A&A 450, 295-303 (2006)
DOI: 10.1051/0004-6361:20054316
C. G. Bassa1 - M. H. van Kerkwijk2 - S. R. Kulkarni3
1 - Astronomical Institute, Utrecht University, PO Box 80 000,
3508 TA Utrecht, The Netherlands
2 - Department of Astronomy and Astrophysics, University of
Toronto, 60 Saint George Street, Toronto, ON M5S 3H8,
Canada
3 - Palomar Observatory, California Institute of Technology
105-24, Pasadena, CA 91125, USA
Received 7 October 2005 / Accepted 29 December 2005
Abstract
We present optical and near-infrared observations with Keck
of the binary millisecond pulsar PSR J0751+1807. We detect a faint,
red object - with R=25.08
0.07, B-R=2.5
0.3, and
R-I=0.90
0.10 - at the celestial position of the pulsar and
argue that it is the white dwarf companion of the pulsar. The
colours are the reddest among all known white dwarfs, and indicate a
very low temperature,
K. This implies that
the white dwarf cannot have the relatively thick hydrogen envelope
that is expected on evolutionary grounds. Our observations pose two
puzzles. First, while the atmosphere was expected to be pure
hydrogen, the colours are inconsistent with this
composition. Second, given the low temperature, irradiation by the
pulsar should be important, but we see no evidence for it. We
discuss possible solutions to these puzzles.
Key words: stars: pulsars: individual: PSR J0751+1807 - stars: binaries: close - stars: neutron - stars: white dwarfs
Among the pulsars in binaries, the largest group, the low-mass binary pulsars, has low-mass white dwarf companions. Before the companions became white dwarfs, their progenitors filled their Roche lobe and mass was transferred to the neutron stars, thereby spinning them up and decreasing their magnetic fields. Considerations of the end of this stage, where the white dwarf progenitor's envelope becomes too tenuous to be supported further, allow one to make predictions for relations between the orbital period and white dwarf mass, and orbital period and eccentricity (for a review, e.g., Stairs 2004; Phinney & Kulkarni 1994). Furthermore, after the cessation of mass transfer, two clocks will start ticking at the same time: the neutron star, now visible as a millisecond pulsar, will spin down, while the secondary will contract to a white dwarf and start to cool. Consequently, the spin-down age of the pulsar should equal the cooling age of the white dwarf.
From optical observations of white dwarf companions to millisecond pulsars one can estimate the white dwarf cooling age and compare it with the pulsar spin-down age. Initial attempts to do this (Hansen & Phinney 1998b; Schönberner et al. 2000; Hansen & Phinney 1998a) revealed a dichotomy in the cooling properties of white dwarfs in the sense that some white dwarf companions to older pulsars have cooled less than those of younger pulsars. In particular, the companions of PSR J0437-4715 (van Straten et al. 2001; Danziger et al. 1993) and PSR B1855+09 (van Kerkwijk et al. 2000; Ryba & Taylor 1991) have temperatures of about 4000-5000 K, with characteristic pulsar ages of 5 Gyr. This is in contrast to the companion of PSR J1012+5307 (van Kerkwijk et al. 1996; Lorimer et al. 1995; Callanan et al. 1998), which has a higher temperature (8600 K), while it orbits an older pulsar (8.9 Gyr).
A likely cause for this dichotomy is the difference in the thickness
of the envelope of hydrogen surrounding the helium core of the white
dwarf (Alberts et al. 1996). After the cessation of mass transfer, the white
dwarfs have relatively thick (
)
hydrogen
envelopes which are able to sustain residual hydrogen shell-burning,
keeping the white dwarf hot and thereby slowing the cooling
(Driebe et al. 1998). The shell burning, however, can become unstable and
lead to thermal flashes which can reduce the mass of the
envelope. White dwarfs with such reduced, relatively thin
(
)
hydrogen envelopes cannot burn hydrogen and,
as a result, cool faster. The transition between thick and thin
hydrogen envelopes was predicted to lie near 0.18-0.20
(where heavier white dwarfs have thin envelopes;
Althaus et al. 2001; Alberts et al. 1996; Sarna et al. 2000).
Until recently, PSR J1012+5307, with an orbital period
d, was the only system for which a thick hydrogen
envelope was required to match the two timescales. Given the relation
between the white dwarf mass and the orbital period
(Tauris & Savonije 1999; Rappaport et al. 1995; Joss et al. 1987), companions in similar or closer orbits
should have similar or lower mass, and thus have thick hydrogen
envelopes as well. This was confirmed by the recent discovery of two new, nearby, binary millisecond pulsars with orbital periods similar to that of PSR J1012+5307; PSR J1909-3744 (1.53 d,
Jacoby et al. 2005) and PSR J1738+0333 (0.354 d, Jacoby et al., in prep.; see van Kerkwijk et al. 2005 for preliminary results). For both, the
temperatures and characteristic ages are similar to those of PSR J1012+5307, and thus one is led to the same need for a thick hydrogen
envelope. These discoveries, combined with the thin envelopes inferred
for PSR J0034-0534 (1.59 d) and binaries with longer periods,
suggest that the transition occurs at a mass that corresponds to an orbital period just over 1.5 d (van Kerkwijk et al. 2005). All systems with
shorter orbital periods should have thick hydrogen envelopes.
The two known millisecond pulsars with white dwarf companions that
have shorter orbital periods than PSR J1012+5307 but do not have
optical counterparts, are PSR J0613-0200, with a 1.20 d period, and
PSR J0751+1807, which has the shortest orbital period of all binary
millisecond pulsars with
companions,
0.26 d (Lundgren et al. 1995). The latter system is of particular interest
because the companion mass has been determined from pulsar timing
(
at 95% confidence;
Nice et al. 2005), so that one does not have to rely on the
theoretical period-mass relationship. Intriguingly, for PSR J0751+1807, optical observations from Lundgren et al. (1996) set a limit to
the temperature of 9000 K, which is only marginally consistent with
it having a thick hydrogen envelope. Based on this, Ergma et al. (2001),
suggested the hydrogen envelope may have been partially lost due to
irradiation by the pulsar.
The faintness of the companion to PSR J0751+1807 aroused our curiosity and motivated us to obtain deep observations to test the theoretical ideas discussed above. We describe our observations in Sect. 2, and use these to determine the temperature, radius and cooling history in Sect. 3. In Sect. 4, we investigate irradiation by the pulsar, finding a surprising lack of evidence for any heating. We discuss our results in Sect. 5.
The PSR J0751+1807 field was observed with the 10 meter Keck I and II
telescopes on Hawaii on five occasions. On December 11, 1996 the Low
Resolution Imaging Spectrometer (LRIS, Oke et al. 1995) was used to
obtain B and R-band images, while the Echellette Spectrograph and
Imager (ESI, Sheinis et al. 2002) was used on December 21, 2003 to obtain
deeper B and R-band, as well as I-band images. The R-band
filter used that night was the non-standard "Ellis R'' filter. The
observing conditions during the 1996 night were mediocre, with
0
8-1
1 seeing and some cirrus appearing at the end of the
night. The conditions were photometric during the 2003 night, and the
seeing was good, 0
6-0
8. The third and fourth visit were
with LRIS again, now at Keck I, on January 7 and 8, 2005. The red arm
of the detector was used to obtain R-band images. The seeing on the
first night in 2005 was rather bad, about 1
5 and improved to
about 1
0 on the second night. The conditions on these nights
were not photometric. Finally, a series of 36 dithered exposures, each
consisting of 5 co-added 10 s integrations, were taken through the
filter with the Near Infrared Camera (NIRC;
Matthews & Soifer 1994) on January 26, 2005. The conditions were photometric
with 0
6 seeing. Standard stars (Stetson 2000; Landolt 1992) were
observed in 1996 and 2003, while a 2MASS star (Cutri et al. 2003) in the
vicinity of PSR J0751+1807 was observed to calibrate the NIRC data. A log of the observations is given in Table 1.
The images were reduced using the Munich Image Data Analysis System
(MIDAS). The images were bias-subtracted and flat-fielded using
dome flats. The longer exposures in each filter were aligned using
integer pixel offsets, and co-added to create average images. The
near-infrared images were corrected for dark current using dark frames
with identical exposure times and number of co-adds as those used for
the science frames. Next, a flatfield frame was created by median
combining the science frames. After division by this flatfield, the
science frames were registered using integer pixel offsets and averaged.
Table 1: Observation log.
For the astrometric calibration, we selected 14 stars from the second
version of the USNO CCD Astrograph catalogue (UCAC2; Zacharias et al. 2004)
that overlapped with the 10 s R-band LRIS image of December 1996. Of these, 11 were not saturated and appeared stellar and unblended. The centroids of these objects were measured and corrected
for geometric distortion using the bi-cubic function determined by
J. Cohen (1997, priv. comm.). We
fitted for zero-point position, plate scale and position angle. The
inferred uncertainty in the single-star measurement of these 11 stars
is
and
in right ascension and declination,
respectively, and is consistent with expectations for the UCAC measurements of approximately
for stars of 14th magnitude
and
for stars 2 mag fainter.
This solution was transferred to the 10 min R-band LRIS image using
91 stars that were present on both images and were stellar,
unsaturated and not blended. Again the zero-point position, plate
scale and position angle were left free in the fit and the final
residuals were
and
in right ascension and
declination. The UCAC is on the International Celestial Reference
System (ICRS) to
,
and hence the final systematic
uncertainty with which our coordinates are on the ICRS is dominated by
our first step, and is
in each coordinate.
Our images, with the position of PSR J0751+1807 (Nice et al. 2005) indicated, are shown in Fig. 1. On the 10 min LRIS R-band images from 1996 and 2005, we find a faint object, hereafter star X, at the position of the pulsar. It is also, though marginally, present in the two 5 min R-band images from 1996, but not detected in the 10 min B-band LRIS image of that observing run. Star X is clearly present in the 2003 ESI R and I-band images, and marginally in the B-band image. It is not detected in the near-infrared observations (Fig. 1).
Positions for star X and other objects inferred using the astrometry
of the 10 min LRIS R-band image are listed in Table 2.
The pulsar position at the time of the 1996 LRIS observation, using
the Nice et al. (2005) position and proper motion, is
,
.
We find
that star X is offset from the pulsar position by
in right ascension and
in declination, well within the
uncertainties (including those on the pulsar position). Given the low
density of about 47 stars per square arcminute and the excellent
astrometry, the probability of a chance coincidence in the 95% confidence error circle, which has a radius of
,
is only 0.1-0.2%. Since, as we will see, it is hard to envisage how the
companion could be fainter than the object detected, we are confident
that star X is the companion of PSR J0751+1807.
The DAOPHOT II package (Stetson 1987), running inside MIDAS, was used for the photometry on the averaged images. We followed the recommendations of Stetson (1987): instrumental magnitudes were obtained through point spread function (PSF) fitting and aperture photometry on brighter stars was used to determine aperture corrections.
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Figure 1:
Images of the field of PSR J0751+1807. The upper figure
shows a
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Table 2:
LRIS Astrometry and ESI photometry of the companion of
PSR J0751+1807 and stars in the field. The nomenclature of the
stars is according to Fig. 1. The uncertainties
listed in parentheses are instrumental, i.e., they do not include
the zero-point uncertainty in the astrometric tie (about
in each coordinate) or of
photometric calibration (0.05 mag in B and 0.03 mag in both R and I).
For the calibration of the optical images, instrumental magnitudes of
the standard stars, determined using aperturephotometry, were
compared against the values of Stetson (2000). We used the standard
Keck extinction coefficients of 0.17, 0.11 and 0.07 mag per airmass
for B, R and I, respectively. Colour terms were not required for
the LRIS B and R bands, but were significant for the ESI bands:
0.107 (B-R) for B,
0.083 (B-R) for R, and
-0.004 (R-I) for I, i.e., the ESI B, R are redder than the standard bands, while
ESI I is slightly bluer. The root-mean-square residuals of the ESI calibrations are about 0.05 mag in B, and 0.03 mag in R and I,
while those of the LRIS calibration are 0.08 mag in B and 0.05 mag
in R; we adopt these as the uncertainty in the zero-points. The
near-infrared observations were calibrated through aperture photometry
with 1
5 (10 pix) apertures using the 2MASS star, fitting for a zero-point only, as the difference in airmass between the science and calibration images is small. We adopt an uncertainty in the
zero-point of 0.1 mag.
Calibrated ESI magnitudes for star X and selected other stars in the
field are listed in Table 2. Star X is barely above the
detection limit of the ESI B-band observations, hence the large
error. It is not detected in the LRIS B-band and the NIRC
-band observations, and, scaling from the magnitude of a star with a signal-to-noise ratio of about 10 and 6, we estimate the 3
detection limits at B=26.8 and
,
respectively. The former is consistent with the ESI detection. None
of the stars in Table 2 are covered by the small
field-of-view of NIRC, hence we do not have
near-infrared magnitudes for these.
The 1996 LRIS R-band magnitude is 25.13
0.11, which is
consistent with the ESI measurement. Since the conditions during the
1996 LRIS observations may not have been photometric, however, this
may be a coincidence. To check for variability, we tied the
instrumental LRIS R band magnitudes directly to the ESI R and I ones, using 38 stars that both images had in common and that had
magnitude uncertainties below 0.1 mag. As expected given the
non-standard "Ellis R'' filter on ESI, we required a large colour
term,
,
but with this the fit
was adequate, with root-mean-square residuals of 0.14 mag. Compared to
the fit, the ESI minus LRIS difference in R-band magnitude is
insignificant, -0.03
0.13 mag. Similarly, comparing instrumental
R-band magnitudes from 2005 January 7 with those taken 2005 January 8 and 1996 December 11, fitting for an offset only, results in
magnitude differences of 0.03
0.07 and -0.16
0.12 mag,
respectively. Thus, no large variations in brightness are seen; we will
see in Sect. 4 that this is somewhat surprising.
We use our observations of star X, the companion of PSR J0751+1807, to constrain its temperature, radius, and atmospheric constituents, and discuss our result that the white dwarf does not have the expected thick hydrogen envelope.
We first use the colours of star X to constrain its temperature. The
red colours are largely intrinsic, as the maximum reddening towards
PSR J0751+1807 (l=202.73, b=21.09) is small,
EB-V=0.05
0.01(Schlegel et al. 1998). This value is consistent with the low value found for
the interstellar absorption
1020 cm-2, as estimated from ROSAT X-ray observations of PSR J0751+1807 by Becker et al. (1996). For
comparison, the relation by Predehl & Schmitt (1995) predicts an
1020 cm-2 for the above
reddening. Given the distance of
0.6 kpc (Nice et al. 2005), we
expect most of the reddening to be in the foreground to the
pulsar. Hence, the dereddened colours are
(B-R)0=2.40
0.27 and
(R-I)0=0.86
0.10.
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Figure 2:
a) Colour-colour and b) colour-magnitude diagram
for the companion of PSR J0751+1807, other millisecond pulsar
companions, field white dwarfs, and model predictions. Shown with
error bars are PSR J0437-4715 (Danziger et al. 1993), PSR J1012+5307
(Lorimer et al. 1995), PSR J0218+4232 (Bassa et al. 2003) and PSR J0751+1807
(this work), as well as the ultra-cool field white dwarfs LHS 3250
(Harris et al. 1999), WD 0346+246 (Oppenheimer et al. 2001), and GD 392B
(Farihi 2004). In the colour-colour diagram, also the full sample
of field white dwarfs of Bergeron et al. (2001) is shown, with filled and
open circles indicating white dwarfs with and without H![]() ![]() ![]() |
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In Fig. 2a, we compare the intrinsic colours of star X with
those of other white dwarf companions of millisecond pulsars, other
white dwarfs, and models. We find that the colours of star X are the
reddest for any known millisecond pulsar companion or white dwarf.
The pulsar companion that comes closest is that of PSR J0437-4715
(B-R=2.12
0.06, R-I=0.56
0.02 (Danziger et al. 1993) and negligible
extinction
);
the most similar white dwarf is WD 0346+246 (B-R=2.2
0.1,
R-I=0.76
0.08, Oppenheimer et al. 2001). Thus, star X is likely as cool
or even cooler than the
K inferred for those
two sources (PSR J0437-4715: Danziger et al. 1993; Hansen 2002, priv. comm.; WD 0346+246: Bergeron 2001; Oppenheimer et al. 2001).
Also shown in Fig. 2a are colours expected from model
atmospheres of Serenelli et al. (2001) and of Hansen (2004, priv. comm.),
which are specifically tailored to the low-mass, helium-core
companions of millisecond pulsars, as well as those for updated
low-gravity (), pure hydrogen atmosphere models
of
Bergeron et al. (1995). One sees that the colours of the companion of
PSR J0437-4715, as well as those of the hotter companions of
PSR J1012+5307 and J0218+4232, are consistent with these models. For
star X, however, the colours are not consistent, as the models never
venture redwards of
and
.
The change in direction of the tracks is seen in all models for hydrogen-rich, metal-free atmospheres; it reflects a change in the dominant source of opacity, from bound-free absorption of H- at higher temperatures to collision-induced absorption of H2 at lower ones (Hansen 1998; Lenzuni et al. 1991; Saumon et al. 1994). The latter process is highly non-grey, and leads to absorption predominantly longward of the R-band. As a result, the R-I colour becomes bluer with decreasing temperatures, while B-R remains roughly constant.
Could star X have a different composition? Due to the high gravity of
white dwarfs, metals settle out of the atmosphere. However, some white
dwarfs have atmospheres dominated not by hydrogen, but by helium. For
the latter, the opacity sources are all fairly grey, and hence the
colours continue to redden with decreasing temperatures. Indeed, the
colours of star X are consistent with the predictions of the updated
pure helium models after Bergeron et al. (1995) at
K (Fig. 2a).
From an evolutionary perspective, however, a pure helium atmosphere is not expected. Low-mass white dwarfs such as the companions to millisecond pulsars are all formed from low-mass stars whose evolution was truncated by mass transfer well before helium ignition (for recent models, see Nelson et al. 2004; Tauris & Savonije 1999). As a result, they should have helium cores surrounded by relatively thick, 0.01 to 1% of the mass, hydrogen envelopes (Althaus et al. 2001; Driebe et al. 1998). Indeed, among the low-mass white dwarf companions to pulsars (van Kerkwijk et al. 2005) as well as among low-mass white dwarfs in general (Bergeron et al. 2001), only hydrogen-dominated atmospheres have been observed.
In principle, at low temperatures, the hydrogen envelope might become
mixed in with the helium core. Even if fully mixed, however, the
remaining amounts of hydrogen would strongly influence the spectrum.
Indeed, the effects of collision-induced absorption increase
with increasing helium abundance up to
(Bergeron & Leggett 2002).
From Fig. 2a, it is clear that the predictions for
hydrogen-dominated atmospheres are also a somewhat poor match to the
colours of the cooler normal white dwarfs with hydrogen in their
atmospheres (as inferred from absorption at H,
Bergeron et al. 2001; filled circles in the figure). For most, this appears
to be due to missing blue opacity in the models (see Bergeron et al. 2001
for a detailed study); the visual through infrared fluxes are
reproduced well by the models, and show unambiguously that
collision-induced absorption by H2 is important. Indeed, the
absorption is evident in the optical colours of some objects, in
particular LHS 3250 (shown in Fig. 2) and
SDSS J133739.40+000142.8 (Bergeron & Leggett 2002, and references therein).
For our purposes, however, the case of the ultra-cool white dwarf WD 0346+246 is most relevant. For this source, the colours cannot be reproduced with either pure hydrogen or helium, but require a mixed atmosphere, dominated by helium (with fractional hydrogen abundances ranging from 10-9 to 10-1, depending on assumptions about the contribution of other opacity sources; Bergeron 2001; Oppenheimer et al. 2001, though recent work puts these abundances in to doubt, P. Bergeron 2005, priv. comm.). For all cases, the temperature is around 3700 K. The similarity in the colours of WD 0346+246 and star X would suggest that star X has a similar, maybe slightly lower, temperature.
From the above, we find that we cannot determine the temperature of the companion of PSR J0751+1807 with certainty, since we do not know its composition. Most likely, however, it is somewhere between the temperature inferred for WD 0346+246 and that indicated by the (pure helium) models, i.e. in the range of, say 3500-4300 K.
A more stringent test could be provided by the near-infrared
observations, as the R-K colour (which is similar to
)
differs for different predictions. At a temperature of 4000 K the
Bergeron et al. (1995) models predict R-K colours
of 2.7 and 1.6 for pure helium and pure hydrogen atmospheres,
respectively. For the same temperature, R-K=1.6 is predicted by the
0.196
model by Serenelli et al. (2001). Finally, for WD 0346+246,
with presumably a mixed hydrogen/helium atmosphere, Oppenheimer et al. (2001)
observed R-K=-0.7. Unfortunately, our near-infrared observations
only limit the colour to R-K<3.8, which does not constrain any of
these predictions.
So far, we have only discussed the colours and temperature. We now
turn to the absolute magnitude and radius. In Fig. 2b, we
show MR as a function of R-I. For star X, we computed the
absolute R-band magnitude MR using the parallax of
0.8 mas as measured through radio timing (Nice et al. 2005).
The resulting distance of
0.6+0.6-0.2 kpc is consistent with
that estimated from the dispersion measure which predicts
1.1
0.2 kpc, using a dispersion measure of
30.2489
0.0003 pc cm-3 (Nice et al. 2005) and the recent model
of the Galactic electron distribution of Cordes & Lazio (2002). Correcting for
the reddening, this implies
MR=15.97+0.88-1.51.
Given the similarities in the above absolute magnitude of star X and
that of WD 0346+246 (MR=16.1
0.3; Hambly et al. 1999; Oppenheimer et al. 2001), and
assuming similar temperature, one finds that the radius of star X
should be comparable to the
for WD 0346+246
(Bergeron 2001). However, the large uncertainty in the parallax of
PSR J0751+1807 allows radii between 0.007-0.021
.
For the
white dwarf mass of
inferred from pulse timing
(Nice et al. 2005), this is consistent the
expected from the 0.196
model by (Serenelli et al. 2001).
As can be seen in Fig. 2, the absolute magnitude is also
consistent with the predicted values from the pure helium
model by Bergeron et al. (1995). At a temperature of
K,
this model has a radius of 0.020
and a mass of 0.15
,
somewhat smaller than the observed 0.19
.
To correct for the small difference in mass, we
computed white dwarf radii for the observed temperature and mass of
the companion and used these to scale the absolute magnitudes of the
pure helium track in Fig. 2. At 0.19
and
K, the Panei et al. (2000) helium core white dwarf
mass-radius relation predicts 0.021
.
This is very similar
to the radius predicted by the Bergeron et al. (1995)
pure helium
models, and as such, the absolute magnitudes are comparable. We
conclude that, with in the large uncertainties on the parallax
distance, the absolute magnitude and radius that we derive for the
companion of PSR J0751+1807 are consistent with the predictions for a pure helium atmosphere.
We note that of the models presented in Fig. 2, those of
Bergeron et al. (1995) have been extensively tested to explain the population
of nearby white dwarfs (Bergeron & Leggett 2002; Bergeron et al. 2001; Bergeron 2001) and use a very
detailed description of the white dwarf atmosphere combined with the
latest opacities (P. Bergeron 2005, priv. comm.). This is not the
case for the models of Serenelli et al. and Hansen, and thus we
should be careful in using their models quantitatively. Indeed, as can
be seen from Fig. 2, their models do not reproduce the
observations of cool white dwarfs well. For instance, for the
companion of PSR J0437-4715, which has a well-determined mass of
0.236
and distance of 139
3 pc
(van Straten et al. 2001), the models of Serenelli et al. (2001), while consistent with the
observed B-R and R-I well, do not reproduce R-I and MRsimultaneously. In contrast, the
model of Hansen
(2004, priv. comm.) does pass through the R-I, MR point, but
cannot reproduce both colours. It may be that both problems reflect
uncertainties in the model atmospheres used by Hansen and
Serenelli et al. (2001). It would be worthwhile to couple the evolutionary
models of these authors with the updated, very detailed atmospheric
model of Bergeron et al. (1995).
Despite the uncertainty in the models and in the composition of the
atmosphere, our observations show that the companion of PSR J0751+1807
has cooled much more than expected if the amount of hydrogen was thick
enough for significant residual nuclear burning
(Sect. 1). Indeed, the temperature is as expected if no
residual hydrogen burning occurred. For instance, at the
characteristic age of the pulsar, Gyr (Nice et al. 2005), the
0.196
of Serenelli et al. (2001), which has a thin envelope,
predicts a temperature of about 3200 K, which is roughly consistent
with what is observed. With a pure helium atmosphere, a slightly
colder temperature, of
2500 K, is expected, though this is a less secure estimate due to uncertainties in the opacities (Hansen & Phinney 1998a).
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Figure 3:
The orbital period as a function of companion mass for a selection of low-mass binary
pulsars outside globular clusters (either with
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The presence of a thin (or no) hydrogen envelope is not expected,
however, since thick envelopes are inferred for other optically
identified companions in short-period systems (see
Sect. 1). What could be wrong with this expectation? It
was based on two theoretical ideas: (i) that below a certain critical
mass, no shell flashes occur and hydrogen layers will be thick; and
(ii) that the companion mass monotonously increases with increasing
orbital period. These assumptions appeared to be confirmed by the
available data: for PSR J0751+1807, with a period of 0.26 d, the
companion mass of 0.16-0.21
(95% conf.; Nice et al. 2005)
is similar to what is found for two other short-period systems with
companions for which thick hydrogen envelopes are inferred, and less
than the masses for longer period systems with thin-envelope
companions. Specifically, PSR J1012+5307 (0.60 d,
0.12-0.20
)
and PSR J1909-3744 (1.53 d,
0.19-0.22
)
have thick envelopes while PSR J0437-4715
(5.74 d, 0.20-0.27
)
and PSR B1855+09 (12.33 d,
0.24-0.29
)
have thin envelopes (see Fig. 3
and van Kerkwijk et al. 2005, and reference therein). Thus, while the
uncertainties do not exclude that the companion of PSR J0751+1807 is
so massive that it its envelope was diminished by shell flashes, the
existing data make it unlikely.
Two explanations for a thin envelope remain. First, there may be differences in metallicity among the progenitors of pulsar companions. Serenelli et al. (2002) studied the evolution of low-mass pulsar companions with sub-solar metallicity and found that, since the thermonuclear flashes are induced by the reactions of the CNO-cycle, the threshold mass between thin and thick hydrogen envelopes increases with decreasing metallicity of the white dwarf progenitor. Thus, it may be that the companion of PSR J0751+1807 had a sufficiently higher metallicity that it was above the threshold for shell flashes, while companions in other short-period systems had lower metallicity and hence were below the threshold, despite having higher masses.
The next possibility is that the white dwarf was indeed formed with a thick envelope, which was subsequently removed by an action other than shell flashes. Based on the upper limit on the temperature of Lundgren et al. (1996), Ergma et al. (2001) already argued that the pulsar companion
could not have the thick hydrogen envelope, and they proposed a scenario where part of the envelope was removed by pulsar
irradiation. Ergma et al. found that irradiation driven
mass-loss could remove as much as 0.01
from the thick
hydrogen envelope (mostly while the companion is contracting following
the cessation of mass transfer).
A possible problem with the above suggestions, is that none predict the removal of the entire hydrogen envelope, while the observed colours seem most consistent with a pure helium or at least helium-dominated atmosphere.
Above, we have treated the companion as if it were an isolated object rather than member of a binary system. Might the presence of a relatively energetic pulsar influence our observations?
The observed pulsar period and period derivative imply a spin-down
luminosity
1033 I45 erg s-1 (Nice et al. 2005; Lundgren et al. 1995),
where
is the pulsar moment of
inertia. For a
pulsar and a
companion, the orbital separation is
,
and,
consequently, the irradiative flux of the pulsar wind incident on the
companion is
1010 I45 erg s-1 cm-2. This is about
twice the flux of the companion itself,
1010 erg s-1 cm-2 for
K. Therefore, the presence of the pulsar and
its irradiation may be important.
Given the irradiation, one would expect the side of the companion facing the pulsar to be brighter than the side facing away from it. Thus, from Earth, the companion should appear faintest at phase 0.25 and brightest at phase 0.75 (using the convention that at phase 0, the pulsar is at the ascending node). This is indeed seen in other pulsar binaries, with the black widow pulsar PSR B1957+20 perhaps the most spectacular example (Fruchter et al. 1988; van Paradijs et al. 1988).
For star X, assuming a fraction
of the incident flux is
absorbed and reradiated as optical flux, the flux from the bright side
of the companion should be a factor
brighter (here, the factor
reflects
projection effects). Observationally, the inferred values of
range from 0.1 to 0.6 (Orosz & van Kerkwijk 2003, and references therein), and
thus one expects a maximum change in bolometric flux by a factor 1.13
to 1.8. For the R-band flux, the range is 1.2 to 2.2 (assuming it
scales like a black-body spectrum,
T6 around 3700 K). We
confirmed this using a detailed light-curve synthesis model (described
briefly in Stappers et al. 1999).
For star X, no effect is seen. Using the PSR J0751+1807 ephemeris from
Nice et al. (2005), we find that during the ESI R-band observations the
orbital phase ranged from 0.22 to 0.25, while the 1996 LRIS R-band
images were taken at phases 0.86-0.90, and the 2005 LRIS images at
phases 0.01-0.14 on January 7, and 0.77-0.93 on January 8. Thus,
these observations span the orbital phases necessary to test for any
modulation in brightness. Indeed, using the inclination inferred from
timing,
i=66+4-7 deg (Nice et al. 2005), we find that during the
ESI observations only 4 to 5% of the irradiated part of the companion
surface was in view, while during the 1996 LRIS observations is was
78% to 85%. As a consequence, we expect to see nearly the maximum
change in brightness. Nevertheless, in Sect. 2.2, we
found no significant variation,
0.13; thus, to
99% confidence, the variation is
smaller than 0.3 mag, which implies
.
The lack of observed modulation could be taken to indicate that the
irradiation is not very effective, e.g., because the albedo is large
(i.e.,
is small), the pulsar emission is non-isotropic, or the
spin-down luminosity is overestimated. We believe these options are
not very likely (for a discussion in a slightly different context, see
Orosz & van Kerkwijk 2003), which leads us to consider the only alternative, that
one of the assumptions underlying the above estimates is wrong.
In particular, we assumed implicitly that the irradiated flux is reprocessed and re-emitted instantaneously, i.e., transfer of flux inside and around the companion are assumed to have negligible effect. For the companions of black-widow pulsars, this is reasonable, since for these relatively large objects, tides will have ensured synchronous rotation. Any flux transfer would thus have to be due to winds and/or convection, which plausibly happens on a timescale long compared to the thermal time of the layer in which the pulsar flux is reprocessed.
The companion of PSR J0751+1807, however, is well within its Roche-lobe, and tidal dissipation should be negligible. We can estimate its current rotation period from its prior evolution, following the reasoning used by van Kerkwijk & Kulkarni (1995) for the companion of PSR B0655+64. Briefly, during mass transfer, the companion filled its Roche-lobe and tides ensured the system was synchronised and circularised. Once mass transfer ceased and the companion started to contract to a white dwarf, however, the tides became inefficient, and the rotational evolution of the companion was determined by conservation of angular momentum.
For our estimates, we split the total moment of inertia of the
progenitor into two parts, one from the core,
and one from the envelope,
;
here kis the radius of gyration and
is the radius of the Roche lobe. After contraction of the envelope, one is left with a white dwarf with
.
If we now assume that
and ignore differences in radius of gyration,
conservation of angular momentum yields
.
In reality, the envelope will
be more centrally concentrated than the white dwarf, i.e.,
,
and tidal dissipation will be important
in the initial stages of the contraction. This will reduce the
spin-up. On the other hand, the hot core of the progenitor will be
larger than the white dwarf, i.e.,
.
In any
case, it follows that unless the envelope mass is very small, the
white dwarf should be significantly spun up.
Model predictions for the envelope mass of helium-core white dwarfs
differ. The
model by Serenelli et al. (2001), has an envelope mass of 6.7
(as given in Althaus et al. 2001), whereas a model of similar mass
(
)
by Driebe et al. (1998) has one of
3.1
.
Using these values, taking
,
and
,
and ignoring differences in k, we
find current rotation periods a factor 18-85 faster than the
orbital period, or 20 to 5 min. Given that thick envelopes seem
inconsistent with the low observed temperature
(Sect. 3), the slower end of the range seems more likely.
To estimate the timescale on which the pulsar flux is reprocessed, we
assume that the incident particles are predominantly highly energetic,
and that they penetrate to, roughly, one Thompson optical depth. This
corresponds to a column depth of N=1.5
,
for which the thermal timescale
min, where the numerical estimate is for
K. This is shorter than the rotation periods
estimated above, suggesting that rotation may not be too important.
On the other hand, our estimate is very rough. For instance, at one Thompson depth, the opacity at optical wavelengths is much smaller
than unity for the cool temperatures under consideration
(Saumon et al. 1994). Thus, the material likely radiates less efficiently
than a black body, which would make the thermal timescale longer.
Furthermore, the irradiation will change the temperature and
ionisation structure of the atmosphere, further complicating matters.
(Indeed, could this be the underlying cause for the fact that the
colours deviate so strongly from those expected for a pure hydrogen
atmosphere?) Finally, it might induce strong winds which equalise the
temperature on both hemispheres (as is the case for Jupiter).
We have optically identified the white dwarf companion of the binary
millisecond pulsar PSR J0751+1807. We find that the companion has the
reddest colours of all known millisecond pulsar companions and white
dwarfs. These colours indicate that the companion has a very low
(ultra-cool) temperature of
K. Furthermore, the colours suggest
that the white dwarf has a pure helium atmosphere, or a helium
atmosphere with some hydrogen mixed in, as invoked for the field white
dwarf WD 0346+246 which has similar colours (Bergeron 2001; Oppenheimer et al. 2001).
Our observations are inconsistent with evolutionary models, from which one would expect a pure hydrogen atmosphere. Indeed, as for other short-period systems, the hydrogen envelope is expected to be thick enough to sustain significant residual hydrogen burning, leading to temperatures far in excess of those observed. It may be that the mass of the envelope was reduced due to shell flashes or irradiation by the pulsar, as was proposed by Ergma et al. (2001).
However, we see no evidence for irradiation, despite the fact that the pulsar spin-down flux impinging on the white dwarf is roughly twice the observed thermal flux. Clues to what happens might be found from more detailed studies of the spectral energy distribution, or more accurate phase-resolved photometry.
Finally, a deeper observation at infrared wavelengths would allow one to distinguish between the different atmosphere compositions for the companion: for a pure helium atmosphere, black-body like colours are expected, while if any hydrogen is present, the infrared flux would be strongly depressed (as is seen for WD 0346+246). With adaptive optics instruments, such observations should be feasible.
Acknowledgements
We thank Norbert Zacharias for providing preliminary UCAC2 data. We also would like to thank the referee, Pierre Bergeron, for his useful suggestions and for pointing out the existence of his updated models. The observations for this paper were taken at the W. M. Keck Observatory, which is operated by the California Association for Research in Astronomy, a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. It was made possible by the generous financial support of the W. M. Keck Foundation. MIDAS is developed and maintained by the European Southern Observatory. This research made use of the SIMBAD and ADS data bases and of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. We acknowledge support from NWO (C.G.B.), NSERC (M.H.v.K.), and from NASA and NSF (S.R.K.).