GMU, April 13, The Pros and Cons of Invisible Mass and Modified Gravity. Stacy McGaugh University of Maryland

Transcription

1 GMU, April 13, 2007 The Pros and Cons of Invisible Mass and Modified Gravity Stacy McGaugh University of Maryland

2 What gets us into trouble is not what we don t know. It s what we know for sure that just aint so. - Mark Twain

3 A few things we know for sure... 2 Φ = 4πGρ F = ma which basically means mv 2 /R = GMm/R 2 i.e, V 2 = GM/R ergo... The universe is filled with nonbaryonic cold dark matter.

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5 Rotation Curve Spiral Galaxy

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7 Galaxy Cluster

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9 Large Scale Structure

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11 Past Future Ω m Ω Λ flat ΛCDM open

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13 Pruning the tree Baryonic Dark Matter Many candidates: brown dwarfs Jupiters very faint stars very cold molecular gas warm (~10 5 K) ionized gas Can usually figure out a way to detect them: most have been ruled out.

14 Hot Dark Matter Pruning the tree Obvious candidate: neutrinos neutrinos got mass!......but not enough. Also - neutrinos suppress structure formation - can t crowd together closely enough (phase space constraint)

15 Cold Dark Matter Pruning the tree Some new particle, usually assumed to be WIMPs (Weakly Interacting Massive Particle) don t interact electromagnetically, so very dark. Two big motivations: 1) total mass outweighs normal mass from BBN 2) needed to grow cosmic structure Ω m 6Ω b

16 (2) There isn t enough time to form the observed cosmic structures from the smooth initial conditions unless there is a component of mass independent of photons. t = 1.8 x 10 5 yr t = 1.4 x yr very smooth: δρ/ρ ~ 10-5 very lumpy: δρ/ρ ~ 1 δρ/ρ t 2/3 Both (1) and (2) hold only when gravity is normal.

17 Constraints predating SN, CMB age = 13 Gyr H 0 age (open) age (flat) ΛCDM Ω m

18 ΛCDM Baryons Dark Matter 23% Dark Energy 73%

19 Pros - Invisible Matter Apparently required by wide array of data Provides self-consistent cosmology Explains large scale structure ΛCDM model parameters well constrained

20 We have direct knowledge of < 1% of this stuff. Known Baryons Baryons Dark Matter 23% Dark Energy 73% Cosmologists are often wrong, but never in doubt - Lev Landau

21 ΛCDM problematic ΛCDM OK Baryonic Mass Slope and normalization wrong galaxies Small scatter poses a finetuning problem clusters Circular Velocity

22 On Galaxy Scales... Measure rotation velocity; find Properties depend systematically on Total Baryonic Mass Baryon Distribution Acceleration

23 High Surface Brightness (HSB) Low Surface Brightness (LSB) intercept Σ o slope h -1 Σ(R) = Σ o e -R/h Azimuthally averaged light distribution typically exponential for spiral disks.

24 NGC 2403 Stars HI gas Fraternali, Oosterloo, Sancisi, & van Moorsel 2001, ApJ, 562, L47

25 NGC 6822 (Weldrake & de Blok 2003) V sini = V sys + V c cosθ + V r sinθ

26 NGC 6946 Stars HI gas Boomsma 2005

27 V flat dark matter baryons stars gas

28 Newton says V 2 = GM/R. Equivalently, Σ = M/R 2 V 4 = G 2 MΣ TF Relation Therefore Different Σ should mean different TF normalization. μ = -2.5 logσ +C

29 NGC 2403 UGC 128 Same global L,V Very different mass distributions

30 V p V p R p R p R p 2.2h

31 No Residuals from TF rel n Not even where disk contribution is maximal

32 Requires fine balance between dark & baryonic mass Phys. Rev. Lett. 95, (2005)

33 Cons - Invisible Matter Serious fine-tuning problems Cusp/core problem Missing satellite problem Halo-by-halo missing baryon problem Do dark matter particles actually exist?

34 cusp/core problem ΛCDM predicts too much dark mass at small radii

35 Cons - Invisible Matter Serious fine-tuning problems Cusp/core problem Missing satellite problem Halo-by-halo missing baryon problem Do dark matter particles actually exist?

36 M31 (Gendler)

37 Kravtsov et al Juerg Diemand Via Lactea simulation

38 Cons - Invisible Matter Serious fine-tuning problems Cusp/core problem Missing satellite problem Halo-by-halo missing baryon problem Do dark matter particles actually exist? CDMS, LHC, & GLAST should all see something soon

39 One begins to worry that

40 MOND MOdified Newtonian Dynamics introduced by Moti Milgrom in 1983 instead of dark matter, suppose the force law changes such that for a >> a o, a g N. for a << a o, a (g N a o ) where g N = GM/R 2 is the usual Newtonain acceleration. More generally, these limits are connected by a smooth interpolation fcn (a/a o ) so that (a/a o ) a = g N. MOND can be interpreted as a modification of either inertia (F = ma) or gravity (the Poisson eqn).

41 MOND predictions The Tully-Fisher Relation Slope = 4 Normalization = 1/(a 0 G) Fundamentally a relation between Disk Mass and V flat No Dependence on Surface Brightness Disk Galaxies with low surface brightness provide particularly strong tests Dependence of conventional M/L on radius and surface brightness None of the following data existed in At that time, LSB galaxies which were widely Rotation Curve Shapes thought not to exist. Surface Density ~ Surface Brightness Detailed Rotation Curve Fits Stellar Population Mass-to-Light Ratios

42 The Tully-Fisher Relation MOND predictions Slope = 4 Normalization = 1/(a 0 G) Fundamentally a relation between Disk Mass and V flat No Dependence on Surface Brightness! Dependence of conventional M/L on radius and surface brightness Rotation Curve Shapes Surface Density ~ Surface Brightness Detailed Rotation Curve Fits Stellar Population Mass-to-Light Ratios

43 In MOND limit of low acceleration a = g N a 0 V 2 R = GM R 2 a 0 V 4 = a 0 GM observed TF!

44 MOND predictions The Tully-Fisher Relation Slope = 4 Normalization = 1/(a 0 G) Fundamentally a relation between Disk Mass and V flat No Dependence on Surface Brightness Dependence of conventional M/L on radius and surface brightness Rotation Curve Shapes Surface Density ~ Surface Brightness Detailed Rotation Curve Fits Stellar Population Mass-to-Light Ratios

45 MOND predictions The Tully-Fisher Relation Slope = 4 Normalization = 1/(a 0 G) Fundamentally a relation between Disk Mass and V flat No Dependence on Surface Brightness Dependence of conventional M/L on radius and surface brightness Rotation Curve Shapes Surface Density ~ Surface Brightness Detailed Rotation Curve Fits Stellar Population Mass-to-Light Ratios

46 mass surface density = V 2 /(Gh) Not a fit MOND predictions The Tully-Fisher Relation Slope = 4 Normalization = 1/(a 0 G) Fundamentally a relation between Disk Mass and V flat No Dependence on Surface Brightness Dependence of conventional M/L on radius and surface brightness Rotation Curve Shapes Surface Density ~ Surface Brightness Detailed Rotation Curve Fits Stellar Population Mass-to-Light Ratios surface brightness

47 MOND

48 Sanders & McGaugh 2002, ARA&A, 40, 263

49 Sanders & McGaugh 2002, ARA&A, 40, 263

50 Sanders & McGaugh 2002, ARA&A, 40, 263

51 Residuals of MOND fits

52 MOND predictions The Tully-Fisher Relation Slope = 4 Normalization = 1/(a 0 G) Fundamentally a relation between Disk Mass and V flat No Dependence on Surface Brightness Dependence of conventional M/L on radius and surface brightness Rotation Curve Shapes Surface Density ~ Surface Brightness Detailed Rotation Curve Fits Stellar Population Mass-to-Light Ratios

53 Line: stellar population model (mean expectation)

54 MOND predictions The Tully-Fisher Relation Slope = 4 Normalization = 1/(a 0 G) Fundamentally a relation between Disk Mass and V flat No Dependence on Surface Brightness Dependence of conventional M/L on radius and surface brightness Rotation Curve Shapes Surface Density ~ Surface Brightness Detailed Rotation Curve Fits Stellar Population Mass-to-Light Ratios

55 Those are the pros. You don t know the Power of the Dark Side Can MOND explain large scale structure? Can it provide a satisfactory cosmology? Can it be reconciled with General Relativity? Does it survive other tests? What are the cons? TeVeS Clusters problematic

56 1E bullet cluster (Clowe et al. 2006) direct proof of dark matter?

57 bullet cluster shows same baryon discrepancy in MOND as other galaxy clusters MOND suffers a missing mass problem! unseen baryons? heavy neutrinos?

58 bullet cluster collision velocity observed shock velocity CDM Angus & McGaugh (2007) arxiv:

59 bullet cluster collision velocity observed shock velocity MOND Angus & McGaugh (2007) arxiv:

60 MOND works too well in galaxies to be a coincidence. Either MOND is correct, or Dark Matter mimics MOND Either way, new physics is implicated: - gravity? a 0 ch 0 cλ 1/2 - new properties of dark matter?

61 BBN: ω b = Ω b h 2 η 10

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