Issue |
A&A
Volume 514, May 2010
|
|
---|---|---|
Article Number | A74 | |
Number of page(s) | 9 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361/200911728 | |
Published online | 21 May 2010 |
Long-term timing of four millisecond pulsars
G. H. Janssen1,2 - B. W. Stappers1,2,3 - C. G. Bassa1,4,5 - I. Cognard6 - M. Kramer7,1 - G. Theureau6,8
1 - Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
2 - Astronomical Institute ``Anton Pannekoek'', University of
Amsterdam, Postbus 94249, 1090 GE Amsterdam, The Netherlands
3 - Stichting ASTRON, Postbus 2, 7990 AA Dwingeloo, The Netherlands
4 - SRON, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
5 - Department of Astrophysics/IMAPP, Radboud University Nijmegen,
PO Box 9010, 6500 GL Nijmegen, The Netherlands
6 - Laboratoire de Physique et Chimie de l'Environnement, CNRS,
3A Avenue de la Recherche Scientifique, 45071 Orléans
Cedex 2, France
7 - Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
8 - Galaxies, Étoiles, Physique, Instrumentation, CNRS URA 1757, 92195 Meudon Principal Cedex, France
Received 26 January 2009 / Accepted 15 February 2010
Abstract
We have timed four millisecond pulses, PSRs J1721-2457,
J1745-0952, J1810-2005, and J1918-0642, for up to a total
of 10.5 years each using multiple telescopes in the European
Pulsar Timing Array network: the Westerbork Synthesis Radio
Telescope in The Netherlands, the Nançay Radio Telescope in
France and the Lovell telescope at Jodrell Bank in the UK. The
long time span has enabled us to measure the proper motions of
J1745-0952 and J1918-0642, indicating that they have
transverse velocities of 200(50) and 54(7) km s-1
respectively. We have obtained upper limits on the proper
motion of J1721-2457 and J1810-2005, which imply that they
have transverse velocities less than 140 and 400 km s-1
respectively. In all cases, the velocities lie in the range
typical of millisecond pulsars. We present pulse profiles for
each pulsar taken from observations at multiple frequencies in
the range of 350 to 2600 MHz, and show that J1810-2005 shows
significant profile evolution in this range. Using our
multi-frequency observations, we measured the spectral indices
for all four pulsars, and for J1810-2005 it appears to be
very flat. The flux density of J1918-0642 shows extensive
modulation which we attribute to the combined effects of
refractive and diffractive scintillation. We discuss the
possible use of including J1721-2457 or J1918-0642 in a
pulsar timing array, and find that J1918-0642 will be useful
to include when the timing precision of this pulsar is improved
over the next few years. We have searched archival optical
observations to detect companions of the binary pulsars, but
none were detected. However, we provide lower limits on the
masses of the white dwarf companions of PSRs J1745-0952 and
J1918-0642.
Key words: stars: neutron - pulsars: general - pulsars: individual: J1721-2457 - pulsars: individual: J1745-0952 - pulsars: individual: J1810-2005 - pulsars: individual: J1918-0642
1 Introduction
In this paper we present improved timing solutions for four millisecond pulsars (MSPs): PSRs J1721-2457, J1745-0952, and J1918-0642, discovered by Edwards & Bailes (2001), and J1810-2005, that was discovered by Camilo et al. (2001). Long-term timing of MSPs is an important tool to determine masses of the individual stars in binary systems, and by constraining secular effects like proper motion, it can be used to improve statistics on the evolution of these systems.
In general, masses of pulsars are not easy to determine. In some cases, when the pulsar is in a binary with another compact object, high precision pulsar timing observations on extended timescales can allow for detecting post-Keplerian parameters of the systems, which can be used to separately measure the individual masses of the stars. Space velocities derived from proper motion measurements of radio pulsars give clues about the evolution of these systems and their birth supernovae (e.g. Toscano et al. 1999; Hobbs et al. 2005; Lorimer 2008). It is believed that recycled pulsars have lower space velocities than normal, slowly rotating pulsars. However as MSPs are generally the most stable rotators, the effects of their space velocities on their rotational and orbital parameters will be easier to derive from timing measurements of those systems and could be used to deduce the intrinsic properties of the stars.
Table 1: Timing solutions for the pulsars.
Another interesting and important use of timing MSPs to high precision, is the formation of a pulsar timing array (PTA, e.g. Janssen et al. 2008b; Hobbs et al. 2008). An instrument like this will use an array of MSPs as the endpoints of a Galaxy-scale gravitational wave (GW) detector. Current estimates predict that to detect a GW background, long-term high precision timing of about 20 MSPs is required (Jenet et al. 2005; Van Haasteren et al. 2009). Increasing the number of stable MSPs in the array will improve the detection significance. In order to better understand these systems in general, and to determine their suitability for inclusion in a timing array, their long-term timing behaviour needs to be determined. Moreover, the best frequency at which they should be timed needs to be ascertained. This is a combination of the pulse shape at these frequencies and their intensity. We observed all four pulsars at additional frequencies to find their best possible observing frequency for timing purposes, and discuss their suitability for inclusion in a PTA.
Three of the pulsars that are presented in this paper are in
low-eccentricity binary systems with white dwarf companions (see
Table 1). These systems are usually classified as
low-mass binary pulsars (LMBPs). The LMBPs distinguish themselves
from intermediate-mass binary pulsars (IMBPs) in having shorter
periods (<10 ms), very low eccentricities (<10-5), and they
follow relationships between their orbital period and the eccentricity
of their orbit, and their orbital period and the companion mass
(Thorsett & Chakrabarty 1999). The origin of the difference between these two classes
of binary MSPs is believed to be an evolutionary effect, and mainly
due to the progenitor masses of the companion stars. There are now
65 MSP binary pulsars with probable white dwarf companions known
(e.g. Lorimer 2008) and about 16 of these can be regarded as IMBP
candidates (Jacoby et al. 2006).
Detecting an optical counterpart to one of the binary pulsars allows to derive properties of their white dwarf companions. Because of differences in the cooling properties of white dwarfs in LMBPs and IMBPs, optical observations can in some cases be used to distinguish between the two classes (e.g. van Kerkwijk & Kulkarni 1995). So far, for all three binary pulsars described in this paper, the most recently published limit on optical magnitude of the companion is R>24 (van Kerkwijk et al. 2005).
2 Pulsar timing observations and data analysis
2.1 Westerbork
The pulsars were observed approximately monthly using the pulsar machines at the Westerbork Synthesis Radio Telescope (WSRT): PuMa (Voûte et al. 2002) since August 1999, and PuMaII (Karuppusamy et al. 2008) since August 2006. The WSRT has three frequency ranges allocated for pulsar timing; for observations centred at 350 MHz we use two bands of 10 MHz wide, and observations centred at 1380 or 2300 MHz use 80 MHz of bandwidth, spread in 8 steps of 10 MHz over a range of 160 MHz. The new pulsar machine uses the full 80 MHz bandwidth at the low frequencies, and all of the available 160 MHz bandwidth at 1380 and 2300 MHz. For all four pulsars presented here, we mainly used the 1380 MHz band as the pulsars were detected in this band, and there are no other reports of detections in other bands. Also this is the best available band for timing at the WSRT as it has the best sensitivity. For completeness, we observed all pulsars for one hour at 350 and 2300 MHz, see Fig. 1.
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Figure 1: Profiles for the PSRs at multiple frequencies. All profiles were generated from a single 55 min observation using PuMaII, except the 1380 MHz profiles of PSRs J1721-2457, J1745-0952 and J1810-2005 that used 10 to 12 h of PuMaII observations, and the 2600 MHz profile of PSR J1745-0952 was generated from a 50 min Nançay observation. These profiles are to show their appearance; for timing purposes we used high S/N templates as described in the text. |
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For a complete description of the PuMa data analysis, we refer to
Janssen et al. (2008a). Analysis of the PuMaII data was carried out using the
PSRCHIVE (Hotan et al. 2004) software suite. For both instruments, each
profile was cross-correlated with a standard profile at the
corresponding observing frequency (Fig. 1), obtained
from the summation of high signal-to-noise (S/N) profiles, to
calculate a time of arrival (TOA) for each observation. These were
referred to local time using time stamps from a H-maser at WSRT and
converted to UTC using global positioning system (GPS) maser offset
values measured at the observatory, and GPS to UTC corrections from
the Bureau International des Poids et Mesures (BIPM). The TOAs were converted to the Solar system barycentre using the JPL ephemeris
DE405
.
We used the TEMPO2 timing software package (Hobbs et al. 2006) to analyse
the data.
Flux densities were calculated for the WSRT observations by using the
aforementioned bandwidth and observing times, the measured
S/N ratio for each profile, the gain of the WSRT
(1.2 K/Jy), the pulse duty cycle (10%), the system temperature
and the pulsar specific radiometer equation (Dewey et al. 1985). The total
system temperature was determined from the synthesis data that is
taken in parallel with the pulsar observations.
2.2 Nançay
PSR J1721-2457, J1745-0952 and J1918-0642 were observed roughly every 3 to 4 weeks with the Nançay Radio Telescope (NRT) since 2006.
Equivalent to a 93-m dish, the Nançay Radio Telescope and the BON
(Berkeley-Orléans-Nançay) coherent dedispersor were used for
typical integration times of 45 min. Coherent dedispersion of a
64 MHz band centred on 1398 MHz was carried out on sixteen
4 MHz channels
using a PC-cluster in the period covered by the observations. The
Nançay data are written with timestamps which are directly tied to
UTC(GPS) in realtime, using a Thunderbolt receiver (Trimble Inc.), when
converting from an analogue to digital signal is performed. Differences
between UTC and UTC(GPS) are less than 10 ns at
maximum, and therefore no laboratory clock corrections are needed. One
TOA was calculated from a cross-correlation with a pulse template for
each observation of 45 min.
The flux densities for the Nançay data were calculated in a similar way to those for the WSRT except that the system temperature was determined from the known receiver temperature and sky temperature in the direction of the source. The gain of the NRT is 1.4 K/Jy.
2.3 Jodrell bank
PSR J1810-2005 was observed at Jodrell Bank since November 1997, and PSR J1918-0642 since February 2008. Both pulsars were observed every two weeks at a centre frequency around 1400 MHz. The gain of the Lovell telescope is 1 K/Jy.
The polarized signals from the receiver were were fed into an analogue
filterbank system with
MHz channels, and
filtered and digitised at appropriate sampling intervals and
incoherently dedispersed in hardware. The resulting dedispersed
timeseries were folded on-line with the topocentric pulsar period and
finally written to disc. In the off-line reduction, the two
polarisations were summed to form total-intensity profiles. A standard
high S/N pulse template was used to determine a TOA for each
observation. During this process, TOAs were referred to the local
H-maser time-standard and already corrected to UTC using information
obtained via the GPS.
3 Pulsar timing results and discussion
We present new timing solutions for the pulsars in Table 1, based on 7.5 to 10.5 years of radio pulsar timing as described in Sect. 2. The vast majority of our timing data were taken using a centre frequency around 1380 MHz, and therefore originally only the timing variation across the observing bandwidth was used to measure the dispersion measure (DM) of the four pulsars. As the combined data sets of WSRT and Nançay or Jodrell Bank together cover more than 200 MHz of bandwidth, the DM was already determined with good accuracy using only that data. However, to allow for refining the DM value even more, and to study the pulse shape and flux densities at other frequencies, we also observed the pulsars at 350 MHz and 2.3 GHz. This resulted in a few detections, see Fig. 1.
For PSRs J1745-0952, J1810-2005 and J1918-0642, all in very low-eccentricity binaries, we have used the ELL1 timing model (Lange et al. 2001) to avoid the high degree of covariance between the epoch and longitude of periastron.
We have measured significant proper motions for PSRs J1918-0642:
mas yr-1 and J1745-0952:
mas yr-1. By combining those proper
motions with the DM-derived distances from the Cordes & Lazio (2002) model,
we have calculated transverse velocities for those systems. For the
other two pulsars, we use the marginally significant values from the
timing solution to calculate a limit on their transverse velocities,
see Sect. 3.1.
3.1 Proper motion and velocity
We use our proper motion measurements to derive transverse velocities,
or limits on those, for all four pulsars (see
Table 1). We have a highly significant measurement
of the proper motion of PSR J1918-0642, and a significant detection
in right ascension for PSR J1745-0952. The proper motion values as
presented for the other two pulsars are not significant.
We note that both PSR J1721-2457 and J1810-2005 have
ecliptic latitudes very close to the ecliptic plane (
and
respectively), and therefore their proper motions may
be better and more independently fit in ecliptic parameters. However,
as the coordinate systems are nearly parallel because both
pulsars are near
,
fits in this
coordinate system did not result in an improvement of the limits on
their proper motions, or the significance of their positions. As both
of these pulsars lie quite close to the ecliptic, it may be that they
will show effects due to the solar wind (You et al. 2007). However at
the present timing precision we see no influence on the observed TOAs.
Due to changes in the projected line of sight, transverse motions of
pulsars can affect observed periodicities in the system (Shklovskii 1970).
We present the contributions to the spin period derivative of each
pulsar in Table 2. For completeness, the contributions
to the observed
from accelerations in the Galactic potential
are also presented, although those are not important effects for these
pulsars. To calculate the magnitude of the Shklovskii term we have used the
total proper motion values as presented in Table 1.
For PSR J1918-0642, the contribution to its spin period
derivatives,
,
from proper motion is less than
of
the observed value. However for PSR J1745-0952, the effect
can be as large as 50% of the observed value, leading to an
underestimation of the characteristic age and an overestimation of the
magnetic field. Moreover, as the proper motions for the solitary pulsar
J1721-2457 and PSR J1810-2005 have not been determined
significantly yet, the Shlovskii term may even completely dominate the
observed
for
those pulsars. To calculate an upper limit for the proper motion, and
accordingly a limit to the transverse velocity, we can use the observed
as a maximum:
This yields




Table 2: Contributions to the period derivative.
About 50% of the known solitary and low-eccentricity binary pulsars have measured transverse velocities (Tables 2 and 4 in Lorimer 2008). Hobbs et al. (2005) quote mean values of 2D speeds of 77(16) km s-1 for solitary MSPs and 89(15) km s-1 for binary MSPs. Compared to those, the (limits on) transverse velocities that we have derived from the proper motion measurements represent normal velocities for recycled pulsars.
3.2 Profiles
Apart from our normal timing observing frequency of 1380 MHz, we have observed all four pulsars at additional frequencies: 350 MHz and 2300 MHz. The results are shown in Fig. 1. It is now standard procedure for WSRT timing observations of MSPs to use both pulsar machines, and as we havetwice the bandwidth available in PuMaII, we present the profile of the detected pulsars at 350 MHz and 2.3 GHz from that data, see Fig. 1. Single observations of 55 min were used to generate the profiles at 350 and 2300 MHz. Where no profile is plotted, the pulsar was not seen at that frequency. The profiles at 1380 MHz were generated using one year of regular timing observations and consist of 10 to 12 observations of 25 min, except for PSR J1918-0642, where again one observation of 55 min. was used. PSR J1745-0952 was detected with NRT at 2600 GHz in an observation of 50 min.
As reported by Kramer et al. (1998), for most MSPs there is very little development of pulse profiles with frequency, which can be explained by MSPs having a very compact magnetosphere. For all pulsars except PSR J1810-2005, we indeed see no changes in the pulse profile with changing frequency, except for changes in the ratios of the heights of some components, within the significance of our detections. Compared to its profile at 1380 MHz, the 2300 MHz profile of PSR J1810-2005 appears to have more components in the main peak. Also the profile appears to show a leading component about 70 degrees before the main peak, although higher S/N will be needed to confirm this. Of all the MSP profiles presented by Kramer et al. (1999) none show more complex profiles at higher frequencies than at lower frequencies. Thus a further study of the profile of PSR J1810-2005 and its polarisation properties could reveal more about MSP emission profiles. The extra features in the peak of the high-frequency profiles of PSR J1810-2005 could be an indication that the profile at 1380 MHz suffers from scattering effects. However, the Cordes & Lazio (2002) model predicts very little scattering for this pulsar at both 1380 MHz (0.26 ms) and 2300 MHz (0.03 ms) suggesting that the features in the main peak of the pulse profile are intrinsic to the pulsar. It may turn out that, when better sensitivity can be achieved at higher frequencies, PSR J1810-2005 will give better timing results compared with the more commonly used 1380 MHz as its profile shows more features at higher frequencies.
3.2.1 Useful for pulsar timing array?
PSR J1721-2457 shows very stable rotational behaviour. All parameters of the timing solution presented in Table 1 are consistent with the original timing solution as published by Edwards & Bailes (2001). However, for the present S/N ratio, the wide profile of this pulsar does not allow for the high timing precision that is required for PTA pulsars (Jenet et al. 2005).
In contrast, despite its relatively long spin period compared to most
pulsars considered for PTA studies, PSR J1918-0642 may be worthwile
to include. Already at 1380 MHz the profile has a very sharp peak,
allowing for very precise timing over 7.5 years (rms = 2.3 s).
Furthermore, it is possible that better results for pulsar timing
arrays may be deduced by including not only the best-timing pulsars,
but extending the PTA pulsar set with pulsars that have timing
solution with rms
1
s (Jenet et al. 2005; Van Haasteren et al. 2009). The pulse
profile as shown in Fig. 1
was generated by the
PuMaII machine in WSRT, promising even better timing precision in the
ongoing timing programme. Observations with PuMaII use twice the
bandwidth of those with PuMaI and so give an increase in the
sensitivity. Moreover, because PuMaII uses coherent dedispersion, it
yields a sharper profile. The combination of these effects should lead
to an improvement in the timing precision of a factorbetween 2 and
4 for this pulsar over the next five years which may bring it to
the
required level for a PTA pulsar.
3.3 Flux density and scintillation
Table 3: Flux densities and spectral index.
We calculated flux densities for the four pulsars as described in Sect. 2.1, based on the profiles as shown in Fig. 1, see Table 3. We note that apart from those at 21 cm, the profiles are generated from single observations only, and therefore the resulting flux densities should not be regarded as accurate measurements, but are indicative of the intensities of the pulsars at the observed frequencies. The spectral indices for these pulsars are normal except for PSR J1810-2005, which appears to have a relatively flat spectrum. We observed this pulsar a couple of times at 2.3 GHz, and the resulting flux densities were varying by a factor 2, indicating that the brightness of this pulsar may be affected by scintillation.
Not long after we began our observations of PSR J1918-0642 we noticed that there were a number of occasions when we either did not detect the pulsar at all or it was extremely bright. A plot of the flux densities determined from all observations is shown in Fig. 2.
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Figure 2: Flux density variations of PSR J1918-0642 obtained with the WSRT and NRT from observations made at 21 cm. The left panel shows the distribution of flux densities from the two observatories, where the leftmost column represent all non-detections. In the right panel we show the individual flux density values as a function of time, where the length of the line in each case is proportional to the flux density, as indicated in the legend. Observations where there was no clear detection (ND) of the pulsar and thus only an upper limit on the flux density can be determined, are plotted with a cross. |
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The left hand panel shows a histogram of flux values from both Nançay and WSRT observations with the non-detections in the WSRT data shown in the far left hand bin. The right hand panel shows the variation in flux density as a function of time indicating the variations are typically on short timescales, although a long period of non-detections can be seen in 2006-2007. We note that the pulsar is not detected in approximately 20% of all WSRT observations. The pulsar is always detected, although sometimes with very low S/N ratio, in the Nançay data. This is not suprising due to the higher gain and longer integration times for the Nançay observations meaning that the NRT is approximately 30% more sensitive than the WSRT for this pulsar.
If these flux variations are due to scintillation then the quite frequent non-detections would suggest that the scintillation bandwidth must be at least as wide as the PuMaI bandwidth of 80 MHz. For the dispersion measure of this pulsar at this observing frequency such a large scintillation bandwidth seemed too large to be diffractive (Rickett 2001). Checking the literature, we found four pulsars with similar dispersion measures which had measured diffractive scintillation bandwidths in the range 15-70 MHz (Wang et al. 2005; Johnston et al. 1998) at 21 cm. While this is a large range the diffractive scintillation bandwidth would need to be above the highest measured value to explain the observed flux variations.
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Figure 3: Dynamic spectra of PSR J1918-0642 plotted as a greyscale of intensity as a function of time and frequency. Darker pixels correspond to higher intensity values and the intensity scales linearly with the levels of grey. The dynamic spectra are from two observations made using PuMaII on 23 February 2008 ( left) and 24 March 2008 ( right). |
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Using the improved bandwidth of our PuMaII measurements we were able to better explain the scintillation properties of PSR J1918-0642. In Fig. 3 we show the dynamic spectra from two observations of PSR J1918-0642, separated by just one month. The left hand side shows a classic case of scintillation with a scintillation bandwidth of approximately 5 MHz. Comparing this value to the range of bandwidths seen for similar dispersion measure pulsars, as discussed earlier, it is a factor of three smaller than the lowest measured scintillation bandwidth. In contrast, the right hand plot shows just a single scintle, which is perhaps somewhat broader than 5 MHz, across the full 160 MHz of bandwidth. It may be possible that these variations are purely statistical in nature, although the lack of any scintles in the band of at least 80 MHz in width, appears to happen about 20% of the time. We note that Gupta et al. (1994) explain variations in the scintillation properties like this as being to the refractive modulation of the diffractive interstellar scintillation pattern. While beyond the scope of this paper, the techniques outlined by Gupta et al. (1994) could be used to further examine the relationship between the velocities in this system and the interstellar medium along the line of sight. We note also that very wide bandwidth observations of this pulsar provide the best opportunity to do high precision timing, as when the pulsar is bright it can be timed to high precision.
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Figure 4:
|
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4 Optical observations
We have analysed archival observations of PSR J1745-0952 and
PSR J1810-2005. These observations were obtained with the ESO
Multi-Mode Instrument (EMMI) at the 3.6 m telescope of the European
Southern Observatory at La Silla, Chile on March 15th, 2004. The
instrument has two 2K 4K detectors
which were read out with
binning, providing a pixel scale
of
pix-1. The observations consisted of two 10 min.
R-band exposures of PSR J1745-0952 and two 5 min. R-band
exposures for PSR J1810-2005. For both pulsars, these long
exposures were preceded by short (10 s) exposures, also in the
R-band. The seeing during these observations was about
to
.
All images were bias-subtracted and flat-fielded using
twilight flats. The two deep images of each pulsar were averaged and
used for further analysis.
The short 10 s observations were astrometrically calibrated against
the 2nd version of the USNO CCD Astrograph Catalog (UCAC2,
Zacharias et al. 2004). For the PSR J1745-0952 observations, 34 UCAC2
stars overlapped with the chip on which the pulsar was located, of
which 26 were not saturated and appeared stellar and unblended, giving
rms residuals of
in right ascension and
in
declination. A secondary astrometric catalog was created from the
stars on the short exposure and used to calibrate the average of the
two 10 min exposures. For the transfer, about 300 stars were used,
giving residuals of
in right ascension and
in declination. Combined with the uncertainty on the timing position
of the pulsar, the quadratic uncertainty of the pulsar position on the
deep optical image is
in right ascension and
in declination. For PSR J1810-2005, we used 23 of the 32 overlapping UCAC2 stars, giving rms residuals of
in right
ascension and
in declination. The transfer of the
secondary catalog to the deeper average of the two 5 min
180 secondary standards, giving residuals of
in right
ascension and
in declination. The final uncertainty on
the pulsar position on the deep image is
in right
ascension and
in declination. No sources are present in
the error circles of both pulsars, as shown in Fig. 4.
In order to determine upper limits on the brightness of the pulsar
companions, we performed PSF photometry on the averaged deep images
using DAOPHOT II (Stetson 1987). The resulting instrumental magnitudes
were calibrated against 47 standard stars in the PG 1525-071 using
the calibrated magnitudes of Stetson (2000). Since only R-band
observations were taken, only the zeropoint was fitted for the
calibration, giving rms residuals of 0.02 mag. The standard La Silla
R-band extinction of 0.07 mag per airmass was used to correct for
extinction between the standard observations taken at an airmass of
1.08 and the pulsar observations taken at an airmass of 1.34 (for
PSR J1745-0952) and 1.25 (for PSR J1810-2005). Based on the
magnitudes and uncertainties of faint stars in the images, we estimate
the 3
detection limit at R>24.49 for PSR J1745-0952 and
R>24.02 for PSR J1810-2005.
4.1 Model predictions
Though no optical counterparts to PSR J1745-0952, PSR J1810-2005 and PSR J1918-0642 (R>24, see van Kerkwijk et al. 2005) were detected, it is still worthwhile to compare the upper limits on the white dwarf magnitudes with those predicted by models. To convert the upper limits on the apparent magnitudes to limits on the absolute magnitude, we need estimates for the distance and absorption. Estimates for the distance to each pulsar using the observed dispersion measure and the Cordes & Lazio (2002) model for the Galactic distribution of electrons are given in Table 1. The V-band absorption AValong the line-of-sight and at the distance of each pulsar was estimated using the Drimmel et al. (2003) model for Galactic extinction and converted to R-band absorption AR using the extinction coefficients of Schlegel et al. (1998) ( AR=0.819AV). We estimate upperlimits on the absolute R-band magnitude of MR>11.3 for PSR J1745-0952, MR>3.3 for PSR J1810-2005 and MR>12.7 for PSR J1918-0642.
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Figure 5:
Absolute R-band magnitude and cooling age
predictions. Shown are helium-core white dwarf cooling tracks
by Rohrmann et al. (2002) and carbon-oxygen white dwarf cooling tracks
with hydrogen-rich atmospheres by Bergeron et al. (1995) ( |
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In Fig. 5 we show predictions of absolute magnitude
and cooling ages from the white dwarf cooling tracks by Rohrmann et al. (2002)
and Bergeron et al. (1995). The helium-core white dwarf cooling tracks show a
dichotomy in the cooling properties of helium-core white dwarfs caused
by differences in the thickness of the hydrogen layer surrounding the
helium core of these white dwarfs (see,
e.g. Althaus et al. 2001; Schönberner et al. 2000). White dwarfs heavier than
0.18-0.20
have thin envelopes and cool faster than lighter
white dwarfs which have thick envelopes. Cooling tracks appropriate
for heavier carbon-oxygen white dwarfs with hydrogen-rich atmospheres are even
fainter.
Under the assumption that the characteristic pulsar ages are equal to
the white dwarf cooling ages, we plot the upper limits on our white
dwarf pulsar companions and detections of others in
Fig. 5. Because of the large distance and absorption
towards PSR J1810-2005, the limit does not constrain any white
dwarf parameters. For PSR J1745-0952 and PSR J1918-0642 the
upper limits exclude white dwarfs with thick hydrogen envelopes. As
such, the mass of the white dwarf in these systems is constrained to
.
For PSR J1745-0952 this mass
limit, combined with the low massfunction of the system, constrains
the inclination of the binary orbit to the low value of
(assuming
). Should this pulsar have a
carbon-oxygen white dwarf, which is not excluded by the optical
observations, the limit on the inclination will be even lower.
5 Conclusions
Using the WSRT, NRT and Lovell telescopes, we have timed four MSPs for 7.5 to 10.5 years. We have presented updated timing solutions, pulse profiles at multiple frequencies for each pulsar, and scintillation parameters for PSR J1918-0642. We have measured transverse velocities for PSRs J1745-0952 and J1918-0642, and set limits on the velocities of PSRs J1721-2457 and J1810-2005. All velocities are consistent with previously published distributions for solitary and binary MSPs.
We have analysed archival optical observations for the binary MSPs and
found no companions to the pulsars. From the magnitude limits we
deduce for the companions, we can exclude white dwarfs with thick
atmospheres. This indicates that the companions must be heavier than
about 0.2 .
At this point, the mass restrictions as well as the optical magnitude
limits give no conclusive information to classify PSRs J1745-0952
or J1810-2005 as either LMBPs or IMBPs.
For low-eccentricity binary pulsars, the only post-Keplerian parameter that is likely to be measurable is the Shapiro delay. The upper limit for inclination of PSR J1745-0952, i < 34, suggests that the effect of Shapiro delay in timing will be very low and therefore we can not expect to use pulsar timing analyis to disentangle the individual masses of this system. However, the expected luminosity of MR>11.3 indicates that using a dedicated optical observation, the companion of this pulsar may be detectable, and this will therefore be the most promising way of deducing the pulsar and companion masses.
AcknowledgementsThe Westerbork Synthesis Radio Telescope is operated by ASTRON (Netherlands Foundation for Research in Astronomy) with support from the Netherlands Foundation for Scientific Research NWO. The Nançay radio Observatory is operated by the Paris Observatory, associated to the French Centre National de la Recherche Scientifique (CNRS). The Nançay Observatory also gratefully acknowledges the financial support of the Region Centre in France.
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Footnotes
- ... (BIPM)
- http://www.bipm.org
- ...
DE405
- ftp://ssd.jpl.nasa.gov/pub/eph/export/DE405/de405iom.ps
All Tables
Table 1: Timing solutions for the pulsars.
Table 2: Contributions to the period derivative.
Table 3: Flux densities and spectral index.
All Figures
![]() |
Figure 1: Profiles for the PSRs at multiple frequencies. All profiles were generated from a single 55 min observation using PuMaII, except the 1380 MHz profiles of PSRs J1721-2457, J1745-0952 and J1810-2005 that used 10 to 12 h of PuMaII observations, and the 2600 MHz profile of PSR J1745-0952 was generated from a 50 min Nançay observation. These profiles are to show their appearance; for timing purposes we used high S/N templates as described in the text. |
Open with DEXTER | |
In the text |
![]() |
Figure 2: Flux density variations of PSR J1918-0642 obtained with the WSRT and NRT from observations made at 21 cm. The left panel shows the distribution of flux densities from the two observatories, where the leftmost column represent all non-detections. In the right panel we show the individual flux density values as a function of time, where the length of the line in each case is proportional to the flux density, as indicated in the legend. Observations where there was no clear detection (ND) of the pulsar and thus only an upper limit on the flux density can be determined, are plotted with a cross. |
Open with DEXTER | |
In the text |
![]() |
Figure 3: Dynamic spectra of PSR J1918-0642 plotted as a greyscale of intensity as a function of time and frequency. Darker pixels correspond to higher intensity values and the intensity scales linearly with the levels of grey. The dynamic spectra are from two observations made using PuMaII on 23 February 2008 ( left) and 24 March 2008 ( right). |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Absolute R-band magnitude and cooling age
predictions. Shown are helium-core white dwarf cooling tracks
by Rohrmann et al. (2002) and carbon-oxygen white dwarf cooling tracks
with hydrogen-rich atmospheres by Bergeron et al. (1995) ( |
Open with DEXTER | |
In the text |
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