# Presentation: 243376

## What happened to the r-modes?

- Nils Andersson
- University of Southampton
- Santa Fe July 2003

- The gravitational-wave driven instability of the inertial r-modes may
-  	govern the spin evolution of nascent neutron stars
-  	halt the accretion induced spin-up of NS in LMXBs
-  	lead to detectable gravitational waves
- but, despite five years of effort, we still do not understand the details of this mechanism well enough to draw any definite conclusions...

## The r-mode instability

- The l=m=2 r-mode grows on a timescale of a few tens of seconds, and leads to a strong instability.

- What are the dissipation mechanisms that affect the instability?
-  		- crust-core boundary layers
-  		- hyperon bulk viscosity
-  		- superfluid mutual friction
- 		- magnetic field effects
- What is the mechanism that saturates the mode, and at what _[amplitude](file:///C:/WINDOWS/Desktop/work/presentations/astro%20seminar/pics/final.mov)__[ does](file:///C:/WINDOWS/Desktop/work/presentations/astro%20seminar/pics/final.mov)_ this happen?
-  		- nonlinear mode coupling may limit the
- 		  r-modes to small amplitudes
- Will the mode survive saturation?
- What is the backreaction of the
- mode on the star - will radiation reaction and/or non-linear effects  lead to differential rotation?

- The instability is counteracted by shear and bulk viscosity, leading to a “window of opportunity” around 109 K.

## “Exotic” viscosity

- Then the nuclear reactions that lead to the macroscopic bulk viscosity are suppressed...
- ... and the effect on the instability may not be so great after all.

- “Exotic” viscosity

- Hyperon bulk viscosity may suppress the r-mode instability significantly.

- In order to study the effects of exotic particles we need to understand the oscillations of fully relativistic, possibly superfluid, NS!

- A conglomerate of s,d,u quarks may be the most stable form of matter.
- Strange matter also has a very strong bulk viscosity: In a strange star the r-mode instability window is located at lower temperatures.

- While accreting NS are likely to undergo a thermo-gravitational runaway, accreting strange or hybrid stars may reach quasi-equilibrium and radiate persistent GWs.

## Superfluid hydrodynamics

- The simplest model for a superfluid star consists of two fluids coupled via entrainment. At a basic level, the system is analogous to **two coupled oscillators**.
- The two dynamical degrees of freedom
- lead to independent sets of modes which
- tend to be such that the fluids are co- and
- counter-moving.
- Deviation from chemical equilibrium provides the main restoring agent for the superfluid modes.
- The presence of vortices leads to entrainment and “mutual friction” between interpenetrating superfluids. These are key mechanisms that needs to be understood.

- YES!

- Two-stream instability

## The saturation amplitude

- The r-mode growth phase can be described by linear theory, but nonlinear effects soon become important.
- _Phenomenology_:
- At some point the mode “saturates” and as excess angular momentum is radiated away the star spins down.
- Model using  and  and evolution equations from the conservation of energy and angular momentum:
- Note: Early estimates used =1 which is _very_ large, corresponding to

- Current evidence: r-mode GWs would be detectable within our galaxy provided signal can be integrated for two weeks.

## Some challenges

- Our understanding of the r-mode instability is still far from satisfactory. We need to face up to several difficult challenges.
**Theory:**
-  Must improve our models of exotic physics in NS cores: Are	hyperons 			and/or deconfined quarks present?
-  Need better models of superfluid dynamics and the associated viscosities.
-  Need independent determination of saturation amplitude. Numerical 				evolutions are difficult because of the need to resolve short lengthscales. 		What happens in stratified or superfluid stars?
-  Should study role of magnetic field in detail (secular drift leads to wind-up, 		magneto-viscous boundary layer may suppress instability).
**Observations:**
-  Does the presence of an instability in the core fluid affect the EM signal?
-  Are data for young and recycled radio PSRs and LMXBs consistent with the 		presence of a strong instability?  What about the temperature?
-  Need to develop GW detection strategies that account for evolution of 			source, eg. due to variation in accretion rate.

- Observations may provide a probe of exotic physics!