The Pulsar-White Dwarf-Planet System in Messier 4: Improved Astrometry

Abstract

A young and undermassive white dwarf has been identified as the possible companion to the millisecond pulsar PSR B1620-26 in Messier 4. This association is important as it then helps constrain the mass of the third body in the system to be of order a few times that of Jupiter. The presence of this planet in M4 has critical implications for planetary formation mechanisms in metal-poor environments such as globular clusters and the early Universe. The identification of the white dwarf is purely via the agreement in position between it and the pulsar and was limited by the accuracy of the pointing of HST which is +/-0.7 arcsec. We have redetermined the position of the white dwarf using ground-based data tied to USNOB-1.0 and find that the pulsar and white dwarf are now coincident to within 0.12 +/- 0.13 arcsec further strengthening the case for association between the two. We have also attempted to improve the proper motion measurement of the white dwarf by a maximum likelihood analysis of the stellar positions measured over a baseline of 5 years. While the errors are reduced by almost a factor of 6 from our previous work, we still have not resolved the cluster's intrinsic dispersion in proper motion. Thus the proper motion of the white dwarf with respect to the cluster itself is still not known although it is very small and is within 2-sigma of that of the cluster internal dispersion. Comment: 9 pages, 2 figures, accepted for publication in the Astrophysical Journal (Letters)

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arXiv:astro-ph/0309502v1 17 Sep 2003
Submitted to The Astrophysical Journal Letters August 19, 2003.
THE PULSAR-WHITE DWARF-PLANET SYSTEM IN MESSIER 4:
IMPROVED ASTROMETRY1
Harvey B. Richer2, Rodrigo Ibata3, Gregory G. Fahlman4, Mark Huber2
ABSTRACT
A young and undermassive white dwarf has been identified as the possible companion
to the millisecond pulsar PSR B1620-26 in Messier 4. This association is important as
it then helps constrain the mass of the third body in the system to be of order a few
times that of Jupiter. The presence of this planet in M4 has critical implications for
planetary formation mechanisms in metal-poor environments such as globular clusters
and the early Universe. The identification of the white dwarf is purely via the agreement
in position between it and the pulsar and was limited by the accuracy of the pointing
of HST which is ±0.7′′. We have redetermined the position of the white dwarf using
ground-based data tied to USNOB-1.0 and find that the pulsar and white dwarf are
now coincident to within 0.12 ± 0.13′′further strengthening the case for association
between the two. We have also attempted to improve the proper motion measurement
of the white dwarf by a maximum likelihood analysis of the stellar positions measured
over a baseline of 5 years. While the errors are reduced by almost a factor of 6 from
our previous work, we still have not resolved the cluster’s intrinsic dispersion in proper
motion. Thus the proper motion of the white dwarf with respect to the cluster itself is
still not known although it is very small and is within 2σ of that of the cluster internal
dispersion.
Subject headings: globular clusters: individual (Messier 4) – stars: astrometry, white
dwarfs, pulsars: individual (PSR B1620-26)
1Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science
Institute, which is operated by AURA under NASA contract NAS 5-26555. Based on observations with the Canada-
France Hawaii Telescope, which is operated by the National Research Council of Canada, the Centre National de la
Recherche Scientifique of France and the University of Hawaii.
2Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC
V6T 1Z1, Canada. richer@astro.ubc.ca, mhuber@astro.ubc.ca
3Observatoire de Strasbourg, 11 rue de l’Universite, F-67000 Strasbourg, France. ibata@newb6.u-strasbg.fr
4National Research Council, Herzberg Institute of Astrophysics, 5071 West Saanich Road, RR5, Victoria, BC V9E
2E7, Canada. greg.fahlman@nrc-cnrc.gc.ca

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1.Introduction
Messier 4 contains a unique stellar/planetary system. It consists of a central tight binary
composed of an 11 msec pulsar (PSR B1620-26) and a stellar companion (thought to be the white
dwarf that spun up the neutron star) together with a distant object possessing either a planetary
mass in a low eccentricity orbit or a stellar companion in a highly eccentric one (Lyne et al. 1987;
McKenna & Lyne 1988; Backer, Foster & Sallmen 1993, Michel 1994, Rasio 1994, Thorsett et al.
1999, Ford, Joshi & Rasio 2000). The former scenario was deemed early on to be the more probable
one. The existence of this triple system is of great cosmogonic significance as, if primordial, it could
suggest the presence of numerous solar systems that formed early in the history of the Universe.
The close-in stellar companion to PSR B1620-26 had escaped detection until recently when
Sigurdsson et al. (2003) showed that an undermassive and young white dwarf was the likely partner.
The properties of this object seemed to fit a pre-existing scenario for the history of this triple wherein
an exchange reaction in the core of M4 captured both the white dwarf’s progenitor and its planetary
companion into an orbit around a neutron star (Sigurdsson 1992, 1993, 1995).
While the identification of the companion to the pulsar is highly suggestive, it does have its
limitations. The positional agreement is constrained by how well the coordinates of the HST guide
stars are known. The uncertainty in their location limits the accuracy of the absolute position
of the white dwarf to ±0.7′′. The pulsar position by contrast is known to about 0.003′′through
pulsar timing (Thorsett et al. 1999). The system should have been ejected on almost a radial
orbit from the core after the exchange interaction. The energy available for this recoil originated
in the increased binding energy of the newly formed binary as the new stellar companion was more
massive than the original one. The recoil velocity of the system is expected to be 10 − 15 km/sec
(Sigurdsson 1993) which is near the escape velocity from the cluster. The orbit of the triple system
within the cluster evolved via dynamical friction and orbital diffusion and it is expected to return to
the cluster core on a timescale of ∼ 109yrs (Sigurdsson et al. 2003). This suggests that the system
could have a somewhat higher velocity with respect to the cluster than equilibrium dynamics would
suggest. It is of interest then to look for this in the system’s proper motion.
Both the position and proper motion of the system are addressed in this Letter with improved
measurements of both. The significant orbital velocity of the white dwarf around the neutron star
could also be used as a definitive test of the association between the two but this awaits future
observations.
2.The Data
The data analyzed are composed of both ground-based and HST images. The ground-based
observations are short exposure (5×2 sec averaged into a master image with high pixels removed
by an average sigma clip) CFHT 12K I-band data centered on M4. The complete HST data set

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analyzed here consists solely of images in F814W so that effects of different bandpasses play no part
in the analysis. The earliest images, 9×800 sec in F814W, were secured in 1995 as part of GO 5461
from cycle 4 (Richer et al. 1995, 1997; Ibata et al. 1999). The second epoch exposures came from
the HST archives (GO 8153) and consist of 8×700 sec exposures giving images of approximately
equal depth to the cycle 4 ones. All images were secured with the same roll angle and in all cases
the pulsar/white dwarf fall on WF3. The images from GO 6166 obtained in 1999 were not used as
they were much shallower than those mentioned above and were secured so that the pulsar/white
dwarf were on the PC. This could cause further difficulties with potential proper motion reductions
from WF data because of the scale difference. The HST images were all preprocessed according to
the recipe given in Stetson et al. 1998.
3.Positional Astrometry
In order to construct an appropriate reference frame, we carried out photometry on the CFHT
images using the DAOPHOT (Stetson 1987) suite of programs. In total 16240 stars in the direction
of M4 were measured on a single CFHT 12K chip. The location of these stars is shown in Figure 1.
These were converted into standard coordinates centered on 16h23m35.41s−26◦31′31.9′′(J2000).
Within this area of the chip we also selected all of the stars on the USNOB-1.0. There were 816 of
these (circled in Figure 1). We then cross-identified these two lists, keeping only those stars that had
no neighbors closer than 3.0′′, that had I < 18 and whose photometry satisfield |ICFHT−IUSNO| <
1.5. This latter constraint may appear overly generous, but the USNO photometry near the faint
end of this range is rather poor. We iteratively refined a 6-coefficient polynomial transformation
while rejecting cross-identifications with large residuals. This resulted in 274 cross-identified stars,
with an RMS in the ensuing transformations of 0.12′′.
This process was then repeated using the CFHT data (now on the USNOB-1.0 system) and
our existing HST WF3 astrometry (Ibata et al. 1999). In this case any object detected on both
the CFHT images and the HST ones were used without regard to their relative magnitude mea-
surements. Here 428 stars were matched (larger dots in Figure 1) and the resultant RMS in the
transformation was 0.06′′. Combining the 2 transformations gave a position for the white dwarf at
16h23m38.217s−26◦31′53.662′′, that is 0.126 ± 0.13′′from the pulsar. This result does not include
any systematic uncertainty coming from the USNOB-1.0.
Note from these results that the red main sequence star mentioned as a possible pulsar com-
panion in Sigurdsson et al. (2003), is now about 6σ away from the nominal pulsar position and is
very unlikely to be associated with the pulsar/planetary system.

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4.Proper Motion Measurements
The velocity dispersion near the core of M4 is about 3.5 km/sec (Peterson, Rees & Cudworth
1995). At the distance of M4 (1.73 kpc) this corresponds to a (2-dimensional) proper motion
dispersion of 0.6 mas/yr. Our measurements in the inner (Richer et al. 2003) and outer (Richer et
al. 2002) regions of the cluster have yielded errors in the range of 3 mas/yr for faint stars. As was
shown originally by Cudworth and Rees (1990), M4 has a high proper motion with respect to the
field population. Building on this, our goal has been simply to be able to distinguish cluster from
field stars so as to produce proper motion selected color magnitude diagrams. However, Bedin et
al. 2003 are interested in the internal dynamics of globular clusters and have a long term program
to resolve the dispersion. They currently claim a measurement precision of about 0.02 pixels which,
when coupled with long baselines, may make this goal eventually possible.
The measurement uncertainty which we have achieved in our earlier work is about 0.15 pixels
for stars down to V = 27.5 (Richer et al. 2003). With the more sophisticated analysis discussed
below we improve this to about 0.03 pixels at the expense of not reaching stars as faint. However,
this is not a concern for the present analysis as the white dwarf has V = 24.0.
A reference frame for the cluster was constructed by first selecting only cluster members from
our earlier work. Photometry was carried out for these objects on all the individual HST frames
using ALLSTAR. The frames were then transformed onto the sky using the Trauger et al. (1995)
corrections. This effectively corrects for the optical distortions in the WFPC2 camera. All the
frames from both epochs were then transformed to a single reference frame. The RMS of this
solution was typically 0.08 pixels, and with generally about 500 stars in each frame, this resulted
in a positional uncertainty of about 3.6 mas.
Using the maximum likelihood method described in Ibata & Lewis (1998), we find the positions
of the white dwarf and red dwarf mentioned in Sigurdsson et al. (2003) as listed in Table 1. From
this Table we derive that the proper motion of the white dwarf companion to PSR B1620-26 with
respect to the cluster is about 0.9±1.1 mas/yr. Similarly the red main sequence star has a proper
motion of 1.1±1.0 mas/yr so that neither exhibits significant peculiar motion with respect to M4.
In fact if the cluster proper motion dispersion is 0.6 mas/yr as expected then neither exceeds this
by more than about 2σ.
5. Other Considerations
It is clear that a much longer baseline (about 15 years) than we currently have will be required
to both resolve the M4 proper motion dispersion and measure the motion of the white dwarf
companion to PSR B1620-26 with respect to the cluster. This may eventually be an important
check on the dynamical history of this system (Sigurdsson et al. 2003, Sigurdsson 1992, 1993,
1995). However, other tests are currently possible. With an orbital period of only 191 days, the

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white dwarf will exhibit a velocity amplitude of about 40 km/sec which should, with a determined
effort, be capable of detection. This velocity curve will be critical datum toward an independent
measurement of the mass of its Pop II neutron star companion. A spectroscopic mass determination
of the white dwarf itself would also provide an important confirmation of the mass estimated from
fitting its location in the M4 CMD to model cooling curves (Sigurdsson et al. 2003).
The case for the association of the white dwarf with PSR B1620-26 has been strongly strength-
ened by the present results, supporting the conclusion that the third body is most likely of planetary
mass (Sigurdsson et al. 2003). Since this system has the metal abundance of M4 (30 times less
than that of the Sun) it is strongly suggestive that a mode of planetary formation that does not
rely on planetesimals has been in operation as the entire proto-planetary disk out of which this
object formed would only have contained a few Earth masses of metals. Such models, relying on
disk instability mechanisms, have been suggested for more than a decade now and were recently
reviewed by Boss (2002). This would produce planets much earlier in the Universe than one which
relied on a mechanism that required high metallicity. The implications here for a potential early
rise to life in the Universe are thus obvious.
The research of HBR and GGF is supported in part by the Natural Sciences and Engineering
Research Council of Canada. HBR extends his appreciation to the Killam Foundation and the
Canada Council for the award of a Canada Council Killam Fellowship.
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