[figure]capposition=bottom, floatwidth=0.8 [table]capposition=top

New features of the pulsar B0950+08 radiation
at the frequency of 111 MHz

V. M. Malofeev, I. F. Malov, O. I. Malov, D. A. Teplykh

P.N.Lebedev Physical Institute of the Russian Academy of Sciences,
Leninskii pr. 53, Moscow, 119991, Russia;
<EMAIL_ADDRESS>
Accept 13-Dec-2021

###### Abstract

Results of long time observations of the pulsar B0950+08 are given. These
observations were carried out at the LPA radio telescope at the frequency of
111 MHz from January of 2016 to May of 2019 (450 days). A strong variability
in emission of this pulsar has been detected with changes of signal to noise
ratios hundreds of times. Part of the long-time flux density variability can
be explained by refractive scintillations in the interstellar medium. The
existence of radiation between the interpulse (IP) and main pulse (MP) was
confirmed. It was more powerful than at high frequencies. We detected the
unusual interpulse and precursor (Pr) radiation on August 1, 2017. On the base
of strong 65 interpulses we found the correlations between energies of IP and
Pr and between the phase of IP and the distance Pr-IP. It is shown that the
observed peculiarities of this pulsar can be explained in the frame of the
aligned rotator model. We estimated distances of radiation levels from the
center of the neutron star. The calculated value of the initial period of 0.2
sec means that not all pulsars are born with millisecond periods. The large
age of the pulsar (6.8 millions of years) and the small angle between its
magnetic moment and the rotation axis (less than 20∘) confirm the suggestion
on the pulsar evolution to an alignment.

keywords: pulsars: individual B0950+08

##  1 Introduction

Most of the known 3000-plus radio pulsars (Manchester et al., 2005) are
characterized by an average pulse width of order of several percents of the
period. However, there are pulsars emitting in the wider longitude range. This
is specific particularly for radiation at low frequencies. In this case
emission is generated at large distances from the surface of the neutron star
where the emission cone expands markedly. If the angle between the magnetic
moment and the rotation axis is small then the line of sight can be inside the
emission cone for a long time. We believe that such a case takes place for the
pulsar B0950+08 emitting sometimes during the whole period. For example, such
observations were made at 408 MHZ (Hankins & Cordes, 1981 and Perry & Lyne,
1985) and at 111 MHz (Smirnova, 2012). Some features of this pulsar are
discussed in our paper. In addition to the main pulse (MP) and interpulse
(IP), this pulsar has the bridge and the precursor located between MP and IP
(see, for example, Hankins & Cordes, 1981). They analysed the complex time-
frequency structure both of integrated pulses and of individual ones in this
pulsar. The frequency dependences of the width of MP and IP as well the
distances between IP and MP were presented also. The discussion about the
arising of MP and IP from opposite magnetic poles or from a single magnetic
pole (the aligned rotator) takes place in a number of papers (see, for
example, Perry & Lyne, 1985 and Hankins & Cordes, 1981).

The LPA antenna was upgraded in 2014 and its sensitivity became two times
higher. As the result the time-frequency resolution was improved significantly
and about 60 new pulsars and RRATs were discovered (Tyul’bashev et al., 2016,
Tyul’bashev et al., 2017, Tyul’bashev et al., 2018, Tyul’bashev et al., 2020).
There was the possibility to carry out new observations of the pulsar B0950+08
and detect some interesting features in its radiation. Further we describe the
results of these new observations.

The reminder of the paper is organized as follows. In Section 2 we discuss
some details of our observations. Section 3 contains the results and their
analysis. In Section 4 the interpretation of these results and the discussion
are given. In Section 5 the conclusions are summarized.

##  2 Observations

All observations were carried out using the meridional radio telescope LPA
(Large Phase Array). Its antenna is the phased array composed of 16384
dipoles. The geometric area of this antenna is more than 70 000 $m^{2}$ and
the effective area is ${47000\pm 2500\,m^{2}}$ (Tyul’bashev et al., 2016).
Antenna has 128 space beams with the size of one beam $0.9^{\circ}\times
0.5^{\circ}$. The duration of an observing session is $3.5/cos\,\delta$
minutes, where $\delta$ is the declination. The measurement series lasting
about 10-20 days each were carried out from 2016 to 2019. For the processing
460 channels of the 512 channel digital receiver are used. The single channel
bandwidth is 4.88 kHz, and the time resolution is 1.23 msec, the total
bandwidth is 2.245 MHz. All data is stored in the server. For the processing
the special program has been worked out (Malofeev et al., 2012). We have
rather good RFI (radio frequency interference) situation on our radio
telescope, especially during night time. We have the dynamic spectrum of every
pulsar period and can detected a pulse RFI in the frequency domain and in the
time domain. There are two regular radio stations in our frequency band (2.245
MHz). They occupy 2-3 frequency channels (the band is equaled to 10-15 kHz).
Sometimes we see sporadic pulse RFI which occupy a part of our frequency band
or even the entire band. To clean the data, we removed from the reduction such
frequency channels. Our estimations show, that the fraction of RFI data occupy
no more than 2% of the observation time. Here we present the analysis of
integrated profiles and single pulses for the pulsar B0950+08. The focus is on
the unique event that took place on August 1, 2017.

##  3 Results and analysis

Figure 1: S/N variation of emission during 3.5 years of observations.

Figure 1 shows the dependence of the signal to noise ratio (S/N) in integrated
pulses on the date of observations from January of 2016 to May of 2019 (450
days). In our case, the value S/N is the ratio of the pulse amplitude to sigma
of the noise. To calculate $\sigma$ we used the time interval with minimum
radiation in the integrated profile of pulsar. This interval is shown in Fig.
4b. It is evident that S/N or flux densities of integrated pulses are
extremely variable. Integrated pulses were constructed on the base of 3.2
minutes of observations (764 pulsar periods). These pulses change the
intensities on the time scales from one to five days and show power bursts
when S/N grows up to the values of 2000 in individual pulses. There are also
long quasi-periodic variations of flux densities with scales of several
months.

We detected the unusual changes of the flux densities of this pulsar on August
1, 2017. These changes took place on both millisecond scales inside the period
(Fig. 2) and second-minute scales (Fig. 3) for the observation session
duration of 3.2 min. Most likely these changes are caused by the radiation
mechanism itself, however, some of them are possibly due to scintillations
caused by inhomogeneities of the interstellar plasma.

###  3.1 Influence of interstellar scintillations and polarization

There are two types of interstellar scintillations, namely, diffractive (DISS)
and refractive (RISS) ones. The first ones are characterized by short periods,
the second ones by long times. Shishov et al. (1995) have given the empirical
expressions for estimations of a decorrelation bandwidth ($\Delta\nu_{d}$), a
decorrelation time ($\tau_{d}$) and a scintillation index ($m$) describing
diffractive scintillations. These expressions have been obtained on the base
of the large number of measurements of the parameters mentioned at the number
of frequencies for dozens of pulsars located at different distances or
different dispersion measures, see the references in Shishov et al. (1995). We
will use the following equalities:

$\Delta\nu_{d}(\text{kHz})=8.8\left(\frac{\nu}{\nu_{0}}\right)^{4}\left(\frac{DM}{DM_{0}}\right)^{-1.45}\,\text{for}\,DM\leq
20\,pc\cdot cm^{-3}$ (1)

and

$\tau_{d}(\text{min})=10\left(\frac{\nu}{\nu_{0}}\right)^{1.1}\left(\frac{DM}{DM_{0}}\right)^{-0.4}\text{for}\,DM\leq
30\,pc\cdot cm^{-3},$ (2)

where $\nu_{0}=1$ GHz, $DM_{0}=30\,pc\cdot cm^{-3}$. Using $DM=2.97\,pc\cdot
cm^{-3}$ from Manchester et al. (2005) for the pulsar B0950+08 we have
$\Delta\nu_{d}$ = 38 kHz and $\tau_{d}$ = 2.2 min at the frequency of $\nu$ =
111 MHz. Smirnova (2006) has given $\Delta\nu_{d}$ = 200 kHz and $\tau_{d}>$
3.3 min. Using results of measurements at frequency of 60 MHz (Kuiack et al.,
2020) and the value of $\Delta\nu_{d}=32$ kHz at this frequency we obtain 480
kHz for this quantity at our frequency on the base of equations (1) and (2).
Measurements of Bell et al. (2016) at 154 MHz give $\Delta\nu_{d}$ =4.1 MHz
and $\tau_{d}$ =28.8 min. Then we have $\Delta\nu_{d}$ =350 kHz, $\tau_{d}=21$
min at 111 MHz. Almost the same results are obtained, if we use the
dependences from (Cordes, 1986): $\Delta\nu_{d}=(\nu/\nu_{0})^{4}$,
$\tau_{d}=(\nu/\nu_{0})^{1.2}$. The scintillation index decreases markedly due
to the smoothing of scintillations with the decorrelation bandwidth $\sim$ 38
kHz inside of our receiver bandwidth (2.3 MHz). As was shown by Sutton (1971)
the scintillation index decreases to 0.25 for the ratio of these two bands
equaled to 60. Hence, diffractive scintillations can not explain not only
millisecond and second intensity variations but minute ones as well. Let us
estimate an influence of refractive scintillations. For this process Shishov
et al. (1995) obtained formulas for the scintillation index ($m_{r}$) and the
decorrelation time ($\tau_{r}$) on the base of long time measurements by Gupta
et al. (1993) at the frequency of 74 MHz:

$m_{r}=0.6\left(\frac{\nu}{\nu_{0}}\right)^{1/2}\left(\frac{DM}{DM_{0}}\right)^{-1/3}$
(3)

and

$\tau_{r}(\text{days})=40\left(\frac{\nu}{\nu_{0}}\right)^{-2}\left(\frac{DM}{DM_{0}}\right)^{1.5}$
(4)

Figure 2: Examples of successive individual pulses on August 1, 2017.: changes
of intensity for all components from one pulse to another (A), relative
stability of radiation during several periods (B) and the case when IP
stronger than MP (C). The numbers of individual pulses are shown.

As the result we have $m_{r}=0.42$, $\tau_{r}=101$ days. Let us compare these
values with the results of measurements at fairly close frequencies. Gupta et
al. (1993) have given $m_{r}=0.45$, and $\tau_{r}=3^{d}.4$ at 74 MHz.
Conversion to frequency of 111 MHz using equations (3) and (4) gives
$m_{r}=0.55$ , and $\tau_{r}=1^{d}.5$. Bell et al. (2016) obtained
$\tau_{r}=20^{h}.9$ at 154 MHz. Conversion to 111 MHz leads to
$\tau_{r}=1^{d}.8$. Hence, the estimate of the scintillation index (RISS) from
equation (3) is very close to the corresponding value at 74 MHz. However,
values of $\tau_{r}$, obtained by equation (4) differ by more than 50 times.
This problem has been discussed already by Gupta et al. (1993). They predicted
$\tau_{r}=98^{d}$ using the equations valid for an extended medium model and a
Kolmogorov spectrum without an inner scale (Rickett et al., 1984). This value
differed by 30 times from the measured one $\tau_{r}=3^{d}.2$. The authors
concluded that "It is not clear whether the results for PSR 0950+08 are part
of the same trend for the predicted RISS time scales to overestimate the
observed values, or whether it presents a special case". Thus, we have two
time scales for RISS at 111 MHz. Both scales are seen in our data (Fig.
1).These scales are several days and several months. Perhaps we have deal
indeed with a special case in the direction to this pulsar. Hence, the
observed variations of flux densities in the pulsar B0950+08 at the scales of
order of a few days and months can be explained by RISS.

Analyzing intensity variations we must take into account that the LPA radio
telescope received radiation with a linear polarization. It is known that the
position angle in the pulsar B0950+08 changes smoothly by $180^{\circ}$
between MP and IP (Backer & Rankin, 1980). High degree of polarization is
observed at frequencies lower than 200 MHz For example, it is $67\pm 6\,\%$ at
the frequency of 39 MHz (Suleimanova et al., 1983). The rotation measure of
this pulsar is $4\,\text{rad}\,m^{-2}$ and the period of the intensity
modulation due to the Faraday rotation is 6 MHz at the frequency of 111 MHz
(Shabanova & Shitov, 2004). Since the receiver bandwidth is 2.35 MHz the angle
of rotation is $70^{\circ}$. This leads to the noticeable and different
intensity variations in two components of MP. (Shabanova & Shitov, 2004)
showed that the ratio of flux densities of these components could be up two
times depending on the degree of the linear polarization. Since the position
angle between MP and IP changes approximately by $180^{\circ}$ the ratio of
amplitudes of MP and IP must be unchanged for different observation days.
However, intensities of the bridge and the precursor will change from day to
day. We have analyzed the precursor (Fig. 4), taking into account its high
intensity of $29\%$ comparing to MP (August 1, 2017, Table 1, Fig.4). The
detailed description of errors of each considered component is given in
Section 3.5. We have taken into account here one linear polarization of our
antenna. The small sample of days with strong emission of the bridge does not
allow us to make the detailed analysis of intensity variations of this
feature. It is known that MP in this pulsar contains the orthogonal component
manifested in the position angle (see, for example, Manchester et al., 1980).
This can explain the rear cases when we see IP and Pr but there is no MP
(pulses 179 and 741 in Fig. 2).Sometimes we observe only one component of MP,
as a rule C2. Figure 2 shows such cases.

###  3.2 Integrated profiles

One of the main aims of our work was the detailed analysis of the pulsar
emission for August 1, 2017. Let us compare the integrated profile of this day
with other days. We constructed three groups dividing they by their
intensities. Pulses in the first group have on average $<S/N>$ = 250, for the
second one $<S/N>$ = 590, the third one is characterized by $<S/N>$ = 1100
(Table 1). Further we compare phases of MP and IP, their relative intensities,
distances between MP and IP and their widths by the level 50%.

Figure 3: Relative intensity of radiation during the observation session on
August 1, 2017. The grey blocks (A, B, C) are the pulses shown in Fig. 2.
Figure 4: Integrated profile of the PSR B0950+08 on August 1, 2017 (a) and
outside the main pulse, 85% of the whole period at a scale of 10% of the
amplitude of MP (b). The zero level is marked by the segment between
$114^{\circ}$ and $150^{\circ}$ of the pulse longitude (b).

Figure 4a shows the integrated profile for August 1, 2017 (sum of 764 pulses).
This day was unique among all 450 observation days. The pulsar emitted
practically during all time (see, for example, some successive pulses in Fig.
2). Perry & Lyne (1985) and Hankins & Cordes (1981) gave the integrated
profile of the pulsar B0950+08 at the frequency of 408 MHz and declared that
emission was observed almost during the entire period (83%) and individual
interpulses were occasionally as strong as 60% of the average main pulse. It
follows from Fig. 4b demonstrating 85% of the whole period without the main
pulse and drawn at a scale of 10% of the amplitude of MP that the interpulse
emission (IP and the bridge) is on average at least 2.5% of the MP intensity
and this radiation occupies about 90% of the entire period. Fig. 4 shows
clearly that the IP emission passes smoothly into the bridge and then through
the precursor into MP. The similar effect was noted earlier by Smirnova &
Shabanova (1988) at the frequency of 102.5 MHz, but their estimate was
approximately two times lower (1.3%). Since our estimate has been obtained on
the whole period but not at the specific phase inside it we declare the much
more intense effect. Moreover this estimate exceeds the mean level for all
three groups mentioned earlier (Table 1). As can be seen from this table the
increasing of the MP intensity correlates with the decreasing of the
intensities for Pr and IP. Comparison of intensity on August 1, 2017 with
other days shows that it is several times higher than S/N for the third most
power group.

Table 1: Observed intensities for three groups mentioned. Data | S/N | Intensity of precursor | Relative intensity
---|---|---|---
|  | in relation to | of IP/MP, (%)
|  | the main pulse,(%) |
07.10.2018 | 225 | 3.9 | $<0.5$
04.11.2018 | 297 | 7.0 | 1.0
03.01.2019 | 247 | 10.5 | 2.5
02.03.2019 | 211 | 5.0 | $<0.5$
11.09.2018 | 481 | 2.6 | 2.5
01.12.2018 | 568 | 12.3 | $<0.5$
04.12.2018 | 571 | 5.3 | 2.5
05.04.2019 | 648 | 5.9 | 1.2
05.05.2019 | 688 | 6.3 | 1.2
10.05.2019 | 585 | 2.7 | 2.5
13.07.2017 | 1656 | 9.6 | 0.8
01.08.2017 | 980 | 29.0 | 3.5
05.08.2017 | 1368 | 5.2 | 1.3
06.03.2018 | 984 | 8.2 | 0.8
14.03.2018 | 795 | 3.4 | 1.8
03.07.2018 | 982 | 2.8 | 1.0
07.09.2018 | 1159 | 3.2 | 0.7
13.09.2018 | 1276 | 11.1 | 0.8
12.02.2019 | 948 | 16.8 | $<0.5$
10.03.2019 | 1014 | 7.3 | 2.3

It is worth noting that in the pulsar considered it is difficult to determine
the level where there is no radiation (Hankins & Cordes, 1981). We took for
the zero level an area with minimum radiation intensity. The duration of zero
longitudes is $36^{\circ}$ for all days. The zero level is shown in Fig. 4b.

###  3.3 Individual pulses

Strong jumps in intensity have been observed on August 1, 2017 both in the
separate components of MP and in the interpulse space. Fig. 2 shows series of
individual successive pulses for this day. The central part of the window
contains IP. This feature can be as strong as MP (Fig. 2(B), 389) and even
stronger than MP (Fig. 2(C), 741).

As a rule the structure of pulses and their intensity changes sharply from one
pulse to another (see Fig. 2(A), where four successive pulsar periods are
illustrated). However, sometimes radiation is stable during 3-4 periods (Fig.
2(B)). As for the interpulse emission it changes markedly from one period to
another. In Figure 2 grey blocks show the phase boundaries of the components
relative the integral form (Fig. 4). These are : IP = 175 - 230 deg, Pr = 300
- 323 deg, MP = 324 - 360 deg with the boundary between C1 and C2 at the phase
of 342 deg. All series of pulses are marked by the grey blocks at Figure 3.The
interval of our observations (13.07.2017 - 10.03.19) is inside of the interval
of observations of this pulsar using LOFAR at the frequency of 60 MHz (Kuiack
et al., 2020). They showed that the flux density increased in 2018 comparing
to 2017. The similar effect has been observed at our frequency 111 MHz as well
(see Fig. 1). Moreover, at 60 MHz 275 giant pulses (GPs) have been detected
during 90 hours of observations, that is 3 GPs per hour. Tsai et al. (2015)
have detected 5 GPs during one hour observations at 39 MHz. At our frequency
about 250 strong pulses have been detected by Smirnova (2012) during one hour
observation also. However, it is not clear can we consider these pulses as
GPs. Singal & Vats (2012) declared that about 1 % of pulses at 103 MHz are
GPs. We found no one GP during 20 days (64 minutes) of observations (Table 1).
Such large discrepancy in the rate of GPs at close frequencies can be
explained by the strong day-to-day variation of this rate (Singal & Vats,
2012).

As can be seen from Fig. 2 some individual pulses can give emission during the
whole period of the pulsar. The maximal value of S/N for one of the individual
MP is more than 2000. The mean value of S/N is 980. We carried out the
quantitative analysis of the individual behavior of IP, Pr and MP for each of
20 days given in Table 1.

###  3.4 Main pulse

To find out how the day of August 1, 2017 is unique we construct three groups
of integrated pulses with different values of S/N. They are listed in Table 1.
The first group corresponds to 4 days of observations, the second one to 6
days and the third to 10 days. All 20 days are inside the interval between
July 13, 2017 and May 5, 2019. First of all we counted numbers of individual
pulses in 9 intervals of the signal to noise ratios from S/N $\geq 5$ to S/N
$\geq 1280$, for each next interval S/N is two times higher. Then we analyzed
dependences of these numbers on S/N in integrated pulses for all 9 intervals.
Fig.5 shows the dependences for two intervals. It is obtained that for small
values of S/N (Fig. 5a) the number of pulses decreases with the growth of S/N.
For strong pulses (S/N = 320 - 640) the dependence is opposite. There is not a
correlation for intermediate values of S/N.

Figure 5: Numbers of individual pulses for S/N = 5-10 (a) and S/N = 320-640
(b).The mean S/N ratio is shown at the abscissa (see Table 1). Three groups of
days from Table 1 are shown by different marks: the first group by the
asterisks, the second one by the grey triangles and the third one by the
circles. Figure 6: Distributions of phases for IP, Pr, C1 and C2.

We analyzed differential distributions of pulse numbers for each range of
values of S/N. The maximum of the distribution for the first weak group
corresponds to S/N $\geq 5-10$, and 66% of pulses have amplitude with S/N
$\geq 5$. In the third strong group the maximum of the distribution is located
in the range S/N $\geq 10-40$, and the total fraction of visible pulses is of
order of 90%. Hence, an amplitude of an integrated pulse depends not only on a
number of individual pulses with an amplitude greater than the specified one
but on an intensity of these pulses.

###  3.5 Interpulse, precursor and main pulse

The unique day 01.08.2017 is located in the middle of the strong integrated
pulses (the third group) in Figure 5. However, the maximal value of the IP and
Pr amplitudes were recorded just on 01.08.2017 both in the integrated profile
and in individual pulses. Smirnova (2006) analysed the precursor and MP at the
frequency of 111 MHz and then searched for giant pulses in this pulsar. We
give detailed analysis of IP and its connection with Pr and MP for the first
time. We analyzed 4 components of individual pulses, namely, IP, Pr, C1 and C2
of MP. The following parameters of these components have been investigated:
phases, amplitudes, durations at level 50%, and integrated energies. Besides,
we considered the energy of the previous MP, since Hankins & Cordes (1981)
found the connection of this component with IP. These parameters are listed in
Table 2. Most of our flux density measurements was made using the calibration
discrete sources and the calibration signal, which was recorded synchronously
in the beginning of every period of the pulsar. Such method was used earlier
for the measurements of flux densities for 235 pulsars at 102.5 MHz (Malofeev
et al., 2000). In the present work we tried to investigate the pulsar profile
during entire period without any calibration signal. Therefore, we used new
LPA pulsar flux calibration hardware and software, described in Tyul’bashev et
al. (2016); Tyul’bashev et al. (2020). Daily measurements of the noise flux
densities, using 6 calibration sources were carried out. The calibration
signal was recorded in the form of OFFONOFF. The temperatures of ON and OFF
signals were $2400\,K$ and $\sim 300\,K$, respectively. Sigma of noises was
calculated in the interval with minimum radiation in the pulsar period (Fig.
4b). We obtained $\sigma=1.3\pm 0.2Jy$, with the parameters of observations:
time resolution - 1.23 msec and the total bandwidth - 2.245 MHz. The
processing of data gave S/N for single pulses and we could calculate the
energy of all components. In Table 2 all 65 individual pulses with the signal
to noise ratio more than 4 are collected. The first column contains the pulse
numbers. From the second column to the fifth one we give phases of 4
components. The sixth and seventh ones present the phase differences D with
their errors (in brackets). The eighth column shows for which component value
of D is calculated, when the amplitudes of components C1 and C2 not equal. For
examples, there are pulses 386, 387 (Fig. 2b), where we can see component C2
only. From the ninth column to the twelfth one energies are given. Fig. 6
shows the distributions of phases for all four components. We can note two
features in these distributions. Firstly, three components (Pr, C1 and C2) can
be approximated by gaussians. Secondly, the size of the distribution for IP is
approximately equaled to the total size of the Pr+MP distribution. We search
for connections between IP and other components (Pr, MP, and separately C1 and
C2). More than 20 paired relationships between parameters of different
components (phases, amplitudes, durations, and energies) were analyzed. The
strong inverse correlation between the phase of IP and the difference D of
phases (Pr-IP) has been detected (Fig. 7a).

The correlation coefficient for 62 pairs is K = - 0.92. The probability of the
random distribution in Figure 7a $p<0.0001$. The linear approximation of the
relationship in Figure 7a can be described by the following equation:

$D=(-1.02\pm 0.06)\text{Phase(IP)}+(318\pm 11),$ (5)

There is also the inverse dependence between phases of IP and MP-IP (Fig. 7b).
It shows the high correlation coefficient $K=-0.85$ and the probability of the
random distribution $p<0.0001$. It is very important to know which component
connects with IP. We conclude that this is Pr. Firstly, we can see (Table 1,
Fig. 4) that the intensity of Pr in the integral pulse on 01.08.2017 is much
higher than during other days and is about 29% of MP. Secondly, when IP
appears Pr, as a rule, is observed also (62 cases from 65 ones) (Table 2). In
the same time we see 57 C2 and 32 C1 only. Fig. 2 shows clearly that all 7
pulses have IP and Pr simultaneously , and only 4 MPs in the same time. Third,
there are positive correlations between energies of different components (Fig.
8). For 62 pairs of Pr and IP we obtained:

$\log E(\text{Pr})=(0.48\pm 0.11)\log E(\text{IP})+(1.49\pm 0.24),$ (6)

with the correlation coefficient $K=0.49$ and the probability of the random
distribution $p<0.0001$. For other two relationships we have for 60 pairs of
MP and IP $K=0.17$, $p=0.18$, for 55 pairs of IP and the previous MP $K=0.26$,
$p=0.05$.

We have calculated the similar relationships for 3 other days (11.09.2018,
10.03.2019 and 10.05.2019) with intensities of IP more than 2.3% comparing to
MP (Table 1). The total number of Pr-IP pairs was equal to 23. The mean value
of the correlation coefficient ($<K>=0.44$) is very close to the mentioned
value of $K=0.49$ for 01.08.2017. For 53 IP-subsequent MP pairs $K=0.30$, and
for 52 IP-previous MP pairs $K=0.36$. These values are somewhat higher than
$K=0.26$ for 01.08.2017. It is important to note that obtained values of $K$
(0.26 and 0.36) for IP-previous MP pairs are close to the values from Hankins
& Cordes (1981), where this quantity changes from 0.14 to 0.34 for 3 series
counting 200 pulses.

Figure 7: Relationship between phases of IP and Pr (a); between IP and MP (b).

Let us discuss the problem of energy measurement errors taking into account
the registration of signals by the linearly polarized antenna As follows from
Section 3.1 IP and MP are 150 degrees apart and have the same phase of the
position angle (the difference is equal to 180 deg.). However, paying
attention to the rather wide distributions of phases for different components
of pulses (Fig. 6), we must take into account the corresponding changes of
position angles when estimate errors in values of energy. We have estimated
the mean statistical errors of the measured values of energy. These are for IP
$\varepsilon=\frac{22^{\circ}}{75^{\circ}}\times 70\%=21\%$, for MP
$\varepsilon=\frac{25^{\circ}}{75^{\circ}}\times 70\%=23\%$ . Here 22 deg and
25 deg are the widths of IP and MP distributions, and 75% is the part of the
period where the changes of the position angle are equal to 90 deg. The degree
of the pulsar linear polarization is 70% at our frequency (see Section 3.1).
The situation is not so clear for the IP-Pr pair. If we suggest that the Prs
are on the average 112 deg. apart from IPs (Fig. 6), then the error of the
measured energy in Pr consists of two quantities. The first one is caused by
the phase variations for Pr $\frac{12^{\circ}}{75^{\circ}}\times 70\%=11\%$,
the second by the difference of position angles of these two components
$\frac{112^{\circ}-75^{\circ}}{75^{\circ}}\times 70\%=35\%$. These errors are
independent and their mean is $37\%=(11^{2}+35^{2})^{1/2}$. Also, there are
errors of measurements of energy itself caused by noises. This one is no more
than 15%. Therefore the total errors in energy are 26% for IP and 28% for MP.
The error is equal to 40% for Pr. We don’t know the position angle location
for the IP-Pr pairs during our observations and have taken the mean value of
the error for both components $\frac{26\%+40\%}{2}=33\%$. We present 3
relationships between energies of IP-Pr, IP-MP and IP-previous MP in Fig. 8.
We did not show errors. They greatly burden the presented pictures, but don’t
change the obtained dependences and values of the correlation coefficients.

Figure 8: Relationship between energies of Pr and IP (a); MP and IP (b);
previous MP and IP (c).

We can conclude that there are correlations both between intensities of IP and
Pr and between their phases. This picture reminds the complex relation between
the interpulse and the second component of the main pulse in the pulsar
B1822-09 (Gil et al., 1994) where the correlations between spectra and
durations of these features have been detected.

##  4 Discussion

Hankins & Cordes (1981) have given the following arguments for the assumption
on the pulsar B0950+08 as an aligned rotator. 1) There is emission between MP
and IP. 2) There is the correlation between intensities of MP and IP. 3) The
distance between MP and IP differs from $180^{\circ}$. 4) The position angle
of linear polarization changes smoothly from MP to IP. 5) The microstructures
in MP and IP have the similar time scales: $130\,\mu$sec in MP and
$90\,\mu$sec in IP (Backer et al., 1973). We believe that these arguments
exclude the possibility of a description of observed peculiarities in the
frame of the orthogonal rotator model. Malov & Nikitina (2013) estimated
values of the angle $\beta$ between the magnetic moment and the rotation axis
in the pulsar B0950+08 by several methods and gave the mean value of this
angle $<\beta>=18.9^{\circ}$. For the angle between the rotation axis and the
line of sight they obtained $\zeta=6.7^{\circ}$. For these angles the model
path of the position angle of linear polarization is in a good agreement with
the observed one. Earlier the similar values of these angles have been
obtained by Narayan & Vivekanand (1983), namely $\beta=10^{\circ}$ and
$\zeta=5^{\circ}$. Indirect argument for the aligned rotator in the case of
PSR B0950+08 is its age. Malov & Nikitina (2013) showed that orthogonal
rotators had ages several times less than aligned ones. The investigated
pulsar locates far enough from the Galactic plane, its height is $z=0,18kpc$.
The low radio luminosity of this pulsar ($L=27.41mJy\cdot kpc^{2}$) shows also
that it is the decaying source. Moreover using its transverse velocity
$V=36.55km/sec$ (Manchester et al., 2005) and suggesting that its moving is
isotropic, i.e. $V_{z}=25.84\,km/sec$, we can estimate its kinematic age as
$\tau=z/V_{z}=6.8$ millions of years. This means that it is the old pulsar.
Suggesting that the braking of the pulsar provided with the constant rate
$dP/dt=2.3\cdot 10^{-16}$ (Manchester et al., 2005) and its real age equals to
the kinematic one we can estimate its initial period obtained in the moment of
its birth $P_{0}=P-\tau dP/dt\approx 0.2\,sec$. This means that the pulsar
B0950+08 was born as a long periodic object, and that not all pulsars were
born with millisecond periods. If PSR B0950+08 is a typical object among
pulsars we can conclude that old pulsars have small values of the angle
$\beta$ and, hence, these angles decrease with the age. Such a conclusion was
made earlier by Malov (1990) and by Philippov et al. (2014).

Figure 9: Proposed explaining of the obtained dependences between parameters
of MP and IP at two frequencies in the frame of the single pole model. a)
Relative distribution of spots at the surface of the neutron star, rotation
($\Omega$), magnetic axes ($\mu$) and line of sight at the level where
radiation at the frequency of 1400 MHz is generated are shown. Axes $\Omega$
and $\mu$ are perpendicular to the plane of the Figure. b) MP and IP emission
is generated in the cones connected with some spots. Here it was assumed that
the angle between the magnetic moment and the rotation axis
$\beta=18.9^{\circ}$ and between the line of sight and the rotation axis
$\zeta=6.7^{\circ}$. For the clarity the top cone angular size is shown not in
the same scale.

The possible geometry explaining the peculiarities of observed emission is
shown in Figure 9. We use further values $\beta=18.9^{\circ}$ and
$\zeta=6.7^{\circ}$. Some active areas (spots) can exist in a polar cap of the
pulsar. They are formed as a result of the surface sparking causing the
generation of unsteady electric field (Ruderman & Sutherland, 1975).Their
radiation then spreads through the narrow columns with angular sizes
increasing away from the surface of the neutron star. It is variable due to
changes with time of concentrations and energies of emitting charges. Such a
variability reveals itself in sharp changes of all observed components (MP,
IP, Pr and emission between them). At low frequencies the main pulse consists
of two components, at enough high ones one of them is out of sight. The
angular distance between MP and IP can remain unchanged if the location of the
spots mentioned is not changed.

We suggest here that the generation of emission at the chosen distance from
the center of the neutron star occurs at the local plasma frequency

$\nu_{p}=\left(\frac{2n_{p}e^{2}}{\pi m}\right)^{1/2},$ (7)

where $n_{p}$ is the concentration of the secondary electron-positron plasma.
Let us suggest that during the cascade process of the plasma birth all energy
of the primary beams transferred to new electrons and positrons:

$\gamma_{b}n_{b}mc^{2}=2\gamma_{p}n_{p}mc^{2}$ (8)

Here $\gamma_{b}$ and $\gamma_{p}$ are Lorentz-factors of the primary
particles and the new born electrons, respectively, and

$n_{b}=\frac{B}{Pce}$ (9)

is the concentration of charges in the primary beam (Goldreich & Julian,
1969).

For the dipolar magnetic field we have

$\nu_{p}=2.37\cdot
10^{3}\left(\frac{B\gamma_{b}R_{*}^{3}}{P\gamma_{p}r^{3}}\right)^{1/2}$ (10)

Substitution of $P=0.253$ sec and magnetic field at the magnetic pole, two
times higher than the value of $B=2.44\cdot 10^{11}G$ from the ATNF catalogue
(Manchester et al., 2005) and using values of $\gamma_{b}=10^{7}$ and
$\gamma_{p}=100$ give

$\nu_{p}=10^{12}\left(\frac{R_{*}}{r}\right)^{3/2}$ (11)

We calculated distances where emissions at frequencies 1400 and 111 MHz are
generated: $\left(\dfrac{r}{R_{*}}\right)_{1400}=90$,
$\left(\dfrac{r}{R_{*}}\right)_{111}=489.$

The light cylinder radius $r_{\text{{\tiny{LC}}}}=\dfrac{cP}{2\pi}$ is
$1.2\cdot 10^{9}\,cm=1200\,R_{*}$ for the pulsar B0950+08. The equation of the
last open field lines for the dipole geometry is

$\frac{r}{sin^{2}\theta}=r_{\text{{\tiny{LC}}}}$ (12)

They form the emission cone in the frame of the polar cap model. Equation (12)
determines the angular radii of this cone at the calculated levels:
$\theta_{1400}=15.9^{\circ}$, $\theta_{111}=39.7^{\circ}$. These values have
been used in Figure 9.

Our observations show the noticeable variations of the distance between IP and
MP (Fig. 10).

Figure 10: Distribution of observed distances between IP and MP.

The maximum of the distribution of D = IP-MP is $146.5^{\circ}$, and this
distribution can be well described by the following Gaussian:

$N=24exp\left\\{-\left(\frac{146.5-D}{16.4}\right)^{2}\right\\}$ (13)

Variations of D, the wide distribution of this distance and the mentioned
difference from $180^{\circ}$ are the strong additional arguments in favor of
the alignment of this pulsar. These are mentioned here for the first time. For
an orthogonal rotator D must be very near $180^{\circ}$ with minor deviations
from this value. Variability in aligned objects can be caused by different
intensities of separate parts of corresponding spots and by their movement on
the surface of the neutron star caused by oscillations of the surface and
waves spreading over it. Figure 9 shows how we can reconcile our model with
the observed dependences of features in MP and IP on frequency given by
Hankins & Cordes (1981).

In our model distances between sub-pulses of MP are determined by the
structure of magnetic field lines in spots (Fig. 9a). At high frequencies near
the surface of the neutron star this distance is almost constant. When we move
away from the surface lines of force diverge, the angular radius of the
emission cone increases and the distance between sub-pulses increases also.
This effect explains similarly the width of MP at different frequencies. At a
some distance from the neutron star one of the spots is out of sight and one
of the components becomes invisible. The width of MP changes abruptly at
higher frequencies and is determined by the width of the reminder component.
The distance between IP and MP as is declared earlier is determined by the
almost unchanged distance between the corresponding spots. They are connected
by magnetic field lines (see Fig. 9), and this explains the weak radiation at
longitudes between MP and IP.

##  5 Conclusions

Some results of long-term observations of the pulsar B0950+08 using radio
telescope LPA at the frequency of 111 MHz are given.

A strong variability of the intensity was revealed in radiation of the pulsar
showing the changes of signal to noise ratio hundreds times at different time
scales. This variability is caused mainly by peculiarities of the emission
mechanism. However, long-term fluctuations with the characteristic time of
several days and months can be explained by RISS in the interstellar medium.

The analysis of the integrated profile of MP shows that the amplitude of its
radiation depends on both number of pulses and their intensities. The
existence of radiation between IP and MP has been confirmed. It is more
intense comparing to the higher frequencies. We carried out the detailed
analysis of the unique event on 1.08.2017 showing strong radiation in the
almost entire interpulse space.

We detected the high correlations both between changes of intensities of Pr
and IP and between phases of IP and Pr. New peculiarities of the pulsar
emission such as the correlation between parameters of IP and Pr, the rather
wide distribution of IP phases and distances between IP and MP can be
explained in the frame of the aligned rotator model. The empirical version of
such a model of the pulsar magnetosphere is proposed. We believe that there
are some spots at the surface of the central neutron star in the pulsar
B0950+08. They determine the structure of emission cones at different
frequencies. Particularly, such a model explains qualitatively the complex
picture of emission at low frequencies and gives the possibility to calculate
distances where the observed emission is generated.

We estimated also the initial period of the pulsar acquired at birth
($P_{0}\approx 0.2s$). This means that not all pulsars are born with
millisecond periods. The large age of the pulsar (6.8 millions of years) and
the small angle between the magnetic moment and the rotation axis are the
evidences of the evolution of pulsars to aligned rotators.111When our
manuscript was ready for the submission the preprint by Bilous et al. (astro-
ph HE 2109.08500) appeared. There some similar problems concerning variations
of radiation of the pulsar B0950+08 at other frequencies (55 MHz and 1.4 GHz)
are discussed. The detection of the rather strong feature between MP and IP
described in this preprint is the additional argument for the aligned rotator
model.

## Acknowledgements

The authors thank T.V. Smirnova for the useful discussions and S.V. Logvinenko
for the technical support of observations and data processing.

Table 2: Characteristics of some components of individual pulses. Pulse | Phase (deg) | D (deg) | Component | Energy ($Jy\cdot msec$)
---|---|---|---|---
number | IP | Pr | C1 | C2 | Pr - IP | MP - IP | of MP | IP | Pr | MP | MPprev
85 | 199 | 317 | 343 |  | 118(2) | 144(5) | C1 | 92 | 169 | 130 | 43
93 | 215 |  |  |  |  |  |  |  |  |  |
109 | 191 | 311 |  | 350 | 120(2) | 159(5) | C2 | 184 | 268 | 256 | 180
128 | 198 | 313 | 338 | 352 | 115(6) | 154(6) | C2 | 107 | 152 | 450 | 2454
145 | 206 | 313 | 338 | 360 | 107(4) | 143(4) |  | 79 | 238 | 246 |
146 | 198 | 313 | 338 | 352 | 115(1) | 147(6) |  | 500 | 390 | 2231 | 246
177 | 195 | 317 |  | 350 | 122(2) | 155(5) | C2 | 346 | 346 | 253 | 383
178 | 188 | 305 |  | 359 | 117(4) | 171(6) | C2 | 114 | 823 | 453 | 253
179 | 178 | 318 |  |  | 140(3) |  |  | 113 | 478 | 293 | 453
191 | 191 | 324 |  | 348 | 133(5) | 157(3) | C2 | 117 | 673 | 6593 | 466
211 | 205 | 315 |  | 355 | 110(3) | 150(7) | C2 | 376 | 376 | 167 | 83
214 | 196 | 319 |  | 355 | 123(4) | 159(6) | C2 | 120 | 250 | 496 | 153
224 | 207 | 317 |  | 347 | 110(3) | 140(6) | C2 | 266 | 150 | 929 | 1692
228 | 189 | 319 | 340 | 348 | 130(4) | 159(5) | C2 | 133 | 316 | 2850 | 186
232 | 205 | 321 | 336 | 352 | 116(3) | 139(5) |  | 242 | 827 | 3926 | 1765
248 | 195 | 305 | 336 | 352 | 110(3) | 149(5) |  | 103 | 120 | 509 | 120
250 | 217 | 315 | 340 | 352 | 98(3) | 129(3) |  | 30 | 333 | 260 | 473
271 | 204 | 306 |  | 347 | 102(3) | 143(3) | C2 | 58 | 152 | 87 | 67
273 | 198 | 315 |  | 350 | 117(3) | 152(5) | C2 | 225 | 225 | 1136 | 413
300 | 220 | 313 |  |  | 93(2) |  |  | 170 | 40 |  | 1462
301 | 187 | 318 |  | 354 | 131(3) | 167(4) | C2 | 83 | 92 | 100 |
341 | 200 | 317 | 343 |  | 117(3) | 143(4) | C1 | 47 | 87 | 47 | 17
346 | 193 | 308 |  | 360 | 115(1) | 167(3) | C2 | 85 | 180 | 40 | 73
374 | 208 | 315 |  | 352 | 107(3) | 144(4) | C2 | 133 | 549 | 226 |
379 | 177 | 313 | 334 | 357 | 136(4) | 169(5) |  | 65 | 300 | 719 | 541
386 | 199 | 308 |  | 353 | 109(4) | 154(3) | C2 | 157 | 616 | 133 | 67
387 | 207 | 313 |  | 348 | 106(3) | 141(4) | C2 | 260 | 866 | 450 | 133
388 | 193 | 313 |  | 356 | 120(2) | 163(7) | C2 | 300 | 842 | 120 | 450
389 | 195 | 317 |  | 354 | 122(4) | 159(4) | C2 | 55 | 233 | 117 | 120
391 | 215 | 308 | 343 | 354 | 93(5) | 134(5) |  | 63 | 400 | 563 | 25
392 | 187 | 312 | 333 | 354 | 125(3) | 151(6) |  | 93 | 493 | 799 | 563
394 | 208 | 317 |  | 358 | 109(2) | 150(5) | C2 | 133 | 290 | 260 | 266
408 | 220 | 310 | 331 | 348 | 90(1) | 128(6) | C2 | 45 | 653 | 2045 | 390
416 | 228 | 305 |  | 353 | 77(2) | 125(4) | C2 | 107 | 210 | 80 | 60
428 | 200 | 310 | 340 | 352 | 110(2) | 146(5) |  | 186 | 1865 | 346 | 1941
429 | 222 | 312 | 338 | 354 | 90(3) | 124(5) |  | 2198 | 4928 | 1399 | 3468
430 | 200 | 322 | 336 | 350 | 122(5) | 136(4) |  | 433 | 3040 | 2957 | 1399
431 | 208 | 312 |  | 350 | 104(2) | 142(5) | C2 | 1432 | 1332 | 80 | 2957
432 | 226 | 318 |  | 358 | 92(3) | 132(3) | C2 | 55 | 373 | 653 | 80
438 | 210 | 313 | 338 | 357 | 103(2) | 138(6) |  | 133 | 403 | 706 |
441 | 208 | 315 |  | 361 | 107(2) | 153(4) | C2 | 112 | 216 | 390 | 346
442 | 189 | 311 | 333 | 357 | 122(2) | 152(5) |  | 310 | 350 | 53 | 390
444 | 205 | 308 |  | 352 | 103(2) | 147(3) | C2 | 60 | 646 | 286 | 57

Table 2. (Continued)  Pulse Phase (deg) D (deg) Component Energy ($Jy\cdot
msec$) number IP Pr C1 C2 Pr - IP MP - IP of MP IP Pr MP MPprev 447 201 317
338 352 116(3) 144(5) 160 320 2338 193 457 199 315 359 116(3) 160(4) C2 230
1439 67 140 473 200 322 355 122(2) 155(5) C2 93 230 30 483 184 308 329 355
124(2) 158(4) 93 133 326 453 494 192 320 342 359 128(3) 159(4) 93 226 763 497
198 310 355 112(4) 157(4) C2 120 293 147 120 508 193 322 337 355 129(4) 153(4)
64 85 38 130 533 205 310 334 355 105(3) 140(5) 100 110 70 549 192 308 355
116(3) 163(4) C2 130 882 253 40 579 227 315 336 352 88(2) 117(4) 158 250 504
90 601 190 305 332 115(4) 142(5) C1 117 157 53 1758 621 204 306 339 350 102(3)
141(5) 9 173 370 706 647 213 322 334 354 109(2) 131(2) 117 113 455 460 658 213
320 361 107(1) 148(3) C2 60 117 67 24 667 193 317 341 353 124(2) 154(3) 47 120
653 60 669 203 317 353 114(3) 150(2) C2 45 306 47 1605 674 202 341 350 144(3)
93 1382 554 678 195 313 340 355 118(2) 152(3) 18 140 140 704 206 47 73 705 205
313 339 349 108(2) 139(5) 40 266 546 741 194 324 130(2) 886 117 93 754 187 315
331 354 128(2) 155(3) 80 526 167 67

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