Presentation in the Science Coffee hosted by the Advanced Concepts Team of the European Space Agency on the 12.01.2024. Speaker: Benoit Famaey (CNRS - Observatoire astronomique de Strasbourg) Title: Modified Newtonian Dynamics Abstract: Presentation around the topic of MOND / tests of MOND

1. Modified Newtonian
Dynamics
Benoit Famaey
CNRS - Observatoire astronomique de Strasbourg

2. The actual need for Dark Matter
- CMB+large-scale structure => existence of a non-baryonic collisionless fluid
- Whatever it is: must reproduce (the successes of) ΛCDM on large scales
- Is cosmology solved? Is something missing? Is the devil in the details?
Dodelson 2011

3. Regularities in the
dynamics of galaxies
Tully & Fisher 1977
Half of the velocity width at 20% of the peak flux = proxy for rotational velocity
L Δv α
α = 2.5 – 4
(slope of 6.25-10
in mag)

4. Regularities in the
dynamics of galaxies
Armed with this knowledge 40 years ago, Milgrom proposed his
MOND paradigm, or just Milgrom’s relation:
-If observed RCs are flat, then gravity must effectively fall like 1/r
-The discrepancy sets in at different radii in different galaxies, so a
more relevant scale than radius is the centripetal acceleration
a0 ~ 10-10 m/s2

5. ÞVelocity predicted to be flat (until the external field dominates),
and Tully-Fisher relation predicted to be a relation between the
total baryonic mass of galaxies and the asymptotic circular
velocity, with a slope of 4, with no dependence on secondary
parameters such as baryonic surface density
Very strong, bold and unintuitive predictions at the time!

6. Very strong, bold and unintuitive predictions at the time!
In Newtonian gravity, assume that one has a fixed factor between the
total mass and the baryonic one at fixed baryonic mass Mb, one
would then expect something like V4 ∼ Mb
2/R2 ∼ Mb Σb where Σb is
the surface density, but what is predicted is V4 ∼ Mb , with no
dependence on size or Σb

7. Verified prediction: Baryonic TF
n Log Mb = α log Vf – log β
n α ≈ 3.9
n Intrinsic scatter
~ 6%
Lelli et al. 2019

8. Famaey & McGaugh 2012

9. Halo mass-concentration relation &
abundance matching
Halo mass-concentration relation
(with some scatter)
Match stellar mass
function to halo
mass function by
assigning n(>M*)
to n(>Mh)

10. Stellar-to-halo mass relation (SHMR)
Behroozi et al. (2013)
Typical scatter ~ 0.15 dex
ÞAdding the gas, the
intrinsic BTFR scatter
cannot go below
0.05 dex
(Desmond 2017)
feedback
(hopefully?)
~30% of
cosmic
fraction
Scatter of BTFR twice too high!
(3.6 sigmas discrepancy)
+ no bending at high masses

11. Milgrom (1983)
The real elephant in the room:
a priori prediction of the diversity of
rotation curves as a function of
baryonic surface density

12. Ghari, Famaey,
et al. (2019)

13. « galaxies not only share a global Vf (Mb); the entire shape of the
rotation curve V(R/Rd|Mb) is similar » (McGaugh 2014)
But how can that be?

14. Not a priori expected in ΛCDM
Dark matter halos are (almost) a one-parameter family (driven by mass)

15. too many cores
Too many cusps
Galaxy formation simulations
in trouble
Ghari, Famaey,
et al. (2019)

16. Modifying gravity?
Ñ. [ µ (½ÑF½/a0) ÑF] = 4 pG rbar AQUAL: Bekenstein & Milgrom (1984)
or
Ñ2 F = Ñ. [ n (½ÑFN½/a0) ÑFN] QUMOND: Milgrom (2010)
g = gN if g>>a0
g = (gN a0)1/2 if g<<a0
MOND
Milgrom 1983
A characteristic acceleration scale present in the BTFR and diversity
- Most fine-tuning problems in rotation curves disappear (see, e.g.,
Famaey & McGaugh 2012) : no BTFR tightness problem or diversity problem…

17. Modifying gravity?
Famaey & McGaugh (2012)
Galaxy rotation curves: it
works! No problem of
diversity or BTFR tightness

18. Modified gravity: weak-field
=>
=>
Ñ2 F = Ñ. [ n (½ÑFN½/a0) ÑFN]
Other version (« QUMOND »):
(« AQUAL »)

19. Modified gravity: covariant version
ÞAdd some « k-essence » like scalar + a vector field for lensing (TeVeS)
Classical action:
Bekenstein & Milgrom (1984); Bekenstein (2004)

20. Modified gravity: covariant version
ÞAdd some k-essence like scalar + a vector field for lensing
ÞLatest version by Skordis & Zlosnik (2021), « AEST »:
Classical action:
Bonus: GW and light speeds are equal

21. The CMB
Skordis & Zlosnik (2021)

22. Weak lensing
Brouwer et al. (2021)
External field
effect (EFE) ?

23. Now the troubles
Desmond
(2023)
n=1

24. Now the troubles
Gravitational field of the Milky Way acting on Solar
neighbourhood ~ 1.8 x a0
For local Wide Binaries with mutual attraction below a0
n=1 => (<gr >/gN)1/2 ~ 1.2
hence a 20% enhancement of relative velocities
In the Solar System, AQUAL/QUMOND also creates a
quadrupole field (e pointing towards the Galactic center) :

25. Now the troubles
Gaia DR3 provides parallaxes, prop. motions and vlos for ~3.3 x 107 stars
Isolate ~104 wide binaries (within 300 pc from the Sun, mass ranging
from 0.2 to 1.3 Msun) with separations up to ~0.15 pc
Model their relative velocities with a 6 parameters model :
+ fraction of close binary contamination and their maximum semi-major
axis + line-of-sight Galactic contamination
=> Likelihood ratio favours Newton over n=1 MOND interpolating
function by orders of magnitude (Banik et al. 2024)

26. Now the troubles
Cassini (Hees et al. 2014) :
𝝳
Desmond, Hees & Famaey (2024)

27. Now the troubles
Cassini (Hees et al. 2014) :
Desmond, Hees & Famaey (2024)

28. k-mouflage as a possible way out?
A possible « natural » way out: adding a new length scale
MOND effects suppressed below the Vainshtein radius
Babichev et al. (2011)

29. Temperature profiles of X-ray emitting gas in clusters:
Globally, a factor of 2 of
residual missing mass
Can easily reach a factor of 10
in central parts
Angus, Famaey & Diaferio (2010)
Famaey & McGaugh (2012)
Now the troubles :
on large (galaxy cluster) scales

30. The discrepancy seems to be related with the depth of the potential
well => EMOND (Zhao & Famaey 2012) where a0 becomes a0(ϕ)
BUT then hard to also make the « residual mass » collisionless !!
Now the troubles :
on large (galaxy cluster) scales

31. What remains:
-Hot dark matter ? Probably not …
(HDM, e.g., sterile neutrinos, Angus 2009)
But halo mass function completely off !
(Angus et al. 2013) => ruled out …
-Cluster baryonic dark matter (CBDM,
Milgrom 2008), cold dense H2 clouds
- AEST? Durakovic & Skordis (2024)
Now the troubles :
on large (galaxy cluster) scales

32. Dynamics of ultra-diffuse galaxies
in the Coma cluster as a clue ?
Freundlich, Famaey et al. (2022)
- The agreement of the velocity dispersions
with MOND are impressive !
- But the EFE ruins the agreement if
d<5Mpc (d > 5Mpc would require a very
peculiar observer-dependent bias in
spatial distribution)
- Needs the new d.o.f. making up the
residual missing mass (same as sourcing
structure in AEST?) to not couple to the
field generating MOND in the UDGs

33. Conclusion
Baryonic Tully-Fisher relation between baryonic mass of spiral galaxies and
asymptotic velocity is captured by Milgrom’s relation, while the high-end slope
and the scatter remain challenging in ΛCDM
The diversity of RC shapes driven by the surface density of baryons is also
captured by Milgrom’s relation, and remains challenging for simulations that
either produce too few or too many cores
MOND is successful at predicting the dynamics of galaxies, especially
rotationally-supported ones: the question is why does it make successful
predictions ?
- Emergence in ΛCDM?
- Fundamental nature of DM?
- Modified gravity?
- All of the above or something even more exotic?
The interpolating function seems to be scale-dependent (wide binaries, solar
system) and the external field effect seems to be screened in clusters => gives a hard
time to model-builders…