Infrared observations of the candidate double neutron star system PSR  J1811$-$1736

No near-IR observations of the PSR J1811$-$1736 are available in either the ESO¹¹1http://archive.eso.org or the Gemini²²2www.gemini.edu Science Data Archives. Thus, we searched for near-IR data of the PSR  J1811$-$1736 field in the image archive of the UK Infrared Deep Sky Survey (UKIDSS) performed with the Wide Field Camera (WFCAM) at the UK Infrared Telescope (UKIRT) at the Mauna Kea Observatory (Hawaii). WFCAM (Casali et al. 2007) is a mosaic detector of four 2048$\times$2048 pixel Rockwell devices, with a pixel scale of 0$\text{aas}@@fstack\prime \prime$4 and covering a field–of–view of 0.21 square degrees. A general description of the UKIDSS survey is given in Lawrence et al. (2007). The UKIDSS survey covers several regions, with a different sky coverage, and sensitivity limits in the $ZYJHK$ UKIRT photometric system (Hewett et al. 2006). The field of PSR  J1811$-$1736 is included in the Galactic Plane Survey (GPS; Lucas et al. 2008) which covers about 1800 square degrees in $JHK$ down to sensitivity limits which are more than a factor of ten deeper than 2MASS. Like all the UKIDSS data, the GPS images are processed through a dedicated pipeline (Hambly et al. 2008) developed and operated at Cambridge Astronomical Survey Unit (CASU) which performs basic reduction steps (dark subtraction, flat fielding), image de-jittering, stacking, and mosaicing. The pipeline also runs a source detection algorithm and produces source catalogues. Astrometry and photometry calibration are performed using 2MASS stars as a reference (Hodgkin et al. 2009). We searched for the reduced science images of the PSR  J1811$-$1736 field and associated object catalogues through the WFCAM Science Archive (WSA)³³3http://surveys.roe.ac.uk/wsa/ interface accessible via the Royal Observatory Edinburgh. We queried the most recent UKIDSS Data Release (version 9 Plus) made available on October 25th 2011. The field was observed on July 18 2006. We downloaded $10\text{arcmin}\times 10\text{arcmin}$ $J$, $H$, $K$-band stacks around the pulsar position and the associated multi-band object catalogues.

For the search for the companion star to PSR J1811$-$1736, we assumed as a reference its radio timing coordinates. We note that the pulsar radio timing solution presented by Corongiu et al. (2007) is based on data taken in the epoch range MJD=50842–53624 and does not include the determination of the pulsar’s proper motion, an essential parameter for recomputing its position at a given epoch. For this reason, we re-analysed the data presented in Corongiu et al. (2007) adding the proper motion to the timing model, to obtain a new radio timing position at a reference epoch (MJD=53624) closest to that of the UKIDSS observation (MJD= 53934). Thus, we obtained ${\alpha }_{J2000}={18}^h{11}^{m}55\text{aas}@@fstacks0385\pm 0\text{aas}@@fstacks0029$ and ${\delta }_{J2000}=-{17}^{\circ }36\text{arcmin}38\text{aas}@@fstack\prime \prime 45\pm 0\text{aas}@@fstack\prime \prime 41$ for the position and ${\mu }_{\alpha }cos\left(\delta \right)=18.3\pm 9.7$ mas yr${}^{-1}$ and ${\mu }_{\delta }=-176\pm 100$ mas yr${}^{-1}$ for the proper motion, where all quoted uncertainties are at $1\sigma$ level. The extrapolated timing position at the epoch of the UKIDSS observation (MJD= 53934) is, then: ${\alpha }_{J2000}={18}^h{11}^{m}55\text{aas}@@fstacks054\pm 0\text{aas}@@fstacks009$ and ${\delta }_{J2000}=-{17}^{\circ }36\text{arcmin}38\text{aas}@@fstack\prime \prime 60\pm 0\text{aas}@@fstack\prime \prime 42$, with an uncertainty radius of 0$\text{aas}@@fstack\prime \prime$44 (1$\sigma$) that accounts for the position uncertainty due to the proper motion extrapolation. For comparison, by applying the same timing model as above but without adding the proper motion, we obtain ${\alpha }_{J2000}={18}^h{11}^{m}55\text{aas}@@fstacks0337\pm 0\text{aas}@@fstacks0014$ and ${\delta }_{J2000}=-{17}^{\circ }36\text{arcmin}37\text{aas}@@fstack\prime \prime 80\pm 0\text{aas}@@fstack\prime \prime 19$, where the choice of the reference epoch (MJD=53624) within the range spanned by the timing data is, in this case, arbitrary. Although this position has a nominal uncertainty radius (0$\text{aas}@@fstack\prime \prime$19; 1$\sigma$) that is smaller than obtained in the previous case, assuming it as a reference at the epoch of the UKIDSS observations would introduce an unknown systematic uncertainty due to the neglected pulsar proper motion. For this reason, it is formally less correct than the radio position obtained by fitting the proper motion, despite the latter having a larger uncertainty radius. Nonetheless, in the following section we conservatively consider both positions in our search for the PSR  J1811$-$1736 counterpart. In computing the overall uncertainty on the PSR  J1811$-$1736 position in the UKIDSS images we also accounted for systematics associated with the nominal accuracy on the UKIDSS astrometry calibration (0$\text{aas}@@fstack\prime \prime$05 rms at low Galactic latitudes; Lawrence et al. 2007), the internal astrometric accuracy of 2MASS ($\text{la}$0$\text{aas}@@fstack\prime \prime$2 for stars with $15.5\le K\le 13$), and the accuracy on the link of 2MASS to the International Celestial Reference System (0$\text{aas}@@fstack\prime \prime$015; Skrutskie et al. 2006).

The UKIDSS $K$-band image of the PSR  J1811$-$1736 field is shown in Fig. 1 (bottom) compared to the corresponding 2MASS image (top). For comparison, we plotted the two pulsar positions derived from the radio timing solution, with and without fitting the proper motion. As seen, no object is detected within the two $1\sigma$ radio position error circles (0$\text{aas}@@fstack\prime \prime$44 and 0$\text{aas}@@fstack\prime \prime$19 radii, respectively). However, a star ($K=15.46\pm 0.02$), unresolved in the 2MASS image but clearly detected in the much higher resolution UKIDSS one, is detected within the proper motion-corrected $3\sigma$ radio error circle (1$\text{aas}@@fstack\prime \prime$32 radius). Thus, its association with the pulsar cannot be ruled out a priori and needs to be investigated. The star is also detected in the $J$ and $H$ bands, with magnitudes of $J=18.61\pm 0.37$ and $H=16.65\pm 0.03$. No other star is detected at, or close to, the computed $3\sigma$ radio pulsar positions down to $3\sigma$ limiting magnitudes of J$\sim 20.5$, H$\sim 19.4$ and K$\sim 18.6$, as computed from the rms of the sky background (Newberry 1991). Given the high star density along the Galactic plane, however, the match can be the result of a chance coincidence. We computed this probability as $P=1-\exp (-\pi \rho r^2)$, where $r$ ($\sim 1\text{aas}@@fstack\prime \prime 32$) is the matching radius, assumed equal to the $3\sigma$ uncertainty on the proper motion-corrected pulsar radio position, and $\rho$ is the density of stellar objects within an area of $10\text{arcmin}\times 10\text{arcmin}$ around the pulsar. We found that $\rho \sim 0.057$ arcsec${}^{-2}$, which gives $P\sim 0.27$. Such a high chance coincidence probability suggests that the star is likely unrelated to the pulsar, although we need a direct piece of evidence to firmly rule out the association.

We investigated whether the characteristics of the star detected close to the PSR  J1811$-$1736 position are compatible with it being its companion star. To this end, we tried to determine its spectral type from its colours. Fig. 2 shows the colour-magnitude diagram (CMD) $(H-K)$–$K$ and the colour-colour diagram $(K-H)$ vs. $(J-K)$ built from the photometry of field stars detected within a $10\text{arcmin}\times 10\text{arcmin}$ area around the pulsar position, as derived from the UKIDSS object catalogue. We also plotted the location of the star detected close to the PSR  J1811$-$1736 position (Fig. 1, bottom), whose location in both diagrams is consistent with the sequence of field stars. Thus, determining its spectral type from the comparison of its colours and flux with those of field stars is not obvious. Moreover, the determination of the star’s intrinsic colours is affected by the substantial interstellar extinction towards the pulsar, which is located in the Galactic plane ($l={12.828}^{\circ };b={0.435}^{\circ }$). In particular, the CMD is very broadened, suggesting that the field is affected by a quite high, and probably differential, extinction.

The interstellar extinction towards PSR  J1811$-$1736 is uncertain, and this affects our estimate of the upper limits on the companion star luminosity. A first estimate of the interstellar extinction can be derived from the integrated Hydrogen column density along the line of sight to the pulsar. This is $N_H=(1.24-1.64)\times {10}^{22}$, as computed using the heasarc tool webpimms⁴⁴4http://heasarc.nasa.gov/cgi-bin/Tools/w3nh/w3nh.pl according to the Dickey & Lockman (1990) and Kalberla et al. (2005) Hydrogen maps. This gives $E(B-V)=2.2$–2.9, according to the relation of Predhel & Schmitt (1995). However, PSR  J1811$-$1736 is closer than the edge of the Galaxy, at a distance $D={5.7}_{-0.71}^{+0.84}$ kpc, estimated from the radio pulse dispersion measure (DM=$476\pm 5$ pc cm${}^{-3}$; Corongiu et al. 2007) and the Galactic free electron density along the line of sight (Cordes & Lazio 2002). This would suggest a lower interstellar extinction. According to the Galactic extinction maps of Hakkila et al. (1997), the pulsar distance and Galactic coordinates would imply an interstellar extinction $E(B-V)\sim 1.9$. However, these estimates are only indicative mainly because of the uncertainties on the extinction maps on smaller angular scales. Unfortunately, the PSR  J1811$-$1736 field has not been observed in X-rays, so that no independent measurement of the interstellar extinction can be inferred from the hydrogen column density $N_H$ directly derived from the fits to the X-ray spectra. In principle, an independent measurement of the $N_H$ can be obtained from the DM itself assuming an average ionisation fraction of the interstellar medium (ISM) along the line of sight. In the case of PSR  J1811$-$1736, a DM=$476\pm 5$ pc cm${}^{-3}$ would correspond to $N_H\sim 1.5\times {10}^{22}$ cm${}^{-2}$, for a 10% ionisation fraction. This would imply an $E(B-V)\sim 2.7$. However, this method is usually applied to pulsars closer than $\sim 300$ pc (e.g., Pavlov et al. 2009; Tiengo et al. 2011) and is intrinsically affected by a much larger uncertainty for pulsars at larger distances, such as PSR  J1811$-$1736.

We tried to derive an independent estimate on the reddening along the line of sight by comparing the CMDs and colour-colour diagrams of field stars with those in a reference region of very low reddening, such as the Baade’s Window. As we did for the PSR  J1811$-$1736 field, we extracted from the UKIDSS data the object catalogues relative to a $10\text{arcmin}\times 10\text{arcmin}$ area centred around the Baade’s Window, for which we assumed the coordinates of the globular cluster NGC  6522: ${\alpha }_{J2000}={18}^h{03}^{m}34\text{aas}@@fstacks08$ and ${\delta }_{J2000}=-{30}^{\circ }02\text{arcmin}02\text{aas}@@fstack\prime \prime 3$ (Di Criscienzo et al. 2006). Fig. 3, shows the same diagrams as in Fig. 2 but with the UKIDSS data for the BaadeÕs Window region overlaid. From the comparison of the two sets of diagrams, we derived an estimate of the interstellar extinction towards the pulsar. Firstly, we computed the average of the distribution in the colour-colour space for the Baade’s Window region, applying a $3\sigma$ clipping. Secondly, we did the same for the pulsar field but selecting a region of 50″ radius around the pulsar position not to be affected by the differential extinction in the field. Then, from the difference between the two values we estimated an $E(B-V)=5.7\pm 1.9$ for the pulsar field. This value is a factor of 2 larger than the Galactic interstellar extinction inferred from the Hydrogen column density maps in the pulsar’s direction. However, we note that the $N_H$ value reported above is a weighted average relative to a 1${}^{\circ }$ radius area around the pulsar coordinates, which does not rule out the presence of patches of higher Hydrogen column density on angular scales smaller than 0.4${}^{\circ }$, which are not resolved by the available maps.

Indeed, it has been found that the interstellar extinction towards the Galactic bulge region is not uniform and shows strong variations, or granularities, on angular scales as small as 1′ (see, e.g. Gosling et al. 2006). We used the UKIDSS J, H, and K${}_s$-band images of the PSR  J1811$-$1736 field to measure the granularity of the interstellar extinction in the region, following the method described in Gosling et al. (2006). We considered a region of $500\text{arcsec}\times 500\text{arcsec}$ centred on the PSR  J1811$-$1736 position. We divided the region in cells with dimension variable between 8″ and 500″ to sample the granularity in the field on different angular scales. For each cell dimension, we calculated the $y$ parameter (see Eqn. 1 in Gosling et al. 2006), which gives a quantitative estimate of the granularity of the field and is defined as the variance of the number of stars in all cell normalised to the mean number of stars per cell. We computed the $y$ parameter for the J, H, and K${}_s$-band images. For the region considered in our analysis, we found that the $y$ parameter, hence the granularity, decreases as a function of wavelength (see Fig. 4), as in the case of one of the test fields used by Gosling et al. (2006). Thus, the high level of granularity in the pulsar field seems to be correlated with a high and variable reddening, explaining the large scatter in the CMD and colour-colour diagram of the field stars (Fig. 2). We note that the measured angular scale of the granularity in the PSR  J1811$-$1736 field (see Fig. 4) is comparable to the 50″ radius region that we used to estimate the extinction in the pulsar’s direction from the CMD and colour-colour diagram analysis (see previous paragraph). Thus, we are confident that our procedure does not under/overestimate the assumed extinction value along the line of sight to the pulsar.

Under the hypothesis that the star seen close to the PSR  J1811$-$1736 position is its companion, we tried to determine its spectral type assuming the range of reddening values computed above. We considered a range of distances within the computed $1\sigma$ uncertainty range on the PSR  J1811$-$1736 distance based on the DM ($D$=4.9–6.54 kpc), and an age range of 1–13.2 Gyr, consistent with the ages of the stellar populations in the Galactic centre region (e.g. Zoccali et al. 2003), where the pulsar is located. We also considered different values of the metallicity $Z$. For older populations, we considered both $Z=0.008$ and $Z=0.02$, while for the younger populations we considered only $Z=0.02$. Then, for different values of metallicity, age, and distance we determined the best $E(B-V)$ values in the range $E(B-V)=3.8$–7.6 that minimise the sum of the projected distances of the star location in the $J$–$(J-H)$ and $K$–$(H-K)$ CMDs from the isochrones computed from the stellar models of (Marigo et al. 2008; Girardi et al. 2010). From the best combinations of metallicity, age, distance, and reddening, we then derived the corresponding mass ($M_C$) and radius ($R_C$) of the candidate companion star to PSR  J1811$-$1736, from the comparison with the isochrones. Finally, we combined the computed mass of the candidate companion star with the mass function of the pulsar system (Corongiu et al. 2007) and its total mass ($M_{tot}=2.57\pm 0.10M_{\odot }$). In this way, we derived the pulsar mass ($M_P$) and the orbital inclination angle $i$ of the system for each combination of metallicity, age, distance, reddening, and mass of the candidate companion star. We filtered out combinations for which it resulted $\sin i>1$. We also selected the acceptable combinations for the conditions that the companion mass $0.93M_{\odot }\le M_C\le 1.5M_{\odot }$ and the pulsar mass $1.17M_{\odot }\le M_P\le 1.6M_{\odot }$, as it results from the PSR  J1811$-$1736 timing analysis (Corongiu et al. 2007), where the lower limit on $M_P$ corresponds to the minimum measured value for the mass of a neutron star (Janssen et al. 2008). The different parameter combinations are summarised in the first eight columns of Table 1 and 2. These parameters are consistent, for a reddening $E(B-V)=4.5$–5, with a companion star still on the main sequence (MS) and close to the turn-off or on the lower Red Giant Branch (RGB), with an inferred mass $M_C\approx 1$–1.3 $M_{\odot }$ and radius $R_C\approx 4.3$–5.8 $R_{\odot }$.

All the combination of parameters reported in Tab. 1 and 2 have been further checked against the lack of eclipses at superior conjunction (orbital phase $\varphi$ = 0.25) in the radio timing observations. This check is grounded on the fact that the pulsar cannot be eclipsed at a given orbital phase if the corresponding pulse’s time of arrival (ToA) has been determined, since ToA determination strictly requires the detection of the pulse. Hence, we calculated the orbital phases for each ToA presented in Corongiu et al. (2007), and we obtained that the closest available ToAs before and after superior conjunction correspond to an orbital phase $\varphi$ = 0.191366 and $\varphi$ = 0.277151, respectively. A parameters’ combination is acceptable only if, at both orbital phases, the projected distance $d$ of the pulsar to the centre of the companion, computed on the plane perpendicular to the line of sight, is larger than the companion radius, i.e. $d/R_C>1$. Columns 9 and 10 of Tab. 1 and 2 report the values of $d/R_C$ for the two values of the orbital phase computed above, with the possible combinations flagged YES and NO for the cases $d/R_C>1$ and $d/R_C<1$, respectively. Our calculation shows that for only 4 out of the 63 possible combinations of selected parameters the required condition is satisfied at both orbital phases. These combinations imply a $\approx 5$ Gyr companion star, with mass $M_C\approx 1.3M_{\odot }$ and radius $R_C\approx 5R_{\odot }$, at a distance of $\sim 5.5$ kpc and with a reddening $E(B-V)\approx 4.9$. This corresponds to a pulsar mass $M_P\approx 1.3M_{\odot }$ and inclination angle for the system of $\approx {45}^{\circ }$. Thus, according to the constraints on the masses and orbital inclination of the binary system, it is theoretically possible that the star detected at the radio position is, indeed, the companion to the pulsar. In this case, PSR  J1811$-$1736 would not be a DNS.

A $\approx 5$ Gyr MS companion would be compatible with the pulsar spin-down age (${\tau }_{SD}=1.9$ Gyr) but not much so with the recycling scenario and the pulsar orbital parameters. In principle, the high orbital eccentricity of PSR  J1811$-$1736 ($e=0.828$) can be seen as the signature of a supernova explosion that changed all binary system parameters. Since PSR  J1811$-$1736 is a recycled pulsar, the orbit must have been circularised during the recycling process (Battacharya & van den Heuvel 1991) and its orbital eccentricity could have been produced by a second supernova explosion, i.e. that of the companion star. In this case, both the spin period and the orbital eccentricity values of PSR  J1811$-$1736 would be the highest among DNSs and consistent with the correlation between these two parameters observed in such systems (Faulkner et al. 2005) and recovered under the hypothesis of a low-amplitude neutron star kick (${\sigma }_v\sim 20$km s${}^{-1}$) at birth (Dewi et al. 2005).

We investigated whether the MS companion scenario would be indeed compatible with the pulsar spin and orbital parameters. We compared in Fig. 5 the eccentricity, spin period, and orbital period of PSR  J1811$-$1736 to those of binary pulsars with identified companions, whose masses are in the same range as the PSR  J1811$-$1736 companion. We selected our sample from the Australia Telescope National Facility (ATNF) pulsar data base⁵⁵5http://www.atnf.csiro.au/people/pulsar/psrcat/ (Manchester et al. 2005). Our sample is summarised in Table 3. In our analysis, we focused on the comparison with recycled binary pulsars only, whose evolutionary path can be compared to that of PSR  J1811$-$1736. As seen, the only known pulsar–MS star system in the selected companion mass range is PSR  J1903+0327 (Khargharia et al. 2012). However, this is a fully–recycled ms-pulsar ($P_s=2.5$ ms), whereas PSR  J1811$-$1736 is a mildly-recycled pulsars with a much longer spin period ($P_s=104$ ms) and a much shorter orbital period ($P_{orb}=18.8$ d) than PSR  J1903+0327 ($P_{orb}=95.2$ d). Moreover, the eccentricity of PSR  J1811$-$1736 ($e=0.828$) is much larger than PSR  J1903+0327 ($e=0.436$). Thus, there are no known pulsar–MS star systems in the selected companion mass range with spin and orbital parameters comparable to those of PSR  J1811$-$1736. This might suggest that such systems, if they do exists, are quite rare, although the very small sample currently available prevents us to draw firm conclusions. There is one pulsar system, PSR  J0514$-$4002A in the globular cluster NGC 1851 (Freire et al. 2004), with a possible white dwarf (WD) companion (Freire et al. 2007), that has both orbital period and eccentricity comparable to PSR  J1811$-$1736 (Fig. 5, lower panel). However, like PSR  J1903+0327, also PSR  J0514$-$4002A is a fully–recycled pulsar, with a spin period $P_s=4.99$ ms. Moreover, since PSR  J0514$-$4002A is in a globular cluster, its original companion might have been exchanged through a close encounter with another star in the cluster. Thus, the evolutionary history of this system might not be directly comparable to PSR  J1811$-$1736. A firm classification of the PSR  J0514$-$4002A companion would help to evaluate the pulsar–MS star scenario for PSR  J1811$-$1736.

If the companion star of PSR  J1811$-$1736 is undetected in the UKIDSS data, the derived upper limits on its flux can be used to constrain its nature. From the interstellar extinction coefficients of Fitzpatrick (1999), an $E(B-V)=5.7\pm 1.9$ would correspond to $A_J\sim 3.3$–6.6, $A_H\sim 2.0$–4.0 and $A_K\sim 1.4$–2.8. From our derived detection limits (J$\sim 20.5$, H$\sim 19.4$ and K$\sim 18.6$) these values imply extinction-corrected fluxes of $J_0\text{ga}13.9$, $H_0\text{ga}15.4$, and $K_0\text{ga}15.8$, where we conservatively assumed the largest values of the interstellar extinction. At the estimated pulsar distance ($D={5.7}_{-0.71}^{+0.84}$ kpc) these values correspond to absolute magnitudes $M_J\text{ga}6.9$, $M_H\text{ga}8.4$, and $M_K\text{ga}8.8$, allowing us to rule out a companion of spectral type earlier than a mid-to-late M-type MS star. Thus, our constraints on the companion star are far more compelling that those derived by Mignani (2000) on the basis of the DSS data alone. Moreover, those constraints should be now revised upward since the reddening towards the pulsar measured in this work is at least twice as large than assumed by Mignani (2000) from the Galactic extinction maps (Hakkila et al. 1997). As a matter of fact, these were the only resources available at the time to determine the reddening in the pulsar direction. 2MASS data of the pulsar field, which could be used to determine the reddening from the CMD technique, as we did with the UKIDSS data, were only released after the Mignani (2000) paper was published. Our new limits are also not deep enough to rule out a WD companion star. As done in the previous section, we investigated whether the PSR  J1811$-$1736 spin and orbital parameters would fit those of recycled pulsar–WD systems. As seen from Fig. 5, most recycled pulsar–WD systems have circular orbits and both orbital and spin periods shorter than PSR  J1811$-$1736. There is only one recycled pulsar–WD system, PSR  J1750$-$3703A in the globular cluster NGC  6397 (D’Amico et al. 2001), that has both spin ($P_s=0.111$ s) and orbital parameters ($P_{orb}=17.33$ d; $e=0.712$) close to PSR  J1811$-$1736. Thus, it is possible that PSR  J1811$-$1736 is, indeed, a pulsar–WD system and not a DNS. However, since also PSR  J1750$-$3703A is in a globular cluster, the same caveats as discussed above for PSR  J0514$-$4002A apply in this case. The identification of other pulsar–WD systems with spin and orbital parameter close to PSR  J1811$-$1736, but located in the Galactic plane, would help to determine the nature of the PSR  J1750$-$3703A system. We note that the other pulsar–WD system PSR  B2303+46 (Dewey et al. 1985; Thorsett et al. 1993; van Kerkwijk & Kulkarni 1999) with orbital parameters ($P_{orb}=12.33$ d; $e=0.658$) similar to PSR  J1811$-$1736 (Fig. 5, lower panel) is not a recycled pulsar, which means that it is either on a different evolutionary path or evolutionary stage.