11institutetext:  ASTRON, Netherlands Institute for Radio Astronomy, Oude
Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands 22institutetext:
Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010,
6500 GL Nijmegen, The Netherlands 33institutetext: Jodrell Bank Centre for
Astrophysics, Department of Physics and Astronomy, University of Manchester,
Manchester M13 9PL, UK 44institutetext: LPC2E - Université d’Orléans/CNRS,
France 55institutetext: ORN, Observatoire de Paris, Université PSL, Univ
Orléans, CNRS, 18330 Nançay, France 66institutetext: Anton Pannekoek Institute
for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam,
The Netherlands 77institutetext: Department of Physics, Massachusetts
Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
88institutetext: MIT Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA
02139, USA 99institutetext: Department of Physics, McGill University, 3600 rue
University, Montréal, QC H3A 2T8, Canada 1010institutetext: McGill Space
Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7,
Canada 1111institutetext: INAF - Cagliari Astronomical Observatory, Via della
Scienza 5, I–09047 Selargius (CA), Italy 1212institutetext: Max-Planck-
Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany Bonn,
Germany 1313institutetext: Fakultät für Physik, Universität Bielefeld,
Postfach 100131, 33501 Bielefeld, Germany 1414institutetext: Department of
Space, Earth and Environment, Chalmers University of Technology, Onsala Space
Observatory, 439 92 Onsala, Sweden 1515institutetext: Max-Planck-Institut für
Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
1616institutetext: Ruhr University Bochum, Faculty of Physics and Astronomy,
Astronomical Institute, 44780 Bochum, Germany 1717institutetext: Oxford
Astrophysics, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, UK
1818institutetext: Manly Astrophysics, 15/41-42 East Esplanade, Manly, NSW
2095, Australia 1919institutetext: SKA Observatory, Jodrell Bank, Lower
Withington, Macclesfield, SK11 9FT, United Kingdom 2020institutetext:
Department of Physics and Astronomy, University of the Western Cape,
Bellville, Cape Town, 7535, South Africa 2121institutetext: Leibniz-Institut
für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany

# The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an
overview of the properties of the LOFAR pulsar discoveries

E. van der Wateren<EMAIL_ADDRESS>LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35
radio pulsars and an overview of the properties of the LOFAR pulsar
discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and
an overview of the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-
Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the
properties of the LOFAR pulsar discoveries C. G. Bassa The LOFAR Tied-Array
All-Sky Survey: Timing of 35 radio pulsars and an overview of the properties
of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of
35 radio pulsars and an overview of the properties of the LOFAR pulsar
discoveries S. Cooper The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveriesThe
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveries J. -M. Grießmeier The LOFAR
Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the
properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveriesThe
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveries B. W. Stappers The LOFAR Tied-
Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the
properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveries J. W. T. Hessels The LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveriesThe
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveries V. I. Kondratiev The LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveries D.
Michilli The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and
an overview of the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-
Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the
properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveries C.
M. Tan The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an
overview of the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array
All-Sky Survey: Timing of 35 radio pulsars and an overview of the properties
of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of
35 radio pulsars and an overview of the properties of the LOFAR pulsar
discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and
an overview of the properties of the LOFAR pulsar discoveries C. Tiburzi The
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveries P. Weltevrede The LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveries A.
-S. Bak Nielsen The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveriesThe
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35
radio pulsars and an overview of the properties of the LOFAR pulsar
discoveries T. D. Carozzi The LOFAR Tied-Array All-Sky Survey: Timing of 35
radio pulsars and an overview of the properties of the LOFAR pulsar
discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and
an overview of the properties of the LOFAR pulsar discoveries B. Ciardi The
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveries I. Cognard The LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveriesThe
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveries R. -J. Dettmar The LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveries A.
Karastergiou The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars
and an overview of the properties of the LOFAR pulsar discoveriesThe LOFAR
Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the
properties of the LOFAR pulsar discoveries M. Kramer The LOFAR Tied-Array All-
Sky Survey: Timing of 35 radio pulsars and an overview of the properties of
the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35
radio pulsars and an overview of the properties of the LOFAR pulsar
discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and
an overview of the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-
Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the
properties of the LOFAR pulsar discoveries J. Künsemöller The LOFAR Tied-Array
All-Sky Survey: Timing of 35 radio pulsars and an overview of the properties
of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of
35 radio pulsars and an overview of the properties of the LOFAR pulsar
discoveries S. Osłowski The LOFAR Tied-Array All-Sky Survey: Timing of 35
radio pulsars and an overview of the properties of the LOFAR pulsar
discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and
an overview of the properties of the LOFAR pulsar discoveries M. Serylak The
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35
radio pulsars and an overview of the properties of the LOFAR pulsar
discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and
an overview of the properties of the LOFAR pulsar discoveries C. Vocks The
LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of
the properties of the LOFAR pulsar discoveriesThe LOFAR Tied-Array All-Sky
Survey: Timing of 35 radio pulsars and an overview of the properties of the
LOFAR pulsar discoveries O. Wucknitz The LOFAR Tied-Array All-Sky Survey:
Timing of 35 radio pulsars and an overview of the properties of the LOFAR
pulsar discoveriesThe LOFAR Tied-Array All-Sky Survey: Timing of 35 radio
pulsars and an overview of the properties of the LOFAR pulsar discoveries

The LOFAR Tied-Array All-Sky Survey (LOTAAS) is the most sensitive untargeted
radio pulsar survey performed at low radio frequencies (119–151 MHz) to date
and has discovered 76 new radio pulsars, among which the 23.5-s pulsar
J0250+5854, up until recently the slowest-spinning radio pulsar known. Here,
we report on the timing solutions of 35 pulsars discovered by LOTAAS, which
include a nulling pulsar and a mildly recycled pulsar, and thereby complete
the full timing analysis of the LOTAAS pulsar discoveries. We give an overview
of the findings from the full LOTAAS sample of 76 pulsars, discussing their
pulse profiles, radio spectra and timing parameters. We found that the pulse
profiles of some of the pulsars show profile variations in time or frequency
and while some pulsars show signs of scattering, a large majority display no
pulse broadening. The LOTAAS discoveries have on average steeper radio spectra
and have longer spin periods ($1.4\times$) as well as lower spin-down rates
($3.1\times$) compared to the known pulsar population. We discuss the cause of
these differences, and attribute them to a combination of selection effects of
the LOTAAS survey as well as previous pulsar surveys, though can not rule out
that older pulsars tend to have steeper radio spectra.

###### Key Words.:

pulsars: general – ephemerides – surveys

##  1 Introduction

Radio pulsars are uniquely useful sources to study the Galactic neutron star
population, because their radio emission holds information about their
rotation and relative motion, as well as the signal propagation. These
properties, which are mostly unknown for other types of neutron stars, can be
used to derive parameters which are essential to describe the population, such
as the characteristic age, the magnetic field, and the spin-down energy
(Lorimer & Kramer, 2012). Models for population synthesis rely on information
about the currently known population. So far, the ATNF Pulsar
Catalogue111http://www.atnf.csiro.au/research/pulsar/psrcat (version 1.67,
Manchester et al. 2005), consists of 3320 pulsars (Manchester et al., 2005),
which is expected to be only a small proportion of the full Galactic pulsar
population (Keane et al., 2015). Surveys searching for new pulsars and
exploring new parameter spaces are therefore necessary to get a complete
picture of the full Galactic neutron star population. Recent discoveries
resulting from radio pulsar surveys include the double pulsar (Burgay et al.,
2003; Lyne et al., 2004; Kramer et al., 2021), the fastest and heaviest
Galactic neutron star (Bassa et al., 2017; Romani et al., 2022), and unusually
long-period radio sources (Hurley-Walker et al., 2022; Caleb et al., 2022).

A large proportion of pulsars have been discovered in surveys at observing
frequencies around 1.4 GHz and by predominantly surveying the Galactic plane,
such as the Parkes multi-beam pulsar survey (Manchester et al., 2001) and the
PALFA survey (Cordes et al., 2006; Lazarus et al., 2015). More recently, there
have been several wide area pulsar surveys at lower observing frequencies,
including the Green Bank North Celestial Cap (GBNCC) survey, observing at 350
MHz (Stovall et al., 2014), AO327, a survey with Arecibo at 327 MHz (Deneva et
al., 2013), the Giant Metrewave Radio Telescope (GMRT) High Resolution
Southern Sky Survey at 322 MHz (Bhattacharyya et al., 2016), and the Pushchino
Multibeam Pulsar Search (PUMPS) at 111 MHz (Tyul’bashev et al., 2022). As the
currently known pulsar population is a reflection of the surveys with which
they were found, searching at different frequencies may shed light on new
pulsar populations.

Pulsars, which were originally discovered at the low observing frequency of
81.5 MHz (Hewish et al., 1968), have generally steep radio spectra
($S_{\nu}\propto\nu^{-1.57\pm 0.62}$; Jankowski et al. 2018) and hence are
brighter at lower frequencies. Therefore, many pulsars may still be waiting to
be discovered, being only observable at lower frequencies. However, pulsar
surveys at low observing frequencies are challenging because these
observations are more severely affected by dispersion and interstellar
scattering, which scale with frequency $\nu$ as $\nu^{-2}$ and $\nu^{-4}$,
respectively. Additionally, because of the $\nu^{-2.6}$ sky temperature
spectrum (e.g. Price, 2021), low frequency observations also suffer more from
high sky temperatures. For these reasons, pulsar surveys at low frequencies
are less sensitive to pulsars in the Galactic plane, where dispersion,
scattering and sky temperatures are all higher compared to higher Galactic
latitudes.

The LOFAR Tied-Array All-Sky Survey (LOTAAS) was aimed at searching for radio
pulsars and fast transients at very low observing frequencies. This untargeted
all-sky survey of the northern hemisphere operated at frequencies between 119
and 151 MHz with long 1-hour integration times per pointing (Sanidas et al.,
2019). Full timing solutions and spectra of 41 pulsars discovered by LOTAAS
have been presented by Tan et al. (2018), Michilli et al. (2020), and Tan et
al. (2020), which include the 23.5-s pulsar J0250+5854, up until recently the
slowest spinning radio pulsar known. Other discoveries were a mildly recycled
binary pulsar and a Rotating Radio Transient (RRAT; McLaughlin et al. 2006).

By investigating the pulsars discovered by LOTAAS at very low observing
frequencies, we gain a unique insight into a new parameter space of the pulsar
population. In this paper, we report on the properties of 32 pulsars
discovered by LOTAAS (Sanidas et al., 2019) and two pulsars discovered by its
pilot survey, the LOFAR Tied-Array Survey (LOTAS; Coenen et al. 2014). We also
included PSR J1958+2214, which was discovered as PSR J1958+21 as part of the
LOTAAS survey after the publication of the overview paper by Sanidas et al.
(2019). In § 2, we combine the LOFAR observations with observations from other
telescopes to perform a multi-frequency analysis, hence obtaining the full
timing solutions of all 35 pulsars. The pulse profiles at different
frequencies were inspected for signs of interstellar scattering and profile
variation. Additionally, we calculated flux densities and performed spectral
analysis to constrain the spectral index. As this paper completes the full
timing analysis of all pulsars discovered by LOTAAS, we also give an overview
of the findings of all LOTAAS pulsar discoveries in § 3, and discuss their
properties compared to the known pulsar population in § 4.

##  2 Observations and analysis

###  2.1 Observations

Timing observations of the LOTAAS pulsars were obtained with the LOFAR Core,
the International LOFAR stations in Germany, France, Sweden, and the United
Kingdom, the Lovell telescope at Jodrell Bank Observatory (JBO) in the United
Kingdom, and the Nançay Radio Telescope in France. For each pulsar, we used
the best-known celestial position, spin period, and dispersion measure
($\mathrm{DM}$) from their discovery or follow-up gridding observations
(Coenen et al., 2014; Sanidas et al., 2019) to point the telescopes and obtain
timing observations.

For the LOFAR Core observations, the high-band antennas (HBAs) from the 24
Core stations were digitally beamformed with the cobalt correlator/beamformer
(Broekema et al., 2018) to create a single tied-array beam pointing towards
the pulsar (see Stappers et al. 2011 for a description of LOFAR’s beam-formed
modes). Nyquist sampled, dual polarisation complex voltages were recorded for
400 subbands of 0.1953125 MHz each, covering observing frequencies from 110 to
188 MHz. The complex voltages were coherently dedispersed and folded using
dspsr (van Straten & Bailes, 2011) through the LOFAR pulsar pipeline
(Kondratiev et al., 2016) to produce folded pulse profiles in the psrfits
format for 10-s sub-integrations and 0.1953125 MHz channels. We used clfd
(Morello et al., 2019) to automatically remove the majority of the radio
frequency interference (RFI). Remaining residual RFI was removed manually with
the psrzap tool from the psrchive software suite (Hotan et al., 2004).

The observations from the LOFAR stations of the German LOng Wavelength
consortium (GLOW) were processed following the procedure described in Donner
et al. (2020). For the observations of the French LOFAR station FR606, voltage
data was recorded between 102.34 and 197.46 MHz in subbands of 0.1953125 MHz
and processed with a pipeline based on dspsr producing folded pulse profiles
in the psrfits format for 10-s sub-integrations. Frequencies below 109.96 MHz
and above 187.89 MHz were discarded. RFI was automatically removed using
CoastGuard (Lazarus et al., 2016), followed by a manual inspection and RFI
removal where needed. The pre-processing of the observations from the Swedish
LOFAR station SE607 was done similarly to the FR606 procedure, with the
additional steps of removing data between 181 and 186 MHz and injecting
improved ephemeris before cleaning the observations. The UK LOFAR station at
Chilbolton (UK608) uses the ARTEMIS222Advanced Radio Transient Event Monitor
and Identification System backend Karastergiou et al. (2015). Observations
were typically 1 h in duration, spanned 48 MHz, centred at 162 MHz, and
divided in to channels of approximately 12.2 kHz. The data were folded with a
pipeline based on dspsr and further analysis was done using psrchive. The
majority of RFI was automatically removed using clfd and the remainder was
removed manually with psrzap

Observations with the LOFAR Core were obtained at an approximately monthly
cadence, while the International LOFAR stations observed at an approximately
weekly or semi-weekly cadence. Integration times of the LOFAR Core
observations were between 10 and 20 min while the lower-collecting-area
International LOFAR stations observed between 1 and 4 hr.

At higher observing frequencies, the majority of the LOTAAS pulsars were
observed with the Lovell telescope at 334 MHz and 1532 MHz to constrain their
spectra. For those pulsars detected at 1532 MHz, further timing observations
were obtained at a weekly to monthly cadence. These observations were obtained
using the Digital Filterbank (DFB) with observed bandwidths of 64 MHz at 334
MHz, and 384 MHz at 1532 MHz. The integration times were between a few minutes
and an hour depending on the pulsar brightness. The Nançay Radio Telescope
observed at 1484 MHz with the NUPPI backend (Guillemot et al., 2016). The
integration times were between a few minutes and an hour with a bandwidth of
512 MHz. As only a few JBO observations at 334 MHz and NRT observations were
obtained per pulsar, these were not used for timing, but only to determine
flux densities and pulse widths. An overview of all observations is provided
in Table 1.

Table 1: Overview of the radio observations. Pulsar names are provided based on the timing positions, as well as the discovery designation with which they were reported in Coenen et al. (2014) and Sanidas et al. (2019) (disc.). The observation time span is given by $t_{\mathrm{span}}$ and the number of observations from LOFAR Core (c), International Stations (i) the Lovell telescope at 334 MHz (P-band), 1532 MHz (L-band) and the Nançay telescope at 1484 MHz (L-band) is as indicated. Pulsar | Pulsar | $t_{\mathrm{span}}$ | $N_{\mathrm{obs}}$
---|---|---|---
| (disc.) | (yr) | LOFAR | Lovell | NRT
|  |  | (c) | (i) | (P) | (L) | (L)
J0039+3546 | J0039+35 | 6.5 | 34 | 242 | 1 | 8 | 9
J0059+6956 | J0059+69 | 2.4 | 33 |  |  |  | 3
J0139+5621 | J0140+5622 | 7.9 | 50 |  | 2 | 57 |
J0305+1123 | J0305+11 | 5.1 | 67 |  | 1 | 7 |
J0317+1328 | J0317+13 | 3.1 | 37 |  | 1 | 3 | 1
J0613+3731 | J0613+3731 | 9.0 | 56 | 416 | 3 | 84 |
J0811+3729 | J0811+37 | 4.1 | 43 |  | 2 | 6 | 3
J0813+2202 | J0813+22 | 2.0 | 29 |  |  | 11 | 5
J0828+5304 | J0827+53 | 2.4 | 64 |  |  | 24 | 3
J0928+3039 | J0928+30 | 2.6 | 31 |  | 1 | 6 | 5
J0935+3312 | J0935+33 | 3.9 | 39 | 50 | 3 | 6 | 10
J1303+3815 | J1303+38 | 1.7 | 24 |  |  | 17 | 3
J1334+1005 | J1334+10 | 1.7 | 24 |  |  |  | 5
J1427+5211 | J1426+52 | 2.4 | 34 |  |  | 14 | 5
J1529+4050 | J1529+40 | 7.1 | 38 | 203 | 2 | 104 | 4
J1707+3556 | J1707+35 | 1.9 | 25 |  |  |  | 3
J1715+4603 | J1715+46 | 2.5 | 32 |  | 1 | 29 | 3
J1722+3519 | J1722+35 | 2.4 | 28 |  | 1 | 5 | 4
J1740+2715 | J1740+27 | 6.0 | 32 | 210 | 1 | 52 | 3
J1745+4254 | J1745+42 | 5.8 | 52 |  | 1 | 49 | 2
J1809+1705 | J1809+17 | 3.0 | 41 |  | 1 | 8 | 3
J1814+2224 | J1814+22 | 6.8 | 33 | 258 | 1 | 77 | 1
J1910+5655 | J1910+56 | 3.0 | 53 |  |  | 18 | 4
J1953+3014 | J1953+30 | 2.4 | 34 |  |  | 46 | 4
J1958+2214 | J1958+21 | 2.2 | 26 |  |  |  |
J1958+5650 | J1958+56 | 2.3 | 34 |  |  | 37 | 1
J2006+2205 | J2006+22 | 2.7 | 32 |  | 1 | 5 | 6
J2022+2112 | J2022+21 | 2.0 | 28 |  |  | 5 | 3
J2053+1718 | J2053+17 | 2.5 | 32 |  |  | 5 | 4
J2057+2128 | J2057+21 | 3.1 | 42 |  |  |  | 6
J2123+3624 | J2123+36 | 2.4 | 33 |  |  | 15 | 3
J2209+2117 | J2209+22 | 6.2 | 33 |  |  | 121 | 3
J2306+3124 | J2306+31 | 6.2 | 28 | 213 |  | 140 | 3
J2336$-$0151 |  J2336$-$01 | 3.1 | 43 |  | 1 | 4 | 9
J2350+3140 | J2350+31 | 3.6 | 36 | 38 | 1 | 7 | 14
Table 2: Pulsar timing solutions.

PSR | $\alpha_{\mathrm{J2000}}$ | $\delta_{\mathrm{J2000}}$ | Epoch | $P$ | $\dot{P}$ | $\mathrm{DM}$ | $\mathrm{N_{TOA}}$ | $\mathrm{RMS}$ | $\mathrm{\chi^{2}_{red}}$
---|---|---|---|---|---|---|---|---|---
|  |  | (MJD) |  ($\mathrm{s}$) |  ($\mathrm{10^{-15}}$) |  ($\mathrm{pc\,cm^{-3}}$) |  |  ($\upmu$s) |
J0039+3546 | $00^{\mathrm{h}}39^{\mathrm{m}}08\aas@@fstack{s}8171(6)$ | $+35\degr 46\arcmin 16\aas@@fstack{\prime\prime}432(10)$ | 58461 | 0.53668651031180(15) | 0.063385(4) | 53.0249(3) | 244 | 139 | 1.36
J0059+6956 | $00^{\mathrm{h}}59^{\mathrm{m}}39\aas@@fstack{s}617(3)$ | $+69\degr 56\arcmin 31\aas@@fstack{\prime\prime}34(2)$ | 58556 | 1.1459097060823(13) | 0.14070(15) | 63.4768(5) | 33 | 127 | 0.74
J0139+5621 | $01^{\mathrm{h}}39^{\mathrm{m}}38\aas@@fstack{s}577(16)$ | $+56\degr 21\arcmin 36\aas@@fstack{\prime\prime}38(16)$ | 57835 | 1.775356366845(11) | 79.1067(4) | 101.83(4) | 102 | 1954 | 8.01
J0305+1123 | $03^{\mathrm{h}}05^{\mathrm{m}}07\aas@@fstack{s}291(6)$ | $+11\degr 23\arcmin 24\aas@@fstack{\prime\prime}9(3)$ | 58055 | 0.862062679407(4) | 0.30478(12) | 27.830(17) | 67 | 455 | 1.41
J0317+1328 | $03^{\mathrm{h}}17^{\mathrm{m}}48\aas@@fstack{s}66(2)$ | $+13\degr 28\arcmin 34\aas@@fstack{\prime\prime}0(1.2)$ | 57673 | 1.974239666372(14) | 0.1696(9) | 12.57(18) | 37 | 885 | 2.31
J0613+3731 | $06^{\mathrm{h}}13^{\mathrm{m}}12\aas@@fstack{s}137(3)$ | $+37\degr 31\arcmin 38\aas@@fstack{\prime\prime}53(13)$ | 58128 | 0.6191987768316(6) | 3.237300(16) | 18.9677(10) | 544 | 1279 | 797.45
J0811+3729 | $08^{\mathrm{h}}11^{\mathrm{m}}15\aas@@fstack{s}095(13)$ | $+37\degr 29\arcmin 13\aas@@fstack{\prime\prime}8(6)$ | 58238 | 1.248264327889(10) | 0.7458(5) | 17.100(4) | 34 | 1003 | 19.02
J0813+2202 | $08^{\mathrm{h}}13^{\mathrm{m}}51\aas@@fstack{s}94(2)$ | $+22\degr 02\arcmin 16\aas@@fstack{\prime\prime}3(1.3)$ | 58626 | 0.5313827887886(19) | 0.0777(2) | 52.2555(20) | 29 | 333 | 0.83
J0828+5304 | $08^{\mathrm{h}}28^{\mathrm{m}}25\aas@@fstack{s}69737(20)$ | $+53\degr 04\arcmin 43\aas@@fstack{\prime\prime}053(3)$ | 59065 | 0.0135273958162361(13) | $2.597(9)\times 10^{-5}$ | 23.10340(6) | 60 | 16 | 1.7
J0928+3039 | $09^{\mathrm{h}}28^{\mathrm{m}}59\aas@@fstack{s}360(9)$ | $+30\degr 39\arcmin 26\aas@@fstack{\prime\prime}5(3)$ | 57270 | 1.045756634409(18) | 0.3629(4) | 22.3(3) | 31 | 628 | 14.09
J0935+3312 | $09^{\mathrm{h}}35^{\mathrm{m}}07\aas@@fstack{s}799(4)$ | $+33\degr 12\arcmin 36\aas@@fstack{\prime\prime}62(13)$ | 57512 | 0.961553419242(3) | 0.37797(15) | 18.33(2) | 87 | 548 | 1.49
J1303+3815 | $13^{\mathrm{h}}03^{\mathrm{m}}19\aas@@fstack{s}3477(5)$ | $+38\degr 15\arcmin 03\aas@@fstack{\prime\prime}167(7)$ | 58681 | 0.39627397772729(20) | 0.34938(3) | 18.99746(14) | 23 | 31 | 1.6
J1334+1005 | $13^{\mathrm{h}}34^{\mathrm{m}}32\aas@@fstack{s}626(13)$ | $+10\degr 05\arcmin 41\aas@@fstack{\prime\prime}5(4)$ | 58688 | 0.911092162286(13) | 0.7415(16) | 23.868(3) | 24 | 780 | 0.85
J1427+5211 | $14^{\mathrm{h}}27^{\mathrm{m}}07\aas@@fstack{s}711(3)$ | $+52\degr 11\arcmin 11\aas@@fstack{\prime\prime}96(2)$ | 58555 | 0.995864060026(2) | 0.4744(2) | 25.3107(9) | 34 | 205 | 1.48
J1529+4050 | $15^{\mathrm{h}}29^{\mathrm{m}}16\aas@@fstack{s}526(6)$ | $+40\degr 50\arcmin 57\aas@@fstack{\prime\prime}79(6)$ | 58032 | 0.4764184320778(13) | $2.65(3)\times 10^{-3}$ | 6.484(3) | 330 | 1767 | 3.21
J1707+3556 | $17^{\mathrm{h}}07^{\mathrm{m}}02\aas@@fstack{s}7328(3)$ | $+35\degr 56\arcmin 36\aas@@fstack{\prime\prime}522(4)$ | 58656 | 0.15976470098275(6) | $8.52(7)\times 10^{-4}$ | 19.23798(11) | 25 | 24 | 3.36
J1715+4603 | $17^{\mathrm{h}}15^{\mathrm{m}}43\aas@@fstack{s}770(7)$ | $+46\degr 03\arcmin 59\aas@@fstack{\prime\prime}15(7)$ | 57782 | 0.548097027876(2) | 0.0484(3) | 19.767(2) | 31 | 527 | 0.68
J1722+3519 | $17^{\mathrm{h}}22^{\mathrm{m}}09\aas@@fstack{s}5067(6)$ | $+35\degr 19\arcmin 18\aas@@fstack{\prime\prime}591(8)$ | 57795 | 0.8216175744405(4) | 0.54474(5) | 23.8766(2) | 27 | 54 | 4.72
J1740+2715 | $17^{\mathrm{h}}40^{\mathrm{m}}32\aas@@fstack{s}5712(10)$ | $+27\degr 15\arcmin 21\aas@@fstack{\prime\prime}470(16)$ | 58300 | 1.0582099056193(11) | 0.21430(3) | 35.522(5) | 281 | 348 | 1.54
J1745+4254 | $17^{\mathrm{h}}45^{\mathrm{m}}50\aas@@fstack{s}1197(13)$ | $+42\degr 54\arcmin 37\aas@@fstack{\prime\prime}895(17)$ | 58333 | 0.3050545538470(2) | $9.851(8)\times 10^{-3}$ | 37.931(9) | 92 | 227 | 1.0
J1809+1705 | $18^{\mathrm{h}}09^{\mathrm{m}}07\aas@@fstack{s}483(7)$ | $+17\degr 05\arcmin 44\aas@@fstack{\prime\prime}54(17)$ | 57663 | 2.066649687618(13) | 3.0727(12) | 47.187(3) | 38 | 951 | 1.14
J1814+2224 | $18^{\mathrm{h}}14^{\mathrm{m}}29\aas@@fstack{s}9046(5)$ | $+22\degr 24\arcmin 40\aas@@fstack{\prime\prime}183(10)$ | 58153 | 0.25371005873953(6) | 0.354845(2) | 62.2999(19) | 357 | 230 | 1.14
J1910+5655 | $19^{\mathrm{h}}10^{\mathrm{m}}53\aas@@fstack{s}64(3)$ | $+56\degr 55\arcmin 33\aas@@fstack{\prime\prime}5(2)$ | 58980 | 0.341858932039(4) | 0.2048(2) | 20.658(5) | 51 | 2306 | 7.45
J1953+3014 | $19^{\mathrm{h}}53^{\mathrm{m}}52\aas@@fstack{s}445(2)$ | $+30\degr 14\arcmin 30\aas@@fstack{\prime\prime}63(3)$ | 58555 | 1.271207766231(3) | 0.3852(3) | 43.5777(11) | 34 | 225 | 1.48
J1958+2214 | $19^{\mathrm{h}}58^{\mathrm{m}}45\aas@@fstack{s}284(9)$ | $+22\degr 14\arcmin 26\aas@@fstack{\prime\prime}11(18)$ | 59299 | 1.050380009903(12) | 4.5748(13) | 87.665(4) | 26 | 927 | 0.65
J1958+5650 | $19^{\mathrm{h}}58^{\mathrm{m}}06\aas@@fstack{s}981(6)$ | $+56\degr 50\arcmin 07\aas@@fstack{\prime\prime}57(4)$ | 58570 | 0.3118323776425(10) | 0.17214(12) | 58.1231(14) | 33 | 364 | 0.7
J2006+2205 | $20^{\mathrm{h}}06^{\mathrm{m}}44\aas@@fstack{s}802(5)$ | $+22\degr 05\arcmin 26\aas@@fstack{\prime\prime}06(10)$ | 57736 | 1.741873881197(8) | 5.8099(7) | 130.4831(19) | 30 | 549 | 1.78
J2022+2112 | $20^{\mathrm{h}}22^{\mathrm{m}}27\aas@@fstack{s}649(3)$ | $+21\degr 12\arcmin 38\aas@@fstack{\prime\prime}64(7)$ | 58626 | 0.803551296937(3) | 0.9048(4) | 73.5194(14) | 28 | 334 | 1.86
J2053+1718 | $20^{\mathrm{h}}53^{\mathrm{m}}49\aas@@fstack{s}4814(2)$ | $+17\degr 18\arcmin 44\aas@@fstack{\prime\prime}731(6)$ | 57765 | 0.11926776027515(3) | 0.000301(3) | 26.97952(18) | 31 | 24 | 3.87
J2057+2128 | $20^{\mathrm{h}}57^{\mathrm{m}}38\aas@@fstack{s}237(14)$ | $+21\degr 28\arcmin 05\aas@@fstack{\prime\prime}4(3)$ | 57669 | 1.166639603609(12) | 0.5229(10) | 73.12(17) | 40 | 1679 | 0.9
J2123+3624 | $21^{\mathrm{h}}23^{\mathrm{m}}58\aas@@fstack{s}407(12)$ | $+36\degr 24\arcmin 39\aas@@fstack{\prime\prime}30(19)$ | 58556 | 1.294029820771(13) | 2.1008(14) | 108.525(4) | 30 | 1069 | 1.25
J2209+2117 | $22^{\mathrm{h}}09^{\mathrm{m}}59\aas@@fstack{s}7239(11)$ | $+21\degr 17\arcmin 58\aas@@fstack{\prime\prime}49(2)$ | 58335 | 1.776960679496(5) | 5.07777(11) | 46.3741(4) | 104 | 213 | 1.69
J2306+3124 | $23^{\mathrm{h}}06^{\mathrm{m}}19\aas@@fstack{s}2039(7)$ | $+31\degr 24\arcmin 20\aas@@fstack{\prime\prime}364(13)$ | 58234 | 0.34160250343014(13) | 0.222456(4) | 46.15171(20) | 307 | 219 | 2.8
J2336$-$0151 | $23^{\mathrm{h}}36^{\mathrm{m}}32\aas@@fstack{s}07(17)$ | $-01\degr 51\arcmin 56^{\prime\prime}.7(5.8)$ | 57669 | 1.029839015486(4) | 0.3448(3) | 19.622(13) | 39 | 630 | 0.99
J2350+3140 | $23^{\mathrm{h}}50^{\mathrm{m}}41\aas@@fstack{s}200(3)$ | $+31\degr 40\arcmin 47\aas@@fstack{\prime\prime}24(5)$ | 57778 | 0.5080916900926(7) | 0.35236(5) | 39.141(14) | 74 | 353 | 2.06
333The spin period and spin period derivative are referenced to the quoted
Epoch. Figures in parentheses are the nominal $1\sigma$ tempo2 uncertainties
in the least-significant digits quoted multiplied by the square root of the
reduced $\chi^{2}$. For PSRs J0828+5304 and J2053+1718, significant
measurements of proper motion were obtained.

###  2.2 Pulsar timing

For each pulsar, we aimed to obtain a phase-coherent timing solution which
accounts for all rotations of the pulsar over the observing time span and
allows for prediction of the arrival time of pulses as a function of time and
observing frequency. As all pulsars described in this work, except PSR
J0828+5304, are isolated, the timing models required fitting for the
astrometric position (right ascension $\alpha_{\mathrm{J2000}}$ and
declination $\delta_{\mathrm{J2000}}$), the spin period $P$, the spin period
derivative $\dot{P}$, and the dispersion measure $\mathrm{DM}$, which we
assumed to be constant.

We used an iterative procedure to obtain phase-coherent timing solutions using
tools from psrchive and tempo2 (Hobbs et al., 2006). First, to obtain phase-
coherence over the observing time span we started with the LOFAR Core
observations, folded and dedispersed at the discovery parameters (Coenen et
al., 2014; Sanidas et al., 2019), as these have the highest signal-to-noise
and generally the longest timing baselines. For each pulsar, we selected the
highest signal-to-noise observation, averaged it in time and frequency, and
modelled the resulting profile as the sum of several von Mises functions (with
different positions, heights, and widths) using the paas tool to obtain an
analytical template profile. Times-of-arrival (TOAs) were determined by cross-
correlating the fully time- and frequency-averaged pulse profiles from LOFAR
Core observations against this analytical template profile with pat, using the
Fourier domain with Markov chain Monte Carlo algorithm (Taylor, 1992).

Due to the uncertainties in the discovery spin period and celestial position,
the uncertainty in the predicted time of arrival between consecutive LOFAR
Core observations was generally much larger than the spin period, making it a
priori not possible to phase-connect consecutive observations. Instead, we
used the algorithm described in Michilli et al. (2020), which folds the TOAs
with tempo2 over a range of spin periods around the discovery spin period,
keeping the celestial position and DM fixed to the discovery values and the
spin period derivative to zero. The resulting residual plots were inspected
manually to identify spin periods which yielded phase coherence over part of
the timing baseline. These spin periods were used to extend phase coherence
over the entire timing baseline by iteratively fitting for and improving the
spin period, the spin period derivative, and the celestial position.

This approach yielded phase-coherent timing solutions for the majority of the
isolated pulsars, except for four pulsars (PSRs J1745+4254, J1910+5655,
J2053+1718, and J2306+3124) for which the algorithm had to be repeated for a
range of celestial positions before finding phase coherence. In the case of
the faint pulsar J1814+2224, neither approach yielded partial phase coherence.
Instead, we used the Lovell observations at 1532 MHz, which were obtained at a
cadence of a few days during 2014, to find the initial phase-coherent timing
solution, which was then improved and extended by using the LOFAR Core
observations.

For the binary pulsar J0828+5304, we also included parameters describing the
binary orbit: the orbital period $P_{\mathrm{b}}$, the projected semi-major
axis of the orbit $x$, the time of ascending node passage $T_{\mathrm{asc}}$,
and the Laplace-Lagrange parameters $\eta=e\sin\omega$ and
$\kappa=e\cos\omega$, with $e$ the eccentricity and $\omega$ the longitude of
periastron. The Laplace-Lagrange parameters are from the ELL1 binary model
(Lange et al., 2001), which models orbits with small eccentricities. We used
13 LOFAR Core observations obtained over the course of one orbital period of
about 5.9 days to first obtain phase coherence over one orbit. Initial values
for $P$, $P_{\mathrm{b}}$, $x$, and $T_{\mathrm{asc}}$ (assuming a circular
orbit) were obtained by fitting a sinusoid to spin period measurements
determined with pdmp. Using these initial values, a brute force search over
all four parameters was used to fit TOAs over the same time span against a
timing model with a circular orbit to find values for $P$, $P_{\mathrm{b}}$,
$x$, and $T_{\mathrm{asc}}$ that yielded phase coherence and minimal residuals
over a single orbit. Once found, the timing solution was manually extended to
all observations by including the celestial position and spin period
derivative when fitting the TOAs with tempo2.

Once we had obtained initial phase coherent timing solutions for all pulsars,
the observations from all telescopes were refolded using the new timing
parameters and new template profiles were constructed for each telescope by
fully averaging profiles from all observations in time and frequency and
fitting von Mises functions to the averaged profiles. For each pulsar observed
with different telescopes, the templates were aligned using the pas tool. In
the case of PSR J1529+4050, its pulse profile displays two components of which
the leading component diminishes towards higher frequencies. For this reason,
the templates at 334 and 1532 MHz were aligned against the second component of
the template at 149 MHz. To measure DM, all observations were averaged to two
frequency channels from which TOAs were calculated. The LOFAR Core
observations had centre frequencies of 129 and 166 MHz, the GLOW observations
were at 136 and 170 MHz, the Chilbolton observations were at 150 and 174 MHz,
the FR606 and SE607 observations were at 129 and 167 MHz, and the JBO
observations were at 1447 and 1630 MHz. The resulting TOAs were fitted for all
timing parameters. Phase offsets were included in the timing solutions to take
into account any remaining time delays between template profiles from
different instruments. We note that for PSR J0811+3729, which displays nulls
(see § 3.2), only sub-integrations which show emission were used to construct
templates and calculate TOAs.

The resulting timing solutions, now with updated DM values, were used to
refold and re-dedisperse the observations, which were again fully averaged in
time and frequency to determine TOAs. These TOAs were fitted for all timing
parameters except DM to obtain the timing models provided in Tables 2 and 3
and the timing residuals shown in Fig. 1. After inspection of the timing
residuals of all pulsars, we also included parameters describing the proper
motion of PSRs J0828+5304 and J2053+1718, as this improved the $\chi^{2}$
value of their fit and yielded significant detections of proper motion (see
Section 3.1). All timing solutions were referenced to the Solar-system
barycentre with the DE436 solar system ephemeris (Folkner & Park, 2016) and
the Terrestrial Time standard (BIPM2011; Petit 2010) using Barycentric
Coordinate Time (TCB).

Table 3: Binary parameters for PSR J0828+5304. Orbital period, $P_{b}$ (d) | 5.899255592(5)
---|---
Projected semi-major axis of orbit, $x$ (lt-s) | 13.147610(3)
Time of ascending node passage $T_{\mathrm{asc}}$ (MJD) | 58886.8001661(3)
$\eta=e\sin\omega$ |  $-$2.2(5)$\times 10^{-6}$
$\kappa=e\cos\omega$ |  $-$1.1(6)$\times 10^{-6}$

###  2.3 Pulse profiles

The profiles at different frequencies were aligned by applying the model in
Table 2 and then rotated such that the highest peak of the LOFAR pulse profile
was located at a phase $\phi=0.25$.

The averaged pulse profiles from the pulsars presented here are shown in Fig.
2. Most pulse profiles were modelled with one, two or three von Mises
functions. All pulsars display a profile with a single main pulse, except for
PSRs J0613+3731 and J0828+5304. PSR J0613+3731 shows a very faint interpulse
in the FR606 data, which is only just visible in the LOFAR Core data and is at
a phase $\Delta\phi=0.4$ from the main pulse. The binary pulsar J0828+5304
displays a clear interpulse at $\Delta\phi=0.5$ of the main pulse.

We calculated full pulse widths at 10% ($W_{10}$) and 50% ($W_{50}$) of the
peak intensity of the fully frequency and time averaged profiles at 149 MHz,
334 MHz, and 1484 or 1532 MHz, if available. Pulse widths were determined
using tools from PSRSalsa (Weltevrede, 2016), which models the profiles with
analytical templates composed of one or more von Mises functions and
calculates pulse widths from the added components. For the observations that
were used for timing, we applied the templates that were created to calculate
TOAs, while for all other observations, new templates were constructed.
Uncertainties on the pulse widths were determined by generating a width
distribution composed of simulated pulse profiles with randomly added noise
from the off-pulse region of the added profiles and then calculating the
standard deviation of the simulated width distribution. The pulse widths and
duty cycles can be found in Table 4.

Table 4: Pulse widths and duty cycles at 10% and 50% of the pulse amplitude at different frequencies. Measurements with * were measured at 1484 MHz. The uncertainties in the parentheses represent the standard deviations of simulated width distributions (see text). PSR |  W10 (ms) |  $\delta_{10}$ (%) |  W50 (ms) |  $\delta_{50}$ (%)
---|---|---|---|---
| 149 | 334 | 1532 | 149 | 334 | 1532 | 149 | 334 | 1532 | 149 | 334 | 1532
| MHz | MHz | MHz | MHz | MHz | MHz | MHz | MHz | MHz | MHz | MHz | MHz
J0039+3546 | 17.6(3) | 9.1(1.5) | 22(4) | 3.28(5) | 1.7(3) | 4.2(7) | 6.95(5) | 5.7(9) | 17.7(1.1) | 1.296(10) | 1.07(16) | 3.3(2)
J0059+6956 | 65.4(6) | $-$ | $-$ | 5.71(5) | $-$ | $-$ | 8.21(14) | $-$ | $-$ | 0.716(12) | $-$ | $-$
J0139+5621 | 81.3(8) | 74(10) | 83(3) | 4.58(4) | 4.2(6) | 4.69(19) | 40.2(6) | 52(7) | 43.5(1.8) | 2.26(3) | 2.9(4) | 2.45(10)
J0305+1123 | 35.7(6) | $-$ | $-$ | 4.14(7) | $-$ | $-$ | 19.3(3) | $-$ | $-$ | 2.24(4) | $-$ | $-$
J0317+1328 | 34.4(6) | 40(7) | $-$ | 1.74(3) | 2.0(3) | $-$ | 18.9(3) | 19(3) | $-$ | 0.956(17) | 0.96(17) | $-$
J0613+3731 | 24.0(4) | 29.1(8) | 38.2(4) | 3.87(7) | 4.70(13) | 6.17(6) | 9.721(3) | 15.0(4) | 20.58(19) | 1.5700(5) | 2.42(6) | 3.32(3)
J0811+3729 | 56.0(7) | $-$ | $-$ | 4.49(6) | $-$ | $-$ | 28.3(2) | $-$ | $-$ | 2.271(20) | $-$ | $-$
J0813+2202 | 52.3(1.5) | $-$ | $-$ | 9.9(3) | $-$ | $-$ | 14.1(5) | $-$ | $-$ | 2.66(9) | $-$ | $-$
J0828+5304 | 1.6(1.8) | $-$ | $-$ | 12(13) | $-$ | $-$ | 0.55(2) | $-$ | $-$ | 4.09(17) | $-$ | $-$
J0928+3039 | 43.9(4) | $-$ | $-$ | 4.20(4) | $-$ | $-$ | 25.412(16) | $-$ | $-$ | 2.4300(15) | $-$ | $-$
J0935+3312 | 37.8(2) | $-$ | $-$ | 3.93(2) | $-$ | $-$ | 20.56(13) | $-$ | $-$ | 2.138(13) | $-$ | $-$
J1303+3815 | 15.39(15) | $-$ | $-$ | 3.88(4) | $-$ | $-$ | 1.89(3) | $-$ | $-$ | 0.477(7) | $-$ | $-$
J1334+1005 | 28.3(1.1) | $-$ | 43(3)* | 3.11(12) | $-$ | 4.7(3)* | 16.8(4) | $-$ | 23(2)* | 1.84(4) | $-$ | 2.6(3)*
J1427+5211 | 45.6(5) | $-$ | 13.8(1.6) | 4.58(5) | $-$ | 1.38(16) | 9.70(10) | $-$ | 6.5(9) | 0.974(10) | $-$ | 0.65(9)
J1529+4050 | 161.6(9) | 108(10) | 96(5) | 33.91(19) | 23(2) | 20.2(1.1) | 121.0(6) | 52(4) | 47.7(1.0) | 25.40(14) | 10.9(8) | 10.0(2)
J1707+3556 | 10.5(1.1) | $-$ | $-$ | 6.6(7) | $-$ | $-$ | 1.843(15) | $-$ | $-$ | 1.154(10) | $-$ | $-$
J1715+4603 | 22.3(1.0) | $-$ | 31(6) | 4.07(18) | $-$ | 5.7(1.1) | 15.1(5) | $-$ | 20(2) | 2.76(9) | $-$ | 3.6(4)
J1722+3519 | 30.68(6) | 28.0(1.4) | $-$ | 3.733(7) | 3.41(17) | $-$ | 23.08(3) | 18.4(1.6) | $-$ | 2.810(4) | 2.24(19) | $-$
J1740+2715 | 37.9(7) | 25(4) | 42.8(1.3) | 3.58(6) | 2.4(4) | 4.04(13) | 14.63(12) | 14.5(1.6) | 23.7(7) | 1.383(11) | 1.37(15) | 2.24(7)
J1745+4254 | 18.8(4) | 7.6(1.0) | 9.1(4) | 6.15(13) | 2.5(3) | 2.98(15) | 9.08(17) | 3.9(3) | 5.1(3) | 2.98(6) | 1.29(11) | 1.67(9)
J1809+1705 | 48.3(8) | $-$ | $-$ | 2.34(4) | $-$ | $-$ | 26.8(4) | $-$ | $-$ | 1.295(19) | $-$ | $-$
J1814+2224 | 8.7(3) | 15.3(1.6) | 7.08(15) | 3.44(12) | 6.0(6) | 2.79(6) | 4.64(19) | 4.5(8) | 3.79(8) | 1.83(7) | 1.8(3) | 1.50(3)
J1910+5655 | 138.0(7) | $-$ | $-$ | 40.4(2) | $-$ | $-$ | 72.1(4) | $-$ | $-$ | 21.09(10) | $-$ | $-$
J1953+3014 | 54.0(3) | $-$ | 58(5) | 4.25(3) | $-$ | 4.6(4) | 43.0(5) | $-$ | 33(2) | 3.38(4) | $-$ | 2.59(17)
J1958+2214 | 41.7(1.1) | $-$ | $-$ | 3.97(10) | $-$ | $-$ | 23.2(6) | $-$ | $-$ | 2.21(6) | $-$ | $-$
J1958+5650 | 24.2(3) | $-$ | 14.1(1.5) | 7.76(11) | $-$ | 4.5(5) | 13.14(18) | $-$ | 8.6(8) | 4.21(6) | $-$ | 2.7(3)
J2006+2205 | 62.3(1.1) | $-$ | 49(4)* | 3.58(6) | $-$ | 2.8(3)* | 28.2(4) | $-$ | 26.4(1.2)* | 1.62(2) | $-$ | 1.52(7)*
J2022+2112 | 35.2(6) | $-$ | $-$ | 4.39(8) | $-$ | $-$ | 20.9(2) | $-$ | $-$ | 2.60(3) | $-$ | $-$
J2053+1718 | 2.53(6) | $-$ | $-$ | 2.12(5) | $-$ | $-$ | 1.138(11) | $-$ | $-$ | 0.954(9) | $-$ | $-$
J2057+2128 | 54(3) | $-$ | $-$ | 4.6(3) | $-$ | $-$ | 35.0(1.3) | $-$ | $-$ | 3.00(11) | $-$ | $-$
J2123+3624 | 250(6) | $-$ | $-$ | 19.3(5) | $-$ | $-$ | 81(5) | $-$ | $-$ | 6.3(4) | $-$ | $-$
J2209+2117 | 36.45(19) | $-$ | 31.7(1.4) | 2.051(11) | $-$ | 1.78(8) | 9.26(14) | $-$ | 16.6(8) | 0.521(8) | $-$ | 0.93(4)
J2306+3124 | 22.8(4) | $-$ | 30.6(2.0) | 6.67(10) | $-$ | 9.0(6) | 7.07(8) | $-$ | 10.0(5) | 2.07(2) | $-$ | 2.93(15)
J2336-0152 | 70.2(5) | 61(5) | $-$ | 6.81(5) | 6.0(5) | $-$ | 38.5(3) | 36(3) | $-$ | 3.73(2) | 3.5(3) | $-$
J2350+3140 | 25.9(3) | $-$ | $-$ | 5.09(7) | $-$ | $-$ | 13.36(16) | $-$ | $-$ | 2.63(3) | $-$ | $-$

Figure 1: The residuals from the timing model in Table 2 for all 35 pulsars.
The different colours represent different instruments as indicated in the
bottom-right corner. The black bars on the right side of each panel show the
scale of the proportion of the spin period. Figure 2: Pulse profiles averaged
over all observations of the pulsars presented here at 149 MHz (black), 334
MHz (red), and 1532 MHz (blue) with bandwidths of 78, 64 and 384 MHz. The
profiles were aligned by applying the model in Table 2. Then, all profiles
were rotated such that the highest peak of the LOFAR pulse profile is located
at phase $\phi=0.25$. The pulse profiles at 149 MHz have 1024 phase bins,
while the profiles at 334 and 1532 MHz were rebinned from 512 and 1024 to 256
and 512 phase bins, respectively. Figure 3: Mean flux densities (dots and
circles) and upper limits for flux densities (triangles) as reported in Table
5 for the 29 pulsars whose timing positions fall within the FWHM of the LOFAR
Core tied-array beam. Filled dots and triangles are flux density measurements
for which five or more observations were available, while empty circles and
triangles are measurements from less than five observations. The black lines
represent fitted spectral indices, which are the mean values for the spectral
index $\alpha$ and the flux density on the reference frequency of 149 MHz
$S_{0}$ from the emcee samples. The shaded regions represent the uncertainty
on $\alpha$ and $S_{0}$ propagated to flux densities between 90 and 2100 MHz.
For the spectral index fit, only flux density measurements with five or more
observations were used.

###  2.4 Flux densities and spectral analysis

Mean flux densities were determined from the LOFAR Core, Lovell, and Nançay
observations. Observations from LOFAR were fully averaged in time and split in
two subbands with centre frequencies of 129 and 166 MHz. For each pulsar, all
observations at these frequencies were combined and flux densities were
calculated using the radiometer equation following the method from Kondratiev
et al. (2016). This approach models the LOFAR beam, the system temperature,
and the beamformer coherence, combined with sky temperatures taken from Price
(2021). We found that, on average, between 5 and 10% of the dipoles in the
LOFAR High Band Antennas were not in operation, reducing the effective area
(Kondratiev et al., 2016). We used a conservative estimate of 5% of broken
antennas for all flux density calculations as to not overestimate the flux
densities of the pulsars. For observations during which 10% of the dipoles
were not operational, this would result in an underestimation of the flux
density which is much lower than the uncertainty from other factors. We
assumed a systematic uncertainty due to RFI, scintillation, and fluctuating
tied array beam gain and system temperatures of 50%, as suggested in
Kondratiev et al. (2016).

Note that we do not attempt to correct the LOFAR flux densities for positional
offsets of the pulsars with respect to the centre of the LOFAR Core tied-array
beam. Positional offsets are introduced by ionospheric effects, which can
introduce random displacements of the order of $\sim 1\arcmin$ compared to the
$3\aas@@fstack{\prime}5$ full width half maximum (FWHM) of the tied-array beam
during observations, but more importantly, there are systematic offsets
between the final timing position and the position determined from gridding
and used to obtain the timing observations. For six pulsars, the gridding
positions place them outside of the FWHM of the tied-array beam. While the
corrections using a squared $\mathrm{sinc}$ function were used to correct flux
densities of known pulsars in Sanidas et al. (2019), this approach is not
suitable here, as the FWHM of a tied-array beam from the LOFAR Core stations
is a factor 6 smaller than that from the stations on the LOFAR Superterp.
Hence, we caution the reader to treat the LOFAR flux densities as indicative
and that they should not be used for detailed studies. We expect that accurate
flux densities of the LOTAAS pulsars will become available with the continued
data releases from the LOFAR continuum imaging survey (Shimwell et al., 2017).

For PSRs J0059+6956, J0305+1123, J0813+2202, J0828+5304, J0935+3312,
J1427+5211, J1953+3014, J1958+5650, and J2123+3624, the observing position was
updated part way through the observing time span, resulting in smaller
positional offsets for the later observations. Only the later observations
with improved gridding position were used to determine flux densities for
these pulsars.

From the Lovell observations, we obtained flux densities at 334 and 1532 MHz.
For each pulsar, the observations were fully averaged in time and frequency
and combined using psradd. Flux densities were calculated from the radiometer
equation using a gain of 0.8 K Jy-1 for both centre frequencies, an elevation-
dependent system temperature to take into account spill-over, and sky
temperatures from Price (2021). The NRT observations were calibrated using a
noise diode which injected white noise into the receiver to allow for the
transfer of the flux scale using observations of flux calibrators. To estimate
the uncertainty on the flux density measurements $\sigma_{S}$ in the Lovell
and Nançay observations, we applied a simplification of the method used in
Jankowski et al. (2018): $\sigma_{S}=\sqrt{(0.2S)^{2}+(0.3S)^{2}/N}$, with $S$
the measured flux density for each pulsar, and $N$ the number of observations,
which assumed a systematic uncertainty of 20% and a typical modulation index
due to scintillation of 30%. In the case of non-detections in the Lovell and
Nançay observations, upper limits were determined by averaging all
observations and calculating the $3\sigma$ limit on the root-mean-square noise
of the pulse profile.

For those 29 pulsars whose timing positions fall within the FWHM of the LOFAR
Core tied-array beam, we used Bayesian methods to model the radio spectra from
both the flux density measurements as well as the upper limits. We used emcee
(Foreman-Mackey et al., 2013) to maximise the likelihood function for
detections and non-detections as described by Laskar et al. (2014, Eqn. 1 to
3). We assumed that the radio spectra can be modelled with a single power law
$S_{\nu}=S_{0}\left(\nu/\nu_{0}\right)^{\alpha}$, where $S_{\nu}$ are the
observed mean flux densities or upper limits at their respective observing
frequencies $\nu$, with $\alpha$ as the spectral index for a flux density
$S_{0}$ at reference frequency $\nu_{0}=149$ MHz. Flat priors were assumed in
$S_{0}$ and for $-9<\alpha<3$. We note that the simplification of a single
power law may not be valid for all pulsars, as some pulsars may have spectra
which are better described by a broken power law (e.g. Bilous et al., 2016;
Jankowski et al., 2018).

##  3 Results

###  3.1 Timing

The timing residuals shown in Fig. 1 using the timing models from Table 2 and
3 are generally noise-like (i.e., uncorrelated and around the same level as
the TOA uncertainties) for the majority of pulsars. The residuals of PSRs
J0139+5621, J0613+3731, and J2306+3124 display time-dependent trends, while
the timing residuals of PSRs J0811+3729, J0928+3039, J1722+3519, and
J1910+5655 show non-Gaussian noise, resulting in timing solutions with high
reduced $\chi^{2}$ values.

In the case of PSR J0139+5621, the residuals of the LOFAR observations
obtained after the observational gap between 2018 May and 2019 June show a
downward trend, indicating the possibility of a glitch, a sudden increase in
the spin frequency, which is often followed by a recovery towards the pre-
glitch frequency (Radhakrishnan & Manchester, 1969; Reichley & Downs, 1969).
Fitting the spin-frequency $\nu$ with the TOAs before and after MJD 58257
separately, we obtained a fractional glitch size $\Delta\nu/\nu$ of $3.3\times
10^{-10}$, which is near the lower values of the observed range of glitch
sizes of $10^{-11}$ and $10^{-5}$ (Espinoza et al., 2011; Yu et al., 2013;
Basu et al., 2022). As glitches are predominantly seen in younger pulsars, and
since PSR J0139+5621 is the youngest pulsar in our sample, with a
characteristic age $\tau_{c}$ of $3.6\times 10^{5}$ yr (see below for further
explanations on $\tau_{c}$), we consider it likely that a glitch occurred in
PSR J0139+5621.

We considered the possibility that the long-term trends seen in the residuals
for PSRs J0613+3731 and J2306+3124 could be due to magnetic dipole braking.
This would yield a measurable second spin-frequency derivative
$\ddot{\nu}=n\dot{\nu}^{2}/\nu$ for spin-frequency $\nu$ and spin-frequency
derivative $\dot{\nu}$ with $n=3$. However fitting for $\ddot{\nu}$ in the
timing solutions of PSRs J0613+3731 and J2306+3124 yields unrealistically
large values for $|n|$, indicating that the observed trends are likely due to
timing noise, which is seen in the majority of normal pulsars timed over long
time spans (e.g., Hobbs et al., 2010).

We found that the noise in the timing residuals of PSRs J0811+3729,
J0928+3039, J1722+3519, and J1910+5655 is caused by nulling and pulse-to-pulse
profile variations that do not average out over the length of the observation,
see Fig. 4. We discuss some of these pulsars in § 3.2.

For the majority of the pulsars the offset between the timing position and the
gridded position used to obtain the timing observations (Table 5) fall within
the $1\aas@@fstack{\prime}75$ half-width at half maximum (HWHM) of the tied-
array beams with the LOFAR Core. For PSR J0305+1123, the position used to
obtain the observations was updated in 2017 November, resulting in higher
signal-to-noise detections and more precise TOAs afterwards (Fig. 1). Of the
six outliers (PSRs J0317+1328, J1814+2224, J1958+2214, J2006+2205, J2057+2128,
and J2306+3124), all have offsets below $2\aas@@fstack{\prime}5$, except for
PSR J1958+2214, which is offset by $16\aas@@fstack{\prime}3$ and located in
the far side-lobes of the LOFAR Core tied-array beam. The origin of this large
offset was traced back to the LOTAAS survey observation in which PSR
J1958+2214 was discovered, which showed several high signal-to-noise
detections at widely separated tied-array beams. These odd side-lobe
detections were noted at the time, and the choice was made to perform follow-
up gridding observations using more narrow tied-array beams towards the
detections of two neighbouring tied-array beams in the centre of the hexagonal
grid of 61 LOFAR Superterp tied-array beams, while the actual position of PSR
J1958+2214 turned out to be consistent with one of the detections in the outer
ring of the hexagonal grid.

Significant measurements of proper motion were obtained for PSRs J0828+5304
and J2053+1718. The proper motion of PSR J0828+5304 is
$\mu_{\alpha}\cos\delta=4.8\pm 1.8$ mas yr-1 and $\mu_{\delta}=-14\pm 3$ mas
yr-1, yielding transverse velocities of 63 and 110 km s-1 for the 0.9 and 1.6
kpc distances predicted by the NE2001 (Cordes & Lazio, 2002) and YMW16 (Yao et
al., 2017) Galactic electron density models. For PSR J2053+1718, with
$\mu_{\alpha}\cos\delta=-31\pm 5$ mas yr-1 and $\mu_{\delta}=15\pm 9$ mas
yr-1, the transverse velocities are 315 and 344 km s-1 at the NE2001 distance
of 1.9 kpc and the YMW16 distance of 2.1 kpc. This pulsar, PSR J2053+1718, was
first discovered by Arecibo (Ray et al., 1996) and a timing solution has
recently been published by Brinkman et al. (2018). They obtained significantly
lower transverse velocities of 63 and 69 km s-1 for the NE2001 and YMW16
distances, over a longer timing baseline. As Brinkman et al. (2018) reports DM
variations on the order of $5\times 10^{-3}$ pc cm-3, we attribute the larger
LOTAAS proper motion measurement, as well as the high reduced $\chi^{2}$ of
the LOTAAS timing solution to unmodelled DM variations affecting the arrival
time measurements. Based on the short spin period and low magnetic field,
Brinkman et al. (2018) propose that PSR J2053+1718 may be a disrupted recycled
pulsar, a pulsar which was spun up in a binary system with a massive stellar
companion which got disrupted and unbound when the companion went supernova.
This origin could explain the low magnetic field of this system, which are
typically seen in double neutron star systems (DNSs; see Tauris et al. 2017
for a review on DNSs).

The period and period derivative from the timing models were used to calculate
the characteristic age $\tau_{\mathrm{c}}$, the surface magnetic field
strength $B$, and the intrinsic spin-down energy $\dot{E}$ (see the rightmost
columns in Table 5. Here, we assumed a canonical neutron star with a radius of
10 km and a moment of inertia of $10^{45}\,$ g cm2. Furthermore, we assumed
that the initial spin is negligible and that magnetic dipole radiation is
responsible for the spin-down throughout the pulsar’s lifetime (see Lorimer &
Kramer 2012 for details).

###  3.2 Pulse profile variations

The pulse profiles of some of the LOTAAS pulsars show profile variations in
time or frequency. Figures 4 and 5 highlight these variations.

PSR J0811+3729 is the most extreme case by displaying nulling, a relatively
common phenomenon where the pulsed emission temporarily ceases, with nulls
lasting between a single pulsar rotation up to several weeks (e.g Kramer et
al. 2006; Young et al. 2015; Basu et al. 2017). In the absence of observations
with single pulse integrations, we analysed the energy distributions of the
5-s sub-integrations, where each sub-integration covers just over almost
exactly 4 individual pulses. For each sub-integration, we determined if pulsed
emission was present by applying the criteria from Wang et al. (2020), which
compare the emission in the on-pulse region with the standard deviation of the
emission in the off-pulse region. We found that for the total observation
length of PSR J0811+3729 of 14.4 h, 80.1% of 5-s sub-integrations were in a
null state. The mean length of a null state was 105 s with the longest null
lasting a full observation of 20 min. The average time between nulls was
approximately 29 s and the longest time the pulsar was in an emission state
was 5.67 min.

For PSR J0928+3039, the 5-s sub-integrations covered 3.43 individual pulses
and, as shown in a representative observation in Fig. 4, these revealed strong
variability on time-scales of tens of seconds. The strong variations appear to
occur primarily in the leading half of the profile. Pulsed emission was also
absent for occasional sub-integrations, indicating that this pulsar may be
nulling for a few rotations at a time. No evidence for drifting sub-pulses was
visible, but would require observations of individual pulses to completely
rule out.

The profile of PSR J1722+3519 at 149 MHz shows two narrow components whose
amplitude varies between observations, resulting in the additional noise seen
in the timing residuals. In most observations the leading component of the
averaged pulse profile has half the amplitude of the trailing component, but
in some observations both components have comparable amplitudes. The 5-s sub-
integrations (6.08 individual pulses) reveal that these variations in the
averaged profiles are caused by pulse-to-pulse variations between the
individual pulse components. To understand the profile variability of PSR
J1722+3519, a 1 hr observation where individual pulses were recorded was
obtained and analysed. This reveals a highly variable intensity of the two
profile peaks with a relatively long timescale of $\sim 100$ pulse periods. A
fluctuation spectrum analysis using the methods described in Weltevrede (2016)
confirmed the presence of this modulation timescale. For many pulsars,
periodic intensity modulation can be associated with drifting sub-pulses (e.g.
Song et al., submitted). However, for PSR J1722+3519, only evidence for
amplitude modulation is found. Given the long timescale of the modulation,
even longer observations would be beneficial in order to reveal any associated
phase variations. Another possible explanation for the profile variation and
the large root-mean-square (RMS) residuals is short timescale mode switching,
as seen in for example Stairs et al. (2019).

In the case of PSR J1910+5655, 14.63 individual pulses were averaged into the
5-s sub-integrations, which still show significant variability between sub-
integrations. The relatively low signal-to-noise of the profile in the 5-s
sub-integrations, combined with the averaging of many pulses per sub-
integration and the single wide component (21% duty cycle) make it difficult
to classify these variations.

The pulse profile of PSR J1529+4050 displays multiple components at 149 MHz,
and in the LOFAR band between 110 and 188 MHz, the leading component decreases
in brightness with increasing frequency compared to the trailing component
(Fig. 5). At 334 MHz and 1532 MHz, only the trailing component remains (Fig.
2), indicating that the leading component has significantly steeper spectra
compared to the trailing component. In a study comparing the pulse profiles of
a hundred pulsars observed by the LOFAR HBAs as well as the Lovell telescope
at L-band, Pilia et al. (2016) found pulse profiles with more profile
components at HBA frequencies compared to L-band frequencies to be less common
than the other way around. More components at HBA frequencies may be explained
by a wider pulsar beam at lower frequencies (Cordes, 1978), resulting in more
components coming into view. Pilia et al. (2016) note a slight indication that
pulsars with more components at HBA frequencies than at L-band frequencies may
be older and have a longer period. With a characteristic age of $2.8\times
10^{9}$ yr, PSR J1529+4050 is the fourth oldest pulsar in our sample.

Figure 4: Pulse profile variations with time for four pulsars at 149 MHz. The
figures display multiple rotations per sub-integration. A portion of the full
rotation is shown here and the profiles are rotated such that the highest peak
is centred, at phase $\phi=0.25$ or $\phi=0.5$. The flux scale is normalised
for each pulsar separately. White bars indicate where RFI was removed from the
data. Figure 5: Pulse profile variations in frequency between 110 and 188 MHz
in four pulsars. A portion of the full rotation is shown here and the profiles
are rotated such that the highest peak is centred, at phase $\phi=0.25$ or
$\phi=0.5$. The flux scale is normalised for each pulsar separately. White
bars indicate where RFI was removed from the data.

###  3.3 Pulse widths

Figure 6 shows the pulse widths at 50% of the peak profile intensity of all
LOTAAS discoveries, combining the $W_{50}$ values from this paper with those
reported in Michilli et al. (2020), Tan et al. (2018), and Tan et al. (2020).
Because the $W_{50}$ of PSRs J0250+5854 and J1658+3630 were reported at
slightly different observing frequencies, we used the $W_{50}$ value at a
frequency nearest to the frequencies reported here. We found that, on average,
the pulse widths are somewhat wider at 149 MHz than at the higher frequencies,
with a mean $W_{50}$ at 149 MHz of 29 ms and a standard deviation of 33 ms,
compared to $24\pm 20$ ms and $27\pm 28$ ms at 334 and 1532 MHz, respectively.

The intrinsic profile of pulsars will be broadened by the effects of
interstellar scattering, resulting in exponential tails at the trailing edge
of the pulse profiles. Four pulsars from the sample reported here, PSRs
J1745+4254, J2006+2205, J2123+3624, and J2306+3124, show these effects in the
pulse profiles at 149, 334, and/or 1484 or 1532 MHz (see Fig. 2 and Fig. 5),
suggesting that these may be scatter broadened. These pulsars are indicated in
Fig. 6, as are eight pulsars that Michilli et al. (2020) and Tan et al. (2020)
reported as showing signs of scatter broadening. All these pulsars are at DMs
above 20 pc cm-3, as expected, since scatter broadening is caused by material
in the interstellar medium and hence is roughly correlated with the dispersion
measure (DM).

Figure 6 also displays the scatter broadening predictions at 149, 334, and
1532 MHz from the empirical relations between scattering and DM found by Bhat
et al. (2004) and Geyer et al. (2017). Most pulse widths displayed in Fig. 6
are around the same order of magnitude as the scatter broadening predicted by
Bhat et al. (2004) and Geyer et al. (2017) for the typical scattering indices
of $\alpha_{\mathrm{S}}\sim-4$ or $-4.4$ (for scattering timescales
$\tau_{\nu}\propto\nu^{\alpha_{\mathrm{S}}}$) from the thin-screen
approximation (Williamson, 1972). Hence, the scattering relations predict that
the pulse profiles of the majority of the pulsars in our sample should be
affected by interstellar scattering. However, most pulse profiles in Fig. 2,
as well as the pulse profiles from the previous LOTAAS timing papers, do not
show signs of scattering, suggesting that there is a less steep frequency
scaling ($\alpha_{\mathrm{S}}>-4$) or that the scattering timescales may be
smaller than predicted by Bhat et al. (2004) and Geyer et al. (2017).

To test this, we modelled the frequency dependence of the LOFAR pulse profiles
of the pulsars that show exponentially trailing edges, PSRs J1745+4254,
J2006+2205, J2123+3624, and J2306+3124, with the wideband pulsar timing code
PulsePortraiture by Pennucci (2019), which simultaneously measures TOAs, DM,
and scattering, by fitting frequency dependent templates. With this method, we
constrained a scattering time $\tau_{\mathrm{S}}$ and scattering index
$\alpha_{\mathrm{S}}$ for these four pulsars by modelling the intrinsic
profile as a single Gaussian function and the pulse broadening as a one-sided
exponential function. We fitted this model to an averaged pulse profile
combining all LOFAR observations, which were fully averaged in time and
partially averaged in frequency to 100 frequency channels.

We found that the LOFAR profile of PSR J1745+4254 is best modelled with a
large scattering index of $\alpha_{\mathrm{S}}=-1.10\pm 0.12$ and a scattering
timescale of $\tau_{\mathrm{S}}=5.49\pm 8$ ms. Similarly, PSR J2006+2205, has
a large scattering index of $\alpha_{\mathrm{S}}=-2.18\pm 15$ for
$\tau_{\mathrm{S}}=15.8\pm 3$ ms, while PSR J2123+3624 has a more typical
scattering index of $\alpha_{\mathrm{S}}=-3.55\pm 9$ for
$\tau_{\mathrm{S}}=89.6\pm 1.0$ ms. We note that the profile of PSR J2306+3124
displays a similar exponential tail at both 149 MHz and 1532 MHz, with no
discernible frequency evolution between the observing bands, indicating its
intrinsic profile may have an exponential tail. The large scattering indices
of PSRs J1745+4254 and J2006+2205 confirm that the effect of scatter
broadening in the LOFAR pulse profiles is less pronounced compared to
predictions from the typical $-4$ and $-4.4$ scattering index values,
behaviour also reported in other pulsars at low observing frequencies (Geyer
et al., 2017).

Figure 6: The relations between pulse broadening and DM as found by Bhat et
al. (2004) (dashed lines) and Geyer et al. (2017) (solid lines) at 149, 334,
and 1532 MHz in black, red, and blue respectively. The functions from Geyer et
al. (2017) are shown with scattering indices between $-4$ and $-2$, while the
function from Bhat et al. (2004) is displayed with the best-fitting index of
$-3.68$. Shown as dots, circles and squares are the $W_{50}$ pulse widths from
this study, as well as from the previous LOTAAS reports Tan et al. (2018),
Michilli et al. (2020), and Tan et al. (2020) at different frequencies. These
measurements represent upper limits on pulse broadening due to interstellar
scattering. Pulse widths from the same pulsar at different frequencies are
connected with grey, vertical lines. The pulsars discussed in § 3.3 are marked
with arrows. The pulse widths at 149 MHz of eight pulsars from Michilli et al.
(2020) and Tan et al. (2020) which may be affected by scattering are marked
with grey circles.

###  3.4 Spectral index

Table 5 displays the flux densities and the spectral indices and Fig. 3 shows
the mean flux densities and the spectral power laws. For the 29 pulsars
investigated, here, we obtained a mean spectral index of $\alpha=-2.8\pm 1.5$,
with the uncertainty representing the standard deviation, which is consistent
with the values of $\alpha=-2.4\pm 0.9$ and $\alpha=-1.9\pm 0.5$ from Michilli
et al. (2020) and Tan et al. (2020), respectively, despite slightly different
treatments of the flux calibration and spectral fitting. Of the pulsars with
spectral index measurements, PSR J2336$-$0152 displays a notably steep
spectrum with a spectral index of $-5\pm 2$, due to the large difference
between the measured flux densities at 129 and 166 MHz. However, these flux
densities have large uncertainties and a much flatter spectrum is also
consistent with our results. We caution that a simple power law may be
insufficient to describe the spectra of some pulsars.

Table 5: The results from the spectral analysis and parameters derived from the timing model in Table 2. Mean flux densities and upper limits on the mean flux densities $S_{\nu}$ are shown with observing frequencies in MHz indicated in subscript. The inferred spectral indices $\alpha$ were fitted with a single power law of the form $S_{\nu}\propto\nu^{\alpha}$. Flux densities for which less than five observations were available are indicated in italics and were not used in the spectral fit. The Offset in arcminutes refers to the difference between the centre of the telescope beam and the position reported in Table 2. For six pulsars, the spectral index was not calculated due to the large position offset. We determined the characteristic age $\tau_{\mathrm{c}}$, the surface magnetic field strength $B$, and the intrinsic spin-down energy $\dot{E}$ assuming a canonical neutron star with a radius of 10 km and a moment of inertia of $10^{45}\,$ g cm2. Furthermore, we assumed that the initial spin is negligible and that the spin-down is due to magnetic dipole radiation throughout the pulsar’s lifetime. See Lorimer & Kramer (2012) for further details. PSR |  S129 |  S166 |  S334 |  S1484 |  S1532 | $\alpha$ | Offset | $\mathrm{\tau_{c}}$ | $\mathrm{B}$ | $\mathrm{\dot{E}}$
---|---|---|---|---|---|---|---|---|---|---
| mJy | mJy | mJy | mJy | mJy |  | arcmin | (yr) | (G) |  (erg s${}^{-1})$
J0039+3546 | $7(3)$ | $3.3(1.7)$ | $\it{0.34(12)}$ | $<1.4$ | $0.14(3)$ | $-1.5(3)$ | $1.12$ | $1.3\times 10^{8}$ | $1.9\times 10^{11}$ | $1.6\times 10^{31}$
J0059+6956 | $1.9(1.0)$ | $1.3(6)$ | $-$ | $<\it{2.5}$ | $-$ | $-2(3)$ | $1.61\times 10^{-3}$ | $1.3\times 10^{8}$ | $4.1\times 10^{11}$ | $3.7\times 10^{30}$
J0139+5621 | $3.8(1.9)$ | $2.3(1.1)$ | $\it{1.8(5)}$ | $-$ | $0.17(3)$ | $-1.2(2)$ | $7.7\times 10^{-1}$ | $3.6\times 10^{5}$ | $1.2\times 10^{13}$ | $5.6\times 10^{32}$
J0305+1123 | $3.9(2.0)$ | $2.0(1.0)$ | $<\it{0.06}$ | $-$ | $<0.006$ | $-4.8(1.8)$ | $5.7\times 10^{-1}$ | $4.5\times 10^{7}$ | $5.2\times 10^{11}$ | $1.9\times 10^{31}$
J0317+1328 | $2.0(1.0)$ | $1.1(5)$ | $\it{0.9(3)}$ | $<\it{2.7}$ | $<\it{0.21}$ | $-$ | $1.84$ | $1.8\times 10^{8}$ | $5.9\times 10^{11}$ | $8.7\times 10^{29}$
J0613+3731 | $24(12)$ | $12(6)$ | $\it{1.9(5)}$ | $-$ | $1.4(3)$ | $-1.0(2)$ | $4.3\times 10^{-2}$ | $3.0\times 10^{6}$ | $1.4\times 10^{12}$ | $5.4\times 10^{32}$
J0811+3729 | $6(3)$ | $2.4(1.2)$ | $<\it{0.86}$ | $\it{0.41(15)}$ | $<0.13$ | $-4.4(1.9)$ | $1.16$ | $2.7\times 10^{7}$ | $9.8\times 10^{11}$ | $1.5\times 10^{31}$
J0813+2202 | $2.9(1.5)$ | $1.2(6)$ | $-$ | $<\it{2.1}$ | $<0.3$ | $-4(2)$ | $2.2\times 10^{-1}$ | $1.1\times 10^{8}$ | $2.1\times 10^{11}$ | $2.0\times 10^{31}$
J0828+5304 | $3.1(1.5)$ | $1.7(8)$ | $-$ | $<\it{1.4}$ | $<0.099$ | $-4.0(1.9)$ | $2.4\times 10^{-4}$ | $8.3\times 10^{9}$ | $6.0\times 10^{8}$ | $4.1\times 10^{32}$
J0928+3039 | $8(4)$ | $3.4(1.7)$ | $<\it{1.1}$ | $<\it{1.6}$ | $<0.15$ | $-4.3(1.9)$ | $8.5\times 10^{-1}$ | $4.6\times 10^{7}$ | $6.2\times 10^{11}$ | $1.3\times 10^{31}$
J0935+3312 | $4(2)$ | $1.8(9)$ | $<\it{0.77}$ | $<\it{2.2}$ | $<0.22$ | $-4.2(2.0)$ | $1.01$ | $4.0\times 10^{7}$ | $6.1\times 10^{11}$ | $1.7\times 10^{31}$
J1303+3815 | $2.8(1.4)$ | $1.5(7)$ | $-$ | $-$ | $<0.12$ | $-3.9(1.9)$ | $1.25$ | $1.8\times 10^{7}$ | $3.8\times 10^{11}$ | $2.2\times 10^{32}$
J1334+1005 | $2.0(1.0)$ | $0.9(5)$ | $-$ | $0.21(5)$ | $-$ | $-0.9(6)$ | $5.8\times 10^{-1}$ | $1.9\times 10^{7}$ | $8.3\times 10^{11}$ | $3.9\times 10^{31}$
J1427+5211 | $3.0(1.5)$ | $1.2(6)$ | $-$ | $0.24(6)$ | $0.10(2)$ | $-1.1(3)$ | $4.8\times 10^{-3}$ | $3.3\times 10^{7}$ | $7.0\times 10^{11}$ | $1.9\times 10^{31}$
J1529+4050 | $13(6)$ | $10(5)$ | $\it{1.7(5)}$ | $\it{0.62(16)}$ | $0.56(11)$ | $-1.3(2)$ | $1.29$ | $2.8\times 10^{9}$ | $3.6\times 10^{10}$ | $9.7\times 10^{29}$
J1707+3556 | $8(4)$ | $5(2)$ | $-$ | $<\it{2.7}$ | $-$ | $-2(3)$ | $5.3\times 10^{-1}$ | $3.0\times 10^{9}$ | $1.2\times 10^{10}$ | $8.3\times 10^{30}$
J1715+4603 | $1.2(6)$ | $0.7(4)$ | $<\it{0.069}$ | $<\it{1.6}$ | $0.0010(2)$ | $-2.9(3)$ | $9.7\times 10^{-1}$ | $1.8\times 10^{8}$ | $1.6\times 10^{11}$ | $1.2\times 10^{31}$
J1722+3519 | $21(11)$ | $11(5)$ | $\it{1.4(5)}$ | $\it{0.7(2)}$ | $<1.5$ | $-4(2)$ | $5.5\times 10^{-1}$ | $2.4\times 10^{7}$ | $6.8\times 10^{11}$ | $3.9\times 10^{31}$
J1740+2715 | $5(2)$ | $3.4(1.7)$ | $\it{1.2(4)}$ | $\it{0.8(2)}$ | $0.41(9)$ | $-0.99(20)$ | $1.57$ | $7.8\times 10^{7}$ | $4.8\times 10^{11}$ | $7.1\times 10^{30}$
J1745+4254 | $2.2(1.1)$ | $1.6(8)$ | $\it{0.8(3)}$ | $\it{0.23(7)}$ | $0.24(5)$ | $-0.9(2)$ | $1.5$ | $4.9\times 10^{8}$ | $5.5\times 10^{10}$ | $1.4\times 10^{31}$
J1809+1705 | $1.5(7)$ | $1.2(6)$ | $<\it{3.3}$ | $\it{0.59(17)}$ | $<0.081$ | $-3.5(1.9)$ | $1.74$ | $1.1\times 10^{7}$ | $2.6\times 10^{12}$ | $1.4\times 10^{31}$
J1814+2224 | $1.1(5)$ | $1.3(7)$ | $\it{0.8(3)}$ | $\it{0.28(10)}$ | $0.20(4)$ | $-$ | $2.4$ | $1.1\times 10^{7}$ | $3.0\times 10^{11}$ | $8.6\times 10^{32}$
J1910+5655 | $10(5)$ | $5(2)$ | $-$ | $<\it{3.7}$ | $<0.14$ | $-4.3(1.8)$ | $1.22$ | $2.6\times 10^{7}$ | $2.7\times 10^{11}$ | $2.0\times 10^{32}$
J1953+3014 | $5(3)$ | $2.2(1.1)$ | $-$ | $\it{0.37(13)}$ | $0.16(3)$ | $-1.3(3)$ | $1.92\times 10^{-3}$ | $5.2\times 10^{7}$ | $7.1\times 10^{11}$ | $7.4\times 10^{30}$
J1958+2214 | $0.6(3)$ | $0.8(4)$ | $-$ | $-$ | $-$ | $-$ | $1.63\times 10^{1}$ | $3.6\times 10^{6}$ | $2.2\times 10^{12}$ | $1.6\times 10^{32}$
J1958+5650 | $1.1(6)$ | $0.6(3)$ | $-$ | $-$ | $0.063(13)$ | $-1.1(2)$ | $3.0\times 10^{-3}$ | $2.9\times 10^{7}$ | $2.3\times 10^{11}$ | $2.2\times 10^{32}$
J2006+2205 | $3.7(1.9)$ | $3.0(1.5)$ | $<\it{2.3}$ | $0.19(7)$ | $<0.12$ | $-$ | $2.0$ | $4.8\times 10^{6}$ | $3.2\times 10^{12}$ | $4.3\times 10^{31}$
J2022+2112 | $5(2)$ | $2.7(1.4)$ | $-$ | $<\it{2.8}$ | $<0.009$ | $-4.6(1.7)$ | $8.8\times 10^{-1}$ | $1.4\times 10^{7}$ | $8.6\times 10^{11}$ | $6.9\times 10^{31}$
J2053+1718 | $4(2)$ | $2.5(1.3)$ | $-$ | $<\it{1.4}$ | $<0.015$ | $-4.4(1.7)$ | $7.4\times 10^{-1}$ | $6.3\times 10^{9}$ | $6.1\times 10^{9}$ | $7.0\times 10^{30}$
J2057+2128 | $1.6(8)$ | $0.8(4)$ | $-$ | $<3.0$ | $-$ | $-$ | $2.3$ | $3.5\times 10^{7}$ | $7.9\times 10^{11}$ | $1.3\times 10^{31}$
J2123+3624 | $6(3)$ | $4(2)$ | $-$ | $<\it{1.4}$ | $<1.6$ | $-3(2)$ | $8.2\times 10^{-3}$ | $9.8\times 10^{6}$ | $1.7\times 10^{12}$ | $3.8\times 10^{31}$
J2209+2117 | $5(3)$ | $3.7(1.9)$ | $-$ | $\it{0.18(5)}$ | $0.29(6)$ | $-1.17(19)$ | $6.8\times 10^{-1}$ | $5.5\times 10^{6}$ | $3.0\times 10^{12}$ | $3.6\times 10^{31}$
J2306+3124 | $6(3)$ | $3.3(1.7)$ | $-$ | $\it{0.18(7)}$ | $0.18(4)$ | $-$ | $2.0$ | $2.4\times 10^{7}$ | $2.8\times 10^{11}$ | $2.2\times 10^{32}$
J2336$-$0151 | $9(5)$ | $2.8(1.4)$ | $\it{1.2(4)}$ | $<1.4$ | $<\it{0.44}$ | $-5(2)$ | $1.54$ | $4.7\times 10^{7}$ | $6.0\times 10^{11}$ | $1.2\times 10^{31}$
J2350+3140 | $5(3)$ | $1.9(1.0)$ | $<\it{1.2}$ | $<1.2$ | $<0.2$ | $-4.2(2.0)$ | $1.01$ | $2.3\times 10^{7}$ | $4.3\times 10^{11}$ | $1.1\times 10^{32}$

###  3.5 PSR J0828+5304

PSR J0828+5304 is a binary millisecond pulsar with a spin period of 13.52 ms
at a DM of 23.103 pc cm-3. Table 3 provides the binary parameters of this
pulsar. The orbital period of $P_{\mathrm{b}}=5.899$ d and projected semi-
major axis of $x=13.147$ lt-s yield a mass-function of 0.07 M⊙, constraining
the binary companion mass to 0.65 M⊙ for an edge-on orbit, or 0.79 M⊙ for a
median orbital inclination of 60$\degr$, assuming the pulsar has a canonical
mass of 1.4 M⊙. With this companion mass and spin period, PSR J0828+5304 can
be classified as an intermediate mass binary pulsar (van Kerkwijk et al.,
2005) where the neutron star is partially recycled due to unstable mass
transfer from a binary companion which will leave a CO or ONeMg-core white
dwarf (Tauris et al., 2012). The Laplace-Lagrange parameters of the ELL1
binary model for nearly circular orbits yield an orbital eccentricity of
$2.5(7)\times 10^{-6}$, in line with predictions from tidal orbital
circularisation (Phinney, 1992; Phinney & Kulkarni, 1994).

No optical counterpart is present at the pulsar timing position of PSR
J0828+5304 in the Pan-STARSS1 survey (PS1; Chambers et al. 2016); the nearest
catalogued PS1 source is $24\arcsec$ offset. The nominal PS1 $5\sigma$
detection limit of r-band magnitude $r=23.2$ provides absolute magnitude
limits of $M_{r}>12.2$ for the 0.9 and 1.6 kpc distances estimated from the
observed DM and the NE2001 (Cordes & Lazio, 2002) and YMW16 (Yao et al., 2017)
Galactic electron density models, respectively. At this limit, cooling
models444http://www.astro.umontreal.ca/b̃ergeron/CoolingModels by Bergeron et
al. (2011) and Tremblay et al. (2011) for 0.7 M⊙ white dwarfs with either
hydrogen or helium atmospheres predict effective temperatures and white dwarf
cooling ages of $T_{\mathrm{eff}}<12000$ K and $\tau_{\mathrm{cool}}>0.5$ Gyr,
ruling out young and hot white dwarf companions.

##  4 Discussion and conclusions

We present the properties of 35 pulsars discovered with LOFAR as part of the
LOTAAS (Sanidas et al., 2019) and LOFAR pilot surveys (Coenen et al., 2014).
We expand this sample with the properties of 41 LOFAR-discovered pulsars
reported by Michilli et al. (2020), Tan et al. (2018), and Tan et al. (2020),
all of which were discovered by the LOTAAS survey. We excluded PSR J0815+4611,
whose timing parameters were presented in Michilli et al. (2020), as it was
discovered as a steep spectrum polarised point source in continuum images of
the 3C 196 field (Jelić et al., 2015). Similarly, we excluded radio pulsars
discovered with LOFAR and presented by Pleunis et al. (2017), Bassa et al.
(2017, 2018) and Sobey et al. (2022) as these pulsars were discovered through
the use of coherent dedispersion and by targeting the locations of Fermi
$\gamma$-ray sources or polarised point sources from the LOFAR imaging survey
(Shimwell et al., 2017) and will have different survey selection effects
compared to LOTAAS.

Figure 7: Cumulative distributions of the spectral index, the spin period, and
the period derivative of the pulsars discovered by the LOTAAS survey (black).
The upper plot displays spectral indices from Jankowski et al. (2018) (blue)
and Bilous et al. (2016) (orange). We caution that, due to the uncertainties
in the flux calibration of the LOTAAS obervations, the LOTAAS spectral indices
should not be used for detailed studies. The lower plots show the LOTAAS
redetections (red), the known pulsar population (grey), and a subset of the
known pulsar population limited to $P>0.02$ s and $\mathrm{DM}<200\,$pc cm-3
(blue).

The spectral properties of the LOTAAS sample have a mean spectral index,
assuming power law spectra of the form $S_{\nu}\propto\nu^{\alpha}$, of
$\alpha=-2.5$ with a standard deviation of 1.2 (for 66 pulsars), see Fig. 7.
On average, these spectra are steeper compared to the sample studied by
Jankowski et al. (2018), which has $\alpha=-1.57\pm 0.62$ for 441 radio
pulsars at radio frequencies between 728 and 3100 MHz, as well as those of
single power law spectral fits by Bilous et al. (2016), which have
$\alpha=-1.4\pm 0.7$ for 124 pulsars, all with observations from the LOFAR
band between 110 and 188 MHz, the same band used for the LOTAAS timing
observations presented here.

The steeper radio spectra of LOTAAS-discovered pulsars are readily explained
as a selection effect, as pulsars with flatter spectra will already have been
discovered by earlier pulsar surveys at higher frequencies. In particular, the
LOTAAS survey overlaps with the GBNCC survey of the Northern sky using the
Green Bank telescope (Stovall et al., 2014), which started in 2009 and reaches
a sensitivity of 1.1 mJy at 350 MHz, the AO327 survey with Arecibo, reaching
0.4 mJy at 327 MHz for declinations between $-1\degr$ and $28\degr$, which
started survey observations in 2011 (Deneva et al., 2013), and PUMPS with the
Large Phased Array at Pushchino, which started in 2014 at 111 MHz with
sensitivities up to 0.1 mJy for declinations between $-9\degr$ and $42\degr$
(Tyul’bashev et al., 2022). Of the 311 known radio pulsars redetected with
LOTAAS, 47 and 6 were earlier discoveries from the GBNCC and AO327 surveys,
respectively (Sanidas et al., 2019), indicating that these pulsars would have
been new discoveries for LOTAAS in the absence of the GBNCC and AO327 surveys.
Similarly, those pulsars discovered with LOTAAS and detected at 334 MHz with
the Lovell telescope have 334 MHz flux densities near the sensitivity limits
of the GBNCC and AO327 surveys, indicating they likely were below their
detection thresholds.

The timing solutions of the LOTAAS pulsars show that they have, on average,
longer spin periods and lower spin period derivatives in comparison to the
known population of radio pulsars. These findings confirm the results from
Sanidas et al. (2019), who already noted the statistical discrepancy of the
LOTAAS discovery spin periods being longer than those from the known
population. To compare the LOTAAS spin periods and spin period derivatives
with those of the known pulsar population, we constructed three pulsar
samples; I) the LOTAAS discoveries; II) known pulsars that were redetected in
the LOTAAS survey and III) known radio pulsars that were not detected in
LOTAAS, and that have $P>0.02$ s and $\mathrm{DM}<200$ pc cm-3, to take into
account some of the selection biases of LOTAAS, namely the increased
sensitivity towards slower pulsars and decreased sensitivity for pulsars at
high DM (Sanidas et al., 2019). We queried the ATNF pulsar
catalogue555http://www.atnf.csiro.au/research/pulsar/psrcat (version 1.67,
Manchester et al. 2005) for the properties of the known pulsars to construct
samples II and III, where we excluded pulsars that were associated with
globular clusters. For sample II, the redetected pulsars presented in Sanidas
et al. (2019), spin period and spin period derivatives were available for 253
out of the 311 pulsars, while sample III consists of 891 pulsars.

Figure 7 shows the cumulative distributions of the spin period and spin period
derivatives of the three samples, as well as the entire known pulsar
population. Using two-sample Kolmogorov-Smirnov (KS) tests, we found that the
probability that the spin periods and spin period derivatives of sample I, the
LOTAAS discoveries, are drawn from the selection-bias-corrected known pulsar
population (sample III) is low, at $p=0.73$% and 0.039%, respectively. As
these probabilities are $p<1$%, we can reject the null hypothesis that the
samples were drawn from the same underlying distribution. For comparison, the
probability that the known pulsars redetected by LOTAAS, sample II, are drawn
from sample III is significantly higher, $p=33$% for the spin period
distribution and 30% for the spin period derivative distribution.

Assuming that the spin period $P$ and spin period derivative $\dot{P}$
distributions from Fig. 7 both follow a log-normal distribution, we found
$\log_{10}P=-0.040\pm 0.421$ and $\log_{10}\dot{P}=-15.43\pm 1.10$ for the
median spin period ($P$ in s) and spin period derivatives ($\dot{P}$ in s s-1)
of the LOTAAS discoveries (sample I), compared to $\log_{10}P=-0.20\pm 0.43$
and $\log_{10}\dot{P}=-14.94\pm 1.18$ for the known pulsar population with
$P>0.02$ s and $\mathrm{DM}<200$ pc cm-3 (sample III). Hence, the LOTAAS-
discovered pulsars have spin periods and spin-down rates which are, on
average, a factor 1.4 longer and a factor 3.1 lower, respectively, compared to
the known pulsar population.

Figure 8: $P-\dot{P}$ diagram of the pulsars discovered (black dots) and
redetected (red circles) by the LOTAAS survey and the known pulsar population
(grey dots). The grey dotted and dashed diagonals represent the characteristic
ages and the spin-down luminosities, respectively. The solid lines are
deathlines from Chen & Ruderman (1993) and Zhang et al. (2000).

When plotted in a $P-\dot{P}$-diagram, Fig. 8, the LOTAAS discoveries have
higher characteristic ages $\tau_{\mathrm{c}}$, lower spin-down luminosities
$\dot{E}$ and are generally located closer to the pulsar deathlines where
pulsar emission ceases (e.g. Chen & Ruderman, 1993; Zhang et al., 2000). The
cause of these offsets in spin period and spin period derivative is not
immediately obvious, though Sanidas et al. (2019) remarked that the 3600 s
integration times of LOTAAS, significantly longer than those of many other
pulsar surveys, will increase its sensitivity towards longer period pulsars.

The offsets may also be related to the low observing frequency of the LOTAAS
survey compared to previous surveys, making LOTAAS more sensitive to pulsars
with steeper radio spectra. Jankowski et al. (2018) found strong correlations
of the spectral index $\alpha$ with the spin-down luminosity $\dot{E}$,
magnetic field at the light-cylinder $B_{\mathrm{LC}}$, the spin frequency
derivative $\dot{\nu}$, and the characteristic age $\tau_{\mathrm{c}}$. They
found the maximum Spearman correlation coefficient between $\alpha$ values of
276 pulsars and a parameterisation of their spin frequency $\nu$ and
$\dot{\nu}$ in the form of $\log_{10}\left(\nu^{a}|\dot{\nu}|^{b}\right)$ for
values which have $b/a=0.55$. Converting this parameterisation from $\nu$ and
$\dot{\nu}$ to $P$ and $\dot{P}$ using
$\log_{10}\left(\nu^{a}|\dot{\nu}|^{b}\right)\propto\log_{10}\left(P^{r}\dot{P}^{q}\right)$,
we found that the $b/a=0.55$ correlation corresponds to $r/q=-0.26$ (as
$r/q=(-a/b-2)^{-1}$). This indicates that for 1 dex in $P$, $\dot{P}$
decreases by 0.26 dex in the $P-\dot{P}$ diagram of Fig. 8, and that pulsars
with steeper radio spectra generally have longer spin periods and lower spin
period derivatives.

Longer spin periods and lower spin period derivatives are also seen for
pulsars recently discovered with the GBNCC survey (Lynch et al., 2018) as well
as those from the SUPERB survey (Spiewak et al., 2020) with Parkes. While the
GBNCC survey observing at 350 MHz will also be biased towards pulsars with
steeper radio spectra, the SUPERB survey, observing at 1382 MHz (Keane et al.,
2018) will not, as the majority of pulsars making up the known pulsar
population were discovered at those observing frequencies (Edwards et al.,
2001; Manchester et al., 2001; Cordes et al., 2006; Keith et al., 2010). For
the GBNCC survey, population synthesis modelling by McEwen et al. (2020)
revealed that this bias is introduced through the GBNCC’s reduced sensitivity
towards pulsars at low Galactic latitudes, due to increased sky temperatures
and scattering, while young radio pulsars have not had enough time to move
away from their birthplaces in the Galactic plane (Faucher-Giguère & Kaspi,
2006). Hence, the GBNCC survey is biased towards finding pulsars at higher
Galactic latitudes, which will predominantly be older pulsars. This is also
the case for the SUPERB discoveries as this survey specifically targets higher
Galactic latitudes ($|b|>15\degr$; Keane et al. 2018), as well as LOTAAS,
which has worse sensitivity in the Galactic plane compared to the GBNCC survey
due to increased sky temperatures and the effects of scattering.

We consider it likely that all three effects combined, sensitivity to longer
spin periods, steeper radio spectra and the reduced sensitivity towards young
pulsars in the Galactic plane, play a role in discovering pulsars with longer
spin periods and lower spin down rates. However, we can not rule out that
older pulsars have, on average, steeper radio spectra. Pulsar population
synthesis modelling would be required to estimate the impact of each of these
effects separately and separate those from any intrinsic pulsar properties,
such as a correlation between age and the steepness of the pulsars radio
spectra. This task goes beyond the scope of this paper, as these simulations
would benefit from using new and updated models of the Galactic electron
distribution, the global sky temperature, and scattering (e.g. Yao et al.,
2017; Price, 2021; Geyer et al., 2017) to properly model the sensitivity for
the low observing frequencies of the LOTAAS survey.

###### Acknowledgements.

The paper is based (in part) on data obtained with the International LOFAR
Telescope (ILT) under project codes LC1_003, LT3_001, LC4_004, LT5_003,
LT5_004, LC9_021, LC9_041, LT10_015 and LT14_005. LOFAR (van Haarlem et al.,
2013) is the Low Frequency Array designed and constructed by ASTRON. It has
observing, data processing, and data storage facilities in several countries,
that are owned by various parties (each with their own funding sources), and
that are collectively operated by the ILT foundation under a joint scientific
policy. The ILT resources have benefitted from the following recent major
funding sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans,
France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI),
Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The
Netherlands; The Science and Technology Facilities Council, UK. We acknowledge
the use of the Nançay Data Center computing facility (CDN – Centre de Données
de Nançay). The CDN is hosted by the Nançay Radioastronomy Observatory (ORN)
in partnership with Observatoire de Paris, Université d’Orléans, OSUC and the
CNRS. The CDN is supported by the Région Centre-Val de Loire, département du
Cher. The Nançay Radio Observatory is operated by the Paris Observatory,
associated with the French Centre National de la Recherche Scientifique
(CNRS). This research was made possible by support from the Dutch National
Science Agenda, NWA Startimpuls – 400.17.608. CGB, JWTH, VIK, and DM
acknowledge support for this work from the European Research Council under the
European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant
Agreement nr. 337062.

## References

  * Bassa et al. (2017) Bassa, C. G., Pleunis, Z., Hessels, J. W. T., et al. 2017, ApJ, 846, L20
  * Bassa et al. (2018) Bassa, C. G., Pleunis, Z., Hessels, J. W. T., et al. 2018, in Pulsar Astrophysics the Next Fifty Years, ed. P. Weltevrede, B. B. P. Perera, L. L. Preston, & S. Sanidas, Vol. 337, 33–36
  * Basu et al. (2022) Basu, A., Shaw, B., Antonopoulou, D., et al. 2022, MNRAS, 510, 4049
  * Basu et al. (2017) Basu, R., Mitra, D., & Melikidze, G. I. 2017, The Astrophysical Journal, 846, 109
  * Bergeron et al. (2011) Bergeron, P., Wesemael, F., Dufour, P., et al. 2011, ApJ, 737, 28
  * Bhat et al. (2004) Bhat, N. D. R., Cordes, J. M., Camilo, F., Nice, D. J., & Lorimer, D. R. 2004, ApJ, 605, 759
  * Bhattacharyya et al. (2016) Bhattacharyya, B., Cooper, S., Malenta, M., et al. 2016, ApJ, 817, 130
  * Bilous et al. (2016) Bilous, A. V., Kondratiev, V. I., Kramer, M., et al. 2016, A&A, 591, A134
  * Brinkman et al. (2018) Brinkman, C., Freire, P. C. C., Rankin, J., & Stovall, K. 2018, MNRAS, 474, 2012
  * Broekema et al. (2018) Broekema, P. C., Mol, J. J. D., Nijboer, R., et al. 2018, ArXiv e-prints [arXiv:1801.04834]
  * Burgay et al. (2003) Burgay, M., D’Amico, N., Possenti, A., et al. 2003, Nature, 426, 531
  * Caleb et al. (2022) Caleb, M., Heywood, I., Rajwade, K., et al. 2022, Nature Astronomy, 6, 1
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Chen & Ruderman (1993) Chen, K. & Ruderman, M. 1993, ApJ, 402, 264
  * Coenen et al. (2014) Coenen, T., van Leeuwen, J., Hessels, J. W. T., et al. 2014, A&A, 570, A60
  * Cordes (1978) Cordes, J. M. 1978, ApJ, 222, 1006
  * Cordes et al. (2006) Cordes, J. M., Freire, P. C. C., Lorimer, D. R., et al. 2006, ApJ, 637, 446
  * Cordes & Lazio (2002) Cordes, J. M. & Lazio, T. J. W. 2002, astro-ph/0207156
  * Deneva et al. (2013) Deneva, J. S., Stovall, K., McLaughlin, M. A., et al. 2013, ApJ, 775, 51
  * Donner et al. (2020) Donner, J. Y., Verbiest, J. P. W., Tiburzi, C., et al. 2020, A&A, 644, A153
  * Edwards et al. (2001) Edwards, R. T., Bailes, M., van Straten, W., & Britton, M. C. 2001, MNRAS, 326, 358
  * Espinoza et al. (2011) Espinoza, C. M., Lyne, A. G., Stappers, B. W., & Kramer, M. 2011, MNRAS, 414, 1679
  * Faucher-Giguère & Kaspi (2006) Faucher-Giguère, C.-A. & Kaspi, V. M. 2006, ApJ, 643, 332
  * Folkner & Park (2016) Folkner, W. M. & Park, R. S. 2016, JPL planetary and lunar ephemeris DE436
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306
  * Geyer et al. (2017) Geyer, M., Karastergiou, A., Kondratiev, V. I., et al. 2017, MNRAS, 470, 2659
  * Guillemot et al. (2016) Guillemot, L., Smith, D. A., Laffon, H., et al. 2016, A&A, 587, A109
  * Hewish et al. (1968) Hewish, A., Bell, S. J., Pilkington, J. D. H., Scott, P. F., & Collins, R. A. 1968, Nature, 217, 709
  * Hobbs et al. (2010) Hobbs, G., Lyne, A. G., & Kramer, M. 2010, MNRAS, 402, 1027
  * Hobbs et al. (2006) Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, MNRAS, 369, 655
  * Hotan et al. (2004) Hotan, A. W., van Straten, W., & Manchester, R. N. 2004, PASA, 21, 302
  * Hurley-Walker et al. (2022) Hurley-Walker, N., Zhang, X., Bahramian, A., et al. 2022, Nature, 601, 526
  * Jankowski et al. (2018) Jankowski, F., van Straten, W., Keane, E. F., et al. 2018, MNRAS, 473, 4436
  * Jelić et al. (2015) Jelić, V., de Bruyn, A. G., Pandey, V. N., et al. 2015, A&A, 583, A137
  * Karastergiou et al. (2015) Karastergiou, A., Chennamangalam, J., Armour, W., et al. 2015, MNRAS, 452, 1254
  * Keane et al. (2015) Keane, E., Bhattacharyya, B., Kramer, M., et al. 2015, in Advancing Astrophysics with the Square Kilometre Array (AASKA14), 40
  * Keane et al. (2018) Keane, E. F., Barr, E. D., Jameson, A., et al. 2018, MNRAS, 473, 116
  * Keith et al. (2010) Keith, M. J., Jameson, A., van Straten, W., et al. 2010, MNRAS, 409, 619
  * Kondratiev et al. (2016) Kondratiev, V. I., Verbiest, J. P. W., Hessels, J. W. T., et al. 2016, A&A, 585, A128
  * Kramer et al. (2006) Kramer, M., Lyne, A. G., O’Brien, J. T., Jordan, C. A., & Lorimer, D. R. 2006, Science, 312, 549
  * Kramer et al. (2021) Kramer, M., Stairs, I. H., Manchester, R. N., et al. 2021, Physical Review X, 11, 041050
  * Lange et al. (2001) Lange, C., Camilo, F., Wex, N., et al. 2001, MNRAS, 326, 274
  * Laskar et al. (2014) Laskar, T., Berger, E., Tanvir, N., et al. 2014, ApJ, 781, 1
  * Lazarus et al. (2015) Lazarus, P., Brazier, A., Hessels, J. W. T., et al. 2015, ApJ, 812, 81
  * Lazarus et al. (2016) Lazarus, P., Karuppusamy, R., Graikou, E., et al. 2016, MNRAS, 458, 868
  * Lorimer & Kramer (2012) Lorimer, D. R. & Kramer, M. 2012, Handbook of Pulsar Astronomy (Cambridge University Press)
  * Lynch et al. (2018) Lynch, R. S., Swiggum, J. K., Kondratiev, V. I., et al. 2018, ApJ, 859, 93
  * Lyne et al. (2004) Lyne, A. G., Burgay, M., Kramer, M., et al. 2004, Science, 303, 1153
  * Manchester et al. (2005) Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005, VizieR Online Data Catalog, VII/245
  * Manchester et al. (2001) Manchester, R. N., Lyne, A. G., Camilo, F., et al. 2001, MNRAS, 328, 17
  * McEwen et al. (2020) McEwen, A. E., Spiewak, R., Swiggum, J. K., et al. 2020, ApJ, 892, 76
  * McLaughlin et al. (2006) McLaughlin, M. A., Lyne, A. G., Lorimer, D. R., et al. 2006, Nature, 439, 817
  * Michilli et al. (2020) Michilli, D., Bassa, C., Cooper, S., et al. 2020, MNRAS, 491, 725
  * Morello et al. (2019) Morello, V., Barr, E. D., Cooper, S., et al. 2019, MNRAS, 483, 3673
  * Pennucci (2019) Pennucci, T. T. 2019, ApJ, 871, 34
  * Petit (2010) Petit, G. 2010, Highlights of Astronomy, 15, 220
  * Phinney (1992) Phinney, E. S. 1992, Philosophical Transactions of the Royal Society of London Series A, 341, 39
  * Phinney & Kulkarni (1994) Phinney, E. S. & Kulkarni, S. R. 1994, ARA&A, 32, 591
  * Pilia et al. (2016) Pilia, M., Hessels, J. W. T., Stappers, B. W., et al. 2016, A&A, 586, A92
  * Pleunis et al. (2017) Pleunis, Z., Bassa, C. G., Hessels, J. W. T., et al. 2017, ApJ, 846, L19
  * Price (2021) Price, D. C. 2021, Research Notes of the American Astronomical Society, 5, 246
  * Radhakrishnan & Manchester (1969) Radhakrishnan, V. & Manchester, R. N. 1969, Nature, 222, 228
  * Ray et al. (1996) Ray, P. S., Thorsett, S. E., Jenet, F. A., et al. 1996, ApJ, 470, 1103
  * Reichley & Downs (1969) Reichley, P. E. & Downs, G. S. 1969, Nature, 222, 229
  * Romani et al. (2022) Romani, R. W., Kandel, D., Filippenko, A. V., Brink, T. G., & Zheng, W. 2022, ApJ, 934, L18
  * Sanidas et al. (2019) Sanidas, S., Cooper, S., Bassa, C. G., et al. 2019, A&A, 626, A104
  * Shimwell et al. (2017) Shimwell, T. W., Röttgering, H. J. A., Best, P. N., et al. 2017, A&A, 598, A104
  * Sobey et al. (2022) Sobey, C., Bassa, C. G., O’Sullivan, S. P., et al. 2022, A&A, 661, A87
  * Spiewak et al. (2020) Spiewak, R., Flynn, C., Johnston, S., et al. 2020, MNRAS, 496, 4836
  * Stairs et al. (2019) Stairs, I. H., Lyne, A. G., Kramer, M., et al. 2019, MNRAS, 485, 3230
  * Stappers et al. (2011) Stappers, B., Hessels, J., Alexov, A., et al. 2011, in American Institute of Physics Conference Series, Vol. 1357, Radio Pulsars: An Astrophysical Key to Unlock the Secrets of the Universe, ed. M. Burgay, N. D’Amico, P. Esposito, A. Pellizzoni, & A. Possenti, 325–330
  * Stovall et al. (2014) Stovall, K., Lynch, R. S., Ransom, S. M., et al. 2014, ApJ, 791, 67
  * Tan et al. (2018) Tan, C. M., Bassa, C. G., Cooper, S., et al. 2018, ApJ, 866, 54
  * Tan et al. (2020) Tan, C. M., Bassa, C. G., Cooper, S., et al. 2020, MNRAS, 492, 5878
  * Tauris et al. (2017) Tauris, T. M., Kramer, M., Freire, P. C. C., et al. 2017, ApJ, 846, 170
  * Tauris et al. (2012) Tauris, T. M., Langer, N., & Kramer, M. 2012, MNRAS, 425, 1601
  * Taylor (1992) Taylor, J. H. 1992, Philosophical Transactions of the Royal Society of London Series A, 341, 117
  * Tremblay et al. (2011) Tremblay, P. E., Bergeron, P., & Gianninas, A. 2011, ApJ, 730, 128
  * Tyul’bashev et al. (2022) Tyul’bashev, S. A., Tyul’basheva, G. E., & Kitaeva, M. A. 2022, arXiv e-prints, arXiv:2208.04578
  * van Haarlem et al. (2013) van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2
  * van Kerkwijk et al. (2005) van Kerkwijk, M. H., Bassa, C. G., Jacoby, B. A., & Jonker, P. G. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 328, Binary Radio Pulsars, ed. F. A. Rasio & I. H. Stairs, 357
  * van Straten & Bailes (2011) van Straten, W. & Bailes, M. 2011, PASA, 28, 1
  * Wang et al. (2020) Wang, P. F., Han, J. L., Han, L., et al. 2020, A&A, 644, A73
  * Weltevrede (2016) Weltevrede, P. 2016, A&A, 590, A109
  * Williamson (1972) Williamson, I. P. 1972, MNRAS, 157, 55
  * Yao et al. (2017) Yao, J. M., Manchester, R. N., & Wang, N. 2017, ApJ, 835, 29
  * Young et al. (2015) Young, N. J., Weltevrede, P., Stappers, B. W., Lyne, A. G., & Kramer, M. 2015, MNRAS, 449, 1495
  * Yu et al. (2013) Yu, M., Manchester, R. N., Hobbs, G., et al. 2013, MNRAS, 429, 688
  * Zhang et al. (2000) Zhang, B., Harding, A. K., & Muslimov, A. G. 2000, in American Astronomical Society Meeting Abstracts, Vol. 195, American Astronomical Society Meeting Abstracts #195, 133.03