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Modified Newtonian Dynamics: a phenomenological review
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Transcript of Modified Newtonian Dynamics: a phenomenological review
Modified Newtonian Dynamics: a phenomenological review
Benoit Famaey (ULB, Brussels)
The old missing mass problem
• 1781: William and Caroline Herschel discover Uranus
• 1792: Delambre publishes orbit of Uranus, non-Newtonian even after taking the perturbations of other planets into account
• 1834: Hussey proposes new planet, Airy believes in new gravitational law
• 1846: Le Verrier calculates the position of the new planet
Galle discovers Neptune
• 1859: perihelion precession of Mercury of 43 arcsec per century, Leverrier postulates the existence of the small planet Vulcan
But correct answer for Mercury found by Einstein in 1915
The modern-day missing mass
• 1933: Zwicky observes velocity dispersion of individual galaxies in the Coma cluster, and finds M/Mvis ≈ 20
• 1973: Rubin & Ford measure the asymptotically FLAT rotation curve of M31 (Andromeda) instead of a Keplerian 1/√r falloff
Doppler Shift: (-0)/0 = Vr / c
CDM and the cusp problem
• Simulations of clustering CDM halos (e.g.Diemand et al.) predict a central cusp r- , with > 1
• Feedback from the baryons makes the problem worse
• Angular momentum transfer from the bar
• WDM?• Other solutions?• Hiding cusps by triaxiality of
the halo? arXiv:astro-ph/0608376 No
0
200
ESO79-G14 (Gentile et al. 2004)
CDM and the « conspiracy » problem
• Each time one sees a feature in the light, there is a feature in the rotation curve (Sancisi’s rule)
• Baryonic Tully-Fisher relation
V∞4 Mbar (tight->triaxiality of halo?)
• Amount of DM determined by the distribution of baryonsat all radii and wiggles of rotation curves even follow wiggles of baryons (TF at all radii)
• Tidal Dwarf Galaxies with DM?Tidal Dwarf Galaxies with DM?(Bournaud et al. 2007 Science(Bournaud et al. 2007 Science)
Tidal dwarf galaxiesNumerical simulations of tidal dwarf galaxies formation:
Barnes & Hernquist (1992)
Tidal dwarf galaxies are formed out of material
that was in a rotating disk.
They have virtually
no collisionless dark matter !
The NGC 5291 systemBournaud et al. (2007) show HI VLA observations
of the NGC 5291 system
Several tidal dwarf galaxies
are found
Only 3 are large enough
for mass modelling
(N5291N, N5291S,
N5291SW)
blue: HI
white: optical
red: UV
Bournaud et al. (2007)
The NGC 5291 systemBournaud et al. derive the rotation curves of these 3 tidal dwarf galaxies:
visible
These galaxies show a mass discrepancy
According to CDM there should be almost no dark matter (5-10% at most).
Bournaud et al.: baryonic dark matter e.g. in the form of cold H2 molecules?
CDM
expectation
The conspiracy in other galaxies can be summarized by MOND
• Correlation summarized by this formula in galaxies (Milgrom 1983):
(g/a(g/a00) g) g = g= gN barN bar where a0 ~ cH0 ~ c1/2
(V(V22/ra/ra00) V) V22/r/r = g= gN barN bar
with (x) = x for x « 1
(x) = 1 for x »1
• Until we reproduce a relation like this from simulations, we cannot yet claim to fully undertstand DM
• OK for the Milky Way TVC (Famaey & Binney 2005, Wu et al. 2008, McGaugh 2008)
• No cusp problem + explains the RC wiggles following the baryons
• Tully-Fisher relation (observed with small scatter): V∞4 = GMbara0
• Predicts that the discrepancy always appear at V2/r ~ a0 => in LSB where << a0/G
• Mbar(r)/Mtot(r) = (halo-by-halo missing baryons problem: ≠ cosmic ratio at large radii)
• Predicts the correct order of magnitude for the local galactic escape speed
~ (x) = x/(1+x)
Famaey et al. 2007
Phys.Rev. D75 (2007) 063002
arXiv:astro-ph/0611132
M*/L ratios
The NGC 5291 system
In Gentile et al. (2007, A&A, 472, L25) we see how MOND does
(first assuming an inclination of 45o):
MOND
Red curve: baryonic contribution
Black curve: MOND curve (*not* at fit, zero free parameters!)
We also took into account the external field effect from NGC 5291
Conspiracy 108 -> 1012 baryonic Msun
i=45° for TDGs of NGC5291
i=45° Newton
((Gentile et al. Gentile et al. A&A 472 L25)
Why does the formula work in CDM and CDM-free galaxies???
• At least, the MOND formula might tell us something we are not yet understanding in galaxy formation (« gastrophysical » feedbacks). Surprising regularity!
• Non-standard: a) fundamental property of DM (see Blanchet)b) modification of « inertia »
(Milgrom 1994, not clear what to do at relatvistic level, non-metric theory?)
c) modification of gravityd) all of the above
. [ (/a0) ] = 4 π G bar
• Modifying GR to obtain MOND in static weak-field limit: dynamical 4-vector field UU = –1, with free function in the action playing the role of (Bekenstein 2004; Zlosnik et al. 2007; Bruneton & Esposito-Farese 2007; Halle, Zhao & Li 2008)
• Double-imaged strong lenses well fitted, except a few outliers in groups and clusters (Shan et al. 2008 arXiv:0804.2668)
Conclusions
• « DM » is distributed in galaxies in a regular and predictive manner (not as messy as expected)
• One formula fits >2000 galaxy rotation curves data points
• RCs of TDGs of NGC 5291 are difficult to understand in the CDM framework but MOND fits them very well