Numerical Evolu.on of Soliton Stars Dr. Jayashree Balakrishna (HSSU Saint Louis, Missouri)

Transcription

1 Numerical Evolu.on of Soliton Stars Dr. Jayashree Balakrishna (HSSU Saint Louis, Missouri) Collaborators: M. Bondarescu (Ole Miss. ), R. Bondarescu (Penn. State), G. Daues (N.C.S.A), F.S. Guzman (Mexico), E. Seidel (LSU, NSF)

2 Overview What is Dark MaPer? Possible Dark MaPer Candidates. What are soliton stars role in dark maper cosmology: halos, compact objects. forma.on of soliton stars. proper.es of compact soliton stars. In spherical Symmetry. In Full 3D GR gravita.onal radia.on.

3 Dark MaPer Dark maper: maper whose presence is inferred by its gravita.onal effects even though it cannot actually be seen.

4 Dark MaPer: Galac.c Rota.on Curves

5 Direct Proof of Dark MaPer

6 Hubble Expansion: Relevance of scalar fields in cosmology Redshi[ in light (distant galaxies) propor.onal to distance. Expansion of the universe: co moving distance between points (difference in their coordinates) remains constant but physical distance between points increases.

7 Dark MaPer and Dark Energy Hubble Telescope observa.ons 1998 of distant supernovae showed that the expansion of the universe was accelera.ng rather than slowing down. Postulated dark energy (non zero cosmological constant working like a repulsive force). Present es.mates are about 70% of the energy density is provided by this dark energy. Only about 5% of the density is luminous maper leaving about 25% being dark maper.

8 Nature of Dark MaPer Primordial Nucleosynthesis: Current es.mates of light element abundances fit predic.ons of BBN to a high degree. This is an es.mate of baryon (protons+neutrons) abundances. These es.mates show that dark maper is essen.ally non baryonic.

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10 Axions as Dark MaPer Why they are preferred? i) They are non baryonic ii) They are predicted by par.cle physics as a solu.on to the lack of CP viola.on in strong interac.ons. iii) They are light and behave as cold dark maper and can explain galaxy forma.on and large scale structure.

11 Axion Mass Range Lower bound 10 6 ev /c to keep the density cri.cal density Upper bound 10 3 ev /c to prevent excessive energy loss in stars and supernovae. 2 M Pl The mass of a compact star ~ where m is m the mass of the par.cle it is made of

12 Detec.on? Extremely light scalar par.cles ( ) could ev in principle form dark maper halos. Heavier par.cles can form compact objects. Can there be stars made of scalar par.cles that have signatures that could be detected? Gravita.onal Radia.on

13 What is an axion star? Axions are scalar par.cles that can be described by real fields. These par.cles could clump together by a Jeans instability mechanism to form stars called soliton stars. There are also scalar par.cles that can be described by complex scalar fields (also possible dark maper candidates) that could form stars by the same mechanism. Such hypothe.cal stars are called bosonstars. These stars held together by a balance between the aprac.ve force of gravity and the dissipa.ve nature of the uncertainity principle (field).

14 Boson and Soliton Stars: Equa.ons, Configura.ons and Evolu.ons. Spherically Symmetric Boson Stars: E. Seidel, and W. M Suen, Phys. Rev. D. 42, (seidelsuen Boson) Soliton Stars: Ground State and Forma.on: E. Seidel and W. M. Suen, Phys. Rev. Le=., 66, 1659 (1991). (seidel suen Soliton) Soliton Stars Ground State: M. Alcubierre, R. Becerril, F. S. Guzman Class.Quant.Grav. 20, 2883, (2003). (Alcubierre et al) Boson Stars: Spherically Symmetric and 3D evolusons: J. Balakrishna, PhD thesis Washington University Boson Stars on a 3D Grid: F. S. Guzman, Phys. Rev. D. 73, (R) (2006)

15 Recent Work Evolu.on of 3D Boson Stars with Waveform Extrac.on: J. Balakrishna: R. Bondarescu, G. Daues, F. S. Guzm an and E. Seidel Class. Quant. Grav. 23, 2631 (2006). (J.B. et al boson) Numerical Simula.ons of Oscilla.ng SolitonStars: Excited States in Spherical Symmetry and Ground State Evolu.ons in 3D: J. Balakrishna, R. Bondarescu, G. Daues, M. Bondarescu Phys. Rev. D. 77, , (J.B. et al. soliton)

16 The equa.ons Coupled Einstein Klein Gordon system: Ac.on: Metric (spherical symmetry+ polar slicing):

17 Solu.ons Boson Stars (complex field).me dependent field,.me independent metric with energy density being.me independent. Soliton Stars (real field) no equilibrium configura.on. Fields and metrics have.me dependence. Asympto.cally Flat: φ(r = ) = 0 => φ 1,3,.. (r = ) = 0. A 0 ( ) =1, A 2,4,.. = 0. C 2 j = eigenvalue

18 Soliton Star Profile (Alcubierre et. Al)

19 Boson Star Profile (Seidel Suen Boson)

20 Mass Profile: Boson Star

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22 Ground State S Branch Boson Star Evolu.on (Seidel Suen boson unpert. M=0.33, phi(0)=0.1))

23 Star Radius: Perturbed Stable Star

24 Mass Loss

25 Mass Profile: Ground State Soliton Star

26 Soliton Stars Expected to be unstable (No equilibrium configura.ons). Truncated solu.on as a small perturba.on:

27 S branch Soliton Star: M=.5726, phi1(0)=0.2828, jmax=3 (Alcubierre et al) Mass loss < 0.003% of the original mass by t=5000.

28 Excited States (j.b et al.): Oscillatons Role of Excited States in Cosmology: could be intermediate states in the forma.on process of these stars. Are they stable?

29 Mass Profile: First Excited State

30 S branch Excited State star collapsing to a black hole In the polar slicing condi.on we use the radial metric rises sharply as an apparent horizon forms signaling the onset of black hole forma.on. Phi(0)=0.2828, dr= 0.1 perturba.on is due to discre.za.on of the grid.

31 S branch star going to the ground state: Ini.al configura.on

32 Mass Profile Evolu.on of S branch n=1 star going to ground state.

33 Metric at the end of the run compared to the metric of a ground state star close to the one it seples down to. The mass of the star at the end of the run is M =.44M 2 Pl /m The profile shown in comparison has a mass of M =.43M 2 Pl /m

34 Decay Times If an excited state S branch star can lose enough mass it goes to the ground state otherwise it collapses to a black hole. A comparison of.me scale of collapse of n=1 S branch stars with the same numbers of grid points (~ 187) covering the star is shown.

35 Cascading Stars: 5 node star

36 5 node star: Density profile with intermediate 4 node state

37 FULL 3D EVOLUTIONS 3D evolu.ons take longer (more equa.ons): resolu.on, convergence issues. instabili.es and assymetries d/dx d/dy versus d/dy d/dx Gauge issues how to step through space.me (more degrees of freedom). SO WHY? More realis.c

38 Cactus Code: deveoped by AEI LSU It is a modular code. The modules are called thorns. (We changed the ini.al data and added gauge condi.on. We also had an ini.al value solver for the Boson Star.) It uses a BSSN formalism for the evolu.on equa.ons with and without maper. Special credit to F. Siddhartha Guzman for his scalar field evolver.

39 Boson Stars versus Soliton Stars Challenges for Soliton Star. Gravita.onal Waves have a high damping rate allowing full extrac.on on a short.me scale (compared to Neutron Stars). *S. Yoshida, Y. Eriguchi, T. Futamase, Phys. Rev. D. 50, 6235 (1994).

40 Gravita.onal Waveform

41 Gravita.onal Wave: Newman Penrose Scalar

42 Soliton Star 3D (J.B. et al. PRD 2008) Code Test

43 Newman Penrose scalar: Metric Y20 perturba.on of stable soliton star.

44 Zerilli Func.on Stable Star

45 Energy Output

46 Conclusion We have seen that, in principle, scalar par.cles can form stable stars. They have ground states and excited states. The excited states although inherently unstable can cascade to a stable ground state configura.on losing mass via emission of scalar radia.on. Excited states can be intermediate states during the forma.on of these stars. They have gravita.onal wave signatures that damp on a short.me scale.

47 Cri.cal Density The smooth universe has a geometry ini.ally parallel free trajectories 2 Flat: stay parallel, Closed: converge, H 2 = ȧ = 8ΠGρ kc2 a 3 a 2 + Λc2 3 Open: diverge. ρ cr = 3H 2 8πG

48 How do we know there is dark maper Theore.cal: The cri.cal density is needed for infla.on and its predic.ons to work. Luminous maper is 5% of this. There must be nonluminous stuff. If 70 % is dark energy then 25% must be dark maper. Rota.on curves of stars shows the speeds do not match what they would be if the observed mass was all there was.

49 Friedmann Robertson Walker Metric. ds 2 = a(t) 2 2 ds 3 dt 2 a(t) = scale factor. H 2 = ȧ a 2 = 8ΠGρ kc2 3 a 2 + Λc2 3 Ḣ+ H 2 = ȧ. a = 4ΠG 3p (ρ + 3 c 2 ) + Λc2 3 Λ = Cosm.const. k / a 2 = curvature G = grav.const. from oo component of Einstein s equa.on from trace of Einstein Field Eqns.

50 (perfect fluid \MaPer dominated: w=0 => Radia.on dominated w=1/3 => p = wρc 2 => a(t) = a 0 t 2 3(w+1) a(t) t 2/3 a(t) t 1/2