High Precision Measurements of Interstellar Dispersion Measure with the upgraded GMRT
M. A. Krishnakumar, P. K. Manoharan, Bhal Chandra Joshi, Raghav Girgaonkar, Shantanu Desai, Manjari Bagchi, K. Nobleson, Lankeswar Dey, Abhimanyu Susobhanan, Sai Chaitanya Susarla, Mayuresh P. Surnis, Yogesh Maan, A. Gopakumar, Avishek Basu, Neelam Dhanda Batra, Arpita Choudhary, Kishalay De, Yashwant Gupta, Arun Kumar Naidu, Dhruv Pathak, Jaikhomba Singha, T. Prabu
AAstronomy & Astrophysics manuscript no. InPTAhighprecDM © ESO 2021January 18, 2021
High Precision Measurements of Interstellar Dispersion Measurewith the upgraded GMRT
M. A. Krishnakumar (cid:63) , P. K. Manoharan , Bhal Chandra Joshi , Raghav Girgaonkar , Shantanu Desai , ManjariBagchi , , K. Nobleson , Lankeswar Dey , Abhimanyu Susobhanan , Sai Chaitanya Susarla , Mayuresh P. Surnis ,Yogesh Maan , A. Gopakumar , Avishek Basu , Neelam Dhanda Batra , , Arpita Choudhary , Kishalay De ,Yashwant Gupta , Arun Kumar Naidu , Dhruv Pathak , , Jaikhomba Singha , T. Prabu Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany Arecibo Observatory, University of Central Florida, Arecibo, PR 00612, USA National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Ganeshkhind, Pune 411007, Maharashtra, India Department of Physics, Indian Institute of Technology Hyderabad, Kandi, Telangana 502285, India The Institute of Mathematical Sciences, C. I. T. Campus, Tharamani, Chennai 600113, Tamil Nadu, India Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, Maharashtra, India Department of Physics, BITS Pilani Hyderabad Campus, Hyderabad 500078, Telangana, India Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Mumbai 400005,Maharashtra, India Indian Institute of Science Education and Research Thiruvananthapuram, Vithura, Kerala 695551, India Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands Department of Physics, Indian Institute of Technology Delhi, New Delhi-110016, India Cahill Center for Astrophysics, California Institute of Technology, 1200 E. California Blvd. Pasadena, CA 91125, USA University of Oxford, Sub-Department of Astrophysics, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, United King-dom Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India Raman Research Institute, Bengaluru 560080, Karnataka, IndiaReceived XXX XX, XXXX; accepted YYY YY, YYYY
ABSTRACT
Context.
Pulsar radio emission undergoes dispersion due to the presence of free electrons in the interstellar medium (ISM). Thedispersive delay in the arrival time of pulsar signal changes over time due to the varying ISM electron column density along the lineof sight. Correcting for this delay accurately is crucial for the detection of nanohertz gravitational waves using Pulsar Timing Arrays.
Aims.
We aim to demonstrate the precision in the measurement of dispersion delay achieved by combining 400 −
500 MHz (
BAND3 )wide-band data with those at 1360 − BAND5 ) observed using the upgraded GMRT, employing two di ff erent templatealignment methods. Methods.
To estimate the high precision dispersion measure (DM), we measure high precision times-of-arrival (ToA) of pulses usingcarefully generated templates and the currently available pulsar timing techniques. We use two di ff erent methods for aligning thetemplates across frequency to obtain ToAs over multiple sub-bands, and therefrom measure the DMs. We study the e ff ects of thesetwo di ff erent methods in detail on the measured DM values. Results.
We present in-band and inter-band DM estimates of four pulsars over the timescale of a year using two di ff erent templatealignment methods. The DMs obtained using both these methods show only subtle di ff erences for PSR J1713 + − ff set is seen in the DM of PSR J1939 + − ff set between the DMs obtained. Irrespective of the template alignment methods followed, the precision on the DMs obtained is about10 − pc cm − using only BAND3 and 10 − pc cm − after combining data from BAND3 and
BAND5 of the uGMRT. In a particularresult, we have detected a DM excess of about 5 × − pc cm − on 24 February 2019 for PSR J2145 − Key words. pulsars:general – ISM:general – Gravitational Waves – Sun:coronal mass ejections
1. Introduction
Pulsars are rotating neutron stars that emit broadband radiationreceived as pulsed signals by the observers. The pulsar radiationreaches the observer after propagating through the ionised inter- (cid:63)
E-mail: [email protected] stellar medium (IISM) which disperses the pulsed signal, therebydelaying the times of arrival (ToAs) of pulses as a function of theobserving frequency (Lorimer & Kramer 2004). This dispersiondelay is directly proportional to the integrated column density offree electrons in the IISM, usually referred to as the dispersionmeasure (DM), and inversely proportional to the square of the
Article number, page 1 of 11 a r X i v : . [ a s t r o - ph . H E ] J a n & A proofs: manuscript no. InPTAhighprecDM observing frequency ( ν ). Precise measurements of the DM cantherefore be made by measuring the pulse ToAs simultaneouslyat di ff erent observing frequencies (e.g. Backer 1996; Ahuja et al.2005, 2007).The DM of a pulsar can vary with time due a number ofreasons that include the relative motion of the pulsar with re-spect to the observer, solar wind, terrestrial ionosphere, and thedynamical nature of the IISM. Typical DM variations observedin pulsars range from 10 − – 10 − pc cm − (Kumar et al. 2013;Alam et al. 2020; Donner et al. 2020). If these variations arenot accounted for, systematic errors of the order of 1 µ s or morecan arise while correcting for the DM delay to generate infinite-frequency ToAs in the solar system barycentre (SSB) frame(Hobbs et al. 2006; Edwards et al. 2006). Such unaccounted sys-tematics have the potential to degrade the ability of millisecondpulsars (MSP) to act as very accurate celestial clocks (Hobbset al. 2019). The technique of pulsar timing that creates such ce-lestial clocks requires us to model and characterize correctly thepulse propagation e ff ects (Edwards et al. 2006). This techniqueis crucial for the rapidly maturing Pulsar Timing Array (PTA)e ff orts to detect nanohertz gravitational waves (Foster & Backer1990; Arzoumanian et al. 2020). PTAs pursue timing of tens ofMSPs to detect mainly a stochastic nanohertz gravitational wavebackground due to an ensemble of merging supermassive blackhole binaries (Burke-Spolaor et al. 2019).There are three established PTA e ff orts and they are theParkes Pulsar Timing Array (PPTA: Hobbs 2013; Kerr et al.2020), the European Pulsar Timing Array (Kramer & Champion2013; Desvignes et al. 2016), and the North American NanohertzObservatory for Gravitational Waves (NANOGrav: McLaughlin2013; Alam et al. 2020). In addition, PTA e ff orts are gatheringpace in India under the auspices of the Indian Pulsar Timing Ar-ray (InPTA: Joshi et al. 2018). The International Pulsar TimingArray (IPTA) consortium combines data and resources from var-ious PTA e ff orts to enable faster detection of nanohertz GWs(Perera et al. 2019). It should be noted that high precision DMmeasurements are essential for reaching the desired sensitivitiesof existing PTAs as precise pulse ToA estimates depend on ac-curate DM measurements. While PPTA mostly relies on dataabove 800 MHz, NANOGrav uses narrow band (25 −
50 MHz)low frequency observations (430 MHz), in addition to the highfrequency observations (1.4 GHz and above) in their campaign.On the other hand, InPTA covers the low frequencies with wide-band receivers, where the dispersion is most prominent. This al-lows precision in-band DM estimates (for example, see Liu et al.2014). When combined with simultaneous higher frequency ob-servations, high precision DM estimates are possible. In this pa-per, we assess the usefulness of this combination for high preci-sion DM measurements.It is therefore of utmost importance to such experiments thatthe pulsar DMs are measured to high precision. As the DM de-lay scales with the observing frequency as ∆ DM ∝ DM ν − , highprecision DM measurements are possible at lower observing fre-quencies, although one must be mindful of certain caveats suchas the frequency dependence of DM due to multi-path propaga-tion through the IISM (Cordes et al. 2016; Donner et al. 2019)as well as the e ff ect of variable scatter broadening of the pulseprofiles observed at low radio frequencies while applying lowfrequency DM measurements to correct ToAs measured at highfrequencies.With the advent of a new-generation of upgraded telescopesand their wide-band receivers, the attainable precision in DMmeasurements has greatly improved in recent years (e.g. Kauret al. 2019; Tiburzi et al. 2019; Donner et al. 2020). The Giant Metre-wave Radio Telescope (GMRT: Swarup et al. 1991) hasrecently gone through a major upgrade of its receivers and back-end instrumentation (uGMRT: Gupta et al. 2017; Reddy et al.2017), which has enabled an almost seamless frequency cover-age from 120 to 1450 MHz. This improvement in the frequencycoverage along with its capability of simultaneously observing asource at di ff erent frequency bands using multiple subarrays hasgreatly enhanced the precision with which the uGMRT can mea-sure pulsar DMs. This enables uGMRT to play an important rolein eliminating low frequency DM noise in PTA experiments.In our technique, we use multiple profiles obtained acrosswide bandwidths for DM estimation. The DM obtained with thismethod will be insensitive to profile evolution over frequenciesas the model template will also be similarly frequency resolved.One important factor in getting the correct DM is the alignmentof the sub-band profiles in the template. Small di ff erences in thealignment can cause a systematic o ff set in the measured DM,and will make it di ffi cult to combine with other PTA datasetsor to apply at higher frequencies. In this paper, we discuss twodi ff erent ways of aligning the wide-band profiles to measurein-band ( BAND3 alone) and inter-band (
BAND3 and
BAND5 combined) DMs using data obtained by the uGMRT (details ofthe band definitions can be found in Section 2).The four pulsars for which we present our initial analysis arePSRs J1713 + − + − −
2. Observation and data processing
In this work, we use observations of four MSPs conducted be-tween April 2018 and March 2019 as part of the InPTA cam-paign. PSRs J1713 + − + − + − BAND3 (400 − BAND5 (1360 − BAND4 (650 − simultane-ously at every epoch. The data in each band were acquired usinga 100 MHz band-pass with 1024 sub-bands, where BAND3 and
BAND5 data were coherently dedispersed using a real-time co-herent dedispersion pipeline (De & Gupta 2016) to the known
Article number, page 2 of 11rishnakumar et al.: InPTA: Precision DM estimates with uGMRT
Table 1: Summary of the observations used in this work. The ta-ble lists the duration of a single observation, the median signalto noise (S / N) ratio obtained in
BAND3 and
BAND5 after re-moving the non-detections, and the total number of observationsfor each pulsar. The observations were carried out over a timeperiod from April 2018 to March 2019.PSR Observation Median S / N No. ofduration (mins) BAND3 BAND5 EpochsJ1713 + − + − µ s sampling time and recorded for further process-ing. In this work, we only used the coherently dedispersed dataobtained with BAND3 and
BAND5 , as the incoherently dedis-persed
BAND4 data were of much lower sensitivity for the in-band analysis described later. Further details on the availableuGMRT configurations may be found in Gupta et al. (2017) andReddy et al. (2017).The timing mode data generated by the uGMRT wererecorded using the GMRT Wide-band Backend (GWB: Reddyet al. 2017) in a raw data format without any metadata, whichrequires preprocessing before it can be analysed by widelyused pulsar software such as
PSRCHIVE (Hotan et al. 2004).We convert this raw data to the
Timer format (van Straten &Bailes 2011) using a pipeline named pinta (Susobhanan et al.2020) developed for the InPTA campaign. pinta performs ra-dio frequency interference (RFI) mitigation using either gptool (Chowdhury & Gupta 2021) or RFIClean (Maan et al. 2020),and folds the data using DSPSR (van Straten & Bailes 2011),while supplying the required metadata (such as observing fre-quency and bandwidth) based on the observatory settings underwhich the observation was carried out. We supplied
DSPSR withthe pulsar models available from the IPTA Data Release 1 (Ver-biest et al. 2016) for folding. In the analysis presented in thiswork, we exclusively use
RFIClean for RFI mitigation, whichis designed to remove periodic RFI such as the RFI caused bythe 50 Hz power distribution grid as well as narrow band andspiky RFI.The details of the observations and the achieved profilesignal-to-noise (S / N) ratios over the entire band are summarizedin Table 1. Both in-band and inter-band estimates of the DMare presented in this work, which required reasonably high S / N( >
30) within individual sub-bands, and this was achieved onmost epochs. A plot of the frequency evolution of the four pul-sars used in this work and their integrated profiles at both thebands are shown in Figure 1. Multiple high S / N ratio observa-tions were added together to obtain the data plotted in this figure.
3. Data Analysis
The data folded with
DSPSR after removing the RFIs using
RFIClean are directly used for estimating the DM. Due to thelimited time span of the dataset ( ∼ https://github.com/abhisrkckl/pinta https://github.com/ymaan4/rficlean mating DM. The first requirement for obtaining a high precisionDM measurement using a wide-band data like ours is to obtaina frequency resolved high S / N ratio template and aligning thesub-band profiles properly so that there is no residual DM de-lay in the template. If this correction is not done properly, theDMs estimated using such a template will be biased. We haveused two di ff erent methods to align the sub-band profiles in thetemplate to check their e ff ectiveness on the DM measurementsas described in Section 3.1 below. We used these frequency re-solved templates to obtain ToAs and measure DM using TEMPO2 (Hobbs et al. 2006). A python based script was developed for thispurpose using the
PSRCHIVE tools. We have also implemented anoutlier rejection algorithm for removing large outlier ToAs usingHuber Regression (Huber 1964) following Tiburzi et al. (2019).Details of our DM measurements are given in Section 3.2.
In our first method (
METHOD1 ), we selected an epoch where theS / N ratio of the observation is comparatively high at both bands(
BAND3 and
BAND5 ). We estimated the DM at
BAND3 us-ing the pdmp program available with
PSRCHIVE . Although theprecision with which pdmp reports the DM is not very high, itis su ffi cient to align the sub-band profiles well in most cases.If the precision in the DM measurement reported by pdmp isworse than the change in DM from the ephemeris (with whichthe data is dedispersed), we did not update the DM (This is thecase with PSR J1909 − BAND3 and
BAND5 data. Smoothed tem-plates were created from these files with the psrsmooth pro-gram in
PSRCHIVE using the wavelet smoothing algorithm (De-morest et al. 2013). These smoothed templates were later usedto estimate the DM.It is possible that
METHOD1 could bias the DM measure-ments as the alignment of the templates is performed using pdmp
DM, which tries to maximise the S / N ratio while obtaining thebest DM. To circumvent this issue, we employed a di ff erentmethod ( METHOD2 ) for alignment using an analytic template de-rived from the data. To do this, we added some of the high S / Nratio observations at both the bands to create high S / N ratio data.A frequency and time averaged profile was produced from thesedata at
BAND3 . We used the
PSRCHIVE tool paas to create ananalytic template by fitting multiple Gaussian functions to thisprofile. The noise-free template created with the best fit obtainedwith paas was then used to estimate the DM of the high S / Nratio
BAND3 data we have produced above using the methodexplained in section 3.2. The sub-band profiles in the high S / Nratio data were then aligned using this DM for both the bands.We then used psrsmooth as in the previous case to obtain noisefree frequency resolved template. The frequency resolved tem-plates produced using both the methods described above werethen used to obtain the DM time series as described in the fol-lowing section.The DMs obtained using
METHOD2 have, in general, an orderof magnitude better uncertainties than the ones obtained with
METHOD1 . We also note that, in some cases, the actual DM valueobtained using the two methods were slightly di ff erent. Addi-tionally, it is possible for METHOD2 to give a biased DM for pul-sars that show significant profile component evolution within theband as the initial alignment is obtained using a frequency aver-aged profile.
Article number, page 3 of 11 & A proofs: manuscript no. InPTAhighprecDM
J1713+0747 F r e q u e n c y ( M H z ) J1909-3744 J1939+2134 J2145-0750 F r e q u e n c y ( M H z ) Pulse Phase
Fig. 1: A collage of the frequency evolution seen in the pulse profiles of the four pulsars presented in this work, along with theirfrequency averaged profiles. Top panel shows the data from
BAND5 and bottom panel shows
BAND3 data. The data for the plotwas obtained after adding multiple observations together using the known ephemeris of each pulsar.
To measure the DM, we have used frequency resolved templatesprepared as explained in Section 3.1. This approach removes theneed of fitting other frequency dependent parameters while fit-ting for DM as the pulsar profile shape at a given frequency re-mains very much invariant (except for mode changes or scatter-ing variations). The DMs reported in this paper are obtained us-ing the
TEMPO2 package. We have made use of the python inter- face of
PSRCHIVE for obtaining the ToAs and also for removingthe outliers. Most of the data processing was performed with thisPython interface except for obtaining the ToA residuals and forfitting DM which were performed using
TEMPO2 . The procedurefor performing the outlier rejection we use here closely followsthat by Tiburzi et al. (2019). A Python based tool,
DMcalc wasdeveloped for performing the above operations.
Article number, page 4 of 11rishnakumar et al.: InPTA: Precision DM estimates with uGMRT F r e q u e n c y ( M H z ) Pulse Phase (bins) I n t e n s i t y T o A R e s i d u a l s ( s ) Prefit: Filtered400 420 440 460 480 500
Frequency (MHz)
Source: PSR J2145-0750; MJD: 58538.2306; Prefit Wrms: 17.71 s; Postfit Wrms: 6.35 sMedian ToA Err: 7.31 s; DM: 9.010648 ± ; Reduced : 0.50 Fig. 2: A sample analysis plot of
DMcalc using the observation of PSR J2145 − BAND3 on 24 February 2019, when anexcess DM was seen towards this pulsar (See Section 4 for the discussion). Details of the fit can be found at the top of the plot.
Right panel : The top plot shows the pre-fit residuals obtained from
TEMPO2 as gray circles and the Huber Regression fit to it asdashed line in red. The middle panel shows the prefit ToAs after removing the outliers. The bottom panel shows the ToAs afterfitting for DM using
TEMPO2 . The details of the analysis method can be found in Section 3.2.
Left panel : The top panel shows animage of the frequency spectra of the pulse profiles of a 25 min observation after applying the DM correction and the bottom showsthe frequency and time averaged profile of the observation.We used the latest parameter files published by Alam et al.(2020) for obtaining the DM. We have removed the DM and theDMX parameters from the parameter files as this could other-wise bias the measured DM values. FD parameters were alsoremoved as we perform frequency resolved ToA estimation inthis work. We have also kept the electron density due to thesolar wind (NE_SW) as zero so as to not get biased with thisvalue. The DM in the parameter file was updated to the onethat is obtained using either
METHOD1 or METHOD2 for use inboth the methods. The ToAs with the given frequency resolu-tion for each pulsar were obtained at both the bands by usingthe
ArrivalTime class of
PSRCHIVE available with the Pythoninterface. We used the classical Fourier phase shift estimationmethod (Taylor 1992) implemented in
PSRCHIVE as PGS forobtaining the ToAs. The ToAs thus obtained were then used toobtain frequency resolved timing residuals using the general2 plugin of
TEMPO2 . A fit of ν − , where ν is the barycentric fre-quency of the ToAs was performed to these residuals using Hu-ber Regression (Huber 1964). A robust median absolute devia-tion (MAD) of the ToA residuals after removing the above fitfrom the residuals is calculated and the ToAs beyond three timesthe MAD value on both sides of the ToA residuals were removed.This outlier rejection method is e ff ective in removing the large outliers which are otherwise present due to RFI or other issuesin the data (for example, scintillation will make data of somechannels almost unusable due to very low S / N ratio), which willcorrupt the DMs obtained. These filtered ToAs were then usedto fit for DM with
TEMPO2 .An example analysis plot of PSR J2145 − BAND3 and
BAND5 separatelyas well as in a combined
BAND3 + BAND5 mode to obtainDMs. The addition of the data (or ToAs) without the require-ment of having any jumps between the two bands is justifiedas these were observed simultaneously and processed with the
Article number, page 5 of 11 & A proofs: manuscript no. InPTAhighprecDM same pipelines, where the relative delay was experimentally de-termined to be zero (Susobhanan et al. 2020). The procedure wasthen repeated for all the observations to obtain the DM time se-ries as shown in the Figure 3. In the case of inter-band DM mea-surements, the data of both the bands were aligned using thepulsar ephemeris before obtaining the ToAs and DM.The four pulsars presented in this work have di ff erent fre-quency evolution of their parameters like flux density, profileshapes, scintille sizes and scatter broadening. To illustrate this,frequency resolved profiles for all the four pulsars are shown inFigure 1. As a result, we had to obtain ToAs with di ff erent fre-quency resolution for each of them as described in Section 4.
4. Results & Discussions
The DM time series obtained using the methods described inSection 4 for the four pulsars are shown in Figure 3. The leftpanel shows the DM measured using
METHOD1 and the rightpanel shows DM obtained using
METHOD2 . The median DM val-ues and their uncertainties for the four pulsars are listed in Ta-ble 2. We have only reported the measurements for which a re-duced χ <
10 is obtained with
TEMPO2 . Some epochs showreduced χ values worse than 10, but looking at each of themindividually showed that they were a ff ected by heavy RFI. Al-though we put a higher limit on χ for getting the good mea-surements, most of them have reduced χ much less than 10and close to 1. The median value of the DMs estimated using METHOD1 and
METHOD2 di ff ers slightly for PSRs J1713 + − ff set between the DMsfor PSRs J1939 + − ff erence is the underlying di ff erence in the profile align-ment methods used.In the present work, we have used the data obtained by ob-serving simultaneously at both BAND3 and
BAND5 using a100 MHz bandwidth. The fractional bandwidth at
BAND5 isa factor of ∼ BAND5 . But a better fractional bandwidth at
BAND3 enablesus to get a good handle on the DM. The DM precision we can ob-tain in general by using this dataset with the
BAND3 data aloneis ∼ − and while combining the two bands it gets better by anorder of magnitude to ∼ − . In particular, we achieve an orderof magnitude better precision of 10 − with BAND3 and 10 − with BAND3 and
BAND5 for PSR J1939 + ff erent IISM the rays of these two bandspass through (Cordes et al. 2016).Comparing our results obtained using the two methods de-scribed in this work to that of the recently published ones byAlam et al. (2020) and Donner et al. (2020) show interestingtrends. For two pulsars, J1713 + − + ∼ × − pc cm − from NANOGravresults. For J2145 − METHOD1 shows a dif-ference of ∼ × − pc cm − , whereas the ones obtainedwith METHOD2 show consistency with the other two datasets. ForJ1909 − + − ff erent due to their inherent di ff erences in obtain-ing it. A di ff erence of ∼ × − pc cm − in the DM applied inthe template caused the di ff erence in the obtained DM using ourtwo methods. Both of these measurements will have a small biasif the NANOGrav DM time series is extrapolated to cover ourepochs. For J1939 + METHOD1 as well as
METHOD2 , could create a bias due to scattering. A com-pletely di ff erent method taking care of the scattering evolutionfor each observation has to be used in such a case, which willbe taken up in a follow up work. In summary, both these align-ment methods can be useful in getting DMs, but a systematicbias could be possible in either of the methods which will bevery much pulsar specific. Below we discuss in detail the resultsof each of the pulsars studied in this paper. This is one of the most precisely timed pulsars in PTA datasets.Apparently, the pulsar has so wide scintillation bandwidth at
BAND5 that at several epochs we could not detect the pulsaracross the full 100 MHz bandwidth. This essentially reducedour DM precision at
BAND5 and also made some of the ob-servations essentially unusable for our analysis. We collapsedthe data to 16 channels at both the bands for obtaining the DMs.Both methods give similar DMs at both the bands, but the com-bined estimate shows a small bias. The DMs used for aligningthe templates using both the methods are slightly di ff erent, by ∼ − . From Figure 3, it can be seen that the DM mea-surements at some epochs are missing in the left panel. This isbecause the reduced χ of those fits are beyond the cuto ff valueand were removed from the plot. The average DM obtained inthis work is consistent with that obtained by Donner et al. (2020)using LOFAR data, but is slightly higher than the DMs obtainedby Alam et al. (2020) by about 2 × − pc cm − . This smallbias from Alam et al. (2020) could be due to a frequency depen-dence of the DM (or scattering), as both BAND3 and LOFARfrequency bands are close to each other. The median ToA preci-sion obtained at
BAND5 is close to 1 µ s. Similar to the previous pulsar, this one is also a precisely timedpulsar with PTAs. Here also we collapsed the data to 16 chan-nels at both the bands for DM measurement. The average DMobtained using the two methods, after combining the two bandsshow a slight di ff erence. This small bias, as in the previous case,could be due to the initial DM used for aligning the templates(they di ff er by 3 × − ). The pulse shape remains the same (with-out any major profile evolution) at both BAND3 and
BAND5 . Itis possible that we are unable to detect any small profile evo-lution due to the coarse sampling of the pulse phase. This pre-vented us from getting a better analytic profile for obtaining theDM with which the template was aligned. The DM time seriesreported in Alam et al. (2020) does not cover the epochs of ourobservations, but extrapolating their measurements to ours showa better alignment with the DMs obtained using
METHOD1 and asmall di ff erence of ∼ × − pc cm − with that of METHOD2 ,as evident from the di ff erence in their average DMs. The ToAprecision is similar at both the bands. Article number, page 6 of 11rishnakumar et al.: InPTA: Precision DM estimates with uGMRT
Table 2: Results. The table shows the ToA uncertainty for each pulsar when using frequency and time averaged profiles using theanalytic template created with
METHOD2 for both bands. The median DM and DM uncertainty obtained from the DM time series ofeach pulsar using
METHOD1 and
METHOD2 are also given.PSR σ TOA ( µ s) DM [ METHOD1 ] (pc cm − ) DM [ METHOD2 ] (pc cm − )BAND3 BAND5 BAND3 BAND5 Combined BAND3 BAND5 CombinedJ1713 + − + − J1713+0747
J1909-3744
J1939+2134
J2145-0750
Modified Julian Day D M ( p c c m ) J1713+0747
J1909-3744
J1939+2134
J2145-0750
Modified Julian Day D M ( p c c m ) Fig. 3: The plots show the DM time series of the pulsars presented in this work. Left panel shows the DM time series obtained by
METHOD1 and Right panel shows the DM time series obtained by
METHOD2 . Black filled circles represent DM obtained from
BAND3 and Cyan triangles indicate DM obtained by combining bands 3 and 5. The median DM obtained from combining the two bands(Refer Table 2) are subtracted from the DM values to produce this plot. The DMs obtained with only using
BAND5 data is notshown in the plot as their uncertainties are large.
This is one of the longest timed millisecond pulsar by all thePTAs (Kaspi et al. 1994; Verbiest et al. 2016). It shows timingnoise in its ToA residuals and its timing data cannot be used forGW analysis without proper noise modeling. Since the pulsar isone of the brightest MSPs in our set, the precision in DM thatcan be achieved is quite high. Due to this, we used 128 chan-nels at
BAND3 and 32 channels at
BAND5 in the DM analysis.One limitation this pulsar has for using the
BAND3 data for es- timating DM is that it has very strong scatter broadening. Due tothis reason, the initial DM obtained by the two di ff erent methodswe used di ff er by about ∼ × − pc cm − . This is exactly thedi ff erence between the average DMs reported in Table 2 for thecombined bands. There is a small di ff erence of ∼ × − be-tween the BAND3
DMs and the combined ones obtained using
METHOD2 . This is probably due to the presence of scattering at
BAND3 . The DM obtained using both the methods show di ff er-ences even after taking these biases into account. This indicatesthat the scatter broadening present in the pulsar signal is also Article number, page 7 of 11 & A proofs: manuscript no. InPTAhighprecDM
Solar Elongation (degrees) D i s p e r s i o n M e a s u r e ( p c c m ) Fig. 4: The DM time series of PSR J2145 − TEMPO2 .time varying. A proper analysis of scatter broadening and simul-taneous measurement of DM is required to disentangle the DMgetting biased by the extra delay caused by scattering. This willbe taken up in a future study. The DM time series obtained using
METHOD1 follows the trend seen in Alam et al. (2020), althoughthe DMs reported here su ff er from scattering bias. The ToA pre-cision we obtain are the best for this pulsar in our sample, whichis also indicative of the DM precision we could achieve. This is one of the brightest pulsars in our sample. It shows strongprofile evolution across both of the bands. Moreover, this pul-sar’s line of sight passes close to the Sun at a solar elongation of ∼ BAND3 data, we collapsed it to 16 channels to reduce the e ff ect of scin-tillation. At BAND5 , we used 8 channels across the band. Themedian DMs obtained using the two methods shown in Table 2di ff er by about 1 . × − pc cm − for the combined bands. Eventhough the S / N ratio of the data used for generating the templatewas good, the precision in DM using
METHOD1 is worse than thedi ff erence quoted above. This is possibly due to change in rel-ative amplitudes of profile components with frequency, whichincreases uncertainty while maximising S / N in pdmp . This is notan issue for
METHOD2 which obtained a precision in the fourthdecimal place for the profile alignment using the analytic tem-plate. Although this creates a constant bias between the DMtime series obtained using the two methods, the trend in it is notmuch a ff ected as can be seen in Figure 3. The DMs obtained with METHOD2 show better alignment with the ones from Alam et al.(2020) and Donner et al. (2020), while the ones obtained with
METHOD1 have an o ff set. The median ToA precision we couldobtain is about 4 µ s at BAND5 .Since the line of sight to this pulsar passes close to the Sun(between January – March), we compare the observed DM timeseries as a function of solar elongation (obtained from
TEMPO2 as solarangle You et al. 2007) as shown in Figure 4. The red curve in the figure shows the expected DM excess caused by thebackground solar wind as predicted by the model incorporatedin
TEMPO2 . We have only two observations as the line of sightto the pulsar passed close to the Sun, respectively, at solar elon-gations ∼ ∼
10 degrees. In Figure 4, it is seen that the DMmeasurement on 10 February 2019 (MJD: 58524) at a solar elon-gation of ∼ ∼
40 solarradii) away from the Sun on 24 February 2019 (MJD: 58538)shows a DM excess of about an order of magnitude higher thanthe model. The
DMcalc fit for this excess DM observed is shownin the Figure 2. To find the cause of this excess DM, we care-fully examined the various solar datasets and solar wind mea-surements available during this epoch.The examination of solar images from the Solar DynamicObservatory (SDO: Pesnell et al. 2012) revealed the onsets oftwo eruptions, i.e., coronal mass ejections (CMEs) at ∼
10 de-grees west of the Sun’s center between 03 and 24 UT on 23February 2019. The ahead spacecraft of the Solar TErrestrialRElations Observatory (STEREO-A: Kaiser et al. 2008) was lo-cated 99 degree east of the Sun-Earth line and it observed theabove eruptions at about 20 degree behind the west limb of theSun. Since these CMEs originated close to the disk center andwere relatively narrow, they did not fill and show their expansionoutside the field of view of the occulting disk of the coronagraphat the near-Earth spacecraft. In addition to these CMEs, the SDOimages showed the presence of a large coronal hole ∼
30 degreewide, extending from the origin of the CME to the east nearlyalong the equatorial region of Sun. The high-speed streams fromthe coronal hole were likely to interact with the slow speed solarwind as well as CMEs.Figure 5 shows the typical geometry of the line of sight to thepulsar with respect to the Sun, the possible propagation directionof CMEs, and slow solar wind along the Parker (Archimedean)spiral. The analysis of the interplanetary magnetic field and solarwind plasma from the OMNI datasets revealed an interplanetaryshock at 07:35 UT on 27 February associated with the interac-tion between the slow- and high-speed solar wind streams. Fig-ure 6 shows a 3-day period solar wind and interplanetary mag-netic field measurements from 26 to 28 February 2019, obtainedfrom the OMNI database . From top to bottom, the figure showsthe solar wind proton density, velocity, temperature, plasma beta( β ), and the magnitude of interplanetary magnetic field. The ar-rival of the shock is indicated by a vertical dotted line. The av-erage ambient solar wind speed of ∼
300 to 350 km / s, observedduring the later half of February 2019, suggests that the inter-action by the high-speed streams of speed ∼
600 to 650 km / s,would have been formed and developed well ahead of its arrivalat the Earth. The shock was followed by an intense interactionregion, which was more than an order of magnitude denser thanthe ambient solar wind as well as about a half day wide in time.In the interaction region, the magnetic field exhibited large inten-sity fluctuations and the plasma beta, which is the ratio betweenthe gas and magnetic pressures, also showed a large peak. Thetemperature, density and velocity measurements after the inter-action region showed clear characteristics of the streams fromthe coronal hole. The backward projection of the interaction re-gion suggests that the interaction would have crossed the pulsarline of sight on 24 February around 2 to 8 UT.In the case of the ambient solar wind, the density decay withthe distance from the Sun can be considered to be R − , typical for https://omniweb.gsfc.nasa.gov Article number, page 8 of 11rishnakumar et al.: InPTA: Precision DM estimates with uGMRT
Earth
Sun
PulsarLine of Sight
Parker Spiral ~41 solar radii
Region of Influence on DM
CME-High Speed Wind Interaction Region
NE W N CME
WE NS
Fig. 5: A sketch showing the geometry of line of sight to the pul-sar with respect to the Sun on 24 February 2019. The interactionregion with excess electrons can be large in size while crossingthe line of sight. The inset image shown at the top is the run-ning di ff erence EUV image of the Sun taken at 03:32 UT on 23February 2019 by the SDO AIA telescope at 171 Å.a spherically symmetric expansion of the solar wind, where R isthe heliocentric distance. However, when the high density solarwind structures, such CMEs and / or high speed stream interac-tions are involved, a radial density gradient of R − . or steeperhas been observed (e.g., Bird et al. 1994; Elliott et al. 2012).Assuming the R − relation, it can be estimated that this inter-action region had a density of ∼ × cm − , taking 45 cm − as the density at Earth (1 AU). This density region (assuming thesame extent of the interaction region at 41 solar radii) will createan excess DM of 1 × − pc cm − . If we assume the steeper den-sity gradient of R − . , a DM excess of 3 × − pc cm − can beobtained. Another point to be considered is that the eastern sideof the interaction region likely crossed the Earth and it was pos-sibly a little less dense than the nose of the interaction region,as indicated by the in situ measurements. Thus, the excessiveDM observed probably corresponds to the density enhancementcaused by the interactions between high-speed and slow-speedsolar wind and CMEs.The solar wind stream interactions as well as stream-CMEinteractions are expected when the Sun is dominated by the mid-latitude and equatorial coronal holes. The vast sets of PTA andother pulsar observations available are likely to include many Fig. 6: In situ measured OMNI data for a 3-day period, from26 to 28 February 2019, during the passage of interaction re-gion associated with the high-speed solar wind streams and slowCME / ambient wind. From the top to bottom the following dataare plotted: solar wind proton density ( N p ), velocity ( V p ), tem-perature ( T p ), magnitude of the interplanetary magnetic field( | B | ) and plasma beta ( β ). The vertical dashed line indicates thearrival of the interplanetary shock associated with the interactionregion. The time immediately after the shock shows the intenseinteraction region, which is followed by the clear signatures ofthe high-speed streams from the coronal hole.such events. A coordinated analysis of selected data sets wouldbe of interest in understanding the e ff ects of enhanced densitystructures of the solar wind on the DM variations as functions ofsolar o ff set and possibly also the phase of the solar cycle.
5. Summary & Conclusions
In this paper, we compared the two possible methods for aligningthe frequency resolved pulsar profile templates and probed theire ff ects on the resulting DM measurements. We used four InPTApulsars observed by the uGMRT for a period of a year (two ob-serving cycles at GMRT). These observations were done simul-taneously at BAND3 and
BAND5 of uGMRT with a 100 MHzbandwidth. For a uniform and systematic processing, we havedeveloped a Python based tool,
DMcalc , utilizing the
PSRCHIVE
Python interface and
TEMPO2 for estimating DM using the tem-plates from the above two methods. We regularly obtained a DMprecision of ∼ − pc cm − at BAND3 and ∼ − pc cm − when combining it with BAND5 data while using both of ourtemplate alignment methods.We find that both the methods are useful for aligning thetemplates, but
METHOD2 could show a constant bias if the pul-sar has scatter broadening. For pulsars that have no detectable
Article number, page 9 of 11 & A proofs: manuscript no. InPTAhighprecDM scatter broadening, the DMs obtained by
METHOD1 show a con-sistent bias from that obtained with
METHOD2 . This is essentiallydue to the use of two di ff erent methods for template alignment.The METHOD1 uses an algorithm that aligns the multi-channeldata by maximising the S / N ratio while the
METHOD2 uses an an-alytic model derived from the frequency averaged profile of thedata. We have compared the DMs obtained by these two methodswith the other recently published results (Alam et al. 2020; Don-ner et al. 2020). Our DM measurements for PSRs J1713 + − METHOD2 compare very well with theirs,while those from
METHOD1 show a bias. In the cases of PSRsJ1909 − + + METHOD1 , while
METHOD2 shows a clear constant o ff set.An improved method that takes care of the scattering bias whileestimating the DM will be able to remove any bias created byscattering. For J1909 − ff set fromthat of the NANOGrav data using both the methods, althoughthe DMs obtained with METHOD1 may have smaller bias than theother.We could obtain a ToA precision of ∼ µ s or better for all thepulsars at both the bands, which is highly encouraging. We seethe e ff ect of scattering on DM measurements of J1939 + ff ects to obtainbetter DM estimates.We infer that the DM measurement at MJD 58538 of PSRJ2145 − ∼ ◦ was enhanced byan interaction region formed by a CME and high speed solarwind from a coronal hole close to the origin of the CME. Similarevents can be of interest to both the pulsar and the solar windcommunity and our results show that such studies can be pursuedusing high precision data from the uGMRT.The present observations used a 20 – 25 mins scan for eachpulsar. A much better precision on both ToAs and hence DMcan be achieved by using longer integrations and wider band-widths of the uGMRT. We have started doing observations usinga bandwidth of 200 MHz at both BAND3 and
BAND5 simulta-neously and also increased the observation duration in additionto increasing the number of antennas at each band (by skipping
BAND4 , and utilizing the antennas at the other two bands). Afactor of three improvement in the precision of DM is expected at
BAND3 in general with this increased bandwidth as compared tocurrent results. Initial results show vast improvement in the S / Nratio of the pulsars. The data from these observations are undervarious stages of processing and will be reported elsewhere.Following the encouraging results from the work presentedhere, we plan to apply these techniques to our full sample ofpulsars observed during the last four years. Additionally, e ff ortsare being pursued for developing other methods to make the DMmeasurements even more precise and reliable, and therefore em-ployable for the on-going gravitational wave analysis by the var-ious PTAs. Data Availability
The data used in this paper will be made avail-able on reasonable request. The SDO 171Å imagesused for the solar wind analysis can be found at https://cdaw.gsfc.nasa.gov/movie/make_javamovie.php?date=20190223&img1=sdo_a304&img2=lasc2rdf
Thecode used for measuring DM in this work,
DMcalc is publiclyavailable at https://github.com/kkma89/dmcalc . Acknowledgements
MAK is thankful to Caterina Tiburzi and Joris Verbiest for theirvaluable inputs and useful discussions at various stages of thiswork. AS, AG, BCJ, LD, and YG acknowledge the support ofthe Department of Atomic Energy, Government of India, underproject Identification / WOS-A / PM-1031 / ff of the GMRTwho made our observations possible. GMRT is run by the Na-tional Centre for Radio Astrophysics of the Tata Institute of Fun-damental Research. The open data policy of STEREO and SDOteams is acknowledged. The solar wind and interplanetary datasets have been obtained from the OMNI database. References
Ahuja, A. L., Gupta, Y., Mitra, D., & Kembhavi, A. K. 2005, MNRAS, 357, 1013Ahuja, A. L., Mitra, D., & Gupta, Y. 2007, MNRAS, 377, 677Alam, M. F., Arzoumanian, Z., Baker, P. T., et al. 2020, arXiv e-prints,arXiv:2005.06495Arzoumanian, Z., Baker, P. T., Blumer, H., et al. 2020, ApJ, 905, L34Backer, D. C. 1996, in Compact Stars in Binaries, ed. J. van Paradijs, E. P. J. vanden Heuvel, & E. Kuulkers, Vol. 165, 197Bird, M. K., Volland, H., Paetzold, M., et al. 1994, ApJ, 426, 373Burke-Spolaor, S., Taylor, S. R., Charisi, M., et al. 2019, Astronomy and Astro-physics Review, 27, 5Chowdhury, A. & Gupta, Y. 2021, In preparationCordes, J. M., Shannon, R. M., & Stinebring, D. R. 2016, ApJ, 817, 16De, K. & Gupta, Y. 2016, Experimental Astronomy, 41, 67Demorest, P. B., Ferdman, R. D., Gonzalez, M. E., et al. 2013, ApJ, 762, 94Desvignes, G., Caballero, R. N., Lentati, L., et al. 2016, Monthly Notices of theRoyal Astronomical Society, 458, 3341Donner, J. Y., Verbiest, J. P. W., Tiburzi, C., et al. 2020, arXiv e-prints,arXiv:2011.13742Donner, J. Y., Verbiest, J. P. W., Tiburzi, C., et al. 2019, A&A, 624, A22Edwards, R. T., Hobbs, G. B., & Manchester, R. N. 2006, Monthly Notices ofthe Royal Astronomical Society, 372, 1549Elliott, H. A., Henney, C. J., McComas, D. J., Smith, C. W., & Vasquez, B. J.2012, Journal of Geophysical Research (Space Physics), 117, A09102Foster, R. S. & Backer, D. C. 1990, ApJ, 361, 300Gupta, Y., Ajithkumar, B., Kale, H. S., et al. 2017, Current Science, 113, 707Hobbs, G. 2013, Classical and Quantum Gravity, 30, 224007Hobbs, G., Guo, L., Caballero, R. N., et al. 2019, Monthly Notices of the RoyalAstronomical Society, 491, 5951Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, Monthly Notices ofthe Royal Astronomical Society, 369, 655Hotan, A. W., van Straten, W., & Manchester, R. N. 2004, Publications of theAstronomical Society of Australia, 21, 302–309Huber, P. J. 1964, Ann. Math. Statist., 35, 73Joshi, B. C., Arumugasamy, P., Bagchi, M., et al. 2018, Journal of Astrophysicsand Astronomy, 39, 51Kaiser, M. L., Kucera, T. A., Davila, J. M., et al. 2008, Space Sci. Rev., 136, 5Kaspi, V. M., Taylor, J. H., & Ryba, M. F. 1994, ApJ, 428, 713Kaur, D., Bhat, N. D. R., Tremblay, S. E., et al. 2019, ApJ, 882, 133Kerr, M., Reardon, D. J., Hobbs, G., et al. 2020, Publications of the AstronomicalSociety of Australia, 37, e020Kramer, M. & Champion, D. J. 2013, Classical and Quantum Gravity, 30, 224009Kumar, U., Gupta, Y., van Straten, W., et al. 2013, in Neutron Stars and Pulsars:Challenges and Opportunities after 80 years, ed. J. van Leeuwen, Vol. 291,432–434Liu, K., Desvignes, G., Cognard, I., et al. 2014, MNRAS, 443, 3752
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