To put new constraints on the r-mode instability window , we analyse the formation of millisecond pulsars ( MSPs ) within the recycling scenario , making use of three sets of observations : ( a ) X-ray observations of neutron stars ( NSs ) in low-mass X-ray binaries ; ( b ) timing of millisecond pulsars ; and ( c ) X-ray and UV observations of MSPs .
As shown in previous works , r-mode dissipation by shear viscosity is not sufficient to explain observational set ( a ) , and enhanced r-mode dissipation at the red-shifted internal temperatures T ^ { \infty } \sim 10 ^ { 8 } K is required to stabilize the observed NSs .
Here , we argue that models with enhanced bulk viscosity can hardly lead to a self-consistent explanation of observational set ( a ) due to strong neutrino emission , which is typical for these models ( unrealistically powerful energy source is required to keep NSs at the observed temperatures ) .
We also demonstrate that the observational set ( b ) , combined with the theory of internal heating and NS cooling , provides evidence of enhanced r-mode dissipation at low temperatures , T ^ { \infty } \sim 2 \times 10 ^ { 7 } K. Observational set ( c ) allows us to set an upper limit on the internal temperatures of MSPs , T ^ { \infty } < 2 \times 10 ^ { 7 } K ( assuming a canonical NS with the accreted crust ) .
Recycling scenario can produce MSPs at these temperatures only if r-mode instability is suppressed in the whole MSP spin frequency range ( \nu \lesssim 750 Hz ) at temperatures 2 \times 10 ^ { 7 } \lesssim T ^ { \infty } \lesssim 3 \times 10 ^ { 7 } K , providing thus a new constraint on the r-mode instability window .
These observational constraints are analysed in more details in application to the resonance uplift scenario of ( 48 ; 47 ) .