HERSCHEL AND SPITZER OBSERVATIONS OF SLOWLY ROTATING, NEARBY ISOLATED NEUTRON STARS

Herschel observations of eight isolated NSs were carried out over a period of ∼1 yr using the Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010). We obtained the images in mini-map mode in the blue (60–85 μm) and red (130–210 μm) bands with the respective PACS bolometer arrays operated in parallel. The mini-map mode is a particular case of the scan-map mode, where two observations (scan and cross-scan) are carried out that have scan angles in array coordinates along the two array diagonal directions, 70° and 110°. An individual scan-map observation has a pattern of parallel, overlapping scan lines connected by turnaround loops. The mini-map mode provides a good point-source sensitivity with a relatively large homogeneous coverage (about 50'' in diameter).⁵ Our observations were performed with medium scan speed (20'' s⁻¹), and the mapping parameters were 10 scan legs with scan lengths of 3' with a separation of 4'' between them. A repetition factor of 12 was chosen to reach point-source sensitivities close to the expected confusion noise (for a details about the confusion noise in the PACS bands and its estimation, see, e.g., the Herschel Observers' Manual,⁶ Chapter 4.3. and the HERSCHEL-HSC-DOC-0886⁷ document by C. Kiss). Our observations are listed in Table 1. Overall, each Astronomical Observation Request (AOR) was 7 ks. The beam sizes FWHM of the blue and red band at medium speed are 55 × 58 and 105 × 1202, respectively (Poglitsch et al. 2010).

Table 1. List of Herschel Observations

Object	Date	ObsIDs	PointAcca
RX J0420.0–5022	2012 Jan 7	1342236938/9	11
RX J0720.4–3125	2011 Nov 10	1342232218/9	11
RX J0806.4–4123	2011 Oct 29	1342231572/3	11
RX J1308.6+2127	2011 Jul 11	1342223951/2	15
RX J1605.3+3249	2011 Jul 20	1342224486/7	15
RX J1856.5–3754	2011 Mar 15	1342216058/9	24
PSR J1848–1952	2012 Mar 13	1342241353/4	11
RX J2143.0+0654	2012 Apr 23	1342244870/1	11

Note. ^a1σ absolute pointing accuracy; see Section 4.1.

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We observed RX J0720.4–3125 with the Spitzer Space Telescope⁸ (Werner et al. 2004) during the post-cryogenic mission in 2011 January (PI: Posselt). The observations were done with the Infrared Array Camera (IRAC; Fazio et al. 2004) at 3.6 μm and 4.5 μm. We used a frame time of 100 s and 31 dither positions in each band. We also consider here some of the NS observations of another Spitzer program (PI: Wachter), which searched for fallback disks around a large number of nearby pulsars using the IRAC 4.5 μm channel. Those observations were performed from 2011 September to 2012 December. In each observation, a 100 s frame time and 30 dither positions were used. The Spitzer observations discussed in this paper are listed in Table 2. The IRAC field of view is 52 × 52, the native IRAC pixel size is 12, and the FWHM of the point-spread function at 3.6 μm and 4.5 μm is 166 and 172, respectively (Fazio et al. 2004).

Using the Herschel Interactive Processing Environment (HIPE), v9.0,⁹ we reduced the data based on the deep-survey scan-map pipeline scripts of the PACS photometer pipeline. The PACS calibration file set PACS_CAL_41_0¹⁰ was applied. We reprocessed the data from the Level 0 to the final maps (Level 2.5) applying the usual processing steps outlined in Poglitsch et al. (2010) and Lutz et al. (2011).

A critical step in the data processing is the removal of the 1/f noise, the heavy flicker noise of the PACS readout system. In the case of a point-source observation, a high-pass filter along the time line of the observation allows one to remove most of the 1/f noise, which increases the sensitivity of the observation. The effects of the high-pass filter on the PACS point-spread function and the noise, the resulting flux removal, and mask strategies to avoid the former are discussed in detail by Popesso et al. (2012). According to this study, the high-pass filter most efficiently removes noise in the case of high data redundancy, i.e., large repetition factors. Flux losses of point sources are reduced best by putting circular mask patches on prior source positions. The filter width and patch sizes need to be carefully chosen since their influences dominate the global and local noise in the PACS maps. In our data processing, we checked maps produced with a masking technique where only sources above a certain threshold are masked before the combined map is produced. This method can be expected to have the highest sensitivity for faint point-source identification. However, not all observations show a PACS source near the isolated neutron star (INS) position. Aiming to reduce flux losses in our flux (limit) estimates, we therefore masked a region with radius 10'' around each expected INS position for our final map productions.

The pixel noise of individual pixels in a PACS photometer map is correlated due to the 1/f noise and due to the applied drizzle projection method by Fruchter & Hook (2002) during the map creation process. Popesso et al. (2012) calculated the individual noise contributions in dependence of the high-pass filter width, the output pixel size, and the pixel drop fraction used in the drizzle method. In general, the noise level is lower in the high data redundancy case compared to the low data redundancy case, and smaller pixel sizes and smaller pixel drop fractions can be chosen in the former case to achieve the same noise limit. We checked different sets of parameters. As a good final choice for all our maps, we used pixel sizes of 1'' in the blue band, 2'' in the red band, a pixel drop fraction of 0.04 in both bands, and high-pass filter widths of 15 readouts in the blue band and 25 readouts in the red band.

The expected positions of the INSs at the time of the Herschel observations were calculated from positions and proper motions (if known) in the literature, and they are listed in Table 3. Position errors are usually below 1''. We comment on individual INS uncertainties in Section 5 and Appendix A if there are close neighbor sources in the Herschel images. The Herschel absolute pointing error ranges from 1σ ≈ 24 for our earliest Herschel observation (RX J1856) to 1σ ≈ 11 for our latest Herschel observations, according to the Herschel calibration and HIPE teams.¹¹ The pointing errors are listed in Table 1.

We use apertures with sky annuli to measure source fluxes and apply the corresponding aperture corrections using the respective HIPE tasks. The calibration study by Popesso et al. (2012) provided a method to calculate aperture flux errors from the coverage of individual map pixels by considering the chosen data reduction parameters. First, the coverage-error map relation as well as the cross-correlation factor are calculated in dependence on the chosen pixel size, pixel drop fraction, and high-pass filter width. Then, the coverage is used to calculate the error of the individual map pixels. The pixel errors are quadratically added for the respective aperture size. Finally, the cross-correlation factor is applied. This cross-correlation correction factor accounts for both components in the correlation noise, the projection itself, and the residual 1/f noise not removed by the high-pass filter. Since we give aperture-corrected fluxes, we apply the aperture correction factor to the estimated error as well. We checked whether the determined final error was of the same order as the variance of background apertures in nearby source-free regions and found this to be the case. We list 5σ errors for the aperture-corrected fluxes in Table 5.

If there is no source at the INS position, we consider several apertures to measure the standard deviation of the background in the central, source-free region of the map (close to the INS) where the exposure coverage is reasonably homogeneous. Depending on how crowded the field is, we usually obtain results from 7 to 15 apertures with radii of 5'' or 7''. We list 5σ values for the flux limits in Table 5.

We neglect the PACS photometer color corrections (for estimates of the monochromatic flux densities for different spectral shapes) because they are close to one for a wide range of expected disk temperatures (30–1000 K). However, if highly accurate fluxes for a particular disk model are desired, we refer to the respective Herschel PACS Technical Note PICC-ME-TN-038.¹²

For the data reduction of the Spitzer IRAC data, we used Spitzer's MOsaicker and Point source Extractor package, MOPEX,¹³ v.18.5.6. In the following, we give an exemplary description of the data reduction for the IRAC data of RX J0720.4–3125 (two bands). The data reduction for the 4.5 μm data of the other INSs is performed following the same procedures.

In each case, we start from the artifact-corrected basic calibrated data (cBCD) frames. We removed one cBCD frame from the 3.6 μm data set of RX J0720.4–3125 because it had a bad column at the target position. From the respective 4.5 μm data set, we removed five frames due to artifacts, possibly the so-called column pull-up, at or close to the source position. Using the mosaic task, we obtained a combined image with a pixel size of 06. We checked the alignment of the IRAC mosaic astrometry with the 2MASS Point Source Catalog (Skrutskie et al. 2006) using 114 2MASS sources with the highest quality flag AAA in the field. The astrometric accuracy of the 3.6 μm and the 4.5 μm mosaics of RX J0720.4–3125 are 027 and 028, respectively. Similar astrometric accuracies are found for the other INS Spitzer mosaics. The expected INS positions were calculated for the times of the respective Spitzer observations using known positions and proper motions as described for Herschel in Section 4.1.

The IRAC Point Response Function (PRF) is essentially the convolution of a box the size of the image pixel, with the point-spread function (e.g., MOPEX user guide, chapter 8.9¹⁴). To consider a PRF that is variable in the field of view, one uses the so-called PRF maps, which are provided by the Spitzer Science Center¹⁵ for the IRAC channels. The PRF is required for point-source fitting photometry, which we performed with the apex multi-frame task on each individual cBCD frame. Applying then the apex-qa task, we subtracted the fitted point sources from the individual cBCD frame to obtain a residual mosaic. Such residual mosaics are useful if neighboring sources contaminate the flux at the source position.

We use aperture photometry to determine IRAC fluxes and flux limits. We apply aperture radii of 2 native IRAC pixels, corresponding to 4 mosaic pixels, and aperture correction factors of 1.21 and 1.22 for the 3.6 μm and the 4.5 μm measurements, respectively (Reach et al. 2005). To obtain an upper limit, we determine not only the source aperture flux, F_SRC, but also the background level, F_BG, and the standard deviation, σ, of several (usually 8–10) source-free apertures close to the source position. If necessary and possible, we use the residual mosaics for these measurements. In the case of a non-detection, we define the upper flux limit F_5σ = F_SRC − F_BG + 5σ.

The derived IRAC fluxes are in Jy and correspond nominally to those fluxes one expects to measure in the respective IRAC channel for a source with F_ν∝ν⁻¹. Sources with different spectral shapes and, in particular, very red sources, require a color correction. The IRAC Instrument Handbook¹⁶ (Section 4.4) lists color corrections for different power law indices and blackbody temperatures. In Sections 5.1 and 5.2, and Appendices A.1–A.6, we give the aperture-corrected flux values without color correction, while in Table 5 we exemplarily apply the color corrections for a T = 200 K blackbody as an approximation for the spectral shape of potential warm disk emission.

The Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) mapped the sky in 2010 at 3.4 (W1), 4.6(W2), 12(W3), and 22 (W4) μm with an angular resolution of 61, 64, 65, and 12'', respectively. We use the all-sky atlas images and the WISE Source Catalog to investigate the regions of our INSs. We cross-checked for astrometric shifts between the positions of known 2MASS sources or sources in our previous H-band VLT observations and source positions in WISE bands, as well as for noticeable astrometric shifts between WISE sources and the Herschel sources. While the astrometric calibrations of the first three WISE bands generally agree well with NIR astrometry, there are often noticeable shifts in the fourth band that are most easily seen when comparing the last two WISE bands. Astrometric biases in the WISE all-sky atlas images are discussed on the IPAC Web page.¹⁷ While we suspect a shifted W4 astrometry for several of our fields, we do not attempt to improve the W4 astrometric calibration because the scarcity, faintness, and spatial extent of the W4 sources hinder a good, unique astrometric calibration. We ignore the W4 band in the following.

We searched for potential WISE counterparts of the INSs or neighboring Herschel sources in the remaining bands and discuss our findings in the respective subsections. In Table 4 we provide the WISE field limits measured in Vega magnitudes. The limits correspond to the requirement that the IR sources have signal-to-noise ratios (S/N) ⩾5 in the respective band. To obtain these limits, we considered all WISE sources in a box area 1° × 1° around the INS (usually around 20,000 sources). Sources with S/N =5 usually have a magnitude uncertainty of ≈0.22 mag.

To convert the Vega magnitudes into flux density units such as Jy, one has to know and account for the source spectrum in the respective WISE band by applying a color correction. Due to the wide WISE bands, these color corrections can be very different for stars and much cooler blackbody-like sources (asteroids, disks); see, e.g., Cutri et al. (2012), Section IV.4.h, and Wright et al. (2010). As an example, we give fluxes for a T = 200 K blackbody additionally to the Vega magnitudes in Table 4, but caution that flux limits should in principle be more carefully calculated for any specific (disk) models under investigation.

The Spitzer IRAC2 (4.5 μm) observation of RX J0806.4–4123 is well aligned with previous NIR observations (e.g., 2MASS point sources), with a 1σ astrometric accuracy of 02 (using 196 AAA 2MASS sources). Posselt et al. (2009) investigated VLT ISAAC H-band images of this region. Figure 1 shows that the major H-band sources correspond well to the Spitzer sources. The Chandra X-ray position of RX J0806.4–4123 has a positional uncertainty of 06 (90% confidence; Haberl et al. 2004). Together with the upper limit on the INS proper motion at the time of the Spitzer observation (088 (2σ); Motch et al. 2009), the overall positional uncertainty of the expected RX J0806.4–4123 position in IRAC2 is about 09 (90% confidence level) in the worst case.

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There appears to be faint emission in the 4.5 μm band within this range in the northwest direction of the nominal INS position; see source A in Figure 1. The emission is so faint that we were not able to detect it with the MOPEX PRF-fitting methods. It may be spurious emission; however, there are similarly faint sources that correspond to known NIR sources (e.g., source C in Figure 1). We were not able to produce a reasonable apex-qa residual mosaic in which the brighter sources would be reliably subtracted. As the H-band contours show, the IRAC2 emission may contain several IR sources that are not recognized by the PRF fit. For example, it would be useful to subtract source B, but this source is not even recognized as an individual source in our PRF fits. If we do flux aperture measurements at the INS position (with a radius of 2 native IRAC pixels), we nominally obtain an aperture-corrected flux of F^4.5 μm = 5.2 ± 1.9 (1σ) μJy. Since one can argue about the reliability of such 2.8σ emission, we also estimated the aperture-corrected upper flux limit $F^{4.5\, \mu \rm m}_{5\sigma }=14.7$ μJy. We note that there is a very faint NIR source at the INS position in the 2004 VLT H-band data too, but the NIR emission is below the 3σ significance level as well (Posselt et al. 2009).

In the Herschel PACS blue band, there is no significant emission around the position of RX J0806.4–4123. Using apertures in different source-free regions and at the target position, we determined the 5σ upper flux limit for the INS as $F^{\rm blue}_{5\sigma } = 4.9$ mJy. There is, however, emission around the INS position in the Herschel PACS red band; see Figure 2. We use the X-ray position of RX J0806.4–4123 from Haberl et al. (2004). This position has an uncertainty of 06 (90% confidence). In addition, an uncertainty of 083 needs to be considered due to the 2σ upper limit on the proper motion, 86 mas yr⁻¹. In the Herschel field of view, there is only one unambiguous point source in common with other infrared data, e.g., VLT H-band or WISE. The positions of this point source agree well. Comparing the extended emission with the WISE data, we conclude that the nominal Herschel PACS pointing accuracy of 1σ ≈ 11 can be assumed. The PACS red emission around the INS could either consist of several point sources or include extended emission. The peak closest to the INS has a spatial separation of ≈25 from the X-ray position. We use a 5'' aperture for the flux measurement and 10 other apertures on source-free regions to measure the background. Using an aperture correction of 3.4, we estimate a flux of F^red ≈ 10 ± 5 (5σ) mJy at the position of the INS. In Section 6.1, we discuss the likelihood of the Herschel PACS red band emission being not associated with the NS.

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We use the previous H-band image for cross-checks with the WISE W1–W3 data; see Figure 3. There is no noticeable astrometric shift between these bands. There is no apparent counterpart in the WISE data to the emission in the Herschel PACS red band. Higher spatial resolution is required to investigate the Herschel emission around the INS position.

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The position of RX J2143.0+0654 is known with an accuracy of 02 from optical observations (Schwope et al. 2009), but its proper motion is unknown. Comparing the Chandra, XMM-Newton, and optical positions from different epochs as shown by Schwope et al. (2009), one can infer that the proper motion must be smaller than 700 mas yr⁻¹. Thus, at the time of the Herschel and Spitzer observations, the INS could have moved from the optical position by <32 and <37, respectively.

There is no emission at the position of RX J2143.0+0654 in the Spitzer IRAC 4.5μm mosaic image; see Figure 4. There are, however, four Spitzer sources within <37 of the nominal NS position. Since the same sources were detected as faint H-band sources in the 2003 VLT observations by Posselt et al. (2009), none of them can be the NS counterpart. The aperture-corrected 5σ upper flux limit at the nominal NS position is $F^{4.5\, \mu \rm m}_{5\sigma }=3.0$ μJy.

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The field around RX J2143.0+0654 is densely populated in the infrared and includes several common sources in the Herschel PACS bands, Spitzer IRAC, the WISE W1 and W2 bands, and in the VLT ISAAC H-band observations of Posselt et al. (2009); see Figures 4–6. This allows us to confirm that the absolute pointing error of the Herschel observation is not larger than the expected value of 11.

There is emission in the red PACS band at the position of the INS, consisting of a blend of at least one southern and one brighter northern source (see Figure 5; the southern source is marked with a box and was also detected by WISE). In the blue PACS band, there is very faint emission northwest of the INS. The peak position of the 160 μm emission is 37 north of the optical INS position, about 26 from the closest N(IR) source. Considering the unknown NS proper motion, we cannot rule out the possibility that this source is the counterpart of the INS. However, it appears unlikely that RX J2143.0+0654 has the implied large proper motion (>06 yr⁻¹). While the INS distance is unknown, it is expected to be larger than 300 pc (Posselt et al. 2007). For comparison, the closest of the XTINSs, RX J1856.5–3754 (D = 140 pc), also has the largest proper motion (330 mas yr⁻¹) of those four of the XTINSs for which proper-motion measurements or limits were reported.

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Part of the red band emission at the INS position is likely to come from the bright infrared southwestern source that is seen in several bands. Given the proximity of the sources, their faintness, and the FWHM in the red band of 105 × 1202, it is not possible to remove sources with the necessary accuracy to search for residual 160 μm emission at the optical position of the INS. We used an aperture with radius of 5'' at the position of the INS to measure the flux at this position. The aperture-corrected flux is F^red = 7.8 ± 4.8 (5σ) mJy. Due to the surrounding sources, this value must be regarded with caution and it can be an overestimate of any actual flux from the INS position. In Section 6.1, we discuss the likelihood of the Herschel PACS red band emission not being associated with the NS.

In the blue band, there is no prominent source emission at the INS position. Using apertures in different source-free regions and at the target position, we determined the 5σ upper limit for RX J2143.0+0654 flux to be $F^{\rm blue}_{5\sigma } = 5.0$ mJy.

We used the VLT ISAAC H-band image by Posselt et al. (2009), Spitzer, and 2MASS point sources for cross-checks with the WISE W1–W3 data; see Figures 4 and 6. There is no noticeable astrometric shift between these bands. The W1 emission west of the INS position is probably related to the southwestern sources seen with Spitzer, and no enhanced emission is detected at the INS position. In W3, there is no emission peak at the INS position, although there is an eastern source at ≈8'' and a faint southern source at ≈5'' from the nominal NS position. Since the astrometry of sources in these WISE images agree well with those of N(IR) sources, we conclude that RX J2143.0+0654 is undetected in the WISE W1–W3 data.

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In Sections 5.1 and 5.2, we reported on Herschel red band emission at or near the positions of RX J0806.4–4123 and RX J2143.0+0654. How likely is the emission in the Herschel PACS red band to be associated with a source different from the INS? Confusion from faint Galactic stars is negligible for the PACS red band.¹⁸ The main two components of sky background confusion noise in the long-wavelength bands of Herschel are extragalactic sources and interstellar cirri. Sibthorpe et al. (2013) showed that, for a given Herschel PACS flux level, results from typical extragalactic fields can be used to estimate the background source numbers in typical debris disk surveys. They used the results from the PACS Extragalactic Probe (Berta et al. 2011; Lutz et al. 2011) to estimate the expected background source number density for given flux and flux uncertainty levels. Following the approach by Sibthorpe et al. (2013), we estimate the chance probability of detecting an F_red ≈ 10 mJy extragalactic source in a circle with a radius of r = 5'' as 0.5%. For RX J2143.0+0654, we estimate the respective chance probability of detecting an F_red = 7.8 mJy extragalactic source in a circle with a radius of r = 5'' as 0.7%. Given these chance probabilities, the binomial probability that we detect background sources in two of eight overall XTINS fields is at maximum 1% for 7.8 mJy sources, but the probability of detecting one background galaxy at one of the eight XTINS positions is already 5%.

Gáspár & Rieke (2014) argued that Sibthorpe et al. (2013) underestimate the confusion noise probabilities, mainly because galaxies fainter than a considered flux limit may also contribute to the overall confusion noise. We used the Monte Carlo Code by Gáspár & Rieke (2014) to estimate the probabilities for N_excess unrelated "excess sources" in the photometry apertures of our eight NSs. We realized 10⁶ data sets of eight sources with our detection requirement of ≳ 5σ (Table 5, i.e., 5 mJy for RX J0806.4–4123) in a r = 5'' photometry aperture. In a nutshell, the code by Gáspár & Rieke (2014) simulates background sources in a single large field (0.5 deg²), then properties for eight random positions from this field are estimated 10⁶ times. The latter step includes the consideration of noise from interstellar cirri using a probability distribution with standard deviation σ_cirrus, which is calculated from the observed far-infrared interstellar medium (ISM) flux background. For details on the code and the assessment of its statistical performance, we refer to Gáspár & Rieke (2014). For our simulations, we used a cirrus noise value of σ_cirrus = 0.84 mJy, which corresponds to the median value of the ISM background flux of 11.74 MJy sr⁻¹, as estimated by using Hspot¹⁹ for the observing dates and positions of our eight NSs. The resulting probability plot is shown in Figure 7. The probability to detect no, one, or two excess source(s) among our eight NSs is 86%, 13%, and 1%, respectively. Thus, it seems unlikely that both our detections are excess sources.

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Kaplan et al. (2011) investigated RX J0806.4–4123 with the Hubble Space Telescope (HST) and found no source other than the NS within 2'' of the INS position using the Advanced Camera for Surveys, Wide Field Channel/filter F475W down to an ST magnitude of 27.92 ± 0.22. Considering the Herschel pointing accuracy (11, Section 5.1) and its large FWHM (≈11'' for the red band), there are, however, several HST sources that currently cannot be excluded as potential Herschel background galaxy counterparts.

There is also another alternative explanation for the Herschel PACS red band source: interstellar cirrus. In fact, the ISM background flux in the direction of RX J0806.4–4123 is estimated by Hspot to be about a factor of 10 higher than the median value of the remaining seven NS fields. Illustrating the higher ISM background, the recent 3D maps of the local ISM distribution by Lallement et al. (2014) show a local ISM cloud clump in the direction of RX J0806.4–4123. A typical interstellar cirrus has been found to have temperatures of about ∼20 K with a range of about 4 K around this value (Veneziani et al. 2013; see also Gáspár & Rieke 2014)—a temperature range very reminiscent of the one inferred for our Herschel detection around RX J0806.4–4123 (see Section 6.2). If we consider explicitly the higher ISM background flux for this one source in the Monte Carlo simulation by Gáspár & Rieke (2014), we obtain 63%, 33%, and 3% as the probabilities for detecting no, one, or two excess source(s) among our eight NSs, respectively. The probability of one excess source among the eight NSs has nearly tripled, but the probability for no excess sources in the sample is still a factor of 2 higher.

In the case of RX J2143.0+0654, the HST observations are not constrained with respect to excluding obviously present galaxies as counterparts to the faint Herschel emission either. Regarding interstellar cirri, the ISM background flux in the direction of RX J2143.0+0654 is nearly the same as the median value for the seven NS fields (excluding RX J0806.4–4123). Thus, the probability for an excess source due to an ISM cirrus is less than in the case of RX J0806.4–4123.

In the following, we assume that the detected Herschel emission originated from dust associated with the XTINS. We summarize the Herschel and Spitzer results of the previous subsections in Table 5. Assuming the emitting dust to be optically thin at submillimeter wavelengths, we can use the Herschel 160 μm measurements to calculate the dust mass, assuming a single temperature for all dust grains:

$$\begin{equation} M_d=\frac{F_{\nu } D^2}{B_{\nu }(T_d) {\kappa }^d_{\nu }}, \end{equation} \tag{ 1 }$$

where ν = 1.9 × 10¹² Hz is the frequency, F_ν is the measured flux density (limit), D is the distance, B_ν(T_d) is the Planck function at a dust temperature T_d, and ${\kappa }^d_{\nu }$ is the dust mass absorption coefficient. We use ${\kappa }^d_{\rm 160\,\mu m}=13$ cm² g⁻¹ for the PACS red band, which we calculated from the optical constants by Dorschner et al. (1995), assuming dust grains consisting of amorphous magnesium silicate with a grain density ρ_g = 2.7 g cm⁻³. The dust composition and, therefore, the dust mass absorption coefficient is in general highly uncertain (by a factor of three to five, e.g., Posselt et al. 2010). Additionally, the dust likely has a temperature distribution, not a single temperature. The composition and dimensions of a fallback disk around a ∼1 Myr old NS are unknown, too. Thus, the derived dust masses in Table 5 and Figure 9 are only crude estimates.

In Figures 8 and 9, we show the ratios of the IR/submillimeter fluxes (limits) to the X-ray fluxes of the XTINSs. The obtained flux ratios (limits) are usually in the range 10⁻⁴ to 10⁻³ for the H-band and the Spitzer 4.5 μm data, but 0.01 to 0.1 for the Herschel data. For comparison, we refer to similar plots of three CCOs by Wang et al. (2007a, for optical and IR fluxes only). At the Spitzer wavelengths, flux ratio limits of 10⁻² to 10⁻⁴ were reached for the CCOs, but no disks were detected. Wang et al. (2007a) also showed a comparison plot for the only magnetar where a disk is thought to be detected—4U 0142+61 (Wang et al. 2006). For this magnetar, the flux ratio at Spitzer IRAC wavelengths is ≈6 × 10⁻⁵. This comparison might indicate that our limits are simply not deep enough. On the other hand, the single object 4U 0142+61 might not be defining for all potential NS disks. Our Herschel detections of emission around RX J0806.4–4123 and RX J2143.0+0654 could indicate predominantly cold dust around these (older) NSs. Spitzer 4.5 μm observations are not sensitive enough to detect such cold dust.

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Dust emission at long wavelengths can be described in the Rayleigh limit if λ > max (2πa, λ_Res), where a is the (spherical) grain size radius, and λ_Res is the largest resonance wavelength of the complex refractive index as tabulated in the DOCCD.²⁰ If this condition is fulfilled, the flux density F_ν∝ν² (see Appendix B), and assuming optically thin conditions for the grain as well as the overall medium (e.g., dusty disk or cloud), we can write

$$\begin{equation} F_{\nu }=\frac{B_{\nu } (T_d)}{B_{\nu _0} (T_d)} \left(\frac{\nu }{\nu _0}\right)^2 F_{\nu _0}, \end{equation} \tag{ 2 }$$

where ν₀ ≪ 10¹³ Hz is the reference frequency. Here, we choose the Herschel red band (ν₀ = 1874 GHz) as reference band and show the constraints on the expected dust fluxes at long wavelengths in Figures 8 and 9. In the former, we use an exemplary temperature T_d = 20 K, and in the latter, we illustrate the effect of choosing different temperatures.

In the wavelength regime of W1–W3, Spitzer IRAC, and the H band, the dust absorption and emission properties are highly non-monotonic functions of λ (see, e.g., the laboratory absorption coefficient measurements of dust grains by Dorschner et al. 1995), and the dust medium is in general not optically thin for (its own) emission at such wavelengths. Realistic flux models would require the application of the Mie theory for the radiation transport calculation for a distribution of dust grains. Given that we deal only with flux limits at these wavelengths, such modeling is beyond the scope of this paper. To estimate at least the maximal upper limits on the luminosity ratios, we assume blackbody emission. For blackbody emission, the dust luminosity limits, L_dust(T_d), are related to the measured flux density limits, F_ν,

$$\begin{equation} F_{\nu } =\frac{B_{\nu }(T_d) L_{\rm dust} }{4 D^2 \sigma _{SB} {T_d}^4 }, \end{equation} \tag{ 3 }$$

where σ_SB is the Stefan–Boltzmann constant. The right plot in Figure 9 shows the blackbody luminosity constraints for RX J0806.4–4123.

For hν₀ ≫ 2.8kT, optically thin dust conditions, and uniform properties of the dust grains as well as a uniform temperature, we derive for the total luminosity of the dust:

$$\begin{eqnarray} L_{\rm dust}(T_d)&=& \frac{160}{21}\pi ^2 \left(\frac{kT_d}{h\nu _0}\right)^2 \kappa ^d_{\nu _0} M_d \sigma _{SB} T_d^4 \nonumber \\ &=& F_{\nu } D^2 \frac{160}{21} \pi ^2 \left(\frac{k}{h\nu }\right)^2 \frac{\sigma _{SB}}{B_{\nu } (T_d)} T_d^6, \end{eqnarray} \tag{ 4 }$$

where k is the Boltzmann constant and h is the Planck constant. The middle plot of Figure 9 shows the constraints on $L_{\rm dust}(T_d)/L^{NS}_X$ from the Herschel red band value and blue band limit. We see that only low dust temperatures (T_d < 25 K) are allowed considering the detection and non-detection in the red and blue band, respectively.

In the previous section, we discussed only in general the constraints on the dust associated with the XTINSs. Here, we discuss constraints on different properties of potential disks assuming that the detected Herschel fluxes are indeed due to emission from dust around the NSs. Bryden et al. (2006) noted that only the brightest debris disks detected with Spitzer have L_dust/L_{bol, *} ⩾ 10⁻⁴. The recent Herschel DUNES survey by Eiroa et al. (2013) reported L_dust/L_{bol, *} ranging from 10⁻⁶ to 3 × 10⁻⁴ for Herschel debris disk candidates around solar-type stars. If the Herschel 160 μm detections for two XTINSs and the marginal Spitzer 4.5 μm and H-band detections of emission around RX J0806.4–4123 are confirmed to come from disks, the luminosity ratios would be two to three orders of magnitudes higher than the values seen for non-degenerate stars. The implied large absorption cross section of the disk appears questionable. In contrast to the luminosities of main sequence stars, most of the XTINSs' luminosity is emitted in soft X-rays (<1 keV). In contrast to other wavelengths, soft X-ray photons are very efficiently absorbed and re-emitted by all dust grains (≈100% of each incident soft X-ray photon; e.g., Dwek & Smith 1996). The absorption cross section of a putative disk cannot, however, be larger than the geometric cross section of that disk. Hence, even if one accounts for an exceptionally high dust heating efficiency, geometric arguments exclude a thin flared disk from gobbling up 20% of the stellar luminosity. The implied geometric shape for an assembly of dust grains surrounding the NS would be rather a dusty torus or an envelope.

We use the Rayleigh approximation to estimate the possible location of the dust around the NS. As outlined in Appendix B, the temperature distribution, T_g(r), of amorphous magnesium silicate dust grains with sizes a can be calculated as:

$$\begin{equation} T_\mathrm{g}(r)= 39 \left(\frac{L_{\mathrm{bol},30}}{a_{\mu \mathrm{m}}} \right)^{1/6} \left(\frac{1}{r_{14}} \right)^{1/3}\,\mathrm{K}, \end{equation} \tag{ 5 }$$

where the NS luminosity, L_{bol, 30}, is normalized to 10³⁰ erg s⁻¹, and the distance, r₁₄, between the NS and the grain is normalized to 10¹⁴ cm. Note that this equation is only valid for $T<\min {(96\,\mathrm{K},2300 a^{-1}_{\mu \mathrm{m}}\,\mathrm{K})}$.

As shown in Section 6.2 and Figure 9, the inferred temperature for potential circumstellar dust around, e.g., RX J0806.4–4123, is in the range of 10–22 K. A dust grain with such temperatures would be expected at radii of $r_d= 2.3 \times 10^{16} a_{\mu \mathrm{m}}^{-1/2}$ cm to $2.2 \times 10^{15} a_{\mu \mathrm{m}}^{-1/2}$ cm, corresponding to $1600\, a_{\mu \mathrm{m}}^{-1/2}$ AU and $150 \, a_{\mu \mathrm{m}}^{-1/2}$ AU, respectively. At a distance of ≈250 pc, this translates into angular sizes of about 6'' and 1'', i.e., the source would be still unresolved in the Herschel red band, which is consistent with the observations. Thus, we cannot rule out such temperatures based on the expected emission extension for RX J0806.4–4123. For RX J2143.0+0654, the inferred radii would be a factor of 2.8 larger due to its higher X-ray luminosity, although the angular scales are probably similar because of the likely larger distance of this XTINS. The implied orbital radii of the 22 K dust grains with sizes a ≲ 1 μm are larger than the radii commonly considered for (young and gas-rich) fallback disks, R_FD ≈ 10¹⁰–10¹⁴ cm (e.g., Perna et al. 2014). After removal of the gas in the possible disks around the relatively old INSs, however, the dust is difficult to remove by ISM drag (see also below), and a pure dust or debris disk could, in principle, expand to larger radii. Looking at our own solar system, there are the following reminiscent large structures: the Kuiper Belt at 30–60 A.U. with lateral coverage of up to 40° (e.g., Brown 2001) and the hypothesized near-spherical Oort Cloud with radii from 10⁴–10⁵ A.U. (e.g., Dones et al. 2004). The formation of the Kuiper Belt and the Oort Cloud are not fully understood, but in general it is believed that gravitational interactions of belt/cloud objects with the newly formed giant planets were of major importance (Morbidelli et al. 2008; Dones et al. 2004). Survival or formation of giant planets around an NS are unlikely, and a mechanism for the extension of an initial compact fallback disk would be needed if the emitting dust grains are smaller than 10 μm. Constraints on the emitting grain size could be obtained by additional investigations at submillimeter wavelengths.

The smallest grains are the hottest and contribute most to the observed dust luminosity. If, in the case of cicumstellar dust, already ≈20% of the NS luminosity is re-emitted by cold dust, but the upper limit at Spitzer wavelengths is less than 1% (because of blackbody assumption; see Figure 9), it follows that there are no significant amounts of small hot dust grains around RX J0806.4–4123. An explanation for this finding could be the effect of the Poynting–Robertson (P-R) drag (e.g., Phillips & Chandler 1994). In Figure 10, we plot lines corresponding to the P-R drag and different dust temperatures (for the latter we use Equation (5)). The black line corresponds to the P-R drag limit for a putative disk around an NS with radius of R_NS = 10 km and a disk age of 0.5 Myr. Dust grains below that line are removed for the respective radius in a putative disk. We see that small grains close to the NS are effectively eliminated. Dust grains with size ∼1 μm can exist only at radii r > 3 × 10¹³ cm. In Figure 10, we also plot the effects of the ISM drag experienced by the dust grains when they move together with the NS disk/belt through the ISM (e.g., Phillips & Chandler 1994). The ISM drag depends on the inclination of the putative disk/belt with respect to the direction of proper motion. We use different inclination angles. If the putative disk moves edge-on in the direction of the proper motion, the inclination angle is 0°. This assumption allows us to obtain an upper limit for the smallest grain size, represented by the red line in Figure 10. An inclination angle of 89° corresponds to the putative disk moving nearly face-on in the direction of the proper motion. This scenario is more likely because many NSs have a spin-velocity alignment and angles <10° are most probable. In Figure 10, this scenario is represented by the green line. We assumed a disk age of 0.5 Myr, an NS velocity of 100 km s⁻¹, a number density of ISM gas particles 1 cm⁻³, and a dust grain density of 3 g cm⁻³ for our calculations. The ISM drag is the dominating force on the dust grains at large distances. Similar to the P-R line, grains below the ISM drag lines in Figure 10 would be removed. In the case of face-on disk motion, this mechanism would remove grains smaller than ∼1 μm at all distances. Overall, it appears likely that any dust around RX J0806.4–4123 consists of predominantly large, a > 1 μm, grains—if the Herschel emission indeed comes from a dusty torus around the XTINS.

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There is no IR emission at the position of RX J0420.0–5022 in the Spitzer 4.5 μm IRAC image; see Figure 11. The aperture-corrected 5σ upper limit is $F^{4.5\, \mu \rm m}_{5\sigma }=2.8$ μJy.

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At the position of RX J0420.0–5022, we detect no source in the Herschel blue and red band (see Figure 12). Using apertures in different source-free regions and at the target position, we determined the 5σ upper flux limits at the INS position as $F^{\rm blue}_{5\sigma } = 4.5$ mJy and $F^{\rm red}_{5\sigma } = 7$ mJy. There are several common sources in the Herschel bands and WISE bands W1 to W3. There is no noticeable astrometric shift between these bands. The W1 and W3 images for the field around RX J0420.0–5022 are shown in Figure 13. There is very faint emission east and northwest of the INS in the W3 band, but no entry in the WISE source catalog at these positions. Slightly enhanced emission at the same positions might be suspected in the red band (Figure 12). However, these potential W3 sources are separated by at least 58 from the expected INS position and are therefore unassociated with the INS.

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We first consider the Spitzer observations. The IRAC mosaics are very crowded, and there appears to be a faint source close to the position of RX J0720.4–3125 (Figure 14). The expected position of the INS at the time of the Spitzer observation, MJD 55582, is $\alpha = 7^{\rm h} 20^{\rm m} 24\buildrel{\mathrm{s}}\over{.}{904}; \delta = -31^\circ 25^\prime 49{\buildrel{\prime\prime}\over{.}} {63}$. It is calculated using the latest, MJD = 54477, optical position of the NS and its proper motion, μ_α = −93.2 ± 5.4 mas yr⁻¹ and μ_δ = 48.6  ±  5.1 mas yr⁻¹, listed by Eisenbeiss et al. (2010). The radial positional uncertainty of the expected INS position at the time of the Spitzer observation is 62 mas (90% confidence level). The 1σ astrometric accuracy of the 3.6 μm and 4.5 μm mosaics is 027 and 028, respectively (Section 4.2). The faint IRAC 3.6 μm source closest to RX J0720.4–3125 seems to be a blended source and has a spatial separation of at least 13. From our previous VLT ISAAC H-band observations (Posselt et al. 2009), two individual NIR sources are known close to the position of the faint IRAC source(s). From the spatial separation and the NIR identification of the faint IRAC source(s), we conclude that the IRAC source is not the counterpart of the INS. Thus, RX J0720.4–3125 is undetected at 3.6 μm and 4.5 μm.

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To obtain an upper limit, we determine the background level and the standard deviation of 10 source-free apertures close to the source position. We use the residual mosaics (Section 4.2) for these measurements. We chose apex-qa task parameters, which result in a good removal of point sources in the immediate surrounding of the INS. The northern part of the faint blended source close to the INS is detected as individual point sources and removed in both IRAC channels. A small flux enhancement remains in both channels at the position of the southern ISAAC source and slightly increases the derived upper limits, which are computed by the measured source aperture flux above the background plus five times the standard deviation of the 10 source-free apertures (Section 4.2). The aperture-corrected 3.6 μm and the 4.5 μm upper flux limits at the position of RX J0720.4–3125 are $F^{3.6\, \mu \rm m}_{5\sigma }=4.9$ μJy and $F^{4.5\, \mu \rm m}_{5\sigma }=4.5$ μJy, respectively.

There is no obvious infrared source in the Herschel blue and red band at the position of RX J0720.4–3125 (see Figure 15). The closest possible source in the red band is at least 6'' from the INS position. Using apertures in different source-free regions and at the target position, we determine the 5σ upper flux limits for the INS to be $F^{\rm blue}_{5\sigma } = 5.2$ mJy and $F^{\rm red}_{5\sigma } = 9.4$ mJy.

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The spatial resolution and sensitivity of the two Spitzer IRAC images are superior to the first two channels of the WISE data, but the W3 and W4 band provide new wavelength coverage. Nothing is seen in W3 or W4 at the position of the INS. Because of the uncertainty in the W4 astrometry, only W3 is shown in Figure 16. The closest, very faint 12 μm source to the east of the INS has a spatial separation from the INS of ∼5''. Given the good astrometric compliance of major W3 sources with Spitzer IRAC sources, this faint source is unlikely to be the INS counterpart.

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There is no IR emission at the position of RX J1308.6+2127 in the Spitzer 4.5 μm IRAC image; see Figure 18. The aperture-corrected 5σ upper limit is $F^{4.5\, \mu \rm m}_{5\sigma }=1.6$ μJy.

In the Herschel PACS blue band, there is no significant emission around the position of RX J1308.6+2127; see Figure 17. Using apertures in different source-free regions and at the target position, we determine the 5σ upper flux limit for the INS as $F^{\rm blue}_{5\sigma } = 1.7$ mJy. In the Herschel PACS red band, there is no significant emission at the position of RX J1308.6+2127, but there is faint emission southwest and west of it (Figure 17). The spatial separation of this faint emission and the XTINS position is 10''. The positional uncertainty of the NS at the 90% confidence level in the Herschel observation is smaller than 07, accounting for the uncertainty of the Chandra position (Kaplan et al. 2002; Hambaryan et al. 2002) and the uncertainty of the proper motion (Motch et al. 2009). We checked for common sources in the Herschel observation, 2MASS point-source catalog, and Spitzer IRAC 4.5 μm data. Based on this comparison, we confirm that the absolute Herschel pointing accuracy is better than 15 for this observation, as expected from the works by the Herschel calibration and HIPE teams (see above). Thus, all the faint sources in the Herschel PACS red band can be excluded as INS counterparts. Using apertures in different source-free regions and at the target position, we determine the 5σ upper flux limit in the red band for the INS as $F^{\rm red}_{5\sigma } = 5.2$ mJy.

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We compared the WISE W1–W3 data to the Spitzer IRAC 4.5 μm data. There is no noticeable astrometric shift between Spitzer IRAC 4.5 μm and WISE W1 and W2. For WISE W3, there are only few clear common sources, and three of them are 2MASS point sources. There is no noticeable astrometric shift for these sources. Interestingly, there is faint emission in WISE W3 at a position consistent with the INS position within positional accuracy; see Figure 18. There is no source reported in the WISE All-Sky Source Catalog at this position, and no such emission is seen in any other WISE band, the Spitzer IRAC 4.5 μm, or the Herschel PACS bands. Due to its faintness, the W3 emission can be a noise feature. Confirmation by similar observations is necessary before any conclusions regarding the INS can be drawn. In principle, emission at such wavelengths is particularly interesting, because—if real—it could indicate potential silicate emission in the 8–12 μm region reminiscent of white dwarf debris disks (e.g., in the case of the spectacularly debris-polluted white dwarf GD 362, one-third of the debris disk emission is carried by a strong 10 μm silicate emission feature; Jura et al. 2007).

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There is very faint IR emission at the position of RX J1605.3+3249 in the Spitzer 4.5 μm IRAC image; see Figure 19. However, the INS position is located between two IR sources whose PRFs affect any measured flux at the INS position. We found that the faint 4.5 μm emission has a significance of only 1.3σ if we employ PRF subtraction of the two sources in the vicinity (2.9σ otherwise). Hence, there is no significant emission at 4.5 μm from the INS. The aperture-corrected 5σ upper limit is $F^{4.5\, \mu \rm m}_{5\sigma }=3.6$ μJy.

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There are several common sources in the Herschel bands and WISE bands W1–W3. There is no noticeable astrometric shift between these bands. There is no source in the Herschel blue and red bands at the position of RX J1605.3+3249 (see Figure 20). North of the INS, there is a faint source in the red band that is at least 56 separated from the expected INS position and is therefore unassociated with the INS. Using apertures in different source-free regions and at the target position, we determine the 5σ upper limits as $F^{\rm blue}_{5\sigma } = 6.1$ mJy and $F^{\rm red}_{5\sigma } = 12.2$ mJy. The WISE W1 and W3 images for the field around RX J1605.3+3249 are shown in Figure 21. While there is large-scale extended emission in W3, no point source is seen at the position of RX J1605.3+3249 in any of the WISE bands.

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The positions of RX J1856.5–3754 at the time of the Spitzer and Herschel observations were estimated from the position and proper motion values listed by Walter et al. (2010). The accuracy of the determined positions are better than 01. The astrometry of the Spitzer IRAC2 (4.5 μm) image of RX J1856.5–3754 is well aligned with the astrometry of previous H-band observations (Figure 22). There is no prominent emission centered at the expected INS position, but there is strong IR emission north of RX J1856.5–3754, starting at ≈1'' from the INS. From the NIR, we know this source consists of at least four individual sources that are, however, not discernible with Spitzer. We were not able to completely remove the IR emission of these northern sources by PRF fitting. Thus, our subsequently derived aperture-corrected 5σ upper limit for RX J1856.5–3754, $F^{4.5\, \mu \rm m}_{5\sigma }=11.6$ μJy is a very conservative estimate.

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Comparing Herschel PACS and WISE sources, we were not able to identify enough unique common sources to check the astrometry of the Herschel observations. Therefore, we assume the astrometric error to be the absolute pointing error of ≈24. This value was listed by the Herschel calibration team as the average value for a time window that includes our observations.²¹ In the Herschel blue band, there is very faint emission at ≈46 northeast from the INS position. In the Herschel red band, the INS position is located within a larger faint emission region that probably consists of several sources and extends to the northeast and north (see Figure 23). We cannot exclude that the INS contributes to the faint PACS 160 μm band emission. However, it appears likely that most of that emission actually comes from the same NIR sources that are also detected by Spitzer. We measured the flux at the INS position in an aperture with radius 5''. The aperture-corrected flux is F^red = 3.1 mJy, which corresponds to ≈3σ above the background. The nominal 5σ flux limit for the position of RX J1856.5–3754 in the red band is $F^{\rm red}_{5\sigma }=7.8$ mJy. In the blue band, we used apertures in different source-free regions and at the target position to determine the 5σ upper flux limit at the INS position as $F^{\rm blue}_{5\sigma } = 7.7$ mJy.

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Comparing sources in the WISE W1–W3 band images with H-band sources from a deep VLT observation (Posselt et al. 2009), there is no apparent astrometric shift between these bands (see Figure 24). The IR sources observed with W1 and W2 correspond to the ones seen with Spitzer IRAC 4.5 μm. Nothing is detected around the INS position in W3.

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The position of PSR J1848–1952 at MJD 48695 is known with a 2σ accuracy of 06 in right ascension, but 7'' in declination (Hobbs et al. 2004). The proper motion is unknown for this pulsar. PSR J1848–1952 was recently observed for 38 ks with XMM-Newton (ObsId: 0653300101, PI: Kaspi). Unfortunately, the pulsar was not detected (Olausen et al. 2013), and the closest X-ray source to the pulsar radio position has an angular separation of ≈165. Thus, the X-ray observations cannot be used to determine the current position of PSR J1848–1952 with higher accuracy. Hobbs et al. (2004) gave the following proper motion values: μ_αcos δ = 39(157) mas yr⁻¹ and μ_δ = −1200  (1900) mas yr⁻¹. While the error in declination is too large to be used for a reasonable upper limit on the expected pulsar proper motion, we use the error in right ascension to determine the maximal angular separation of the possible pulsar position in this direction at the time of the Herschel observation as 31 (2σ). The mean 2D speed of pulsars is ≈250 km s⁻¹, and PSR B2224+64 has the highest inferred 2D speed of ≈1600 km s⁻¹ (Hobbs et al. 2005). We assume this most extreme 2D speed to determine the maximal expected shift in declination for PSR J1848–1952. Its DM =18.23 cm⁻³ pc translates to a distance of 750 pc using the NE2001 model for the Galactic distribution of free electrons (Cordes & Lazio 2002). We estimate the upper limit of the proper motion of PSR J1848–1952 as 045 yr⁻¹. Thus, at the time of the Herschel observation, the maximal expected shift is 9''. We assume this value as the upper limit on the proper motion in the direction of declination.

The sky region around PSR J1848–1952 is densely populated with infrared sources. Comparing 2MASS, WISE, and our Herschel observation, it is difficult to pin down common sources. However, we found at least three common sources between these bands. From the comparison of their positions, the expected absolute pointing error of 11 for the Herschel observation seems to be a reasonable estimate. There is no source in the Herschel blue and red band at the position of RX J1848–1952 (see Figure 25). There is a faint southern source that is inside the box of proper motion upper limits. However, this source has a counterpart in other bands, in particular in 2MASS. Therefore, it is not the counterpart of the pulsar. Using apertures in different source-free regions and at the target position, we determine the 5σ upper flux limits at the INS position as $F^{\rm blue}_{5\sigma } = 3.6$ mJy and $F^{\rm red}_{5\sigma } = 5.9$ mJy.

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The WISE W1 and W3 images for the field around PSR J1848–1952 are shown in Figure 26. Except for the southern 2MASS source, there is no WISE point source detected in the region of PSR J1848–1952.

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