We study the field millisecond pulsar population to infer its intrinsic distribution in spin period and luminosity and to determine its spatial distribution within the Galaxy .
Our likelihood analysis on data from extant surveys ( 22 pulsars with periods < 20 ms ) accounts for the following important selection effects : ( 1 ) the survey sensitivity as a function of direction , spin period , and sky coverage ; ( 2 ) interstellar scintillation , which modulates the pulsed flux and causes a net increase in search volume \sim 30 % ; and ( 3 ) errors in the pulsar distance scale .

Adopting power-law models ( with cutoffs ) for the intrinsic distributions , the analysis yields a minimum period cutoff { P _ { min } > 0.65 } ms ( 99 % confidence ) , a period distribution \propto P ^ { -2.0 \pm 0.33 } and a pseudo-luminosity distribution \propto L _ { p } ^ { -2.0 \pm 0.2 } ( where L _ { p } = flux density \times distance ^ { 2 } , for L _ { p } \geq 1.1 mJy kpc ^ { 2 } ) .

We find that the column density of millisecond pulsars ( uncorrected for beaming effects ) is \sim 50 ^ { +30 } _ { -20 } kpc ^ { -2 } in the vicinity of the solar system .
For a Gaussian model the z scale height is 0.65 ^ { +0.16 } _ { -0.12 } kpc , corresponding to local number density 29 ^ { +17 } _ { -11 } kpc ^ { -3 } .
( For an exponential model the scale height becomes 0.50 ^ { +0.19 } _ { -0.13 } kpc and the number density 44 ^ { +25 } _ { -16 } kpc ^ { -3 } . )
Estimates of the total number of MSPs in the disk of the Galaxy and for the associated birthrate are given .
The contribution of a diffuse halo-like component ( tracing the Galactic spheroid , the halo or the globular cluster density profile ) to the local number density of MSPs is limited to \mathbin { \lower 3.0 pt \hbox { $ \hbox to 0.0 pt { \raise 5.0 pt \hbox { $ \char 60 $ } } % \mathchar 29208 $ } } 1 % of the midplane value .

We consider a kinematic model for the MSP spatial distribution in which objects in the disk are kicked once at birth and then orbit in a smooth Galactic potential , becoming dynamically well-mixed .
The analysis yields a column density 49 ^ { +27 } _ { -17 } kpc ^ { -2 } ( comparable to the above ) , a birth z kick velocity 52 ^ { +17 } _ { -11 } km s ^ { -1 } and a 3D velocity dispersion of \sim 84 km s ^ { -1 } .
MSP velocities are smaller than those of young , long-period pulsars by about a factor of 5 .
The kinematic properties of the MSP population are discussed , including expected transverse motions , the occurrence of asymmetric drift , the shape of the velocity ellipsoid and the z scale height at birth .
If MSPs are long-lived then a significant contribution to observed MSP z velocities owes to diffusive processes that increase the scale height of old stellar populations ; our best estimate of the 1D velocity kick that is unique to MSP evolution is \sim 40 km s ^ { -1 } if such diffusion is taken into account .

The scale heights of millisecond pulsars and low-mass X-ray binaries are consistent , suggesting a common origin and that the primary channel for forming both classes of objects imparts only low velocities .
Binaries involving a common envelope phase and a neutron-star forming supernova explosion can yield such objects , even with explosion asymmetries like those needed to provide the velocity distribution of isolated , nonspunup radio pulsars .

Future searches for MSPs may be optimized using the model results .
As an example , we give the expected number of detectable MSPs per beam area and the volumes of the Galaxy sampled per beam area for a hypothetical Green Bank Telescope all sky survey .
Estimates for the volume that must be surveyed to find a pulsar faster than 1.5 ms are given .
We also briefly discuss how selection effects associated with fast binaries influence our results .