• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    An Estimation of the Geometrical Structure of Polar Cap and Emission Property of Radio Pulsar: A Treatment from an Analytical Approach

    2023-05-29 10:12:42TridibRoy

    Tridib Roy

    1 Indian Institute of Astrophysics, Sarjapur Main Road, Koramangala 2nd Block, Bangalore 560034, India; tridibroy.12@gmail.com

    2 SN Bose National Cenre for Basic Science, Saltlake, Sector 3, JD Block, Kolkata 700106, India

    Abstract Pulsars are believed to be one of the most interesting objects in the universe.The emission mechanism of pulsars is still a conundrum to physicists,as there is no completely acceptable theory that can establish a consensus between theory and observation.Pulsars possess a gigantic magnetic field,to the order of 1012 Gauss, and generate a very powerful radio beam from the magnetic pole.However,the powerful radio beam is generated by some complicated coherent plasma processes and acceleration in the pulsar magnetosphere.The location of the origin of the radio waves has been predicted to come out exclusively from the polar cap zone, whose boundary is defined by the footprint of the last open field line.However, in this paper, we mainly try to generate the shape of the polar cap structure from an analytical solution and discuss how it gets distorted for different geometrical parameters due to the presence of perturbation such as polar cap current flow.Also, apart from that, we try to emphasize understanding the variation of radio emission height and polarization angle with respect to different geometryrelated parameters as well as with frequency.

    Key words: (stars:) pulsars: general – stars: neutron – radiation mechanisms: non-thermal

    1.Introduction

    Pulsars are rapidly rotating neutron stars (NSs), radio transients and highly gravitating compact objects which originate as a stellar remnant during the end phase of the evolution of a massive stellar progenitor.Pulsars are regarded as ubiquitous objects,as they not only generate powerful radio beams but measuring the radio signal from pulsars also helps one to trace the magnetic field in the intervening Galactic medium.The physical appearance of a pulsar is inferred from the observed or physical characteristics of rapidly spinning NSs, possessing a hugely powerful magnetic field to the order of 108–1012Gauss.In each epoch of rotation, radio flashes from pulsars pass our line of sight, and we receive a series of periodic signals, similar to what happens in a lighthouse.

    The main motivation of this paper is to unravel the polar cap(PC) structure and its modification due to the presence of perturbation.Apart from that, I have tried to explore some of the properties associated with polarization angle(PA)and radio emission altitude to get more insights into the topics theoretically.Principal results are discussed in more detail in the subsequent part of this paper.Before that, let us revisit some crucial and very important results done in the field of pulsar astronomy.The pulsar paradigm is quite rich and is regarded as one of the most important discoveries in astrophysics.Although a copious amount of theory has been dedicated to probing the emission physics of radio pulsars,it is still a long-standing debated mystery.Most physicists believe that pulsar radio emission is mainly generated via the coherent curvature radio emission mechanism (CCRM)(see Sturrock 1971; Ruderman & Sutherland 1975; Buschauer& Benford 1976; Wang et al.2012; Roy & Gangadhara 2019;Cooper et al.2021; Gangadhara et al.2021), but some alternative models have convinced researchers to deduce the emission properties of radio pulsars by introducing the inverse Compton scattering(ICS)model in the annular gap regime(see Du & Han 2011; Lv & Wang 2011).In this context some recent critiques regarding plasma processes involved in the pulsar magnetosphere have been summarized by Melrose et al.(2021), where the merits and intricacies of all the possible plasma processes,as present in the pulsar magnetosphere,have been well documented.

    The emission mechanism of a radio pulsar is a broadband and coherent process.The brightness temperature of a radio pulsar corresponds to a huge temperature of 1025K, which infers that the emission mechanism of pulsars is coherent.In this context some recent literatures (see Roy &Gangadhara 2019; Cooper et al.2021; Lyutikov 2021b) have tried to estimate the brightness temperature and derived constraints involved in the bunch topoology by satisfying the coherent condition.The theory of pulsar emission physics associated with the polar gap, sparks and coherent microwave radiation has been well documented in many classical literatures (Sturrock 1971; Ruderman & Sutherland 1975;Melrose 1978).However, the incoherent theory was not sufficient to explain the high brightness temperature of pulsars in the radio band.Soon the need to develop a consistent theory of coherent radio emission for pulsars was realized and Buschauer & Benford (1976), Benford & Buschauer (1977)first gave an elaborate formulation of it.Very recently, some advanced simulation has generated an integrated pulse profile of pulsars based on the theory of an accelerating, coherently emitting extended plasma source and tried to reach brightness temperature as close to the values predicted by observation as possible (Roy & Gangadhara 2019; Gangadhara et al.2021).However, in this paper, I will try to mainly constrain some of the theoretical aspects in the framework of coherent curvature radiation to ponder some thoughts toward generating PC structure under perturbation and attempt to explore some of the emission height and PA related properties.

    A pulsar’s paradigm is quite rich, and in the last 50 yr after its discovery, this field has seen an unprecedented level of success, and its application became diversified into different streams such as gravitational waves,nuclear physics and so on.Most of the literature recognizes pulsars’radio emission mechanism to be a broadband process and coherent as well,as inferred from the very high brightness temperature (≈1025K) in the radio band.However, the emission mechanism is a multi-stage process which is determined by both radio emission geometry and kinematics of electron-positron pair plasma.Several instabilities, such as two-stream instability, probably act in the pulsar magnetosphere to generate Langmuir waves,and, finally, these waves get converted to transverse propagating modes by some complicated propagation effect in the quasi-tangential zone(Asseo&Porzio 2006;Wang et al.2012;Roy 2021).Curvature photons arising from the acceleration of primary charged particles interact with the magnetic field and generate secondary charged particles, which generate strong radio pulses from the PC region of pulsars (Sturrock 1971;Ruderman & Sutherland 1975).Now with the advent of modern astronomy, global 2D kinetic plasma simulation of magnetic reconnection has been performed,to illustrate a more clarified picture of the coherent emission mechanism.Such advanced simulation has shown that beyond the light cylinder and close to the equatorial zone of an NS,current sheets form a plasmoid unstable regime,where current sheets get fragmented and form a dynamic chain of small plasmoids, which eventually interact with each other as well as with the magnetic field and finally a radio nano-shot emits from the magnetosphere(Philippov et al.2019,2020).Such pioneering advanced simulation has definitely had a significant impact on our further understanding about the involved emission mechanism of a pulsar.Apart from it, recently a model by Lyutikov (2021a)and Lyutikov (2021b) has demonstrated promising results based on a nonlinear plasma physics analytical solution,which generates coherent radio emission in the Crab pulsar,magnetars and fast radio bursts (FRBs), produced by a reconnectiongenerated beam of particles via a variant of the free electron laser mechanism, operating in a weakly turbulent, guide fielddominated plasma, with emission frequencies ν that depend mostly on the scale λtof turbulent fluctuations and the Lorentz factor of the reconnection-generated beam,but it is independent of the underlying magnetic field.

    Now very briefly I discuss the polarization of a radio pulsar.A pulsar radio beam, which is generated from the magnetic pole,has a hollow nested conal structure (Rankin 1993).Individual polarization profiles in a pulsar are highly fluctuating and timevarying, with a degree of polarization that varies from 10%–100%.De-dispersion, Faraday rotation correction over different frequency channels and folding of thousands of individual pulses lead to the generation of a stable average pulse profile.However, the polarization profile of different radio pulsars is different; each of them has a unique shape and the polarization profile is definitely diverse in nature.The shape and structure of the integrated polarization profile is a unique signature of each pulsar.In this context,recently Johnston&Karastergiou(2019)did a comprehensive analysis to predict a correlation between pulse width and other frequently measured parameters such as spin period, magnetic field, etc.; such an analysis would really help one to probe pulsar emission physics in more detail.

    Since this work is based on Kumar & Gangadhara (2012a),first I try to highlight some aspects of the works done in the paper and some possible follow ups.Kumar & Gangadhara(2012a) had shown that field aligned induced toroidal current over the PC region perturbs the dipolar field line, and hence influences the emission geometry.This field aligned current introduces asymmetry on the curvature, in the emission zone,which is reflected as an asymmetry in the phase location of trailing and leading components with respect to the meridional point.By analyzing the PC current perturbed dipole, Kumar &Gangadhara(2012a)systematically computed the changes of the coordinates of the colatitude, azimuth and curvature associated with the emission points, with respect to the unperturbed case,and subsequently deduced the integrated pulse profiles,including intensity, linear and circular polarization and PA by summing over the emission region from each field line.PC current flow does not lead to a phase shift at the inflection point(IP)of the PA curve,but it causes a vertical offset in the rotation phase diagram.However, the details of their simulation show that, in the presence of PC current perturbation and modulation, it makes a significant difference on IP, which in turn affects the polarized emission.However in this work, I have tried to deduce the PC structure due to PC induced field aligned current,which was not included in Kumar & Gangadhara (2012a).Except for the PC diagram, almost a complete model of polarization including the full emission geometry of a radio pulsar was developed by them.

    It is quite familiar from existing literature that pulsar radio emission exclusively originates from a zone called the PC,whose boundary is defined by the footprint of the last open field line.Here I have tried to generate the structure of the PC and its modification under plasma current.Also,I have tried to explore the behavior of radio emission altitude and PA related properties briefly based on our analytical formulation.The contents of the paper are arranged in the following sections.In Section 2,the mathematical expression of the PC is given,and next in Section 3 emission altitude is formulated, followed by what I discuss about the property of PA in Section 4, finally ending up with a discussion and conclusion in Section 5.

    2.Generic Property of the Polar Cap of Radio Pulsars: A Treatment to Deduce Polar Cap Formulation

    The work is mainly categorized into three parts: (1) PC formulation,where details on the formulation and PC structure are summarized for both unperturbed and perturbed cases.(2)Radio emission height related calculation,and(3)PA related properties of pulsars, which are described in the subsequent sections.

    In the context of emission of radio pulsars, the PC is regarded as a very important zone.Radio emission of pulsars is a multistage process,and most of the literature claims that it is associated exclusively with the PC region.The combined action of rapidly spinning, superconducting magnetospheric condition, and the very powerful magnetic field of an NS,generates a huge gap potential across the PC, which in turn leads to the extraction of charged particles and generates primary plasma; that primary plasma further undergoes pair multiplicity and generates secondary plasma, whose Lorentz factor lies in the range of 100–1000 (Ruderman &Sutherland 1975;Roy&Gangadhara 2019).The PC boundary is defined by the locus of the last open field line.Here I have tried to give the formulation of the PC and discuss the modification of the PC structure under the presence of PC current, which may be the advanced part of this paper.Rather than tracing the open field line, I have tried to determine the locus from the last closed field line as it could probably give a better estimation.So, the last closed field line would be tangent at the light cylinder surface, which implies thatd=rct- (rct·Ω?)Ω? , where|d|=rLcis the radius of the light cylinder,and Ω? is a unit vector,parallel to the spin axis of the NS.The expression of position vector rctof an arbitrary charged particle on the magnetic field line in the stationary frame of an observer was reported by Gangadhara (2004).By applying the above condition,one can derive the expression of the polar angle associated with the locus of the PC as

    whereA= cos ( 2(α-φ) ) - 2 cos ( 2φ) + cos ( 2(α+φ)), α is the inclination angle of magnetic dipole moment with respect to spin axis and φ is the magnetic azimuth.Now for the range of π/2 ≤φ ≤3π/2, colatitude will be replaced by π ?θsol.

    where rLc=P c/(2π) is the light cylinder radius, P is the spin period of the pulsar and c is the speed of light in a vacuum.As pulsar magnetic field line topology can be roughly approximated as purely dipolar, at least in the radio emission regime,the dipolar field line constant corresponding to the last open field line can be derived by using the dipolar field line equationr=resin2(θ) as follows

    Next, we will try to understand the influence of PC current,which may be a potential source for distorting PC structure.As was first shown by Hibschman&Arons(2001),if there is any longitudinal current flow across the PC, it will add an extra azimuthal component and break the dipolar field line symmetry.Due to the symmetry breaking, field lines get twisted (Kumar & Gangadhara 2012a).In the spherical polar coordinate system (r, θ, φ) centered on the magnetic axis, the unperturbed dipole field is written as

    where μ is the magnetic moment,θ is the colatitude and r is the radial distance from the origin.Most of the PC models of pulsar emission attribute the current flow due to the streaming of secondary charged particles along open magnetic field lines,which is approximately equal to the Goldreich–Julian current density JGJ

    Here Ω? is the direction of rotation of the spin axis andB?0is the direction of unperturbed magnetic field, and ξp=J/JGJis the scale factor associated with plasma flow, which is responsible for generating the azimuthal component of magnetic field and twisting.By assuming axisymmetric current flow, the induced magnetic field due to field aligned current was first derived by Hibschman & Arons (2001) as

    So,the total magnetic field due to perturbation will be the sum of the contributions from Equations (7) and (9), i.e.,B=B0+BP.The differential equation of a dipolar magnetic field line is given by

    From Equation(10),one can deduce the following two equations;one connects the radial coordinate with polar angle and another one connects the azimuthal coordinate with polar angle

    where K is an integration constant.From Equation (12), one can derive

    where the notations stand for their usual meanings.Finally,the expression for δφ is written as a function of magnetic azimuth by taking the first-order approximation with the help of equation (11) as given in Gangadhara (2004).So, the expression of magnetic azimuth φ in Equation (1) has to be replaced by φ+δφ to account for the PC effect in the current scenario.After calculating the shift, the modification of the shape of the PC is computed and is shown in Figure 1, for different values of misalignment parameters and geometrical configurations.

    In this section, I have tried to elaborate on the physical explanations associated with Figures (1–2), as shown in this paper.Let us first look at the complex Figure 1, where I have generated the PC boundary in the presence of a PC current perturbation, which is demarcated with red color and overlaid with an unperturbed PC diagram(shown in blue).The presence of longitudinal current flow across the PC distorts the symmetric dipolar magnetic field structure.It is more pronounced to say that higher plasma current flow leads to the generation of azimuthal components associated with the magnetic field,which can definitely result in the formation of a twisted magnetic field structure.From Figure 1, we can easily notice that the smaller values of α and misalignment parameter ξpdo not lead to a significant deviation of the PC structure compared to the unperturbed one.Here ξpcharacterizes the ratio of the plasma current flow with respect to the background Goldreich–Julian current.It is clear from panels (a) and (e) of Figure 1 that, even though plasma current for this case gets enhanced by a factor of 10, the smaller value of α suppresses the deviation.Now I discuss another two interesting cases associated with Figure 1: (i) Case 1, ξpis fixed to 1, where I have tried to discuss the trends of the PC with the increment of α.For this case,we can see that for lower α value,deviation of the structure of PC in the presence of polar cap current (PCC)perturbation is very minimal,but as α increases,PCC perturbed PC structure gets well separated with respect to the unperturbed one;it shows a fixed intersection point along the x-direction for each panel.The structure remains almost quasi-elliptical, and the orientation of the elliptical region along the y-direction gets slightly shifted.(ii) Case 2, where ξpis fixed to 10, and I analyze the changes in the structure with the increment of α.It is very clear from panels (e)–(h) of Figure 1 that, for higher α value,orientation of the major axis of the PC in the presence of PCC perturbation almost gets shifted by a significant amount,and the structure also gets deviated from well recognized elliptical geometry.This all has been understood to be happening because of the influence of the higher-order plasma current, which leads to the breaking of the symmetry of the dipolar magnetic field line, hence resulting in the shift of the emission coordinate and distortion.

    Figure 1.Above figure shows the PC diagram in the presence of perturbation, marked with a red contour for different geometrical configurations.To compare the changes of the PC boundary in the presence of plasma current perturbation, they are overlaid with the unperturbed cases; unperturbed cases are marked with blue contours.Top panels, (a)–(d), correspond to case of scale factor ξp=1 and magnetic axis inclination angle varies from 10° to 70°, with a step size of 20°, whereas bottom panels,(e)–(h),correspond to the case ξp=10 and α varies all the way from 10°to 70°,with a step size of 20°.The x-axis ranges of the PC for the unperturbed case from panels (a)–(d) are ±142.6 m, ±125 m, ±93 m, ±50 m respectively, whereas panels (e)–(h) have the same set of ranges for the unperturbed case, as they have the same set of α, and also the y-axis range for the PC remains constant for all unperturbed cases, which is ±145 m.Following that, the (x, y)-axis ranges for perturbed PC cases:panels(a)–(h)are(±142.6 m,±145 m),(±125.5 m,±142 m),(±93.4 m,±139.9 m),(±50 m,±138 m),(±143.3 m,±142.3 m),(±138.2 m,±121.7 m), (±125 m, ±92 m) and (±70 m, ±61 m) respectively.A point to note is that for perturbed cases, the ranges have been taken strictly by analyzing the intersection points with the x, y axis respectively, but due to the perturbation, the boundary can expand beyond the point of intersection.Other common parameters taken for computing the above profiles are spin period of pulsar P=1 s and radius of pulsar, i.e., RNS=10 km.

    Next I move forward to explain Figure 2.Figures 2(a)–(d)show the PC boundary for the spin period 5 ms, which is generated with the help of Equation (1).If you notice panels(a)–(d) in Figure 2,it is evident that for a higher inclination of the magnetic axis, the dimension of the PC along the xdirection gets contracted, whereas the y dimension remains fixed.This happens because, for a higher inclination angle of the magnetic axis,more number of magnetic field lines close to the magnetic axis get bounded.As a consequence, the volume of the open magnetic field line regime gets contracted.The shape of the PC is quasi-elliptical in general, and also it is verified that the formula given here shows good agreement for the case of pulsar PSR 0329+54 (α=30°, P=0.71 s), with the x-dimension 164 m and y-dimension 171 m (Biggs 1990;Gangadhara 2004).It is evident from Figure 2 that the dimensions of the PC significantly get enlarged for millisecond pulsars, which happens purely due to the contraction of light cylinder radius.

    Figure 2.Above diagram panels(a)–(d)show the PC boundary of a millisecond pulsar.Beside each panel the corresponding inclination angle α has been indicated.From panels(a)–(d),the corresponding x-axis ranges are ?2028 m ≤x ≤2028 m,?1782 m ≤x ≤1782 m,?1325 m ≤x ≤1325 m and ?705 m ≤x ≤705 m,and the dimension along the y-axis remains constant for all cases,i.e.,?2075 m ≤y ≤2075 m.Other parameters chosen are spin period of pulsar P=5 ms and radius of pulsar RNS=10 km.

    However, a point to note is that, in order to distinguish the difference between unperturbed and perturbed cases in Figure 1, I only have considered the changes of azimuthal coordinate on polar angle(see solution in Equations(1),(15)).But in reality, the expression for ηp(see Equation (2)) can be affected, due to the shift of azimuthal coordinate in the presence of PCC perturbation.Once ηpgets changed,subsequently, the expressions for re,lof, θp(see Equations (4), (5) respectively) can also get modified, hence leading to a slight change in PC estimation.However, in this paper I only consider the prime contribution of coordinate shift due to perturbation on θsol(see Equation (1)), and effect of coordinate changes on ηpwas neglected for the sake of simplicity.But in reality, the field line constant gets changed due to changes in polar angle shift as well as due to azimuthal angle shift (see Equation (13)), so one needs to consider it precisely for more accurate calculation of the PC.Second,for PC calculation I have considered some average emission height to calculate plasma current parameter Δ,but in reality it should be chosen very close to the NS surface for more fine tuned adjustment.Now this assumption has implication over three limits:(i)magnitude of current sheets is strong near the surface, due to the presence of a multipolar magnetic field component, hence it is highly probable that in that regime, magnetic reconnection processes are more active, hence plasma current perturbation is also strong.These reconnection processes are important in the sense that these processes are responsible for generating longitudinal plasma mode and radio nano-shot, and later these waves get coupled and amplitude gets enhanced via nonlinear wavewave or wave-mode interaction process and attain some highly unstable state with time.Finally, waves get converted to transverse escaping mode, near the wind-zone, close to the light cylinder (Philippov et al.2020).(ii) Second for an orthogonal rotator, i.e., α=90°, the effect of perturbation on PC structure is very minimal, no matter how strong the current circulation is near to PC zone, and as for this case Δ ≈0.(iii) For a millisecond pulsar, the effect of rapid spin period amplifies the perturbation (evident from the expression of Δ),but for normal period or long period pulsars,the effect of plasma current perturbation on PC structure is expected to be suppressed.So one needs to be very careful to choose a proper value of emission height, while estimating the PC.

    3.Radio Emission Height Formulation

    The pulsar radio emission is generally believed to be coherent curvature radiation emitted by secondary-pair plasma streaming along the dipolar magnetic field lines.The characteristic frequency of curvature radiation, at which the emission peaks, is given by Ruderman & Sutherland (1975)

    Once we substitute the expression of radius of curvature ρ from Gangadhara (2004), one can derive the expression of emission height as a function of emitted frequency and geometricalparameters as follows

    Next, I move forward to discuss different properties associated with emission height as well as with PA.First, I discuss the variation of emission altitude, which is shown in Figure 3.Profiles in Figure 3 are generated with the help of Equation (17).Variation of emission altitude is plotted with respect to rotation phase for each panel(a-c)in Figure 3.Panel(a) displays the plot of emission height versus rotation phase for different frequencies but with fixed values of α and σ,which demonstrates that radio emission does not come from a fixed height; rather, it comes from a range of heights.Figure 3(a) also confirms the radio frequency mapping; the frequency component at 300 MHz comes from the range close to 0 up to a maximum height of 4500 km,whereas the emission height associated with the frequency component at 600 MHz and at 1.4 GHz is limited to up to maximum height 2000 km and 1000 km respectively.Similarly,panel(b)also depicts the inverted Gaussian shape, but the curves intersect with each other, whereas panel (a) curves do not intersect each other.Panel (b) shows the variation of emission height with rotation phase for different values of α but with fixed values of impact factor, Lorentz factor and frequency.For α=30°, maximum emission height is limited to 2000 km, which is comparatively lower than the height as predicted for α=50° and 70°.For α=50° and 70°, maximum height is limited to 4000 km and 8000 km, respectively.All these variations associated with emission altitude happen due to the geometrical mapping and can be attributed to the interdependence of geometrical parameters.The last profile associated with emission height is displayed in Figure 3(c), which also shows similar trends as in panel (b).Panel (c) demonstrates that, corresponding to σ=0°, its minimum height is confined very close to the surface, and it spans up to a maximum height of 2000 km,whereas for σ=?8°and 8°,maximum heights are confined up to 1700 km and 2500 km respectively.But unlike zeroemission height for the case of σ=0°, minimum emission height for σ=?8°,8°does not occur very close to the surface of the NS; rather, it comes from some finite height.

    4.Polarization Angle Property of Radio Pulsar

    In this section I discuss the property of PA and its behavior elaborately,as doing so will really help one to have a confident estimation of emission height associated with different pulse components of a radio pulsar at multiple bands.Once we are able to measure the shift of polarization position angle IP(PPAIP), one can easily get the phase shift of the pulse component induced by aberration-retardation (A/R) or PCC effect.This method yields strong implications for confidently estimating emission altitude by using the relativistic phase-shift method.The expression of PA with relativistic effect was given in Blaskiewicz et al.(1991), Thomas & Gangadhara (2010)

    where ζ=α+σ.It was predicted from earlier literature that,due to the occurrence of emission at fniite height,PPAIP shifts to the later phase, and peak emission shifts toward the earlier phase;due to the A/R effect,PPAIP shifts by an amountφ′ ≈remrLc(see Blaskiewicz et al.1991; Thomas & Gangadhara 2010).Once we take the derivative of Equation (18), and substituteφ′ =remrLc,we can derive the maximum slope associated with the PA curve for the σ=0 case as

    Figure 4.PA is plotted vs.rotation phase for different emission heights.Other fixed parameters are mentioned in the box.

    Next, I try to explain Figure 4, where PA is plotted versus rotation phase for different emission heights with the help of Equation (18).We can clearly see that for higher emission altitude, PPAIP gets shifted toward the later phase.The measurement of the PPAIP has implications on estimating emission height.The phase shift of the peak location of pulse profile due to different relativistic effects such as A/R is exactly equal to the value of PPAIP, but carries an opposite sign.Therefore one can easily estimate the emission height of core and conal components for different pulsars,once the α, σ values are known.From an observational analysis, one can actually extract the values of α, σ by fitting the PA data with a theoretically predicted formula, i.e., rotating vector model(RVM) and BCW models respectively (Radhakrishnan &Cooke 1969;Blaskiewicz et al.1991).In general,pulsars show a high degree of linear polarization with a systematic “S”-shaped polarization position angle (PPA) swing, which is a characteristic property of a pulsar signal.The RVM of Radhakrishnan & Cooke (1969) attributes this characteristic“S”curve to an underlying geometry, wherein the magnetic field is assumed to be mainly dipolar, and relativistic beaming is in the direction of field line tangents.From an observational approach, an observer usually tries to make a best chi-square fitting of well calibrated pulsar data with an RVM curve of pulsar PA profiles to constrain the underlying emission geometry, hence extracting the information on magnetic axis inclination angle, and the line of sight impact angle with respect to the rotation axis.However, this method cannot always give confident estimates of the emission geometry related parameters as in reality (i) PA data of a pulsar are expected to be a function of emission height at a particular frequency, and(ii)second fitting of PA data with RVM model gives a degenerate solution of the emission geometry parameters.However,some pulsars show that the PA behavior deviates from the standard S curve, particularly in millisecond pulsars, where the polarization sweep is noisy and flatter on average (Xilouris et al.1998).Apart from that, several relativistic and plasma effects have been proposed to understand these deviations, such as (i) plasma propagation effects(Barnard&Arons 1986;McKinnon 1997),(ii)aberration of the beaming direction from strict parallelism (Blaskiewicz et al.1991;Dyks 2008;Kumar&Gangadhara 2012b),(iii)distortion of the underlying dipole field due to the field-aligned PCC(Hibschman & Arons 2001; Kumar & Gangadhara 2012a),or (iv) multiple interacting orthogonal polarization modes(McKinnon & Stinebring 1998).

    Figure 5.In panel (a),the slope of the PA is plotted vs.rotation phase for different emission heights.To generate panel (a),I used a fixed value α=10°.Panel (b)shows the plot of maximum of the slope of PA vs.emission height as a fraction of light cylinder for different inclination angles of the magnetic axis;for this plot the chosen value of impact angle is σ=0°.

    Figure 6.In the above figure,panels(a)and(b)show the generalized contour representations of the slope maxima associated with PA in the(σ,rem/rLc)and(α,σ)plane respectively.To generate panel (a), a fixed value of α=10° is chosen, whereas for panel (b) a fixed value of fractional emission altitude is rem/rLc ≈0.5.

    Next, I move forward to explain the profile, i.e., Figure 5,which is generated with the help of Equation (18) and Equation (19).Figure 5 is something new and an important result which has potential synergies with pulsar emission physics.Such results as derived from theoretical formulation have strong relevance to interpreting observational data.Carrying such analysis and making a good connection with theory intuitively helps one to get a confident estimation of PPAIP associated with PA curves, hence relating the connection with the emission height.One can see from Figure 5(a)that the peak of the slope of the PA curve gets shifted to the right side, with respect to the rotation phase, as the emission height progresses.Also, another important feature associated with Figure 5(a) is, with the enhancement of fractional emission height, the magnitude of the slope of PA decreases.On the other hand, Figure 5(b) displays the variation of the slope maximum of PA curve with the fractional emission altitude for different values of α.One can clearly see from Figure 5(b)that the locus of slope maximum of PA curves corresponding to different α remains constant until the light cylinder, but if one analyzes their nature up to r ≈7 rLc, one can see that curves slowly get merged at a point close to r=3.4 rLcand start to oscillate after reaching this turning point, but slowly the amplitude of oscillation gets attenuated as fractional emission height progresses; but initial value of the amplitude of such oscillation is quite less for higher value of α.Also, such study implies that the polarity of a particular emitted mode get reversed after a few light cylinder radii,naturally reflecting the property of propagation effect and which can explain several observational features associated with mode propagation of radio pulsars.Figure 6 presents the contour plots, showing the contour representation of the slope maximum associated with PA.A point to note is that Figure 5 is very specific in the sense that it has been generated for the σ=0 case to get a simplified expression, whereas Figure 6 is generated for generalized values of α, σ, rem/rLc.Since the generalized expression of(δψ δφ′ )Maxis quite big, I avoided presenting it here, but for the sake of completeness the locus of the slope maximum corresponding to PA swing has been presented as a contour diagram and is displayed in Figure 6.From a common point of view, one can derive the generalized expression of slope maxima by suitably choosing the initial value ofφ′ iteratively,such thatwhere the ψbcwexpression is given in Equation(18).The constraints,corresponding to the set of contour rings or z sliced representation of isochrone curves, associated with both the panels of Figure 6, a third variable, have been marked with color graded index, suitably placed adjacent to each panel.In the contour representation,slopes of the adjacent curves are relatively steeper,than the far away curves,which generally reflects the property of curvature radiation associated with the curvature of a dipolar magnetic field line configuration (see Dyks & Harding 2004; Kumar &Gangadhara 2012a).But in the presence of plasma current perturbation, field line structure gets twisted.Hibschman &Arons(2001),showed that a plasma current perturbation due to spark discharge associated with primary plasma current causes field line distortion,which in turn gives the polarization curves a vertical offset, but does not necessarily make any change on the coordinate of PPAIP in rotation phase space.A recent simulation by Kumar & Gangadhara (2012a) confirmed this fact, but they claimed that the presence of plasma modulation along the azimuthal direction can lead to a drastic change in PPAIP coordinate.In the caption of Figure 6, details of the parameter values have been mentioned.PA of the emitted radiation manifests the orientation of the the plane of the magnetic field line as projected onto the equatorial plane.One usually derives it from the detailed treatment of the Fourier component of the radiation electric field, integrated over the emission region and followed by the component of the corresponding quantity being segregated along the direction of two orthogonal basis vectors in the plane of the sky to reconstruct the final Stokes vector.Consequently,such contour representation as depicted in Figure 6 generally reflects the standard dipolar magnetic field line topology and is very consistent with the standard radio emission geometry of a pulsar magnetosphere (Gangadhara 2004; Roy &Gangadhara 2019).Another intriguing fact for the realistic pulsar case, phase shift of the pulse components, is that the PPAIP depends on the emitted frequency band and on the absolute emission location of the respective component in the pulsar magnetosphere, which has been predicted by earlier literatures(Blaskiewicz et al.1991;Gangadhara 2005;Thomas& Gangadhara 2010), whereas the RVM model shows a solution of the slope maximum of the PA curve, for zero emission height approximation for all pulse components to be(δψ δφ′ )max= sinαsinσ(Radhakrishnan & Cooke 1969).Thus one needs to consider the effect of finite emission height corresponding to each pulse component separately, for estimating absolute emission height (Thomas &Gangadhara 2010).

    5.Discussion and Conclusion

    Here I vividly try to summarize some of the important results below.(i) In the manuscript, distortion of the PC shapes for different plasma current parameters and geometrical parameters are shown in Figure 1,based on an analytical approach,which is the main result of the paper.Figure 1 clearly affirms that,as magnetic axis inclination angle (α) and plasma current parameter(ξp)both get enhanced,PC structure slowly becomes distorted into an arbitrary structure from a regular elliptical shape,and also orientation of the major axis of the PC begins to precess.In another part of the PC formulation, structure of the PC for the millisecond pulsar case is displayed in Figure 2 and all relevant explanations are presented in the previous section.From general comparison, it is evident that the area of the PC for a millisecond pulsar is quite larger than the case for a normal pulsar.Expansion of the area of a PC of a millisecond pulsar happens purely because of a geometrical reason.As the effect of plasma current perturbation is much stronger for the millisecond perturbation case, it requires much more refined calculation.For interpreting the PC formulation of a normal period pulsar, I have used some numerical approximation,which can indirectly influence geometrical parameters, hence limiting our understanding about PC structure.As perturbation is expected to be strong for the millisecond pulsar case, the formula needs to be refined much more precisely based on the prevailing geometrical description.In this short paper, it is beyond the scope to interpret all those results in detail, so the plan is to work on those in a subsequent paper.

    In the second stage of the paper,geometrical dependency of emission height variation in the rotation phase space is shown,for different radio frequencies,magnetic axis inclination angles and line of sight impact angle parameters in Figure 3, which demonstrates that emission of radio pulsars comes from a wide range of height, and its detailed description is given in the section on radio emission height.In literature, two main methods to estimate emission height of pulsars have been proposed: (i) geometrical method (Blaskiewicz et al.1991)and(ii)relativistic phase-shift method (Dyks&Harding 2004;Gangadhara 2004, 2005; Dyks 2008; Thomas &Gangadhara 2010).Both the methods have their merits and shortcomings as well.The first method, i.e., geometrical method, postulates that (a) all pulse components emit at a constant height,and(b)pulse edge corresponds to the last open field line.This method has an ambiguity in terms of predicting the pulse edge corresponding to the last open field line, as in some cases it is highly probable that the whole PC does not emit.The first method predicts that the centroid of the peak advances to an earlier phase by rem/rLc,whereas PPAIP lags to a later phase by an amount 3rem/rLc.The second method predicts that due to a geometrical limitation and relativistic effect associated with emitting blobs in the pulsar magnetosphere, the observer does not receive all the components at a constant height.Due to the combined effect associated with rotation and retardation(i.e.,A/R effect),it creates asymmetry on the phase location of leading and trailing components with respect to the meridional plane.The meridional plane is an invariant entity, which contains a rotation axis and magnetic axis both at zero rotation phase.This combined A/R effect leads to a phase shift in the centroid of the peak, advancing to an earlier phase by an amount 2rem/rLc,whereas PPAIP lags to a later phase by an amount 2rem/rLcin the rotation phase diagram.This method is called the relativistic phase-shift method, where it is assumed that core and conal components emit at different heights and emission height is determined from the asymmetry of the phase location of core and conal components.Although this method gives a very confident estimation of emission height for most cases,in some cases it is quite difficult to identify the core and conal components from pulsar data.

    In the third stage of the work,PA and its slope variations are shown for different emission heights and geometrical parameters in Figures 4–6.In Figure 4,it is shown that PPAIP gets shifted for different emission heights.Next in Figures 5 and 6,slopes of PA curves are plotted with respect to rotation phase and fractional emission height respectively for a fixed geometry.In Figure 5, it is shown that the peak of the slope of PA gets shifted in rotation phase space as emission height progresses,while on the other hand Figure 6 demonstrates that slope maximum of the PA curve almost remains constant until the light cylinder radius.Relevant explanations on the nature of all the curves associated with the predicted results can be well explained with the conventional geometrical scenario of curvature radiation of radio pulsars.

    Below, I have tried to give some limitations or incompleteness on the model, and also discuss some future scope and other perspectives.For the sake of completeness, Kumar &Gangadhara (2012a) presented a full geometry under PCC perturbation, which shows the difference between the unperturbed (dashed line) and perturbed magnetic field line (solid line).Due to the presence of extra azimuthal component (i)field lines becoming twisted and(ii)emission coordinate being changed, i.e., tangent vector, radius of curvature of field lines,curvature vector and other radio emission geometry related parameters on which emission property depends,gets affected,which naturally leads to a phase shift in the peak of intensity profile (see Kumar & Gangadhara 2012a).Results shown in this paper are based on some new formulations (see Equation (1), which determines the PC structure and coordinate), which are firmly connected with existing literatures, so I believe that the results are genuine and carry potentially good impact as far as the pulsar emission mechanism is concerned.Although I have tried to revisit some new and old formulas, until it is implemented and justified thoroughly with reliable data sources, intricacies and drawbacks will not be revealed.Also,in the current analysis,I have neglected the rotation of pulsars.It is evident that rotation can also modify the PC structure.In a subsequent paper I plan to add this effect.Among all the perturbation effects that are present in a pulsar magnetosphere,it is believed that A/R is the dominant one, which leads to shifting the centroid of intensity peak to an earlier phase by 2rem/rLcand PPAIP to be shifted to a later phase by 2rem/rLc, with respect to the meridional plane(see Gangadhara 2005), where remis the emission height and rLcis the light cylinder radius.However,earlier prediction(see Blaskiewicz et al.(1991),named the BCW model)claimed the phase shift of the location of the centroid of the core of the pulse profile to advance in phase by rem/rLcand delay PPAIP to a later phase by 3rem/rLc.This was derived based on the assumptions of(i)first order approximation of rotational effect and(ii)constant emission height across the full pulse longitude,which does not give a confident estimation of phase shift(both PPAIP and centroid peak of intensity)and frequency dependent emission height, as initial assumptions do not seem to be realistic.

    Here I try to highlight some of the limitations of the model associated with PC estimation.First limitation: (i) while computing the PC in the quadrant π/2 ≤φ ≤3π/2, δφ is not computed at the shifted azimuthal location at π ?φ.But in principle for accurate estimation of PC,δφ should be estimated at π ?φ in the second quadrant, as δφ is also an explicit function of φ.Second limitation: (ii) while estimating ηlof, I have not substituted φ by φ+δφ, as it can iteratively generate unnecessary numerical errors or indeterminate numerical value at some particular phase location.Third limitation: (iii) while estimating the contribution of PC current perturbation I have assumed some average emission height, i.e., r ≈0.5rLC, but in general one should trace the field line constant at a specific value,which corresponds to the last open field line for a given set of emission geometries, or one can roughly take emission height to r ≈RNS, the radius of an NS, as the PC boundary is constructed by the projection of the last open field line on the surface of the NS.However, the aforementioned value sometimes can overestimate or underestimate the PC boundary and one needs to justify it from pulsar data.

    Nevertheless,there are some other effects like magnetic field sweep back(mfsb)(see Dyks&Harding 2004),but it has been proved that this effect is a third-order effect,proportional to rn3,where rnis emission height as a fraction of light cylinder radius.By using the expression of phase-shift due to mfsb δ φmfsb(see Dyks & Harding (2004)), Gangadhara (2005)estimated the value of δφmfsbfor rotation phaseφ′ = 0° , line of sight impact angle 0°and magnetic axis inclination angle 10° and 90° respectively, and he found that compared to the A/R and PCC effects, mfsb is far too weak in the regime rn≤0.2.Hence it can be claimed that, among all perturbation effects,the A/R and PCC effects are among the most dominant ones (see Gangadhara (2005) for a more detailed discussion).However mfsb can become dominant close to the light cylinder.Still now, the relativistic phase shift method as prescribed by Gangadhara (2005) seems to be a very powerful and accurate method,which was practically applied by Thomas& Gangadhara (2010) to estimate the emission height associated with the multi-component profile of three pulsars,at 610 MHz and 1.4 GHz.In the near future I have a plan to implement the technique over a wider population of radio pulsars and carry out the emission height analysis at multiple bands.

    Acknowledgments

    I personally thank Prof.R.T.Gangadhara(affiliated with the Indian Institute of Astrophysics, Bangalore) for several illuminating discussions.The author also acknowledges the SNBNCBS institute, Kolkata for providing research infrastructure and Department of Science and Technology,Govt.of India for providing financial assistance to carry out research.Also I would like to thank the anonymous referee for carefully going through the manuscript and pointing out some important issues that improved the quality of the manuscript.

    精品国产乱子伦一区二区三区| 一区二区三区激情视频| 一区二区日韩欧美中文字幕| 亚洲中文av在线| av网站在线播放免费| 久久国产精品影院| 一级片免费观看大全| 久久久久国产精品人妻aⅴ院| 琪琪午夜伦伦电影理论片6080| 伦理电影免费视频| 国产精品影院久久| 日韩欧美免费精品| 美国免费a级毛片| 男女做爰动态图高潮gif福利片 | 亚洲男人的天堂狠狠| 99国产极品粉嫩在线观看| 亚洲成国产人片在线观看| 亚洲人成77777在线视频| 久久天堂一区二区三区四区| 99久久99久久久精品蜜桃| 精品乱码久久久久久99久播| 日韩大尺度精品在线看网址 | 两性午夜刺激爽爽歪歪视频在线观看 | 久久草成人影院| 久久久久国产精品人妻aⅴ院| 免费高清视频大片| 久久久精品国产亚洲av高清涩受| 亚洲人成网站在线播放欧美日韩| 亚洲av美国av| 欧美成人免费av一区二区三区| 亚洲精品中文字幕在线视频| 亚洲人成电影免费在线| 在线国产一区二区在线| 精品乱码久久久久久99久播| 怎么达到女性高潮| 啦啦啦 在线观看视频| 麻豆一二三区av精品| 国产av一区二区精品久久| 99热国产这里只有精品6| 欧美日韩瑟瑟在线播放| 欧美人与性动交α欧美精品济南到| 免费看a级黄色片| 国产亚洲欧美精品永久| 日韩中文字幕欧美一区二区| 欧美日韩视频精品一区| 在线观看舔阴道视频| 18禁美女被吸乳视频| 高清在线国产一区| 啦啦啦免费观看视频1| 免费人成视频x8x8入口观看| 黑人欧美特级aaaaaa片| 韩国精品一区二区三区| 99在线视频只有这里精品首页| 国产成人欧美| 很黄的视频免费| 色老头精品视频在线观看| 婷婷六月久久综合丁香| 国产精品一区二区免费欧美| a级片在线免费高清观看视频| 久久热在线av| 亚洲五月天丁香| 精品一区二区三区视频在线观看免费 | 一级毛片女人18水好多| 国产有黄有色有爽视频| 国产伦一二天堂av在线观看| 欧美日韩福利视频一区二区| 国产成年人精品一区二区 | 国内毛片毛片毛片毛片毛片| 亚洲熟妇中文字幕五十中出 | 日本wwww免费看| 日韩三级视频一区二区三区| 在线观看66精品国产| 操美女的视频在线观看| 婷婷六月久久综合丁香| 国产极品粉嫩免费观看在线| 波多野结衣高清无吗| 精品久久久久久久久久免费视频 | 黄色女人牲交| 久久久久精品国产欧美久久久| av在线天堂中文字幕 | 欧美日韩av久久| 在线观看免费日韩欧美大片| 少妇被粗大的猛进出69影院| 手机成人av网站| www.精华液| 热99re8久久精品国产| 老司机午夜十八禁免费视频| 国产av精品麻豆| 中文亚洲av片在线观看爽| 国产成人影院久久av| 久久国产精品男人的天堂亚洲| 黄色怎么调成土黄色| 国产熟女午夜一区二区三区| 国产又色又爽无遮挡免费看| 亚洲va日本ⅴa欧美va伊人久久| 免费搜索国产男女视频| 伊人久久大香线蕉亚洲五| 老司机深夜福利视频在线观看| 丝袜人妻中文字幕| 天天躁狠狠躁夜夜躁狠狠躁| 亚洲国产精品合色在线| www.熟女人妻精品国产| 久久性视频一级片| 在线天堂中文资源库| 成人av一区二区三区在线看| 欧美大码av| 日韩av在线大香蕉| 久久久国产欧美日韩av| 欧美久久黑人一区二区| 亚洲aⅴ乱码一区二区在线播放 | 亚洲精华国产精华精| 久久久久久人人人人人| xxx96com| 国产成人影院久久av| 国产av一区二区精品久久| a级毛片黄视频| 97超级碰碰碰精品色视频在线观看| 欧美黄色片欧美黄色片| 老熟妇乱子伦视频在线观看| 国产精品秋霞免费鲁丝片| 深夜精品福利| 欧美不卡视频在线免费观看 | 国产精品国产av在线观看| 一区二区三区激情视频| 亚洲欧美日韩高清在线视频| 国产精华一区二区三区| 久久久国产精品麻豆| 亚洲国产毛片av蜜桃av| 亚洲中文日韩欧美视频| 国产97色在线日韩免费| 日本a在线网址| 国产成年人精品一区二区 | 亚洲人成电影观看| avwww免费| 久久久久久久久中文| www.www免费av| 日韩欧美一区视频在线观看| 在线观看舔阴道视频| 精品午夜福利视频在线观看一区| 久久中文字幕人妻熟女| 麻豆久久精品国产亚洲av | 日本黄色视频三级网站网址| 最新美女视频免费是黄的| a在线观看视频网站| 国产欧美日韩一区二区三| 久久香蕉精品热| 久久伊人香网站| 久久精品成人免费网站| 18禁国产床啪视频网站| 最好的美女福利视频网| 热re99久久精品国产66热6| 午夜两性在线视频| 成人三级黄色视频| 久久久水蜜桃国产精品网| 国产精品久久视频播放| 欧美黄色淫秽网站| 啦啦啦在线免费观看视频4| 9热在线视频观看99| 久久欧美精品欧美久久欧美| 欧美午夜高清在线| 精品免费久久久久久久清纯| 欧美日韩一级在线毛片| www.熟女人妻精品国产| 亚洲一区中文字幕在线| 天天躁狠狠躁夜夜躁狠狠躁| а√天堂www在线а√下载| 亚洲欧美激情综合另类| 亚洲欧美精品综合一区二区三区| 90打野战视频偷拍视频| xxx96com| 美女午夜性视频免费| 久久性视频一级片| 亚洲一区中文字幕在线| 免费高清在线观看日韩| 国产日韩一区二区三区精品不卡| 一级a爱片免费观看的视频| 丝袜人妻中文字幕| 日韩国内少妇激情av| 亚洲,欧美精品.| 视频区图区小说| 免费日韩欧美在线观看| 亚洲,欧美精品.| 免费不卡黄色视频| 黄色 视频免费看| 极品教师在线免费播放| 国产精品一区二区免费欧美| 亚洲国产精品999在线| 丝袜人妻中文字幕| 欧美国产精品va在线观看不卡| 88av欧美| 多毛熟女@视频| 日韩免费av在线播放| 日本a在线网址| 久久人妻av系列| 黑人巨大精品欧美一区二区蜜桃| av超薄肉色丝袜交足视频| 国产精品野战在线观看 | av网站在线播放免费| 丝袜在线中文字幕| 中文字幕人妻丝袜制服| 久久午夜综合久久蜜桃| 国产精品影院久久| 久久精品91无色码中文字幕| 中文字幕人妻熟女乱码| 精品熟女少妇八av免费久了| 亚洲av成人一区二区三| 免费少妇av软件| 大香蕉久久成人网| 真人做人爱边吃奶动态| 在线视频色国产色| 午夜精品久久久久久毛片777| 我的亚洲天堂| 人人妻,人人澡人人爽秒播| 老鸭窝网址在线观看| 亚洲avbb在线观看| 国产成人欧美| 啦啦啦免费观看视频1| 国产熟女午夜一区二区三区| 亚洲欧美一区二区三区久久| 一区福利在线观看| 国产单亲对白刺激| 免费日韩欧美在线观看| 他把我摸到了高潮在线观看| 免费在线观看黄色视频的| 9191精品国产免费久久| 91成人精品电影| 久久人妻福利社区极品人妻图片| 成人手机av| 热99国产精品久久久久久7| 亚洲成人免费av在线播放| 天天添夜夜摸| 国产精品亚洲av一区麻豆| 看片在线看免费视频| 国产av一区二区精品久久| 久久精品亚洲av国产电影网| 老司机亚洲免费影院| 日本欧美视频一区| 午夜福利在线观看吧| 在线国产一区二区在线| 久久久久久人人人人人| 最近最新免费中文字幕在线| 亚洲精品国产色婷婷电影| 国产三级在线视频| 亚洲国产精品一区二区三区在线| 亚洲av片天天在线观看| 国产精品香港三级国产av潘金莲| 嫁个100分男人电影在线观看| 成人18禁高潮啪啪吃奶动态图| 亚洲国产毛片av蜜桃av| 国产精品久久久久久人妻精品电影| 亚洲男人的天堂狠狠| 欧美精品亚洲一区二区| 色综合站精品国产| 99久久综合精品五月天人人| 一级a爱视频在线免费观看| 99国产精品免费福利视频| 国产欧美日韩综合在线一区二区| 国产高清videossex| 欧美日韩黄片免| 99在线人妻在线中文字幕| 多毛熟女@视频| 在线观看免费视频日本深夜| 国产精品九九99| 久9热在线精品视频| 手机成人av网站| 亚洲成人国产一区在线观看| 人人妻人人澡人人看| 91在线观看av| 女生性感内裤真人,穿戴方法视频| 狠狠狠狠99中文字幕| 欧美中文综合在线视频| 成人特级黄色片久久久久久久| 免费看a级黄色片| 69精品国产乱码久久久| 在线观看舔阴道视频| 午夜福利欧美成人| 91av网站免费观看| 黑人欧美特级aaaaaa片| 老熟妇仑乱视频hdxx| 一二三四社区在线视频社区8| 国产亚洲欧美精品永久| 中文亚洲av片在线观看爽| 啦啦啦 在线观看视频| 精品熟女少妇八av免费久了| 999精品在线视频| 精品久久久久久成人av| 免费在线观看影片大全网站| 一二三四社区在线视频社区8| svipshipincom国产片| 国产高清视频在线播放一区| 如日韩欧美国产精品一区二区三区| 看黄色毛片网站| 亚洲久久久国产精品| 18禁黄网站禁片午夜丰满| 精品国产超薄肉色丝袜足j| 国产精品一区二区三区四区久久 | 久久久国产一区二区| 亚洲三区欧美一区| 日韩人妻精品一区2区三区| 黄片播放在线免费| 久久婷婷成人综合色麻豆| 视频在线观看一区二区三区| 国产1区2区3区精品| 亚洲,欧美精品.| 免费在线观看黄色视频的| 99国产精品一区二区三区| 天天添夜夜摸| 久久热在线av| 亚洲国产精品sss在线观看 | 香蕉久久夜色| 国产一卡二卡三卡精品| 中文欧美无线码| 亚洲精品成人av观看孕妇| 亚洲成av片中文字幕在线观看| 久久这里只有精品19| 一区二区三区国产精品乱码| 亚洲精品粉嫩美女一区| 法律面前人人平等表现在哪些方面| 亚洲熟女毛片儿| 欧美在线一区亚洲| 丁香六月欧美| 国产一区在线观看成人免费| 久久久精品国产亚洲av高清涩受| 欧美日韩精品网址| 国产黄a三级三级三级人| 精品久久蜜臀av无| 亚洲av五月六月丁香网| 日本黄色日本黄色录像| 精品日产1卡2卡| 国产亚洲av高清不卡| 90打野战视频偷拍视频| 国产成人免费无遮挡视频| 国产三级在线视频| 午夜免费激情av| 日韩精品中文字幕看吧| 国产免费现黄频在线看| 色尼玛亚洲综合影院| 99国产精品一区二区三区| 久久中文字幕一级| 制服人妻中文乱码| 天天影视国产精品| 成熟少妇高潮喷水视频| 日韩精品青青久久久久久| 亚洲aⅴ乱码一区二区在线播放 | 国产日韩一区二区三区精品不卡| 国产一卡二卡三卡精品| 精品无人区乱码1区二区| 亚洲av五月六月丁香网| 久久久久久久午夜电影 | 成人三级黄色视频| 久久性视频一级片| 脱女人内裤的视频| 一a级毛片在线观看| 别揉我奶头~嗯~啊~动态视频| 自拍欧美九色日韩亚洲蝌蚪91| 老熟妇仑乱视频hdxx| 亚洲精品中文字幕一二三四区| 国产成人av激情在线播放| 午夜福利,免费看| 操美女的视频在线观看| 精品国产亚洲在线| 露出奶头的视频| 成人影院久久| 国产xxxxx性猛交| 狂野欧美激情性xxxx| 女同久久另类99精品国产91| 叶爱在线成人免费视频播放| 伦理电影免费视频| 精品久久久久久,| 这个男人来自地球电影免费观看| 欧美 亚洲 国产 日韩一| 国产伦人伦偷精品视频| 黄片播放在线免费| 一a级毛片在线观看| 久久性视频一级片| 国产无遮挡羞羞视频在线观看| 成在线人永久免费视频| 久久久久久久久免费视频了| 九色亚洲精品在线播放| 国产成人精品无人区| 欧美最黄视频在线播放免费 | 亚洲熟妇熟女久久| 亚洲精品久久午夜乱码| 国产高清激情床上av| 日本一区二区免费在线视频| 最好的美女福利视频网| 一级作爱视频免费观看| 国产精品免费视频内射| 超色免费av| 日韩免费高清中文字幕av| 91精品三级在线观看| www国产在线视频色| 亚洲中文字幕日韩| 99精品久久久久人妻精品| 欧美精品亚洲一区二区| 午夜福利免费观看在线| 色尼玛亚洲综合影院| 免费看a级黄色片| 香蕉国产在线看| 丁香六月欧美| 亚洲狠狠婷婷综合久久图片| 国产aⅴ精品一区二区三区波| 久久国产乱子伦精品免费另类| 国产97色在线日韩免费| 少妇粗大呻吟视频| 一级,二级,三级黄色视频| 在线观看66精品国产| 大陆偷拍与自拍| 两个人看的免费小视频| 日本黄色日本黄色录像| 黄色丝袜av网址大全| 久久人人97超碰香蕉20202| 无人区码免费观看不卡| 精品少妇一区二区三区视频日本电影| 少妇裸体淫交视频免费看高清 | 最新美女视频免费是黄的| 午夜免费成人在线视频| aaaaa片日本免费| 激情视频va一区二区三区| 亚洲人成77777在线视频| 波多野结衣一区麻豆| 一边摸一边做爽爽视频免费| 久久人妻熟女aⅴ| 国产人伦9x9x在线观看| 天堂√8在线中文| 欧美成人免费av一区二区三区| 少妇粗大呻吟视频| x7x7x7水蜜桃| 成人特级黄色片久久久久久久| 大型av网站在线播放| 亚洲精品成人av观看孕妇| 亚洲性夜色夜夜综合| 欧美大码av| 日韩三级视频一区二区三区| 亚洲av成人一区二区三| 亚洲成av片中文字幕在线观看| 真人做人爱边吃奶动态| 亚洲精品中文字幕一二三四区| 又黄又爽又免费观看的视频| 香蕉丝袜av| av国产精品久久久久影院| 国产精品日韩av在线免费观看 | 免费在线观看影片大全网站| 黄片大片在线免费观看| 黄色 视频免费看| 亚洲一区二区三区欧美精品| 一边摸一边做爽爽视频免费| 久久久久国内视频| 成人特级黄色片久久久久久久| 国产精品久久视频播放| 日本黄色视频三级网站网址| a在线观看视频网站| 久久久久久人人人人人| 成年人黄色毛片网站| 国产99白浆流出| 麻豆av在线久日| 激情视频va一区二区三区| 在线观看午夜福利视频| 国产成人免费无遮挡视频| 精品国产美女av久久久久小说| 97超级碰碰碰精品色视频在线观看| 美女午夜性视频免费| 久久久久久亚洲精品国产蜜桃av| 18禁观看日本| 久久草成人影院| 国产男靠女视频免费网站| 后天国语完整版免费观看| 亚洲精品在线观看二区| 三级毛片av免费| 亚洲专区字幕在线| 日韩人妻精品一区2区三区| 欧美国产精品va在线观看不卡| 又大又爽又粗| 国产精品99久久99久久久不卡| 香蕉丝袜av| 麻豆成人av在线观看| 久久亚洲真实| 久久伊人香网站| 国产精品免费一区二区三区在线| 国产人伦9x9x在线观看| 琪琪午夜伦伦电影理论片6080| 人人澡人人妻人| 80岁老熟妇乱子伦牲交| 日日夜夜操网爽| 亚洲精品一二三| 亚洲欧美精品综合久久99| 亚洲第一青青草原| 日本三级黄在线观看| 精品人妻1区二区| 免费不卡黄色视频| 日本五十路高清| 亚洲精品国产一区二区精华液| 波多野结衣av一区二区av| 日韩有码中文字幕| 搡老岳熟女国产| 久久这里只有精品19| 每晚都被弄得嗷嗷叫到高潮| 少妇的丰满在线观看| 自线自在国产av| 99国产综合亚洲精品| 女人爽到高潮嗷嗷叫在线视频| 免费高清在线观看日韩| 又紧又爽又黄一区二区| 啪啪无遮挡十八禁网站| 无限看片的www在线观看| 国产成人影院久久av| 国产精品98久久久久久宅男小说| 高清黄色对白视频在线免费看| 不卡一级毛片| 成人手机av| 无遮挡黄片免费观看| 久久久久久亚洲精品国产蜜桃av| 乱人伦中国视频| 国内久久婷婷六月综合欲色啪| 国产在线观看jvid| 国产精品亚洲av一区麻豆| 亚洲第一青青草原| 91老司机精品| 中文字幕人妻丝袜制服| 亚洲专区字幕在线| 极品教师在线免费播放| 亚洲三区欧美一区| 中文欧美无线码| 天天躁狠狠躁夜夜躁狠狠躁| 日本撒尿小便嘘嘘汇集6| 久久人人97超碰香蕉20202| 欧美中文综合在线视频| 国产免费av片在线观看野外av| 日日摸夜夜添夜夜添小说| 亚洲久久久国产精品| 久久影院123| 丝袜美腿诱惑在线| 老司机深夜福利视频在线观看| 欧美精品一区二区免费开放| 国产一区二区三区视频了| 久久久久九九精品影院| 亚洲成人精品中文字幕电影 | 成人精品一区二区免费| 亚洲黑人精品在线| 久热爱精品视频在线9| 亚洲人成伊人成综合网2020| 久久欧美精品欧美久久欧美| 一边摸一边抽搐一进一小说| 亚洲精品一区av在线观看| 别揉我奶头~嗯~啊~动态视频| 777久久人妻少妇嫩草av网站| 视频区图区小说| 婷婷精品国产亚洲av在线| 中文字幕最新亚洲高清| 久久中文看片网| 在线av久久热| 亚洲男人天堂网一区| 久久热在线av| 久久精品国产亚洲av高清一级| 国产精品国产高清国产av| 在线看a的网站| 久久婷婷成人综合色麻豆| 精品熟女少妇八av免费久了| 日韩欧美一区视频在线观看| 国内久久婷婷六月综合欲色啪| 男女午夜视频在线观看| 精品一区二区三区av网在线观看| 亚洲第一青青草原| 两性午夜刺激爽爽歪歪视频在线观看 | 中文字幕色久视频| 男女午夜视频在线观看| 我的亚洲天堂| 亚洲av美国av| 午夜免费鲁丝| 19禁男女啪啪无遮挡网站| 无限看片的www在线观看| 天堂√8在线中文| 国产1区2区3区精品| 中国美女看黄片| 妹子高潮喷水视频| 熟女少妇亚洲综合色aaa.| 男女下面进入的视频免费午夜 | 精品国产亚洲在线| 狂野欧美激情性xxxx| 亚洲自拍偷在线| 亚洲第一欧美日韩一区二区三区| 国产真人三级小视频在线观看| 国产亚洲欧美精品永久| av中文乱码字幕在线| 久久久国产一区二区| 巨乳人妻的诱惑在线观看| 亚洲色图综合在线观看| 国产一区二区激情短视频| 国产精品99久久99久久久不卡| 免费看十八禁软件| 成人三级黄色视频| 日韩欧美在线二视频| 黄片小视频在线播放| 国产激情欧美一区二区| 精品人妻在线不人妻| 日韩免费高清中文字幕av| 亚洲aⅴ乱码一区二区在线播放 | 亚洲美女黄片视频| 人人妻人人添人人爽欧美一区卜| 在线天堂中文资源库| 亚洲欧美日韩另类电影网站| 亚洲色图 男人天堂 中文字幕| 日韩欧美一区视频在线观看| 精品第一国产精品| 中文字幕另类日韩欧美亚洲嫩草| www日本在线高清视频| 五月开心婷婷网| 黄网站色视频无遮挡免费观看| av福利片在线| 亚洲第一青青草原| 9色porny在线观看| 久久久久久久久久久久大奶| 亚洲欧美激情在线| 校园春色视频在线观看| 亚洲成人国产一区在线观看|