modified dark matter in galaxy clusters

Modified dark matter in galaxy clusters

Douglas Edmonds Emory & Henry College

Miami 2015

Collaboration

D. Farrah Virginia Tech

C.M. Ho Michigan State

University

D. Minic Virginia Tech

Y.J. Ng University of

North Carolina

T. Takeuchi Virginia Tech

D. Edmonds Emory & Henry

College

Modified Dark Matter (MDM)

� What is MDM? �  MDM from entropic gravity

� What is the mass profile of an MDM halo? � Does MDM resolve mass discrepancies?

�  Observed galactic rotation curves �  Observed vs. dynamical mass in Galaxy

clusters

Outline

MoNDian Modified dark matter (MDM) is dark matter

i.e., it is an EXTRA source

(beyond the baryonic source)

MDM is NOT

a modification of gravity

MDM

via entropic gravity

entropic force from 1st and 2nd laws of thermodynamics

Bekenstein-Hawking formula for black hole entropy (at event horizon)

Unruh temperature

Newton’s 2nd law (Vector from gradient of entropy)

Verlinde, 2010 [arXiv:1001.0785]

MDM Theory

FΔx = TΔS

ΔS = 2πk mc!Δx

kT = !a2πc

!Fentropic =m

!a

Along with

Consider a quasi-local (spherical) holographic screen with area and temperature

Verlinde, 2010 [arXiv:1001.0785]

A = 4πr2 T

Equipartition of energy: , being the total number of degrees of freedom (bits) on the screen

E = NkT / 2N = A / lP

2 = Ac3 / (G)

Unruh temperature for a uniformly accelerating (Rindler) observer

kT = a2πc

E =Mc2

Mc2 =Ac2a4πG

=r2c2aG

⇒ a = GMr2 Newton’s law of gravity

MDM Theory via entropic gravity

Unruh temperature measured by an inertial observer, where

Unruh temperature measured by a non-inertial observer with accleration

Deser & Levin [arXiv:gr-qc/9706018]; Jacobson [arXiv:gr-qc/9709048]; Ho, Minic & Ng [arXiv:1005.3537]

Generalization to de Sitter space:

TdS =a02πkc a0 = c Λ / 3

TdS+a = a2 + a0

2

2πkc

T ≡ TdS+a −TdS =

2πkca2+a20 −a0

#$%

&'(

Net temperature measured by a non-inertial observer

Fentropic = T =m a2+a20 −a0

"#

$%Verlinde’s approach ⇒


a

Consider a quasi-local (spherical) holographic screen with area and effective temperature

Ho, Minic & Ng [arXiv:1005.3537]; [arXiv:1105.2916]; [arXiv:1201.2365]

A = 4πr2 T

a2 + a02 − a0 =

2πck T

=2πck

2 ENk"

#$

%

&'= 4π

MGA

"

#$

%

&'=

G Mr2

Unruh equipartition Einstein

where represents the total mass enclosed within the volume. , where is the dark matter mass.

M

M =M +M ' M '

What is the MDM mass profile?


Ho, Minic & Ng [arXiv:1005.3537]; [arXiv:1105.2916]; [arXiv:1201.2365]

What is the mass profile?

Fentropic = T =m a2+a20 −a0

"#

$%

For , consistency with flat rotation curves (v independent of r) and the observed Tully-Fisher relation ( ) requires that

a >> a0, Fentropic ≈ ma; a << a0, Fentropic ≈ ma2 / (2a0 )

a << a0

v4 ∝M a ≈ (2aNa30 /π )

1/4

The entropic force for the low acceleration regime is then

Fentropic ≈ma2

2a0≈ m aNac ≈ FMoND

where is the critical acceleration in MOND, and we have used the fact that a0 ≈ 2πac

ac

MDM Theory observational constraints

Galactic rotation curves suggest:

Ho, Minic & Ng [arXiv:1005.3537]; Jacobson [1995; Phys. Rev. Lett. 75]

What is the mass profile? MDM Theory

M ' =M 1π

a0a

!

"#

$

%&2'

())

*

+,,

observational constraints

Note: This form is also suggested by introducing a fundamental acceleration which is related to the cosmological constant into Jacobson’s rewriting of GR as a form of thermodynamics

Galactic Rotation Curves

ρ ' r( ) = acr

!

"#

$

%&2 ddr

Ma2!

"#

$

%&

ρ ' r( ) = ρ0rrs1+ r

rs

!

"#

$

%&

2 v r( ) = v200ln 1+ cx( )− cx / 1+ cx( )x ln 1+ c( )− c / 1+ c( )"# $%

Fentropic =m a2+a20 −a0"#

$% =

mGMr2

1+ a0a

&

'(

)

*+2"

#,

$

%- =

mv2

r

Solve the force equation for circular orbits for a(r) and v(r)

Once we have a(r), we can find the MDM density profile

We compare MDM fits to CDM (using NFW profile)

Observations

DE, Farrah, Ho, Minic, Ng & Takeuchi, 2014 [arXiv:1308.3252]


Data – black squares

Stars – blue line

Gas – green line

[Sanders & Verheijen, 1998]

MDM – red line

CDM (NFW) – black line

Fitting parameters:

MDM – M/L

CDM – c , V200 , M/L


Observations


MDM – red line

CDM (NFW) – black line

Fitting parameters:

MDM – M/L

CDM – c , V200 , M/L


Observations

Galactic rotation curves suggest:

What is the mass profile? MDM Theory

M ' =M 1π

a0a

!

"#

$

%&2'

())

*

+,,

observational constraints

M ' = α1+ r / rs

!

"#

$

%&a20a2M

But, the mass profile above does not work for galaxy clusters.

In principle, the mass profile may be modified in any number of ways – search for mass profiles which are consistent with thermodynamics.

A better profile for galaxy clusters:

Note: This mass profile also works for galactic rotation curves.

M (r) = kT (r)rµmpG

d lnρgd ln r

+d lnT (r)d ln r

!

"#

$

%&

spherical symmetry and hydrostatic equilibrium (Sarazin 1988)

ρg =1.2mp nenp

Galaxy Clusters

Observations

Vikhlinin et al. (2006)

modification of traditional β- model

T (r) = T0tcool (r)t(r)

Allen et al. (2001)

MN (r) =kT (r)rµmpG

d lnρgd ln r

+d lnT (r)d ln r

!

"#

$

%&

Dynamical (virial) mass: (implied by Newton)

MMOND =Mbaryonic

1+ ac / a( )2

MOND effective mass (mass required in Newtonian dynamics to give the same observed acceleration as MOND):

MMDM =Mbaryonic 1+α

1+ r / Rs

!

"#

$

%&a20a2

'

()

*

+,Total mass with MDM:

Galaxy Clusters

Observations

Observations

Galaxy Clusters black solid: virial mass dashed: gas mass

green solid: MDM dash-dotted: CDM dotted: MOND

A133 A262 A1795 A1991

A383

A907

A478

A1413

A2029

RX J1159+5531

A2390

MKW 4

USGC S152

Summary �  By generalizing entropic gravity to deSitter space,

we are led to a form of dark matter which naturally accounts for Milgrom’s scaling.

�  The mass profile is not uniquely determined – we choose mass profiles that are consistent with thermodynamics.

�  We have tested the MDM model at galactic and cluster scales, and it fares well.

�  We can fit galactic rotation curves and galaxy cluster dynamics with the same dark matter mass profile up to a constant scale factor.

�  We not only fit the average cluster mass, but the shape of the mass profile as well.

Conclusion

Future Work

� Can we better constrain the mass profile? � The Bullet Cluster; How strongly coupled is

MDM to baryonic matter? How does MDM self-interact?

� Acoustic oscillations measured in the CMB � Simulations of structure formation: Hard? � “Particle” physics: MDM is (likely) non-local

– How does one detect such a thing?

Conclusion

Thank you!

Ho, Minic & Ng, 2010, Phys. Lett. B, 693, 567

Ho, Minic & Ng, 2011, Gen. Rel. and Grav., 43, 2567

Ho, Minic & Ng, 2012, Phys. Rev. D, 85, 104033

DE, Farrah, Ho, Minic, Ng & Takeuchi, 2014, ApJ 793, 41

DE, Farrah, Ho, Minic, Ng & Takeuchi, arXiv 2015?

Conclusion

modified dark matter in galaxy clusters

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