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martes 21 de febrero de 2012

Tonatiuh Matoshttp://www.fis.cinvestav.mx/~tmatos/

http://www.iac.edu.mx

The Status of the Scalar Field Dark Matter Model


http://www.fis.cinvestav.mx/~tmatos/

http://www.fis.cinvestav.mx/~tmatos/

http://www.iac.edu.mx/

http://www.iac.edu.mx/

2


L =√−g

�R− 1

2(∇Φ)2 − V (Φ)− e−2αΦF 2

�

Fuzzy, BEC, Ultra-light, Scalar Field DM

2

A brief Review of the Scalar Field Dark Matter model. Juan Magana, Tonatiuh Matos, Victor Robles, Abril Suarez. arXiv:1201.6107


http://inspirehep.net/record/1086647


http://inspirehep.net/author/Magana%2C%20Juan?recid=1086647&ln=es


http://inspirehep.net/author/Matos%2C%20Tonatiuh?recid=1086647&ln=es


http://inspirehep.net/author/Robles%2C%20Victor?recid=1086647&ln=es


http://inspirehep.net/author/Suarez%2C%20Abril?recid=1086647&ln=es


Ideas

Matos-Guzman 2000

P. J. E. Peebles 2000


Ideas

Matos-Guzman 2000

P. J. E. Peebles 2000

Ureña-Lopez-et. al. 2000

Ureña-Lopez-Liddle 2007

Perez-Lorenzana-et. al. 2007

Cervantes-Rodriguez 2001


4


SFDM

4

Same predictions for CMB and MPS

Behaves like dust at cosmological lebel













SFDM

4



Clusters form by hierarchy Same predictions for structure formation













SFDM

4


Galaxies form by condensation of the SF

Galaxies haloes form erlier and are similar















SFDM

4






Haloes are BEC drops Galaxies are core













SFDM

4







MPS has a natural cut off Substructure is restricted














5

HereL =

√−g

�R− 1

2(∇Φ)2 − V (Φ)− e−2αΦF 2

�A brief Review of the Scalar Field Dark Matter model. Juan Magana, Tonatiuh Matos, Victor Robles, Abril Suarez. arXiv:1201.6107












L =√−g

�R− 1

2(∇Φ)2 − V (Φ)

�


5

HereA brief Review of the Scalar Field Dark Matter model. Juan Magana, Tonatiuh Matos, Victor Robles, Abril Suarez. arXiv:1201.6107












V (Φ) = V0 +11!

V �Φ +12!

V ��Φ2 +13!

V ��Φ3 +14!

V ivΦ4 + · · ·

L =√−g

�R− 1

2(∇Φ)2 − V (Φ)

�


5













L =√−g

�R− 1

2(∇Φ)2 − V (Φ)

�


5

Here

V (Φ) = V0 +12!

V ��Φ2 +14!

V ivΦ4 + · · ·













V (Φ) = Λ− 12m2Φ2 +

λ

4Φ4 + · · ·

L =√−g

�R− 1

2(∇Φ)2 − V (Φ)

�


5













�Φ +dV

dΦ= 0

Φ + 3HΦ +dV

dΦ= 0

kBTc =2π�2

m53

�ρ

g 32(1)

� 23

Bose-Einstein CondensatesA brief Review of the Scalar Field Dark Matter model. Juan Magana, Tonatiuh Matos, Victor Robles, Abril Suarez. arXiv:1201.6107












The CosmologyΦ2 as Dark Matter. T. Matos, A. Vázquez & J.A. Magaña. MNRAS, 389, (2009) 13957.


http://pelusa.fis.cinvestav.mx/tmatos/Publicaciones/84.pdf




Φ2 as Dark Matter. T. Matos, A. Vázquez & J.A. Magaña. MNRAS, 389, (2009) 13957.

The Cosmology




9

The Cosmology


9

-1000

0

1000

2000

3000

4000

5000

6000

0 200 400 600 800 1000 1200

l(l+1

)Cl (µ

K)2

Multipole l

CMB anisotropies

TT

1000

10000

0.1

P(k)

(h-3

Mpc

3 )

k/h

Power Spectrum

SDSS2df

I. Rodriguez, A. Pérez-Lorenzana, E. de la Cruz, Y. Giraud-Héraud and TM. Bosonic Cosmic Dark Matter. arXiv:1110.2751

The Cosmology


http://arxiv.org/abs/1110.2751

http://arxiv.org/abs/1110.2751

δΦ + 3HδΦ− 1a2∇2

δΦ + V,ΦΦ δΦ + 2V,Φ φ = 0

Galaxy FormationTonatiuh Matos and Luis A. Ureña. Phys Rev. D63, (2001), 063506. Available at: astro-ph/ 0006024


http://pelusa.fis.cinvestav.mx/tmatos/CV/Publicaciones/52.pdf


http://arxiv.org/abs/astro-ph/0006024


http://pelusa.fis.cinvestav.mx/arXiv.org/abs/astro-ph/0003364


¨δΦk + 3H ˙δΦk +�

k2

a2+ V,ΦΦ

�δΦk + 2V,Φ φk = 0

Galaxy FormationTonatiuh Matos and Luis A. Ureña. Phys Rev. D63, (2001), 063506. Available at: astro-ph/ 0006024








Galaxy Formation

11


VT (Φ) = −12m2Φ2 +

λ

4Φ4

Galaxy Formation

11


T > Tc

VT (Φ) = −12m2Φ2 +

λ

4Φ4+

λ

8T 2Φ2 − π2

90T 4

Galaxy Formation

11


Tc =2m√

λ

VT (Φ) = −12m2Φ2 +

λ

4Φ4+

λ

8T 2Φ2 − π2

90T 4

Galaxy Formation

11


Tc =2m√

λ

T < Tc

VT (Φ) = −12m2Φ2 +

λ

4Φ4+

λ

8T 2Φ2 − π2

90T 4

Galaxy Formation

11


0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0.001 0.01 0.1 1 10T/Tc

12

Galaxy Formation

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.1 1T/Tc


0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0.001 0.01 0.1 1 10T/Tc

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.1 1T/Tc

13

Galaxy Formation

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.1 1T/Tc


0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0.001 0.01 0.1 1 10T/Tc

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.01 0.1 1T/Tc

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.1 1T/Tc

14

Galaxy Formation


15

M.Alcubierre, F. S. Guzmán, T. Matos, D. Núñez, L. A. Ureña and P. Wiederhold. Galactic Collapse of Scalar Field Dark Matter. CQG 19(2002)5017. arXiv:gr-qc /0110102.


15

Scalar Field Fluctuation = HaloM.Alcubierre, F. S. Guzmán, T. Matos, D. Núñez, L. A. Ureña and P. Wiederhold.

Galactic Collapse of Scalar Field Dark Matter. CQG 19(2002)5017. arXiv:gr-qc /0110102.


16









http://arxiv.org/abs/gr-qc/0110102


M ∼ 0.06√

λm3

pl

m2Tc =

2m√λ



J. Balakrishna, E. Seidel and W. Suen. PRD 58(1998)104004

Pau Amaro-Seoane, Juan Barranco, Argelia Bernal and Luciano Rezzolla. Constraining scalar fields with stellar kinematics and collisional dark matter. JCAP11 (2010)002






M ∼ 0.06√

λm3

pl

m2

λ = 1× 10−6

M ∼ 1014 M⊙

Tc =2m√

λ

Tc ∼ 2000 eV



J. Balakrishna, E. Seidel and W. Suen. PRD 58(1998)104004

Pau Amaro-Seoane, Juan Barranco, Argelia Bernal and Luciano Rezzolla. Constraining scalar fields with stellar kinematics and collisional dark matter. JCAP11 (2010)002

m ~ 1eV






18

Galaxy Formation


18


k2

a2+ V,ΦΦ

�δΦk + 2V,Φ φk = 0

Galaxy Formation



k2

a2−m

2 +λ

4T

2

�δΦk = 0

Φmin

18

In

Galaxy Formation


Φmin

18

In

Galaxy Formation

¨δΦk + 3H ˙δΦk + m2

�k

2

m2a2− 1 +

T2

T 2c

�δΦk = 0


Φmin

18

In

Galaxy Formation

¨δΦk + 3H ˙δΦk + m2

�k

2

m2a2− 1 +

T2

T 2c

�δΦk = 0

T << Tc

Tonatiuh Matos and Luis A. Ureña. Phys Rev. D63, (2001), 063506. Available at: astro-ph/ 0006024








T. Harko & C. G. Bhömer JCAP 0706:025,(2007) arXiv:0705.4158

Galaxy Formation


Galaxy Formation


A. Bernal, TM, D. Nunez. Rev. Mex. A.A. 44, (2008), 149-160Galaxy Formation


-2.5

-2

-1.5

-1

0.5

0 0.2 0.4 0.6 0.8

Log(

[Ms/

pc3 ])

Log(Radio [Kpc])

U11819= -0.64

BECISO

NFW 0

20

40

60

80

100

120

140

160

0 2 4 6 8

Velo

cida

d [K

m/s

]

Radio [Kpc]

U11819

observacionalBECISO

NFW

22-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0

Log(

[Ms/

pc3 ])

Log(Radio [Kpc])

U11583= - 0.2

BECISO

NFW 0

10

20

30

40

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Velo

cida

d [K

m/s

]

Radio [Kpc]

U11583

observacionalBECISO

NFW

V. H. Robles and TM. MNRAS 392, (2012) in press. arXiv:1201.3032

Galaxy Formation


-2.5

-2

-1.5

-1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Log(

[Ms/

pc3 ])

Log(Radio [Kpc])

U11557

= 0.20

BECISO

NFW

0

20

40

60

80

0 1 2 3 4 5 6 7

Velo

cida

d [K

m/s

]

Radio [Kpc]

U11557

observacionalBECISO

NFW

23


Galaxy Formation


-2.5

-2

-1.5

-1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Log(

[Ms/

pc3 ])

Log(Radio [Kpc])

U11557

= 0.20

BECISO

NFW

0

20

40

60

80

0 1 2 3 4 5 6 7

Velo

cida

d [K

m/s

]

Radio [Kpc]

U11557

observacionalBECISO

NFW

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Log(µ

B 0 [M

s /pc

2 ])

N

23


Galaxy Formation


Abril Suarez and TM MNRAS 311, (2011), 87

Structure Formation


δΦ + 3HδΦ− 1a2∇2

δΦ + V,ΦΦ δΦ + 2V,Φ φ = 0

δΦ =�

ρ cos�

mc2 t

� + S

��v ≡ �

m∇S


Structure Formation


25


Structure Formation


�v ≡ �m∇S

∂ρ

∂t+

1a2∇ · (ρ�v) + 3H ρ

− �m

ρ

�S + 3HS

�− �

m

ˆρS = 0

∂�v

∂t+

1a2

�v∇ · �v +∇φ +�2

2m2∇

��√ρ√ρ

�

− �m

S∂�v

∂t= 0,

25


Structure Formation


�v ≡ �m∇S

25

∂ρ

∂t+

1a2∇ · (ρ�v) + 3H ρ = 0

∂�v

∂t+

1a2

�v∇ · �v +∇φ +�2

2m2∇

��√ρ√ρ

�= 0,


Structure Formation


�v ≡ �m∇S

26

∂ρ

∂t+

1a2∇ · (ρ�v) + 3H ρ = 0

∂�v

∂t+

1a2

�v∇ · �v +∇φ +�2

2m2∇

��√ρ√ρ

�= 0,


Structure Formation


�v ≡ �m∇Sρ = ρ(t) S = S(t)

26

∂ρ

∂t+

1a2∇ · (ρ�v) + 3H ρ = 0

∂�v

∂t+

1a2

�v∇ · �v +∇φ +�2

2m2∇

��√ρ√ρ

�= 0,


Structure Formation


�v ≡ �m∇Sρ = ρ(t)

∂ρ

∂t+ 3H ρ = 0

S = S(t)

26


Structure Formation


�v ≡ �m∇Sρ = ρ(t)

∂ρ

∂t+ 3H ρ = 0

ρ ∼ 1a3

S = S(t)

26


Structure Formation


�v ≡ �m∇S

27


Structure Formation


�v ≡ �m∇S

27

∂ρ

∂t+

1a2∇ · (ρ�v) + 3H ρ = 0

∂�v

∂t+

1a2

�v∇ · �v +∇φ +�2

2m2∇

��√ρ√ρ

�= 0,


Structure Formation


�v ≡ �m∇S

∂ρ

∂t+

1a2∇ · (ρ�v) = 0

∂�v

∂t+

1a2

�v∇ · �v +∇φ +�2

2m2∇

��√ρ√ρ

�= 0,

27


Structure Formation


28


Structure Formation


�v1 = λ�k + �v2

∂ρ1

∂t+ 3Hρ1 + i

ρ0

a2k

2λ = 0

∂λ

∂t+ i(

v2q

ρ0− 4πG

a2

k2)ρ1 = 0,

28

ρ = ρ0 + ρ1(t) exp(i�k · �x/a)

�v = �v0 + �v1(t) exp(i�k · �x/a)

φ = φ0 + φ1(t) exp(i�k · �x/a)


Structure Formation


�v1 = λ�k + �v2

∂ρ1

∂t+ 3Hρ1 + i

ρ0

a2k

2λ = 0

∂λ

∂t+ i(

v2q

ρ0− 4πG

a2

k2)ρ1 = 0,

d2δ

dt2+ 2 H

dδ

dt+

�v2qk

2

a2− 4πGρ0

�δ = 0,

δ =ρ1

ρ

28

SFDM

ρ = ρ0 + ρ1(t) exp(i�k · �x/a)

�v = �v0 + �v1(t) exp(i�k · �x/a)

φ = φ0 + φ1(t) exp(i�k · �x/a)


Structure Formation


�v1 = λ�k + �v2

∂ρ1

∂t+ 3Hρ1 + i

ρ0

a2k

2λ = 0

∂λ

∂t+ i(

v2q

ρ0− 4πG

a2

k2)ρ1 = 0,

d2δ

dt2+ 2 H

dδ

dt+

�v2qk

2

a2− 4πGρ0

�δ = 0,

d2δ

dt2+ 2 H

dδ

dt+

�v2sk

2

a2− 4πGρ0

�δ = 0,

δ =ρ1

ρ

28

SFDM

CDM

ρ = ρ0 + ρ1(t) exp(i�k · �x/a)

�v = �v0 + �v1(t) exp(i�k · �x/a)

φ = φ0 + φ1(t) exp(i�k · �x/a)

v2q =

�2k2

4a2m2


Structure Formation


29


Structure Formation


SFDM

30









Conclusion


Conclusion

• Scalar Fields are so far good candidates to be the Dark Matter of

the Universe













SFDM


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