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On the bimodality of the kick velocity distribution of
radio pulsars
S.B. Popov
Universit’a di Padova, via Marzolo 8, 35131, Padova, Italy;
Sternberg Astronomical Institute, Universitetski pr. 13, 119992 Moscow,
Russia
I. Bombaci
Universit’a di Pisa, via F. Buonarroti 2, 56127 Pisa, Italy
Abstract. We propose that the bimodal nature of the kick velocity distribu­
tion of radio pulsars is connected to the dichotomy between hadronic stars (i.e.
neutron stars with no quark matter content) and quark stars. Bimodality can
appear due to di#erent mechanisms of explosion which lead to the formation of
two types of compact stars or due to two di#erent sets of parameters driving a
particular kick mechanism. The low velocity maximum (at # 100 km s -1 ) is
associated with hadronic star formation, whereas the second peak corresponds
to quark stars. In the model of delayed collapse of hadronic stars to quark stars
(Berezhiani et al. 2003) quark deconfinement leads to a second energy release,
and to a second kick, in addition to the kick imparted to the newly formed
hadronic star during the supernova explosion. If the electromagnetic rocket
mechanism can give a significant contribution to pulsar kicks, then the high ve­
locity peak can be associated with the shorter initial spin periods of quark stars
with respect to hadronic stars.
An important property of the compact stars usually called neutron stars
(NSs) is their spatial velocity distribution. At the present time the most widely
accepted velocity distribution is the one obtained by Arzoumanian, Cherno# &
Cordes (2002) . It is a bimodal distribution with two Maxwellian components.
Here we propose a scenario in which the low­velocity part of the distribution
is connected with normal (hadronic) compact stars, and high­velocity part is
formed by objects with some amount of quark matter inside (hybrid or strange
stars).
The fact that we are dealing with radio pulsars tells us that to produce
di#erent kicks we cannot use ideas which involve physical conditions in which
radio pulsars do not exist (for example, too low magnetic fields, or too long
initial rotational periods). Binaries also cannot explain this bimodality (they
do not produce enough high­velocity NSs if isolated and binary progenitor stars
produce PSRs with comparable probabilities). So we come to a conclusion that
some significant dichotomy among normal single (isolated) radio pulsars is re­
quired. The strongest theoretically known dichotomy in compact stars is the
dichotomy between pure hadronic stars (HSs) and quark stars (QSs). Among
many di#erences between HSs and QSs, typical kick velocities for the members
of these two families of compact stars can be di#erent too.
1

2 Popov and Bombaci
A quark star can be formed in a delayed collapse (see Berezhiani et al. 2003)
or in a direct collapse with additional energy release. In both cases additional
energy release and, correspondently, additional kick can be expected. As we
suggest that about one half of all PSRs are QSs, then most of QSs should be
formed due to fall­back or directly in the SN explosion (so that the delay time is
significantly shortened), since the outcome of NSs from binary systems is rather
small to constitute #1/2 of the total PSR population. Anyway, an additional
energy release can produce a bimodal distribution of many physical properties
of the compact stars which we usually call just NSs.
We suggest that the delayed stellar conversion process of a pure HS to a QS,
triggered by quark deconfinement, can give a second kick to the compact star.
Thus, the low velocity component of the pulsar velocity distribution receives
contributions mainly from ``normal'' NSs (hadronic stars) which have passed
through a single explosion (the SN explosion). The high velocity part is mostly
composed of QSs which have received a second kick due to the energy release
associated with the stellar conversion process.
Of course, as far as both explosions produce distributions of velocities, it is
possible to find low velocity QSs which experienced two kicks, and high velocity
HSs which received just a single natal kick. Also, among mid­ and high­velocity
objects there can be a contribution of HSs from massive binaries.
More details can be found in a recent paper Bombaci & Popov (2004).
Compact object with di#erent velocities can be very similar to each other
if they belong to the same peak of the velocity distribution (i.e. there will be no
correlations of di#erent parameters vs. velocity if NSs belong to the same com­
ponent of the distribution). However, if our hypothesis is correct low­velocity
objects on average can be distinct from high­velocity ones. They can have di#er­
ent average values of some parameters, or demostrate di#erences in behaviour,
especially if it is connected with their internal structure. An interesting problem
is the possibility of glitches in QSs. As internal structure of QSs and HSs are
di#erent, it is reasonable to expect that glitches of the two types of compact
objects are di#erent too (see recent discussion in Horvath 2004). At present
more than 100 glitches from about 35 PSRs have been reported (see Shemar &
Lyne 1996, Krawczyk et al. 2003 and references therein). For 9 of these objects
transverse velocities are available. For the two­component distribution of Arzou­
manian et al. (2002), contribution of the low velocity component dominates up
to # 300 km s -1 , which corresponds to the transverse velocity V t # 250 km s -1 .
All but two velocity measurements of glitchers are below this limit. The best
known glitchers -- Crab and Vela -- definitely represent the low­velocity compo­
nent. High velocity glitchers can be products of disruption of close binaries.
Full text of the poster is available at http://xray.sai.msu.ru/” polar/.
References
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Berezhiani, Z., Bombaci, I., Drago, A., Frontera, F., & Lavagno, A. 2003, ApJ 586, 1250
Bombaci, I., & Popov, S.B. 2004, A&A 424, 627
Horvath, J.E. 2004, astro­ph/0404324
Krawczyk, A., Lyne, A.G., Gil, J.A., & Joshi, B.C. 2003, MNRAS 340 1087
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