The Relativistic Binary Programme on MeerKAT: Science objectives and first results
M. Kramer, I.H. Stairs, V. Venkatraman Krishnan, P.C.C. Freire, F. Abbate, M. Bailes, M. Burgay, S. Buchner, D.J. Champion, I. Cognard, T. Gautam, M.Geyer, L. Guillemot, H. Hu, G. Janssen, M.E. Lower, A. Parthasarathy, A. Possenti, S. Ransom, D.J. Reardon, A. Ridolfi, M. Serylak, R.M. Shannon, R. Spiewak, G. Theureau, W. van Straten, N. Wex, L.S. Oswald, B. Posselt, C. Sobey, E.D. Barr, F. Camilo, B. Hugo, A. Jameson, S. Johnston, A. Karastergiou, M. Keith, S. Oslowski
MMNRAS , 1–21 (2021) Preprint 11 February 2021 Compiled using MNRAS L A TEX style file v3.0
The Relativistic Binary Programme on MeerKAT: Science objectives andfirst results
M. Kramer , ★ , I.H. Stairs , V. Venkatraman Krishnan , P. C. C. Freire , F. Abbate , M. Bailes , ,M. Burgay , S. Buchner , D. J. Champion , I. Cognard , , T. Gautam , M. Geyer , L. Guillemot , ,H. Hu , G. Janssen , M. E. Lower , , A. Parthasarathy , A. Possenti , , S. Ransom , D. J. Reardon , ,A. Ridolfi , , M. Serylak , R. M. Shannon , , R. Spiewak , , G. Theureau , , W. van Straten , N. Wex ,L. S. Oswald , B. Posselt , , C. Sobey , E. D. Barr , F. Camilo , B. Hugo , , A. Jameson , ,S. Johnston , A. Karastergiou , M. Keith , S. Osłowski , Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany Jodrell Bank Centre for Astrophysics, University of Manchester, M13 9PL, UK Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada Centre for Astrophysics and Supercomputing, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav) INAF - Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius (CA), Italy South African Radio Astronomy Observatory, 2 Fir Street, Black River Park, Observatory 7925, South Africa Station de Radioastronomie de Nançay, Observatoire de Paris, CNRS/INSU, Université d’Orléans, 18330, Nançay, France Laboratoire de Physique et Chimie de l’Environnement, CNRS, 3A Avenue de la Recherche Scientifique, 45071, Orléans Cedex 2, France ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD, Dwingeloo, The Netherlands CSIRO Astronomy & Space Science, Australia Telescope National Facility, P.O. Box 76, Epping, NSW 1710, Australia Universitá di Cagliari, Dipartimento di Fisica, S.P. Monserrato-Sestu Km 0,700 - 09042 Monserrato (CA), Italy National Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA 22903, USA Institute for Radio Astronomy & Space Research, Auckland University of Technology, Private Bag 92006, Auckland 1142, NZ Oxford Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK Department of Astronomy & Astrophysics, Pennsylvania State University, 525 Davey Lab, 16802 University Park, PA, USA CSIRO Astronomy and Space Science, PO Box 1130 Bentley, WA 6102, Australia Rhodes University: Department of Physics and Electronics, Rhodes University, Artillery Road, Grahamstown, South Africa Gravitational Wave Data Centre, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia
Last updated; in original form
ABSTRACT
We describe the ongoing Relativistic Binary programme (RelBin), a part of the MeerTime large survey project with the MeerKATradio telescope. RelBin is primarily focused on observations of relativistic effects in binary pulsars to enable measurements ofneutron star masses and tests of theories of gravity. We selected 25 pulsars as an initial high priority list of targets based on theircharacteristics and observational history with other telescopes. In this paper, we provide an outline of the programme, presentpolarisation calibrated pulse profiles for all selected pulsars as a reference catalogue along with updated dispersion measures.We report Faraday rotation measures for 24 pulsars, twelve of which have been measured for the first time. More than a third ofour selected pulsars show a flat position angle swing confirming earlier observations. We demonstrate the ability of the RotatingVector Model (RVM), fitted here to seven binary pulsars, including the Double Pulsar (PSR J0737 − − − − − − − Key words: pulsars:general, instrumentation:interferometers, stars:neutron ★ E-mail: [email protected] © a r X i v : . [ a s t r o - ph . H E ] F e b Kramer et al.
Pulsars are remarkable laboratories for studying fundamentalphysics. When the rotation of a pulsar in a binary system is trackedwith high precision using a technique called pulsar timing, we canstudy the orbit of the pulsar about the centre of mass that it shareswith a companion object. If the orbit is compact enough, timing mayreveal a number of relativistic effects that depend on the masses ofthe pulsar and its companion, apart from the Keplerian parametersof the orbit that are readily measured. Consequently, studying bi-nary radio pulsars enables us to probe relativistic gravity as well asprecisely measure masses of neutron stars (e.g. Taylor & Weisberg1982; van Straten et al. 2001; Kramer et al. 2006; Weisberg & Huang2016).In both the highly relativistic interior and the vicinity of a pulsar(and its binary companion, in the cases of double neutron star systemsor potential pulsar-black hole systems) space-time may significantlydeviate from the predictions of General Relativity (GR; Damour &Esposito-Farèse 1996). Pulsar timing therefore is a rare tool for prob-ing gravity in the (mildly-relativistic) strong-field regime, enablinghigh-precision tests of GR or alternative theories of gravity (Damour& Taylor 1992; Will 2018). Perhaps best known precision tests ofGR are the ones performed using the compact orbits of double neu-tron star (DNS) systems, such as the PSR B1913+16 (Weisberg &Taylor 1984) or the unique “Double Pulsar” (Kramer et al. 2006).Binary pulsars with white dwarf companions enable tests of someof the fundamental properties of gravity such as a possible viola-tion of the universality of free fall (e.g. PSR J0337 − − Pulsar timing registers the pulse arrival times of pulsar signals atEarth and transforms these topocentric times of arrival (ToAs) via ahypothetical ToA at the Solar System Barycentre (barycentric ToAs)into the reference frame of the pulsar. This allows us to preciselycount the number of rotations of the neutron star with the help of atiming model. Using this, we can measure the relevant timing param-eters, the precision of which increases with the number and precisionof the ToAs as well as the total time span of the observations (Lorimer& Kramer 2012). If the pulsar has a companion, the impact on theToAs from the corresponding orbital motion can be described, inthe simplest case, with five Keplerian parameters. Deviations from asimple Keplerian orbit due to astrophysical or relativistic effects canbe described by the addition of theory-independent phenomenologi-cal “post-Keplerian” (PK) parameters (Damour & Taylor 1992). Forany metric theories of gravity, these PK parameters can be writtenas functions of the well-measured Keplerian parameters and the un-known masses of the pulsar and its companion. Measuring 𝑛 PK = 𝑛 PK >
2, the set of available equations is over-determined. Inthis case, one can check for the self-consistency of a theory of gravity,allowing 𝑛 PK − MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme of the components, as in the case of PSR J1141 − 𝑃 b ∼ fewhours) and orbital campaigns with cadence of a few hours for longerorbits. For orbits of a few days (e.g. PSR J1017 − − In order to obtain 𝑛 PK > − − − − − − − Our objectives are both to improve on existing mass determinationsand to derive new measurements. The binary systems considered formass measurements can then be split into the following categories: - Pulsars in nearly circular orbits with likely white dwarf (WD)companions, for which we expect to obtain Shapiro delay measure-ments.- Millisecond pulsars (MSPs) that are also timed as part of Meer-Time in a “Pulsar Timing Array” (PTA) programme (Spiewak etal. in prep.). The RelBin observations complement the regular PTAmonitoring by dedicated sessions aimed on optimising orbital phasecoverage. Shapiro delay measurements obtained in this way may becombined with potential measurements of the PK parameters (cid:164) 𝜔 and (cid:164) 𝑥 , i.e. periastron advance and change in the projected semi-majoraxis, respectively. These effects cannot only be caused by relativisticgravity but, for instance, by kinematic effects.- Eccentric MSPs, where we will be able to measure periastronadvance, (cid:164) 𝜔 , and Shapiro delay (J0955 − − − − − (cid:164) 𝑃 b . We provide here a brief introduction to the telescope and the backendsystem used for the MeerTime project. For further details on theinstrumentation for pulsar observations, see Bailes et al. (2020).
The MeerKAT telescope is a 64-dish interferometer situated in Ka-roo region of South Africa and is operated by the South AfricanRadio Astronomy Observatory (SARAO). Each dish is 13.9 m indiameter and currently has two operational receivers in its focus, inan offset-Gregorian configuration, with a gain of 2.8 K/Jy. The first“L-band” receiver operates with a bandwidth of 856 MHz centred ata frequency of 1284 MHz, and it is the instrument used for most of thepulsar observations presented in this paper. The receiver has a verylow system temperature of ∼
18 K, making it one of the most powerfulinterferometers around 1.4 GHz. The second “UHF-receiver” is cen-tred at a frequency of 816 MHz with a bandwidth of 544 MHz. It hasrecently been installed with commissioning and testing observationsunderway. A third receiver suite, the “S-band” receivers (operatingat 1.75–3.5 GHz) have been designed and built by the Max-Planck-Institut für Radioastronomie (MPIfR). The receivers are currentlybeing delivered to the telescope and commissioned upon arrival.Given that S-band observations promise significant improvement intiming precision for a number of sources (as detailed further below),RelBin will make extensive use of the MPIfR S-band system once itis fully operational in the next 12–18 months.The signals from all 64 antennas are first amplified by chain ofradio frequency amplifiers, and are sampled at radio frequency (nodown-conversion) to produce complex voltage streams that are sent tothe correlator-beamformer engine (CBF) via a 40-Gbps switch. TheCBF coherently adds the voltages, channelizes to either 1024 or 4096channels, beamforms up to 4 tied-array beams (TAB) and streams thechannelized time series to the Pulsar Timing User Supplied Equip-ment (PTUSE) machines. The steps in the observing procedure asfollows.Before every pulsar observing session, calibration observations areperformed to phase up the array and obtain polarisation calibration
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Table 1.
Basic parameters of the sources in the MeerKAT Relativistic binary programme. We list the spin and orbital periods, the eccentricity and the massfunction. We also list the initial Time-of-Arrival (ToA) measurement precision achieved for all the pulsars with a 2048 second, full-band integration. The valuesare obtained using a standard processing pipeline with a single template for the whole band. Hence these estimates are conservative, unless pulsar was highlyscintillating up. We compare this precision with the currently best available TOA precision (using values to the best of our knowledge based on literature and ourown data sets regardless of observing frequencies, see last column), adjusted for the same integration time as here. For Southern-sky sources, these improvementsare about one order of magnitude. The penultimate column lists the science goals that we expect to achieve with our observations. See Table footnotes and textfor more details.PSR Name Spin period, Orbital period, Eccentricity, Mass Function, TOA Precision Science Goals Ref. 𝑃 ( ms ) 𝑃 b (days) 𝑒 𝑀 f ( 𝑀 (cid:12) ) ( 𝜇 s)/ improvementJ0737 − > × S, GW, EOS, E, LB,DTH, SO (1)J0955 − > × OM, S, M (2)J1017 − > × OM, S, M (3) † J1141 − > × S, SO, M (4) † J1157 − > × OM, S, M (5)J1227 − > × OM, S, M (6)J1435 − > × S, M (7)J1454 − > × OM, S, M (7)J1528 − > × OM, S, M (8) † J1603 − > × S, GW, INC (3) † J1618 − > × OM, S, M (9)J1727 − > × OM, S, M (10)J1732 − > × S, M (3) † J1748 − ∼ × OM, S, M (11) † J1753 − > × OM, S, M (12)J1756 − > . × OM, S, GW, M (13)J1757 − > . × OM, GW, S, M, DTH, EOS (14)J1757 − < . > × GW, S, M (5)J1802 − < . > . × GW, S, M (15)J1811 − > × OM,S, M (16)J1811 − < . > . × S, M (17)J1930 − > . × OM, S, M (18)J1933 − < . > × S, M (19) † J2129 − > × S, M (3) † J2222 − > . × OM,S,GW, M (20)Abbreviations of science goals: S - Shapiro delay measurement, OM - Periastron advance via (cid:164) 𝜔 , GW - Gravitaional wave damping via (cid:164) 𝑃 b , M - Massmeasurements, SO - spin-orbit coupling (classical and relativistic spin and orbital precession), EOS - Equation of state, INC - constraints on inclinationfrom proper motion, LB - Light - Bending effect, DTH - relativistic deformation of the orbit via 𝛿 𝜃 , E - Eclipse studies.The references for the previously achieved ToA precision are (1) Hu et al. (2020), (2) Camilo et al. (2015), (3) Kerr et al. (2020), (4) Venkatraman Krishnanet al. (2020), (5) Edwards & Bailes (2001), (6) Bates et al. (2015), (7) Camilo et al. (2001), (8) Jacoby et al. (2007), (9) Octau et al. (2018), (10) Lorimeret al. (2015), (11) Freire et al. (2008), (12) Keith et al. (2009), (13) Ferdman et al. (2014), (14) Cameron et al. (2018) (15) Ferdman et al. (2010), (16)Corongiu et al. (2007) (17) Ng et al. (2020), (18) Swiggum et al. (2015), (19) Graikou et al. (2017), (20) Cognard et al. (2017). For pulsars marked with † we compare the MeerKAT ToA precision to the best data from other telescopes that we have access to; these are significantly better than the data in thelatest published reference. solutions. This includes observations of a calibrator source with wellcharacterised flux and polarisation for a wide range of frequencies.During these observations, signal from a noise diode is injected intothe voltage stream just before RF amplification in every antenna.The sources often used are PKS J0408 − − − ring buffer in the CPU memory. The data fromthis ring buffer is asynchronously processed by the pipelines in thedspsr software library (van Straten & Bailes 2011). The pipelineeither records full-Stokes, search mode data at a sampling time of9.57 𝜇𝑠 (which can be configured to scrunched down up to 38 𝜇𝑠 ),or folds the data (i.e. computes the phase-resolved average of thepolarised flux) at the topocentric pulse period with 1024 phase binsand 8-s integration lengths. Both search and fold-mode acquisition https://psrdada.sourceforge.net http://ascl.net/1010.006 MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme Table 2.
Measurements of DM and RM meas for the RelBin list of sources. The measurements are obtained from the longest observation of the pulsar performedin the course of Relbin. In order to derive at the rotation measure of the pulsar, RM
PSR , we correct for ionospheric contributions, RM
Iono , which are computedusing ionFR (Sotomayor-Beltran et al. 2013). We provide the RM values from psrcat (Manchester et al. 2005) where available.PSR Name Observation DM RM meas RM iono RM PSR RM psrcat epoch, (MJD) (pc cm − ) (rad m − ) (rad m − ) (rad m − ) (rad m − )J0737 − − ( ) J0955 − − − − −− J1017 − − − − − ( ) J1141 − − − − − ( ) J1157 − − − − − ( ) J1227 − − −− J1435 − − − − −− J1454 − − −− J1528 − − − − − ( ) J1603 − − ( ) J1618 − − −− J1727 − − − − − ( ) J1732 − − − − − ( ) J1748 − − − − −− J1753 − − −− J1756 − − − − ( ) J1757 − − − − −− J1757 − − −− J1802 − − ( ) J1811 − − − − −− J1811 − − ( )† J1930 − − −− J1933 − − −− J2129 − − . ( ) J2222 − − . ( . )† psrcat’s values for this pulsar were not up to date. The latest estimates come from (Ng et al. 2020) andis 21(9) rad m − which is consistent with our measurements. can be configured to run with or without coherent dedispersion. Datashown here are obtained in coherent dedispersion mode. The pulsar fold-mode and search-mode data from the PTUSE ma-chines are periodically transferred to the OzStar supercomputingcluster at Swinburne University of Technology in Australia. The fold-mode archives are fed through a pipeline (meerpipe) which performsautomated RFI excision and polarisation calibration. The RFI exci-sion is performed using a modified version of coastguard (Lazaruset al. 2016) and the Jones matrices for polarisation calibration areobtained from the phase up observation of the telescope (see 3.1).The cleaned, calibrated files are decimated to the required time andfrequency resolution, and the Times of Arrival (ToAs) of the pulsesare obtained using the pat programme in the psrchive softwaresuite (Hotan et al. 2004).We used the longest observation taken on each pulsar to computethe updated dispersion and rotation measures (DMs and RMs) pro-vided in Table 2. The DM of the pulsar was obtained using the pdmpprogram that provides the dispersion measure that maximises thesignal to noise ratio. The RM was obtained using the rmfit program.rmfit obtains the best RM by brute-force searching for the maximumsignal-to-noise ratio for the linearly polarised flux, 𝐿 = √︁ 𝑄 + 𝑈 ,as a function of trial RM. The range of RMs trialled and the step size http://ascl.net/1105.014 is automatically determined such that the change in position angle(P.A.) over the band, P.A. < Observing cadence, significant orbital coverage and long timing base-line are crucial for the measurement of several relativistic effects andthe masses of the component stars. In order to achieve this, we notethat the RelBin programme on MeerKAT reported here is supportedby further dedicated observing campaigns. In particular, we havean ongoing support project with the Parkes radio telescope where asubset of our pulsars is timed with the Ultra Wide-Band Low (UWL)receiver (Project ID P1032; PI Venkatraman Krishnan). These ob-servations will not only help with gaining better orbital coverage butthe ultra wide bandwidth of 4 GHz will also help in obtaining betterconstraints on orbital and temporal dispersion measure variations ofthe pulsar, an effect known to bias estimates of the relativistic pa-rameters. These data will be included in subsequent publications ontiming results for specific sources.
We present the first results of our RelBin observations with MeerKATby first reviewing the sample properties, before commenting on thespecific sources in the next section.
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Figures 1, 2, 3, 4, 6, 8 and 11 show the L-band polarisation profilesand the corresponding position angle swings of their linear polarisa-tion for all the pulsars. In order to demonstrate the relative brightnessof the sources, and hence the expected timing precision, all profilesshown in Figs. 1 - 6 have been obtained with the same observinglength of 2048 seconds. All profiles are well resolved, but those ofPSRs J1811 − − − − − − − − − − Our measurements of DM and RM are obtained from the longestobservation of each pulsar taken over the last year. The updated val-ues along with the epoch of the observation are provided in Table2, including new RM measurements for 12 pulsars. We use the pub-licly available software package, ionFR (Sotomayor-Beltran et al.2013), to obtain the ionospheric Faraday rotation measure (RM Iono )to the measured RMs (RM meas ) corresponding to each observation(Sotomayor-Beltran et al. 2013). The software uses inputs from theInternational Geomagnetic Reference Field and the InternationalGNSS service vertical total electron content maps to obtain RM Iono for each epoch. The corrected RM, RM
PSR , is then obtained by sub-tracting RM iono from RM meas . In general, we find our DM precisionto be better than a few × . − except for PSR J1811 − (cid:46) 𝜎 . Inspecting the polarisation properties of the obtained profiles canreveal potential calibration problems that would negatively affect thetiming precision and often introduce systematics. The profiles shownhere will therefore also serve as a reference to compare with duringcontinuing timing observations. However, as we will demonstrate,they can also be helpful to achieve our science goals. http://ascl.net/1303.022 ftp://cddis.nasa.gov/pub/gps/products/ionex/ Overall, all pulsars show only a modest degree of polarisation. Thelinear polarisation is much lower than seen, for instance, in youngpulsars (see e.g. Karastergiou et al. 2005). The exception is PSRJ1157 − − The large degree of linear polarsiation observed in PSR J1157 − − − − − − − | 𝑑 P . A . / 𝑑 Φ | ,as a function of pulse period. It is notable that a formal fit reveals aweak dependence on the period as | 𝑑 P . A . / 𝑑 Φ | ∝ 𝑃 . ± . , sug-gesting that pulsars with smaller periods tend to show a shallowerslope. Whether this dependence is significant and confirmed withadditional data remains to be seen. We will defer the answer ofthis question to a more detailed and larger study in a later publicationwhere we cannot only increase the sample size by adding non-RelBinsources, but where we can also benefit from longer observing spansthan available here. Longer integration time may reveal additionalP.A. values that may deviate from a flat P.A. swing observed here. Alarger sample can also look at possible physical origins, should thistrend be confirmed, e.g. the possible dependence on the amount ofaccreted matter and other source-specific parameters. This is beyondthe scope of this paper.With the currently available data set, for all cases shown in Table 3the magnitude of the slope is less than 2 deg/deg which is extremelyflat, sometimes measured even over a wide range of longitudes. Thisis indeed difficult to explain in a geometrical model, although wecannot rule out that some P.A. swings are the result of extremeaberration effects (which could also depend on period) or can be MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme P . A . ( d e g )
100 200 3000.000.450.90 N o r m a li s e d f l u x J0737-3039A
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50 100Pulse Longitude (deg)0.000.450.90 N o r m a li s e d f l u x J1603-7202
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Figure 1.
Pulse profiles for the relativistic binaries with a complex P.A. swing or where the P.A. swing is not well defined. Apart from PSR J0737 − simply explained by sharp unresolved 180 degree swings for a centralcut, both of which would still indicate a potentially valid geometricalinterpretation of the P.A. swings. Also, as discussed, flat PAs maystill be representing the geometry of a grazing beam, as we believeis the case for PSR J1141 − − MNRAS000
Pulse profiles for the relativistic binaries with a complex P.A. swing or where the P.A. swing is not well defined. Apart from PSR J0737 − simply explained by sharp unresolved 180 degree swings for a centralcut, both of which would still indicate a potentially valid geometricalinterpretation of the P.A. swings. Also, as discussed, flat PAs maystill be representing the geometry of a grazing beam, as we believeis the case for PSR J1141 − − MNRAS000 , 1–21 (2021)
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300 325 3500.000.450.90 N o r m a li s e d f l u x J1930-1852
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Figure 2.
As Fig. 1 continued.
Table 3.
List of pulsars in our sample that show a flat P.A. swing. We listthe measured slope, its uncertainty and the reduced- 𝜒 value to indicate howwell the data can be described by a simple straight P.A. model.PSR Period (ms) P.A. Slope (deg/deg) 𝜒 J1157 − − − − − − − − − − − − with a slope of 3.82(5) deg/deg and a spin period of 394 ms. Thiswould result in a slightly steeper power law index of + . ( ) . For a number of pulsars with a noticeable P.A. swing, combinedwith a sufficiently large number of well defined P.A. values, we haveattempted to apply the RVM because recent results of the relativisticbinary PSR J1906 + 𝛼 ,the viewing angle 𝜁 and the pulse phase, 𝜙 . We show its modifiedform as presented in Johnston & Kramer (2019):P . A . = P . A . + arctan (cid:18) sin 𝛼 sin ( 𝜙 − 𝜙 − Δ ) sin 𝜁 cos 𝛼 − cos 𝜁 sin 𝛼 cos ( 𝜙 − 𝜙 − Δ ) (cid:19) (1)Here, 𝜙 is the pulse longitude at which PA=PA and 𝜁 = 𝛼 + 𝛽 (see Fig. 7). The additional Δ term is present to deal with cases inwhich the emission heights are different between the main pulse anda potentially observed interpulse.We present the results of our RVM fits in the form of the determinedmagnetic inclination angle 𝛼 and the viewing angle 𝜁 in Table 4 andFigs. 6 and 8. We note that we have not been successful in modelingthe P.A. swings using the RVM for PSRs J1017 − − − − − − 𝜁 of recycled pulsars is of interest. For fully recycled pulsars,from evolutionary arguments, we expect the spin vector of the pul-sar to be aligned with the orbital momentum vector. For systemsthat show relativistic spin-precession, we may be able measure theangle between pulsar spin and orbital momentum vector, 𝛿 , as forPSR J1906 + 𝛿 = ± − 𝛿 < 𝜁 with the orbital inclination angle, 𝑖 . Hence, determining 𝜁 via a successful RVM fit offers a way todetermine 𝑖 independently of a Shapiro delay measurement, whichonly allows a measurement of sin 𝑖 . Hence, apart from providing im-portant information for tests of gravity or mass measurements (e.g.,solving the mass function), RVM fitting may indeed also enable usto solve the corresponding 𝑖 or 180 − 𝑖 ambiguity of a Shapiro delaymeasurement.Comparing the value of 𝜁 with the orbital inclination angle requirescaution. We stress that depending on the convention used for themeasurement of the position angle and the applied RVM equation, MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme P . A . ( d e g )
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Figure 3.
Pulse Profiles for the relativistic binary pulsars with flat P.A. swings. See text for details. The data properties and panel descriptions are the same asFig. 1. one needs to identify 𝜁 either with 𝑖 or 180 − 𝑖 . We will demonstratethe power of this additional information with two specific examples,namely the Double Pulsar and PSR 1811 − 𝛼 and the viewing angle, 𝜁 , or thethe impact angle 𝛽 , where 𝜁 = 𝛼 + 𝛽 (see Fig. 7). Importantly, thedefinition of 𝜁 in the RVM binds it to the definition of 𝑖 . Using adefinition of orbital geometry as shown in Fig. 7, which is derivedfrom Damour & Taylor (1992) (see also Kramer & Wex 2009a), MNRAS000
Pulse Profiles for the relativistic binary pulsars with flat P.A. swings. See text for details. The data properties and panel descriptions are the same asFig. 1. one needs to identify 𝜁 either with 𝑖 or 180 − 𝑖 . We will demonstratethe power of this additional information with two specific examples,namely the Double Pulsar and PSR 1811 − 𝛼 and the viewing angle, 𝜁 , or thethe impact angle 𝛽 , where 𝜁 = 𝛼 + 𝛽 (see Fig. 7). Importantly, thedefinition of 𝜁 in the RVM binds it to the definition of 𝑖 . Using adefinition of orbital geometry as shown in Fig. 7, which is derivedfrom Damour & Taylor (1992) (see also Kramer & Wex 2009a), MNRAS000 , 1–21 (2021) Kramer et al. P . A . ( d e g )
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J1757-1854
Figure 4.
Fig. 3 continued. and, crucially, also implemented in the timing software Tempo andTempo2 , we identify 𝜁 = − 𝑖, (2)when pulsar spin axis and the orbital angular momentum vectorare aligned. We call this definition also the “DT92” convention andrefer to the definition of the corresponding position angles as the“RVM/DT92” convention.As Everett & Weisberg (2001) before, we strongly recommend torefer to the pulsar geometry angles in the RVM/DT92 convention. http://ascl.net/1509.002 http://ascl.net/1210.015 Figure 5.
Magnitude of the slopes measured from P.A. swings as listed inTable 3 as a function of pulse period. See text for details.
This can be easily identified. The impact angle is positive , 𝛽 > 𝜁 > 𝛼 , when the slope in the position angles derived by theobserver’s PSR/IEEE convention (as for psrchive) and measured atits steepest gradient (at the centroid or fiducial plane) is negative , andvice versa.As Eqn. 1 is written in the RVM/DT92 convention, fitting it to P.A.smeasured in the PSR/IEEE convention (as in our figures) requires animportant prior step. Either one inverts the P.A. values by multiplyingthem by −
1, or one modifies Eqn. 1 such that one fits for the arguments ( 𝜙 − 𝜙 ) rather than ( 𝜙 − 𝜙 ) , where we set Δ = 𝛼 and 𝜁 caused by the struc-ture of Eqn. 1, the uncertainties of the angles derived from RVM fitsare usually very large if the range of fitted pulse longitudes is lim-ited (see e.g. discussion by Everett & Weisberg 2001 and Lorimer& Kramer 2012). However, when the pulses are wide, and especiallywhen interpulse emission is seen, the precision in the derived anglesis much improved. This can also be seen for the results shown inTable 4. The angles of PSRs J0737 − − − 𝛼 and 𝜁 . The implied orbital inclination an-gle of 𝑖 = ± 𝜁 is still consistent with a range from71 to 99 deg, and the orbital inclination correspondingly. Includingmore P.A. values from the wings of the profile, pushes the solutionto smaller 𝜁 (and 𝛼 ) values, which is a systematic uncertainty thatis not yet reflected in the quoted statistical uncertainties. To gaugethe impact on the overall result, we mark the P.A. values included ineach fit in Fig. 6, so that readers can form their own opinion aboutthe reliability of the results. MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme P . A . ( d e g )
300 320 3400.000.450.90 N o r m a li s e d f l u x J1454-5846
100 125 150
J1727-2946 P . A . ( d e g )
100 2000.000.450.90 N o r m a li s e d f l u x J1757-5322
220 240 260
J1802-2124 P . A . ( d e g ) N o r m a li s e d f l u x J1811-2405
100 200Pulse Longitude (deg)
J1933-6211
Figure 6.
Pulse profiles for relativistic binary pulsars, where we try to model the P.A. with a Rotating Vector Model (RVM) . The data properties and paneldescriptions are the same as Fig. 1. The sub panels showing the P.A.s also show the best-fit rotating vector model as a dash-dotted brown line. The black pointsin the panel are the original P.A. points - now made semi-transparent for clarity. The blue ones are the points that are considered for the RVM fitting. The redpoints are the original locations of some P.A. points that had to be shifted by 90 degrees to account for an orthogonal polarised mode transition, or shifted by180 degrees for fitting convenience. The cyan star is the best-fit position of ( 𝜙 , P.A. ) - see text for more details. We emphasize that one way of constraining the uncertainties isby using an informed non-uniform prior on 𝜁 . With 𝜁 = − 𝑖 foraligned spin and orbital momentum vectors, we can take into accountthat a face-on orbit (small 𝑖 ) is less likely be found than an inclinedorbit, by using a uniform prior on cos 𝜁 . Similarly, if we have goodconstraints on the pulsar and/or companion mass (e.g. from opticalobservations of the companion), one can also use the mass function to construct a prior on 𝑖 and, hence, 𝜁 . Implementing this had littleimpact on our results compared to those obtained with a uniformprior, but there are clearly cases, where such strategies will be usefulas we demonstrate for PSR J0737-3039A in Section 5.1.1. Similarly,one may also adopt non-uniform priors for 𝛼 , for instance in studiesthat include a possible variation of the magnetic inclination angle MNRAS000
Pulse profiles for relativistic binary pulsars, where we try to model the P.A. with a Rotating Vector Model (RVM) . The data properties and paneldescriptions are the same as Fig. 1. The sub panels showing the P.A.s also show the best-fit rotating vector model as a dash-dotted brown line. The black pointsin the panel are the original P.A. points - now made semi-transparent for clarity. The blue ones are the points that are considered for the RVM fitting. The redpoints are the original locations of some P.A. points that had to be shifted by 90 degrees to account for an orthogonal polarised mode transition, or shifted by180 degrees for fitting convenience. The cyan star is the best-fit position of ( 𝜙 , P.A. ) - see text for more details. We emphasize that one way of constraining the uncertainties isby using an informed non-uniform prior on 𝜁 . With 𝜁 = − 𝑖 foraligned spin and orbital momentum vectors, we can take into accountthat a face-on orbit (small 𝑖 ) is less likely be found than an inclinedorbit, by using a uniform prior on cos 𝜁 . Similarly, if we have goodconstraints on the pulsar and/or companion mass (e.g. from opticalobservations of the companion), one can also use the mass function to construct a prior on 𝑖 and, hence, 𝜁 . Implementing this had littleimpact on our results compared to those obtained with a uniformprior, but there are clearly cases, where such strategies will be usefulas we demonstrate for PSR J0737-3039A in Section 5.1.1. Similarly,one may also adopt non-uniform priors for 𝛼 , for instance in studiesthat include a possible variation of the magnetic inclination angle MNRAS000 , 1–21 (2021) Kramer et al. orbital plane sky plane JI I = i j
To ObserverPulsar emission cone
K = K = - n o ^ Ω asc Magnetic axis (µ) . J ^^ Figure 7.
Definition of angles relevant for the viewing geometry of binary pulsars in a coordinate system defined by Damour & Taylor (1992). The plane definedby ˆ i and ˆ j form the orbital plane which is inclined at an angle 𝑖 to the sky plane and rotated in azimuth by the longitude of the ascending node ( Ω asc ). The skyplane is the plane perpendicular to the line of sight vector, ˆ 𝑛 = − K , defined from the pulsar to the observer. The spin angular momentum vector of the pulsaris given by S , here seen to be along the same direction of the orbital angular momentum vector, K . This is true for some binaries where the pulsar has beenfully recycled by a phase of mass accretion from the companion during its evolutionary history. For the cases where this is not true, please see Damour & Taylor(1992) and Venkatraman Krishnan et al. (2019). The magnetic axis of the pulsar ( μ ) is inclined from the spin axis by an angle 𝛼 . The radio emission conesubtends an angle 𝜌 from μ . The closest approach of the observer’s line-of-sight to μ marks the impact parameter 𝛽 , which relates to the total viewing angle as 𝜁 = 𝛼 + 𝛽 . The angle subtended by S and K is 𝜆 , which for pulsars with no spin-orbit misalignment follows 𝜆 = − 𝜁 = 𝑖 . Note that the polarisation angle Ψ is defined as the angle subtended by the projection of S on the sky plane from I in the clockwise direction as viewed from the +K direction, which is theopposite sense to the observer’s convention - see text. on long timescales. The results shown in Table 4 were obtained withuniform priors on the angles, except in the case of PSR J0737-3039A.In summary, we clearly recommend treating the results of RVMfits, especially to mildly or fully recycled pulsars with care. On theother hand, we do have a number of pulsars the RVM fits are com-pelling: We discuss PSR J0737-3039A using a polarisation profilebased on a longer observation (see Figure 8) in more detail in Sec-tion 5.1.1. We further discuss PSR J1811 − 𝑖 ambiguity or estimating whethera Shapiro delay measurement may be possible at all. Indeed, the us-age of the “pulse structure information” – given by the profile andits polarisation properties – can be very powerful. This informationcomplementary to the timing, cannot only help to determine orbitalinclination angles for mass determinations, but especially also fortests of gravity. This is demonstrated here, consistent with the recentwork by Desvignes et al. (2019) or earlier by Stairs et al. (2004). Table 4.
Viewing geometry as derived from fits of the RVM to a subset ofthe pulsars. The magnetic inclination angle 𝛼 and the viewing angle 𝜁 aregiven. Their values and uncertainties quoted correspond to the median andthe 16 and 84 percentiles of the posterior distribution, respectively. The lastcolumn lists the orbital inclination angle, 𝑖 , as implied from the obtained 𝜁 value (see text for details).PSR 𝛼 (deg) 𝜁 (deg) Implied 𝑖 (deg)J0737 − ∗ − − − − − − ∗ The priors for 𝜁 were restricted using existing timingconstraints on the inclination angle.MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme P . A . ( d e g )
100 200 300Pulse Longitude0.00.20.40.60.81.0 N o r m a li s e d f l u x J0737-3039A
Figure 8.
Fit of the modified RVM model given in equation 1 to the P.A.of PSR J0737 − Our science goals and measurement strategy as outlined in Section 2usually require an extended timing baseline, which for all sourcesselected for RelBin at this point can be provided from previous ob-servations with other telescopes. In order to reliably predict the ex-pected measurement precision for the PK parameters and masses thatwe want to measure within RelBin, dedicated studies like those byHu et al. (2020) need to be conducted. However, as indicated in Sec-tion 2, we can already gauge the potential of RelBin by comparing thetiming precision that we obtained with MeerKAT thus far, with thatpresented for each pulsar in prior literature. We emphasize that this isa conservative estimate, since our values listed in Table 1 are obtainedfor a standard observing and processing set-up. In a final analysis,the choice of receivers (“UHF”, “L-Band” or “S-Band”) and analysispipeline (e.g. frequency-evolving templates for our wide-band data)will be optimized for every source individually. Hence, the alreadyvisible, often large improvement in the timing precision is impressiveand fills us with great confidence that we can achieve our objectives.We comment on selected individual cases below and also refer tothe PTA programme (Spiewak et al. in prep.) and future publicationsdedicated to the various sources for more details. − The Double Pulsar is a unique double neutron star system whereboth component neutron stars in the system are active radio pulsars.Due to relativistic spin-precession, the radio pulse of the companion (J0737 − ∼ . × better at UHF than at L-band. The im-proved timing precision compared to less-sensitive observations andbetween L-Band and UHF that has been achieved already, suggeststhat Double Pulsar timing will not be limited by pulse jitter, at leastuntil the SKA comes online (Hu et al. 2020). With MeerKAT wewill continue to time the pulsar at both frequency bands, as sig-nificant DM variations are observed (Kramer et al., in prep.). Thisdual-frequency approach allows us to better connect our MeerKATdata with existing data sets from other telescopes.The polarisation profile shown in Fig. 1 confirms the polarisationdata presented by Kramer & Stairs (2008) and is specifically consis-tent in the degree of polarisation, the sense of circular polarisationand the direction of the P.A. swing. We note that this is in contrastto earlier polarisation data published by Demorest et al. (2004) orHotan et al. (2005). In order to determine the geometry, Demorestet al. (2004) applied RVM fits to their data with the conclusion thatthey favoured an aligned (small 𝛼 ) geometry. In contrast, Guillemotet al. (2013) attempted to fit a standard RVM to the polarisaton dataof Kramer & Stairs (2008) and derived values for 𝛼 and 𝜁 close to90 deg. An orthogonal geometry was also derived by Ferdman et al.(2013), based on considerations of the profile stability in the pos-sible context of spin-precession. We decided to improve further onthe pulse profile shown in Fig. 1 with additional observing time. Theresulting profile is shown, also with more detail, in Fig. 8. FittingEqn. 1 to these data results in the geometry presented in Table 4. Weconfirm that the pulsar is in fact an orthogonal rotator, i.e. we seethe emission from opposite magnetic poles. As we explain below, inorder to derive this result, we used the information that is availableon the orbital inclination angle, i.e. we observe an edge-on orbit. Themeasurement of a Shapiro delay gives a value of 𝑖 = . (− . , + . ) deg, or 𝑖 = . (− . , + . ) as measured by Kramer et al. (2006),whereas an extended data set suggests an angle somewhat closerto 90 deg (but consistent with the previous value, Kramer et al., inprep.) and by modelling of the relativistic spin-precession of pulsarB (J0737 − − − MNRAS000
Fit of the modified RVM model given in equation 1 to the P.A.of PSR J0737 − Our science goals and measurement strategy as outlined in Section 2usually require an extended timing baseline, which for all sourcesselected for RelBin at this point can be provided from previous ob-servations with other telescopes. In order to reliably predict the ex-pected measurement precision for the PK parameters and masses thatwe want to measure within RelBin, dedicated studies like those byHu et al. (2020) need to be conducted. However, as indicated in Sec-tion 2, we can already gauge the potential of RelBin by comparing thetiming precision that we obtained with MeerKAT thus far, with thatpresented for each pulsar in prior literature. We emphasize that this isa conservative estimate, since our values listed in Table 1 are obtainedfor a standard observing and processing set-up. In a final analysis,the choice of receivers (“UHF”, “L-Band” or “S-Band”) and analysispipeline (e.g. frequency-evolving templates for our wide-band data)will be optimized for every source individually. Hence, the alreadyvisible, often large improvement in the timing precision is impressiveand fills us with great confidence that we can achieve our objectives.We comment on selected individual cases below and also refer tothe PTA programme (Spiewak et al. in prep.) and future publicationsdedicated to the various sources for more details. − The Double Pulsar is a unique double neutron star system whereboth component neutron stars in the system are active radio pulsars.Due to relativistic spin-precession, the radio pulse of the companion (J0737 − ∼ . × better at UHF than at L-band. The im-proved timing precision compared to less-sensitive observations andbetween L-Band and UHF that has been achieved already, suggeststhat Double Pulsar timing will not be limited by pulse jitter, at leastuntil the SKA comes online (Hu et al. 2020). With MeerKAT wewill continue to time the pulsar at both frequency bands, as sig-nificant DM variations are observed (Kramer et al., in prep.). Thisdual-frequency approach allows us to better connect our MeerKATdata with existing data sets from other telescopes.The polarisation profile shown in Fig. 1 confirms the polarisationdata presented by Kramer & Stairs (2008) and is specifically consis-tent in the degree of polarisation, the sense of circular polarisationand the direction of the P.A. swing. We note that this is in contrastto earlier polarisation data published by Demorest et al. (2004) orHotan et al. (2005). In order to determine the geometry, Demorestet al. (2004) applied RVM fits to their data with the conclusion thatthey favoured an aligned (small 𝛼 ) geometry. In contrast, Guillemotet al. (2013) attempted to fit a standard RVM to the polarisaton dataof Kramer & Stairs (2008) and derived values for 𝛼 and 𝜁 close to90 deg. An orthogonal geometry was also derived by Ferdman et al.(2013), based on considerations of the profile stability in the pos-sible context of spin-precession. We decided to improve further onthe pulse profile shown in Fig. 1 with additional observing time. Theresulting profile is shown, also with more detail, in Fig. 8. FittingEqn. 1 to these data results in the geometry presented in Table 4. Weconfirm that the pulsar is in fact an orthogonal rotator, i.e. we seethe emission from opposite magnetic poles. As we explain below, inorder to derive this result, we used the information that is availableon the orbital inclination angle, i.e. we observe an edge-on orbit. Themeasurement of a Shapiro delay gives a value of 𝑖 = . (− . , + . ) deg, or 𝑖 = . (− . , + . ) as measured by Kramer et al. (2006),whereas an extended data set suggests an angle somewhat closerto 90 deg (but consistent with the previous value, Kramer et al., inprep.) and by modelling of the relativistic spin-precession of pulsarB (J0737 − − − MNRAS000 , 1–21 (2021) Kramer et al. . . . . . . . . . . . . . . . O r b i t a l ph a s e ( d e g ) L-band . . . . . . UHF-band
Figure 9.
A plot of the pulsed intensity modulation of J0737 − ∼
180 ms). It can be clearly seen that the modulation is at the spin period of the companion, which is ∼
20 40 60 80 100 120Time (mins)9001000110012001300140015001600 F r e q u e n c y ( M H z ) Figure 10.
Dynamic Spectrum of the Double Pulsar, obtained from a 2-hrobservation of the pulsar. The stretching and squeezing of the blobs of powerare caused due to the pulsar’s orbital motion. relativistic spin-precession of and a sixth independent test of gravitywith the Double Pulsar (Breton et al. 2008).We can demonstrate the increased sensitivity of MeerKAT in Fig- ure 9, where the eclipse seen with the UHF-receiver has a S/N almostthree times better than the eclipse measured with the MeerKAT L-band receiver. We note that the UHF-eclipse is also measured threetime better than with the GBT at the same frequency range (dueto larger sensitivity and less spill-over contribution to the systemtemperature). Combined with the improved polarisation purity ofMeerKAT, these observations will enable detailed studies of spectro-polarimetric variations in the pulses of PSR J0737 − − Ω B , when compared tothe results of Breton et al. (2008). We find that we can obtain ameasurement of Ω B with comparable precision using only two inde-pendently measured eclipses separated by 1.5 years. By combiningthese eclipses with the results of Breton et al. (i.e. referring back toDecember, 2003), we can expect to measure Ω B to about 1% accu- MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme racy, thereby improving the precision of this gravity test by aboutan order of magnitude or more. These estimates are somewhat con-servative, as we will have many more eclipses available from ourmonthly observations, in addition to current work on improving theeclipse analysis tools.We indicated that the RVM modelling presented in Section 4.3.2was done with an uniform prior on 𝜁 between ( . − . − . ) deg and ( . + . + . ) deg. Extending the prior range by anadditional 3 deg, beyond the 0 . 𝛿 < Δ = − . ( ) deg value can be interpreted as a significant loweremission height for the interpulse, when compared to the main pulse.In order to check the robustness of the result, we also modelled the twopoles separately, with separate RVMs. Interestingly, the obtained 𝛼 values, and even the P.A. values (which is not necessarily expected)are perfectly consistent, not only with each other but also with thejoint fit presented earlier, albeit with larger uncertainties as expected.As a further check, we can see if the pulse widths are consistentwith the obtained geometry. For both main and inter pulse, we mea-sure a pulse width at a 10%-intensity level of about 𝑊 ∼
72 degusing a method described by Kramer et al. (1994). We can use thefollowing relationshipcos 𝜌 = cos 𝛼 cos 𝜁 + sin 𝛼 sin 𝜁 cos ( 𝑊 / ) (3)(Gil et al. 1984) to infer the beam radius, 𝜌 . We obtain 𝜌 MP = . 𝜌 IP = . 𝜌 that we expect if the pulsar followsa known 𝜌 = 𝑘 × 𝑃 − . scaling relationship, whereas 𝑘 ranges from4.9 to 6.5 deg s . , resulting in an uncertainty that is larger than thatof the measured width (see the discussion by Venkatraman Krishnanet al. 2019). Nevertheless, if this can be applied here, we expect 𝜌 tobe between 33 and 44 deg, which is in excellent agreement with ourestimate derived from the RVM. It is also notable that the geometryderived from the RVM allows naturally for the poles to have thesame beam radius and a resulting equal pulse width. This cannot benecessarily expected (from random combinations of 𝛼 and 𝜁 ) butagrees with the observations.Despite the prior for 𝜁 ranging uniformly between ∼
85 deg to ∼ 𝜁 = . ± . 𝑖 = . ( ) >
90 deg. We note that thisvalue is larger than an updated timing value reported later (Kramer etal. in prep.), but most importantly it is inconsistent with the result byRickett et al. (2014) who used scintillation measurements to derive 𝑖 = . ( ) <
90 deg .Indeed, the Double Pulsar is among a small number of binarysystems for which the system geometry can also be inferred frominterstellar scintillation properties using a method that was pioneeredby Lyne (1984). The dynamic spectrum in Figure 10 shows variationin pulsar A’s flux due to interstellar scintillation. The scintillationtimescale varies with orbital phase, owing to the changing transversecomponent of the pulsar’s orbital velocity. Long term monitoring ofthis scintillation provides a way to uniquely determine parameters ofthe orbit including the inclination angle 𝑖 and longitude of ascendingnode Ω (Lyne 1984; Ord et al. 2002; Rickett et al. 2014; Reardonet al. 2019). As Figure 10 shows, we can clearly apply the method to P . A . ( d e g ) N o r m a li s e d f l u x J1141-6545
Figure 11.
A high time-resolution plot of the polarised intensity profileof PSR J1141 − the Double Pulsar, which will allow us to either confirm the earlierresults by Rickett et al. (2014) or decide in favour of the RVMestimate. We note that a geometrical model of scattering is required inorder to correct for any significant time-variability in the spatial scaleof the scintillation pattern (Cordes & Rickett 1998). Measurementsof the scintillation over wide bandwidths, for example with near-simultaneous L-band and UHF observations, can be used to improvethis model. If the geometry can be understood, modelling of thedynamic spectrum can also be used to estimate the pulsar distanceand proper motion (Reardon et al. 2019). − PSR J1141 − . (cid:46)
200 s) of the whitedwarf companion (Venkatraman Krishnan et al. 2020). This is thefirst known binary pulsar where the astrophysical interpretation of the
MNRAS000
MNRAS000 , 1–21 (2021) Kramer et al. orbital dynamics requires contributions from relativistic spin-orbitcoupling, known as the Lense-Thirring effect; this is non negligiblefraction of the total observed spin-orbit coupling. Further timing ofthis pulsar will help to better constrain the spin period of the whitedwarf (cf. Wex 1998; Wex & Kopeikin 1999).The pulsar also undergoes geodetic precession, leading to a secularchange in its pulse shape. Geodetic precession of PSR J1141 − 𝜇 son April 8th 2020. The data were folded at the best known topocentricperiod of the pulsar with 8192 bins across its rotational phase, afterwhich it was calibrated for polarisation and scrunched in frequencyand time. Figure 11 shows the pulsar polarisation profile and theP.A. swing. It can be seen from the figure that a 90 degree phasejump of the P.A. swing occurs, accompanied by a sudden dip in thelinear polarisation. Combined, these show that the jump is indeed anOPM transition, solving the degeneracy faced by the earlier analysiswith lesser S/N data from the Parkes telescope. This deduction canbe fed back as a prior information to the full precessional RVManalysis to further understand its geodetic precession. As discussedin Section 4.3, such a flat P.A. curve is in principle difficult to describewithin the RVM, but its changes with time (especially in the measuredabsolute value of the P.A.) due to relativistic spin precession stillprovides valuable additional information. − PSR J1756 − . (cid:164) 𝑃 b that was reportedly inconsistent withthe value predicted by GR at the 2 − 𝜎 confidence level. Motivatedby this result, we had included this source in the RelBin programme.The observations are already successful, as shown in Figure 12 wherewe demonstrate the measurement of the Shapiro delay in the systemwith a single 8-hour long ( ∼ full orbit) observation of the pulsar.This is in contrast to the Shapiro delay measurement presented byFerdman et al. (2014) for their whole available dataset (see theirFigure 3). Holding other parameters fixed and fitting for spin period,DM, orbital phase, and the Shapiro delay PK parameters, we measure 𝑟 = . ± . 𝑀 (cid:12) and 𝑠 ≡ sin 𝑖 = . ± .
04, of similar precisionas and consistent with Ferdman et al. (2014). p o s t - f i t r e s i d u a l s ( m s ) J1756-2251
Orbital phase p o s t - f i t r e s i d u a l s ( m s ) Figure 12.
Shapiro delay signature in PSR J1756 − ∼ . 𝜇𝑠 . Fitting for theKeplerian orbital parameters absorb part of the Shapiro delay leading to animprovement in the RMS to ∼ 𝜇𝑠 . Fitting for the Shapiro delay parametersfurther improves the RMS to ∼ . 𝜇𝑠 in the bottom panel. As of November 2020, we have completed orbital campaigns for 10pulsars, where we performed long observations over superior con-junction, followed by observations filling other parts of the orbit, andregular observations over the year to obtain a better timing baseline.Here, we only present some highlights for a subset of them, in or-der to demonstrate the ability of MeerKAT and the prospects of theRelBin programme. − PSR J1757 − − hour binary sys-tem around an optically identified white dwarf companion (Edwards& Bailes 2001; Jacoby et al. 2006). The pulsar shows remarkablespectral features due to interstellar scintillation, owing to its proxim-ity. This presents yet another avenue to measure some of the orbitalparameters through scintillometry.Here, we present secondary spectrum (Fourier transform of thedynamic spectrum) from a 90 minute observation of this pulsar isshown in Figure 13. This reveals a parabolic scintillation arc. Thedegree of curvature for this arc depends on the distance to the sourceof scattering in the interstellar plasma, as well as the transversevelocity of the line of sight through this plasma. The dependence MNRAS , 1–21 (2021) he MeerKAT Relativistic Binary Programme f t (mHz)050010001500200025003000 f ( m ) Figure 13.
Secondary spectrum of J1757 − on velocity causes the arcs to change in curvature with the pulsar’sbinary velocity as a function of orbital phase. Measurements of thisorbital modulation can be used to precisely determine 𝑖 and Ω (asin Reardon et al. submitted ). This measurement shows that we willbe able to check the validity of our RVM results (see Section 4.3.2),even though initial timing efforts suggest that any Shapiro delaysignal is weak. This result also demonstrates the good prospects ofthis method for other RelBin sources, on which we will report later. − PSR J1811 − ∼ . 𝑀 p = . + . − . 𝑀 (cid:12) . We undertookobservations of this pulsar with MeerKAT with the aim of obtaininga better detection of the Shapiro delay. We recorded a total of ∼ ∼
14 months, including a dense orbital campaign.During the orbital campaign, the pulsar was observed for 1 hourevery day for a 7 day period ( ∼ 𝜎 error bars includes all regionsbetween ∼ . 𝑀 (cid:12) , we can obtain insight for the WD com-panion: its mass is only 2- 𝜎 compatible with the prediction of Tauris& Savonije (1999) of ∼ . 𝑀 (cid:12) , which assumes the companion is Table 5.
Shown are the post-fitting model parameter values forPSR J1811 − ± 𝜎 uncertainties.Spin and astrometric parametersRight ascension, 𝛼 (J2000) 18:11:19.85405(3)Declination, 𝛿 (J2000) − 𝜇 𝛼 (mas yr − ) 0.6(1)Spin frequency, 𝜈 (Hz) 375.856020042883244(7)Spin down rate, (cid:164) 𝜈 (s − ) -1.8895(3) × − Dispersion measure, DM (cm − pc) 60.615(1)Rotation measure (rad m − ) 30.3(2)Binary parametersOrbital period, 𝑃 orb (days) 6.27230620515(7)Projected semi-major axis, 𝑥 (lt-s) 5.705656754(4)Epoch of periastron, 𝑇 (MJD) 56328.98(2)Longitude of periastron, 𝜔 ( ◦ ) 62(1)Orbital eccentricity, 𝑒 × − Orthometric amplitude, ℎ ( μ s) 0.70(3)Orthometric ratio, 𝜍 𝑀 c ( 𝑀 (cid:12) ) 0 . + . − . Pulsar mass from Bayesian analysis, 𝑀 p ( 𝑀 (cid:12) ) 1 . + . − . Orbital inclination from Bayesian analysis, 𝑖 ◦ . + ◦ . − ◦ . Timing modelBinary model DDFWHESolar System ephemeris DE435Reference epoch of period (MJD) 56330.0Reference epoch of dispersion and rotation mea-sure measurements (MJD) 58750.6First ToA (Rounded MJD) 55871Last ToA (Rounded MJD) 58948Weighted RMS residuals ( μ s) 0.583Reduced 𝜒 a He WD. If the WD companion really is much more massive thanthat, then it might be a CO WD instead. In this case the MSP couldalso be substantially more massive than the ∼ . 𝑀 (cid:12) that it wouldhave if the companion mass were 0.22 𝑀 (cid:12) .Future orbital campaigns of this system with MeerKAT with theUHF (where the pulsar is brighter) and the S-band (where the pulseprofile is known to have narrow features) receivers have the potentialto improve the current estimates of the masses, and resolve both theissue of the nature of the WD companion and provide a more preciseestimate of the pulsar mass.We use this pulsar also to demonstrate how an RVM fit discussed inSection 4.3 can be used to break the sin 𝑖 ambiguity of the Shapiro de-lay measurement. We point out that Ng et al. (2020) already obtainedan RVM fit to Parkes data. Our data and solution presented here aremore precise but fully consistent with the earlier result. As shown inTable 4, our RVM fit done with a uniform prior for 𝜁 over the full 0 to180 deg range, results in an estimate for an orbital inclination angleof 𝑖 = . ( ) deg. This does not only break the sin 𝑖 ambiguitybut is also in perfect agreement with the Shapiro delay measurementin numerical value. This is indeed both the case when fitting for anon-zero Δ parameter as in Eqn. 1 (obtaining Δ = . ± . Δ =
0, with entries as in Tab. 4). Consequently,we list the inclination angle in Table 5 as 𝑖 = ◦ . + ◦ . − ◦ . deg. MNRAS000
0, with entries as in Tab. 4). Consequently,we list the inclination angle in Table 5 as 𝑖 = ◦ . + ◦ . − ◦ . deg. MNRAS000 , 1–21 (2021) Kramer et al.
T&S99 T&S99 ς ς h h Figure 14.
Mass and orbital inclination constraints for PSR J1811 − ℎ ) in solid blue and the orthometric ratio ( 𝜍 ) in dottedblue (Freire & Wex 2010). The solid black contours represent the 2-D probability distribution with their marginalized 1-D distributions represented in the topand right panels. The orange dotted lines indicate the nominal companion mass for the given orbital period as predicted by Tauris & Savonije (1999) for binarypulsars with Helium white dwarf companions. : 1.52 ± 0.07 ms0.94 GHz J1227-6208 : 0.92 ± 0.07 ms0.94 GHz
J1757-1854 : 51 ± 10 ms0.94 GHz
J1811-1736 : 0.67 ± 0.02 ms1.23 GHz : 0.38 ± 0.02 ms1.23 GHz : 21.6 ± 0.7 ms1.23 GHz
Time (ms) : 0.24 ± 0.02 ms1.62 GHz
Time (ms) : 0.13 ± 0.07 ms1.62 GHz
Time (ms) : 8.2 ± 0.2 ms1.62 GHz N o r m a li z e d I n t e n s i t y Figure 15.
Measurements of scattering timescales at three selected sub-bands for PSRs J1227 − − − , 1–21 (2021) he MeerKAT Relativistic Binary Programme ^^^ Figure 16.
Measured scattering times measured for PSRs J1227-6208,J1757 − Our initial results presented above suggest that MeerKAT will pro-vide superior data compared to those already available from lesssensitive telescopes. This includes wide-bandwidth full-polarisationdata of the observed pulse profiles as well as high-precision timingdata. We have used “pulse structure” data to obtain additional in-formation that is useful for undertaking tests of relativistic gravity,as was first suggested by Damour & Taylor (1992). We have alsoshown that the simultaneous dynamic spectra obtained over largebandwidths yield yet another dimension that can be explored for ourscience goals. Finally, the well-calibrated, high S/N pulse profiles al-low us to obtain a measured timing precision, which scales with bothincreased S/N as well as our ability to resolve narrow pulse features(e.g. Lorimer & Kramer 2012). Despite these impressive improve-ments available with MeerKAT we point out that the already existingdata sets obtained with other telescopes will remain an essential inputin the timing analysis presented in dedicated publications elsewhere, as they provide the long timing baseline that is essential to measuresecular PK parameters.We have demonstrated the performance of MeerKAT at L-Bandand UHF frequencies; the RelBin programme will also make excel-lent use of the upcoming S-band system. Some pulsars have beenfound to have improved timing precision at these higher frequen-cies (e.g. PSR J1757 − − − − − − 𝜏 ∝ 𝑓 − ˆ 𝛼 . The results of those fits is shownin Fig. 16. The spectral indices, ˆ 𝛼 , found are all near − (cid:46) 𝜇 s precision for observations with the upcoming S-band system.Even for PSR J1811 − 𝜇 s. This result is consistentwith Corongiu et al. (2007), who also measured the same scatteringindex of − . ( ) and already suggested that timing at higher fre-quencies will provide superior precision of the timing parameters.With this in mind, we expect to be able to make an improved mea-surement of (cid:164) 𝜔 and a first measurement of the Shapiro delay, andpotentially the PK parameter 𝛾 for PSR J1811 − − − − MNRAS000
Measured scattering times measured for PSRs J1227-6208,J1757 − Our initial results presented above suggest that MeerKAT will pro-vide superior data compared to those already available from lesssensitive telescopes. This includes wide-bandwidth full-polarisationdata of the observed pulse profiles as well as high-precision timingdata. We have used “pulse structure” data to obtain additional in-formation that is useful for undertaking tests of relativistic gravity,as was first suggested by Damour & Taylor (1992). We have alsoshown that the simultaneous dynamic spectra obtained over largebandwidths yield yet another dimension that can be explored for ourscience goals. Finally, the well-calibrated, high S/N pulse profiles al-low us to obtain a measured timing precision, which scales with bothincreased S/N as well as our ability to resolve narrow pulse features(e.g. Lorimer & Kramer 2012). Despite these impressive improve-ments available with MeerKAT we point out that the already existingdata sets obtained with other telescopes will remain an essential inputin the timing analysis presented in dedicated publications elsewhere, as they provide the long timing baseline that is essential to measuresecular PK parameters.We have demonstrated the performance of MeerKAT at L-Bandand UHF frequencies; the RelBin programme will also make excel-lent use of the upcoming S-band system. Some pulsars have beenfound to have improved timing precision at these higher frequen-cies (e.g. PSR J1757 − − − − − − 𝜏 ∝ 𝑓 − ˆ 𝛼 . The results of those fits is shownin Fig. 16. The spectral indices, ˆ 𝛼 , found are all near − (cid:46) 𝜇 s precision for observations with the upcoming S-band system.Even for PSR J1811 − 𝜇 s. This result is consistentwith Corongiu et al. (2007), who also measured the same scatteringindex of − . ( ) and already suggested that timing at higher fre-quencies will provide superior precision of the timing parameters.With this in mind, we expect to be able to make an improved mea-surement of (cid:164) 𝜔 and a first measurement of the Shapiro delay, andpotentially the PK parameter 𝛾 for PSR J1811 − − − − MNRAS000 , 1–21 (2021) Kramer et al.
We presented the science case and initial results from the MeerTimerelativistic binary programme (RelBin) with the MeerKAT telescope.Our observations demonstrate that MeerKAT is an powerful pulsarinstrument, and is capable of delivering high fidelity data that willyield tests of theories of gravity as well as a large sample of newor significantly improved mass measurements. This is made possibleby superior timing precision in combination with additional infor-mation derived from polarisation profiles and dynamic spectra. Wedemonstrated this by presenting a rare collection of well calibratedpolarisation profiles of suitable pulsars and their analysis. We demon-strate the utility of dynamic spectra to determine system geometriesby modelling changes in the scintillation properties. Full-polarisationinformation is also crucial for achieving the anticipated timing pre-cision (van Straten 2006). Hence, it is important to also confirm thatthe polarisation properties of the instrument are consistent across theobserving bands, while the long term timing stability ensures highprecision pulsar timing. Our observations through the lifetime ofMeerTime hence have the potential to significantly contribute to ourknowledge of neutron star masses and further understanding gravity.Finally, we indicated the potential of high-precision timing observa-tions with the S-band system. We will report on first results with thissystem when available. With the initial results presented here, we areconfident that RelBin can achieve the science goals it has set out toattain.
ACKNOWLEDGEMENTS
The MeerKAT telescope is operated by the South African RadioAstronomy Observatory, which is a facility of the National ResearchFoundation, an agency of the Department of Science and Innova-tion. SARAO acknowledges the ongoing advice and calibration ofGPS systems by the National Metrology Institute of South Africa(NMISA) and the time space reference systems department depart-ment of the Paris Observatory. MeerTime data is housed on theOzSTAR supercomputer at Swinburne University of Technology.The Parkes radio telescope is funded by the Commonwealth of Aus-tralia for operation as a National Facility managed by CSIRO. Thisresearch has made extensive use of NASAs Astrophysics Data Sys-tem (https://ui.adsabs.harvard.edu/) and includes archived data ob-tained through the CSIRO Data Access Portal (http://data.csiro.au).Parts of this research were conducted by the Australian ResearchCouncil Centre of Excellence for Gravitational Wave Discovery (Oz-Grav), through project number CE170100004 and the Laureate fel-lowship number FL150100148. The MeerTime Pulsar Timing Arrayacknowledges support of the Gravitational Wave Data Centre fundedby the Department of Education via Astronomy Australia Ltd. andADACS. MBu, APo, and AR used resources from the research grant“iPeska” (P.I. Andrea Possenti) for this work, funded under the INAFnational call Prin-SKA/CTA approved with the Presidential Decree70/2016. RMS acknowledges support through Australian ResearchCouncil fellowship FT190100155. LO acknowledges funding fromthe UK Science and Technology Facilities Council (STFC) GrantCode ST/R505006/1. MK, VVK, PCCF, FA, DJC, TG, AP, NW, andEDB acknowledge continuing valuable support from the Max-PlanckSociety.
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author.
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