Neutron stars as laboratories for exotic physics

Ian Jones Neutron stars as laboratories for exotic physics 1/20 Neutron stars as laboratories for exotic physics Ian Jones D.I.Jones@soton.ac.uk General Relativity Group, Southampton University

Context Ian Jones Neutron stars as laboratories for exotic physics 2/20 Many different physical inputs required to build a realistic neutron star model: Shear modulus and breaking strain of crust (and core?). Thermal and electrical and viscosity coefficients. Superfluidity/superconductivity. High density equation of state P = P(ρ, T). All in the context of a rapidly rotating relativistic object.

Overview Ian Jones Neutron stars as laboratories for exotic physics 3/20 Will concentrate on the role of superfluidity in two particular contexts: 1. Free precession & radio astronomy. 2. Steady rotation & gravitational wave astronomy.

Basics: Superfluid neutron stars Ian Jones Neutron stars as laboratories for exotic physics 4/20 Can model star as a mixture of 1. Superfluid neutrons 2. Charged particles (protons & electrons) The superfluid neutrons rotate by forming an array of vortices: Ω x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

Evidence for vorticity: glitches Ian Jones Neutron stars as laboratories for exotic physics 5/20 Some spinning neutron stars undergo occasional glitches. Leading theory relies on pinned vorticity: some of the superfluid vortices are rigidly attached to the solid phase, preventing them from undergoing smooth spindown. When a sufficiently large angular velocity lag has built up catastrophic unpinning occurs, corotation is established, spinning up the charged part of the star.

Part 1: Free precession & radio astronomy Ian Jones Neutron stars as laboratories for exotic physics 6/20 Free precession is the most general motion of a rigid body. Classically, determined by moment of inertia tensor I ab. Characteristic timescale of order P fp P ǫ, where ǫ is dimensionless asymmetry in I ab. P fp months years for a typical pulsar.

Free precession plus superfluidity Ian Jones Neutron stars as laboratories for exotic physics 7/20 A pinned superfluid component changes the picture radically. Angular momentum now given by J a = I ab Ω b + J SF a. The pinned superfluid acts like a gyroscope, sewn into the star (Shaham 1977). Find P fp minutes or less!

The free precession conundrum Ian Jones Neutron stars as laboratories for exotic physics 8/20 Best evidence for precession comes from PSR B1828-11, with P fp 500 days! (Stairs, Shemar & Lyne 2000). What is going on? Do we need to redraw our picture of neutron star interiors? (Link 2006)

Vortex dynamics Ian Jones Neutron stars as laboratories for exotic physics 9/20 Vortices are acted upon by two forces: 1. A Magnus force, sourced by v vortex a v n a difference 2. A drag force, R(va vortex va), p caused by charged/magnetic component scattering off the vortex core. This results in a mutual friction force, fa MF, coupling the neutrons and protons: dv n a dt dva p dt = a (µ n + Φ) + f MF a, = a (µ p + Φ) fa MF /x p We therefore have a two-component coupled system.

An instability Ian Jones Neutron stars as laboratories for exotic physics 10/20 Consider a rotating star, and allow the protons to have some velocity w along the neutron vortices. Find a short wavelength instability for sufficiently fast relative flow, e.g. in weak drag limit (Sidery, Andersson & Comer, 2008): w > 2Ωn k This corresponds to perturbation having a speed intermediate between the neutron and proton fluids; analogue of Donnelly-Glaberson instability in helium. Will this instability occur in neutron stars?

Free precession and the instability Ian Jones Neutron stars as laboratories for exotic physics 11/20 Free precession automatically generates a flow w along the vortices. Find that, for sufficiently strong drag, precession triggers the instability, (probably) destroying the pinning (Glampedakis, Andersson & DIJ, 2008). So, premature to conclude that conventional view of neutron star interior is wrong! To make progress, need to: 1. Obtain more realistic model of vortex dynamics. 2. Investigate instability in non-linear regime.

Overview Ian Jones Neutron stars as laboratories for exotic physics 12/20 Will concentrate on the role of superfluidity in two particular contexts: 1. Free precession & radio astronomy. 2. Steady rotation & gravitational wave astronomy.

Part 2: Steady rotation & gravitational wave astronomy Ian Jones Neutron stars as laboratories for exotic physics 13/20 So much for the precessional solutions. We already know about their GW significance: If no precesion in radio data, look only at 2Ω. If precession in radio data, look at multiple frequencies. (e.g. DIJ & Andersson 2000, Van Den Broeck 2005). Let s think about the (simpler) case of non-precessional ones, from the gravitational wave point of view. Will model the star as a triaxial body containing a pinned superfluid component.

The steady rotation solutions Ian Jones Neutron stars as laboratories for exotic physics 14/20 Can identify non-precessional solution as one where Ω C a is parallel to J a. Can then plug this motion into mass quadrupole approximation to General Relativity to calculate GW emission (Jones 2009). Key quantities are the multipole moments: Q lm = δρ lm (r)r l+2 dr. Tedious calculation leads to Q 21 and Q 22 in terms of stellar parameters. Key point is that both Q 21 and Q 22 non-zero if pinning axis doesn t coincide with a principal axis of I ab.

The gravitational wave emission Ian Jones Neutron stars as laboratories for exotic physics 15/20 Find components at both f and 2f. Signal-to-noise ratio is of the form ρ = h T obs Sh (f gw ), which leads to ρ Ω (ι) = ρ 2Ω (ι) = A Sh (Ω) Q 21 sinι(1 + cos 2 ι) 1/2, A Sh (2Ω) Q 22 2[(1 + cos 2 ι) 2 + 4 cos 2 ι] 1/2, where ( π A = 4 15 ) 1/2 T 1/2 obs Ω2.

The gravitational wave emission cont... Ian Jones Neutron stars as laboratories for exotic physics 16/20 Pictorially: 4 2 K2 K1 0 1 2 K2 K4 In sky-averaged sense, Q 22 is about 4 times stronger than Q 21. Conversely, for a source of known spin-down rate, a Q 21 -dominated source is about 2 times stronger than a Q 22 -dominated one.

What limits the wave emission? Ian Jones Neutron stars as laboratories for exotic physics 17/20 There are a number of possible limiting factors: Finite breaking strain of crust. Finite strength of pinning. Superfluid vortex instabilities. None of these seem to be killers (Jones 2009).

Significance for GW searches Ian Jones Neutron stars as laboratories for exotic physics 18/20 Crucial point is multiple frequency GW emission possible, even if rotation appears to be completely steady. Of interest for both targeted and all-sky blind searches. Ω component intrinsically not as strong as 2Ω one. Exist addition failure mechanisms as compared to 2Ω case. Signal more complex than conventional 2Ω one. Will presumably need large SNR for confident detection. Computational burden of search very low.

Open issue Ian Jones Neutron stars as laboratories for exotic physics 19/20 Open issue: will necessary asymmetry exist in Nature? Where or not multiple frequency search ultimately worthwhile depends upon what sources Nature chooses to provide. I would argue certainly worth looking for: existence of Q 21 multipole doesn t seem any less plausible than Q 22 one! Need to break axisymmetry in either case. Magentic field might be the symmetry breaking agent.

Summary Ian Jones Neutron stars as laboratories for exotic physics 20/20 1. Precession: Existing radio observations of precession have provoked lively debate. They seem to imply that either our existing model of neutron star interiors is seriously flawed or vortex instabilities are operative. 2. Steady rotation: Multiple frequency GW emission possible, even if rotation appears to be completely steady. An observation of multiple frequency GW emission from a steadily rotating star would provide evidence in favour of pinned superfluidity.