dark matter, galactic dynamics, and gaia - testing ......moschella (princeton) galactic dynamics aps...

Dark Matter, Galactic Dynamics, and GaiaTesting Alternative Theories

Matthew MoschellaPrinceton University

APS DPF 2019

Image: ESA/Gaia/DPAC

arXiv:1812.08169 & work in progresswith M. Lisanti, N. Outmezguine, O. Slone

Evidence for Dark Matter on Many ScalesGalaxies

Galaxy Clusters CosmologyEilers et al. (2018); Planck Collaboration (2018); Chandra X-Ray Observatory (2006)

Moschella (Princeton) Galactic Dynamics APS DPF 2019 2 / 34

The Missing Mass Problem in Galaxies

• Flat Rotation Curves

• Local Velocity Dispersions

• “Small Scale Crisis”• Missing Satellites• Too Big to Fail• Core vs. Cusp

• Dynamical Correlations with Baryons• Baryonic Tully-Fisher Relation• Diversity of Rotation Curves• Radial Acceleration Relation

Eilers et al. (2018);


The Diversity of Rotation Curves

• Diversity of inner rotation curves for galaxies with similar halo mass• Correlates with surface brightness (baryons)

Ren et al. (2018)


The Radial Acceleration Relation

• SPARC: rotation curves for 175disk galaxies

• Observe a tight correlation:

a =

{aN aN � a0√a0aN aN � a0

• a0 ∼ 10−10 m s−2Lelli et al. (2017); McGaugh et al. (2016)


Solutions to the Missing Mass Problem in Galaxies

Which is most consistent with observed Milky Way dynamics?


MOND-like Forces

• Built to reproduce rotation curves:

a =

{aN aN � a0√a0aN aN � a0

a0 ≈ 10−10 m s−2

• Regardless of theoretical mechanism, the empirical target is:

a = ν

(aN

a0

)aN

• For simplicity, we assume this relation holds going forward.

Milgrom (1983); Famaey, McGaugh (2012)


MOND-like Forces vs. Dark Matter

• MOND-like forces predict a in the same direction as aN

• Dark Matter predicts a = aN + aDM

• In the Milky Way, aN is disk-like, but aDM is spherical

• Need to look at vertical acceleration to distinguish kinematically

• If you could measure a and aN, this is all you need – sincemeasurements are imperfect, the real situation is morecomplicated.

Image: ESO/NASA/JPL-Caltech/M. Kornmesser/R. Hurt


A Teaser: The Direction of the Gravitational Acceleration

Data requires more enhancement in aR than in az

slope ∼ azaR


A Generalized Framework

Bayesian Approach: marginalize over model parameters

ρB = ρ∗,bulge + ρ∗,disk + ρg,disk

Bland-Hawthorn, Gerhard (2016); Image: Wikipedia


Milky Way Observables

For self-consistency, we must use only measurements that come fromdirect photometric observations, rather than dynamical fitting.

• Baryonic Surface Density

• Disk Scale Radius/Height

• Stellar Bulge Mass

• Rotation Curve

• Vertical Velocity Dispersions

σz(z)2 = − 1

n(z)

∫ ∞z

n(z′) az(z′) dz′

• probes vertical acceleration

• requires assumption ofequilibrium (Jeans equation)

• requires modelling the tracernumber density n(z)

Zhang et al. (2013); Read (2014)


A MOND-like Force Model

• adopt interpolation function that fits the radial acceleration relation

ν(aN/a0) =1

1− e−√aN/a0

a0 = 1.20± 0.24× 10−10 m

s2

McGaugh et al. (2016)

• Compare Models:

BIC = k log n− 2 log L̂

• k: num. of model parameters• n: num. of data points• L̂: maximum likelihood

Table: Camarena, Marra (2018)

• Comparing to a reference DM model, we find that ∆BIC = 10.4• very strong preference for dark matter


A Generalized MOND-like Force Model

• avoid dependence on a particular parametrization of ν(aN/a0)• expand ν(aN/a0) about the local value: aN,ref . v2

0/R0 ∼ a0

ν

(aN

a0

)≈ ν0 + ν1 · aN

• Comparing to a reference DM model, ∆BIC = 4.1• positive, but not strong, preference for dark matter

• Prefers very small enhancements ν ≈ 1

• Does not fit the radial accelerationrelation


Superfluid Dark Matter

• Dark matter condenses to a superfluid core inside galaxies• In superfluid phase, phonons mediate a long-range MOND-like force

a = aN + aDM + aphonon

• Work in Progress: Because ρDM is small, expect to be similar topure MOND-like force scenario

Berezhiani, Khoury (2015); Berezhiani et al. (2017);


Solutions to the Missing Mass Problem in Galaxies

Which is most consistent with observed Milky Way dynamics?


Conclusions

• Local galactic observables can be used to test models withMOND-like forces precisely where they are most successful

• MOND-like forces appear in tension with existing data and are unableto simultaneously reproduce the observed radial and verticalaccelerations

• Currently working on applying this framework to Superfluid DarkMatter – similar results expected


Thank You


Supplementary Material


The (Baryonic) Tully-Fisher Relation

• Look at many galaxies

• Observe Mb ∝ v4f

• Mb: total baryonic mass (luminosity)• vf : asymptotic rotational velocity

• Mb ∼ aNR2, vf ∼√Ra

⇒ a ∝ √aN• proportionality constant: Ga0

• a0 ≈ 10−10 m s−2

Milgrom (1983); McGaugh et al. (2016)







• Rotation Curve


Σ1.1j = 2

∫ 1.1 kpc

0ρj(R0, z

′) dz′Σ1.1∗,obs = 31.2± 3.0 M� pc−2

Σ1.1g,obs = 12.6± 1.6 M� pc−2

McKee et. al. (2015); Flynn et. al. (2006)







• Rotation Curve


ρ∗,disk = ρ̃∗ e−R/h∗,Re−|z|/h∗,z

h∗,z,obs = 300± 50 pc

h∗,R,obs = 2.6± 0.5 kpc

Bland-Hawthorn, Gerhard (2016); Juric et. al. (2008)







• Rotation Curve


ρ∗,bulge(r) =M∗,b

2π

r∗,br

1

(r + r∗,b)3

• Existing measurements have alarge variance

• Conservative range:0 < M∗,b < 2× 1010 M�

M∗,b,obs = 1.50± 0.38× 1010 M�

Licquia, Newman (2015); Calchi Novat et. al. (2008)







• Rotation Curve


vc(R0) =√R0 · a(R0)

∣∣∣z=0

vc,obs = 229± 12km

s

(dvc/dR)obs = −1.7± 0.47km

s kpc

Eilers et. al. (2018)


A Reference DM Model

• For our baseline DM model, wetake an NFW Profile:

ρDM(r) =ρ̃DM

(r/rs)α (1 + r/rs)

3−α

and the dynamics are:

a = aN + aDM ∇ · aDM = −4πGρDM

Navarro et. al. (1996);


Superfluid DM

a = −∇Φ +αΛ

MPl∇φ

∇2Φ = 4πG(ρDM + ρB)

ρDM =2√

2m5/2Λ(

3 (β − 1) µ̂+ (3− β) (∇φ)2

2m

)3

√(β − 1) µ̂+ (∇φ)2

2m

(∇φ)2 + 2m(

2β3 − 1

)µ̂√

(∇φ)2 + 2m (β − 1) µ̂∇φ = αMPlaN

Berezhiani, Khoury (2015); Berezhiani et al. (2017);


A Lagrangian Formulation of MOND

• Gravitational Lagrangian:

LN = − 18πG (∇ΦN )2 ⇒ L = − a20

8πGF(

(∇Φ)2

a20

)• µ(x) = ∂F

∂x2 : an arbitrary function up to asymptotes• a = −∇Φ

• Equation of Motion:

∇ · [µ (a/a0)a] = −4πGρB

µ(a/a0)a = aN + S

• ∇ · S = 0, but S 6= 0 in general• For spherical (one dimensional) symmetries, S = 0• For disk-like potentials, S ≈ 0 outside of the disk

Bekenstein, Milgrom (1984); Brada, Milgrom (1994)


Quasilinear MOND

• Gravitational Lagrangian:

L = − 18πG

(2∇Φ ·∇ΦN − a2

0Q(

(∇ΦN )2

a20

))• ν(x) = ∂Q

∂x2 : an arbitrary function up to asypmtotes• ΦN : Newtonian potential (∇2ΦN = 4πGρb)• a = −∇Φ, aN = −∇ΦN

• Equation of Motion:

∇ · a = ∇ · [ν(aN/a0)aN]

a = ν (aN/a0)aN + S

Milgrom (2010)


Is S Small?

0.04

0.04

0.04

0.04

0.04

0.04

0.07

0.07

0.07

0.07

0.07

0.07

0.07

0.09

0.09

0.09

0.09

2 4 6 8 10 12

-3

-2

-1

0

1

2

3

R [kpc]

z[kpc]

δ=|S |/|ν(aN) aN|


Is the Interpolation Function Linear?


Results: Dark Matter Parameters

ρDM(R0) = 0.29± 0.06 GeV cm−3

α < 1.1 at 90% confidence


Results: MOND Parameters

• Red: Our analysis• Gray: ν(aN/a0) = 1

1−e−√

aN/a0, a0 = 1.20± 0.24× 10−10 m s−2

excluded at ∼ 95% confidenceMcGaugh et al. (2016)Moschella (Princeton) Galactic Dynamics APS DPF 2019 32 / 34

Model Parameters and Priors

• rs = 19 kpc

• r∗,bulge = 600 pc

• h∗,z = 300 pc

• hg,z = 130 pc

• hg,R = 2h∗,R• Also enforce that ν0 + ν1 · aN > 1 and that the baryon-only rotation

curve reaches its maximum before R = 5 kpc


Systematic Checks


dark matter, galactic dynamics, and gaia - testing ......moschella (princeton) galactic dynamics aps...

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