How bumpy can neutron stars be?:
How bumpy can neutron stars be? Ellipticity e = (Ixx – Iyy)/Izz ~ Q22/Izz
Elastic deformations
Solid matter folded, spindled, and mutilated
Max determined by breaking strain, shear modulus
Traditional answer: emax ~ few x 10-7 (LIGO-S1 PRD 2004)
New crazy answer: emax ~ few x 10-4 (Owen astro-ph/0503399)
New not-so-crazy answer: emax ~ 10-5 (Owen astro-ph/0503399)
Hydromagnetic deformations
Accreting matter (maybe not solid) bottled by magnetic field
Max determined by field strength, matter conductivity (flow-thru)
New answer: emax ~ 10-5 (Melatos & Payne astro-ph/0503287)
Elastic deformations:
Elastic deformations Solid crust (all stars)
Ushomirsky et al MNRAS (2000)
Neutron-rich nuclei
Conservative physics
Solid core (hybrid star)
Glendenning PRD (1992)
Gradual phase transition
(-) quark droplets in (+) baryonic background
Up to 8km solid core
Not-so-crazy physics
All-solid (strange quark) star
Xu ApJL (2003)
s quark clustering
Crazy physics
Hydromagnetic deformations:
Hydromagnetic deformations Melatos & Phinney PASP (2000)
Accreting ms pulsars only
Accreted matter funnels towards magnetic pole
Matter crosses field lines slowly (Ohmic diffusion)
Depends on conductivity of matter at low density
Field lines hold up mountain that would collapse under its own weight
Good news for searches:
Good news for searches S2 known pulsars
9 pulsars e < few x 10-4 (solid strange star) – mildly interesting
(These have no competing spindown upper limit)
S5 known pulsars
(Extrapolating SRD sensitivity and 1yr integration time)
9 “original” pulsars e < 10-5 (hybrid star) – interesting!
O(10) more have e < 10-5 and O(100) have e < few x 10-4
S5 all-sky
Solid strange star emax visible in most of galaxy (beyond core)
Hybrid star emax visible to few kpc (Gould belt, not galactic core)
Detection: e too big for normal star
Many non-detections: render a model unlikely
Don’t party just yet…:
Don’t party just yet… Many radio pulsars have e < 10-8 from spindown (probably even in globular clusters)
How to get to emax?
How to keep at emax?
Stars with big e don’t last long in the LIGO band
Hydromagnetic: accreting millisecond pulsars in LMXBs have e ~ 10-7 from x-ray flux and torque balance; have we seen them all?
Conclusions:
Conclusions Limits on e < 10-4 (S2) are already (mildly) interesting
Limits on e < 10-5 (S5) get us to where we might detect something in a reasonable theory
Enough non-detections will let us confront, though not rule out, some theories of dense matter