Stellar and terrestrial observations from the mean. MANJARI BAGCHI PDF, TIFR, Mumbai. MONIKA SINHA PDF, SINP, Kolkata SUBHARTHI RAY PDF, IUCAA, PUNE

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1 Stellar and terrestrial observations from the mean field QCD model MANJARI BAGCHI PDF, TIFR, Mumbai MONIKA SINHA PDF, SINP, Kolkata SUBHARTHI RAY PDF, IUCAA, PUNE Mira & Jishnu Dey, Presidency College, Kolkata 1

2 Aspects of QCD : Asymptotic Freedom (AF) Confinement Chiral Symmetry Restoration 2

3 Modeling QCD Properties: We can build a phenomenological model representing QCD properties. In that case, we can represent quark-quark interactions by a phenomenological potential which incorporates AF and confinement into its structure. 3

4 Richardson Potential Nc π Vq ( ) = 1 2N c N f q2 ln(1 + q ) Λ 2 N + 1 6π Vr r f r () = c 2 2Nc 33 2Nf Λ ( Λ ) α f() t = dx exp( xt) x {ln( x 1)} + π Λ 400 MeV J. Richardson, Phys. Lett. B 82 (1979) 272 H. W. Crater, P. Van Alstine, PRL 53 (1984) 1527 Dey et al, Phys. Rev. D 34 (1986) 2104 Dey et al, PLB 438 (1998) 123 Λ 100 MeV 4

5 Modified Richardson Potential Nc + 1 Vq ( ) 12π = 1 Λ + Λ 2Nc 33 2N f q2ln(1 q ) q q + Λ Λ= 100 MeV ; Λ = 350 MeV N + 1 6π Vr= Λ r f Λr () c 2 2Nc 33 2Nf ( ) α f() t = dx exp( xt) x {ln( x 1)} + π Original Richardson Potential Modified Richardson Potential AF and Confinement are inbuilt with correct scales. 5

6 Test of modified Richardson Potential in baryonic sector : Bagchi et al, NPA 740 (2004) 109. Bagchi et al, Europhys. Lett. 75 (2006) 548. Λ= 100 MeV ; Λ = 350 MeV 6

7 Test of modified Richardson Potential in baryonic sector : 7

8 Test of modified Richardson Potential in baryonic sector : M = E T CM 8

9 Test of modified Richardson Potential in baryonic sector : Baryonic magnetic moments ( μ B ) are found by combining μ q s with the help of baryonic wave function 9

10 Test of modified Richardson Potential in baryonic sector : 10

11 Test of modified Richardson Potential in baryonic sector : 11

12 Application of modified Richardson potential for study of strange star properties : 12

13 What is a Strange Star? Strange stars are stars composed of strange quark matter i.e. a very high density strange quark phase consisting of deconfined u, d and s quarks. In our model, strange stars are more compact than neutron stars. 13

14 Mean Field Model : Modified Richardson potential as interquark potential Screening of potential due to medium dependence on density and temperature Density dependent quark mass Charge neutrality, beta equilibrium condition (hard part) Relativistic HF formalism to obtain EOS. Finite temperature through Fermi function TOV equations are solved to obtain the mass-radius of the stars 14

15 fermi function F i ( T) k, i = exp 1 ( f ε ) i εi T 3 3 n = k 2 F dk ε = φ k 2 F dk i i i i i i π 2 0 i π 2 0 i φ is single particle energy comes from interquark potential entropies 3 2 ( ) ( ( ))( ( )) ( ( )) i = - k 2 i i i, ln i i, 1 i i, ln 1 i i, i π 0 S F k T F k T F k T F k T dk free energies pressure f = ε TS i i i fi Pi = ni fi ; P = P i n Bagchi et al, Astron. & Astrophys. 450 (2006) 431. i i 15

16 Original Richardson Potential Modified Richardson Potential Screened Richardson Potential 16

17 2 2 2 q q + D 1 2α ( ) 2 0 f f 2 D = mg = ki ki + mi α 0T π i= u, d, s 1/2 17

18 Chiral symmetry restoration at high density M q = m q + M sec Q h nb n N 0 18

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20 dp G M () r c 2 + 4π r 3 P( r) = [ Pr ( ) + ε ( r)] dr c 4 2GM() r r 2 1 cr 2 dm = dr 4 π r 2 c ε 2 ( r) 20

21 2 1 1 nu ns nd ne = 0 nq =, n π e = ( f ) ( f k ) q ke 2 2 3π μ = μ μ = μ + μ s d s u e s+ u d + u s u+ e+ ν 21

22 H = α. p + β M + V i i i i ij i i< j dq = TdS = de + PdV μdn P n n = μ ε i i i + μ ε e e e i 22

23 Property of Strange Quark Matter At high density the strange quark matter is hypothesized to be more favorable energetically to normal matter (Bodmer 1971, Witten 1984) 23

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29 Property of Strange Quark Matter 29

30 New results 30

31 80 MeV 90 MeV 50 MeV 70 MeV Temp. Mmax Radius Baryon No. (MeV) (M SUN ) (km) (10 57 ) Bagchi et al, A & A. 450 (2006)

32 New results Witten argued that if strange quark matter is the ground state, then strange stars can be born in the early universe around a temperature of 100 MeV. From our model we found that stable star structure is possible upto a temperature of 80 MeV. This closeness to Witten s hypothesis supports our SS model. Furthermore, the Kovtun, Sons and Starinets bound is also saturated at this temperature ArXiv ! 32

33 Surface Tension Surface tension is the surface energy per unit area. For ordinary fluid, it is the property of the interaction between the media forming an interface and gravitation does not play any significant role. 33

34 Defining Surface Tension SS is a huge drop of strange quark matter, the pressure difference across the surface can be expressed in terms of S. The pressure on top of the surface is zero. dp 2S Δ P = r = R where Δ P r = R = h R dr r= R so S = hr dp 2 dr r= R What is the relevant thickness h?? Interaction radius r 0 of the quarks. P r= R dp dr r= R =

35 surface area of an SS = 4 π R 2 thickness of a shell of one quark layer = r 0 volume of the shell = 4 π R 2 r 0 quark number inside the shell n t = 4 π R 2 r 0 n number density at star surface projection of a quark = π r 0 2 quark number at the surface n s = 4 π R 2 / π r 2 = 4R 2 / r 2 for densely packed system, n s = n t r = 1 1/3 giving π n r 0 ~ 0.5 fm - r 0 at surface does not depend on star size. But for a particular star, r 0 increases from centre to surface interaction radius" of the quarks 35

36 A check of interaction radius σ qq = π r 2 σ pp = 3 σ qq Heiselberg, Pethick, PR D 48 (1993) σ pp =25 mb matches with experiment 36

37 Estimated value of surface tension S 1/3 R 1 dp = 2 π n dr r = R Putting h = r Large value of surface tension upto 140 MeV fm -2 ( 174 MeV 3 ). [Typical values of S used in literature range within MeV fm -2 Heiselberg, Pethick, PRD 48 (1993) 2916 : Iida, Sato, PRC 58 (1998) 2538.] For us S depends on star size!! Gravitation plays an Important role. 37 Bagchi et. al, A & A, 440 (2005) L33.

38 Our Model MIT Bag Model Instead of TOV, putting Newtonian expression for dp/dr, S becomes much lower ~ 50 MeV fm -2 even for our EoS. 38

39 Study of surface wave We have used our estimated value of surface tension to study the properties of surface waves at the surface of a strange star. 39

40 Study of surface wave where 2π x y = h sin λ h > amplitude, v -> velocity, T -> time period, λ -> wavelength b -> radius of curvature ( + ( ) 2 ) 3/ dy/dx vt b = = dy/dx 4π h - at crest, + at trough λ = vt correction to velocity due to circular motion of fluid particle: v v+ 2π b T (crest) v v 2π b T (trough) 40

41 Study of surface wave condition for streamline flow-bernoulli's equation 2 v p gz + + = 0 2 ρ z (R± h) (R± h) 1 R R S h 1/2 ± + at crest, - at trough where S p b Rs R R 1 R ρ ε 2 c 1/2 2GM R S = Schwarzsclild Radius 2 c p Sc ρ εb 2 41

42 Study of surface wave 1/2 Rs Rs GM GM 1 2 R h 1 2 b + π Sc R h 1 2π b Sc + v+ = + v + R+ h 2 T b ε R h 2 T b ε b 2 2 vt = 2GM 2 R 4 π S = h 2 c 1/2 1/2 Rs R s πhv RSc R h R h 5 8 h Sc + π v 3 2T = + R + h R h εt B(v,h,T) A(v,h,T) 42

43 Study of surface wave Type I X-ray bursts are observed from 7 LMXB by RXTE. rise time t rise ~ 1 sec decay time ~ 10 sec a peak in power density spectrum burst oscillation C O U N T M. van der Klis, Ann. Rev. Astron. Astrophys. 38 (2000) 717. Strohmayer et al, Astrophys. J. 469 (1996) L9. 43

44 Study of surface wave The frequency of oscillation is not constant, it increases becomes constant near the burst tail Asymptotic Frequency [light curve in white] frequency shift Δf ~ 1.5 HZ F R E Q U E N C Y C O U N T Δf T I M E 44

45 Study of surface wave We claim this frequency shift is the onset of a surface wave as the burst proceeds and due to the anticoupling of the wave's power to the burst power. Bagchi et al, A & A 440 (2005) L33 v πr t = 1 rise T = ( Δf) 45

46 Study of surface wave Burst from 4U observed by RXTE on February 16 (1996) ; t rise = 0.6 sec, Δf = 1.5 HZ T = 2/3 sec. v = km/sec ( R = 7.05 km) graphical solution gives h = 300 cm 46

47 Application of density dependent mass ansatz 47

48 Application of density dependent mass ansatz 48

49 Application of density dependent mass ansatz f in MeV π G in 10 MeV n B /n 0 49

50 Application of density dependent mass ansatz f π in MeV n B /n 0 50

51 Concluding Remarks Existence of Strange Star is not still well established. We hope further study of x-ray and radio astronomy will help to remove the dispute. But why we are so much interested to Strange Stars? QCD properties are still inaccessible to terrestrial experiments. Experimentalists tried to get signatures of asymptotic freedom and confinement in laboratory RHIC, but could NOT succeed. So Strange Star serves as the lab set up by nature for us to test QCD properties.!! Further study of Strange Star properties will be interesting. Connecting RHIC data to SS is possible through viscosity/entropy ratio. 51

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53 I liked Bob Rutledge s question. The take home for astrophysicists is observations are good. The one for Nuclear Model people is u r doing well. For phenomenologists like us the message is : look for discrepancies and try simple QCD models.