Prospects for High-Precision Pulsar Timing with the New Effelsberg PSRIX Backend

0.45 MB·

by  P. Lazarus

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed26January2016 (MNLATEXstylefilev2.2)
Prospects for High-Precision Pulsar Timing with the New
Effelsberg PSRIX Backend
P. Lazarus1⋆, R. Karuppusamy1, E. Graikou1, R. N. Caballero1,
6
1 D. J. Champion1, K. J. Lee2,1, J. P. W. Verbiest3,1, M. Kramer1,4
0
1Max-Planck-Institut fu¨r Radioastronomie, Auf dem Hu¨gel 69, 53121 Bonn, Germany
2
2Kavli institutefor astronomy and astrophysics, Peking University,Beijing 100871, P.R.China

n 3Fakult¨at fu¨r Physik, Universita¨t Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
a 4Jodrell Bank Centre for Astrophysics, Universityof Manchester, Manchester, M13 9PL, United Kingdom
J

2
2

26January2016
]
M
I ABSTRACT
.
h
p The PSRIX backend is the primary pulsar timing instrument of the Effelsberg
- 100-mradiotelescopesinceearly2011.ThisnewROACH-basedsystemenablesband-
o
widths up to 500MHz to be recorded,significantly more than what was possible with
r
t its predecessor,the Effelsberg-BerkeleyPulsarProcessor(EBPP).We reviewthe first
s
a four years of PSRIX timing data for 33 pulsars collected as part of the monthly Eu-
[ ropean Pulsar Timing Array (EPTA) observations. We describe the automated data
analysis pipeline, CoastGuard, that we developed to reduce these observations. We
1
also introduce TOASTER,the EPTA timing database used to store timing results, pro-
v
cessing information and observation metadata. Using these new tools, we measure
4
9 the phase-averaged flux densities at 1.4GHz of all 33 pulsars. For 7 of these pulsars,
1 our flux density measurements are the first values ever reported. For the other 26
6 pulsars,we compare our flux density measurements with previously published values.
0 By comparing PSRIX data with EBPP data, we find an improvement of ∼2–5 times
. in signal-to-noise ratio achievable, which translates to an increase of ∼2–5 times in
1
0 pulse time-of-arrival (TOA) precision. We show that such an improvement in TOA
6 precisionwillimprovethesensitivityto thestochasticgravitationalwavebackground.
1 Finally, we showcase the flexibility of the new PSRIX backend by observing several
: millisecond-period pulsars (MSPs) at 5 and 9GHz. Motivated by our detections, we
v
discuss the potential for complementing existing pulsar timing array data sets with
i
X MSP monitoring campaigns at these frequencies.
r
a Key words: pulsars: general – stars: neutron – gravitationalwaves
1 INTRODUCTION have also been used to probe the interstellar medium (e.g.
Bhat et al.1998;Berkhuijsen & Mu¨ller2008;Eatough et al.
Pulsarsareextremelyusefultoolsforstudyingvariousfields
2013).Furthermore,collections ofMSPsarebeingobserved
of astrophysics. Many important results are the product
regularly as part of so-called pulsar timing array (PTA)
of regular timing campaigns that are used to determine
projects, which have the ultimate goal of detecting low-
models of pulsars’ rotation capable of accounting for ev-
frequencygravitationalwaves,possiblyarisingfromthecos-
ery rotation of the star. High-precision timing observa-
mic population of super-massive black-hole binaries (e.g.
tions of millisecond-period pulsars (MSPs) have proven to
Sesana 2013) or from cosmic strings (e.g. Sanidas et al.
have a large number of diverse applications, such as test-
2012).
ing of relativistic gravity (e.g. Kramer et al. 2006), con-
To maximise the scientific potential of pulsar timing
straining the equation-of-state of ultra-dense matter (e.g.
observations, high signal-to-noise ratio (S/N) observations
Demorest et al.2010),andstudyingbinarystellarevolution
arerequiredtodeterminepulsetimesofarrival(TOAs)pre-
(e.g. Freire et al. 2011). In general, studies of radio pulsars
cisely.Givenatelescope,theS/N canbeimprovedeitherby
increasing the integration time, which is limited by the to-
⋆ E-mail:[email protected] talavailabletelescopetimeandthenumberofpulsarstoob-
c 0000RAS
(cid:13)
2 P. Lazarus et al.
serve,orbyusingmoresensitiveand/orwiderbandwidthre- design of PSRIX compared to the EBPP, the timing cam-
ceivers. Inorder tofully leverage wider bandwidths,instru- paignsundertakenatEffelsbergusingPSRIXareproducing
ments capable of processing the increased frequency range dataofsuperiorquality,thusenablingevenhigher-precision
must be used. timing studies than previously possible. Moreover, PSRIX
The Effelsberg-Berkeley Pulsar Processor (EBPP) co- may further improve the prospects of high-precision timing
herent dedispersion backend (Backer et al. 1997) has been atEffelsberg bymakingit ispossible toconducttimingob-
running since 1995. Its long, uniform data sets for some servationsofMSPsat5GHzandhigher,helpingtomitigate
MSPshaveenableduniquestudies.Forexample,Shao et al. noise arising from variations of the ISM along the line of
(2013) used EBPP data to constrain profile variations in sight towards the pulsar, a serious impediment to searches
MSPs, and thus improve limits on the violation of local for GWs with PTAs.
Lorentz invariance of gravity by several orders of mag- The EPTA has previously incorporated the 17-year-
∼
nitude relative to previously published limits (see Will long EBPP data set into its timing analyses and GW
1993, and references therein). The EBPP data set has also searches (e.g. Desvignes et al., submitted; Janssen et al.
been a key component of several European Pulsar Timing 2008; Lazaridis et al. 2009, 2011; Lentati et al. 2015). Here
Array (EPTA) projects, such as characterising the noise we describe the PSRIX data and its analysis, which will
properties of MSPs (Caballero et al. 2015), constraining be included in future EPTA projects and be shared with
the low-frequency gravitational wave background (GWB; theInternationalPulsarTimingArray(IPTA)collaboration
Lentati et al.2015),andsearchingforsinglesourcesofgrav- (Verbiest et al., submitted).
itational waves (GWs; Babak et al., accepted). In addition to the monthly observing sessions of many
The EBPP is beginning to show its age. For instance, binarypulsarsandMSPs,severalpulsarshavebeenthetar-
the EBPP bandwidth is limited to only 64–128MHz, de- get of dedicated observing campaigns with PSRIX over the
∼
pending on the integrated Galactic electron content along pastfouryears. Inparticular, PSRIXdatawereincludedin
the line-of-sight to the pulsar (i.e. the pulsar’s dispersion the IPTA effort to observe PSR J1713+0747 continuously
measure,DM),whereasmostcurrentreceiversystemsoper- for 24 hours using the largest radio telescopes around the
atinginthe1–3GHzbandcansimultaneouslyobserveband- Earth (Dolch et al. 2014). Also, PSR J0348+0432, a 2-M⊙
widths of 200–800MHz (e.g. the Greenbank Ultimate Pul- pulsar in a 2.5hr relativistic binary with a white-dwarf
∼
sar Processing Instrument – GUPPI – used at the Green companion (Lynchet al. 2013; Antoniadiset al. 2013), has
Bank Telescope, and its clones PUPPI and NUPPI at the beenregularlyobservedforfullorbitsusingPSRIX.Several
Arecibo and Nan¸cay observatories, respectively Ford et al. full-orbitobservingcampaignsofPSRJ1518+4904, a41-ms
2010), and in the case of the Ultra-Broadband (UBB) re- pulsar in an 8.6-day double-neutron-star binary, have been
ceiver at Effelsberg, 2600MHz. Furthermore, the EBPP conductedwithPSRIXtopreciselymeasurethemassofthe
∼
hardware is becoming increasingly unreliable, and replace- pulsar and its companion (Janssen et al., in prep.).
ment parts are increasingly difficult tocome by. The remainder of this paper is organised as follows.
For these reasons, the EBPP backend was replaced as Section 2 describes the monthly EPTA observations under-
themaindatarecorderforpulsartimingobservationsatEf- takenwiththeEffelsbergtelescopeusingPSRIX.Theanal-
felsberg by the PSRIX backend in 2011 March. PSRIX is ysisof these observationsis detailed in 3,and includesan
§
built around a Reconfigurable Open Architecture Comput- overviewoftheautomateddatareductionsuiteCoastGuard,
ing Hardware (ROACH) system, a programmable platform as well as the timing database TOASTER. Flux density mea-
designed by the Collaboration for Astronomy Signal Pro- surements for 33 pulsars at 1.4GHz and a comparison be-
cessing and Electronics Research (CASPER).1 The EBPP tween PSRIXand the old EBPP backendsare presented in
is still run in parallel with PSRIXwheneverpossible. 4,asaretheresultsofobservationsat5and9GHz.There-
§
PSRIX was originally designed as part of the Large sultsarediscussedin 5andthepaperisfinallysummarised
§
European Array for Pulsars (LEAP) project (Bassa et al. in 6.
§
2015), which has the objective of coherently combining sig-
nals from the five largest European radio telescopes.2 To
meet this goal, the primary mode of operation of PSRIX
2 OBSERVATIONS
is to record baseband data, however, additional modes
were implemented to record coherently dedispersed profiles Every month, the Effelsberg radio telescope is used to ob-
foldedinreal-timeandcoherentlydedispersedsinglepulses. serve bright, stable MSPs as part of the EPTA project.
PSRIX’s coherent-dedispersion modes support bandwidths These observations are conducted with PSRIX in its
upto500MHzandareflexibleenoughtoobserveatdifferent coherent-dedispersion real-time folding mode, evenly divid-
frequencies,takingadvantageofEffelsberg’smanyreceivers. ing the pulse profiles into 1024 phase bins. Each session
Technical details of the backend design and the implemen- typically consists of observations at both 1.4 and 2.6GHz
tation its various modes of operation will be described in a (wavelengths of 21 and 11cm, respectively). The 1.4-GHz
futurepaper. observations use either the central feed of the 7-beam re-
Thanks to the increased bandwidth and more robust ceiver(called“P217mm”)orthesingle-feed1.4GHzreceiver
(“P200mm”).3 Both of these1.4-GHz receiversaresituated
in the primary focus of the Effelsberg telescope. Only one
1 https://casper.berkeley.edu/ ofthe1.4-GHzreceivers isinstalled for anygiven observing
2 Specifically,theLovellTelescope,theWesterborkSynthesisRa-
dio Telescope, the Nanc¸ay Telescope, the Sardinia Radio Tele-
scope,andEffelsberg. 3 http://www.mpifr-bonn.mpg.de/effelsberg/astronomen
c 0000RAS,MNRAS000,000–000
(cid:13)
The Effelsberg PSRIX Pulsar Timing Backend 3
session.Weusewhicheverreceiverisavailable.The2.6-GHz 3 DATA ANALYSIS
observations are done with the “S110mm” secondary-focus
3.1 CoastGuard: An Automated Timing Data
receiver.PSRIXisusedtorecorda200-MHzband,whichis
Reduction Pipeline
dividedintoeight25-MHzsub-bands.InthecaseofP200mm
and S110mm observations, this exceeds the available band- We developed an automated pipeline, CoastGuard,5 to re-
widths of 140MHz and 80MHz, respectively. See Table 1 duce PSRIX data. CoastGuard is written in python and
fordetailsoftheobservingset-upsused.Allofthereceivers is largely built around programs from the psrchive pack-
used in this work havecircularly polarised feeds. age6 (Hotan et al. 2004), using its python wrappers to
Whenever possible, we record data with the EBPP read PSRIX data files, which are psrchive-compatible.
coherent-dedispersionpulsartimingbackendinparallelwith CoastGuard contains components that are sufficiently gen-
PSRIX.Thisallowsforamoreaccuratedeterminationofthe eral for use with psrchive-compatible datafiles from other
timeoffset betweenthetwoinstruments.Wehavealso used observingsystemsdespitethatitwasprimarilydesignedfor
thesesimultaneousobservationstocharacterisetheimprove- Effelsberg PSRIX data. In particular, the radio frequency
ment of PSRIXoverthe EBPP (see 4.3). interference (RFI) removal algorithm described below has
§
Our monthly EPTA observing sessions typically con- been applied to data from the Parkes Telescope (Ng et al.
sist of 24 hours at 1.4GHz and 12–24 hours at 2.6GHz. 2014)andhasalsobeenadoptedbytheLOFARpulsartim-
Eachobservingsessionincludespulsarobservationsof 30– ing data reduction pipeline (Kondratiev et al. 2015).
∼
60min in duration. Polarisation calibration scans are con- CoastGuard contains considerable error checking, log-
ducted prior to each pulsar observation and each consist of ging, logistics, and control logic required to automate large
a2-minintegrationofthereceivernoisediodeoffsetby0.5◦ portions of the pipeline, which is marshalled by a control
fromthepulsarposition.Thediodeispulsedwitha1-srep- script and a MySQL database.
etition rate and a 50% dutycycle. In its coherent-dedispersion real-time folding mode the
Since 2013, at 1.4GHz, we also performed on- and off- PSRIX backend writes data files every 10s for each 25-
sourcescansofaradiosourcewithastable,well-knownflux MHzsub-band.Thesefragments arethen grouped together
density,usually3C218(i.e.HydraA).Thesefluxcalibration and combined using psradd. At this stage, the data are re-
observations use thenoise diode as described above. aligned using an up-to-date pulsar ephemeris, if necessary,
Every month, we observe 45 pulsars at 1.4GHz and and12.5%ofthechannelsattheedgeofeachsub-bandare
∼
20 pulsars at 2.6GHz. Pulsars that are never, or rarely, zero-weighted to reducethe effect of aliasing.
∼
detected at 2.6GHz during a 6–12 month probationary pe- Next, the metadata stored in these consolidated files
riod are dropped from theregular observing schedule. Here are cross-checked against telescope observing logs and all
we focus on the data sets of 33 MSPs and binary pulsars discrepanciesarecorrected.Thisisprimarilytorepairissues
acquired between 2011 and 2015. Tables 2 and 3 show a with the observation metadata that were common during
summary of our 1.4 and 2.6GHz observations of these pul- the commissioning of PSRIX. These issues have since been
sars, respectively. resolved.
As we will discuss in 5.2, since ISM effects weaken The data files are then cleaned of RFI.In thepipeline,
§
withincreasingradiofrequency,high-frequencyobservations our cleaning process excludes RFI by setting the weights
ofpulsarsmaybeextremelyusefultoavoidandmitigatethe of individual profiles to zero. That is, the data from RFI-
effectsofvariabilityintheinterstellarmedium(ISM),which affected sub-integration/channel combinations are ignored
limitthesensitivityofattemptsatdetectingGWswithpul- in the rest of the analysis without altering the data values.
sars.In2015January,weconductedobservationsof12MSPs Therefore,itispossibletoreversetheautomatedRFImask-
at5GHz(6cm)usingthe“S60mm”secondary-focusreceiver ing.
withtheaimofassessingtheirutilitytothePTAs.Weused CoastGuard’s RFI-excision script, clean.py, includes
PSRIXinits500-MHzcoherent-dedispersionreal-timefold- four distinct algorithms that can be chained together to
ingmode for these5 observations. Wealso observed four of clean corrupted data. Each algorithm has several parame-
these pulsars at 9GHz (3.6cm) with the “S36mm”, also a ters that can be used to optimise its performance. In our
secondary-focusreceiver,againwith500MHzofbandwidth. automated data analysis, we use two of the four available
Our high-frequency observations are listed in Table 4. We cleaning algorithms, namely rcvrstd and surgical. The
selectedthepulsarsfortheseexploratoryhigh-frequencyob- othertwoalgorithms,bandwagonandhotbins,areoccasion-
servations based on their 1.4 and 2.6GHz detection signifi- ally applied manually to observations requiring special at-
cances, which we scaled to higher frequencies using the ra- tention. Our standard RFI excision algorithm proceeds as
diometerequation,thereceiverperformance, andpublished follows:
spectral indices. 4 Specifically, we required an estimated First, clean.py’s rcvrstd algorithm is used to zero-
S/N ∼>10 for a 30-min observation when selecting pulsars weightfrequencychannelsbeyondthereceiverresponseand
forthepreliminary5and9-GHzobservationsreportedhere. channels falling within a list of receiver-dependent bad fre-
High-frequencyobservationsofother(fainter)MSPsarebe- quencyintervals.
ing conducted and will be reported elsewhere. Second, thesurgical algorithm is used to find profiles
corrupted by RFI in the folded data cube. To avoid be-
ing biased by the presence of the pulsar signal, the ampli-
4 Forpulsarswithoutspectralindicesavailableintheliterature, 5 Availableathttps://github.com/plazar/coast guard
weusedaspectralindexofα= 2forourestimates. 6 http://psrchive.sourceforge.net/
−
c 0000RAS,MNRAS000,000–000
(cid:13)
4 P. Lazarus et al.
tude and phase of the integrated pulse profile is fit using fluxcalcomparesthepowerlevelsofon-andoff-sourceob-
a least-squares algorithm to individual profiles containing servationsofastandardcandletarget todeterminethesys-
a significant detection and the difference is computed. It is tem equivalent flux density over the observing band. This
thesepulsar-freeresidualsthataretreatedintheremainder information is used to determine the flux density scale of
of the algorithm. Next, RFI-contaminated data are identi- thepolarisation-calibrated pulsar observations.
fiedwithaset offourmetrics, whicharecomputedforeach For this paper we refolded all data with up-to-date
sub-integration/channelpair(i.e.eachtotal-intensityprofile ephemerides.
stored in the data file). These metrics are: 1) the standard
deviation, 2) the mean, 3) the range, and 4) the maximum
amplitude of the Fourier transform of the mean-subtracted 3.2 TOASTER: The TOAs Tracker Database
residuals.Thesefourmetricswereselected duetotheirsen-
We have developed a python package, TOAS TrackER
sitivity to theRFI signals present in Effelsberg data, which (TOASTER),9 for computing and storing TOAs in a fully de-
include,butarenotlimitedto:excessnoise,occasionaldata
scribed and reproducible way. At its core, TOASTER consists
drop-outs,andinfrequently,rapid(sub-ms)periodicbursts.
of an SQL database and full-featured python toolkit for re-
For each metric, a N N -sized matrix of values is
sub × chan liably interacting with thedata and database.
produced.Trendsintherowsandcolumnsofthesematrices
Beyond simply storing TOA information, TOASTER’s
are removed by subtracting piece-wise quadratic functions
database also records information about telescopes and ob-
that were fit to the data. The subtraction of these trends
serving systems, observation information (e.g. frequency,
account for slow variations in time, as well as the shape of
epoch,integrationtime,theephemerisusedforfolding),the
thebandpass.Theserescaledmatricesarethensearchedfor
standard profile used to determine each TOA, as well as
outliers,whicharedefinedasbeing>5σfromthemedianof
versionnumbersofrelevant software, suchaspsrchive and
eithertheirsub-integrationorchannel.Finally,profilesthat
TEMPO2 (Hobbset al. 2006).
areidentifiedasanoutlierbyatleasttwoofthefourmetrics
Once the database is populated, TOASTER can also
are zero-weighted.
launchTOAgenerationprocessesthatuseavarietyof“ma-
The bandwagon algorithm completely removes sub-
nipulators”topreparethedatapriortoautomatically com-
integrations and channels that already have a sufficiently
putingTOAs using standard psrchive tools. The most ba-
large fraction of data masked, and the hotbins algorithms
sicmanipulatorfullyintegratesdatainfrequencyandtime.
replaces outlier off-pulse profile phase-bins with locally
However,moresophisticatedmanipulationscanbeincluded
sourced noise.7 Neither of these two algorithms are part of
to adjust the data according to an updated, possibly time-
our standard automated data reduction.
varying DM, integrate a fixed number of pulses or vari-
Once the observations are cleaned, they are reviewed
able number of pulses depending on the resulting S/N.
before proceeding with the rest of the automated analysis.
Manipulators can also be used to scale the measured pro-
Thisistoidentify observationsthatstillneedtobecleaned
files to have uniform off-pulse variance, as was done by
manually. In practice, only a small fraction of observations
(Arzoumanian et al. 2015). Typically thesetypesof manip-
require additional RFI zapping. This quality-control stage
ulations are included in the data reduction pipelines that
also providesan opportunitytoidentify observations where
prepare observations prior to determining TOAs. By per-
the pulsar is not detected or where the data are contami-
forming these data reduction steps in TOASTER, the details
natedbyRFIbeyondrepair.Observationsfalling intothese
of themanipulations performed on thedataand theresult-
twocategoriesdonotcontinuefurtherinthedatareduction
ing TOAs are logged in the database, making it easy to
process.
storetheresultingTOAs,aswellassystematicallycompare
The above data reduction process (combine, correct,
the effect of different manipulations on the eventual timing
clean, quality control) is also applied to polarisation cali-
analysis. Furthermore,theTOASTER databaseincludesaref-
bration scans of the noise diode. The cleaned and vetted
erence to the template used to compute each TOAs. The
calibration scans are fully time-integrated, and then loaded
endresultisacompletelydescribedandreproducibleTOA-
into the appropriate psrchive pac-compatible “database”
generation procedure. This makes TOASTER a useful tool for
files. The pipeline maintains one calibration database file
high-precisiontimingprojectsliketheEPTAandIPTAthat
for each pulsar.
are constantly adding new data, as well as developing new
Polarisation calibration of the cleaned pulsar data files
data reduction algorithms.
is performed with psrchive’s pac program,8 usingits “Sin-
TheTOASTERtoolkitscriptscanbeusedtoeasilyquery
gleAxis”algorithm,whichappropriatelyadjuststherelative
theinformationstoredinitsdatabase.Forexample,TOASTER
gainandphasedifferenceofthetwopolarisationchannelsby
provides scripts to list and summarise the TOAs in the
applying the technique of Britton (2000). These calibrated
database. These scripts can also be used to generate TOA
observations are manually reviewed a second time to verify
filesinmultipleformats,includingaTEMPO2format thatin-
that no artifacts havebeen introduced.
cludes all the annotations (“TOA flags”) requested by the
Fluxcalibrationhasnotbeenincorporatedintotheau-
IPTA.
tomated dataanalysis pipeline.Nevertheless,wehaveman-
TOASTER can be used to load TOAs directly into the
ually performed flux calibration wherever possible. In our
database (i.e. without information concerning the observa-
analysis we used psrchive’s fluxcal and pac programs.
tions, templates, etc.). This feature is useful for including
7 Becausethehotbinsalgorithmreplacesdata,itisirreversible. 9 TOASTER and its documentation are publicly available at
8 http://psrchive.sourceforge.net/manuals/pac/ https://github.com/plazar/toaster
c 0000RAS,MNRAS000,000–000
(cid:13)
The Effelsberg PSRIX Pulsar Timing Backend 5
previously computed, and finalised, data sets, such as the
J2043+1711
EPTA legacy TOAs (Desvignes et al., submitted). J1640+2224
WesetuptheTOASTERsoftwareanddatabasetomanage J0340+4129
thereduced(i.e.cleanedandcalibrated)PSRIXdata,which J2017+0603
J2322+2057
are automatically loaded into the TOASTER database by the
J1741+1351
data reduction pipeline described in 3.1. J0348+0432
§ J1738+0333
J2229+2643
J0023+0923
4 RESULTS J1853+1303
J2010 1323
−
Over the past four years, we have collected timing data on J2317+1439
J1911+1347
45 pulsars at 1.4 and 2.6GHz using the PSRIX backend
J2234+0944
with the 100-m Effelsberg radio telescope. Here we report J0218+4232
onaselectionof33pulsars.Mostofthesepulsarshavebeen J0751+1807
J0030+0451
monitored monthly in both bands for the entire 4-year pe-
J0621+1002
riod. An overview of our 1.4 and 2.6GHz observations can J1918 0642
−
befound in Tables 2 and 3, respectively. J1600 3053
−
J1744 1134
−
J0613 0200
−
J1024 0719
4.1 Flux Density Measurements −
J1022+1001
J1518+4904
Wemeasuredfluxdensitiesforall33pulsarsat1.4GHz.For J2145 0750
−
each pulsar, we report the mean flux density, S , and the B1855+09
medianfluxdensity,S ,toaccountforobserhvedi modula- J1012+5307
med. J1643 1224
tion due to interstellar scintillation. We estimate the preci- −
J1713+0747
sion of themean fluxdensities as thestandard error on the J1730 2304
−
mean, that is, B1937+21
This work
δhSi=σS/√Ncal., (1) Previously published
where σS is the standard deviations of the individual flux
measurements and N is the number of calibrated obser- 10-1 100 101
cal.
vations. Flux Density, S (mJy)
(cid:0) (cid:2)
The flux densities we measure are reported in Table 2,
along withpreviously measured valuesat 1.4GHz.Sevenof
the pulsars we report flux densities for do not have previ-
Figure 1. Measured 1.4GHz flux densities of 33 pulsars esti-
ouslypublishedmeasurements,andthreeotherpulsarshave
mated from averaging over multiple PSRIX observations (filled
previouslypublishedmeasurementsthatwerenotcalibrated circles).Theuncertaintiesareestimatedasthestandarderroron
againstobservationsofstandardcandlesources.Mostofthe the mean (see Eq. 1). Additional details of the calibration pro-
rest of our flux density measurements are consistent with cess canbefoundin 3and4.1. Thepreviouslypublishedflux
§§
previously reported values (see Fig. 1). Inconsistencies may densities(unfilledcircles)donotallhave properlymeasuredun-
arise from scintillation, which impacts both the observed certainties.SeeTable2fornotes andreferences.
flux density as well as the apparent uncertainty. The effect
of scintillation is most apparent when only a small number
of observations are used to estimate the flux density and signal generator and not re-syncing the phase of the signal
is further exacerbated when observations make use of short afterthesystemwasrestarted.Thethirdoffsetwasdeliber-
integrations and/or small bandwidths. ately introduced on 2014 Mar. 4 when the clock signal was
Data from 2013 Nov. to 2014 Aug. could not be cali- synchronisedtotheoriginal clock phase.Finally,thefourth
brated due to saturation and/or non-linearities in the data offset on 2014 Nov. 20 was also deliberately introduced by
resulting from insufficient attenuation of the telescope sig- installing a new clock signal generator.
nal. Fortunately, this was only an issue when observing ex- Thefirsttwoclockoffsetswereinitiallymeasuredbyfit-
tremely strong sources (e.g. flux calibrators with the noise ting timing data for the orbital phase of PSR J0348+0432.
diode).Wefindnoanomalies in theobserved pulseprofiles, These measurements were sufficiently precise to determine
allowingtheseobservationfromlate-2013tomid-2014tobe theoffsetstowithinonephaserotationofPSRJ0348+0432
used for timing. (P 39ms),allowingthevaluestobefurtherrefinedbyfit-
≃
ting arbitrary time offsets (“JUMPs”) to the timing resid-
uals of PSR J0348+0432 and then with PSR J1744 1134
4.2 Clock Stability −
(P 4.1ms).Thefinalvaluesoftheclockoffsetshavebeen
≃
The PSRIX system suffered four clock offsets over its first measured by fittingJUMPs individually tothetiming data
four years of operation. The first offset occurred between of four pulsars, namely PSRs J0613 0200, J1643 1224,
− −
2012 Oct. 27 and Nov. 10, and was due to switching J1713+0747, and J1744 1134. These were selected on the
−
clock sources without measuring the phase difference be- basis of being of the most precisely timed pulsars in
tween their signals. The second offset, which occurred on the PSRIX data set. The JUMPs were fit simultaneously
2013 July 27, was caused by cutting thepower to the clock with pulsar parameters and noise models using TempoNest
c 0000RAS,MNRAS000,000–000
(cid:13)
6 P. Lazarus et al.
4.3 Comparison With the EBPP Backend
We have compared the S/N derived from data recorded
simultaneously with PSRIX and the old EBPP backend
ete)
offsscal ∆TB (foseuerFMigSP3)s.tIhnatpaarrteicubleasrt, awnedumseodstmfurletqipuleenotlbysetrivmaetdionwsitohf
k to PSRIX, PSRs J0613 0200, J1643 1224, J1713+0747, and
Cloc(Not 0 ∆TA ∆TC ∆TD Jca1n7t4l4y−s1t1r3o4n.geWredehtaevc−teiofnous,nrdouthghatl−yP2S–R5ItXimpersovhiidgehsersiSgn/Nifi-,
than the simultaneously recorded EBPP data. A similar
) comparison of TOA uncertainties derived for simultaneous
s
µ 2 PSRIXandEBPPdataalsoshowsimprovementsofafactor
(
s of 2–5.
l
a 0 There are several reasons why PSRIX outperforms the
u
d EBPP:
i
es−2 1)The200-MHzbandwidthofPSRIXisconsiderablylarger
R 55750 56250 56750 than the EBPP’s usable bandwidth ( 40–50MHz for most
MJD pulsars, and 95MHz for pulsars wit∼h DM ∼< 10pccm−3).
∼
A comparison of the observing bands from both backends
is shown in Fig. 4. PSRIX’s larger bandwidth allows more
Figure2.Top–Aschematicofthefourclockoffsetssufferedby
the PSRIX system. Theoffset values are:∆TA =97.2851(6)ms, signal to beintegrated, reducing radiometer noise, and also
∆TB = 409.2691(8)ms, ∆TC = 0.000612(1)ms, and ∆TD = increases thechance of observing constructive scintels.
0.000127(1)ms. Offsets A and B are larger than the spin peri- 2) The PSRIX data are recorded with 8 bits, making them
odsofthepulsarsreportedhere(P 1–50ms),thusresultingin even more resilient in the presence of strong RFI than the
∼
phase ambiguities and different apparent offsets in residuals for EBPP with its 4-bit data.
differentpulsars.See 4.2fortheoriginsoftheclockoffsetsand 3) The 10-s sub-integrations of PSRIX are much shorter
§
howtheirmagnitudesweredetermined.
thanthe2-minsub-integrationsoftheEBPP.Thus,theex-
Bottom –TimingresidualsfromPSRIXobservations at1.4GHz
pense of removing impulsive RFI is diminished. Also, the
ofPSRJ1713+0747afteraccountingfortheclockoffsets,showing
shorter sub-integrations make re-aligning the pulse profiles
thatnosignificantoffsets remain.
with an updated timing model more accurate.
4)PSRIXisamorerobustinstrumentthantheEBPP.This
(Lentati et al. 2014). The resulting JUMP values, all of is especially true now that the latter is nearly 20 years old,
which were measured relative to the original clock sig- and hardware and networking issues occasionally preclude
nal, were averaged together resulting in measurements of it of recording data. In these instances, data files are cut
∆TA = 97.2851(6)ms and ∆TB = 409.2691(8)ms. These short, or not written at all.
measurements have been confirmed with data from LEAP The increase in bandwidth of PSRIX over the EBPP
by measuring and comparing the phase delays between the is even more apparent when full polarisation information
signals of simultaneous observations with several European is recorded. Polarisation observations with the EBPP are
radio telescopes before and after the epochs of the PSRIX limited to only 28MHz, whereas with PSRIX full polari-
clock offsets (see Bassa et al. 2015, for an overview of the sation information can be recorded for up to 500MHz of
project).10 The third and fourth offsets were directly mea- bandwidth. Moreover, because recording polarisation infor-
sured at the telescope by comparing clock signals with an mation required the EBPP to be set up in a special mode
oscilloscope.Theresultsarehigh-precisionmeasurementsof prior to commencing observations, it is much less flexible
∆TC = 0.000612(1)ms and ∆TD = 0.000127(1)ms, which than PSRIX, which always provides full Stokes parameters
areconsistentwithoffsetvaluesderivedfromfittingJUMPs for timing-mode observations.
to pulsar timing data. Inadditiontoinvestigatingindividualobservations, we
A schematic of the PSRIX clock offsets is shown in alsoexaminedthetimingdataofseveralpulsarstocompare
Fig. 2. The timing residuals of PSR J1713+0747 after the the timing stability achievable with PSRIX vs. the EBPP.
JUMPsareremovedshownoevidenceoftheclockoffsets,as Dependingonthepulsar,wefoundtheweightedroot-mean-
showninthebottompanelofFig.2.Similarly,theresiduals square (RMS) of the PSRIX timing residuals is a factor of
of all other pulsars are also free of the effect of the clock 1.3–3 times better than that of the EBPP over the same
∼
offsets after applyingthe offsets listed above. timeinterval.Inouranalysis,wewhitenedthetimingresidu-
Note that the EBPP uses an independent reference alswiththreefrequencyderivativesandtwoDMderivatives
clock, and thus was not affected by any of the four offsets tonot bebiased by theeffects of pulsar spin noise and DM
seen in the PSRIXdata. variations.11 Wealsoremovedthefourclockoffsetsaffecting
PSRIXdata mentioned in 4.2. The smallest improvement
§
factorwefound(1.3 )wasforPSRJ1744 1134.Thisisbe-
10 TheprecisionoftheLEAP-basedmeasurementsisexpectedto causethepulsar’spa×rticularly lowDMof−3.1pccm−3 made
surpasswhatispossiblewithtiming-basedJUMPmeasurements.
However,theuncertaintiesoftheLEAP-basedmeasurementsare
notyetwelldetermined,soherewereportthevaluesanduncer- 11 ThetimingresidualsfromPSRIXandtheEBPPcloselytrace
taintiesderivedfromthemorestandardandconservative JUMP the residuals from other EPTA telescopes, so we are confident
measurements. thatthesystematictrendsweareremovingarenotinstrumental.
c 0000RAS,MNRAS000,000–000
(cid:13)
The Effelsberg PSRIX Pulsar Timing Backend 7
y
t
i
s
n
e
103 t
n
I
)
z
H
1400
M
N (
/ y
X S 102 nc1350
RI ue
S q1300
P e
r
F
1250
J0613 0200
101 − 0 0.25 0.5 0.75 10 0.25 0.5 0.75 1
J1643 1224 Phase Phase
−
J1713+0747
Figure 4. Left – The integrated pulse profile and frequency
J1744 1134
− vs. phase plot for a 28-min observation with PSRIX of
101 102 103 PSRJ1713+0747on2013Jan6.ThisdetectionhasaS/N =225
thanks toits200MHzbandwidth. Thefrequency channels miss-
EBPP S/N
ing are removed due to interference and roll-off at the edges of
thesub-bands(see 3).
§
Figure3.ComparisonofS/Nforsimultaneousobservationswith Right –Theintegratedpulseprofileandfrequencyvs.phaseplot
the PSRIX and EBPP backends. Equal S/N is shown with the for the same observation of PSR J1713+0747 using data from
dashedline.Thedottedlinesrepresent2 ,5 ,and10 improve- EBPP, which was recording in parallel. The EBPP provides a
× × ×
ments. The one observation of PSR J1713+0747 wherethe S/N significantly weaker detection with S/N = 20, owing to its lim-
is larger in the EBPP observation is due to there being a sin- ited 40MHzbandwidth.
∼
glescintillationmaximumwithinthe200-MHzPSRIXbandthat
falls inside the smaller EBPP observing window. Note that we
didnot weight the frequency channels by S/N when integrating range from 0.1 to 7.5µs at 5GHz and from 5 to 30µs at
theband. 9GHz(see Table 4).
Our 5 and 9-GHz detections show that it is feasible to
monitor some MSPs at these observing frequencies, which
it possible for theEBPP tocoherently dedisperse 95MHz arehigherthanthosetypicallyemployedforlong-termmon-
∼
of usable bandwidth. itoring projects (350–3100MHz; e.g. Desvignes et al., sub-
Despite PSRIX providing better detections than the mitted; Manchester et al. 2013; Arzoumanian et al. 2015;
EBPP,westillobservewithbothbackendsinparallelwhen- Shannonet al. 2015). It is important to note that observ-
everpossible,toextendthelatter’snearly20-yearlongdata ing campaigns will only benefit from high-frequency detec-
set. tionsofpulsarsthataresufficientlybrighttobeabletotake
advantage of the reduced ISM effects. See 5.2 for a more
§
detailed discussion.
4.4 High-Frequency Observations
Our 5 and 9-GHz observations of 12 EPTA pulsars all re-
sulted in detections. The integrated pulse profiles from in- 5 DISCUSSION
dividual high-frequency observations are shown in Fig. 5.
ThenewPSRIXdataset already containsroughlymonthly
PSRs J1012+5307, J1713+0747, B1937+21 were observed
observationsof47MSPs,blackwidowpulsarsandrelativis-
twice at 5GHz, and PSR J2145 0750 was observed twice
− tic binaries at 1.4 and 2.6GHz spanning at least two years,
each 5 and 9GHz. Details of the 5 and 9-GHz observations
includingthe33pulsarssummarisedinTables2and3.This
presented in Table 4.
datasetisthesuccessorofthevenerableEBPPdataset,and
To flux calibrate our observations, we observed 3C 48
includesstrongerdetectionsandmorepreciseTOAsthanks
at both 5 and 9GHz on 2015 Jan. 7 and again on 2015
to thelarger bandwidth and more robust design of PSRIX.
Jan. 24. These observations were used to derive calibrated
flux densities of our observations at these frequencies. We
observedthepulsarstohavefluxdensitiesranging from 0.2
5.1 Improved Sensitivity to a GW Background
to1.5mJy at 5GHz,and from 0.2 to0.3mJy at 9GHz(see
Table 4). We found some variation in the measured flux One of the primary goals of our monthly observations with
densities of the pulsars observed multiple times. However, PSRIXistocontributetotheEPTAandIPTAobjectiveof
these variations are consistent with amplitude modulations detecting the GWB. To this end, we will be combining our
expected from weak scintillation at these frequencies (e.g. observations with theEPTA and IPTA data sets.
Lorimer & Kramer 2004). We haveestimated the improvement to GWB sensitiv-
For each of our high-frequency observations, we com- ity made possible by switching from the EBPP to PSRIX
putedTOAuncertaintiesusingananalytictemplate,which fortwoseparatescenarios:first,assumingallpulsarsexhibit
wasgeneratedbyfittingvonMises-shapedpulsecomponents only pure white noise (e.g. radiometer noise or from pulse
to the summed profile. TOA uncertainties we determined jitter), and second, assuming the pulsars also suffer from
c 0000RAS,MNRAS000,000–000
(cid:13)
8 P. Lazarus et al.
J0751+1807 J1012+5307 J1012+5307 J1022+1001
5 GHz, Jan 28, 2015 5 GHz, Jan 24, 2015 5 GHz, Jan 28, 2015 5 GHz, Jan 24, 2015
Tobs. = 2960 s Tobs. = 3740 s Tobs. = 2060 s Tobs. = 1780 s
J1518+4904 J1600 3053 J1643 1224 J1713+0747
− −
5 GHz, Jan 28, 2015 5 GHz, Jan 28, 2015 5 GHz, Jan 26, 2015 5 GHz, Jan 26, 2015
Tobs. = 1770 s Tobs. = 1770 s Tobs. = 1780 s Tobs. = 1200 s
s
n
o
zi
Hat
Gv
r
5-e J1713+0747 J1730−2304 J1744−1134 B1855+09
s 5 GHz, Jan 28, 2015 5 GHz, Jan 26, 2015 5 GHz, Jan 28, 2015 5 GHz, Jan 26, 2015
b Tobs. = 1780 s Tobs. = 1770 s Tobs. = 1280 s Tobs. = 1780 s
O
B1937+21 B1937+21 J2145 0750 J2145 0750
− −
5 GHz, Jan 07, 2015 5 GHz, Jan 28, 2015 5 GHz, Jan 07, 2015 5 GHz, Jan 25, 2015
Tobs. = 2310 s Tobs. = 1780 s Tobs. = 1780 s Tobs. = 1780 s
s J1022+1001 J1713+0747 J2145 0750 J2145 0750
n − −
9 GHz, Jan 24, 2015 9 GHz, Jan 26, 2015 9 GHz, Jan 07, 2015 9 GHz, Jan 26, 2015
zio Tobs. = 2610 s Tobs. = 1780 s Tobs. = 2950 s Tobs. = 2680 s
Hat
Gv
r
9-e
s
b
O
0 0.5 10 0.5 10 0.5 10 0.5 1
Phase Phase Phase Phase
Figure 5. Integrated pulse profiles from PSRIX observations at 5 and 9-GHz. In all cases, a bandwidth of 500MHz was used. These
detections werecleanedofRFIandpolarisationcalibrated.SeeTable4forobservationdetails.
c 0000RAS,MNRAS000,000–000
(cid:13)
The Effelsberg PSRIX Pulsar Timing Backend 9
red noise following a power-law spectrum (e.g. from intrin-
sicspinnoise oruncorrectedDMvariations). Inbothcases, 4
we considered a 7-pulsar12 hybrid data set that combines η=2
the higher timing precision of the PSRIX TOAs with the or η=3
ct η=5
longevityoftheexistingEBPPdataset.Wethencompared Fa EBPP only
our results for this hybriddata set to a hypotheticalexten- nt 3
e
sion ofthecurrentEBPP data set without havingswitched m
e
to PSRIX. v
o
In our first set of estimates, we assumed pulsars with pr
m2
pure white noise timing residuals. We assumed the timing d I
residuals RMS in EBPP data is RMS = 1µs, and the e
E at
RMS of PSRIX residuals is improved by a factor η (i.e. m
RMSP = RMSE/η). We performed separate estimates for Esti1
η = 2, 3, and 5. For simplicity, we also assumed that the
phase offset between the EBPP-era data and the PSRIX- 2000 2005 2010 2015 2020 2025
eradataisperfectlydetermined.WethenusedtheCram´er- Year
RaoBound(e.g.Fisz1963)tocomputetheminimumGWB
amplituderequired to reject thenullhypothesis, which was Figure 6. Estimated improvement in sensitivity to the GWB
thatthereisnoGWB(i.e.azero-amplitudeGWB)atthe1σ as a function of date provided by including PSRIX data com-
level.AmorecompletedescriptionoftheuseoftheCram´er- pared to a hypothetical extended EBPP-only data set. We have
Rao Bound in the context of estimating PTA sensitivity to assumedwhitenoisewithRMSE=1µsforEBPP-eradata(1997
the GWB can be found in Caballero et al. (2015). In mak- to2011),andRMSP=RMSE/ηforPSRIXdata.Thebaselineof
ourcomparisonassumedEBPPdataonly.ByusingtheCram´er-
ing our estimates, we assumed that the GWB signal has a
RaoBoundwecalculatedtheGWBamplitudeatwhichthedata
power-lawstrainspectrumwithanindexof 2/3,appropri-
− would show a 1σ inconsistency with the no-GWB null hypoth-
ate for an isotropic stochastic background of super-massive
esis. The three black curves correspond to pure white noise and
black hole binaries. Improvement factors were determined improvementfactorsofη=2,3,and5.Theredcurvesincludean
by comparing the GWB amplitude derived for the hybrid additional source of red noise with an amplitude corresponding
data set with the analogous value computed for the pure to RMSred = 100ns and a conservatively flat spectral index of
EBPP-style data set. Our estimated improvement factors αred=−1.5forallpulsars.Seetextforadditionaldiscussion.
forη=2,3,and5asafunctionofdateareshowninFig.6.
Our second set of estimates are determined follow-
2010).Whileitmaynotbepossibletofullyremovethedele-
ing the same procedure described above, but assuming an
terious effect of red noise from pulsar timing data, some of
additional red noise contribution to the timing residuals.
thesenoise processes (e.g. from theISM– see 5.2) can be
We used a red noise spectrum with an amplitude corre-
§
mitigated,furtherimprovingtheprospectsforthedetection
sponding to RMS = 100ns and a spectral index of
red
of theGWB.
α = 1.5 for all pulsars. This optimistically flat value
red
of α is −within the measured range for MSPs, 7 ∼< α ∼< As suggested by Siemens et al. (2013), another way to
1 (e.g. Arzoumanian et al. 2015; Caballero et a−l. 2015).13 counter the loss of sensitivity to the GWB due to pulsars’
− red timing noise is to include other, possibly newly discov-
Even when assuming this nearly best-case red noise spec-
eredMSPsinPTAs.Thisexemplifiestheimportanceofon-
trum, we find the overall improvement in sensitivity to the
going high time and frequency radio pulsar surveys such
GWB is considerably reduced. This is because only the
as the Pulsar Arecibo L-Band Feed Array (PALFA) sur-
powerofthewhitenoiseisreducedbyswitchingtoPSRIX.
vey (Lazarus et al. 2015), the High-Time Resolution Uni-
It is, therefore, the red noise restricts the sensitivity to the
verse(HTRU)surveys(Keith et al. 2010; Barr et al. 2013),
GWB. We also find that the improvement factor saturates
and the Greenbank North Celestial Cap (GBNCC) survey
earlierbecausethelowfrequenciesprobedasthedatasetis
(Stovallet al. 2014).
extendedaredominatedbyrednoise.Thus,inthered-noise
case, these lowest frequencies contribute little sensitivity to
the GWB. The improvement factors for GWB sensitivity
5.2 PTA Monitoring of MSPs at High Frequencies
found for these red noise cases are indicated with the red
curvesin Fig. 6. ISM variations, primarily DM variations, can introduce a
The difference between the black and red curves in significant amount of red noise into the timing residuals of
Fig. 6 is caused by the presence of red noise, which can someMSPs(e.g.Lentatietal.,inprep.;Cordes & Shannon
arise from a variety of sources (see e.g. Cordes & Shannon 2010; Keith et al. 2013; Leeet al. 2014). This can bea ma-
jor hindrance to reliably detecting long-timescale signals in
the data (e.g. the nHz GWB spectrum being searched for
with PTAs). Thus, mitigating ISM variations is of great
12 We used the positions of PSRs J0218+4232, J0613 0200,
− importance. In general, this can be accomplished in two
J1022+1001, J1600 3053, J1713+0747, B1855+09, and
− ways: 1) by avoiding ISM variations, either by discarding
J2145 0750. Because we are computing improvement fac-
− datasetscontaminatedbyISMvariationsorbyobservingat
tors,wefindthereisnosignificantdifferenceintheresultsasthe
frequencieshighenoughthattheamplitudeofISM-induced
numberofpulsarsisincreased.
13 MSPswithverysteepspectralindices(e.g.B1937+21)arenot noiseissufficientlysmall(e.g.aswasdonebyShannon et al.
typicallyusedinsearchesfortheGWB. 2015),and2)byremovingtheISMeffects,eitherbyleverag-
c 0000RAS,MNRAS000,000–000
(cid:13)
10 P. Lazarus et al.
ingmulti-frequencyandwide-bandobservationstomeasure
DMvariations(e.g.Keith et al.2013;Demorest et al.2013;
ArzoTumheaneiffaenctetoafl.th2e01I5S)M. diminishes with increasing ob- Npsr 42
serving frequency: DM delays scale as τ f−2 (e.g.
d ∝ 0
Lorimer & Kramer 2004) and pulse broadening caused by
i2n0t0e4r)s.teTllahrersecfaotrtee,ripnuglssacraletsimaisnτgsd∝atfa−3fr.8o6m±0.h16ig(hB-fhreaqtueetnacly. 102 EEffff.. CS1+10mm EMfef.e UrKBABT
Eff. S60mm Eff. P217mm
observationswill contain lesssignificant redISMnoise. Un-
Eff. LOFAR
fortunately, the radio spectra of pulsars, which are gener-
A
a2stl0le0ye0pd;,eBwscairttihebsesedptebcaytl.raa2l0si1inm3d)pi,cleemspaokofiwn−egr1ilt∼<awdα,iffiS∼<cu∝−lt2ft(αoM,caaorrmoenprlaeetttheaellyr. aled σTO101
c
S
avoid ISM variations while maintaining the S/N required
forhigh-precisiontiming.Thus,inpractice,ISMeffectscan- 100
not be completely ignored by observing at arbitrarily high
frequencies.Someefforttoremovetheseeffectsisnecessary.
When removing DM variations thekey resulting quan-
tity is the infinite-frequency TOA, T∞ (i.e. the DM- Corrected w/ Eff. P217mm
correctedTOA).EstimatesofT∞canbemadebycombining Self-corrected using 2 subbands
multi-frequency observations or by splitting a single wide- (Colours same as above)
bandobservationintomultiplesub-bands(seee.g.Lee et al. 100
2014).TheuncertaintyonT∞ isσ∞ = δT∞2 ,andinthe σ∞
two-band case, is given by(Eq. 12 of Lepehet al.i2014) ed
al
f4σ2+f4σ2 Sc
δT2 = 1 1 2 2, (2)
∞ (f2 f2)2
(cid:10) (cid:11) 1 − 2 10-1
where the fi and σi terms are the centre frequencies and
TOA uncertainties of thetwo bands, respectively.
To measure and remove DM variations, timing data at −3.0 −2.5 −2.0 −1.5 −1.0
1to3GHzaretypicallycomplementedbylow-frequencyob- Spectral index, α
servations (e.g. ∼<350MHz). To illustrate the precision on
T∞ attainable, wehaveestimated therelativeimprovement
in σ∞ from combining observations with the LOFAR inter- Figure7.Top –DistributionofspectralindicesfromtheATNF
nationalstationatEffelsberg,14withPSRIXdataat1.4GHz PulsarCatalogueforthepulsarsinTable2.
to compute. Note that we have neglected the differences in Middle – TOA uncertainties for various existing and future ob-
propagation paths through Galaxy of the lower and high- serving systems scaled to what is achievable with PSRIX using
frequencyradioemissionduetoscattering(seeCordes et al. theP217mmreceiverasafunctionofpulsarradiospectralindex.
Lowervaluesindicatemoreprecise(i.e.better)TOAs.Notethat
2015,foradiscussion ofthiseffect).Weestimated theratio
the estimated TOA precision of the UBB receiver is worse than
ofTOAuncertaintiesderivedfromobservationsofthesame
the P217mm receiver because of the former’shigh SEFD, which
durationwithdifferentobservingsystems,“A”and“B”,us-
willbereducedwhenahigh-passfilterisinstalled.
ing Bottom – The uncertainty of the infinite frequency TOA (i.e.
the uncertainty of the DM-corrected TOA), σ∞, obtained from
σtA = (S/N)B cfroommbianniontgheErffoeblssberevrging1.s4y-GstHemz (rPel2a1ti7vmemto)tdheeteucntcioerntsaiwntiythofdtahtae
σtB (S/N)A self-corrected P217mm observation. The σ∞ values for the self-
= Ssys,A ∆fA fhi,B(α+1)−flo,B(α+1) , (3) correctedobservationsareestimatedassumingthebandisdivided
Ssys,Br∆fB (cid:18)fhi,A(α+1) flo,A(α+1)(cid:19) evenly into two parts. Note, that doubling the integration time
− onlyimprovesσ∞ by√2.
where S is the system-equivalent flux density, ∆f is the
sys
recorded bandwidth, f and f are the low and high fre-
lo hi
quency edges of the recorded band, respectively, and α is
recorded bandwidth issummed to form asingle TOA.This
the spectral index. In deriving Eq. 3, we have ignored the
is a reasonable assumption given recent work on wide-band
effect ofprofileevolution across theband,which isminimal
template matching (Pennucci et al. 2014; Liu et al. 2014).
forMSPs(Kramer et al.1999),aswellaspulsebroadening,
In fact, by using these new wide-band TOA determination
whichcanbesignificant at150MHz.Wehavealsoassumed
algorithmsitispossibletosimultaneouslyaccountforprofile
that S is constant across the individual bands. Our esti-
sys evolution,DMvariations, scattering, andscintillation while
mates are plotted in Fig. 7 for 3 α 1.
− ≤ ≤− summarising wide-band observations into a single TOA.
For simplicity, in Fig. 7 we have assumed the entire
Clearly, complementing PSRIX TOAs with observa-
tions using the Effelsberg LOFAR station, provides precise
14 Theinternational LOFARstationatEffelsbergisalsoknown DM-corrected TOAs. However, there are some complica-
as“DE601”. tions with using low-frequency data to remove DM varia-
c 0000RAS,MNRAS000,000–000
(cid:13)