Revisiting the birth locations of pulsars B1929+10, B2020+28,and B2021+51
Franz Kirsten, Wouter Vlemmings, Robert M. Campbell, Michael Kramer, Shami Chatterjee
aa r X i v : . [ a s t r o - ph . S R ] M a r Astronomy & Astrophysics manuscript no. ev18-v8-arxiv c (cid:13)
ESO 20187th April 2018
Revisiting the birth locations of pulsars B1929+10,B2020+28, and B2021+51
Franz Kirsten , , , ⋆ , Wouter Vlemmings , Robert M. Campbell , Michael Kramer , and Shami Chatterjee International Centre for Radio Astronomy Research (ICRAR), Curtin University, GPO Box U1987, Perth, WA 6845,Australia Max Planck Institut für Radioastronomie (MPIfR), Auf dem Hügel 69, D-53121 Bonn, Germany Argelander Institut für Astronomie (AIfA), Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory, SE-439 92Onsala, Sweden Joint Institute for VLBI in Europe, Oude Hoogeveensedijk 4, 7991 PD, Dwingeloo, The Netherlands Department of Astronomy, Cornell University, Ithaca, NY 14853, USA7th April 2018
ABSTRACT
We present new proper motion and parallax measurements obtained with the European VLBI Network (EVN) at 5 GHzfor the three isolated pulsars B1929+10, B2020+28, and B2021+51. For B1929+10 we combined our data with earlierVLBI measurements and confirm the robustness of the astrometric parameters of this pulsar. For pulsars B2020+28and B2021+51 our observations indicate that both stars are almost a factor of two closer to the solar system thanpreviously thought, placing them at a distance of . +0 . − . and . +0 . − . kpc. Using our new astrometry, we simulatedthe orbits of all three pulsars in the Galactic potential with the aim to confirm or reject previously proposed birthlocations. Our observations ultimately rule out a claimed binary origin of B1929+10 and the runaway star ζ Ophiuchiin Upper Scorpius. A putative common binary origin of B2020+28 and B2021+51 in the Cygnus Superbubble is alsovery unlikely.
Key words. pulsars: individual: B1929+10, pulsars: individual: B2020+28,pulsars: individual: B2021+51, proper mo-tions, parallaxes, techniques: interferometric
1. Introduction
Typical transverse velocities of isolated pulsars are of theorder of several hundred km s − (Cordes & Chernoff 1998;Arzoumanian et al. 2002; Hobbs et al. 2005), while thoseof their progenitor O- and B-stars are at most several tensof km s − . In the standard neutron star formation scenariothis discrepancy is explained by an asymmetry in the super-nova (SN) explosion that imparts a kick to the forming cen-tral compact object, accelerating it to the observed veloci-ties (e.g. Scheck et al. 2006). As a result of the short lifetimeof SN remnants ( < yr) and the typical characteristicage of young pulsars ( τ c ∼ − Myr), direct associationsbetween SN-remnants and pulsars are rare. Measurementsof accurate proper motions µ and parallaxes π of pulsarscan, however, indicate the birth locations of pulsars. Thecombination of both µ and the distance d = 1 /π yields thephysical transverse velocity, V ⊥ , which, given an estimateof the radial velocity, V r , allows calculating a trajectorythat traces the pulsar back to its possible birth location.Hence, kinematic ages – as opposed to characteristic ages τ c = P/ P – of pulsars can be determined and conclusionsabout neutron star formation scenarios can be drawn. ⋆ [email protected], Member of the InternationalMax Planck Research School (IMPRS) for Astronomy and As-trophysics at the Universities of Bonn and Cologne One of the first to calculate pulsar orbits was Wright(1979), claiming that the pulsars B1929+10 (J1932+1059)and B1952+29 originate from a former binary system. Morerecently, Hoogerwerf et al. (2001) used the 3D space veloc-ity of high-velocity runaway stars and parallax and propermotion measurements of young nearby pulsars to extrapo-late their trajectories back in time. Their simulations indi-cated that the runaway O-star ζ Ophiuchi ( ζ Oph, HIP81377) and the young pulsar B1929+10 were likely tohave been in a binary system in Upper Scorpius (Scorpius-Centaurus association) until about 1 Myr ago. Accordingto their analysis, the system was disrupted when the pro-genitor star underwent a supernova explosion. During thatevent, the space velocity vectors of both ζ Oph and the pul-sar were modified to point away from Upper Scorpius. Theparameter range for which such a scenario is possible is,however, rather small. Improved measurements of µ and π for B1929+10 obtained with the NRAO Very Long BaselineArray (VLBA) led to the conclusion that a common originof the pulsar and ζ Oph is unlikely (Chatterjee et al. 2004).Adopting the measurements of Chatterjee et al. (2004), butincreasing the reported uncertainties by factors between10 and 30, Bobylev (2008) and also Tetzlaff et al. (2010)repeated the simulations of Hoogerwerf et al. (2001), re-postulating a binary origin of B1929+10 and ζ Oph in Up-per Scorpius.
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Table 1: Observing epochs and arrays.Date(s) UT range Array a Notes. ( a ) Ef = Effelsberg, DE, m; Wb = Westerbork Synthesis Radio Telescope, NL, − × m; Jb = Jodrell BankLovell Telescope, UK, m; Jv = Jodrell Bank Mark2 Telescope, UK, m; On = Onsala, SE, m; Mc = Medicina, IT, m;Tr = Torun, PL, m; Ys = Yebes, ES, m; Sv = Svetloe, RU, m; Zc = Zelenchukskaya, RU, m; Bd = Badary, RU, m;Ur = Urumqi, CN, m; Sh = Shanghai, CN, m. Table 2: Calibrator details for each pulsar.Pointing centre Distance to Flux density b Source RA Dec pulsar [deg] [mJy beam − ]B1929+10 19:32:14.0160 10:59:32.868 50J1928+0848 a a a Notes. ( a ) These are the calibrators referred to as primary calibrators in the text. ( b ) For the pulsars this is the apparent pulsarflux density measured by employing pulse gating.
In a similar investigation, Vlemmings et al. (2004) iden-tified the two pulsars B2020+28 and B2021+51 as candi-dates for a common-origin scenario based on proper mo-tion and parallax measurements obtained with the VLBAat 1.4 GHz (Brisken et al. 2002). The authors simulated thetrajectories of the two pulsars back in time and concludedthat they most likely originated from a binary system in theCygnus Superbubble that was disrupted when the youngerof the two pulsars was born in a supernova. The measure-ments by Brisken et al. (2002) are, however, based on fiveobservations covering a time span of only roughly one year.Here, we present new measurements of µ and π forthe three pulsars B1929+10, B2020+28, and B2021+51 ob-tained with the European VLBI Network (EVN) at an ob-serving frequency of 5 GHz. These observations extend thetime baseline to more than ten years, allowing for an ex-tremely high precision in measurements of µ and π for allthree pulsars. We used these data and ran new simulationsof trajectories to shed new light on the proposed binaryorigin of B1929+10/ ζ Oph and B2020+28/B2021+51.
2. Observations and data reduction
The observations described here were conducted with theEVN under project code EV018(A-D). All observationsused a frequency range . − . MHz with dualcircular polarizations and two-bit sampling, for a totalbit-rate of 1 Gbps per station. The 128 MHz frequencyrange in each polarization was split into eight 16 MHzbaseband channels. We conducted four epochs of observa-tions between May 2010 and June 2011, as summarizedin Table 1. This table also lists the EVN stations that successfully participated in the array at each epoch.We observed each of the three pulsars in all four 12-hour epochs, using phase-referencing. Table 2 summarizesthe pulsars and characteristics of their phase-reference cali-brator sources. Our phase-referencing tactics included (i) abasic four-minute cycle alternating between the target pul-sar (2.5 min) and the primary calibrator (1.5 min), and (ii)insertion of an additional 1.5 minute scan of the secondarycalibrator in every second cycle. For bandpass calibration,we observed the quasars J1800+3848 and 3C454.3: theformer about two hours from the beginning and the latterfour hours from the end of each epoch. This observingpattern provides about two hours of integration on eachpulsar per epoch, yielding a nominally expected sensi-tivity of the arrays ranging from 10.9 to 14.8 µ Jy per beam.The data from the telescopes were correlated on theEVN software correlator at the Joint Institute for VLBIin Europe (SFXC; Keimpema et al. 2015). Each of the 16MHz baseband channels was correlated with 32 frequencypoints and one-second coherent integrations. Pulsar scanswere correlated using the gating/binning capability ofSFXC. Because these were the first observations to employthis mode, we devote a few sentences to describe it.Given an ephemeris of a pulsar, SFXC can apply a gate,defined by a start and stop fraction of a period, such thatcorrelation accumulates only during the in-gate interval.Before gating, the pulsar data are de-dispersed. Here, weused incoherent de-dispersion (a constant correction per . ∼ MHz frequency point). Coherent de-dispersion hassubsequently been developed on SFXC. The gate itself
Article number, page 2 of 11ranz Kirsten et al.: Birth sites of three young pulsars A s t r o m e t r i c e rr o r [ m a s ] Fig. 1: Astrometric accuracy as a function of angular sepa-ration between phase calibrator source and target. This is areproduction of Fig. 3 in Chatterjee et al. (2004) (referredto as C04 here) to which we added data from our obser-vations (open and filled stars). Open symbols denote themedian scatter about the average position of the primaryphase calibrator obtained from calibrating its visibilitieswith solutions from the secondary calibrator. Filled symbolsshow the median scatter of the observed positions about thebest-fit model for proper motion and parallax. The 1.6 GHzdata (squares) are taken from Chatterjee et al. (2001) andVlemmings et al. (2003), while the previous 5 GHz data(circles) are taken from Chatterjee et al. (2004). The solidline is a weighted least-squares power-law fit to all 5 GHzdata points. The almost linear relationship between astro-metric error and calibrator throw seems to break down be-yond an angular separation of more than about four de-grees.may be divided further into a number of equal-width bins,each of which produces independent correlator output. Inthis case, there was only one bin. In this way, assumingthe entire pulse falls within the gate, the signal-to-noiseratio (S/N) of the pulsar detections can be increased bya factor of about p P/w , where P is the pulse periodand w is the width of the gate. The pulsar ephemerideswere derived with TEMPO2 (Hobbs et al. 2006). Beforefull correlation, we conducted iterations of gate-fitting,using a full-period gate with 40 bins, to confirm that thepulse profile was stationary over the time-range of a pulsarobservation within an epoch and to optimize the choice ofthe gate start/stop parameters. For these three pulsars,the gate widths used were typically in the range of − of a pulse period, leading to gating gain factors of ∼ − .We performed a mostly automated data reductionand calibration procedure relying on the NRAO Astronom- ical Image Processing System (AIPS) and the scriptinglanguage ParselTongue (Kettenis et al. 2006). Removalof data affected by radio frequency interference (RFI)was made running the RFI-mitigation software SERPent(Peck & Fenech 2013) and some further manual flagging.We first applied the system temperature and gain curvecorrections as determined by the EVN pipeline and alsocorrected for the parallactic angle using the AIPS taskCLCOR. Next we computed ionospheric corrections inTECOR with the help of total electron content mapsas published by the Center for Orbit Determination inEurope . In a first calibration run, we solved for visibilityrates, phases, and delays in FRING for all calibratorsources assuming a simple point source model. Next, weself-calibrated on each source, improving the S/N by a fac-tor of five to ten. For each calibrator we then concatenatedthe calibrated data from all four epochs. This dataset wasimaged to produce a global model of each calibrator source.The dominant CLEAN components of each source modelwere then used as the input model parameters in a secondFRING-run. In this way, we eliminated any systematicscaused by source structure that affected the position of thecalibrator sources in between epochs. For each of the threepulsars the calibration solutions of the primary calibratorwere of much higher quality than those of the secondarycalibrator and, hence, were applied to the respective targetpulsar (Table 2).We used the calibration solutions from the secondarycalibrator to provide independent checks on the achievedastrometric accuracy as a function of angular separationbetween target and calibrator source (‘calibrator throw’),as done by Chatterjee et al. (2004). Similarly to the ear-lier data, our observations imply an almost linear increasein astrometric accuracy with decreasing calibrator throw(Fig. 1). We fitted a power law, y = a · x b , to all datapoints obtained from 5 GHz observations, which yielded ( a, b ) = (0 . ± . , . ± . . This relation, however,seems to only hold for angular separations of up to fourdegrees between calibrator and target.
3. Estimates for astrometric parameters ofB1929+10, B2020+28, and B2021+51
We measured the position of the pulsars in each epochby fitting a 2D Gaussian to the brightness distributionin the image plane (Fig. 2) using the AIPS task IMFIT.As a result of the high S/N ( ∼ ) and small beamsize ( θ ∼ × mas), the formal errors are very small( θ/ (2 ∗ S/N ) ∼ × µ as), certainly underestimating thereal positional uncertainties. In addition to these randomerrors, residual systematic errors caused by the calibratorthrow (Fig. 1), for instance, need to be taken into account.A good estimate for these systematic errors is the decon-volved size θ d of the pulsar, which is zero for a true pointsource. Following the scheme reported in Chatterjee et al.(2001), we estimated the systematic uncertainties usingthe quantity θ d / p ( N ant − ∗ t obs /t iono , where N ant = 11 is the typical number of antennas involved, t obs = 110 minis the total amount of time spent on each pulsar, and t iono = 6 min is the empirically determined atmospheric ftp://ftp.unibe.ch/aiub/CODE/Article number, page 3 of 11 &A proofs: manuscript no. ev18-v8-arxiv Fig. 2: Greyscale plots of the fitted pulsar images. Rows from top to bottom show B1929+10, B2020+28, and B2021+51.Columns from left to right correspond to epochs one to four. Overlaid contours increase in steps of 20 percent of thepeak flux density, where negative values are indicated by dashed contours. The absolute flux density scale (mJy beam − )is indicated above each individual panel, and the beam size and position angle are indicated in the bottom right. Thelarger beam sizes for B2020+28 and B2021+51 compared to that of B1929+10 are due to flagging of baselines to Shand/or Ur. Table 3: Measured positions at MJD 55629.Pulsar RA (J2000) Dec (J2000) S/N beam size [mas × mas]B1929+10 19:32:14.021289(1) 10:59:32.90137(5) 155 . × . B2020+28 20:22:37.06758(1) 28:54:22.7563(2) 142 . × . B2021+51 20:22:49.85890(1) 51:54:50.5005(1) 156 . × . Notes.
Numbers in brackets indicate the uncertainty in the last digit. The larger beam size for B2020+28 is due to flagging ofbaselines to Sh and Ur. coherence time at 5 GHz. For the total positional uncer-tainty we added both the formal and the systematic errorsin quadrature. Table 3 lists the measured positions of allthree pulsars in the third epoch at MJD 55629.To estimate each pulsar’s proper motion and paral-lax, we performed a weighted least-squares-fit to themeasured positions. Here, we measured both parametersin three ways: we considered our position measurementsalone (Fig. 3), we combined our data with those of thepublications listed in Table 4 (Fig. 4), and we employeda bootstrapping technique. For the latter, we randomlysampled the position measurements that are availablefor each individual pulsar. These positions were then fitted and the results were stored. This procedure wasrepeated times, yielding distributions as shown inFig. 5. During the fitting procedure we allow for absolutepositional offsets between the different data sets (typicallyof the order of several mas). Such offsets are expectedfor several reasons: i) the observations were conductedat different frequencies; ii) the different campaigns useddifferent calibrator sources, which may have differentsystematic errors (e.g. Kovalev et al. 2008; Porcas 2009;Sokolovsky et al. 2011) in their ties to the InternationalCelestial Reference Frame (ICRF2, Ma et al. 2009); iii) thedata were obtained at times that are up to ten years apartduring which improvements to the correlator models andEarth orientation parameters introduce offsets; and iv) the Article number, page 4 of 11ranz Kirsten et al.: Birth sites of three young pulsars
Table 4: Previous proper motion and parallax estimates and derived values. µ α µ δ π d V ⊥ Pulsar [mas yr − ] [mas yr − ] [mas] [kpc] [km s − ] ReferenceB1929+10 . ± . . ± . . ± . . +0 . − . +140 − . ± .
26 43 . ± .
15 3 . ± .
09 0 . +0 . − . +6 − . ± .
11 42 . ± .
16 2 . ± .
07 0 . +0 . − . +5 − − . ± . − . ± .
26 0 . ± .
12 2 . +0 . − . +135 − − . ± .
17 11 . ± .
28 0 . ± .
07 2 . +0 . − . +28 − References. (1) Hoogerwerf et al. (2001); (2) Brisken et al. (2002); (3) Chatterjee et al. (2004)
Table 5: Astrometric results and derived values from the estimation strategies.data sets a µ α µ δ π d V ⊥ Pulsar F b B c N obs [mas yr − ] [mas yr − ] [mas] χ red [kpc] [km s − ]B1929+10 C . ± .
52 43 . ± .
06 2 . ± .
14 1 .
34 0 . +0 . − . +11 − C C , C
10 94 . ± .
12 43 . ± .
23 2 . ± .
08 1 .
03 0 . +0 . − . +5 − L, C . ± .
20 42 . ± .
26 2 . ± .
05 0 .
51 0 . +0 . − . +4 − L, C C , C
15 94 . ± .
09 43 . ± .
17 2 . ± .
06 0 .
77 0 . +0 . − . +4 − C C , C
10 94 . +0 . − . . +0 . − . . +0 . − . . +0 . − . +7 − L, C . +0 . − . . +0 . − . . +0 . − . . +0 . − . +8 − L, C C , C
15 94 . +0 . − . . +0 . − . . +0 . − . . +0 . − . +5 − B2020+28 C − . ± . − . ± .
11 0 . ± .
03 0 .
05 1 . +0 . − . +6 − L, C − . ± . − . ± .
21 0 . ± .
08 0 .
53 1 . +0 . − . +25 − L, C − . +0 . − . − . +0 . − . . +0 . − . . +0 . − . +50 − B2021+51 C − . ± .
42 10 . ± .
25 0 . ± .
11 1 .
54 1 . +0 . − . +15 − L, C − . ± .
27 10 . ± .
17 0 . ± .
07 0 .
90 1 . +0 . − . +11 − L, C − . +0 . − . . +0 . − . . +0 . − . . +0 . − . +16 − Notes. ( a ) C refers to the measurements obtained in this campaign, C C denotes the data set from Chatterjee et al. (2004), and Lindicates that the measurements from Brisken et al. (2002) were included in the analysis. ( b ) Results derived from a least-squaresfit of the measured data. ( c ) Median values and confidence interval from fitting bootstrapped realizations of the data. data were taken with different instruments (VLBA andEVN) that use different hardware/software correlators.Table 5 summarizes the estimates of µ and π from theindividual fits, from the different combinations of datasets, and from the bootstrapping method (where we quotethe most compact 68% confidence interval), as well asthe implied pulsar distances and transverse velocities.The latter are corrected for solar motion and differentialGalactic rotation and refer to the local standard of rest(LSR). Regardless of estimation strategy and combinationof available data, all measured values are consistent withintheir uncertainties at the one-sigma level.For pulsar B1929+10 our results confirm the measure-ments of Chatterjee et al. (2004), especially in combinationwith the earlier data. For pulsars B2020+28 and B2021+51our observations indicate that they are located at a distanceof . +0 . − . kpc and . +0 . − . kpc. Hence, they are about . and . kpc closer to the solar system than what was implied by the measurements of Brisken et al. (2002) alone(Table 4). Considering this discrepancy of a factor of about2, we suspect that the uncertainties on the position mea-surements for B2020+28 and B2021+51 as reported by theauthors were underestimated. Accordingly, we did not in-clude these data in the further analysis. Thus, in the follow-ing, for B1929+10 we adopted the astrometric parametersobtained from bootstrapping all available data, while forB2020+28 and B2021+51 we used the parameters as mea-sured with our new 5 GHz data alone. Hence, the analysisbelow is based on the astrometry as listed in Table 6.
4. Simulations of pulsar orbits
To shed new light on possible common origins ofB1929+10/ ζ Oph and B2020+28/B2021+51, we used thepulsar astrometric parameters described above and tracedtheir orbits back in time through the Galactic potential.
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Fig. 3: Relative measured positions of B1929+10 (left), B2020+28 (middle), and B2021+51 (right) with the best-fitproper motion removed. The solid line is the best-fit parallax from our EVN 5 GHz observations. −3−2−10123 ∆ D e c [ m a s ] L-bandC-band-C04 C-band51600 52000 52400−3−2−10123 ∆ R A [ m a s ] MJD
B1929+10 −101 L-band C-band51600 51900−101
MJD
B2020+28 −101 L-band C-band51600 51900−101
MJD
B2021+51
Fig. 4: Same as Fig. 3, but for the fits performed using all available data. Solid dots show the most recent measurements at5 GHz, open stars are the data taken from Brisken et al. (2002), and squares are the data adopted from Chatterjee et al.(2004). For better illustration, we omitted the time span without any observations.For the runaway star ζ Oph we used the latest propermotion and parallax measurements from van Leeuwen(2007) (Table 6) and adopted the value for the radialvelocity V rad = − . ± . km s − from Kharchenko et al.(2007). Our astrometric measurements yield informationabout the transverse motion of the pulsars, but they doTable 6: Astrometric parameters used in the simulations µ α µ δ π Source [mas yr − ] [mas yr − ] [mas]B1929+10 . ± .
17 43 . ± .
16 2 . ± . ζ Oph a . ± .
26 24 . ± .
22 8 . ± . B1952+29 b − ± − ± . ± . B2020+28 − . ± . − . ± .
11 0 . ± . B2021+51 − . ± .
42 10 . ± .
25 0 . ± . Notes. ( a ) From van Leeuwen (2007) ( b ) Proper motion fromHobbs et al. (2004), parallax from the ATNF Pulsar Catalogue(Manchester et al., 2005). not contain any information about the radial velocity.To estimate the full 3D velocity vector, we simulatedthe possible radial component from our measured trans-verse components and the space velocity distributionof young pulsars as empirically derived by Hobbs et al.(2005). To account for the uncertainties of the measuredparameters µ α , µ δ , π , and the unknown radial velocity,we assumed that all parameters are distributed normally(where the half-width of the Gaussian is given by thehigher absolute value of the upper and lower errors ofthe bootstrapping results) and performed three millionMonte Carlo simulations. The obtained velocity vectorswere corrected for the solar motion with respect to theLSR, for differential Galactic rotation, and also for thevelocity of the LSR. The Galactic potential we used in oursimulations is the potential that was described in full detailin Vlemmings et al. (2004), the main parameters of whichwe summarize here in brief. For consistency reasons, thepulsar orbits were traced back through the same Stäckelpotential as in Vlemmings et al. (2004); consisting of athin disk, a thick disk, and a halo component whose axis Article number, page 6 of 11ranz Kirsten et al.: Birth sites of three young pulsars α [mas/yr]0.00.51.01.52.02.53.03.54.0 P D F B1929+10 PM (RA) 42.5 43.0 43.5 44.0µ δ [mas/yr]0.00.51.01.52.02.53.0 B1929+10 PM (Dec) 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2π [mas]01234567 B1929+10 Parallax−5.5 −5.0 −4.5 −4.0 −3.5 −3.0 −2.5µ α [mas/yr]0.00.51.01.52.02.53.03.5 P D F B2020+28 PM (RA) 25.0 24.5 24.0 23.5 23.0 22.5 22.0µ δ [mas/yr]0.00.51.01.52.0 B2020+28 PM (Dec) 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4π [mas]0.00.51.01.52.02.53.03.5 B2020+28 Parallax−6.5 −6.0 −5.5 −5.0 −4.5 −4.0µ α [mas/ r]0.00.51.01.52.02.5 P D F B2021+51 PM (RA) 9.5 10.0 10.5 11.0 11.5 12.0µ δ [mas/ r]0.00.51.01.52.02.5 B2021+51 PM (Dec) 0.2 0.4 0.6 0.8 1.0 1.2π [mas]0123456 B2021+51 Parallax Fig. 5: Probability density functions of fitting results from bootstrapping all available data. From top to bottom:B1929+10, B2020+28, and B2021+51. Columns are from left to right: proper motion in RA, proper motion in Dec,and parallax. The solid and dashed vertical lines indicate the median and the most compact 68% confidence intervals aslisted in Table 5.ratios are . , . , and . , respectively. We kept therelative contributions of thin and thick disks and of thehalo at . , . , and . , respectively. For a completedescription of each parameter of the Stäckel potential,we refer to Famaey & Dejonghe (2003). We adoptedparameters for solar motion from Schönrich (2012): R ⊙ = 8 . kpc and ( U, V, W ) = (13 . , . , . km s − .Each object’s trajectory was sampled at time intervals of yr using a fourth-order Runge-Kutta numerical inte-gration method. For each time step the distances betweenthe two objects under consideration were computed withinthe Galactic reference frame, and we recorded only thesimulation input parameters of trajectories that resulted ina minimum distance of less than 10 pc. In addition to the separation between the individual objects, we also com-puted their distances to the Sun (B2020+28/B2021+51)and to the Upper Scorpius region (B1929+10/ ζ Oph).To compute the latter, we traced the trajectory of UpperScorpius back in time using the astrometric values as listedin Table 2 of de Zeeuw et al. (1999).For consistency checks we used the input parametersof Hoogerwerf et al. (2001) to compute the trajectoriesof B1929+10 and ζ Oph. In total, 37521 of the threemillion sampled trajectories ( . %) cross within pcof each other. This is close to the percentage found inHoogerwerf et al. (2001): 30822 out of three million, or1.0%. The smallest separation we found is . pc (com- Article number, page 7 of 11 &A proofs: manuscript no. ev18-v8-arxiv P D F B1929+10/ζ Oph 0.4 0.5 0.6time [Myr]024681012 B1929+10/ζ Oph 0.015 0.030 0.045 0.060distance to UpSco [kpc]0102030405060 B1929+10/ζ Oph0 2 4 6 8 10minimal distance [pc]0.000.050.100.150.200.250.300.350.400.45 P D F B2020+28/B2021+51 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0time [Myr]0.00.51.01.52.02.53.0 B2020+28/B2021+51 0.4 0.6 0.8 1.0 1.2 1.4distance to Sun [kpc]0.00.51.01.52.02.53.03.54.04.5 B2020+28/B2021+51
Fig. 6: Probability density functions of minimal distances (left column), time of minimal approach (middle column),and distance to Upper Scorpius and the Sun for B1929+10/ ζ Oph (upper row) and B2020+28/B2021+51 (lower row),respectively. The stellar pair to which the figures apply is indicated in the top of each panel.pared to . pc). Furthermore, while Hoogerwerf et al.(2001) reported that in 4214 (0.14%) simulations the tra-jectories of both the pulsar and the runaway star not onlypass within pc of each other, but also pass within lessthan pc of Upper Scorpius, we found that 6816 (0.23%)of our simulations meet these conditions. The differencesin the results are probably due to the different set-upsof the Galactic potentials. We did reproduce the generaltrend found by Hoogerwerf et al. (2001), however. Whenwe ran the simulations using the same input parametersfor B1929+10 as Hoogerwerf et al. (2001), but used thelatest parameters for ζ Oph from van Leeuwen (2007), atotal of 82840 (2.7%) simulated orbits cross within pc,in only 8 of which both the pulsar and the star are lessthan pc away from Upper Scorpius.To test how much the updated solar parameters andthe different radial velocity distributions influence thecomputed trajectories, we also ran the simulations forB2020+28/B2021+51 using the input parameters for µ α , µ δ , and π from Vlemmings et al. (2004) (Table 4). Inour simulations . of trajectories cross within pc(minimal distance of . pc), reproducing the results ofthese earlier simulations well.In the three million simulations that we ran usingour bootstrapping results for B1929+10 and the latestastrometric parameters for ζ Oph, 258272 (8.6%) orbitscross within pc about . Myr ago (Fig. 6). However,none of these orbits yield a minimum separation of lessthan . pc, and neither the pulsar nor the runaway starapproach the centre of Upper Scorpius to within less than We used a one-component velocity distribution, whileVlemmings et al. (2004) used a two-component distribution. pc. The median radial velocity of B1929+10 required forit to approach ζ Oph within pc is +53 − km s − (Fig.7). For completeness, we also tested the hypothesis thatB1929+10 once formed a binary system with the pulsarB1952+29 (Wright 1979). For the latter we assumed theproper motion from Hobbs et al. (2004) and the parallaxfrom the distance derived from the dispersion measure(DM) in the ATNF Pulsar Catalogue and the Galacticelectron density model from Cordes & Lazio 2003 (Table6). We assumed a parallax uncertainty of mas in lieuof a formal error estimate in the DM-based distance.With these parameters, none of the simulated orbitscrosses within pc. The same is true for simulations ranwith the same proper motion parameters, but with thedistance estimate d = 0 . kpc, based on the same DMbut using instead the Galactic electron density model fromTaylor & Cordes (1993).For the putative pulsar pair B2020+28/B2021+51 our newmeasurements imply a minimum possible separation of . pc. Of the three million trajectories, (0.06%) crosswithin pc about . +0 . − . Myr ago (Fig. 6). The impliedmedian radial velocities are +193 − for B2020+28 and +154 − km s − for B2021+51 (Fig. 7).
5. Discussion
Our new astrometric results for the pulsar B1929+10confirm the measurements of earlier VLBI campaigns α [mas yr −1 ]0.00.51.01.52.02.5 P D F B1929+10 42.5 43.0 43.5 44.0µ δ [mas yr −1 ]0.00.51.01.52.02.5 B1929+10 2.4 2.6 2.8 3.0π [mas]012345 B1929+10 −1200 −600 0 600 1200radial velocity [km s −1 ]0.0000.0010.0020.0030.0040.0050.0060.007 B1929+1014.0 14.5 15.0 15.5 16.0 16.5µ α [mas yr −1 ]0.00.20.40.60.81.01.21.41.6 P D F ζ Oph 23.5 24.0 24.5 25.0 25.5 26.0µ δ [mas yr −1 ]0.00.51.01.52.0 ζ Oph 7.5 8.0 8.5 9.0 9.5 10.0π [mas]0.00.51.01.52.0 ζ Oph −40−30−20−10 0 10 20radial velocity [km s −1 ]0.000.010.020.030.040.050.060.070.08 ζ Oph−3.6 −3.4 −3.2µ α [mas yr −1 ]0123456789 P D F B2020+28 −24.5 −24.0 −23.5 −23.0µ δ [mas yr −1 ]0.00.51.01.52.02.53.03.54.0 B2020+28 0.6 0.7 0.8π [mas]02468101214 B2020+28 −1200 −600 0 600 1200radial velocity [km s −1 ]0.00000.00050.00100.00150.00200.0025 B2020+28−6.0 −5.5−5.0 −4.5−4.0µ α [mas yr −1 ]0.00.20.40.60.81.01.21.4 P D F B2021+51 10.0 10.5 11.0 11.5µ δ [mas yr −1 ]0.00.20.40.60.81.01.21.41.61.8 B2021+51 0.4 0.6 0.8 1.0 1.2π [mas]0.00.51.01.52.02.53.03.54.0 B2021+51 −1200 −600 0 600 1200radial velocity [km s −1 ]0.00000.00050.00100.00150.00200.0025 B2021+51 Fig. 7: Probability density function (grey histograms) of astrometric parameters and required radial velocities that resultin a minimum separation of less than pc between B1929+10/ ζ Oph and B2020+28/B2021+51. Columns from leftto right show the results for µ α , µ δ , π, and V rad . For the measured parameters µ α , µ δ , and π , the solid lines indicatethe input parameter distributions derived from assuming Gaussian errors. The solid line in the last column indicatesthe input distribution for V rad as derived from our measured transverse velocity and the empirically determined spacevelocity distribution derived by Hobbs et al. (2005). Objects from top to bottom are B1929+10, ζ Oph, B2020+28, andB2021+51.(Brisken et al. 2002; Chatterjee et al. 2004), and in com-bination with the previous position measurements, weplace robust constraints on the uncertainties of the propermotion parameters. Accordingly, for our adopted parallax π = 2 . +0 . − . our values for the proper motion differ bymore than σ from the parameter space that implies acommon origin of B1929+10 and ζ Oph in Upper Scorpius in Hoogerwerf et al. (2001). Given the new astrometry forthe pulsar and also the updated astrometric parameters forthe runaway star, the minimal possible separation of . pcbetween the two stars is too large to be consistent with acommon origin of both. Moreover, the closest approach ofroughly pc to Upper Scorpius of either of the two objectsin all of the trajectories crossing within pc makes it Article number, page 9 of 11 &A proofs: manuscript no. ev18-v8-arxiv very unlikely that this region is the place of common origin.However, the fraction of simulated orbits that crosswithin pc ( ∼ . ) is surprisingly high and implies thatthe orbits of both objects may have crossed within thatdistance about . Myr ago. The allowed range in radialvelocities for them to pass close by, on the other hand, isvery small and points to a very strong kick imparted to thepulsar at birth. Only a direct measurement of the pulsar’sradial velocity will further constrain the distance of closestapproach of B1929+10 and ζ Oph.Our data in combination with the updated astrome-try for B1952+29 make a binary origin of B1929+10 andB1952+29 highly implausible.
Vlemmings et al. (2004) used the astrometric parametersfrom Brisken et al. (2002) (Table 4) to infer a putativecommon origin of B2020+28 and B2021+51. This conclu-sions seems plausible considering that the pulsars’ 2D mo-tions lie in apparently opposite directions in Galactic co-ordinates (Fig. 1 in Vlemmings et al. 2004) and also be-cause the pulsars have very similar characteristic ages of . (B2020+28) and . Myr (B2021+51). Nevertheless,our new proper motion measurements, in conjunction withour parallax measurements, which place both pulsars al-most twice as close as previous distance estimates, rule outa common origin for these two objects. Vlemmings et al.(2004) determined the percentage of orbits crossing within pc for a known binary disrupted Myr ago as a functionof astrometric uncertainties (see their Fig. 2). These modelsindicate that our improved errors should have yielded of crossing orbit realization (within pc) for B2020+28and B2021+51. However, in our simulations only . oftrajectories cross within that distance, and none of the or-bits yield an approach of less than . pc. Even if we usethe bootstrapping results with their larger errors from Ta-ble 5, only . of the orbits cross within pc. Further-more, the orbits approaching each other within pc doso at a median distance of . +0 . − . kpc to the solar sys-tem. Given the estimated extent of the Cygnus Superbubbleof . − . kpc (Vlemmings et al. 2004), a common originwithin this region is ruled out. In Table 7 we list the distances inferred from our par-allax measurements in comparison with those implied bythe DM and the Galactic electron density models ofCordes & Lazio (2003, NE2001) and Taylor et al. (1993,TC93, both obtained from the ATNF pulsar catalogue).While the NE2001–distance agrees with our measurementfor B1929+10, the same model overestimates the distancesto both B2020+28 and B2021+51 by a factor of about . .The distance estimates for the latter two pulsars as givenby the preceding model, TC93, agree well with our results,however. Hence, in combination with the DM as listed inTable 7, our parallax measurements imply a mean elec-tron density of . +0 . − . , . +0 . − . , and 18 . +2 . − . cm − along Table 7: Parallax- vs. DM-based distancesDM d π a d NE2001 b d TC93 c Source [pc cm − ] [kpc] [kpc] [kpc]B1929+10 .
180 (4) 0 . +0 . − . .
34 0 . B2020+28 .
640 (3) 1 . +0 . − . .
11 1 . B2021+51 .
648 (6) 1 . +0 . − . .
94 1 . Notes. ( a ) Parallax-based distances derived in this work. ( b ) Dis-tance estimate based on the Galactic electron density modelfrom Cordes and Lazio (2003) ( c ) Distance estimate based onthe Galactic electron density model from Taylor et al. (1993).Except for d π , all values were taken from the ATNF pulsarcatalogue. the lines of sight to B1929+10, B2020+28, and B2021+51,respectively.
6. Conclusions
Based on our new astrometry for pulsars B1929+10,B2020+28, and B2021+51 obtained with the EVN at5 GHz, we rule out previously proposed common origin sce-narios for all three sources. Our Monte Carlo simulationsof the past trajectory of B1929+10 throughout the Galac-tic potential show now indication for the pulsar to haveonce been in a binary system with the runaway star ζ Ophin Upper Scorpius. Similar simulations for B2020+28 andB2021+51 also rule out a binary origin of the pulsars in theCygnus Superbubble.
Acknowledgements.
We appreciate the comments of the anonymousreferee that helped us to improve the manuscript. We would like tothank Walter Brisken for providing us with his position measurementsat 1.5 GHz. F.K. acknowledges partial funding by the Bonn CologneGraduate School of Physics and Astronomy. The European VLBI Net-work is a joint facility of European, Chinese, South African and otherradio astronomy institutes funded by their national research councils.This work has been supported by the European Commission Frame-work Programme 7, Advanced Radio Astronomy in Europe, grantagreement No. 227290.
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