaxies’ location. Conversely, the EFE is not detected in control galaxies residing in the weakest external gravitational fields, as expected.
2.
The EFE is statistically detected at more than 4σ through a blind test using 153 SPARC galaxies. The mean value of the external gravitational field among the SPARC galaxies is again consistent with the independent estimate from the average distribution of mass in the nearby universe.
3.
The EFE also manifests as a small (≳0.05 dex), downward deviation from the empirical RAR occurring around 0.1g†. This behavior is not predicted by any of the existing galaxy formation models in ΛCDM that were proposed to “naturally” reproduce the RAR. In contrast, this downward deviation is predicted by the MOND modified gravity at the right acceleration scale.
Our results suggest a breakdown of the SEP: the internal dynamics of a gravitational system in freefall is affected by a uniform external gravitational field. This sheds new light on the dark-matter problem and paves the way for relativistic theories of modified gravity in the weak-field regime of gravity g ≲ 10−10 m s−2.
We thank the organizers of the conference Bonn-Gravity 2019 (Pavel Kroupa and Indranil Banik) where several of these issues were brought to light. We thank Andrey Kravtsov for providing a code to calculate tidal radii of ΛCDM halos.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1F1A1062477). H.D. is supported by St John’s college, Oxford, and acknowledges financial support from ERC grant No. 693024 and the Beecroft Trust. The Work of S.S.M. is supported in part by NASA ADAP 80NSSC19k0570 and NSF PHY-1911909.
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Einstein proposed his equivalence of gravity and acceleration based on: In a closed system no experiment can be done to distinguish between acceleration and gravity. Theories are not created based on negatives, although they cam be debunked by negatives. In fact experiments were proposed that could distinguish between gravity and acceleration but because Einstein was a superstar celebrity scientist these objections were ignored and the equivalence theory was accepted.
In a closed room if you if a beam of light is reflected between two walls, in a gravity field the position of the light beam will remain constant while in the accelerating container it will move down the walls as the walls move up while the light is in transit between the walls.
About GRAVITY Newton wrote (concluded) near the END of The Principlia (as translated by Motte): “But hitherto I have not been able to discover the cause of those properties of gravity from the phenomena, and I frame no hypothesis; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”
I believe this EXPERIMENTAL PHILOSOPHY is PHYSICAL SCIENCE.
Herb, I ask you (and anyone else). : What phenomena has been observed since Newton’s time which allows anyone to deduce (hypothesize) what the cause of GRAVITY might be???
For without such a phenomenon, Newton clearly stated that any such possible hypothesis has no place in PHYSICAL SCIENCE.
And Richard Feynman stated in a Caltech commencement address give in 1974 (“Surely You’re Joking, Mr. Feynman!”): “There is also a more subtle problem. When you have put a lot of ideas together to make an elaborate theory, you want to make sure , when explaining what it fits are not just the things that gave you the idea for the theory, but that the finished theory makes something else come out right, in addition.”
Now, I believe that this “something else” is a PREDICTION of something not yet OBSERVED (MEASURED), by which the proposed theory might be TESTED. And I understand that without such a PREDICTION the theory (hypothesis) has no place in PHYSICAL SCIENCE!!!
incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX.
Herb Rose
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Einstein proposed his equivalence of gravity and acceleration based on: In a closed system no experiment can be done to distinguish between acceleration and gravity. Theories are not created based on negatives, although they cam be debunked by negatives. In fact experiments were proposed that could distinguish between gravity and acceleration but because Einstein was a superstar celebrity scientist these objections were ignored and the equivalence theory was accepted.
In a closed room if you if a beam of light is reflected between two walls, in a gravity field the position of the light beam will remain constant while in the accelerating container it will move down the walls as the walls move up while the light is in transit between the walls.
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Jerry Krause
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Hi Herb and PSI Readers,
About GRAVITY Newton wrote (concluded) near the END of The Principlia (as translated by Motte): “But hitherto I have not been able to discover the cause of those properties of gravity from the phenomena, and I frame no hypothesis; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”
I believe this EXPERIMENTAL PHILOSOPHY is PHYSICAL SCIENCE.
Herb, I ask you (and anyone else). : What phenomena has been observed since Newton’s time which allows anyone to deduce (hypothesize) what the cause of GRAVITY might be???
For without such a phenomenon, Newton clearly stated that any such possible hypothesis has no place in PHYSICAL SCIENCE.
And Richard Feynman stated in a Caltech commencement address give in 1974 (“Surely You’re Joking, Mr. Feynman!”): “There is also a more subtle problem. When you have put a lot of ideas together to make an elaborate theory, you want to make sure , when explaining what it fits are not just the things that gave you the idea for the theory, but that the finished theory makes something else come out right, in addition.”
Now, I believe that this “something else” is a PREDICTION of something not yet OBSERVED (MEASURED), by which the proposed theory might be TESTED. And I understand that without such a PREDICTION the theory (hypothesis) has no place in PHYSICAL SCIENCE!!!
Have a good day, Jerry
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