# A single pulse study of PSR J1022+1001 using the FAST radio telescope

Yi Feng  CAS Key Laboratory of FAST, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100101, People’s Republic of China
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic
of China  CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW 1710,
Australia  G. Hobbs  CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW
1710, Australia  D. Li  CAS Key Laboratory of FAST, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, People’s Republic
of China  University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China  NAOC-UKZN Computational Astrophysics Centre, University of
KwaZulu-Natal, Durban 4000, South Africa  S. Dai  CSIRO Astronomy and Space
Science, PO Box 76, Epping, NSW 1710, Australia  W. W. Zhu  CAS Key Laboratory
of FAST, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100101, People’s Republic of China  Y. L. Yue  CAS Key Laboratory of
FAST, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100101, People’s Republic of China  P. Wang  CAS Key Laboratory of
FAST, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100101, People’s Republic of China  S.-B. Zhang  Purple Mountain
Observatory, Chinese Academy of Sciences, Nanjing 210008, China  University of
Chinese Academy of Sciences, Beijing 100049, People’s Republic of China  CSIRO
Astronomy and Space Science, PO Box 76, Epping, NSW 1710, Australia  L. Qian
CAS Key Laboratory of FAST, National Astronomical Observatories, Chinese
Academy of Sciences, Beijing 100101, People’s Republic of China  L. Zhang  CAS
Key Laboratory of FAST, National Astronomical Observatories, Chinese Academy
of Sciences, Beijing 100101, People’s Republic of China  University of Chinese
Academy of Sciences, Beijing 100049, People’s Republic of China  CSIRO
Astronomy and Space Science, PO Box 76, Epping, NSW 1710, Australia  S. Q.
Wang  Xinjiang Astronomical Observatory, 150, Science-1 Street, Urumqi, 830011
Xinjiang, China  C. C. Miao  CAS Key Laboratory of FAST, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, People’s Republic
of China  University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China  M. Yuan  CAS Key Laboratory of FAST, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, People’s Republic
of China  University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China  Y.-K. Zhang  CAS Key Laboratory of FAST, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101,
People’s Republic of China  University of Chinese Academy of Sciences, Beijing
100049, People’s Republic of China

###### Abstract

Using the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we
have recorded $\sim 10^{5}$ single pulses from PSR J1022+1001. We studied the
polarization properties, their energy distribution and their times of arrival.
This is only possible with the high sensitivity available using FAST. There is
no indication that PSR J1022+1001 exhibits giant pulse, nulling or traditional
mode changing phenomena. The energy in the leading and trailing components of
the integrated profile is shown to be correlated. The degree of both linear
and circular polarization increases with the pulse flux density for individual
pulses. Our data indicates that pulse jitter leads to an excess noise in the
timing residuals of 67 ns when scaled to one hour, which is consistent with
Liu et al. (2015). We have unsuccessfully trialled various methods to improve
timing precision through the selection of specific single pulses. Our work
demonstrates that FAST can detect individual pulses from pulsars that are
observed in order to detect and study gravitational waves. This capability
enables detailed studies, and parameterisation, of the noise processes that
affect the sensitivity of a pulsar timing array.

pulsars: general — pulsars: individual: PSR J1022+1001 — methods: data
analysis

††software: DSPSR (van Straten & Bailes 2011), PSRCHIVE (Hotan et al. 2004b),
TEMPO2 (Hobbs et al. 2006)

##  1 Introduction

Radio pulsars are known to exhibit a profusion of emission phenomena. For
instance, mode changing (e.g. Bartel et al. 1982, Wang et al. 2007), nulling
(e.g. Backer 1970, Wang et al. 2007), sub-pulse drifting (e.g. Drake & Craft
1968, Weltevrede et al. 2006) and giant pulse (e.g. Staelin & Reifenstein
1968, Hankins et al. 2003) phenomena have been observed in normal pulsars. The
profile shapes of individual pulses vary significantly (e.g. Jenet et al.
2001, Shannon & Cordes 2012), but the summation of a large number of pulses
usually leads to a stable profile. Mode changing is a discontinuous change
where the mean pulse profile abruptly changes between two (or sometimes more)
quasi-stable states. Nulling is where individual pulses in the pulse train are
undetectable. Individual pulses can be tens or hundreds of times brighter than
the average, which is known as giant pulse phenomenon. Giant pulses are much
narrower than the average profile and have durations that range from
nanoseconds to microseconds and follow a power-law energy distribution. With
this definition, giant pulses have been detected in seven pulsars, including
two young pulsars and five millisecond pulsars (e.g. Staelin & Reifenstein
1968, Cognard et al. 1996, Johnston & Romani 2003). Mode changing and nulling
are thought to be linked and are caused by changes in the pulsar magnetosphere
(Lyne et al., 2010; Stairs et al., 2019).

Mode changing, nulling and sub-pulse drifting phenomena are relatively rare in
millisecond pulsars (MSPs). Mode changing has been observed in only one MSP
(Mahajan et al., 2018), nulling has not yet been reported and sub-pulse
drifting has been observed in only three MSPs (Edwards & Stappers 2003, Liu et
al. 2015). This cannot be fully explained by selection biases caused by a lack
of well studied single pulses from MSPs (e.g. Jenet et al. 2001, Shannon &
Cordes 2012, Osłowski et al. 2014, Liu et al. 2016).

In this paper, we carried out a single pulse study of PSR J1022+1001. We have
recorded over $\sim 10^{5}$ single pulses from PSR J1022+1001 with the Five-
hundred-meter Aperture Spherical radio Telescope (FAST, Nan et al., 2011; Li &
Pan, 2016). PSR J1022$+$1001 has a pulse period of 16.45 ms and a dispersion
measure (DM) of 10.2 $\rm{cm^{-3}}\ pc$. The scintillation bandwidth and time-
scale for this pulsar are 65 MHz and 2334 s respectively at 1400 MHz (Keith et
al., 2013). The pulsar is in a binary system with a 7.8-d orbital period with
a white dwarf companion. The average pulse profile obtained from our FAST
observation is shown in Figure 1. The integrated pulse profile of PSR
J1022+1001 consists of two components in the 20-cm band with a highly linearly
polarized trailing component.

The stability of the integrated profile for PSR J1022+1001 has been studied in
detail. Kramer et al. (1999) showed that the amplitude ratio of the two
components evolves on short time-scales (tens of minutes). Hotan et al.
(2004a) argued that profile instability could also arise from improper
polarization calibration because of an imperfect receiver model. Liu et al.
(2015) showed that improper polarization calibration and diffractive
scintillation cannot be the sole reason for the observed profile instability.
Shao & You (2017) argued that profile instability is mainly caused by the
evolution of the pulse profile with frequency combined with the interstellar
scintillation. Recently with long term observations at Effelsberg Radio
Telescope, Padmanabh et al. (2020) found that the pulse shape variations
cannot be fully accounted for by instrumental and propagation effects and
suggested additional intrinsic effects as the origin for the variation.

Our observations and data processing procedures are described in Section 2.
Our results are presented in Section 3. We conclude and discuss our results in
Section 4.

Figure 1: Averaged polarization profile of PSR J1022$+$1001\. The black, red
and blue lines represent Stokes I, the linear polarization and Stokes V,
respectively. We define the phase ranges identifying the leading and trailing
components using the horizontal and vertical lines (chosen to agree with Liu
et al. 2015 and to be the minimum between the two peaks in the profile). The
on-pulse region is taken to be the range delimited by the leading and trailing
components.

##  2 Observation and Data processing

For our analysis, we selected one of the brightest observations of PSR
J1022$+$1001 from a FAST early science project (PID 3005). We obtained
$7.3\times 10^{4}$ single pulses in a 20 minute observation on MJD 58749. The
observation was conducted using the central beam of the 19-beam receiver
(Jiang et al., 2019). The 19-beam receiver, with the frequency range between
1050 and 1450 MHz, provides two data streams (one for each hand of linear
polarization). The data streams are processed with the Reconfigurable Open
Architecture Computing Hardware–version 2 (ROACH2) signal processor (Jiang et
al., 2019). The output data files are recorded as 8 bit-sampled search mode
PSRFITS (Hotan et al., 2004b) files with 4096 frequency channels and with
49.152 $\mu$s time resolution.

We used the DSPSR software package (van Straten & Bailes, 2011) to extract
individual pulses. The “-K” option of the DSPSR software package was used to
remove inter-channel dispersion delays. Polarization calibration was achieved
by correcting for the differential gain and phase between the receptors
through separate measurements of a noise diode signal injected at an angle of
$45^{\circ}$ from the linear receptors. We determined a rotation measure (RM)
of 2.9$\pm$0.2 rad m-2 from our data and the profiles are RM-corrected. The
observations were then flux density calibrated using observations of 3C 286
(Baars et al., 1977). To excise radio frequency interference (RFI), we used
the PSRCHIVE software package (Hotan et al., 2004b) to median filter each
single pulse in the frequency domain. Band-averaged analytical templates were
made using the profile obtained when an entire observation was folded. We used
the PSRCHIVE and TEMPO2 (Hobbs et al., 2006) software packages to determine
pulse times of arrival (ToAs) and timing residuals for each single pulse using
the timing model from Kerr et al. (2020).

Our calibration procedure produces an integrated pulse profile, shown in
Figure 1, that agrees with previously published profiles (for instance, Dai et
al. 2015).

##  3 Results

We first present our results from analysing the single pulse energy
distributions and our search for correlations between the leading and trailing
profile components. We then search for the presence of giant pulse, nulling or
traditional mode changing phenomena. We study the polarization properties of
the single pulses. Finally, we measure the jitter noise and trial various
methods to improve the timing precision by only selecting a sub-set of the
single pulses.

###  3.1 Single pulse statistics

We define the energy of each single pulse (in non-physical units) to be its
integrated flux density. For each pulse, this is determined by measuring the
area across the on-pulse region (see ranges in Figure 1). We also defined an
off-pulse window that was used as a control sample to assess the statistics of
the noise in our measurements. The off–pulse window was chosen to have the
same width as the on-pulse region. We normalised energy of each pulse by the
mean value in the on-pulse region $\left\langle E\right\rangle$. The results
are shown in Figure 2. The yellow histogram shows the off-pulse energy
distribution and the noise in the off-pulse region follows the expected normal
distribution. The blue histogram shows the on-pulse energy distribution, which
is well fit (see red line in Figure 2) by a log-normal distribution of
$N(E)=\frac{A}{E}\exp(-\frac{(\ln E-\mu)^{2}}{2\sigma^{2}})$ where
$\mu=-0.06\pm 0.01$ and $\sigma=0.51\pm 0.01$ and A is normalization factor.

Figure 2: Pulse energy histograms for the off-pulse region (yellow) and on-
pulse region (blue). The pulse energies are normalised by the mean on-pulse
energy. The red line is a log-normal distribution that has been fitted to the
on-pulse energy histogram.

For each single pulse, we also measured the leading component pulse energy,
$E_{l}$, using the area across the leading component region, as defined using
the dotted horizontal line in Figure 1. Similarly, we measured trailing
component pulse energy (defined by the dashed line in the Figure). Figure 3
shows the correlation between the leading component pulse energy, $E_{l}$, and
the trailing component pulse energy, $E_{t}$. The Pearson product-moment
correlation coefficient of $E_{l}$ and $E_{t}$ is 0.38. The points do not fall
on the $E_{t}=E_{l}$ line. The leading component is much wider in general,
and, as a result, the leading component has more energy than that of the
trailing component in most cases.

Liu et al. (2015) showed that the occurrence of subpulses (individual
components of the single pulses) in the leading and trailing components of the
PSR J1022+1001 profile is correlated. Their work was based on 14000 subpulses
obtained over 35-h, which is only 0.2% of the total number of pulses expected
during that time period. They have therefore only selected the brightest
pulses for their analysis. We note from our correlation that if the leading
component energy is large, then the trailing component energy also tends to be
large. This agrees with the results in Liu et al. (2015), but we note from our
data that the components are only partially correlated.

Figure 3: Correlation of the leading component pulse energy and trailing
component pulse energy. The pulse energies are normalised by the mean on-pulse
energy. The vertical and horizontal red dashed lines represent the $3\,\sigma$
noise levels of the leading and trailing component respectively. The black
dashed line represents $E_{t}=E_{l}$.

###  3.2 Nulling and giant pulses

As shown in Figure 2 the energy distribution can be modelled used a single
log-normal distribution. We would expect the energy distribution of nulling
pulses is similar to that of the off-pulse region (the yellow histogram).
However, we see no evidence of this with our data set. If we define nulling
pulses to have on-pulse energy smaller than three times the standard deviation
of the off-pulse energy, then this gives an upper limit of nulling fraction of
0.06%.

The pulse energy for normal pulses typically follows a log-normal or normal
distribution. In comparison, the pulse energy for giant pulses generally
follows a power-law distribution, e.g. the Crab pulsar (Staelin & Reifenstein,
1968), PSR B1937+21 (Cognard et al., 1996) and PSR B0540$-$69 (Johnston &
Romani, 2003). In our data, the brightest pulse is only approximately four
times the average. We therefore have no evidence that PSR J1022+1001 exhibits
the giant pulse phenomenon.

###  3.3 Moding-changing

Mode-changing behaviour has previously only been seen in one other millisecond
pulsar (PSR B1957+20). The switching cadence between the modes for that pulsar
is $\sim$1000 pulses. This is similar to the mode switching time-scales found
in normal, non-millisecond pulsars (but note these time scales are much
shorter than the pulse variations identified for intermittent pulsars; e.g.
Wang et al. 2020).

To determine whether PSR J1022+1001 shows mode-changing, we averaged different
numbers of individual pulses together to form pulse profiles. We then used the
PSRCHIVE software package to compare the averaged pulse profiles with the
template obtained by summing all the available data. We subtracted each
profile from the phase aligned template and determined the root mean square
(RMS) values of the difference in the on-pulse region and in the off-pulse
region. These RMS values are plotted in Figure 4. We fitted a power law,
$\mathrm{RMS}(N)=AN^{\beta}$ (where $N$ is the number of pulses that have been
averaged), to the on-pulse RMS values and obtained that $\beta=-0.49\pm 0.01$.
There is no indication from this Figure that PSR J1022+1001 undergoes profile
changes on a time scale between $\sim 10$ and $\sim 2000$ pulses.

Figure 4: Root mean square (RMS) values obtained from the difference between
the profile formed for a given number of pulses and a template obtained using
all available pulses. The open circles represent the RMS values obtained in
the on-pulse region. The solid black squares are obtained from the off-pulse
region. The solid black line is the best-fitting model for the on-pulse data.
Figure 5: Single pulses from PSR J1022$+$1001\. The first row shows the
integrated pulse profile. The black, red and blue lines represent Stokes I,
the linear polarization and Stokes V, respectively. The vertical dashed line
separates the leading component and the trailing component. The left column
shows three single pulses which have a brighter trailing component than the
leading component. The middle column shows three single pulses which have a
brighter leading component. The right column shows three single pulses which
have multiple peaks.

###  3.4 Single pulse polarization

The single pulses have a large variety of profile shapes. In Figure 5 we show
polarization profiles for a few, representative, single pulses. The top row
shows three copies of the integrated pulse profile. For the remaining nine
panels, the left column contains three single pulses, which have a brighter
trailing component than the leading component. The middle column shows three
single pulses which have a brighter leading component. The right column shows
three single pulses which have multiple peaks. When the leading component
dominates, the trailing component varies from being almost as bright as the
leading component, to being undetectable. The same is true when the trailing
component dominates. We note that the trailing component is always highly
linearly polarized, however, the leading component has a varying degree of
linear polarization.

In order to determine the degree of correlation between the signal-to-noise
(S/N) ratio for each pulse and its polarization fraction, we defined the
degree of linear polarization as
($\Sigma_{i}\sqrt{Q_{i}^{2}+U_{i}^{2}}$)/($\Sigma_{i}I_{i}$) and that of
circular polarization as ($\Sigma_{i}|V_{i}|$)/($\Sigma_{i}I_{i}$), where
$Q,U,V$ are the Stokes parameters and the summation is over the phase bins in
the on-pulse region. We determined the signal to noise ratio (S/N) as the
integrated power in the pulse profile divided by the noise in the baseline. We
then normalised these S/N values by dividing by the mean S/N value (giving
$\mathrm{S/N}_{n}$). Finally we divided the single pulses in
$\mathrm{S/N}_{n}$ ranges in Table 1. Figure 6 shows the relation between
$\mathrm{S/N}_{n}$ and the degrees of linear and circular polarization. The
degrees of both linear and circular polarization increases with
$\mathrm{S/N}_{n}$. This agrees with similar dependencies observed in two
other MSPs (Osłowski et al. 2014, Liu et al. 2016). We note an apparent
increase in the linear polarization fraction at low S/N. This is also seen in
the results presented by Osłowski et al. (2014) for PSR J0437$-$4715\. Using
Equation (22) in Day et al. (2020), we calculated uncertainties on the linear
polarization fraction to be smaller than 0.3% for all points in the upper
panel of Figure 6, thus this may represent some unexpected property of the low
S/N pulses.

Table 1: $\mathrm{S/N}_{n}$ ranges used for Figure 6. Included range | Number of pulses | Fraction of pulses
---|---|---
$0<\mathrm{S/N}_{n}<0.50$ | 18533 | 0.2539
$0.50<\mathrm{S/N}_{n}<0.66$ | 11428 | 0.1565
$0.66<\mathrm{S/N}_{n}<0.87$ | 10923 | 0.1496
$0.87<\mathrm{S/N}_{n}<1.16$ | 9346 | 0.1280
$1.16<\mathrm{S/N}_{n}<1.53$ | 8705 | 0.1192
$1.53<\mathrm{S/N}_{n}<2.03$ | 7359 | 0.1008
$2.03<\mathrm{S/N}_{n}<2.68$ | 4562 | 0.0625
$2.68<\mathrm{S/N}_{n}<3.54$ | 1759 | 0.0241
$3.54<\mathrm{S/N}_{n}<4.69$ | 352 | 0.0048
$4.69<\mathrm{S/N}_{n}<6.2$ | 33 | 0.0005
Figure 6: Polarization fractions of linear (top) and circular (bottom)
component as a function of S/Nn.

###  3.5 Pulse jitter

PSR J1022$+$1001 is observed by pulsar timing array projects (e.g. Hobbs 2013,
Manchester et al. 2013, Manchester & IPTA 2013, Kramer & Champion 2013), which
have the primary goal of detecting ultra-low-frequency gravitational waves.
The sensitivity of such an array depends upon the scatter in the timing
residuals.

On short time-scales the timing residuals are primarily dominated by
radiometer noise (a reasonable representation is given by the ToA
uncertainties) and pulse jitter (e.g. Osłowski et al. 2011, Liu et al. 2012,
Shannon & Cordes 2012, Liu et al. 2015, Shannon et al. 2014, Lam et al. 2016).
Following Shannon et al. (2014), we define the jitter noise level obtained
after $N$ pulses have been averaged together, $\sigma_{\rm J}(N)$, to be the
quadrature difference between the root mean square (RMS) of the timing
residuals and the radiometer noise

$\displaystyle\sigma^{2}_{\rm J}(N)=\sigma_{\rm obs}^{2}(N)-\sigma_{\rm
radiometer}^{2}(N).$ (1)

This assumes that all of the excess error in the arrival time measurements can
be attributed to jitter noise. We used simulated data sets to obtain the
radiometer noise. In these simulated data sets, we formed pulse profiles from
the template obtained by summing all the available pulses and white noise such
that the S/N of the simulated profile matched the S/N of the observed profile.

In Figure 7, we compare estimates of the jitter noise in PSR J1022$+$1001 from
our FAST observation (open circles) with previous Parkes observations (Shannon
et al., 2014), and from Westerbork Synthesis Radio Telescope and Effelsberg
100-m Radio Telescope observations (Liu et al., 2015). We fit a power law,
$\sigma{{}_{\rm J}}(N)=AN^{\beta}$ to the jitter noise measured from our
observations and obtain $\beta=-0.57\pm 0.01$. The jitter noise level when
scaled to one hour is $67\pm 9$ ns. This value is significantly smaller than
the value of $290\pm 15$ ns reported in Shannon et al. (2014) (see black
circles in Figure 7), but is consistent with Liu et al. (2015), which reported
that a jitter noise level of 700 ns based on continuous 1-min integrations
(red square in Figure 7). The discrepancy between our results and Shannon et
al. (2014) may be caused by profile shape variations on hour-long time scales
(which the Shannon et al. 2014 analysis probes). Such variations could be
caused by the evolution of the pulse profile with frequency combined with the
interstellar scintillation (Shao & You, 2017).

Figure 7: Estimates of jitter noise in PSR J1022$+$1001 from the FAST
observation. Open circles are obtained with FAST using all single pulses.
Solid black data points are the results in Shannon et al. (2014). The red
square is the result from Liu et al. (2015). The solid black line is the best-
fitting model for the jitter noise measured with FAST.

###  3.6 Single pulse timing

Figure 8: Left and right panels show the first 1000 timing residuals using
different templates. We used the standard template in the left-hand panel. In
the right-hand panel we used a template obtained from the summation of the
profiles that formed the most negative timing residuals in the left-hand
panel.

In the left-hand panel of Figure 8 we show the timing residuals obtained using
our standard template for this pulsar. This provides the indication of three
differing states. However, the timing residuals change with different
templates. In the right-hand panel we used a template obtained from the
summation of the profiles that formed the most negative timing residuals in
the left-hand panel. We note that the number of residuals in each state (and
the residual level of the states) varies between the two panels.

Osłowski et al. (2014) and Liu et al. (2016) trialled methods to improve the
timing residuals by selecting pulses based on their S/N (for PSRs J0437$-$4715
and J1713$+$0747 respectively). Following these studies, we divided our single
pulses into the following $\mathrm{S/N}_{n}$ ranges: $\mathrm{S/N}_{n}<0.9$,
$0.9<\mathrm{S/N}_{n}<2.0$ and $\mathrm{S/N}_{n}>2.0$. We obtained a template
by summing the single pulses from each $\mathrm{S/N}_{n}$ range, formed
arrival times for the pulse and then timing residuals. The RMS timing residual
is shown in Figure 9 as a function of integration time. The RMS residual
values are higher for all of the $\mathrm{S/N}_{n}$ selections compared with
simply using all of the available pulses. Although Osłowski et al. (2014)
reported marginally reduction of RMS residual by rejecting $\sim 1\%$ of
largest S/N single pulses, PSRs J0437$-$4715 in Osłowski et al. (2014) and
J1713$+$0747 in Liu et al. (2016) agree with our results.

As PSR J1022$+$1001 is a multi-component pulsar and the two components have,
on average, comparable average energies, we also divided the single pulses
according to the energy of the leading component and the trailing component:
the single pulses which have larger leading component energy constitute the
first class and the remainder constitute the second class. We followed the
process above to form new templates from these samples and produced timing
residuals. The RMS timing residuals as a function of integration time are
shown in Figure 10. Again, we identify no improvement in the RMS residuals
through this selection. The single pulses which have larger leading component
energy consist of 91% of all pulses, so the resulting RMS timing residuals are
close to that of all pulses.

Figure 9: RMS timing residuals as a function of integration time obtained
using all available pulses (open circles) and sub-sets determined from the
specific $\mathrm{S/N}_{n}$ ranges (red, blue and yellow symbols). The solid
black line is the best-fitting model for the RMS timing residual versus
integration time determined using all the available pulses.  Figure 10: RMS
timing residuals as a function of integration time obtained using all pulses
(open circles) and sub-sets obtained from the pulses in which the leading
component is larger than the trailing component (red square) and vice versa
(yellow triangle). The solid black line is the best-fitting model to the open
circles.

##  4 Conclusions

We have reported on the detection and analysis of $\sim 10^{5}$ single pulses
from PSR J1022+1001. This is only possible with the high sensitivity available
using FAST. There is no indication that PSR J1022+1001 exhibits giant pulse,
nulling or traditional mode changing phenomena. The energy in the leading and
trailing components of the integrated profile is shown to be correlated. The
degree of both linear and circular polarization increases with the pulse flux
density for individual pulses.

Jitter noise is a limiting source of noise at FAST and we have determined that
the jitter noise for this pulsar, scaled to one hour, is 67 ns. Selecting
single pulses in different $\mathrm{S/N}_{n}$ ranges, or according to relative
energy of the leading and trailing components, does not improve the timing
precision achievable for PSR J1022$+$1001.

FAST provides us with the opportunity to study single pulses from millisecond
pulsars in more detail than previously possible with the previous generation
of radio telescopes. In the near future, FAST will be able to provide a
catalogue of single pulses from millisecond pulsars in the Northern Hemisphere
and MeerKAT (and, in the near future, the Square Kilometre Array) will carry
out similar work in the Southern Hemisphere. A detailed study of such single
pulses may provide the opportunity to improve the sensitivity of pulsar timing
array observations and for other key pulsar-related research, such as pulsar
emission physics and testing theories of gravity.

We would like to thank R. M. Shannon, R. N. Manchester, M. Bailes, W. van
Straten and W. A. Coles for valuable discussions. We also thank the anonymous
referee for providing constructive suggestions to improve the article. This
work is supported by National Key R$\&$D Program of China No. 2017YFA0402600,
by the CAS International Partnership Program No.114- A11KYSB20160008, by the
CAS Strategic Priority Research Program No. XDB23000000, and by NSFC grant No.
11725313 and 11690024. YF is supported by China Scholarship Council. This work
made use of the data from FAST (Five-hundred-meter Aperture Spherical radio
Telescope). FAST is a Chinese national mega-science facility, operated by
National Astronomical Observatories, Chinese Academy of Sciences.

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