Spin-down and emission variations for PSR J0742−2822

Pulsars are the most stable rotators in the universe. They slow down gradually because their rotational energy converts into highly energetic particles and electromagnetic radiations. However, for many pulsars, their slow down is usually disturbed by timing noise, which manifests as a continuous irregular fluctuation in the timing residuals. Hobbs et al. (2010) analyzed the timing irregularities for 366 pulsars and found that the spin-down rates are correlated with the amplitude of timing noise. They also noted that the glitch recoveries usually dominate the timing noise in younger pulsars and a quasi-periodic time-correlated structure is seen in the residuals in many older pulsars. Lyne et al. (2010) studied the timing behaviors of 17 pulsars, which have quasi-periodic timing residuals and their spin-down rates switched between two or more states on a time scale from months to years. They demonstrated that the evolution of spin-down rates for six pulsars is correlated with the evolution of pulse profile. Such correlations indicate that the timing noise might be caused by changes in the magnetospheric state.

Although the spin-down rate ($|\dot{\nu }|$, where $\dot{\nu }$ is the pulsar spin frequency first time derivative) switching between two or more different states has been studied in many pulsars (e.g. Lyne et al. 2010; Kerr et al. 2016; Brook et al. 2016), the correlation between the changes of pulsar spin-down and pulse emission was rarely observed. Usually, $|\dot{\nu }|$ changing from a low state (${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{low}}}$) to a high state (${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{high}}}$) can be triggered by pulsar glitch activities. For example, both the spin-down rate change of PSR J2037+3621 and the first spin-down rate increase of PSR J2021+4026 in October 2011 occurred after a pulsar glitch (Kou et al. 2018; Allafort et al. 2013). However, some pulsars experienced a state change without a glitch. For example, the spin-down rate of PSR J2043+2740 changed from ${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{low}}}$ state to ${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{high}}}$ state and remained in the ${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{high}}}$ state over about 1500 days; after this, it recovered to the ${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{low}}}$ state (Lyne et al. 2010). The spin-down rate of PSR J1001−5507 changed from ${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{low}}}$ state to ${\rm{|}}\dot{\nu }{{\rm{|}}}_{{\rm{high}}}$ state over about 800 days and no glitch was detected before this process (Chukwude & Buchner 2012). Similarly, the second spin down rate increase of PSR J2021+4026 occurred in February 2018 (Takata et al. 2020). Therefor, the spin-down change in these pulsars cannot be explained by the standard glitch model. In addition, the spin-down rate variation of these pulsars is related to the variation of pulse emission (Lyne et al. 2010; Chukwude & Buchner 2012; Allafort et al. 2013; Kou et al. 2018).

PSR J0742−2822 (B0740−28) was identified by the Bologna 408 MHz Pulsar Search Project (Bonsignori-Facondi et al. 1973). This is a radio loud γ-ray pulsar with rotation period P₀ = 0.16676 s, rotation energy loss rate $\dot{\text{E}}\unicode{x223C}1.43\times {10}^{35}\,\,{{\rm{ergs}}}^{{\rm{-1}}}$ and characteristic age τ_c ∼ 1.57 × 10⁵ yr. Eight glitches have been detected in this pulsar up to now (see the Jodrell Bank Pulsar Glitch Table ¹ ). Lyne et al. (2010) studied PSR J0742−2822 and found that $|\dot{\nu }|$ and the pulse profile exhibit rapid oscillation. In addition, the spin-down and pulse shape change has a correlation. The Lomb-Scargle and wavelet spectral analyzes show highly periodic features (broader, less well-defined peaks). Keith et al. (2013) found no correlation between the observed pulse shape and spin-down rate for at least 200 days prior to a glitch at MJD 55020, following which the correlation became strong. These observations indicate that changes in emission state may be caused by the interaction between the interior of the neutron star and the magnetosphere of the pulsar.

In this paper, by combining data from Nanshan and Parkes radio telescopes, we obtained the long-term variation of the spin-down rate and the pulse profile of PSR J0742−2822 over 13 years of data span, and investigated the correlation between them. In addition, we also analyzed the variation of the γ-ray flux and pulse profile of this pulsar with Fermi-LAT data.

2.1. Radio Dta

2.2. Fermi-LAT Data

We consider both Nanshan and Parkes data to investigate the long term variation of $\dot{\nu }$ and the full widths of the pulse profile at 50% of the peak pulse amplitude (W₅₀) (see: Fig. 1(a) and (b)). The correlation between W₅₀ and $\dot{\nu }$ is displayed in Figure 1(c). Using the Fermi-LAT data, we also examined the variation of the γ-ray flux and pulse profile of this pulsar (Fig. 1(d)). Details of the results are as follows.

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3.1. Changes in the Spin-down Rate

Panel (a) of Figure 1 features the variation of $\dot{\nu }$, which exhibits a quasi-periodic structure.Using the auto-correlation function (e.g. Perera et al. 2015), we ascertained that the time scale of the quasi-periodic structure of $\dot{\nu }$ is about 170 d. The values of ν and $\dot{\nu }$ for PSR J0742−2822 were obtained by fitting the timing solutions for subsequent partially overlapping sections of data. Each data section contains 150 d and overlapping 130 d.We also can see that the average values of the frequency first derivatives ($\langle \dot{\nu }\rangle$) have a seemingly permanent change and change among four different states. The time range, the corresponding $\langle \dot{\nu }\rangle$ and increment relative to the previous average value, $\Delta \langle \dot{\nu }\rangle$, are expressed in Table 1. From MJD 54000 to 55225, $\dot{\nu }$ has an average value of $\langle \dot{\nu }\rangle \unicode{x223C}{\rm{-6}}.0436(6)\times {10}^{{\rm{-13}}}{{\rm{s}}}^{{\rm{-2}}}$ (state I). After MJD 55225, $\langle \dot{\nu }\rangle$ reduced by about $\Delta \langle \dot{\nu }\rangle \unicode{x223C}{\rm{-0}}.73(9)\times {10}^{{\rm{-15}}}{{\rm{s}}}^{{\rm{-2}}}$ and changed to a new state (state II). This state continues with $\langle \dot{\nu }\rangle \unicode{x223C}-6.0509(9)\times {10}^{-13}{{\rm{s}}}^{{\rm{-2}}}$ until MJD 56380. Since then, $\langle \dot{\nu }\rangle$ increased to another state, and the corresponding $\langle \dot{\nu }\rangle$ and $\Delta \langle \dot{\nu }\rangle$ are ∼ $-6.0343(9)\times {10}^{-13}{{\rm{s}}}^{-2}$ and 1.7(1) × 10⁻¹⁵ s⁻² (state III), respectively. After MJD 57730, $\langle \dot{\nu }\rangle$ decreased gradually to −6.0448(8) × 10⁻¹³ s⁻², the corresponding increment $\Delta \langle \dot{\nu }\rangle \unicode{x223C}{\rm{-1}}.1(1)\times {10}^{{\rm{-15}}}{{\rm{s}}}^{{\rm{-2}}}$ (state IV), which is consistent with the initial level (∼ MJD 54000-55225) within the uncertainty. Two glitches were reported in the literature, which correspond to our data span at MJD 55020 and MJD 56727, respectively. We found that the changing in $\langle \dot{\nu }\rangle$ from state I to II may be caused by the glitch at MJD 55020. No glitch was detected before $\langle \dot{\nu }\rangle$ changed from state III to IV. Furthermore, we did not detect the permanent-like change in $\dot{\nu }$ after the MJD 56727 glitch.

Table 1. The Average Value of the Frequency First Derivative ($\langle \dot{\nu }\rangle$) and its Increment ($\Delta \langle \dot{\nu }\rangle$) in Four States

State number	Rang (MJD)	$\langle \dot{\nu }\rangle$ (10−13 s−2)	$\Delta \langle \dot{\nu }\rangle$ (10−15 s−2)
I	54000–55225	−6.0436(6)	—
II	55225–56380	−6.0509(9)	−0.73(9)
III	56380–57730	−6.0343(9)	1.7(1)
IV	57730–58700	−6.0448(8)	−1.1(1)

Uncertainties in parentheses are in the last quoted digit and represent 1σ, which are obtained from the standard uncertainty propagation.

3.2. Correlation between the Spin-down Rate and Radio Emission

3.3. Long-term Variation of the γ-ray Flux and Profile

We investigated the long-term evolution of γ-ray flux (0.1–300 GeV) for PSR J0742−2822 in Figure 1(d). Each bin is 40 d and the total data span is from 2008 August 1 to 2019 October 1. The horizontal red dashed lines and red dotted lines in panel (d) represent the average values of γ-ray flux and its 3σ uncertainties, which are from the standard uncertainty propagation, respectively. Table 2 expresses the average value of the 0.1-300 GeV flux (F_Flux) and its increment (Δ F_Flux) and the fractional change ($\displaystyle \frac{{\rm{|}}\Delta {{\rm{F}}}_{{\rm{Flux}}}{\rm{|}}}{{{\rm{F}}}_{{\rm{Flux}}}}$ ) in four states. It is obvious that the uncertainties of flux increments are larger than its value. Therefore, we believe that the γ-ray flux of this pulsar does not change significantly when $\langle \dot{\nu }\rangle$ changes.

Table 2. The Average Value of the 0.1–300 GeV Flux and its Increment in Four States of PSR J0742–2822

State number	Range (MJD)	FFlux (ph cm−2 s−1)	Δ FFlux (ph cm−2 s−1)	$\displaystyle \frac{{\rm{|}}\Delta {{\rm{F}}}_{{\rm{Flux}}}{\rm{|}}}{{{\rm{F}}}_{{\rm{Flux}}}}$ *
I	54700–55225	1.9(2)	—	—
II	55225–56380	2.2(2)	0.2(3)	0.1(2)
III	56380–57730	2.2(2)	0.01(23)	0.003(100)
IV	57730–58700	2.1(2)	−0.1(2)	0.04(10)

Uncertainties in parentheses are in the last quoted digit and are 3σ, which are obtained from the standard uncertainty propagation. ^*The fractional flux change is relative to the previous state.

We have obtained the γ-ray pulse profile for the whole data span and each $\langle \dot{\nu }\rangle$ state (see Figs. 2 and 3). The photons were selected within a 1° radius of the pulsar and the photon energy range was from 0.1–300 Gev. The phase of each photon was assigned by the radio timing solution. In order to compare the differences of the profile in each $\langle \dot{\nu }\rangle$ state with the profile of the whole data span, we normalized all pulse profiles. Panels (a')-(d') of Figure 3 show the residuals of the total integral profile after subtracting the profile in each $\langle \dot{\nu }\rangle$ state. Although the γ-ray pulse profile appears to be different in different states, we cannot confirm these changes because of the small number of photons.

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In this paper, we found that the spin-down rate of PSR J0742−2822 oscillates around an average value ($|\langle \dot{\nu }\rangle |\unicode{x223C}6.0436(6)\times {10}^{{\rm{-13}}}{{\rm{s}}}^{{\rm{-2}}}$) over about three years; after MJD 55225, a permanent-like change was detected in $|\langle \dot{\nu }\rangle |$, which changed to a high state (∼ 6.0509(9)× 10⁻¹³ s⁻²), with the corresponding increment being $\Delta \langle \dot{\nu }\rangle /\langle \dot{\nu }\rangle \unicode{x223C}0.12 \%$. Although the time interval between glitch at MJD 55020 and $|\langle \dot{\nu }\rangle |$ change at MJD 55225 is about 205 d, which exceeds the general glitch recovery time scale, we still cannot rule out the possibility that the glitch active at MJD 55020 lead to the increase of spin-down rate. Keith et al. (2013) found that the correlation between the pulse profile parameters and $\dot{\nu }$ was detected in PSR J0742−2822 after a glitch at MJD 55020. No correlation was present for about 200 d before that and they believe that this was triggered by the glitch at MJD 55020. We also detected the change of correlation between $\dot{\nu }$ and W₅₀ during Keith et al. (2013)'s data span. We ascertained that the correlation disappeared after 1400 d, which coincided with the decrease of spin-down rate. This event did not involve a glitch, as a small glitch occurred 350 d later. During MJD 57730–58700, the $|\langle \dot{\nu }\rangle |$ change to a high state (${\rm{|}}\langle \dot{\nu }\rangle {\rm{|}}\unicode{x223C}6.0448(8)\times {10}^{{\rm{-13}}}{{\rm{s}}}^{{\rm{-2}}}$) and the inverse correlation between $\dot{\nu }$ and W₅₀ gradually becomes strong first and then decays, which is independent of a glitch, as no abrupt jump was detected in spin frequency. Therefore, changes in the $|\langle \dot{\nu }\rangle |$ and the correlation could not be only attributed to the glitch events. Generally, glitches are believed to originate from the interior of the neutron star, but emissions are believed to originate from the magnetosphere. The detected glitch-triggered variation of emission provides us an opportunity to study the interaction of rotation and emission, but for PSR J0742–2822 the connection between pulsar rotation and emission is more complex.

The change of $\dot{\nu }$ reflects the change of external braking torque of the pulsar. The permanent-like relative change of $|\langle \dot{\nu }\rangle |$ can be caused by changes in the inclination angle (Link et al. 1992; Link & Epstein 1997). According to the MHD simulation of Spitkovsky (2006), the relationship between the relative change of spin-down rate ($\Delta \langle \dot{\nu }\rangle /\langle \dot{\nu }\rangle$) and the magnetic angle (α) can be expressed as follows

$$\begin{eqnarray}&&\displaystyle \frac{\Delta \langle \dot{\nu }\rangle }{\langle \dot{\nu }\rangle }=\displaystyle \frac{\sin 2\alpha \Delta \alpha }{(1+{\sin }^{2}\alpha )}.\end{eqnarray} \tag{ 1 }$$

The average increase of $|\langle \dot{\nu }\rangle |$ is 0.12% and 0.18% for the state change at MJD 55225 and 57730, respectively. Therefore, for the relative increase of $|\langle \dot{\nu }\rangle |$ at MJD 55225 and 57730, the corresponding increase in the inclination angle is 0.09° and 0.15° respectively (here, we take α = 37°, Yadigaroglu & Romani (1995)). Moreover, the outflowing particle wind and precession possibly caused the permanent-like relative change of $|\langle \dot{\nu }\rangle |$ (e.g Kou & Tong 2015; Kou et al. 2018; Takata et al. 2020).

Generally, the particle acceleration of a pulsar is thought to occur in the open zone, on the magnetic field line above each pole passing through the light cylinder. The γ-ray emission of the pulsar is produced in an acceleration region near the light cylinder (Abdo et al. 2009). The glitch event affects the structure of the magnetosphere around the light cylinder, which may lead to changes in γ-ray emission. The changes in α result in the change of duration of the line of sight's pass through the pulse emission cone, and hence lead to measurable changes in the pulse profile. According to Link & Epstein (1997), the corresponding increment of the total pulse flux is ∼|Δα|/W_half, where W_half is half of the width of the emission cone. When we use the value of W_half = 5° obtained by Yadigaroglu & Romani (1995), the corresponding changes in flux are ∼ 2% and 3% for the $\langle \dot{\nu }\rangle$ state change at MJD 55225 and 57730 respectively. We do not detect a significant change of γ-ray flux and the γ-ray pulse profile of PSR J0742−2822, which may due to its γ-ray flux being relatively weak (∼ 3.2 ± 0.6 × 10⁻⁸ ph cm⁻² s⁻¹).

In this paper, we have:

• Found that $\langle \dot{\nu }\rangle$ of PSR J0742−2822 changes in four different states.
• Investigated the correlation between $\dot{\nu }$ and W₅₀ and ascertained that the correlation changed with time. However, not all the changes of $\langle \dot{\nu }\rangle$ states and correlations can be associated with the glitch activities.
• Obtained long term evolution of γ-ray flux (0.1–300 GeV) of this pulsar using about 11-years of Fermi-LAT Pass 8 (P8R3) data and did not detect a significant change in γ-ray flux.
• We expect long-term regular radio observation of this pulsar in the future, as well as a more sensitive γ-ray telescope to monitor it, to help us better understand the relationship between spin-down and radiation.

We thank Dr. Rushuang Zhao, Jie Liu and members of the XAO Pulsar Group for useful discussions. This work is supported by the National Key Research and Development Program of China (2016YFA0400804, 2017YFA0402602, 2018YFA0404603 and 2018YFA0404703), the Operation, Maintenance and Upgrading Fund for Astronomical Telescopes and Facility Instruments, budgeted from the Ministry of Finance of China (MOF) and administered by the Chinese Academy of Sciences (CAS), the National Natural Science Foundation of China (Grant Nos. 11873080, U1831102, U1731238, U1938109, U1838104, 11873040, 11573010, 11661161010, U1631103 and U1838102), the Youth Innovation Promotion Association of Chinese Academy of Sciences, the CAS "Light of West China" Program (Nos. 2018-XBQNXZ-B-023, 2018-XBQNXZ-B-025 and 2016-QNXZ-B-24), the Tianshan Youth Program No. 2018Q039, the Open Project Program of the Key Laboratory of FAST, NAOC, Chinese Academy of Sciences, the China Postdoctoral Science Foundation grant (2019M650847), the 2016 and 2018 Project of Xinjiang Uygur Autonomous Region of China for Flexibly Fetching in Upscale Talents and the Science and Technology Fund of Guizhou Province (Grant Nos. (2016)–4008 and (2017) 5726–37). The Parkes radio telescope is part of the Australia Telescope National Facility which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. This paper includes archived data obtained through the CSIRO Data Access Portal.