Invited Perspective published in Science, 311, 1876 (Mar. 31, 2006)
[Note added for astro-ph: In this short introductory commentary on the paper (Hessels et
al 2006, Science, 311, 1901) reporting the discovery of the shortest spin period
millisecond pulsar (MSP) Ter5-ad in the globular cluster Terzan 5, I also point out a new
explanation for possible minimum spin periods, P, of MSPs without requiring
gravitational radiation (or other) slow-down torques. If the accretion of matter required to
spinup a MSP also reduces (buries) the neutron star (NS) magnetic field, B, as commonly
believed, an inverse correlation between neutron star mass, M, and B is expected together
with a positive correlation between P and B. Both are suggested for the 4 MSPs with NS
mass measures reported (Latimer and Prakash 2004, Science, 304, 536) to have ≤10%
uncertainties. The correlations imply the Ter5-ad NS has ~2.5 M?, B ~5 x 107 G and thus
P~3 x 10-21 s/s – which can be tested when a timing solution is found. If confirmed, the
highest spin frequency NSs do not pulse simply because their B fields are too low.]
A Neutron Star in F-sharp
Jonathan E. Grindlay1
Millisecond pulsars are extreme examples of what can happen when stars evolve into
neutron stars in compact binary systems. These rotating objects are spun up by accretion
of matter from their binary companions, producing luminous X-ray emission, and later
become detectable as pulsars with periods of a few milliseconds (1). As a result, these
“fast pulsars” may offer some of the best probes to study matter and space in the
relativistic regime of strong gravity. On page 1901, Hessels et al (2) report the discovery
of pulsar PSR J1748-2446ad in the dense globular cluster Terzan 5 (Ter5-ad). This
object, detected with the Green Bank radio Telescope, holds the new record for the fastest
spinning neutron star (or indeed any object of stellar mass or larger). Its spin period is
only 1.396 ms, even shorter than that of B1937+21 [the first millisecond pulsar
discovered (3)] at1.558 ms. With a rotation frequency of 716 Hz, Ter5-ad reaches a new
high note for the music of the celestial spheres – between F and F sharp, whereas
B1937+21 (at 642Hz) can only hit a note between D-sharp and E.
Since their discovery in 1967, pulsars have been the gateway to the study of matter and
energy at the extremes found only in neutron stars (4). Such stars are nature’s last stable
outposts of matter and only a factor of ~3 larger in radius than what would collapse to a
black hole. With ~1.4-2 solar masses (M?) packed into a ~10-15 km radius, neutron stars
are the ultimate laboratories for astrophysics and physics of the extreme. Neutron stars
can exhibit magnetic fields about 1015 times that of the Earth, as revealed in giant flares
of magnetars. And neutron star – binary pairs merge to produce extremely energetic
events as revealed in short gamma-ray bursts. However it is the oldest, and fastest
1 The author is at the Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138.
pulsars, the millisecond pulsars, that may allow the most direct measures of the ultimate
prize: the mass M and radius R of the neutron star itself, which would fix the equation of
state and the composition of matter at hypernuclear density. The Ter5-ad system is a new
stepping stone to the quest for M and R as well as a constraint on the ultimate rotational
limits that may be revealed by gravitational waves.
A point on the rotation equator of Ter5-ad has velocity nearly one-fourth the speed of
light, assuming R = 15 km. The constraint that the maximum spin frequency ns not
exceed the Keplerian orbital frequency nK at the neutron star surface gives the simple
constraint that ns ≤ 1833(M/M?) R10-3/2 Hz where M is the neutron star mass and R10 is the
radius in units of 10 km. Taking into account general relativistic effects, Lattimer and
Prakash (5) derived a value of 1045 Hz as the maximum spin frequency for a neutron star
with (non-rotating) radius R and mass M less than the maximum mass allowed by its
equation of state. A measured spin frequency ns then sets an upper bound on the neutron
star radius. For Ter5-ad with ns = 716Hz, R is restricted to be ≤ 14.4 to 16.7 km when M
is ≤ 1.4 to 2.2 M? , which is the approximate range encompassed by recent neutron star
mass measurements with quoted uncertainties ≤10% (5). As Hessels et al point out, a
mass measurement -- and thus a constraint on the equation of state -- for the neutron star
in Ter5-ad is conceivable given its eclipsing geometry if the radial velocity of the ≥0.14
M? main-sequence binary companion can be measured. Given likely stellar crowding,
this will be difficult, however: With the ~7 magnitudes of optical extinction to Terzan 5,
the companion must be sought in the in the near-infrared with an expected infrared
magnitude as faint as ~25.
X-ray observations allow complementary constraints on M and R for the neutron stars in
quiescent low mass X-ray binaries (qLMXBs) as well as their millisecond pulsar
descendents. The first Chandra X-ray survey of the globular cluster 47Tuc revealed that
source X7 was one of several qLMXBs (6). Analysis of deeper Chandra observations of
X7 with fits of neutron star atmosphere models (including surface gravities) to its purely
thermal X-ray emission spectrum can be made. These fits yield 90% confidence limits
ranging from R = 12.7 to 16.7 km (for M = 1.4 M?) to R = 10.0 to 15.0 km (for M = 2.2
M?) (7), which are consistent with those for Ter5-ad. Even more accurate constraints of
the gravitational redshift factor M/R (which in turn constrains the equation of state given
measures of M) for neutron stars are possible from studies of the pulsed profiles of
thermal X-ray emission from millisecond pulsars, provided the pulsar distance and
inclination angles are known (8). Unfortunately Ter5-ad may not allow this, since its X-
ray emission is likely dominated by unpulsed non-thermal emission due to the shock
where its pulsar wind encounters gas from its main sequence binary companion, as
recently identified (9) in the similar millisecond pulsar 47Tuc-W.
Hessels et al suggest that even faster millisecond pulsars exist but may be hidden by the
increased likelihood of radio eclipses, because their increased spin-down energy loss rate
and resulting pulsar wind more readily drives matter off their binary companions. Indeed
the distribution (see the figure) of the energy flux from the spin-down energy loss
incident on the binary companion for the 12 fastest millisecond pulsars with binary
companions (10) shows that the eclipsing (radio) systems are generally those with the
largest incident flux. Still faster millisecond pulsars are preferentially hidden (if still in
binaries) from radio surveys but would be detectable as relatively hard X-ray sources
(unpulsed) from their pulsar wind shocks.
A maximum NS spin frequency, nmax ~ 760 Hz, was suggested (11) given the spin
distribution for accretion-powered as well as radio millisecond pulsars. A value for nmax
much less than 1045Hz, the maximum allowed independent of the equation of state (5),
could require a source of angular momentum loss such as gravitational radiation from an
r-mode instability in the neutron star core (12). Another mechanism may be at work: if
the accreting matter spinning up the neutron star is burying its primordial magnetic field,
-- as is generally believed (1) to account for the B ≤ 109 G fields inferred for qLMXBs
and millisecond pulsars -- then the increased accretion and final spin ns imply a lower B
field emerging from the neutron star when accretion stops. The millisecond pulsars that
spin fastest would then have the lowest B fields (above threshold for pulsations) and
largest neutron star mass; neutron stars with larger values of ns and mass have smaller B
and do not pulse. For those millisecond pulsars with neutron star mass estimates (5),
including the 2.2 ±0.2 M? value for the neutron star in the millisecond pulsar
J0751+1807 (13), possible correlations between B vs. P and B vs. M are evident (see the
figure). The implied values for Ter5-ad are ~2.5 M? and ~7 x 107 gauss and thus a
predicted change in spin period
P~3 x 10-21 s/s, which can be tested when a final timing
solution is found. If this were the case, then Ter5-ad would have a mass approaching the
maximum (5) for neutron stars, and it could be singing nearly the highest note without
having made gravitational waves.
1. D. Bhattacharya and E.P.J. van den Heuvel Phys. Rep. 203, 1 (1991).
2. J.W.T. Hessels et al., Science 311, xxx (2006); published online 12 January 2006
3. D.C. Backer, S.R. Kulkarni, C. Heiles, M.M. Davis, W.M. Goss, Nature 300, 615 (1982).
4. Special issue on pulsars, Science 304 (23 April 2004).
5. J.M. Lattimer and M. Prakash, Science 304, 536 (2004).
6. J.E. Grindlay, C.O. Heinke, P.D. Edmonds and S.S. Murray, Science 292, 2290 (2001);
published online 17 May 2001 (10.1126/science.1061135).
7. C.O. Heinke, G.B. Rybicki, R. Narayan and J.E. Grindlay, Astrophys. J., in press (2006).
8. G.G. Pavlov and V.E. Zavlin, Astrophys. J ,490, L91 (1997).
9. S. Bogdanov, J.E. Grindlay, and M. van den Berg, Astrophys. J. 630, 1029 (2005).
10. Australia Telescope National Facility Pulsar Catalogue
11. D. Chakrabarty et al., Nature 424, 42 (2003).
12. R. V. Wagoner, Astrophys. J. 278, 345 (1984).
13. D.J. Nice et al., Astrophys. J. 634, 1242 (2005).
Pulsar properties: (Top) Gas from the normal star in the binary system is prevented from accreting onto the
neutron star at the shock formed where it meets the “wind” of relativistic particles. The shocked gas eclipses
the pulsar for much of the time so that pulsars with the shortest spins (strongest wind) and closest companions
may be permanently hidden at radio frequencies, although unpulsed X-rays are expected. [Adapted from (9)]
(Center) Pulsar wind energy flux of the 12 fastest spinning millisecond pulsars in binary systems that would
be incident on their binary companion stars [parameters from (2) and (10)]. For pulsars without measured
Pdots (including Ter5-ad), an estimated fixed value of 2 x 10-20 s/s is used. The eclipsing systems generally do
have higher pulsar wind flux values though Ter5-ad is not extreme, which implies that still faster systems
could be found. The second-fastest millisecond pulsar, B1937+21, cannot be plotted because it has no binary
companion. The other pulsars marked are B1957+20 (Black Widow), 47Tuc-J, and 47Tuc-W, which are
numbers 3, 10, and 12 in order of increasing spin period (10). The two highest pulsar wind flux pulsars are the
eclipsing system Ter5-O and the noneclipsing system M62-C. (Bottom) Correlations for millisecond pulsars
with neutron star mass [values from (5)]. Correlation between mass and neutron star magnetic field B [blue,
from (10)], and between B and spin period P (purple). Extrapolated values are predicted for Ter5-ad; two other
millisecond pulsars [see (10)] are marked for reference.