With the largest dish Five-hundred-meter Aperture Spherical radio Telescope (FAST),both the mean and single pulses of PSR B2016$+$28, especially including the single-pulse structure, are investigated in detail in this study. The mean pulse profiles at different frequencies can be well fitted in a conal model, and the peak separation of intensity-dependent pulse profiles increases with intensity. The integrated pulses are obviously frequency dependent(pulse width decreases by $\sim$20$%$ as frequency increases from 300 to 750 MHz),but the structure of single pulses changes slightly (the corresponding correlation scale decreases by only $\sim$$1%$).This disparity between mean and single pulses provides independent evidence for the existence of the RS-type vacuum inner gap,indicating a strong bond between particles on the pulsar surface. Diffused drifting sub-pulses are analyzed. The results show that the modulation period along pulse series ($P_3$) is positively correlated to the separation between two adjacent sub-pulses ($P_2$). This correlation may hint a rough surface on the pulsar,eventually resulting in the irregular drift of sparks. All the observational results may have significant implicationsin the dynamics of pulsar magnetosphere and are discussed extensively in this paper.
This work was supported by the National Key R&D Program of China (Grant Nos. 2018YFA0404703, and 2017YFA0402602), the National Natural Science Foundation of China (Grant Nos. 11673002, and 11225314), the Open Project Program of the Key Laboratory of FAST, National Astronomical Observatories, Chinese Academy of Sciences, and the project of Chinese Academy of Sciences (CAS) and the Max-Planck-Society (MPS) collaboration. This work made use of the data from the FAST telescope (Five-hundred-meter Aperture Spherical radio Telescope). FAST is a Chinese national mega-science facility, built and operated by the National Astronomical Observatories, Chinese Academy of Sciences. The FAST FELLOWSHIP was supported by the Special Funding for Advanced Users, budgeted and administrated by Center for Astronomical Mega-Science, Chinese Academy of Sciences (CAMS). YouLing Yue was supported by the National Key RrmD Program of China (Grant No. 2017YFA0402600), and Chinese Academy of Sciences “Light of West China” Program.
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Figure 1
(Color online) The narrow band profiles are fitted with two peaks model (a) and a conal beam function (b). The black curves are the observed pulse profiles (had been normalized) and the red curves are the fitting curves. The blue vertical line is 10 times of the rms (root-mean-square) of fitting residuals. Obviously, the conal beam function gets better fitting results.
Figure 2
Best-fitting parameters of the conal beam model vs. frequency. From top to bottom, the parameters are the conal radius ($\theta_{\mu0}$), the cone wall thickness ($\sigma$), and the conal asymmetry ($k$).
Figure 3
(Color online) Evolution of the conal beam center position. The ordinate is the time delay of conal beam center relative to that at 285 MHz. The evolution is fitted by a correction of DM, and it is shown by the black curve.
Figure 4
(Color online) The statistics of single pulse SNR, and narrow bands with different frequencies are marked with different colors.
Figure 5
(Color online) The mean cross-correlation coefficients of successive pulses are shown as blue dots, and they seems being composed of 3 components. It is tried to fit the coefficients with 3 square hyperbolic secant peaks, and the fitting result is plotted as red curve. The 3 green dashed curves are the 3 peaks, respectively, and the red dashed curve shows the fitting residuals. The centric position $D_i$ and width $\sigma_i$ of 3 peaks are also marked.
Figure 6
(Color online) Part of single pulses are shown in (a), and the drifting sub-pulses are marked as red solid lines. The red dashed lines are fake drift tracks (both solid lines and dash lines corresponds to the red points in (b)). The flux variation at different drift rates is shown in (b), and each maximum point (red point) corresponds to a sub-pulse track.
Figure 7
The drift rates of the extracted 622 sub-pulse tracks variation versus time (a) and the variation spectra of the drifting rate (b).
Figure 8
(Color online) The statistics of the extracted 622 drift rates. The red dashed line marks the division point of the slower and faster drift sub-pulses for Figure
Figure 9
(Color online) The profiles of slower (red curves) and faster (blue curves) drift sub-pulses, and the division point is shown in Figure
Figure 10
(Color online) The total modulation spectra (a) and the flux modulation at different drift rates (b). The red points mark the maximum points along drift rate at different modulation frequency, and the black curve is the fitting result.
Figure 11
The unfolded fluctuation spectra of time-domain data of pulses.
Figure 12
(Color online) The intensity distribution with different $P_3$ (a) and the folded fluctuation spectra of time-domain data of pulses (b). In (b), three distinct areas are marked. In Area 1, the maximum points along vertical axis are marked as blue points and error bars, and the fitting curve is also plotted.
Figure 13
(Color online) The best-fitting parameters $k_h$ and $b_h$ of eq. (
Figure 14
(Color online) The red points in Figure
Figure 15
The ratio of the intensity in Area 1 and Area 2 at different frequencies.
Figure 16
(Color online) The corresponding phase difference $\phi_2-\phi_1$ between adjacent narrow bands at different phase $\phi_1$ is shown in (a). The obviously down trending of each curve shows the shrinking of the single pulse structure. The maximum linearly dependent coefficient at different phase is shown in (b).
Figure 17
(Color online) The evolution of single pulse structure width (black markers) and mean pulse width (FWHM is denoted by blue markers and distance between components in two peaks fitting is denoted by red markers) with frequency is shown. (a) The magnified view of the part between two green dashed lines in (b).
Figure 18
(Color online) The radiation altitude of every magnetic field line which passes polar cap region, and $\theta$ and $\phi$ are the zenith angle and position angle relative to magnetic axis. The black (red) curve denotes the intersection curve of pulsar surface and the last opening field lines (critical field lines).
Figure 19
(Color online) As Figure
Figure 20
(Color online) The simulated single pulse train with a same profile of PSR B2016+28 at 300 MHz (a), and the cross-correlation results (b) similar to Figure
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