Observations of PSR J1357-6429 at 2.1 GHz with the Australia Telescope Compact Array
A. Kirichenko, Yu. Shibanov, P. Shternin, S. Johnston, M. A. Voronkov, A. Danilenko, D. Barsukov, D. Lai, D. Zyuzin
aa r X i v : . [ a s t r o - ph . S R ] N ov MNRAS , 1–9 (2015) Preprint 16 July 2018 Compiled using MNRAS L A TEX style file v3.0
Observations of PSR J1357 − A. Kirichenko, , ⋆ Yu. Shibanov, , P. Shternin, , S. Johnston, M. A. Voronkov, , , A. Danilenko, D. Barsukov, , D. Lai and D. Zyuzin Ioffe Institute, 26 Politekhnicheskaya st., St. Petersburg 194021, Russia Peter the Great St. Petersburg Polytechnic University, 29 Politekhnicheskaya st., St. Petersburg 195251, Russia CSIRO Astronomy and Space Science, Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia Astro Space Centre, Profsouznaya st. 84/32, 117997 Moscow, Russia School of Mathematics and Physics, University of Tasmania, GPO Box 252-37, Hobart, Tasmania 7000, Australia Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
PSR J1357 − γ -rays.It powers a compact pulsar wind nebula with a jet visible in X-rays and a large scaleplerion detected in X-ray and TeV ranges. Previous multiwavelength studies suggestedthat the pulsar has a significant proper motion of about 180 mas yr − implying anextremely high transverse velocity of about 2000 km s − . In order to verify that,we performed radio-interferometric observations of PSR J1357 − ± µ Jy and obtained the most accurate pulsarposition, RA = 13:57:02.525(14) and Dec = − µ <
106 mas yr − . The pulsar shows a highly polarised single pulse, as itwas earlier observed at 1.4 GHz. Spectral analysis revealed a shallow spectral index α ν = 0 . ± .
1. Based on our new radio position of the pulsar, we disclaim its opticalcounterpart candidate reported before.
Key words:
Pulsars: individual: PSR J1357 − Born in supernova explosions, neutron stars (NSs) typicallyobtain velocities orders of magnitude greater than those oftheir stellar progenitors. According to statistical analyses(see Hobbs et al. 2005), the mean three-dimensional veloc-ities of NSs mostly derived from radio data are about 400km s − . The largest firmly established pulsar transverse ve-locity of 1080 ±
100 km s − , which has been determined bydirect proper motion and parallax measurements with theVLBA, belongs to PSR B1508+55 (Chatterjee et al. 2005).Although an initial kick which occurs during supernovaexplosions is generally accepted as the reason for high ve-locities, the origin of the kick is currently unclear. Lai et al.(2001) discuss several classes of kick mechanisms, but it isnot clear whether any of them can fully explain the fastestmoving neutron stars (e.g., Chatterjee et al. 2005). There-fore, new detections of high-velocity pulsars are needed to ⋆ E-mail: [email protected]ffe.ru (AK) put additional constraints on models used in the latest su-pernova explosion simulations (see Wongwathanarat et al.2013). The velocity measurements might be also potentiallyuseful to reveal possible relationship between the velocityand other parameters of NSs (Lai et al. 2001).PSR J1357 − E =3.1 × ergs s − ) radio pulsar with a period of 166ms (Camilo et al. 2004). The pulse profile and polari-sation were studied with the Parkes telescope at 1.4GHz by Camilo et al. (2004); Johnston & Weisberg (2006);Lemoine-Goumard et al. (2011) and Rookyard et al. (2015).The pulsar field was observed in X-rays, where the pul-sar counterpart and a compact tail-like pulsar wind neb-ula (PWN), implying a noticeable pulsar proper motion,were found (Esposito et al. 2007; Zavlin 2007). Thoroughfollow-up high-energy studies have revealed X-ray and γ -raypulsations with the pulsar period (Lemoine-Goumard et al.2011; Chang et al. 2012). A pulsar plerion extended to a fewtens of arcminutes was detected in X-ray and TeV ranges c (cid:13) A. Kirichenko et al. by Abramowski et al. (2011). They also argued that the ex-tended radio emission from the supernova remnant (SNR)candidate G309.8 − − . ′′ ± . ′′
32) of the candidate position fromthe J1357 − ∼ DM = 128 . − byCamilo et al. (2004). Danilenko et al. (2012) performed anindependent distance analysis comparing the interstellarextinction–distance relation along the pulsar line of sightand the absorbing column density obtained from the X-rayspectral analysis. The resulting distance range of 2.0–2.5kpc supports the DM distance estimate. The distance rangeand the candidate offset imply the pulsar transverse veloc-ity to be between 1300 km s − and 2500 km s − , which ishigher than the largest NS velocity precisely measured sofar (Chatterjee et al. 2005). A similar velocity range was es-timated from the comparison of the pulsar X-ray and radio-interferometric positions (Mignani et al. 2011).Aiming to check whether the pulsar velocity is indeedthat high, we performed new radio-interferometric observa-tions with the ATCA to obtain a precise pulsar position foranother epoch. Another reason for the observations was toextend the radio studies of the pulsar itself, which was inves-tigated only at 1.4 GHz, to a higher frequency range. Thedetails of observations and data reduction are described inSect. 2. Our results and reanalysis of the archival data arepresented in Sect. 3 and summarised in Sect. 4. The observations of the pulsar field were carried out withthe ATCA on 2013 June 3. The observing session startedat UT 4:30 and lasted for 9.5 hours. The main goal of theobservations was to measure a precise position of the source.Therefore, the observations were performed with the 6C ar-ray configuration, which has the maximum baseline of nearly6 km. We used the pulsar binning capability of the Com-pact Array Broadband Backend (CABB), which allowed usto perform high time resolution observations (Wilson et al.2011). The binning mode split the 166 ms pulsar periodinto 32 independent rotational phase bins. The observationswere carried out in the 16 cm band centred at 2.102 GHz.The total bandwidth of 2.048 GHz was split into 512 spec-tral channels providing 4 MHz spectral resolution in the1.078–3.126 GHz range. PKS B1934 −
638 was observed atthe beginning of the session as a primary standard for theflux density scale and bandpass calibrations. To account forgain and phase instabilities, we observed two nearby sec-ondary calibrators 1329 −
665 and 1325 −
55 in a ten-minuteloop with the pulsar, where each calibrator was observed forabout two minutes. Two calibrators were used to estimate the systematic errors on the position reference frame. Stan-dard data reduction including Radio Frequency Interference(RFI) flagging and calibration was performed with
MIRIAD package (Sault et al. 1995), and
Karma (Gooch 1996) toolswere used for data visualisation.The data were split into four 512 MHz sub-bands withcentral frequencies of 1.334 GHz, 1.846 GHz, 2.358 GHz and2.870 GHz. The secondary calibration was then performedseparately for each bandwidth partition.The data were imaged using the MIRIAD invert taskwith the “robust” parameter set to zero. It provides a trade-off between better signal-to-noise ratio (
S/N ) and strongersidelobe suppression in the visibility weighting scheme. Thedeconvolution process was performed with the mfclean rou-tine, which accounts for spectral variations across the band-width. For the purposes of absolute astrometry, we used theresulting clean images without further calibration.Phase self-calibration was performed on the data to im-prove the image quality. After the first iteration of mfclean ,model components with flux densities > ∼ − wereused for the initial multi-frequency phase self-calibration,which considerably decreased residual phase errors. Thenthe weaker sources found on clean images were included inthe self-calibration model. As a result, after several clean-self-calibration cycles, the sidelobes of field sources becamecomparable with the thermal noise of ≈ µ Jy beam − forthe 1.334 GHz subband and ≈ µ Jy beam − for thethree other sub-bands.For the lower (1.334 GHz) and higher (2.870 GHz) fre-quency sub-bands, the synthesised beam size was 8 . ′′ × . ′′ . ′′ × . ′′
6, respectively, with the position angle
P A ≈− ◦ . The ATCA primary beam full width at half maxi-mum (FWHM) was 42 ′ for the lowest frequency, decreasingto 15 ′ for the highest frequency. The selected image size forall sub-bands was ∼ ′ × ′ .To confidently measure the pulsar proper motion, weperformed an independent analysis of the available archivalATCA data . The set was obtained on 2000 August 29 in the6A configuration with the baselines close to those of 6C butin 1.376 and 2.496 GHz bands with 128 MHz bandwidthseach split in 14 spectral channels (Camilo et al. 2004) . Thedata processing and imaging were similar to those appliedto our own set, except that no splitting was performed andthe gain calibration was done with the single observed cali-brator 1329 − . ′′ × . ′′ P A ≈ ◦ and 7 . ′′ × . ′′ P A ≈ ◦ for 1.376and 2.496 GHz, respectively. The imaging procedure for the1.376 GHz band revealed a point-like source surrounded byconcentric sidelobe-like rings which were difficult to cleanoff. The source is located close to the phase centre and thepulsar, and was not identified in the 2013 images. Thor-ough data inspection showed that it only appears in chan-nels 13 and 14 near the low frequency sideband and thus islikely spurious. Given its proximity to the pulsar, we usedonly channels 1–12 to eliminate the artifact and its side-lobes which could affect the pulsar position and flux mea-surements. http://atoa.atnf.csiro.au, project CX001. The 2.496 GHz data were not reported by Camilo et al. (2004).MNRAS , 1–9 (2015) bservations of PSR J1357 − D ec SNR candidate G309.8-2.6
MOST 843 MHz
PSR D ec ATCA 1.846 GHz
PSR
Figure 1. ′ × ′ field fragment centred at the PSR J1357 − left ) and the MOST ( right ) at 1.846GHz and 843 MHz, respectively. The positions of the pulsar and the extended emission from the SNR candidate G309.8 − In Fig. 1, we show the self-calibrated image of the pul-sar field in the 1.846 GHz sub-band. For comparison, wealso present the Molonglo Observatory Synthesis Telescope(MOST) image at 843 MHz with a restoring beam size of ≈ ′′ (Murphy et al. 2007). Many MOST point-like ob-jects have their firm counterparts in the ATCA image andvice versa. The pulsar is detected with the ATCA as a point-like source at a 10 σ significance in this sub-band and is alsovisible in the MOST image.Due to significantly higher spatial resolution of theATCA, several MOST sources are resolved as groups of sepa-rate objects. For instance, a bright extended object near thenorth edge of the MOST image is actually a blend of threecompact objects. At the same time, insufficient uv-coverageand the long baseline configuration make the interferom-eter insensitive to large extended structures. That is whythe extended emission from the SNR candidate G309.8 − − To constrain the pulsar proper motion, we used two astro-metric methods. The first one, which we hereafter refer to as“absolute astrometry”, allows to measure source coordinatesrelative to phase calibrators, whose positions are known witha high accuracy, for instance, from the VLBI measurements.The second approach, which we entitle “relative astrome- try”, is based on measurements of the target position shiftbetween observational epochs relative to other sources in thefield.In all cases, to measure the pulsar positions, we usedon-pulse data obtained from the calibrated visibilities. Usingthe
MIRIAD psrfix routine, the pulse-phase bins were phase-adjusted as a function of frequency channel accounting forthe known DM of 128.5 pc cm − and the pulsar period of166 ms. After that, a mean off-pulse baseline value was sub-tracted with the psrbl tool. This considerably decreased thepulsar contamination by backgrounds. We obtained eight positions of the pulsar in the 2013 im-ages, for each of the four spectral sub-bands in both sec-ondary calibrations. They were determined with the
MIRIAD task imfit using the object type “point”. The position un-certainty derived with this task slightly depends on the sizeof a region around the pulsar where the fit is performed.We used a region of about twice the synthesised beam sizein each sub-band. We checked that the resulting positionalerrors were comparable to the size of the beam, divided bytwice the (S/N). The S/N was ≈ −
665 and 1329 − − MNRAS , 1–9 (2015)
A. Kirichenko et al. − , respectively.The best-fit positions and the positional error ellipses areshown in Fig. 2 with crosses and inner thin solid and dashedellipses for 1325 −
65 and 1329 −
55 calibrations, respectively.The positional error ellipse projected on the 1 σ coordinateuncertainty represents only 40 per cent 2D confidence region(e.g., Press et al. 2002). For completeness, we also show 90per cent confidence ellipses, which are by a factor ≈ . ≈ . ′′
12 sys-tematic offset in Dec. We checked that it is consistent withthe shift obtained after cross-calibrating the 1325 −
665 and1329 −
55 standards and measuring their positions. Accord-ing to Fig. 2, the estimated systematic error along the syn-thesized beam major principle axis is comparable with theformal statistical 1 σ uncertainty. Therefore, the two sourcepositions were weighted by the respective covariance matri-ces, in order to account for correlations between the errorsin RA and Dec, and combined. The resulting mean positionwith 40 per cent and 90 per cent uncertainties are shownin Fig. 2 with the bold cross and ellipses. The uncertaintieswere obtained by adding the estimated systematic covari-ance matrix to the weighted mean statistical covariance ma-trix. The final coordinates are RA = 13:57:02.525(14) andDec = − σ errors correspond to theinner bold ellipse in Fig. 2.The derived position appears to be different fromRA = 13:57:02.43(2) and Dec = − ≈
13. At2.496 GHz, the pulsar is found at a significantly lower S/N,making the position measurements less accurate. The de-rived 1.376 GHz coordinates are RA = 13:57:02.546(76) andDec = − . They are consistent with the onesstated by Camilo et al. (2004). However, the published un-certainties appeared to be considerably smaller than the es-timate based on the synthesised beam size and the pulsarS/N. We thereby conclude that the published pulsar positionerrors were severely underestimated.In Fig. 3, we show the pulsar full-band on-pulse im-ages obtained for two epochs using the same calibrator(1329 − ≈ . ′′ µ < ∼
100 mas yr − . . . . - : : . . . RA D ec Figure 2.
Pulsar position uncertainty ellipses measured at 40and 90 per cent confidence levels in 2.1 GHz band. Thin solid anddashed line crosses and ellipses correspond to the calibrations ob-tained with 1329 −
665 and 1325 −
55 standards, respectively. Thebold cross and solid bold line ellipses are the derived weightedmean positions.
Relative astrometry is generally considered as a more robusttool which allows to account for systematic effects which can-not be excluded in advance. For instance, comparing 2000and 2013 positions of various sources in the field, we foundthat they exhibit systematic shifts between the epochs, di-rected roughly radially from the phase centre and increasingwith the offset from it. This stretch could result from band-width smearing which was slightly different for pre-CABBand CABB data. There also can be a small rotation be-tween epochs caused by different ephemeris codes used forpre-CABB and CABB correlators.To increase the image dynamic range and reduce thepositional errors, we used the self-calibrated images for eachof the 2013 sub-bands, as well as for the 2000 epoch. Thepulsar S/N was slightly increased as compared to the non-self-calibrated case and was ≈
18, 9.9, 11.8 and 8.1 for the1.334, 1.846, 2.358 and 2.780 GHz sub-bands, respectively,while in the 2000 image the S/N remained the same. Self-calibration, however, introduced some shift due to an in-complete sky model. The five images were aligned usinga custom-built routine which accounts for shifts, rotationsand stretches. For referencing, we used nine relatively brightpoint-like sources detected in all images with the signal-to-noise ratio > ∼
30. They are shown in Fig. 1 and their posi-tions were determined using imfit routine with an accuracy < ∼ . ′′
07. We found the stretch by a factor of 1.0021(3) anda small rotation by 1.2(6) arcmin for the 2000 image with Herein, the numbers in brackets are 1 σ uncertainties referringto the last significant digits quoted, the equinox is J2000.0. The systematics cannot be accounted here since only one sec-ondary calibrator was observed. MNRAS , 1–9 (2015) bservations of PSR J1357 − . . - : : . . D ec . . - : : . . RA D ec Figure 3. ′′ × ′′ ATCA image fragments with PSR J1357 − top ) and at 1.376 GHz in 2000 ( bottom ) epochsusing the same calibrator and with pixel scales of 0 . ′′
25 and 0 . ′′ respect to the 2013 images. Neither significant stretch norrotation between different sub-bands of 2013 observationswere found. After the transformation, positions of the ref-erence sources in all images became consistent within theuncertainties. The pulsar proper motion was included in theroutine and was fitted simultaneously with the reference so-lution.In Fig. 4, the mean of the pulsar positions in the aligned2013 sub-bands is compared with the 2000 position. We findthat the arrangement of the pulsar error ellipses on epochs2000 and 2013 slightly differs from that provided by theabsolute astrometry (cf., Fig. 3), while again no significantshift between the epochs is seen. The 40, 90 and 99.73 percent confidence regions on the pulsar proper motion µ α cos δ and µ δ are shown in Fig. 5. The 90 per cent upper limit onthe pulsar proper motion, which is the radius of the circularregion containing 90 per cent probability, is µ <
106 masyr − . This value is compatible, but slightly higher than theresult obtained from the absolute astrometry. The reasonfor this is that the positional errors of the 2000 data arein fact underestimated in the absolute astrometry method − − − − ∆ D ec [ a r c s ec ] Figure 4.
40 and 90 per cent pulsar position uncertainty ellipsesafter relative astrometry. The 2013 and 2000 positions are shownby solid and dashed ellipses, respectively. The positions are shownrelative to the mean pulsar position at the 2013 epoch. The offsetsdiffer from those presented in Fig. 3 for the absolute astrometry. − − − µ α cos δ [mas yr − ] − − − µ δ [ m a s y r − ] Figure 5.
40, 90 and 99.73 per cent confidence regions of thepulsar proper motion based on the relative astrometry. cos δ ≈ .
43, where δ is the declination of the phase centre for the 2013epoch data. since the systematic errors are not accessible. Therefore, webelieve that the relative astrometry results are more reliable. To measure the pulsar flux, we used self-calibrated on-pulsevisibilities. To study the spectrum in detail, we additionallysplit each 512 MHz sub-band in half. In order to exclude pos-sible errors introduced by the non-linear cleaning algorithms,we measured the flux directly from the visibility data usingthe MIRIAD uvfit routine. The pulsar position, however,was fixed at the values obtained with the imfit on the cor-responding clean images. The measured fluxes are shown inFig. 6 by solid error-bar crosses. The mean flux over the full2013 band is 212 ± µ Jy. The spectral energy distribution
MNRAS , 1–9 (2015)
A. Kirichenko et al. shows a noticeable flux depression at ≈ . α ν = 0 . ± . χ ≈ . ≈ σ . The inclusion of this point makes the fit unacceptable(reduced χ ≈ . − − are observed (e.g., Minter 2005, and referencestherein). Such features cannot lead to the observed flux de-pression in our case. In addition, we inspected backgroundobjects and found a similar feature at 1.7 GHz in spectra ofthe sources located within ≈ . ′ .The pulsar fluxes on the 2000 data were measured usingthe full-band self-calibrated 1.376 GHz and 2.496 GHz visi-bilities. The respective fluxes of 417 ± µ Jy and 309 ± µ Jyare shown in Fig. 6 by dashed error-bar crosses. Given thelarge uncertainties of the 2000 observations, it is difficultto make any conclusion about the spectral index. However,the 2000 flux values appear to be larger than those of the2013 data, at least for the lower frequency. The pulsar fluxat 1.376 GHz in the 2000 data differs from that in 2013 byabout 2.5 σ including 2 per cent flux calibration uncertain-ties . The difference significance is thus about 99 per cent.It is possible that the flux variability can be at-tributed to the long-term refractive scintillation (e.g.,Lorimer & Kramer 2012). Using the galactic electron den-sity model NE2001 of Cordes & Lazio (2002) we estimatedthe field coherence scale s ≈ l F ≈ . × km and the refractive scale l R = l /s ≈ . × km at 1.376 GHz for the pulsar line of sight. Giventhat l F ≪ l R , the intensity modulation index due to the re-fractive scintillation can be estimated as m R = ( s /l R ) / ≈ .
15 (Lorimer & Kramer 2012). This value is consistent withthe observed 1.376 GHz flux modulation between the twoepochs ( F − F ) / ( F + F ) = 0 . ± .
08. Forthe Kolmogorov turbulence spectrum, the modulation indexscales with the frequency as m R ∝ ν . and at 2.496 GHzis larger by a factor of 1.4 than at 1.376 GHz. This is notexcluded by the data. The timescale of the flux variabilitydue to the refractive scintillation ∆ t R = l R /v tr is inverselyproportional to the pulsar transverse velocity v tr . Using thederived upper limit on the pulsar proper motion we esti-mated the lower limit ∆ t R & We studied the pulse and polarisation profiles of the 2013epoch in the same eight 256 MHz sub-bands. The phase-resolved I , Q , U and V Stokes parameters were extracted According to the operation team, the flux depression can becaused by a correlator issue in the pulsar binning mode. . . . . . . ν [GHz]0 . . . . . . . . . F ν [ m J y ] α ν = . ± . ATCA2013MeanfluxATCA2013ATCA2000
Figure 6.
ATCA spectrum of PSR J1357 − σ uncertainties in sub-bands shown by horizontal solid bars with 256 MHz widths regu-larly spaced within the whole 1.1–3.1 GHz band. The line rep-resents the best fit of the measured fluxes by the power law F ν ∝ ν − α ν with a spectral index α ν shown in the plot. Meanflux densities in the whole 2.102 GHz band measured without di-vision by sub-bands and in 1.376 and 2.496 GHz bands of 2000are shown by dot-dashed and dashed error-bars for comparison.The systematic flux calibration uncertainties of < ∼ using the MIRIAD psrplt routine. The pulsar emission isobservable in five adjacent phase bins. We found no sig-nificant profile width and polarisation changes across thewhole 2.102 GHz band. As an example, the resulting pulseprofiles for the Stokes I , the circular polarisation V andthe linearly polarised component L = ( Q + U ) / in the2.358 GHz sub-band are shown in the lower right panel ofFig. 7. The intensity profile shows a relatively wide sin-gle component. The pulse FWHM of 32 ◦ ± ◦ obtainedusing a Gaussian profile fit, virtually 100 per cent of thelinear polarisation and small amount of circular polarisa-tion are fully consistent with the higher time and spec-tral resolution 1.4 GHz data obtained with the Parkes tele-scope (Johnston & Weisberg 2006; Rookyard et al. 2015).For completeness, in the lower-left panel in Fig. 7 we showthe same profiles for the 1.376 GHz band of the 2000 dataset. These data demonstrate somewhat wider intensity pro-file with FWHM ≈ ◦ ± ◦ . The broader pulse profile ob-served in the 2000 data can partially result from the DMsmearing of ≈ ◦ due to a twice as low spectral resolutionwith the channel width of ≈ ≈ ◦ ,and it does not affect the pulse profiles at higher frequencies.Accounting for the DM smearing and the profile fit uncer-tainties, the 2000 and 2013 intrinsic pulse widths appear tobe consistent.The large bandwidth of the 2013 data allowed us toinfer the rotation measure (RM) along the pulsar line ofsight utilising the λ dependence of the linear polarisationposition angle ψ . The latter values and their errors were de-termined from the Stokes parameters Q and U measured inthe five on-pulse phase bins with the uvfit routine (as de-scribed in Sec. 3.3) for each of the eight spectral sub-bands. MNRAS , 1–9 (2015) bservations of PSR J1357 − . . . − . . . . . . . . F ν [ m J y ] ATCA 20001 .
376 GHz
ILV . . . .
358 GHz
ILV ψ [ d e g ] Figure 7.
Pulse and polarisation profiles ( bottom ), and linear polarisation angle ψ ( top ) for PSR J1357 − left ) and 2.358 GHz ( right ). One full period is shown. Solid, dashed and dot-dashed lines show the total intensity I ,linearly polarised component L = ( Q + U ) / and circular polarisation V , respectively. ψ is corrected for RM and shown for on-pulsephases. Phase of 0.5 is placed at the flux density peak. The linear fit to the observed ψ ( λ ) dependence was per-formed in each phase bin in order to check for the possibleRM variation with phase (Noutsos et al. 2009). The result-ing RM values were found to be consistent within uncer-tainties, therefore the global fit for ψ ( λ ) dependence wasperformed with RM value tied between all five bins. Theinitial regression was not good, with χ = 1 .
79 for 34 de-grees of freedom, indicating that either position angle errorswere underestimated or there exists a non-trivial spectral be-haviour of the position angle. Indeed, the data for two lowestfrequency bands in our set likely show a shallower swing of ψ than in the other six sub-bands. Since the reason for suchbehaviour is unclear, we conservatively increased the errorsof the measured ψ values to make χ of the global fit equalone. The resulting RM of − ± − is smaller, butconsistent with − ± − estimated from the ParkesTelescope 1.4 GHz data obtained with a narrow bandwidth(Johnston & Weisberg 2006). We note also, that the RM fitfor the six upper frequencies is successful without any errorrenormalisation, however giving smaller RM of − ± − . Therefore, we can not exclude the spectral variations ofthe RM, as observed for some pulsars (Dai et al. 2015). Theillustration of the ψ ( λ ) dependence for the central phasebin is shown in Fig. 8. The solid line with grey-hatched re-gion in Fig. 8 show the best-fit linear regression with 68 percent uncertainty region.The phase-dependence of the position angle in the fiveon-pulse bins, corrected for the rotation measure, is shownin the top-right panel in Fig. 7. This dependence is clearlylinear with the slope C = 0 . ± .
03. As expected, theresults for 1.376 GHz data of 2000 observations are con-sistent with the 2013 measurements (Fig. 7, top-left panel).They are also consistent with the higher time resolution dataobtained with the Parkes telescope (Rookyard et al. 2015).The ψ -phase dependence demonstrates almost no curvature. λ [cm ] − − − − ψ [ d e g ] Figure 8.
Polarization angle ψ against the square of the ob-serving wavelength λ . The grey-hatched region shows 68 per centlinear fit uncertainty. Therefore, virtually any pulsar emission geometry can befitted to the data, according to the classical rotation vectormodel (RVM; Radhakrishnan & Cooke 1969). Using a moredetailed ψ curve, Rookyard et al. (2015) obtained loose con-straints on the angle between the magnetic and the rotationaxes α . However, the authors favoured the almost alignedrotator with α ≈ ◦ .While RVM does not provide robust constrains on thepulsar emission geometry from our data, it is neverthelesspossible to invoke additional arguments basing on the ob-served pulse profile width and the statistical data on otherpulsars. Gil et al. (1984) showed that the half-opening angleof the pulsar beam ρ q (at a certain relative intensity level q ) MNRAS , 1–9 (2015)
A. Kirichenko et al. can be related to the pulse width W q at the same level viathe expressioncos ρ q = cos α cos( α + β ) + sin α sin( α + β ) cos( W q / , (1)where β is the angle of the closest impact of the line of sightto the magnetic axis. In addition, the slope of the positionalangle curve at the inflection point is related to the angles α and β via the relationsin α = C sin β (2)(Komesaroff 1970). Utilising these equations and the valuefor the pulse FWHM of W = 32 ◦ , we can find the an-gles α , β and ρ for any line of sight position ζ = α + β .The resulting solution varies in the broad range, howeverthe ratio | β | /ρ , i.e. the value of the impact parameterin units of the emission cone radius, is tied in the narrowrange of 0 . ζ . Similar solutions with W = 70 ◦ give | β | /ρ ∈ (0 . , ρ from the statisti-cal data on other pulsars. The diagram of the pulse widths vs period has a clear low boundary which, in case of thecore component, is thought to represent the value of ρ fororthogonal rotators ( α ≈ π/
2) with low impact parameters( β ≈
0) (Rankin 1990; Maciesiak & Gil 2011). In this case,the main source of the difference of the observed width fromthe minimal value is described by W obs = W min sin α (3)(Rankin 1990; Maciesiak & Gil 2011). Using the low bound-ary from Maciesiak & Gil (2011), we can estimate the incli-nation angle α to be about 10 ◦ on the basis of the W mea-surements alone. Note, that according to Maciesiak & Gil(2011), this method can overestimate α in the close-to-aligned cases (low α ). However, it is more likely that thesingle pulse of PSR J1357 − β issmall. It is not likely in the case of PSR J1357 − α and narrowing with β are not known in advance, we em-ployed the method suggested by Malov & Nikitina (2011).The authors recommend to use the mean value of the ob-served pulse widths W in the sample of pulsars with similarperiods as the conservative estimate for twice the value of ρ . The expression (9) from Malov & Nikitina (2011) yields ρ ≈ ◦ for the PSR J1357 − α ≈ ◦ , in accordance with thesimple estimate from Eq. (3) and the favoured solution ofRookyard et al. (2015). The new ATCA observations of the PSR J1357 − ◦ over the whole 1.078–3.126 GHz frequency range. The ra-diation has a high, almost 100 per cent, linear polarisation,which is typical for young pulsars with ˙ E > ∼ erg s − (Weltevrede & Johnston 2008). We do not detect spectralvariation of the linear polarisation degree. The pulse profileshape and polarisation properties are in agreement with theParkes telescope 1.4 GHz observations (Camilo et al. 2004;Johnston & Weisberg 2006; Lemoine-Goumard et al. 2011;Rookyard et al. 2015) and the ATCA 1.376 GHz observa-tions in 2000. An apparent increase of the observed pulsewidth in the 2000 data set is mainly due to the DM smearingcaused by the worse spectral resolution. The pulsar spectralenergy distribution extracted from the 2013 data demon-strates a shallow spectral index of about 0.5. The ATCA2000 flux values appear to be larger than those of the 2013data, at least for the lower frequency. This variability canresult from the effects of the refractive interstellar scintilla-tion on the timescales significantly larger than the durationof our observations. Detailed monitoring campaign is neces-sary to check this (e.g., Bhat et al. 1999).The rotation measure estimate of − ± − iscompatible within 2 σ with the previous narrow band mea-surements but appears to be more reliable since it is obtainedusing a wider frequency range. Based on the derived RM, weestimated the mean Galactic magnetic field along the pulsarline of sight ¯ B = 1 . × − RM/DM = − . ± . µ G.This is close to the values for most of other pulsars fromthe ATNF catalogue located within a 2 ◦ circle around thepulsar position.On the basis of the absolute and relative astrometrymethods, we did not detect the proper motion of the pul-sar. We estimated a 90 per cent upper limit on it of about100 mas yr − which corresponds to the pulsar transversevelocity v tr < ∼ − if the DM distance of 2.5 kpc isadopted. This does not contradict the value of ∼
650 km s − suggested by Abramowski et al. (2011) based on the offsetof the pulsar from the centre of the extended source HESSJ1356 − < ∼ . ′′ I -band imageadapted from Danilenko et al. (2012) and shown in Fig. 9.The pulsar X-ray positions obtained with Chandra are also , 1–9 (2015) bservations of PSR J1357 − . . . . - : : . . RA D ec VLT I-band Optical candidateChandra/ACIS 2009Chandra/HRC 2005 ATCA 2013
Figure 9.
Fragment of the pulsar field imaged with VLT/FORS2in I -band (Danilenko et al. 2012). The pulsar optical counterpartcandidate position is shown by the cross. Chandra and ATCApulsar positions are shown by 1 σ error ellipses. These ellipsesalso account for the optical astrometric referencing uncertaintyof 0 . ′′ presented. Given a higher accuracy of the ATCA pulsar posi-tion as compared with the X-ray positions, we conclude thatthe optical candidate can be discarded as the pulsar coun-terpart at a 99 per cent significance. A relatively bright staris located in ∼ ′′ southwards the new radio position of thepulsar, and further searching for its faint optical counterpartis only possible with a high spatial resolution imaging pro-vided either by the HST or ground-based optical telescopeswith adaptive optics systems. ACKNOWLEDGEMENTS
We are grateful to the referee Adam Deller for his com-ments which prompted us to reconsider certain parts ofthe manuscript. Authors thank E. B. Nikitina, I. F. Malov,F. Camilo, Serge Balashev and D. E. Alvarez-Castillo foruseful discussions. The work was supported by the Rus-sian Science Foundation, grant 14-12-00316. The AustraliaTelescope Compact Array is part of the Australia TelescopeNational Facility which is funded by the Commonwealth ofAustralia for operation as a National Facility managed byCSIRO.
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