Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Exotic Phases of Matter in Compact Stars

Fredrik Sandin

March 16, 2007

Produced with latex and beamer

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Table of contents

1 Introduction

2 Quark matter

3 Preon stars

4 Research papers

5 Other work

6 Concluding remarks

7 Acknowledgements

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Neutron star in Corona Australis

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Compact stars

Compact stars form when ordinary stars “die”

Stars produce energy by fusion→ thermal pressure

When the fusion reactions diminish thepressure decreases → collapse

(planetary nebula or supernova)

Supernova remnant G11.2-0.3Credit: NASA/McGill/V. Kaspi et al.

1934 Baade (left) and Zwicky (right)suggested that a supernova is thetransition from an ordinary star intoa neutron star

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Compact stars

Two categories

White dwarf stars

Form if 0.1 Msun . Mstar . 8 Msun

Size ∼ EarthMass ∼ Sun (max 1.4 Msun)

Neutron stars

Form if 10 Msun . Mstar . ?Diameter ∼ small cityMass ∼ Sun (max 2–3 Msun)

Sirius BCredit: NASA/CXC/SAO

RX J1856.5-3754Credit: NASA/SAO/CXC/J.Drake et al.

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Compact star sequence

Equation of state (EoS) ofhigh-density matter determinespossible masses and radii

Model EoS → equilibrium sequence

Neutron star sequence expected tobe unique

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Neutron stars

Density ∼ 1015 g/cm3

Properties of interiorunknown

Could contain “exotic”forms of matter

Hydrogen/Heatmosphere

R ~ 10 km

n,p,e, µ

neutron star withpion condensate

quark−hybridstar

hyperon star

g/cm 310 11g/cm 310 6

g/cm 310 14

Fe

−π

K−

s ue r c n d c t

gpo

niu

p

r ot o

ns

color−superconductingstrange quark matter(u,d,s quarks)

CFL−K +

CFL−K0

CFL− 0π

n,p,e, µquarks

u,d,s

2SCCSLgCFLLOFF

crust

N+e

H

traditional neutron star

strange star

N+e+n

Σ,Λ,

Ξ,∆

n superfluid

nucleon star

CFL

CFL

2SC

Novel phases of subatomic matter in a neutron star, assuggested by different theories. F. Weber, Prog. Part. Nucl.Phys. 54, 193 (2005)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Observations of neutron stars

Example

Most neutron stars (NS) haveM∼ 1.4 Msun

Since 2003, NS with higher (andlower) masses have been observed

Measured and estimated masses ofneutron stars in radio binary pulsarsand in x-ray accreting binaries.J. Lattimer & M. Prakash, Phys.Rev. Lett. 94, 111101 (2005)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Observations of neutron stars

Example

RX J1856.5-3754Credit: NASA/SAO/CXC/J.Drake et al.

J. Trumper, V. Burwitz, F. Haberl &V. Zavlin, Nucl. Phys. Proc. Suppl., 132, 560(2004).

Radiation radius R∞ = R ×(1− 2GM

Rc2

)−1/2

Intensity ∝ surface area ∝ R2∞

Neutron star RX J1856, R∞ & 17 km

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Why study neutron stars?

Unique information about the properties of matter at highdensity and “low temperature”

Important piece in the puzzle of fundamental physics

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Structure of matter

Nature has a hierarchical structure

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Building blocks of matter

Except for “a few details” (like theunexplained 95% of the observed energycontent of the universe) matter consists of

6 quarks (2 stable)

3 charged leptons (1 stable)

3 neutrinos (oscillate)

4 force carriers (gravity excluded)

These are the basic objects in thestandard model of particle physics

Particles of the standard model(Higgs excluded)

The Relativistic Heavy-Ion Collider(RHIC)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Comment on mathematics

Example

Kinetic energy, T , andpotential energy, U

The lagrangian isL = T − U

The motion of the pendulum isgoverned by the equation ofmotion

The effective “couplingconstant”, g , has to bedetermined by experiments

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Standard-model lagrangian

L = − 12∂νga

µ∂νgaµ − gs f

abc∂µgaνgb

µgcν −

14g2s f abc f adegb

µgcνgd

µgeν + 1

2ig2

s (qσi γµqσ

j )gaµ + Ga∂2Ga +

gs fabc∂µGaGbgc

µ − ∂νW +µ ∂νW−

µ − M2W +µ W−

µ − 12∂νZ0

µ∂νZ0µ −

12c2

wM2Z0

µZ0µ −

12∂µAν∂µAν −

12∂µH∂µH − 1

2m2

hH2 − ∂µφ+∂µφ− − M2φ+φ− − 12∂µφ0∂µφ0 − 1

2c2w

Mφ0φ0 − βh [ 2M2

g2 + 2Mg

H +

12(H2 + φ0φ0 + 2φ+φ−)] + 2M4

g2 αh − igcw [∂νZ0µ(W +

µ W−ν −W +

ν W−µ )− Z0

ν (W +µ ∂νW−

µ −W−µ ∂νW +

µ ) +

Z0µ(W +

ν ∂νW−µ −W−

ν ∂νW +µ )]− igsw [∂νAµ(W +

µ W−ν −W +

ν W−µ )− Aν (W +

µ ∂νW−µ −W−

µ ∂νW +µ ) +

Aµ(W +ν ∂νW−

µ −W−ν ∂νW +

µ )]− 12g2W +

µ W−µ W +

ν W−ν + 1

2g2W +

µ W−ν W +

µ W−ν + g2c2

w (Z0µW +

µ Z0νW−

ν −Z0

µZ0µW +

ν W−ν ) + g2s2

w (AµW +µ AνW−

ν − AµAµW +ν W−

ν ) + g2sw cw [AµZ0ν (W +

µ W−ν −W +

ν W−µ )−

2AµZ0µW +

ν W−ν ]− gα[H3 + Hφ0φ0 + 2Hφ+φ−]− 1

8g2αh [H4 + (φ0)4 + 4(φ+φ−)2 + 4(φ0)2φ+φ− +

4H2φ+φ−+2(φ0)2H2]−gMW +µ W−

µ H− 12g M

c2w

Z0µZ0

µH− 12ig [W +

µ (φ0∂µφ−−φ−∂µφ0)−W−µ (φ0∂µφ+−

φ+∂µφ0)] + 12g [W +

µ (H∂µφ− − φ−∂µH)−W−µ (H∂µφ+ − φ+∂µH)] + 1

2g 1

cw(Z0

µ(H∂µφ0 − φ0∂µH)−

igs2wcw

MZ0µ(W +

µ φ− −W−µ φ+) + igsw MAµ(W +

µ φ− −W−µ φ+)− ig

1−2c2w

2cwZ0

µ(φ+∂µφ− − φ−∂µφ+) +

igsw Aµ(φ+∂µφ−−φ−∂µφ+)− 14g2W +

µ W−µ [H2 +(φ0)2 +2φ+φ−]− 1

4g2 1

c2w

Z0µZ0

µ[H2 +(φ0)2 +2(2s2w −

1)2φ+φ−]− 12g2 s2w

cwZ0

µφ0(W +µ φ− + W−

µ φ+)− 12ig2 s2w

cwZ0

µH(W +µ φ−−W−

µ φ+) + 12g2sw Aµφ0(W +

µ φ− +

W−µ φ+) + 1

2ig2sw AµH(W +

µ φ− −W−µ φ+)− g2 sw

cw(2c2

w − 1)Z0µAµφ+φ− − g1s2

w AµAµφ+φ− − eλ(γ∂ +

mλe )eλ − νλγ∂νλ − uλ

j (γ∂ + mλu )uλ

j − dλj (γ∂ + mλ

d )dλj + igsw Aµ[−(eλγµeλ) + 2

3(uλ

j γµuλj )−

13(dλ

j γµdλj )] + ig

4cwZ0

µ[(νλγµ(1 + γ5)νλ) + (eλγµ(4s2w − 1− γ5)eλ) + (uλ

j γµ( 43s2w − 1− γ5)uλ

j ) +

(dλj γµ(1− 8

3s2w − γ5)dλ

j )] + ig

2√

2W +

µ [(νλγµ(1 + γ5)eλ) + (uλj γµ(1 + γ5)Cλκdκ

j )] + ig

2√

2W−

µ [(eλγµ(1 +

γ5)νλ) + (dκj C

†λκ

γµ(1 + γ5)uλj )] + ig

2√

2

mλe

M[−φ+(νλ(1− γ5)eλ) + φ−(eλ(1 + γ5)νλ)]−

g2

mλe

M[H(eλeλ) + iφ0(eλγ5eλ)] + ig

2M√

2φ+[−mκ

d (uλj Cλκ(1− γ5)dκ

j ) + mλu (uλ

j Cλκ(1 + γ5)dκj ] . . .

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Not yet brainy enough

The properties of matter in neutron stars,as well as many other unexplainedphenomena, are probably accuratelydescribed by the standard model

However, the answers are hidden in thecomplex equations

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Asymptotic freedom

Protons and neutrons consist ofthree quarks

Quarks are bound by the strongnuclear force

This force becomes weaker withincreasing exchange ofmomentum

Protons and neutrons shouldtherefore dissolve at high

density/temperature

Asymptotic freedom was theoretically discovered byGross (left), Politzer and Wilczek (right) in 1973.They were awarded the Nobel Prize in Physics in2004.

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Signals of quark deconfinement

“Something” strange hasbeen created in heavy-ioncollisions

Not clear if it is aquark-gluon plasma

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

BCS theory

Theory of superconductors

A low-temperature Fermisystem is unstable with respectto formation of Cooper pairs ifan arbitrary weak attractiveinteraction is present

In ordinary superconductors,the attractive interaction ismediated by phonons

BCS theory was developed in 1957 by Bardeen (left),Cooper and Schrieffer (right). They were awardedthe Nobel Prize in Physics in 1972.

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Conjectured phase diagram

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

How to learn more

Observation

Heavy-ion collisions

Compact stars

LHC hall

Theoretical developments

Lattice QCD

Effective models

Visualisation of lattice-QCD result

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Beyond the standard model

The standard model has a potentialto answer many questions, butcertainly not all

For example, > 80% of the mattercontent in the universe is “darkmatter”. What is it?

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Preons

Hypothetical building blocks ofquarks, leptons and (some)gauge bosons

Motivation: conceptualshortcomings of standard model(particle families, unstableparticles, mixing/oscillation,large number of exogenousparameters)

A variety of models exist

First suggested by Pati (left) and Salam(right) in 1974

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Preon stars

If preons exist, a new class of compact stars could exist

Mass . Earth

Radius . m

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Mass and size

Maximum mass and radius dependon the “compositeness scale”, Λ

Mass ∼ 1024 kg(

TeVΛ

)3/2

Radius ∼ 10−3 m(

TeVΛ

)3/2

Density ∼ 1028 g/cm3(

ΛTeV

)3

See Paper VI for details

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Methods to detect preon stars

Possible only if they formed in the earlyuniverse and constitute a significantfraction of cold dark matter

Gravitational (femto-) lensing

Gravitational waves from binaries

Seismic signals from collisions withthe Earth or the Moon?

High-frequency gravitational-wavedetector at the University of Birmingham

Gravitational wave frequency vs.amplitude, see Paper VI for details

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

The point is

If preons exist

We might need a very big (and expensive) particle acceleratorto resolve them

Preon stars could exist, and they could be relatively easy (andinexpensive) to detect

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Paper I

J. Hansson and F. Sandin, Preon stars: a new class of cosmiccompact objects, Physics Letters B616, 1 (2005)

Original publication on preon stars

Estimates for the density, mass andradius

Stability analysis (schematic model)

Brief discussion about detection

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Paper II

F. Sandin, Compact stars in the standard model – and beyond,The European Physical Journal C40 S2, 15 (2005)

Also to appear in How and where to go beyond the standardmodel, proceedings of the International School of SubnuclearPhysics, Erice, ed. A. Zichichi: World Scientific (2007)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Paper III

D. Blaschke, S. Fredriksson, H. Grigorian,A. M. Oztas and F. Sandin, The phase diagram ofthree-flavor quark matter under compact star constraints,Physical Review D72, 065020 (2005)

Model of colour-superconductingquark matter

Phase diagrams

Equations of state

Quark-star sequences

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Paper IV

F. Sandin and A. M. Oztas, Condition for gaplesscolor-antitriplet excitations in Nambu–Jona-Lasinio models,Physical Review C73, 035203 (2006)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Paper V

T. Klahn, D. Blaschke, F. Sandin, Ch. Fuchs,A. Faessler, H. Grigorian, G. Ropke and J. Trumper,Modern compact star observations and the quark matter equationof state, submitted to Physics Letters B; nucl-th/0609067

Based on quark-matter model inPaper III, with the addition of avector-meson interaction

Hybrid-star model consistentwith observations

Equation of state consistentwith data from heavy-ioncollision experiments

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Paper VI

F. Sandin and J. Hansson, The observational legacy of preonstars – probing new physics beyond the LHC, to be submitted;astro-ph/0701768

Observational signals ofpreon stars

Gravitational lensingGravitational wavesSeismic signals (briefly)

Improved estimates for thedensity, mass and radius

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Paper VII

F. Sandin and D. Blaschke, The quark core of protoneutronstars in the phase diagram of quark matter, submitted to PhysicalReview D; astro-ph/0701772.

Based on model in Paper III

Neutrino trapping inquark-matter cores ofprotoneutron stars

Phase diagramsEquations of stateCompact-star sequencesMass defects

Mass defect ∼ energy releasedin supernovæ

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Popular article in “Forskning & Framsteg”

J. Hansson & F. Sandin, Forskn. Frams. 7, 40 (2005)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Popular article in “Popular Astronomi”

J. Hansson & F. Sandin, Pop. Ast. 4, 8 (2005)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

On-line femtolensing calculator

Femtolensing:

Gravitational lensing by acompact object with mass1014 . M

kg . 1017

Produces characteristicfeatures in γ-spectra

Potential means to detectpreon stars

http://femtolensing.dyndns.org

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

On-line femtolensing calculator

Results are available as:

Data in text format

Postscript figure

Grace project file

http://femtolensing.dyndns.org

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

On-line colour-superconductivity calculator

Public interface tocolour-superconductivitysoftware

Low-level code in C++MySQL databaseDistribution over SSHPython command-lineinterface

Powered by Apache andmod-python

http://3fcs.dyndns.org

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

On-line colour-superconductivity calculator

Comparison with results bySteiner et al.

Load example (link)

A. Steiner, S. Reddy & M. Prakash, Phys. Rev.D66, 094007 (2002)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Concluding remarks

Models of quark matter and neutron stars are not yet realistic

The results presented in this thesis add to the qualitativepicture of colour-superconducting phases and the properties ofneutron/protoneutron stars with a quark-matter core

The on-line colour-superconductivity interface is a usefulresource for cross-checking of results as the models continueto improve (∼ become more complicated)

The preon-star hypothesis is gaining momentum – the firstpaper by an independent researcher (Horvath) has beenwritten and it is recognised by some astronomers (it has alsoinspired a song named ‘Exotic Star’)

Introduction Quark matter Preon stars Research papers Other work Concluding remarks Acknowledgements

Acknowledgements

Supervisor: Sverker Fredriksson

Co-Supervisor: Johan Hansson

Collaboration: David Blaschke, Hovik Grigorian,Thomas Klahn and Ahmet Oztas

Thanks to Hans Weber for allowing me to use his FreeBSDcomputer cluster, and to Erik Elfgren and Tiia Grenman formany inspiring discussions

This work was supported by the Swedish Graduate Schoolof Space Technology and the Royal Swedish Academyof Sciences