Hubble Space Telescope observations of the companion to the eclipsing millisecond pulsar PSR J2051-0827 have revealed its "dark" side. The R magnitude at minimum is ~26, while the difference between the side heated by the impinging pulsar radiation and the unirradiated side is ~3.3 mag. For the first time, these data show that there is an asymmetry in the optical light curve of the companion. Furthermore, significant variability is seen in the companion brightness measured after optical maximum on successive orbits. The data are modeled by a gravitationally distorted low-mass secondary star that is irradiated by the pulsar wind. These model fits indicate that the system is only mildly inclined (i ~ 40°) and the unilluminated side of the companion has a temperature likely less than 3000 K

Bell, J. F.

Kulkarni, S. R.

Stappers, B. W.

van Kerkwijk, M. H.

Caltech Authors - Main

L183
The Astrophysical Journal, 548:L183–L186, 2001 February 20
q 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A.
INTRINSIC AND REPROCESSED OPTICAL EMISSION FROM THE COMPANION TO PSR J205120827
B. W. Stappers,1 M. H. van Kerkwijk,2 J. F. Bell,3 and S. R. Kulkarni4
Received 2000 October 13; accepted 2000 December 22; published 2001 February 19
ABSTRACT
Hubble Space Telescope observations of the companion to the eclipsing millisecond pulsar PSR J205120827
have revealed its “dark” side. The R magnitude at minimum is ∼26, while the difference between the side heated
by the impinging pulsar radiation and the unirradiated side is ∼3.3 mag. For the first time, these data show that
there is an asymmetry in the optical light curve of the companion. Furthermore, significant variability is seen in
the companion brightness measured after optical maximum on successive orbits. The data are modeled by a
gravitationally distorted low-mass secondary star that is irradiated by the pulsar wind. These model fits indicate
that the system is only mildly inclined ( ) and the unilluminated side of the companion has a temperaturei ∼ 407
likely less than 3000 K.
Subject headings: binaries: eclipsing — pulsars: individual (PSR J205120827) — stars: neutron
1. INTRODUCTION
The rapidly rotating subclass of pulsars known as millisec-
ond pulsars are thought to have been regenerated through the
process of spin-up by mass accretion from their companions
during an X-ray binary phase (Alpar et al. 1982; Radhakrishnan
& Srinivasan 1982). If isolated millisecond pulsars also form
in this manner, then the companion needs to be removed; this
might occur via a combination of Roche lobe overflow and
ablation. Both these processes can occur at least partially during
the X-ray phase (Ruderman et al. 1989) and then continue once
accretion has stopped and the pulsar begins emitting in the
radio (Rasio, Shapiro, & Teukolsky 1989). The discovery of
the first eclipsing binary millisecond pulsar B1957120, where
there is clear evidence for the ablation of the companion star
(Fruchter, Stinebring, & Taylor 1988), and the more recent
discovery of SAX 1808.423658, an X-ray pulsar spinning at
millisecond periods (Wijnands & van der Klis 1998; Chakra-
barty & Morgan 1998), seem to confirm this formation scenario.
PSR J205120827 is the second known eclipsing binary mil-
lisecond pulsar with an optically identified companion (Stap-
pers, Bessell, & Bailes 1996a). It has a spin period of 4.5 ms
and an orbital period of 0.1 days (Stappers et al. 1996b). There
is evidence that the eclipse region extends beyond the Roche
lobe of the companion. Radio timing studies yield a lower limit
on the companion mass of 0.025 , but no information onM,
its radius relative to its Roche lobe. Optical observations of
the companion provide the best hope of determining this radius.
Furthermore, modeling of the light curve can provide infor-
mation on the degree of heating of the companion star and thus
on how much energy is available for driving a wind from the
companion. It is also possible to place strong constraints on
the inclination of the system and therefore on the companion
mass and the true extent of the eclipse region. A determination
of the companion mass and radius will constrain the nature of
the companion, such as whether it is degenerate or not.
The light curve of PSR J205120827 has been studied pre-
1 Sterrenkundig Instituut “Anton Pannekoek,” Universiteit van Amsterdam,
Kruislan 403, 1098 SJ Amsterdam, The Netherlands; bws@astro.uva.nl.
2 Astronomical Institute, Utrecht University, P.O. Box 80000, 3508 TA
Utrecht, The Netherlands; m.h.vankerkwijk@astro.uu.nl.
3 Australia Telescope National Facility, CSIRO, P.O. Box 76, Epping 1710,
NSW, Australia; jbell@atnf.csiro.au.
4 Palomar Observatory, MS 105-24, California Institute of Technology, Pas-
adena, CA 91125.
viously (Stappers et al. 1996a, 1999), and the companion was
modeled by a gravitationally distorted star, irradiated by the
pulsar wind. These results indicate that 30% of the pulsar’s
spin-down energy, assumed to be in the form of an isotropic
relativistic pulsar wind, which is incident on the companion
star, is reradiated as optical emission. Furthermore, the com-
panion star may underfill its Roche lobe. This provides evi-
dence that (at present in this system) the pulsar wind is the
cause of evaporation of the companion star rather than tidal
dissipation through Roche lobe overflow. A limitation of this
earlier study is that it was only possible to observe the portion
of the companion irradiated by the pulsar. The best constraints
on the stellar radius and therefore on the geometry of the system
and ablation models would come from modeling the complete
light curve, including the cold unirradiated side.
In this Letter, we present Hubble Space Telescope (HST)
observations in which we detect the unirradiated side of the
companion and model the complete light curve. We also show
that there is evidence for variability in the light curve and the
presence of an extra source of emission.
2. OBSERVATIONS AND MODELING
The HST Wide Field Planetary Camera 2 (WFPC2) was used
to obtain a total of 35 images of the PSR J205120827 field,
spread over 12 orbits of the system on 1997 June 24, 25, 28,
29, and 30 and 1997 July 4 and 10. Details of filters and orbital
phases are given in Table 1. Observation times were chosen
to maximize orbital phase coverage when the companion is
faintest. Exposure times were either 400 or 500 s and were
chosen so as to enhance the chance of detection but limit the
variation between each observation. The pointings were ar-
ranged so that the pulsar companion is placed on a portion of
the Planetary Camera (PC) that was free from dead or hot
pixels. Only the PC images are used in our analysis. Analysis
of the images was completed using the IRAF package starting
from the pipeline-calibrated PC images. One of the 35 images
was rejected for further analysis due to a cosmic-ray strike
precisely at the position of the companion. Cosmic-ray masks
were generated by median combining observations from each
orbit. The removal of cosmic rays is most important in this
case for determining accurately the sky contribution in the
region of the companion.
Aperture photometry was performed following the prescrip-
tion of Holtzman et al. (1995). The faintness of the companion
L184 EMISSION FROM COMPANION TO PSR J205120827 Vol. 548
TABLE 1
Summary of HST Observations
of PSR J205120827
Phase Magnitude Error
F675W
0.012 . . . . . . 25.6 0.4
0.049 . . . . . . 25.8 0.5
0.068 . . . . . . 25.1 0.3
0.106 . . . . . . 25.0 0.3
0.107 . . . . . . 25.3 0.3
0.145 . . . . . . 24.5 0.2
0.163 . . . . . . 24.0 0.1
0.163 . . . . . . 23.9 0.1
0.201 . . . . . . 23.8 0.1
0.263 . . . . . . 23.2 0.1
0.736 . . . . . . 22.62 0.05
0.792 . . . . . . 23.17 0.07
0.849 . . . . . . 24.4 0.2
0.849 . . . . . . 23.8 0.1
0.853 . . . . . . 23.9 0.1
0.905 . . . . . . 24.7 0.2
0.967 . . . . . . 25.6 0.3
0.967 . . . . . . 24.6 0.2
0.993 . . . . . . 25.2 0.3
F814W
0.006 . . . . . . 24.0 0.1
0.015 . . . . . . 24.1 0.2
0.062 . . . . . . 24.0 0.1
0.077 . . . . . . 23.9 0.1
0.124 . . . . . . 23.7 0.1
0.224 . . . . . . 22.85 0.07
0.280 . . . . . . 22.54 0.06
0.745 . . . . . . 22.23 0.04
0.801 . . . . . . 22.53 0.06
0.873 . . . . . . 23.4 0.1
0.878 . . . . . . 23.7 0.1
0.929 . . . . . . 23.8 0.1
0.934 . . . . . . 23.8 0.1
0.959 . . . . . . 24.0 0.1
0.996 . . . . . . 24.1 0.1
Note.—Binary phase is defined such that phase
zero occurs when the companion lies between the
Earth and the pulsar.
Fig. 1.—Data in the four observational filters used compared with the best-fit model light curves (as discussed in the text) determined from fitting the complete
light curve (dashed lines) and fitting only the rising part of the light curve (solid lines).
meant that the best signal-to-noise ratio is obtained for rela-
tively smaller apertures. Apertures of different radii were used
on a number of brighter stars in the field to determine aperture
corrections relative to the standard 00.5 (11 pixel) radius ap-
erture. In Table 1, we present these aperture-corrected mag-
nitudes, which have been transferred to the Vega system by
applying a 0.10 mag aperture correction from 00.5 radius to
“nominal infinity” (Baggett et al. 1997). The corrections for
losses due to the charge-transfer efficiency were made follow-
ing the prescription of Whitmore, Heyer, & Casertano (1999).
No correction has been made for the so-called long versus short
anomaly as there is presently no consensus on the nature of
this problem. A recent study by Dolphin (2000) suggests that
the problem is caused by an incorrect determination of the
background in short exposures. Our exposures have a well-
determined background, and so we believe our magnitudes are
unaffected by this problem. However, we note that if a cor-
rection to our magnitudes of the size suggested5 is required,
then our data would need to be remodeled.
As a check on our measurements and transformations,
F675W magnitudes were determined for a faint comparison
star (of similar flux to the mean flux of the PSR J205120827
companion) detected on the PC. Assuming that this star was
intrinsically constant in flux, we obtained a reduced 2x p
, indicating that the uncertainties obtained for the mag-1.06
nitudes are realistic. Previous observations from the Hale
200 inch and the Anglo-Australian Telescope that are also used
in the following analysis have been described in detail by Stap-
pers et al (1999). The complete data set of 53 observations
(shown in Fig. 1) was phased using the known ephemeris for
the binary orbit and then modeled. We note here that there is
excellent agreement between the ground-based magnitudes and
the HST magnitudes converted to Cousins R and I.
A model of a synchronously rotating companion star irra-
diated by the impinging pulsar wind that includes the effects
of gravitational and rotational distortion and gravity darkening
5 See the 1999 June update to the WFPC2 Instrument Handbook for Cycle 9.
No. 2, 2001 STAPPERS ET AL. L185
Fig. 2.—All observations made in the F675W HST filter. Groups of mag-
nitudes that were measured during the same system orbit are indicated by the
same symbol. In total, there are data from seven orbits shown.
TABLE 2
Fit Parameters
Parameter Phases 0.0–1.0 Phases 0.0–0.5
Irradiation efficieny . . . . . .
10.20.320.07
10.20.4520.1
Filling factor . . . . . . . . . . . . .
10.050.9520.02
10.230.4320.16
Temperature (K) . . . . . . . . .
190025002150
160028002200
Inclination (deg) . . . . . . . . .
1203822
194024
Reduced x2 . . . . . . . . . . . . . . . 5.6 0.96
and the inclination of the binary orbit is fitted to the data. The
model also fits for the distance modulus and the extinction in
the direction of the source. As was discussed in Stappers et al.
(1999), we use the dispersion measure–determined distance and
an extinction determined from IRAS maps, and their associated
errors, to constrain these two parameters to (m2M) p0
and , respectively. As the un-10.6 5 0.6 E p 0.06 5 0.03B2V
irradiated side of the companion star is likely very cool, the
emergent spectrum needs to be modeled carefully. Thus, the
model magnitudes were calculated using the most recent low-
temperature stellar atmosphere models of Hauschildt, Allard,
& Baron (1999) and folding them through the appropriate in-
dividual filter functions. Note that the Cousins I and R data
and that recorded in the HST filters were fitted simultaneously
(i.e., the offsets between the magnitudes were considered by
folding through the appropriate filter functions).
3. DISCUSSION
A closer inspection of the phased light curve shown in Fig-
ure 1 shows two important features that were only hinted at
by the ground-based observations. First, there is an asymmetry
apparent in the light curve where the decrease in brightness to
minimum occurs more steeply than does the increase to max-
imum brightness. In other words, the presence of excess emis-
sion after maximum means that the decrease to minimum is
apparent at later phases than would be expected for a symmetric
light curve. Second, the brightness of the companion varies
significantly between orbital phases 0.5 and 1.0 in successive
orbits. Such large variations in brightness are not observed in
the other half of the orbit. This can be seen most clearly in
Figure 2, where all seven orbits obtained in the F675W filter
are shown. The amplitude of these variations is as large as
1 mag, as seen between the observations indicated by the filled
circles and the crosses in Figure 2.
Modeling of the light curve is of course limited by these
complications; a simple synchronously rotating companion re-
sulting in a symmetric light curve is no longer a complete
model. If we fit the complete data set using a symmetric model,
we find that we overestimate the flux in the rising part of the
light curve. The resultant best-fit model is of a Roche
lobe–filling companion star which converts approximately 30%
of the incident pulsar spin-down energy into optical flux. It is
important to note that the distance and extinction do play a
strong role when determining the radius. The range of valid
distances and extinction values allowed are dependent on the
overall quality of the fit. As this quality is lower in this case
than for the fit of Stappers et al. (1999), the radius is also less
well constrained.
Alternatively, we can consider that the variability and asym-
metry that is seen during the falling part of the light curve is
associated with some other source of emission. Assuming the
underlying system must be synchronously rotating and evenly
heated (i.e., no hot spots) and thus has a symmetric light curve,
we fit just the rising part of the light curve. This results in a
model with a significantly improved fit (see Table 2). The com-
panion star fills less than half its Roche lobe and converts up
to 15% more of the incident spin-down energy into optical
emission. The results of this fit are similar to the original model
discussed by Stappers et al. (1999).
The important fit parameters are the following: irradition
efficiency—the percentage of the pulsar’s spin-down energy,
assumed to be radiated isotropically, which is reradiated as
optical emission from the companion; the filling factor—the
ratio of the radii of spheres of equivalent volume to the distorted
companion radius and the Roche lobe radius; the temperature
of the unirradiated face of the companion star; and the incli-
nation of the plane of the orbit to the sky. The values of these
parameters and their 1 j uncertainties are shown for both fits
in Table 2. Despite the limitations on the fitting discussed
above, three parameters are relatively strongly constrained. The
initially most surprising constraint is that on the inclination.
This system is only moderately inclined, that is, , whichi ∼ 407
corresponds to a mass for the companion star of ∼0.04 .M,
A low inclination may help to explain the strong frequency
dependence and large variability observed in the radio eclipses
(Stappers et al. 2001), since in this case the radio beam inter-
cepts only the outer limits of the wind. It is also apparent that
a large fraction, greater than 30%, of the pulsar’s spin-down
energy is converted to optical emission and the backside tem-
perature of the star is very cool, likely less than 3000 K.
Spectroscopic observations and photometry of a number of
contiguous orbits is required to understand better the cause of
the asymmetry and variability in the light curve. If some frac-
tion of the emission that we see is coming from a shock above
the companion’s surface, then that would clearly show up in
a spectrum of the system. The timescale for the variability can
be determined only by more intensive observing sessions than
those possible with the observing constraints of the HST.
The observations were obtained with the NASA/ESA Hubble
Space Telescope at the Space Telescope Science Institute,
which is operated by the Association of Universities for Re-
search in Astronomy, Inc. The reduction of the optical data
was done using the Image Reduction and Analysis Facility
(IRAF), which is developed and maintained by the National
L186 EMISSION FROM COMPANION TO PSR J205120827 Vol. 548
Optical Astronomy Observatories. We acknowledge support of
a NASA Guest Observer grant, a fellowship of the Royal Neth-
erlands Academy of Arts and Sciences (M. H. v. K.), and an
Australian Research Council Fellowship (J. F. B.); B. W. S. is
supported by NWO Spinoza grant 08-0 to E. P. J. van den
Heuvel.
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Intrinsic and Reprocessed Optical Emission from the Companion to PSR J2051_0827

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Intrinsic and Reprocessed Optical Emission from the Companion to PSR J2051_0827

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