Resonant cyclotron scattering (RCS) in pulsar magnetospheres is considered. The photon diffusion equation (Kompaneets equation) for RCS is derived. The photon system is modeled three dimensionally. Numerical calcu...Resonant cyclotron scattering (RCS) in pulsar magnetospheres is considered. The photon diffusion equation (Kompaneets equation) for RCS is derived. The photon system is modeled three dimensionally. Numerical calculations show that there exist not only up scattering but also down scattering of RCS, depending on the parameter space. RCS's possible applications to spectral energy distributions of magnetar candidates and radio quiet isolated neutron stars (INSs) are pointed out. The optical/UV excess of INSs may be caused by the down scattering of RCS. The calculations for RX J1856.5-3754 and RX J0720.4-3125 are presented and compared with their observational data. In our model, the INSs are proposed to be normal neutron stars, although the quark star hypothesis is still possible. The low pulsation amplitude of INSs is a natural consequence in the RCS model.展开更多
Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibr...Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field (10^8 G) could have a lower temper- ature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature, except millisecond pulsar J0437-4715.展开更多
We revisit the problem of radiative transitions of electrons in the presence of a strong magnetic field. We derive fully relativistic cyclotron transition rates for an arbitrary magnetic field, for any orientation of ...We revisit the problem of radiative transitions of electrons in the presence of a strong magnetic field. We derive fully relativistic cyclotron transition rates for an arbitrary magnetic field, for any orientation of electron spin and for any polarization of the emitted radiation. Also, we obtain the transition rates for any value of the initial electron's parallel momentum. For very strong magnetic fields, transitions to the ground state predominate. Transition rates summed over the electron's spin orientation and for unpolarized radiation are also obtained, which confirm previous results by Latal. Transition widths are calculated for different electron spin orientations and different polarizations of radiation. We obtain general expressions for transition rates that reduce to the results for the non-relativistic case and for unpolarized radiation. Additionally we get, for the non-relativistic approximation, the transition rates for any polarization of radiation. As an application, the first five emission lines are evaluated and compared to the X-ray emitting neutron star V0332+53, which has multiple observable cyclotron lines, taking into account gravitational redshift. The most probable polarization is ε(2).展开更多
With a growing sample of fast radio bursts(FRBs),we investigate the energy budget of different power sources within the framework of magnetar starquake triggering mechanism.During a starquake,the energy can be release...With a growing sample of fast radio bursts(FRBs),we investigate the energy budget of different power sources within the framework of magnetar starquake triggering mechanism.During a starquake,the energy can be released in any form through strain,magnetic,rotational,and gravitational energies.The strain energy can be converted from three other kinds of energy during starquakes.The following findings are revealed:(1)The crust can store free magnetic energy of~10^(46)erg by existing toroidal fields,sustaining 10^(6)bursts with frequent starquakes occurring due to crustal instability.(2)The strain energy develops as a rigid object spins down,which can be released during a global starquake accompanied by a glitch.However,it takes a long time to accumulate enough strain energy via spindown.(3)The rotational energy of a magnetar with P■0.1 s can match the energy and luminosity budget of FRBs.(4)The budget of the total gravitational energy is high,but the mechanism and efficiency of converting this energy to radiation deserve further exploration.展开更多
We investigate the population and several properties of radio pulsars whose emission does not null(non-nulling)through simulation of a large pulsar sample.Emission from a pulsar is identified as non-nulling if(i)the e...We investigate the population and several properties of radio pulsars whose emission does not null(non-nulling)through simulation of a large pulsar sample.Emission from a pulsar is identified as non-nulling if(i)the emission does not cease across the whole pulse profile,and(ii)the emission is detectable.For(i),we adopt a model for switching in the plasma charge density,and emission persists if the charge density is non-zero.For(ii),we assume that detectable emission originates from source points where it is emitted tangentially to the magnetic field-line and parallel to the line-of-sight.We find that pulsars exhibiting non-nulling emission possess obliquity angles with an average of 42°.5,and almost half the samples maintain a duty cycle between 0.05 and 0.2.Furthermore,the pulsar population is not fixed but dependent on the obliquity angle,with the population peaking at 20°.In addition,three evolutionary phases are identified in the pulsar population as the obliquity angle evolves,with the majority of samples having an obliquity angle between 20°and 65°.Our results also suggest that emission from a pulsar may evolve between nulling and non-nulling during its lifetime.展开更多
A new mechanism of radiation emission in the polar gap of a pulsar is proposed. It is the curvature radiation emitted by positrons moving towards the surface of the neutron star along inclined magnetic field and refle...A new mechanism of radiation emission in the polar gap of a pulsar is proposed. It is the curvature radiation emitted by positrons moving towards the surface of the neutron star along inclined magnetic field and reflected from the surface. Such radiation interferes with transition radiation emitted from the neutron star when positrons hit the surface. Proposed mechanism explains the mystery of the interpulse shift in the Crab pulsar at high frequencies discovered by Moffett and Hankins twenty years ago. We have found also reflected energy flux and spectrum, discussed coherence and disappearance of interpulse shift with increase of frequency.展开更多
We suggest a short-lived supermassive magnetar model to account for the X-ray flares following short γ-ray bursts. In this model the central engine of the short γ-ray bursts is a supermassive millisecond magnetar, f...We suggest a short-lived supermassive magnetar model to account for the X-ray flares following short γ-ray bursts. In this model the central engine of the short γ-ray bursts is a supermassive millisecond magnetar, formed in coalescence of double neutron stars. The X-ray flares are powered by the dipole radiation of the magnetar. When the magnetar has lost a significant part of its angular momentum, it collapses to a black hole and the X-ray flares cease abruptly.展开更多
Fast radio bursts (FRBs) are puzzling, millisecond, energetic radio transients with no discernible source; observations show no counterparts in other frequency bands. The birth of a quark star from a parent neutron ...Fast radio bursts (FRBs) are puzzling, millisecond, energetic radio transients with no discernible source; observations show no counterparts in other frequency bands. The birth of a quark star from a parent neutron star experiencing a quark nova - previously thought undetectable when born in isolation - provides a natural explanation for the emission characteristics of FRBs. The generation of unstable r-process elements in the quark nova ejecta provides millisecond exponential injection of electrons into the surrounding strong magnetic field at the parent neutron star's light cylinder via β-decay. This radio synchrotron emission has a total duration of hundreds of milliseconds and matches the observed spectrum while reducing the inferred dispersion measure by approximately 200 cm-3 pc. The model allows indirect measurement of neutron star magnetic fields and periods in addition to providing astronomical measurements of β-decay chains of unstable neutron rich nuclei. Using this model, we can calculate expected FRB average energies (- 1041 erg) and spectral shapes, and provide a theoretical framework for determining distances.展开更多
Observations on relativistic jets in radio galaxies, active galactic nuclei, and 'microquasars' revealed that many of these outflows are cylindrical, not conical. So it is worthwhile to investigate the evoluti...Observations on relativistic jets in radio galaxies, active galactic nuclei, and 'microquasars' revealed that many of these outflows are cylindrical, not conical. So it is worthwhile to investigate the evolution of cylindrical jets in gamma-ray bursts. We discuss afterglows from cylindrical jets in a wind environment. Numerical results as well as analytic solutions in some special cases are presented. Our light curves are steeper compared to those in the homogeneous interstellar medium case, carefully considered by Cheng, Huang & Lu. We conclude that some afterglows, used to be interpreted as isotropic fireballs in a wind environment, can be fitted as well by cylindrical jets interacting with a wind.展开更多
Recent INTEGRAL/IBIS hard X-ray surveys have detected about 10 young pulsars. We show hard X-ray properties of these 10 young pulsars, which have a luminosity of 10^33 - 10^37 erg s^-1 and a photon index of 1.6-2.1 in...Recent INTEGRAL/IBIS hard X-ray surveys have detected about 10 young pulsars. We show hard X-ray properties of these 10 young pulsars, which have a luminosity of 10^33 - 10^37 erg s^-1 and a photon index of 1.6-2.1 in the energy range of 20-100 keV. The correlation between X-ray luminosity and spin-down power of Lx ∝ Lsd^1.31 suggests that the hard X-ray emission in rotation-powered pulsars is dominated by the pulsar wind nebula (PWN) component. Assuming spectral properties are similar in 20-100keV and 2-10 keV for both the pulsar and PWN components, the hard X-ray luminosity and flux of 39 known young X-ray pulsars and 8 millisecond pulsars are obtained, and a correlation of Lx ∝ Lsd^1.5 is derived. About 20 known young X-ray pulsars and 1 millisecond pulsars could be detected with future INTEGRAL and HXMT surveys. We also carry out Monte Carlo simulations of hard X-ray pulsars in the Galaxy and the Gould Belt, assuming values for the pulsar birth rate, initial position, proper motion velocity, period, and magnetic field distribution and evolution based on observational statistics and the Lx - Lsd reltions:Lx ∝Lsd^1.31 and Lx∝Lsd^1.5 More than 40 young pulsars (mostly in the Galactic plane) could be detected after ten years of INTEGRAL surveys and the launch of HXMT. So, the young pulsars would be a significant part of the hard X-ray source population in the sky, and will contribute to unidentified hard X-ray sources in present and future hard X-ray surveys by INTEGRAL and HXMT.展开更多
If the binding energy of the pulsar's surface is not so high (the case of a neutron star), both negative and positive charges will flow out freely from the surface of the star. An annular free flow model for 7-ray ...If the binding energy of the pulsar's surface is not so high (the case of a neutron star), both negative and positive charges will flow out freely from the surface of the star. An annular free flow model for 7-ray emission of pulsars is suggested. It is emphasized that: (1) Two kinds of acceleration regions (annular and core) need to be taken into account. The annular acceleration region is defined by the magnetic field lines that cross the null charge surface within the light cylinder. (2) If the potential drop in the annular region of a pulsar is high enough (normally the case for young pulsars), charges in both the annular and the core regions could be accelerated and produce primary gamma-rays. Secondary pairs are generated in both regions and stream outwards to power the broadband radiations. (3) The potential drop grows more rapidly in the annular region than in the core region. The annular acceleration process is a key process for producing the observed wide emission beams. (4) The advantages of both the polar cap and outer gap models are retained in this model. The geometric properties of the 7-ray emission from the annular flow are analogous to that pre-sented in a previous work by Qiao et al., which match the observations well. (5) Since charges with different signs leave the pulsar through the annular and the core regions respectively, the current closure problem can be partially solved.展开更多
Giant pulses(GPs) are extremely bright individual pulses of radio pulsar. In microbursts of Crab pulsar, which is an active GP emitter, zebra-pattern-like spectral structures are observed, which are reminiscent of the...Giant pulses(GPs) are extremely bright individual pulses of radio pulsar. In microbursts of Crab pulsar, which is an active GP emitter, zebra-pattern-like spectral structures are observed, which are reminiscent of the "zebra bands" that are observed in type Ⅳ solar radio flares. However, band spacing linearly increases with the band center frequency of ~5-30 GHz. In this study, we propose that the Crab pulsar GP can originate from the coherent instability of plasma near a light cylinder. Further, the growth of coherent instability can be attributed to the resonance observed between the cyclotron-resonant-excited wave and the background plasma oscillation. The particles can be injected into the closed-field line regions owing to magnetic reconnection near a light cylinder. These particles introduce a large amount of free energy that further causes cyclotron-resonant instability, which grows and amplifies radiative waves at frequencies close to the electron cyclotron harmonics that exhibit zebra-pattern-like spectral band structures. Further, these structures can be modulated by the resonance between the cyclotron-resonant-excited wave and the background plasma oscillation. In this scenario, the band structures of the Crab pulsar can be well fitted by a coherent instability model, where the plasma density of a light cylinder should be ~10^(13-15) cm^(-3), with an estimated gradient of >5.5 × 10~5 cm^(-4). This process may be accompanied by high-energy emissions. Similar phenomena are expected to be detected in other types of GP sources that have magnetic fields of ? 106 G in a light cylinder.展开更多
基金Supported by the National Natural Science Foundation of China
文摘Resonant cyclotron scattering (RCS) in pulsar magnetospheres is considered. The photon diffusion equation (Kompaneets equation) for RCS is derived. The photon system is modeled three dimensionally. Numerical calculations show that there exist not only up scattering but also down scattering of RCS, depending on the parameter space. RCS's possible applications to spectral energy distributions of magnetar candidates and radio quiet isolated neutron stars (INSs) are pointed out. The optical/UV excess of INSs may be caused by the down scattering of RCS. The calculations for RX J1856.5-3754 and RX J0720.4-3125 are presented and compared with their observational data. In our model, the INSs are proposed to be normal neutron stars, although the quark star hypothesis is still possible. The low pulsation amplitude of INSs is a natural consequence in the RCS model.
基金funded by the National Natural Science Foundation of China (NSFC, No. 11347108)the Fundamental Research Funds for the Central Universities (No. 2014QC014)the key program project of the Joint Fund of Astronomy by NSFC and the Chinese Academy of Sciences (No. 11178001)
文摘Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field (10^8 G) could have a lower temper- ature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature, except millisecond pulsar J0437-4715.
基金support from MICIT(Ministry of Science and Technology)support from the Natural Sciences and Engineering Research Council of Canada
文摘We revisit the problem of radiative transitions of electrons in the presence of a strong magnetic field. We derive fully relativistic cyclotron transition rates for an arbitrary magnetic field, for any orientation of electron spin and for any polarization of the emitted radiation. Also, we obtain the transition rates for any value of the initial electron's parallel momentum. For very strong magnetic fields, transitions to the ground state predominate. Transition rates summed over the electron's spin orientation and for unpolarized radiation are also obtained, which confirm previous results by Latal. Transition widths are calculated for different electron spin orientations and different polarizations of radiation. We obtain general expressions for transition rates that reduce to the results for the non-relativistic case and for unpolarized radiation. Additionally we get, for the non-relativistic approximation, the transition rates for any polarization of radiation. As an application, the first five emission lines are evaluated and compared to the X-ray emitting neutron star V0332+53, which has multiple observable cyclotron lines, taking into account gravitational redshift. The most probable polarization is ε(2).
基金supported by the National SKA Program of China(No.2020SKA0120100)the Strategic Priority Research Program of the CAS(No.XDB0550300)+1 种基金support from the National Natural Science Foundation of China(NSFC,Grant Nos.11988101 and 11933004)from the New Cornerstone Science Foundation through the New Cornerstone Investigator Program and the XPLORER PRIZE。
文摘With a growing sample of fast radio bursts(FRBs),we investigate the energy budget of different power sources within the framework of magnetar starquake triggering mechanism.During a starquake,the energy can be released in any form through strain,magnetic,rotational,and gravitational energies.The strain energy can be converted from three other kinds of energy during starquakes.The following findings are revealed:(1)The crust can store free magnetic energy of~10^(46)erg by existing toroidal fields,sustaining 10^(6)bursts with frequent starquakes occurring due to crustal instability.(2)The strain energy develops as a rigid object spins down,which can be released during a global starquake accompanied by a glitch.However,it takes a long time to accumulate enough strain energy via spindown.(3)The rotational energy of a magnetar with P■0.1 s can match the energy and luminosity budget of FRBs.(4)The budget of the total gravitational energy is high,but the mechanism and efficiency of converting this energy to radiation deserve further exploration.
基金supported by the National SKA Program of China No.2020SKA0120200the National Key Program for Science and Technology Research and Development No.2022YFC2205201+2 种基金the National Natural Science Foundation of China(NSFC,grant Nos.12288102,12041303,and 12041304)the Major Science and Technology Program of Xinjiang Uygur Autonomous Region No.2022A03013-2the open program of the Key Laboratory of Xinjiang Uygur Autonomous Region No.2020D04049。
文摘We investigate the population and several properties of radio pulsars whose emission does not null(non-nulling)through simulation of a large pulsar sample.Emission from a pulsar is identified as non-nulling if(i)the emission does not cease across the whole pulse profile,and(ii)the emission is detectable.For(i),we adopt a model for switching in the plasma charge density,and emission persists if the charge density is non-zero.For(ii),we assume that detectable emission originates from source points where it is emitted tangentially to the magnetic field-line and parallel to the line-of-sight.We find that pulsars exhibiting non-nulling emission possess obliquity angles with an average of 42°.5,and almost half the samples maintain a duty cycle between 0.05 and 0.2.Furthermore,the pulsar population is not fixed but dependent on the obliquity angle,with the population peaking at 20°.In addition,three evolutionary phases are identified in the pulsar population as the obliquity angle evolves,with the majority of samples having an obliquity angle between 20°and 65°.Our results also suggest that emission from a pulsar may evolve between nulling and non-nulling during its lifetime.
文摘A new mechanism of radiation emission in the polar gap of a pulsar is proposed. It is the curvature radiation emitted by positrons moving towards the surface of the neutron star along inclined magnetic field and reflected from the surface. Such radiation interferes with transition radiation emitted from the neutron star when positrons hit the surface. Proposed mechanism explains the mystery of the interpulse shift in the Crab pulsar at high frequencies discovered by Moffett and Hankins twenty years ago. We have found also reflected energy flux and spectrum, discussed coherence and disappearance of interpulse shift with increase of frequency.
基金Supported by the National Natural Science Foundation of China.
文摘We suggest a short-lived supermassive magnetar model to account for the X-ray flares following short γ-ray bursts. In this model the central engine of the short γ-ray bursts is a supermassive millisecond magnetar, formed in coalescence of double neutron stars. The X-ray flares are powered by the dipole radiation of the magnetar. When the magnetar has lost a significant part of its angular momentum, it collapses to a black hole and the X-ray flares cease abruptly.
文摘Fast radio bursts (FRBs) are puzzling, millisecond, energetic radio transients with no discernible source; observations show no counterparts in other frequency bands. The birth of a quark star from a parent neutron star experiencing a quark nova - previously thought undetectable when born in isolation - provides a natural explanation for the emission characteristics of FRBs. The generation of unstable r-process elements in the quark nova ejecta provides millisecond exponential injection of electrons into the surrounding strong magnetic field at the parent neutron star's light cylinder via β-decay. This radio synchrotron emission has a total duration of hundreds of milliseconds and matches the observed spectrum while reducing the inferred dispersion measure by approximately 200 cm-3 pc. The model allows indirect measurement of neutron star magnetic fields and periods in addition to providing astronomical measurements of β-decay chains of unstable neutron rich nuclei. Using this model, we can calculate expected FRB average energies (- 1041 erg) and spectral shapes, and provide a theoretical framework for determining distances.
基金Supported by the National Natural Science Foundation of China.
文摘Observations on relativistic jets in radio galaxies, active galactic nuclei, and 'microquasars' revealed that many of these outflows are cylindrical, not conical. So it is worthwhile to investigate the evolution of cylindrical jets in gamma-ray bursts. We discuss afterglows from cylindrical jets in a wind environment. Numerical results as well as analytic solutions in some special cases are presented. Our light curves are steeper compared to those in the homogeneous interstellar medium case, carefully considered by Cheng, Huang & Lu. We conclude that some afterglows, used to be interpreted as isotropic fireballs in a wind environment, can be fitted as well by cylindrical jets interacting with a wind.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10803009 and 10833003)
文摘Recent INTEGRAL/IBIS hard X-ray surveys have detected about 10 young pulsars. We show hard X-ray properties of these 10 young pulsars, which have a luminosity of 10^33 - 10^37 erg s^-1 and a photon index of 1.6-2.1 in the energy range of 20-100 keV. The correlation between X-ray luminosity and spin-down power of Lx ∝ Lsd^1.31 suggests that the hard X-ray emission in rotation-powered pulsars is dominated by the pulsar wind nebula (PWN) component. Assuming spectral properties are similar in 20-100keV and 2-10 keV for both the pulsar and PWN components, the hard X-ray luminosity and flux of 39 known young X-ray pulsars and 8 millisecond pulsars are obtained, and a correlation of Lx ∝ Lsd^1.5 is derived. About 20 known young X-ray pulsars and 1 millisecond pulsars could be detected with future INTEGRAL and HXMT surveys. We also carry out Monte Carlo simulations of hard X-ray pulsars in the Galaxy and the Gould Belt, assuming values for the pulsar birth rate, initial position, proper motion velocity, period, and magnetic field distribution and evolution based on observational statistics and the Lx - Lsd reltions:Lx ∝Lsd^1.31 and Lx∝Lsd^1.5 More than 40 young pulsars (mostly in the Galactic plane) could be detected after ten years of INTEGRAL surveys and the launch of HXMT. So, the young pulsars would be a significant part of the hard X-ray source population in the sky, and will contribute to unidentified hard X-ray sources in present and future hard X-ray surveys by INTEGRAL and HXMT.
基金the National Natural Science Foundation of China.
文摘If the binding energy of the pulsar's surface is not so high (the case of a neutron star), both negative and positive charges will flow out freely from the surface of the star. An annular free flow model for 7-ray emission of pulsars is suggested. It is emphasized that: (1) Two kinds of acceleration regions (annular and core) need to be taken into account. The annular acceleration region is defined by the magnetic field lines that cross the null charge surface within the light cylinder. (2) If the potential drop in the annular region of a pulsar is high enough (normally the case for young pulsars), charges in both the annular and the core regions could be accelerated and produce primary gamma-rays. Secondary pairs are generated in both regions and stream outwards to power the broadband radiations. (3) The potential drop grows more rapidly in the annular region than in the core region. The annular acceleration process is a key process for producing the observed wide emission beams. (4) The advantages of both the polar cap and outer gap models are retained in this model. The geometric properties of the 7-ray emission from the annular flow are analogous to that pre-sented in a previous work by Qiao et al., which match the observations well. (5) Since charges with different signs leave the pulsar through the annular and the core regions respectively, the current closure problem can be partially solved.
基金supported by the China Program of International ST Cooperation 2016YFE 0100300the National Natural Science Foundation of China (Grant Nos. 11473044, 11633004, and 11653003)+10 种基金the Chinese Academy of Sciences (Grant No. QYZDJ-SSW-SLH017)supported by the the National Natural Science Foundation of China (Grant No. 11225314)the Open Project Program of the Key Laboratory of Radio Astronomy, Chinese Academy of Sciencessupported by the National Natural Science Foundation of China (Grant No. U15311243)the National Basic Research Program of China (Grant Nos. 2015CB857101, XDB23010200, 11690024, 11373011)the Max-Planck Partner Groupsupported by the National Key R&D Program of China (Grant No. 2017YFA0402602)the National Natural Science Foundation of China (Grant Nos. 11673002, and U1531243)the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB23010200)supported by the National Natural Science Foundation of China (Grant Nos. 11573039, 11661161015, and 11790301)supported by the Special Funding for Advanced Users, budgeted and administrated by Center for Astronomical Mega-Science, Chinese Academy of Sciences (CAMS)
文摘Giant pulses(GPs) are extremely bright individual pulses of radio pulsar. In microbursts of Crab pulsar, which is an active GP emitter, zebra-pattern-like spectral structures are observed, which are reminiscent of the "zebra bands" that are observed in type Ⅳ solar radio flares. However, band spacing linearly increases with the band center frequency of ~5-30 GHz. In this study, we propose that the Crab pulsar GP can originate from the coherent instability of plasma near a light cylinder. Further, the growth of coherent instability can be attributed to the resonance observed between the cyclotron-resonant-excited wave and the background plasma oscillation. The particles can be injected into the closed-field line regions owing to magnetic reconnection near a light cylinder. These particles introduce a large amount of free energy that further causes cyclotron-resonant instability, which grows and amplifies radiative waves at frequencies close to the electron cyclotron harmonics that exhibit zebra-pattern-like spectral band structures. Further, these structures can be modulated by the resonance between the cyclotron-resonant-excited wave and the background plasma oscillation. In this scenario, the band structures of the Crab pulsar can be well fitted by a coherent instability model, where the plasma density of a light cylinder should be ~10^(13-15) cm^(-3), with an estimated gradient of >5.5 × 10~5 cm^(-4). This process may be accompanied by high-energy emissions. Similar phenomena are expected to be detected in other types of GP sources that have magnetic fields of ? 106 G in a light cylinder.