Constraining standard and nonstandard particle properties using astrophysical data

Transcription

1 Constraining standard and nonstandard particle properties using astrophysical data Juan Barranco Monarca DCI Universidad de Guanajuato XV Mexican Workshop on Particles and Fields Mazatl an, Sinaloa, November 2-6,2015 Constraining standard and nonstandard particle properties using astrophysical data p. 1

2 Outline Bounds extracted from the observation of astrophyiscal objects Bounds extracted from the no-observation of astrophyiscal objects Constraining standard and nonstandard particle properties using astrophysical data p. 2

3 We live in a cavern... The writing of god (by Jorge Luis Borges) The story is narrated by a Mayan priest named Tzinacan, who is tortured by Pedro de Alvarado (who burned the pyramid Qaholom where the protagonist was a magician) and incarcerated, with a jaguar in the adjacent cell. Tzinacan searches for a divine script that will provide him omnipotence, and he hopes to see it in the patterns of the animal s fur. Constraining standard and nonstandard particle properties using astrophysical data p. 3

4 Motivation G µν = 8πGT µν Constraining standard and nonstandard particle properties using astrophysical data p. 4

5 Self-gravitating system made of fermions The equation of state for a free gas of fermions at zero temperature can be directly computed ρ = p = 1 π 2 kf 0 k 2 m 2 F +k2 dk = m4 ( ) f 8π 2 (2z 3 +z)(1+z 2 ) 1/2 sinh 1 (z) = 1 3π 2 kf 0 k 4 m 2 F +k2 m 4 ( ) f 24π 2 (2z 3 3z)(1+z 2 ) 1/2 +3sinh 1 (z) P(Tev/fm 3 ) ρ(tev/fm 3 ) Constraining standard and nonstandard particle properties using astrophysical data p. 5

6 Dark compact objects Solve the TOV equations for such EOS: Normalized variables M = Mm 2 f /m3 p,r = rm 2 f /m p,p = p/m 4 f and ρ = ρ/m 4 f. The equations dm dr = 4πr 2 ρ dp dr = M ρ r 2 (1+ )(1+ p 4πr 3 ρ )(1 2M ρ M r ) 1 The maximum mass for a compact star made of fermionic matter M = 1.6M max ( GeV and the minimum radius m f ( GeV R min = 8.115Km ) 2 M m f ) Mass [Dimensionless units] R [Dimensionless units] Constraining standard and nonstandard particle properties using astrophysical data p. 6

7 DM as motivation The most convincent and direct evidence of the existence for dark matter at the galactic scale comes from the rotational curve velocity, namely the graph of circular velocities of stars and gas as a function of their distance from the galactic center. Constraining standard and nonstandard particle properties using astrophysical data p. 7

8 DM as motivation Furthremore, at galactic scales: Weak modulation of strong lensing around individual massive elliptical galaxies. This provides evidence for substructure on scales of 10 6 M Weak gravitational lensing of distant galaxies by foreground structure The velocity dispersions of dwarf spheroidal galaxies which imply mass to light ratios larger than those observed in our local neighborhood. The velocity dispersions of spiral galaxy satellites which suggest the existence of dark halos around spiral galaxies, similar to our own, extending at galactocentric radii 200 kpc, i.e. well behind the optical disc. This applies in particular to the Milky Way, where both dwarf galaxy satellites and globular clusters probe the outer rotation curve. Constraining standard and nonstandard particle properties using astrophysical data p. 8

9 DM as motivation (WMAP) Constraining standard and nonstandard particle properties using astrophysical data p. 9

10 Planck mision results [Planck results XVI. Arxiv ] Constraining standard and nonstandard particle properties using astrophysical data p. 10

11 DM as motivation Starting from a cosmological model with a fixed number of parameters, the best-fit parameters are determined from the peak of the N-dimensional likelihood surface. From the combined analysis of Planck + WMAP: Ω b h 2 = ± ,Ω M h 2 = ± Including BAO Ω b h 2 = ± Ω M h 2 = ± Conclusive evidence in favor of the existence of dark matter Constraining standard and nonstandard particle properties using astrophysical data p. 11

12 The big problem What is Dark Matter? Constraining standard and nonstandard particle properties using astrophysical data p. 12

13 Remember the selfgravitating fermions... Suppose it is a fermion with no self interaction to Very light DM candidate [Domcke and Urbano, JCAP 1501 (2015) 01, 002] Constraining standard and nonstandard particle properties using astrophysical data p. 13

14 Galactic halo as an ensemble of DM mini-machos log10 t/ys Mini MACHOS Forbidden because of MACHO Microlensing Rich Cluster Mo Large Galaxy Mo Dwarf Galaxy 10 8 Mo Forbidden because of dynamical instability Forbidden because of arguments on massive BHs 10 t = 13.7 Gyr 5 Forbidden because of gravothermal instability log 10 m/mo X. Hernandez, T. Matos, R. A. Sussman and Y. Verbin, Scalar field mini-machos: A new explanation for galactic dark matter, Phys. Rev. D 70, (2004) Clumpy neutralino dark matter M neutralino star 10 7 M. J. Ren, X. Li, H. Shen, Commun.Theor.Phys. 49 (2008) Axions may form such scalar field mini-machos. M axion star < M J. Barranco, A. Bernal, Phys. Rev. D 83 (2011) Constraining standard and nonstandard particle properties using astrophysical data p. 14

15 Formation of dark matter clumps: Neutralino clumps: At the phase transition from a quark-gluon plasma to a hadron gas, the spectrum of density perturbations may develop peaks and dips produced by the growth of hadronic bubbles. Kinematically decoupled CDM falls into the gravitational potential wells provided from those peaks leading the formation of dark matter clumps with masses < M. [Schmid PRD 59 (1999) ] Axion minicluster:the evolution of the axion field at the QCD transition epoch may produce gravitationally bound miniclusters of axions Such minicluster, due to collisional 2a 2a process, it may relax to a selfgravitating system. [Kolb and Tkachev PRL 71 (1993) ] Constraining standard and nonstandard particle properties using astrophysical data p. 15

16 Limits from femtolensing The maximum mass for a compact star made of fermionic dark matter M = 1.6M max ( GeV m f ) 2 M m=1tev m=1.1 x 10 5 TeV New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts exclude the range M M [A. Barnacka, J.F. Glicenstein, R. Moderski Phys.Rev. D 86 (2012) ] This imply a limit for the fermionic dark matter: P(Tev/fm 3 ) ρ(tev/fm 3 ) m f > TeV!!! Constraining standard and nonstandard particle properties using astrophysical data p. 16

17 Self-gravitating system made of axions Axion was originally proposed to solve strong CP problem There is a remnant γ a interaction L = 1 2 ( µ φ µ φ m 2 φ 2 ) 1 4 φ M F µν F µν 1 4 F µνf µν Axion properties GeV f a GeV 10 5 ev m 10 3 ev At late times in the evolution of the universe, the energy density potential is: V(φ) = m 2 f 2 a [ ( )] φ 1 cos,, f a Constraining standard and nonstandard particle properties using astrophysical data p. 17

18 Axion star R = f a σ, r = m p m m f a 4π x, α = 4πf2 a m 2 pm A(x) = 1 a(x) a + a(1+a) x σ + +(1 a) 2 x [( 1 )m B +1 2 σ 2 mσ4 4 ] +α σ 2 (1 a) + σ6 72 ] +α σ 2 (1 a) σ6 72 B + ab [( ) 1 x (1 a)bx B 1 m 2 σ 2 + mσ4 4 ( 2 x + B 2B + a ) [( 1 σ +(1 a) )m 2(1 a) B 1 2 σ + mσ3 3 σ5 24 ] = 0, = 0, = 0 Constraining standard and nonstandard particle properties using astrophysical data p. 18

19 Axion star σ(x) σ(0)=5x10-4 σ(0)=3x10-4 σ(0)=1x10-4 a(x) 0-1e-14-2e-14-3e-14-4e-14-5e-14-6e-14-7e x σ(0) Mass (Kg) R 99 (meters) density ρ (Kg/m 3 ) [J. Barranco, A. Bernal, PRD83, (2011)] Constraining standard and nonstandard particle properties using astrophysical data p. 19

20 Axion star 8e-21 5e-15 M [Solar masses] 6e-21 4e-21 2e-21 4e-15 3e-15 2e-15 1e e+11 4e+11 6e+11 ρ(0)[kg/m 3 ] 0 0 3e+10 6e+10 9e+10 ρ(0)[kg/m 3 ] Axion mass (ev) ρ(0) ( Kg/m 3) Mass (M ) R 99 (meters) m a = m a = [J. Barranco, A. Carrillo-Monteverde,D. Delepine PRD87,(2013) ] Constraining standard and nonstandard particle properties using astrophysical data p. 20

21 Possible γ signal? It is possible axion transform to photons in presence of an external magnetic field! Strong magnetic fields NS > 10 8 Gauss NS in the galaxy Does axion stars collision with Neutron Stars produce a visible effect? Start with Obtain modified Gauss law: L aγγ = cα f PQ π a E B E = cα (ab) f PQ π Energy dissipated in the magnetized conducting media, with averange σ electric conductivity (Ohm s law) W = ABS σe 2 a d3 x = 4c erg/s σ 10 26/s M 10 4 M B 2 (10 8 G) 2 YES! there could be a signal Constraining standard and nonstandard particle properties using astrophysical data p. 21

22 can the dark matter halo be a ensemble of axion stars? The number of collisions per pc 3 per second will be R c = n AS (r) ρ NS (r) S v, n AS is the number of AS per pc 3 and ρ NS is the probability to find a Neutron Star at that point, ρ NS (r) = Ar α 1 /λ α e r/λ. Collisions per year Moore Navarro-Frenk-White Kratsov Isothermal Salucci et al r [Kpc] They fulfill the limits from femtolensing No significant γ signal from the colission of NS with axion stars Constraining standard and nonstandard particle properties using astrophysical data p. 22

23 Other interesting problems The origin of supermassive black holes (SMBH)) at the center of the galaxies is an open question. Most of the numerical and semi-analitycal methods show a lack in time and amount of matter to build SMBH at early times (z 3) The argument that it is a BH is done because there is not viable alternatives... Constraining standard and nonstandard particle properties using astrophysical data p. 23

24 Boson stars with self-interaction M. Colpi, S. L. Shapiro and I. Wasserman, Phys. Rev. Lett. 57 (1986) T µν = 1 2 ( µφ ν Φ + µ Φ ν Φ) 1 2 g µν(g αβ α Φ β Φ +m 2 Φ 2 + λ 2 Φ 4 ). Λ = λm2 p 4πm 2 A A 2 x + 1 x 2 B ABx 1 x 2 σ + ( 1 1 ) [( 1 A ( 1 1 ) [( 1 A ( 1 x + B 2B A 2A )σ B Λ2 ] σ4 + σ 2 A )σ B 1 2 Λ2 ] σ4 + σ 2 A ) [( ] 1 σ +A )σ B 1 Λσ 3 = 0, = 0, = 0 Constraining standard and nonstandard particle properties using astrophysical data p. 24

25 Boson stars with self-interaction M M 99 [m p 2 /mφ ] Λ=20 Λ=60 Λ= Λ σ c σ c M max = Λ 1/2m2 p m Constraining standard and nonstandard particle properties using astrophysical data p. 25

26 Boson stars with self-interaction C(σ c,λ) M 99(σ c,λ) R 99, black hole fluid star C(σ c, Λ) Λ=20 Λ=60 Λ=100 C max (σ c, Λ) boson star σ c Λ 0.0 < C BS (σ c,λ) < 0.158, M max = Λ 1/2 m2 p m. Is there any value of m and λ as to mimic a SMBH? Constraining standard and nonstandard particle properties using astrophysical data p. 26

27 Can a BS mimic SgrA? C min C BS C max C min = M Sgr A R S Constraining standard and nonstandard particle properties using astrophysical data p. 27

28 Can a BS mimic SgrA? 1e+06 1e+03 1e+00 1e-03 m φ (ev) 1e-06 1e-09 1e-12 1e-15 m φ (ev) 1e e-05 1e-10 1e-15 1e-18 1e+07 1e+14 1e+21 1e+28 1e+35 1e+42 Λ 1e-90 1e-80 1e-70 1e-60 1e-50 1e-40 1e-30 1e-20 1e-10 1 λ 1e-20 m φ M min(λ) M SgrA m 2 P M min (Λ) C min R(σ c ) m φ M max(λ) M SgrA m 2 P. [P. Amaro-Seoane, JB, A. Bernal, L. Rezzolla, JCAP 1011 (2010) 002] Constraining standard and nonstandard particle properties using astrophysical data p. 28

29 Evidence of SMBH M BH = M Constraining standard and nonstandard particle properties using astrophysical data p. 29

30 Evidence of SMBH M BH = M M BH 10 9 M Constraining standard and nonstandard particle properties using astrophysical data p. 29

31 SFDM as a viable model for DM Another approach: The Scalar Field Dark Matter model (SFDM) The Dark Matter is modeled by a scalar field with a ultra-light associated particle. (m ev) At cosmological scales it behaves as cold dark matter T. Matos, L.A. Urena-Lopez, Class. Quant. Grav. 17 L75 (2000), V. Sahni and L.M. Wang, Phys. Rev D 62, (2000). At galactic scales, it does not have its problems: neither a cuspy profile, nor a over-density of satellite galaxies. A. Bernal, T. Matos, D. Nuñez, Rev. Mex. A.A. 44, 149 (2008) T. Matos, L.A. Urena-Lopez, Phys. Rev. D 63, (2001) Constraining standard and nonstandard particle properties using astrophysical data p. 30

32 Scalar field in a Schwarzschild background Starting with the Klein-Gordon eqyation ( µ 2 )φ = 0 with := (1/ g) µ ( gg µν ν ) ds 2 = N(r)dt 2 + dr2 N(r) +r2 dω 2, N(r) := 1 2M/r, and we arrive to: φ(t,r,θ,ϕ) = 1 r ψ lm (t,r)y lm (θ,ϕ), l,m [ 1 N(r) 2 t 2 r N(r) ] r +U l(µ,m;r) ψ lm = 0, U l (µ,m;r) := l(l+1) r 2 + 2M r 3 +µ2. Constraining standard and nonstandard particle properties using astrophysical data p. 31

33 Scalar field in a Schwarzschild background We look for stationary solutions: [ N(r) r ψ lm (t,r) = e iω lmt u lm (r), ( N(r) ) ] +N(r)U l (µ,m;r) u(r) = ω 2 u(r), 2M < r <. r By a change in the coordinates to the Regge-Wheeler coordinates r := r +2M ln(r/2m 1), the above equation has the Schrödinger eq. form: ] [ 2 r 2 +V eff (r ) u(r ) = ω 2 u(r ), < r <, with an effective potential V eff (r ): V eff (r ) := N(r)U l (µ,m;r), r = r(r ). Constraining standard and nonstandard particle properties using astrophysical data p. 32

34 The effective potential: M 2 V eff (r * /M) Mµ=0.466 Mµ=0.425 Mµ=0.380 Mµ=0.329 Mµ=0.30 Mµ=0.268 Mµ=0.190 Mµ= It has critical points!!! r * /M Mµ 2 r 3 l(l+1)r 2 +3M ( l 2 +l 1 ) r +8M 2 = 0. Constraining standard and nonstandard particle properties using astrophysical data p. 33

35 Quasi-resonant modes: ρ E n=1 n=2 n=3 n=4 n=5 ρ E µm=0.2 µm=0.25 µm=0.3 µm= r/m r/m ρ E (r) = 1 2 ( 1 N(r) ψ lm t 2 +N(r) ψ lm r 2 +U l (µ,m;r) ψ lm 2 ) [Barranco et al. Phys.Rev. D84 (2011) ] Constraining standard and nonstandard particle properties using astrophysical data p. 34

36 More important! Im (Μω) /6 (Mµ) 10, for l = 1 16 (Mµ) 6, for l = 0 Numerical evolution Leaver s method, l = 1 Leaver s method, l = 0 t 1/2 [years] x10 10 years Mµ Mµ Im (Mω) Schwarzschild black holes can wear scalar wigs [Barranco et al. Phys.Rev.Lett. 109 (2012) ] Constraining standard and nonstandard particle properties using astrophysical data p. 35

37 Scalar wigs! M [Solar Masses] Ultra-light scalar DM Galactic-center black holes Axion DM Primordial black holes t 1/2 =10 10 yrs (l=1) t 1/2 =10 10 yrs (l=0) t 1/2 >10 10 yrs for all l µ [ev] [Barranco et al. Phys.Rev.Lett. 109 (2012) ] Constraining standard and nonstandard particle properties using astrophysical data p. 36

38 The black hole bomb If the BH is rotating, a bosonic field impinging on a rotating black hole can be amplified through superradiant scattering. The scattered wave will then be reflected back and forth between the mass term and the black hole becoming amplified on each reflection. The growth of the field is asserted to be exponential and unstable. A black hole bomb [Press and Teukolsky Nature 238, (28 July 1972)] Constraining standard and nonstandard particle properties using astrophysical data p. 37

39 What about vectorial fields? The Kerr metric in Boyer-Lindquist coordinates ds 2 Kerr ( = 1 2Mr )dt 2 + Σ Σ dr2 4rM2 Σ ãsin2 ϑdϕdt ] + Σdϑ 2 + [(r 2 +M 2 ã 2 )sin 2 ϑ+ 2rM3 Σ ã2 sin 4 ϑ dϕ 2, where Σ = r 2 +M 2 ã 2 cos 2 ϑ, = (r r + )(r r ), r ± = M(1± 1 ã 2 ) and M and J = M 2 ã are the mass and the angular momentum of the BH, respectively. The Proca equation (1) σ F σρ µ 2 A ρ = 0, where A µ is the vector potential, F µν = µ A ν ν A µ and m v = µ is the mass of the vector field. The problem: This equation is not separable in the Kerr background. Constraining standard and nonstandard particle properties using astrophysical data p. 38

40 The strongest limit on photon mass Nevertheless, Pani et al. [Phys.Rev.Lett. 109 (2012) ] solved the Proca equation and found: Mω I γ Sl (ãm 2r + µ)(mµ) 4l+5+2S, J/M m v = ev m v = 2x10-19 ev m v = 4x10-20 ev axial M/M Ȯ It is shown that current supermassive black hole spin estimates provide the tightest upper limits on the mass of the photon (mv < 4x10 20 ev. Constraining standard and nonstandard particle properties using astrophysical data p. 39

41 Conclusions If DM is a fermion with no interaction: either it is too light in order to fit the rotational curves of galaxies or it is too heavy in order to evade the microlensing limits Axion stars may be an important component of dark matter with some possible observational consequences Black holes do not eat everything: They may have wigs, and to avoid the destruction of SMBH, the photon mass should be less than ev. Constraining standard and nonstandard particle properties using astrophysical data p. 40