A&A 541, A22 (2012)
DOI:
10.1051
/0004-6361/201218798
c ESO 2012
Astronomy
&
Astrophysics
Formation of the planet around the millisecond pulsar J1719–1438
L. M. van Haaften
1
, G. Nelemans
1
,2
, R. Voss
1
, and P. G. Jonker
3
,1,4
1
Department of Astrophysics
/ IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
e-mail:
L.vanHaaften@astro.ru.nl
2
Institute for Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
3
SRON, Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA, Utrecht, The Netherlands
4
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
Received 9 January 2012
/ Accepted 12 March 2012
ABSTRACT
Context.
Recently the discovery of PSR J1719–1438, a 5
.8 ms pulsar with a companion in a 2.2 h orbit, was reported. The combination
of this orbital period and the very low mass function is unique. The discoverers, Bailes et al. (2011, Science, 333, 1717), proposed an
ultracompact X-ray binary (UCXB) as the progenitor system. However, the standard UCXB scenario would not produce this system
as the time required to reach this orbital period exceeds the current estimate of the age of the Universe. The detached state of the
system aggravates the problem. The inclination of the system is an important unknown, and Bailes et al. noted that for very low (a
priori very unlikely) inclinations the system is better explained as having a brown dwarf companion rather than an UCXB origin.
Aims.
We want to understand the evolutionary history of PSR J1719–1438, and determine under which circumstances it could have
evolved from an UCXB.
Methods.
We model UCXB evolution varying the donor size and investigate the e
ffect of a wind mass loss from the donor, and
compare the results with the observed characteristics of PSR J1719–1438.
Results.
An UCXB can reach a 2
.2 h orbit within the age of the Universe, provided that 1) the millisecond pulsar can significantly
heat and expand the donor by pulsar irradiation, or 2) the system loses extra orbital angular momentum, e.g. via a fast wind from the
donor.
Conclusions.
The most likely scenario for the formation of PSR J1719–1438 is UCXB evolution driven by angular momentum loss
via the usual gravitational wave emission, which is enhanced by angular momentum loss via a donor wind of >
∼3 × 10
−13
M yr
−1
.
Depending on the size of the donor during the evolution, the companion presently probably has a mass of
∼1–3 Jupiter masses, making
it a very low mass white dwarf as proposed by Bailes et al. Its composition can be either helium or carbon-oxygen. A helium white
dwarf companion makes the long (for an UCXB) orbital period easier to explain, but the required inclination makes it a priori less
likely than a carbon-oxygen white dwarf.
Key words.
pulsars: individual: J1719–1438 – binaries: close – planets and satellites: formation
1. Introduction
Even though the first exoplanets were discovered around a mil-
lisecond pulsar, PSR B1257
+12 (
Wolszczan & Frail 1992
), the
discovery of a companion around PSR J1719–1438 (
Bailes et al.
2011
, hereafter B11) marked the first time a millisecond pulsar
with a very low mass companion in a short orbit has been found.
The orbital period is 2
.177 h (130.6 min) and the mass function
is 7
.85 × 10
−10
M , implying a minimum companion mass of
1
.16 × 10
−3
M (1
.47 × 10
−3
M ) in the case of a 1
.4 M (2 M )
neutron star. The system is detached and there is no information
on the chemical composition of the companion. The minimum
mean density of the companion is 23
.3 g cm
−3
as follows from
the relation between the mean density of the companion Roche
lobe and the orbital period.
B11 stated that the high companion density, the orbital pe-
riod, and the 5
.8 ms spin period of the pulsar are consistent with
a history as an ultracompact X-ray binary (UCXB), which is a
binary consisting of a white dwarf (like) donor transferring mass
to a neutron star, forced by angular momentum loss via gravita-
tional wave emission (
Verbunt & van den Heuvel 1995
).
B11 themselves noted the result by
Deloye & Bildsten
(
2003
) that an UCXB reaches an orbital period of
∼90 min after
5–10 Gyr. The discrepancy between 90 min and 130
.6 min is
very significant, however, because the orbital period increases
slowly at longer orbital periods. Furthermore, B11 did not satis-
factorily answer why the system has become detached. They did
suggest a change in the exponent of the white dwarf mass-radius
relation near the present mass (assuming a near edge-on orbit) as
a natural cause of detachment, but such a change merely changes
the mass transfer rate and cannot lead to detachment.
In this paper, we will investigate two modifications to the
UCXB evolution that could resolve these issues. These are 1)
a larger donor radius and 2) additional angular momentum loss,
apart from that driven by gravitational wave radiation. The actual
scenario may be a combination of these. In Sect.
2
we explain the
problems, and in Sect.
3
we present possible resolutions.
2. Problems with the standard UCXB scenario
Four intrinsic properties of PSR J1719–1438 are known: the or-
bital period, the maximum age of the system (the age of the
Universe, which we take as 13
.75 Gyr,
Jarosik et al. 2011
),
the approximate primary mass as it is a neutron star, and
the radial velocity of the primary. From these, two derived
properties follow: the mass function, which gives an a priori
likely companion mass, and the gravitational wave timescale
τ
GW
= −( J
orb
/ ˙ J
orb
)
GW
with J
orb
the orbital angular momentum.
Article published by EDP Sciences
A22, page 1 of
5
A&A 541, A22 (2012)
Fig. 1.
Timescale for angular momentum loss via gravitational wave
emission as a function of binary inclination for two assumed pulsar
masses, for PSR J1719–1438 with mass function 7
.85 × 10
−10
M . The
upper horizontal axis gives the a priori probability for an inclination
lower than indicated on the lower horizontal axis.
The combination of the values of these parameters is inconsis-
tent with the canonical UCXB scenario (e.g.
Deloye & Bildsten
2003
;
van Haaften et al. 2012
) for the following reasons:
1. Present evolutionary timescale. Even without making as-
sumptions about the companion type, the implied compan-
ion mass is inconsistent with an evolution driven by angular
momentum loss via gravitational wave emission, as shown in
Fig.
1
, where the gravitational wave timescale is a function
of the companion mass M
c
and pulsar mass M
p
via (
Landau
& Lifshitz 1975
)
τ
GW
=
5
32
c
5
G
5
/3
(M
p
+ M
c
)
1
/3
M
p
M
c
P
orb
2
π
8
/3
,
(1)
where P
orb
is the orbital period, c the speed of light,
G the gravitational constant, and M
c
is a function of
the binary inclination i given the measured mass function
(M
c
sin i)
3
/(M
p
+ M
c
)
2
and an assumed pulsar mass. For nor-
mal (close to edge-on) inclinations, the gravitational wave
timescale exceeds the age of the Universe by a large fac-
tor (
∼10−30). The ratio between the gravitational wave
timescale and the age of the Universe needs to be less than or
close to 1, if evolution is driven by gravitational wave emis-
sion, but the corresponding inclinations have a priori proba-
bilities near 0
.1%.
2. Orbital period. If we hypothesize PSR J1719–1438 to have
originated from an UCXB, we can explore the previous ar-
gument in more detail. The orbital period of an UCXB in-
creases during its evolution
1
, at a rate determined by angular
momentum loss via gravitational wave radiation. Figure
2
(solid tracks) shows that an UCXB containing a donor close
to zero-temperature radius (i.e., the radius of a white dwarf
lacking support by thermal pressure) cannot reach the orbital
period of PSR J1719–1438 of 130
.6 min within the age of the
1
The orbital period increases because the exponent
ζ
d
of the mass-
radius relation of the white dwarf donor is lower than 1
/3, correspond-
ing to a decreasing average donor density. This follows from the Roche
lobe geometry and Kepler’s third law.
Fig. 2.
Donor mass versus orbital period for UCXBs. The solid curves
represent a zero-temperature carbon-oxygen (gray) and helium (black)
white dwarf donor. The dashed curves are di
fferent from the solid curves
only in that they have a twice as large donor radius at all masses. The
circles on top of the solid and dashed curves mark the age of the system
since the onset of mass transfer, the numbers associated with the circles
indicate the ages in yr. Filled (open) symbols indicate an initial accretor
mass of 1
.4 M (2 M ). The dotted extensions to the curves go beyond
the point that a UCXB with a 1
.4 M accretor can reach within the
age of the Universe. The vertical solid line shows the present orbital
period of PSR J1719–1438. The overlaying triangles give the a priori
probabilities for the donor mass being higher than indicated, based on
the mass function.
Universe. Donors that are heated have a larger radius, which
results in a longer orbital period at a given age. To gain in-
sight in how a larger radius translates into a longer orbital
period, we simply parameterize a bloated donor by multiply-
ing the radius by a fixed factor for all masses (dashed tracks).
A factor 2 is required for a helium white dwarf donor UCXB
to reach an orbital period of 130
.6 min within the age of
the Universe, and an even larger factor of 2
.5 for a carbon-
oxygen white dwarf donor.
The onset of mass transfer is expected to have occurred sev-
eral gigayears after the Big Bang, so less time is available for
the described evolution, aggravating the problem. Moreover,
it is possible that the system became detached long ago.
3. Detached state. Since an UCXB at all times continues to lose
angular momentum via gravitational waves, the donor will
keep filling its Roche lobe and therefore is not expected to
become detached. B11 suggested that an UCXB becomes de-
tached when the mass-radius relation of the donor becomes
∼0, but this is not the case. The behavior of the system does
not qualitatively depend on the value or the sign of the expo-
nent
ζ
d
of the mass-radius relation of the donor R
d
∝ M
ζ
d
d
, as
long as
ζ
d
is not close to the exponent
ζ
L
≈ −5/3 of the donor
mass-Roche lobe radius relation R
L
∝ M
ζ
L
d
. Here M
d
, R
d
and
R
L
are the donor mass and the donor and Roche-lobe radii,
respectively. The increasing exponent of the mass-radius re-
lation of the donor resulting from its decreasing mass merely
lowers the mass transfer rate (e.g. Eq. (6) in
Savonije et al.
1986
)
2
− ˙
M
d
=
2
ζ
d
− ζ
L
M
d
τ
GW
(2)
2
The simultaneously increasing gravitational wave timescale gener-
ally has a much larger impact on the mass transfer rate.
A22, page 2 of
5
L. M. van Haaften et al.: Formation of the planet around PSR J1719–1438
Fig. 3.
Zero-temperature white dwarf mass-radius relations by Eggleton
(
Rappaport et al. 1987
) for pure helium, carbon and oxygen compo-
sitions (dashed), and the present Roche-lobe radius against mass for
the companion of PSR J1719–1438. Filled circles (neutron star mass of
1
.4 M ) and open circles (neutron star mass of 2 M ) from low to high
companion mass indicate the 1, 0
.1 and 0.01 a priori probabilities for a
companion mass higher than indicated.
and by itself cannot cause detachment, even if this expo-
nent becomes zero or positive (which happens at the donor
masses corresponding to the maxima of the dashed mass-
radius curves in Fig.
3
). A detached state suggests that the
companion has shrunk by itself on a timescale shorter than
the (at this point very long) evolutionary timescale.
3. Possible resolutions
Figure
3
, which is similar to the figure in B11, shows the range
of allowed companion radii as function of its mass and composi-
tion. The zero-temperature radius (dashed) is the lower limit and
the Roche-lobe radius (solid) the upper limit. If the system is ob-
served close to edge-on, a helium white dwarf is too large to fit
inside the Roche lobe, while a carbon-oxygen white dwarf does
fit in as long as it is not much larger than the zero-temperature
radius. However, if we observe the system at an inclination of
less than 31
◦
(41
◦
) (a priori probability 14% (24%)) in the case
of a 1
.4 M (2 M ) neutron star, the companion mass is suffi-
ciently high for even a zero-temperature helium white dwarf to
fit in its Roche lobe. If bloated, a lower inclination is required.
Hydrogen-dominated planets or low-mass brown dwarfs have a
much higher radius (
∼0.1 R ) and therefore require a very low
inclination.
3.1. Bloated donor scenario
The relatively long orbital period may have been reached within
the age of the Universe if the donor has been bloated during a
significant part of its lifetime. Figure
2
shows that the present
companion mass in this scenario is at least
∼0.01 M , which
requires that we observe the system at an a priori unlikely incli-
nation of less than
∼6.6
◦
(0
.7%), assuming a neutron star mass
of 1
.4 M . Alternatively, the ∼0.01 M donor has subsequently
lost a large amount of mass at an almost constant orbital period
near the present orbital period, arriving at a mass of
∼10
−3
M .
Before this mass loss event, the gravitational wave timescale
would have been much shorter and consistent with its maximum
age (the age of the Universe), see Fig.
1
.
Investigation of the mass-radius relation by
Deloye &
Bildsten
(
2003
) showed that bloated factors of 2 or higher, that
would be necessary to explain the current observed properties of
J1719–1438, are unlikely. So the bloated donor scenario can at
most be a partial explanation.
3.2. Additional angular momentum loss scenario
If gravitational wave radiation is not the only mechanism for
angular momentum loss, the real evolutionary timescale is
shorter, or has been shorter in the past. Empirical evidence from
Cataclysmic Variables suggests that the angular momentum loss
in systems below the period gap is higher (by a factor of
∼2.5)
than expected from gravitational wave emission alone (
Knigge
et al. 2011
). Also, SAX J1808.4–3658, a millisecond pulsar ac-
creting from what is probably a
∼0.05 M brown dwarf compan-
ion (
Bildsten & Chakrabarty 2001
), and therefore rather similar
to an UCXB progenitor of J1719–1438, is losing more angu-
lar momentum than expected from gravitational wave radiation
(
di Salvo et al. 2008
).
If the di
fference between the exponents of the mass-radius
relations of the donor and its Roche lobe becomes smaller, mass
transfer is accelerated. This requires either less tendency of the
Roche lobe to expand upon mass transfer (i.e., a higher (less neg-
ative) value of
ζ
L
), or a stronger expansion of the donor (a lower
value of
ζ
d
). The latter is less likely to happen since both cold
and heated white dwarfs tend to either weakly expand or shrink
at low mass
3
. The former is more likely; a higher exponent
ζ
L
of the donor mass-Roche lobe radius relation can be the result
of mass loss from the system because this mass carries angular
momentum, and therefore the semi-major axis will increase less
upon mass transfer.
3.2.1. Donor wind
Mass lost directly from the donor in a fast wind (the Jeans mode)
carries a large amount of specific angular momentum, because
of the high mass ratio. The specific angular momentum of the
donor relative to the orbit is equal to M
a
/M
d
, where M
a
is the
accretor mass
4
. This wind can be caused by high-energy radia-
tion from the millisecond pulsar, such as X-rays, gamma-rays
from magnetosphere-accretion disk interaction and, when ac-
cretion has stopped, an electron-positron wind (
Kluzniak et al.
1988
;
Ruderman et al. 1989
;
Shaham 1992
). Heating by the pul-
sar wind has been observed in the accretion-powered millisec-
ond X-ray pulsars SAX J1808.4–3658 (
Burderi et al. 2009
) and
IGR J00291
+5934 (
Jonker et al. 2008
) in quiescence. Similarly,
heating of the donor by the hot neutron star has been observed
in EXO 0748–676 in quiescence (
Bassa et al. 2009
).
Ratti et al.
(
2012
) found evidence for a wind driven o
ff the donor in this
system.
Figure
4
shows the e
ffect the wind has on accelerating the
evolution. When the wind mass loss rate is very low, reaching
3
If the white dwarf core temperature remains constant due to tidal
heating, the exponent of the mass-radius relation may diverge, leading
to a dynamical instability that disrupts the companion (
Bildsten 2002
).
4
At very high mass ratio the donor even absolutely carries almost all
of the orbital angular momentum of the system in its orbit around the
center of mass. Interestingly, in J1719–1438 the spin angular momen-
tum of the pulsar is significant at
∼1/6 of the orbital angular momen-
tum.
A22, page 3 of
5
A&A 541, A22 (2012)
Fig. 4.
Age of an UCXB with an initially 1
.4 M accretor when its or-
bital period equals the orbital period of PSR J1719–1438 (130
.6 min)
versus donor mass loss rate, which is assumed to be fast and isotropic,
and constant. The donor composition is indicated. The horizontal gray
line gives the maximum age of PSR J1719–1438.
the orbital period of PSR J1719–1438 takes (much) longer than
the age of the Universe, as shown in Sect.
2
. For a donor wind of
∼3 × 10
−13
M yr
−1
, however, evolution proceeds su
fficiently
fast to explain the observed orbital period. If the wind is as-
sumed to commence later, e.g. below a threshold donor mass
of 0
.01 M , the required time increases by only ∼10−20%.
3.3. Detachment at very low donor mass
At the present mass of >
∼10
−3
M , the donor must have shrunk
relatively rapidly to explain why it has become detached. The
cause could be a change in radius not driven by mass loss, ei-
ther due to steadily decreasing heating by the pulsar, which is
expected given the declining accretion rate, pulsar spin period
(at low donor mass,
van Haaften et al. 2012
) and magnetic field
strength, or due to changing thermal properties of the companion
which could allow for more e
fficient cooling.
If the donor has non-degenerate outer layers due to heat-
ing from the pulsar, mass loss would actually shrink the donor,
and if this happens rapidly, the remnant may become detached.
This implies that the remnant must be quite close to the zero-
temperature radius, and certainly much less bloated than the
∼0.01 M object.
3.4. Detachment due to thermal-viscous disk instability
In particular in binaries with a low mass transfer rate, the accre-
tion disk is subject to a thermal-viscous instability (
Osaki 1974
;
Lasota 2001
) and periodically collapses. For a fast, isotropic
wind from either accretor or donor, a (M
a
+ M
disk
+ M
d
)
= const.,
where a is the semi-major axis and M
disk
the disk mass, which
is included because from an orbital dynamics perspective, the
disk can be treated as belonging to the accretor. If we assume
that during an outburst the entire disk is emptied, where al-
most all of the disk mass escapes the system, the orbit will
expand by
Δa/a = M
disk
/( M
a
+ M
d
) (at very low donor mass
Δa ∼ 1 cm which means the donor does not actually detach but
rather insu
fficiently overfills its Roche lobe to be able to pre-
vent the orbit from shrinking). We use the disk description by
Dunkel et al.
(
2006
) for helium and carbon-oxygen composition
to estimate the disk mass. At high mass ratio, the inner disk ra-
dius is taken equal to the speed-of-light cylinder radius, as de-
scribed in
van Haaften et al.
(
2012
).
During the outburst, the donor detaches because its Roche
lobe expands along with the orbit. The time it takes for the
donor to re-attach follows from the orbital decay rate due to
angular momentum loss (via gravitational wave radiation) ˙a
=
2a( ˙
J
/J)
orb
. The re-attachment time is at most
∼1 yr, even for
low viscosity (parameterized by
α = 0.02), low donor mass
(10
−3
M ) and the loss of (almost) the entire disk mass from
the system. The time it takes to rebuild the disk is of the order of
100 yr (
van Haaften et al. 2012
).
The hypothesis that PSR J1719–1438 is a system that at the
present is only temporarily detached as part of a disk instabil-
ity cycle would imply that less than a year before its discovery
this system had a large outburst that caused the detached state,
which would have made the system appear as a transient X-ray
source. Also, the neutron star would still be very hot, and there-
fore bright in X-rays, as its cooling timescale is of the order of
10
4
yr.
4. Discussion and conclusions
In the a priori unlikely case the we observe the millisecond pul-
sar J1719–1438 nearly face-on, the companion could be a brown
dwarf of
∼10−40 Jupiter masses that is being evaporated and
therefore has become detached from its Roche lobe. However,
an optical non-detection of the system makes the presence of a
relatively massive companion less likely (B11).
PSR J1719–1438 is more plausibly explained by having an
ultracompact X-ray binary progenitor. The system could have
started as a regular UCXB of either helium or carbon-oxygen
composition. Cooling due to heat emission and expansion may
have caused the donor radius to eventually approach the zero-
temperature radius, however, radiation from the pulsar can heat
the outer layers of the donor. In particular at low density this ef-
fect can be significant. This heating can lead to a fast stellar wind
from the donor which removes angular momentum from the sys-
tem and accelerates the system’s evolution, allowing longer or-
bital periods and lower companion masses than would be possi-
ble without such a wind. Moreover, the larger size of the donor
also leads to a longer orbital period at a given age.
A combination of bloated donor, donor wind and low inclina-
tion can explain the properties of the system (the relatively long
orbital period, why the present-day gravitational wave timescale
most likely is much longer than the age of the Universe, and why
the system is detached) without requiring an improbable contri-
bution of either of these.
No excess dispersive delays have been found in the radio
light curve (B11), so there is no observational evidence for abla-
tion of the companion. But the required wind mass loss rate we
find is much lower than a donor-evaporating black widow mass
loss rate (
∼10
−10
M yr
−1
,
Burderi et al. 2009
) and therefore may
not be observable.
Neither helium nor carbon-oxygen can be ruled out as the
composition of the companion. A helium composition is a priori
less likely since it requires a relatively special system inclina-
tion (the associated probability is less than 14% in the case of a
1
.4 M neutron star) especially if it is bloated. However, since
UCXBs with helium white dwarf donors have a longer orbital
period than systems with carbon-oxygen white dwarfs, it takes
less heating and angular momentum loss via a donor wind to
explain the long (for UCXB standards) orbital period.
A22, page 4 of
5
L. M. van Haaften et al.: Formation of the planet around PSR J1719–1438
Limited feedback of angular momentum from the accretion
disk to the orbit can in principle cause accelerated mass transfer
over a prolonged period of time, but the occurrence of this pro-
cess is unlikely (
Priedhorsky & Verbunt 1988
;
van Haaften et al.
2012
).
The distance to PSR J1719–1438,
∼1.2 kpc (B11), points to a
Galactic plane environment, so a formation involving dynamical
interaction is not likely.
Acknowledgements. L.M.v.H. is supported by the Netherlands Organisation for
Scientific Research (NWO). G.N., R.V. and P.G.J. are supported by NWO VIDI
grants.
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