The characteristics of millisecond pulsar emission III.From low to high frequencies

a r

X

i

v

:a

s t

r o

-

p

h

/

9

9

6

4

4

2v

1

2

8

J u

n

1

9

9

9

accepted for publication in ApJ The characteristics of millisecond pulsar emission:III.From low to high frequencies Michael Kramer 1,2,Christoph Lange 2,Duncan R.Lorimer 2,3Donald C.Backer 1,Kiriaki M.Xilouris 3,Axel Jessner 2,Richard Wielebinski 2ABSTRACT In this paper we present the ?rst observations of a large sample of millisecond pul-sars at frequencies of 2.7GHz (λ11cm)and 4.9GHz (λ6cm).For almost all sources,these represent the ?rst λ11cm observations ever.The new measurements more than double the number of millisecond pulsars studied at λ6cm.Our new ?ux measurements extend the known spectra for millisecond pulsars to the highest frequencies to date.The coverage of more than a decade of radio spectrum allows us for the ?rst time to search for spectral breaks as so often observed for normal pulsars around 1GHz.The results suggest that,unlike the normal pulsars,millisecond pulsar spectra can be largely described by a single power law.We align the observed millisecond pulsar pro?les with data from lower frequencies to search for indications of disturbed magnetic ?elds and attempt to resolve questions which were raised in recent literature.Deviations from a dipolar magnetic ?eld structure are not evident and absolute timing across the wide frequency range with a single dispersion measure is possible.We seem to observe mainly un?lled emission beams,which must originate from a very compact region.The existence of non-dipolar ?eld components can therefore not be excluded.A compact emission region is also suggested by a remarkably constant pro?le width

or component separation over a very wide frequency range.This observed di?erence to the emission properties of normal pulsars is highly signi?cant.For a few sources,polarization data at 2.7and 4.9GHz could also be obtained which indicate that despite the typically larger degree of polarization at lower frequencies,millisecond pulsars are weakly polarized or even unpolarized at frequencies above 3GHz.The simultaneous decrease in degree of polarization and the constant pro?le width thus question proposals which link de-polarization and decreasing pro?le width for normal pulsars to the same propagation e?ect (i.e.birefringence).

Comparing the properties of core and conal like pro?le components to those of normal pulsars,we?nd less signi?cant patterns in their spectral evolution for the population

of millisecond pulsars.Hence,we suggest that core and conal emission may be created

by the same emission process.

Given the small change in pro?le width,the indicated de-polarization of the radiation and the possible simple?ux density spectra,MSP emission properties tend to resemble

those of normal pulsars only shifted towards higher frequencies.

Subject headings:pulsars:general–radiation mechanisms:non-thermal–stars:evolu-

tion–polarization

1.Introduction

Numerous searches following the discovery of the?rst and still the fastest rotating neutron star PSR B1937+21(Backer et al.1982)have revealed about70millisecond radio pulsars(e.g.Manch-ester1998).This sample has a characteristic age which is on the average two to three orders of magnitude larger than that of normal pulsars,indicating a di?erent evolutionary history.Indeed, millisecond pulsars are considered as being spun-up by mass transfer from a binary companion (Alpar et al.1982).This evolutionary history distinguishes these recycled pulsars,which we will here simply call millisecond pulsars,MSPs,from“normal”pulsars.Chen&Ruderman(1993),for instance,suggested that the recycling process has consequences for the topology of the magnetic ?eld at the surface of the star which could possibly a?ect the emission properties of MSPs.

One of the?rst investigations of the emission properties of MSPs was carried out by Manch-ester(1992).Based upon the small number of MSPs then known,he concluded that they exhibit properties similar to normal pulsars.Lorimer et al.(1995)found the spectra of19MSPs to be slightly steeper than normal pulsars.In a series of papers,we have recently started to study the emission characteristics of a large sample of MSPs in a systematic way.Kramer et al.(1998,Paper

I)found that the spectra of normal and MSPs show great similarities at frequencies up to1.4GHz,

a conclusion which was recently con?rmed by Toscano et al.(1998;hereafter TBMS)for a large sample of MSPs in the southern hemisphere at frequencies between400and1600MHz.In Paper I we also concluded that MSPs tend to be less luminous compared to normal pulsars.They are also found to exhibit narrower emission beams than expected from a period scaling based on data of normal pulsars.Xilouris et al.(1998;hereafter Paper II)noted that pro?les of MSPs develop much less with frequency and often also in an unusual way when compared with a canonical behaviour determined from normal pulsars(Rankin1983,Lyne&Manchester1988).Studying a very large sample of polarization pro?les of MSPs for the?rst time in Paper II,it was also shown that most MSP polarization position angle swings appear much?atter than those of normal pulsars.This observation was recently con?rmed by Sallmen(1998)and Stairs et al.(1999).Their results are

also in agreement with Paper II’s conclusion that MSP pro?les often exhibit a high degree of po-larization which remains almost unchanged up to1.4GHz(i.e.the highest frequency used in both studies).

Although the data already suggest that the emission mechanism for normal and MSPs are essentially identical(see also Jenet et al.1998),there are prominent di?erences in their emission properties,which could be caused by the di?erent evolutionary history(e.g.the existence of addi-tional pulse features in a large fraction of MSPs,see Paper I&II).The most promising approach to further investigate this question is a detailed multi-frequency study.In addition to the data presented in Paper I and II,recent studies provided new high-quality data for various frequencies below2GHz,i.e.Sallmen(1998),Stairs et al.(1999)and TBMS.In contrast,observations of MSPs at frequencies above2GHz are scarce.The examples which can be found in the literature are sum-marized in Table1.Indeed,prior to the observations presented here,only?ve MSPs have been detected above3GHz,viz.PSRs J0437?4715,J1022+1001,J1713+0747,B1855+09and B1937+21 (see Tab.1).Based on this small sample,Kramer(1998)noted that in various respects the emission properties of MSPs up to5GHz tend to mimic those of normal pulsars at very high frequencies.

A study of this apparent trend is essential in understanding the physics of the emission mechanism not only in MSPs but in normal pulsars as well.

The limited number of MSP detections at high radio frequencies prior to this work can be mainly attributed to the fact that due to the decrease in?ux density at higher frequencies,large collecting area and wide observing bandwidths are necessary to obtain su?cient sensitivity to study the emission properties in detail.Although larger bandwidths are often available in principle,the detection of short-period pulsars over large bandwidths is often hampered by the signi?cant amount of dispersive smearing incurred by incoherent detection schemes.Recently,however,a coherent de-disperser has been installed at the100-m radio telescope of the MPIfR in E?elsberg,which provides bandwidths of up to112MHz.Its combination with a large telescope sensitivity makes this site ideally suited for observations of MSPs at high frequencies as shown here.

In this paper we present the?rst observations of a large sample of MSPs at frequencies of2.7 GHz(λ11cm)and4.9GHz(λ6cm).These are the?rstλ11cm observations for almost all MSPs. In this work,we also more than double the number of detections atλ6cm.A description of the observing system is given in Sect.2.Our new?ux measurements presented in Sect.3extend the known spectra of MSPs to the highest frequencies studied so far.In Sect.4we compare our pulse pro?les with low frequency measurements in search for similar frequency dependencies as found for normal pulsars.After studying the polarization properties for a number of sources up to5GHz in Sect.5,we discuss these results and their implications in Sect.6.

2.Observations

All data presented in the following for frequencies above1GHz are the result of observations carried out between July1997to October1998with the100-m E?elsberg radio telescope operated by the Max-Planck-Institut f¨u r Radioastronomie,Bonn,Germany.The observing system used for 1.4GHz was almost identical to the one described in detail in paper I.However,in contrast to Paper I,all pro?les presented here were obtained with the E?elsberg-Berkeley Pulsar Processor (EBPP),a coherent de-disperser.The EBPP obtains signals of two circular polarizations at an intermediate frequency(IF)of150MHz provided by the receiving systems and converts these to an internal IF of440MHz.A bandpass of,at maximum,112MHz is split into four portions for each of the two circular polarizations,which are mixed down to baseband.Each portion is then sub-divided into eight narrow channels via a set of digital?lters(Backer et al.1997).Their outputs are fed into de-disperser boards which in turn perform an on-line coherent de-dispersion.In total 64output signals(or128if full polarization is desired)are detected and integrated in phase with the topocentric pulse period.Sub-integrations of typically180s are transferred to the controlling computer for further o?-line reduction.The total bandwidth of the system is determined by the dispersion smearing of the individual source at the observing frequency and can be up to112MHz. When all four Stokes parameters are requested,the bandwidth of the EBPP is limited to28MHz.

The2.7GHz observations employed a cooled HEMT-receiver operating over an80MHz band-width.The system temperature during the observations was about40K on the cold sky with a telescope gain of about 1.5K Jy?1,comparable to that at1.4GHz.At4.9GHz we used a highly sensitive HEMT receiver with a system temperature of25K on the cold sky whilst the telescope gain is1.45K Jy?1.This receiver provided either an IF of750MHz with a bandwidth of500MHz or an IF of150MHz with a200MHz bandwidth.For most of the observations,we used the narrow band con?guration fed into the EBPP.For some low DM pulsars,we also used an incoherent detection system,i.e.the E?elsberg Pulsar Observing System(EPOS),connected to a80-200MHz multiplying polarimeter in order to obtain an even wider bandwidth than provided by the EBPP.A similar set-up was used particularly for polarimetric observations at2.7and4.9 GHz.For a description of this observing mode we refer to Kijak et al.(1997).The observations are summarized in Table2.

For comparison with lower frequency data we also present some?rst results of E?elsberg observations made at820MHz and1200MHz with the EBPP.The HEMT receiver used for these observations is tunable between800and1300MHz and has a system noise temperature of about 60K on cold sky,providing a150MHz IF connected to the EBPP.Due to the small number of observing sessions,reliable?ux measurements are not available for these particular observations. For all other frequencies,?ux density calibrations were performed in the scheme detailed in Paper I,https://www.wendangku.net/doc/9417412658.html,paring the pulse energy to the output of a switch-able noise diode,which itself was calibrated based on observations of standard?ux calibrators,such as3C123,3C295and NGC7027 (Ott et al.1994).

The selection of millisecond pulsars to be observed was mainly based on considerations about integration time available in a given LST range and the strength of the sources measured at1.4 GHz.Guided by our measurements presented in Paper I,we typically selected those sources which show peak?ux densities of～20mJy or larger at1.4GHz,i.e.we did not make any selection based on spectral index.

3.Flux densities and spectra at high frequencies

The spectral indices calculated in Paper I were based on only those high frequency data which were available at that time.The extension of the frequency coverage to more than a decade of radio spectrum presented in this paper allows us now for the?rst time to study the spectra in search for a steepening in the previously?tted power law spectra as is often observed for normal pulsars around1GHz(e.g.Malofeev et al.1994).

Comparing the results of Paper I to those of TBMS,we?nd that,with the exceptions of PSRs B1620?26,J1643?1224and J2145?0750,all of the derived spectral indices are consistent within the measurement uncertainties.For the three aforementioned pulsars,TBMS’s new measurements at frequencies below1GHz di?er from those values in the literature used for Paper I.The low frequency data of TBMS represent a very large sample of measurements,and thus they should average out scintillation e?ects more e?ectively than previous studies might have done.Our?ux measurements presented in Paper I agree with those of TBMS at the overlapping frequencies,and we adopt TBMS’s results for the low frequencies.We also include their1660MHz?ux densities in the spectra presented here.For some pulsars,we add?ux densities from Stairs et al.(1999)and also results of previously unpublished measurements made at a frequency of820MHz at the43-m telescope of the National Radio Astronomy Observatory4in Green Bank.The observing setup and calibration procedure of the latter observations,carried out in April1997and1998,are identical to those described by Foster et al.(1991).For PSR J2145?0750we also include a?ux measurement made at102MHz by Kuzmin&Losovsky(1996).The high frequency?ux measurements made at E?elsberg typically represent a number of observing sessions of30–60min integration time for each source.This is su?cient to determine a reliable?ux density,since interstellar scintillation e?ects are greatly reduced in amplitude compared to lower frequencies(Malofeev et al.1996).The mean?ux densities,Sν,are summarized in Table3.Resulting spectra are presented in Fig.1(for low frequency data see also Paper I and references therein).Spectral indices were obtained for all observed pulsars by a weighted least-squares?t of the power law expression Sν∝ναand are quoted in Table3.Those sources,which were not detected at2.7or4.9GHz,but for which interesting upper limits on the?ux densities can be derived,are collected in Table4.

The?rst fact which becomes evident from studying Fig.1is that most MSP spectra can be

essentially?tted by a single power law.This is an interesting result given the variety seen in normal pulsar spectra(e.g.Malofeev et al.1994).The fact that a simple power law seems to adequately describe MSP spectra well is visible from the di?erence in spectral indices,?α,derived for power laws separately?tted to data below and above1.4GHz(see Table3)and from the consistency of the spectral indices presented here and in Paper I.Similarly,for pulsars which are common both to our and TBMS’s study,the spectral indices are in good agreement,even though our uncertainties are often smaller due to the larger frequency coverage.The only exception is PSR J1024?0724,for which our observations at4.9GHz imply that its spectrum is?atter than found by TBMS(i.e.a spectral index of?1.4±0.1compared to TBMS’s?1.70±0.12),although it is also well represented by a simple power law.

Given that the spectral indices presented here do not di?er signi?cantly from those in Paper I for all studied sources,we do not expect a change in any of the conclusions drawn in Paper I. Indeed,combining the results of this paper,Paper I and those of TBMS,we still derive a mean spectral index for Galactic?eld MSPs closer than1.5kpc of?1.76±0.14.Obviously we have no reason to believe that the sample of MSPs studied at high frequencies in this paper comprises a special sub-sample of MSPs.In fact,although we did not apply any special criteria to select our sources(apart from a modest peak?ux density at1.4GHz),we detected essentially all MSPs which we tried to observe.The derived upper limits for the non-detections listed in Tab.4are consistent with the?ux densities expected from power law?ts made to the lower frequency data.

4.MSP pro?les at multiple frequencies

In this section we discuss the frequency development of MSP pro?les,viz.their relative arrival time at various frequencies,the change in pro?le and component width,the change in component separation and also the change in relative component amplitudes.For this purpose we align pro?les according to their barycentric arrival times at various frequencies using the TEMPO software pack-age(Taylor&Weisberg1989).This time alignment was performed in a similar way as for pulsars ?rst described by Foster et al.(1991)and later detailed in Kramer et al.(1997),i.e.constructing noise-free templates by describing the pro?le as the sum of a number of Gaussian components (e.g.Kramer et al.1994).In the ideal case,this procedure is perfectly suited for multi-frequency timing measurements.In order to produce a template for an additional observing frequency only the relative amplitudes and widths of the components are adjusted while their locations are kept ?xed.As the chosen?ducial point is therefore the same at all frequencies,a comparison of the pulse times-of-arrival(TOAs)at di?erent frequencies is possible in an unbiased way.The TOAs are corrected for dispersion delays according to their nominal dispersion measures(see Paper I& II and references therein)and then compared to a timing model for the particular source.During this procedure,we usually?t only for the pulse phase,but we also studied the e?ects of adjust-ing the dispersion measure for some cases.Only changes within the nominal uncertainties of the known timing solutions were observed,so that dispersion measures were later kept?xed to their

low frequency values.The results are presented in Figs.2–14,where we add low frequency data taken from the European Pulsar Network(EPN)data base which is freely available on the World-Wide-Web5(Lorimer et al.1998).References to the authors who generously contributed these pro?les to the EPN archive,are given in the corresponding?gure captions.The pro?les of the new measurements presented here are also freely available now from the EPN database.We point out that for the EPN-pro?les timing information was not available.In these cases,alignments were done visually by bringing the outer edges of the lower frequency pro?les in match with the time-stamped data.Before discussing the pro?le development in general,we make a few notes on the individual sources.

In total we present pro?les for?fteen MSPs.For?ve pulsars this is the?rst detection around 5GHz(i.e.J1012+5307,J1024?0719,J1518+4904,J1643?1224and J1744?1134)and also for nine sources at2.7GHz(i.e.J0621+1002,J0751+1808,J1012+5307,J1518+4904,J1640+2224, J1643?1224,J1713+0747,J1744?1134and J2145?0750).Among the eleven MSPs now detected at a frequency as high as5GHz,PSR J0437?4715is the only other source,which is not visible from E?elsberg.In order to complete this study,we therefore include data taken from the EPN data base provided by Bell et al.(1997)and Manchester&Johnston(1995)(see Fig.3).For all sources but PSRs J0751+1807and J1640+2224high radio frequency pro?les are aligned with data obtained at lower frequencies.For the latter two MSPs low frequency data were not available, so that we present their2.7GHz pro?les separately in Fig.15.We also include PSR J0218+4232 here,since our recent measurement at1.41GHz represents the highest frequency for which a pro?le is available.Since the number of observations is too small to exclude scintillation e?ects for this source,we do not quote a?ux density for PSR J0218+4232,but we align its pro?le visually with data from the EPN archive provided by Stairs et al.(1999).Finally,for PSRs B1620?26and J2051?0827we present only spectral information,since the obtained data are su?cient for reliable ?ux measurements but the low signal-to-noise ratio(S/N)of the pro?les does not add any additional knowledge to their pro?le development with frequency.All870,1220and1410-MHz pro?les aligned with the high frequency data were measured in E?elsberg with the EBPP.The575-MHz pro?le of PSR J1012+5307was obtained at Green Bank with the Green-Bank-Berkeley-Pulsar-Processor (Sallmen1998),which is identical to the EBPP.

In the following we brie?y comment on each individual source observed.For this discussion we do not arrange the sources in the usual order of increasing right ascension,but will sort the objects into three groups,i.e.isolated,fast spinning and slowly spinning binary MSPs,respectively.This is done because in Paper I we have found some indications that pro?le properties could be correlated with the mass of the companion star or,alternatively,with the spin period of the pulsar.Although we do not?nd support for these tentative conclusions of Paper I here,we adopt this scheme for the merit of future discussions since it has been suggested(e.g.Chen&Ruderman1993)that the evolutionary history may indeed be re?ected at the emission properties.

4.1.Isolated MSPs

In Paper I we con?rmed the suggestions made by Bailes et al.(1997)that isolated MSPs tend to be less luminous than binary MSPs.Among the eleven sources detected at4.9GHz,three MSPs are isolated objects,i.e.PSRs J1024?0719(Fig.7),J1744?1134(Fig.11)and B1937+21(Fig.13). Pulsar B1937+21is an extraordinarily luminous source,and PSR J1024?0719has a fairly?at spectrum as discussed above.By comparison,the spectrum of PSR J1744?1134is signi?cantly steeper(see Tab.3),while this source also has a smaller luminosity than the average isolated MSP (Paper I).We note that the pro?le of PSR J1744?1134(Fig.11)scarcely changes between410 and4848MHz,although the presently available S/N prevents a detailed investigation of the high frequency data.This is consistent with the pre-cursor,which is detected at410,606and1408 MHz,located at a constant separation of about130?prior to the pulse center.In stark contrast, the pro?le of PSR J1024?0709changes dramatically with frequency as visible from the inversion of the component amplitude ratio.The central component visible at low frequencies weakens at high frequencies,so that only the leading component remains with a weak intensity tail at4.9GHz(see Fig.7).

The pro?le development of PSR B1937+21over the whole spectral range is more di?cult to assess,since at low frequencies the pro?le is severely scattered by inhomogeneities in the ISM. Nevertheless,inspecting the320MHz pro?le presented by Cordes&Stinebring(1984)it seems that the trailing component of the main pulse,which is clearly visible at1.4GHz,is the dominant feature at this low frequency.It is completely disguised by the scattering tail at intermediate frequencies, gradually weakens between1.4,1.7and2.7GHz and eventually fades towards high frequencies (cf.Fig.13).At the same time the amplitude ratio of main and interpulse increases gradually with increasing frequency.While the?rst component of the main pulse appears unchanged and featureless over the whole spectrum,the second component gradually weakens relative to the main pulse(cf.Cordes&Stinebring1984).This additional component is most likely not associated with the observed giant pulses of this pulsar(Jenet et al.,in preparation)which appear generally delayed relative to the position of the main pulse(Backer1995;Cognard et al.1996;Sallmen1998).

4.2.Fast rotating binary MSPs(P<10ms)

The steep spectrum of PSR J0218+4232combined with its large ratio of dispersion measure to period makes it a di?cult source to observe at high radio frequencies.Consequently,the1.4-GHz pro?le shown in Fig.2is the highest frequency pro?le available.Even at1.4GHz this pulsar still emits over essentially the full pulse period.Although wide pro?les are also observed in case of normal pulsars(e.g.PSR B1831+04;Lyne&Manchester1988),the pulse shape of PSR J0218+4232 and its frequency development are interesting.Indeed,the central component in the main pulse feature becomes apparently stronger at higher radio frequencies.At the same time,the weaker pulse component preceding the main pulse obviously fades with frequency.Stairs et al.(1999)

present polarization data of this very weakly polarized pulsar.A determination of the viewing geometry is thus di?cult,and Stairs et al.(1999)suggest an aligned rotator with a wide beam just being grazed.

The unusually complex pro?le of PSR J0437?4715also develops with frequency(see Fig.3and also Fig.5of Navarro et al.1997)in a manner which is di?erent to what is typically observed for normal pulsars.In normal pulsars the outer“conal”components become stronger with increasing frequency compared to the central“core”component,which eventually even fades away(Rankin 1983,Lyne&Manchester1988).In contrast,in the case of PSR J0437?4715the amplitude ratio of the central core to its outer conal components increases from about2to2.5at0.4GHz to more than13at4.6GHz.Nevertheless,the outer components are still traceable at this frequency,which allows us to determine that their separation and the pro?le width are apparently una?ected by a change in frequency.We note however that the position of the core component shifts from a slightly o?-center position to a more centered(earlier)position at high frequencies.This behaviour is comparable to that of the core component of PSR B0329+54(e.g.Kramer et al.1997)which also shows similarities in the overall pulse shape and polarization characteristics.

Figure5shows a clear pro?le development for PSR J1012+5307between0.6and4.9GHz which,however,does not a?ect the pro?le width or component separation.The trailing component of the main pulse becomes the dominant feature above1.4GHz.At the same time,the?rst interpulse feature separated by about120?from the main pulse brightens to about80%of the main pulse amplitude at2.7GHz and is–as far as it can be inferred from the given S/N–as strong as the main pulse at4.9GHz.This trend has already been noticed in Paper II.

The small misalignment in Fig.9of the pro?les of PSR J1643?1224between4.9GHz and the low frequencies is not signi?cant given the relatively low S/N at4.9GHz.Overall,the pro?le seems to change very little between low and high frequencies.Indications of a possible scattering tail in the436MHz pro?le(Bell et al.1997)prevent a careful comparison with higher frequency data(see also Sect.4.4).

The pro?le of PSR J1713+0747(Fig.10)maintains a highly asymmetric shape throughout the whole spectrum.The tail-like feature prominent at low frequencies becomes weaker and almost undetectable at high frequencies(see also Kijak et al.1997).The time alignment suggests a simultaneous arrival at all frequencies.

For PSR B1855+09a distinct pro?le evolution has already been demonstrated by Thorsett &Stinebring(1990)and was extensively discussed in Paper II.Here,we only emphasise that the separation of the main pulse components shrinks signi?cantly between430MHz and2380MHz (see Fig.4of Thorsett&Stinebring1990).This behaviour is comparable to that for the normal pulsars like PSR B1133+16,which also shows the same reverse in amplitude ratio in its outer main pulse components as PSR B1855+09(Phillips&Wolszczan1992).In fact,PSR B1855+09is one of the very rare cases where a MSP shows a frequency development in a manner known from normal pulsars(e.g.Rankin1983and Lyne&Manchester1988).Consistent with that impression

is the observation that PSR B1855+09is also among the very few MSPs,where the position angle is not?at but shows an S-like swing(cf.Paper II and references therein).In this context it is very interesting to compare the pro?les observed at1.4GHz and at4.9GHz(Kijak et al.1997) as done in Fig.12.Relative to the main pulse,the interpulse brightens at high frequencies and bifurcates into two distinct components.Therefore,in both main pulse and interpulse the central component has a steeper spectrum than the outer components.Applying the knowledge gained from normal pulsars(as it is apparently justi?ed for this MSP)this frequency behaviour implies that the observed main and interpulse are created at di?erent magnetic poles.In other words,PSR B1855+09is an orthogonal rotator,which is perfectly consistent with the constant separation of main and interpulse at all frequencies(see also Foster et al.1991)and the observed Shapiro delay (Ryba&Taylor1991;Kaspi,Taylor&Ryba1994).

The2.7-GHz pro?les of PSRs J0751+1807and J1640+2224shown in Fig.15are very similar to those presented in Paper I and II for1.4GHz.As described in Paper II,the amplitude of the ?rst pulse component of PSR J0751+1807decreases compared to that of the trailing part,while the central part seems to disappear completely with increasing frequency.The width of the coherently de-dispersed pro?le presented here is consistent with those of the pro?les at430MHz and1410 MHz(Lundgren,Zepka&Cordes1995,Paper I&II)and the coherently de-dispersed one at1410 shown by Sallmen(1998).

4.3.Slow rotating binary MSPs(P>10ms)

This group of pulsars is distinct from the previous one by having relatively massive binary com-panions,https://www.wendangku.net/doc/9417412658.html,rger than0.5M⊙.All pulsars discussed below are in fact considered to form a single family of sources which are spun-up predominantly during a wind-driven accretion phase,i.e.pro-ducing a non-monotonic random walk in the angular momentum transferred to the recycled pulsar (in contrast to disk accretion with monotonic spin-up;see van den Heuvel1994,Arzoumanian, Cordes&Wasserman1999).

The?rst of this family is PSR J0621+1001for which we present pro?les in Fig.4.The pro?le remains unchanged between410MHz and2695MHz and also the component separation and component amplitude ratio are remarkably constant(see Sect.4.4).

When discussing the pro?le development for PSR J1022+1001,one has to keep in mind that this source is among the sample of MSPs known to exhibit pro?le instabilities.For a detailed discussion we refer the interested reader to Kramer et al.(1999).Pulsar J1022+1001is another example where a MSP exhibits a distinct but unusual pro?le development with frequency.The trailing component,the dominant feature at370MHz,is on average weaker than the leading component at430MHz,but dominates the pro?les up1.4GHz(cf.Fig.6).Then,towards high frequencies,this component weakens again rapidly,being only barely detectable at4.9GHz(see also Kijak et al.1997).A similar case is PSR J1518+4904(Fig.8)where the intensity of the distinct

central component weakens between370and610MHz,but becomes stronger again at higher frequencies,until it is the dominant feature at4848MHz.At the same time,the tail-like feature disappears similarly as in the PSR J1713+0747pro?le.Thus,the leading component appears to have a maximum in its?ux density spectrum around400MHz,which would be consistent with the interpretation that the overall spectrum discussed before shows a low frequency turn-over.

Among the strongest pro?le developments with frequency is the frequency behaviour of PSR J2145?0750:while the leading component is rather weak at102MHz(Kuzmin&Losovskii1996), it becomes the dominant one at higher frequencies.The trailing pulse peak,strongest at102MHz, weakens at frequencies of1.4GHz and higher,and is hardly visible at4.8GHz.The central pulse component does not seem to develop at all as it remains the weakest component throughout the whole observed spectrum.Unlike the normal pulsars,Fig.14indicates that both the pro?le width and the component separation hardly change between100and4850MHz.Kuzmin&Losovsky (1996)however claim to observe an increase in component separation.The fact that the trailing pro?le feature6consists of two overlapping components(cf.Paper I and Sallmen1998)makes a clear statement di?cult although Sallmen(1998)?nds support for a slight increase in component separation.An inspection of all coherently de-dispersed pro?les available between410and1410 MHz(Sallmen1998;Stairs et al.1999;this work)suggests that neither the component separation nor the pro?le width change signi?cantly(see next section).Consistently,the prominent pre-cursor does not change its position as discussed in Paper II.The clear pro?le change between102and436 MHz raises the question as to whether this is common to all MSPs at low frequencies.It would be interesting to obtain high quality measurements of a number of MSPs at these frequencies.

4.4.General frequency behaviour

From the sample of pulse pro?les presented in this paper,two obvious but not necessarily expected facts are evident:?rst,all pro?les align very well up to the highest frequencies,and second, for some pro?les we observe almost no shape changes at all(e.g.PSRs J0621+1002or J1744?1134), while a few pro?les change dramatically which can be most easily described by complete reversals in amplitude ratios of pro?le components(e.g.PSRs J0751+1807or J2145?0750).The particular examples of PSRs J1518+4904and J2145?0750demonstrate that pro?le changes might occur at frequencies below400MHz.However,since such data sets are scarce,we can base any discussion only on the pro?le developments at frequencies of400MHz and above.At the high frequency end between2.7and4.9GHz the observed changes are fairly small,although some development can be still observed in a few cases(e.g.PSR J1022+1001).In total however,we apparently observe an end of pro?le development around3GHz.This frequency seems to be somewhat lower than the typical frequency for normal pulsars which lies usually between5and10GHz(Xilouris et al.1996,Kramer et al.1997)although it is not inconsistent(cf.Sieber,Reinecke&Wielebinski1975).Excluding

some possible low frequency pro?le changes,which may also include scattering e?ects imparted on the pulse pro?le,the data shown here apparently represent the whole frequency development of MSPs in the radio spectrum.

In this light,it is worth emphasising that there is an obvious lack of a change in component separation and MSP pro?le width.This is a signi?cant di?erence to the behaviour of normal pulsars. In order to demonstrate this behaviour clearly,we followed the example of Foster et al.(1991)by measuring the component separation or,if distinct components were not visible,the pro?le width (at a50%level)as a function of frequency,ν,for all MSPs discussed in this work(see Table6and Fig.17).For measuring pro?le widths,we followed the example of Paper I and measured a50% intensity level with reference to the peaks of the outermost resolved components.Consequently, reference points used in this work and that by Foster et al.(1991)di?er for two sources common in both samples,PSRs B1620?26and B1855+09,while for PSR B1937+21both results are in excellent agreement.In addition to the shown pro?les we also used data from the literature(e.g.Paper I),if appropriate(see Tab.6),and marked coherently(incoherently)de-dispersed pro?les with a circle (triangle),respectively.We note that a50%-width is not an ideal measure in some cases(e.g.PSRs J1643?1224and J1713+0747where the existence of additional pulse components at low frequencies obviously in?uence the measurements),but o?ers the possibility for a direct comparison to results published for normal pulsars.For this purpose,the obtained values are modelled to an expression W(ν)=a0+a1·νγby least-squares-?ts as done for normal pulsars by Thorsett(1991)and Xilouris et al.(1996)(see Fig.17).Obtained indices,γ,are given in Tab.6.For most sources,the frequency dependence is so weak that a0and a1are highly correlated.We therefore quote a width/separation interpolated for1GHz instead.We also emphasise that although we measure50%pro?le widths in some cases and component separations in others,we can readily compare the distribution of indices,γ,derived for MSPs and normal pulsars,since both pro?le width and component separation essentially lead to very similar frequency dependencies(cf.Thorsett1991and Xilouris et al.1996). The comparison of histograms is made in Fig.18,which demonstrates very clearly the strikingly di?erent behaviour for both types of objects.A Kolmogorov-Smirnov test even yields a probability of10?8that both samples are drawn from the same parent distribution.

5.Polarization

For the few of the strongest sources at high frequencies or those with a relative low dispersion measure–period ratio,we obtained polarization information between1.7GHz and4.9GHz using the EPOS and the EBPP(see Sect.2).Observations are summarized in Table5,where we quote bandwidth,dispersion smearing and the degree of linear and total polarization(i.e.after adding linear and circular power in quadrature).The pro?les obtained are essentially unpolarized within the uncertainties and will be thus shown elsewhere.This result is interesting as many MSPs show a modest or even high degree of polarization at lower frequencies(Paper II,Sallmen1998).For comparison we compile data from Paper II,Manchester&Johnston(1995),Navarro et al.(1997),

Sallmen(1998),Stairs et al.(1999),Thorsett&Stinebring(1990),and this work,and plot the degree of polarization for the linearly polarized intensity as a function of frequency in Fig.16.In Tab.6we list the de-polarization index,?,which was obtained by?tting the degree of linear polarization as a function of frequency to a simple power law,i.e.ΠL∝ν?.Although the sample is rather small,the data suggest that those sources which are highly polarized,de-polarize rapidly,while the weakly polarized MSPs de-polarize even further but apparently with a slower rate.We stress that the error bars only re?ect instrumental uncertainties which at2.7and4.9GHz nevertheless include estimates of a possible de-polarization due to a bandwidth averaging(cf.Melrose&Macquart1998).This is important since measuring the polarization of MSPs apparently involves larger uncertainties compared to studies of normal pulsars,since we have discovered in Paper II that the polarization characteristics can show signi?cant temporal variations–a result which was later con?rmed by Sallmen(1998;cf.in particular PSRs J1713+0747and J2145?0750)and Stairs et al.(1999).As a result,the degree of polarization can vary signi?cantly for some sources,e.g.occasionally a pro?le is observed which is much more strongly polarized than the average one.Single pulse studies are needed to address this question further,but we believe that an average of many independent observation leads to a representative value.

6.Discussion

We have demonstrated that the time alignment of MSP pro?les presented in our work for frequencies between0.9and4.9GHz7is possible without taking into account timing irregularities caused by e?ects such as aberration,magnetic?eld sweep-back,magnetic multi-poles or retardation. Complementary MSP pro?les borrowed from the literature for the sake of completeness of our work were aligned by visual inspection with the high frequency pro?les.All MSPs have been regularly timed at various observatories in the frequency range between100and1400MHz,which overlaps with the frequency coverage in our study.Irregular frequency dependent timing behaviour has not been reported so far8(see e.g.Cordes&Stinebring1984for PSR B1937+21as the most strongest test).We therefore conclude that,within the resolution and uncertainties of our measurements,we do not observe any abnormal frequency dependent timing behaviour over whole the radio spectrum observed for MSPs.

6.1.Magnetic?eld structure

This absence of any timing irregularities directly re?ects on the magnetic?eld topology in the radio emission region,as such could indicate the existence of aberration e?ects or magnetic multi-poles(cf.Phillips&Wolszczan1992,Kramer et al.1997).Hence,an undisturbed,dipolar structure of the magnetic?eld would be an important result for pulsar emission physics,since the existence of non-dipolar?eld components has been speculated by many authors(e.g.Chen&Ruderman1993) in the past and employed to account for unusual emission phenomena.Among these are(a)the smaller than expected emission beams of MSPs in comparison to normal pulsars,(b)the distorted polarization position angle curves which often exhibit?at slopes,(c)the abnormal pro?le frequency development and(d)polarization properties(cf.Paper I and II and references therein),or also(e)”notches”such as identi?ed in the pro?le of PSR J0437?4715(Navarro&Manchester1996).

Usually,?eld components of higher order than dipolar existing at the surface decay rapidly with increasing distance to the neutron star,so that their signi?cance may be low in the radio emission region.In addition,there are however two direct contributions to the toroidal component of the magnetic?eld:displacement current(as a rotating dipole in vacuum also has“swept back”?eld lines)and the current of the outsreaming plasma.In MSPs there must be a considerable toroidal component present virtually everywhere in the magnetosphere(its relative strength increases as (r/R LC)for small r),so that at the light cylinder all the contributions to the magnetic?eld (vacuum dipole poloidal,vacuum dipole toroidal and due to the?owing current)are of the same order.

Given the compactness of MSP magnetospheres these e?ects could be very well relevant for the observed emission properties.For example,the light cylinder radius,R LC,which ultimately limits the pulsar magnetosphere,is only70km for PSR B1937+21.Hence,any non-zero emission height may be already at a signi?cant fraction of R LC.Nevertheless,as we have seen,all MSP multi-frequency pro?les align perfectly between0.4and5GHz.This can be interpreted in two ways.Either the magnetic?eld in the whole emission region is purely dipolar,i.e.neither higher order multi-poles nor signi?cant toroidal?eld components are present,or the emission region is so compact that we would not notice any deviation from a dipolar structure,i.e.all radio frequencies are virtually emitted from the same location.

6.2.Size of the emission region

With a typical timing accuracy of about50μs depending on resolution and S/N,the simultane-ous arrival of the multi-frequency pro?les sets a limit to the size of the emission region corresponding to a light-travel distance of only2.4km.Estimating the size of the emission region in this manner is rather an oversimpli?cation due to possible non-linear propagation e?ects in pulsar magneto-spheres(e.g.Barnard&Arons1986,Beskin,Gurevich&Istomin1993).Therefore,the size of the emission region is also often estimated from the change in pro?le width(e.g.Cordes1978,Phillips

&Wolszczan1992,Xilouris et al.1996).This approach is based on the observation that the com-ponent separation and pro?le width of normal pulsars typically decreases strongly from low to high frequencies(see e.g.Sieber,Reinecke&Wielebinski1975or Phillips&Wolszczan1992).This behaviour has been explained by the assumption of a frequency dependent location of the emission region within the magnetosphere,a so-called radius-to-frequency mapping(RFM,Cordes1978). The location is changing with frequency either in altitude above the surface or in radial distance from the magnetic axis.(The latter appears less likely given that pro?le width and component separation change simultaneously.)With the additional assumption that the pro?le wings re?ect the extent of the open(dipolar)?eld line region,the width can be directly converted into the height and size of the emission region(cf.Paper I).

An alternative explanation for the narrowing of the pro?le width has been given in terms of a propagation e?ect involving refraction e?ects and birefringence of the plasma above the polar cap (Barnard&Arons1986,McKinnon1997,Gallant1998,von Hoensbroech,Lesch&Kunzl1998). In this model the emission is created at a single altitude,but not all emission can leave the mag-netosphere directly.Instead,one polarization mode?rst propagates through the plasma before it escapes the magnetosphere at a certain radius.The extent of the open?eld line region at this particular,frequency dependent altitude will then be the factor which determines the observed pro?le width.Gallant(1998)gives for the escape radius of the fast O-mode,r esc,an expression

1/3ν?2/3GHz(1)

r esc

P

where R?is the neutron star radius,P the spin period and B12the surface magnetic?eld.Interest-ingly,unless the multiplication factor between the primary and secondary pair plasma,h=104h4, and theγ-factor of the secondaries,γ=102γ2,are very low,this escape radius lies outside the light cylinder radius for most of the MSPs.If the given approximation is correct,one may expect as a consequence to observe only one orthogonal mode of the polarization state.This is generally not the case.Even in the case of normal pulsars,the model implies a separation of the orthogo-nal modes in pulse phase,but there is clear evidence that the modes occur simultaneously at the same phase(e.g.McKinnon&Stinebring1998).In Paper II this occurrence of orthogonal modes was also demonstrated for MSPs,where we observe a discontinuity in the swing of the position angle and a drop in the degree of linear polarization for some sources(see also Sallmen1998and Stairs et al.1999).Besides,according to the above expression the pro?le width should exhibit a frequency dependence of∝ν?2/3(modulo some possible geometrical e?ects).In stark contrast, our observations suggest a minimal frequency dependence for pro?le widths of MSPs.The pro?le width reaches saturation either at very low radio frequencies or does not change with frequency at all.

It is important to emphasise that both models,RFM and birefringence,predict a change in pro?le width with frequency.The di?erence,however,is that in the RFM model the pro?le width re?ects the altitude at which the emission is created,while in the birefringence model it is the altitude where the emission escapes the magnetosphere.The birefringence model has certainly the

advantage that it can explain the occurrence of orthogonal polarization modes in a natural way. Moreover,the RFM model requires the assumption that the overall broad-band pulsar emission mechanism exhibits also some narrow-band features in order to produce a distinct mapping of fre-quency to altitude,which seems di?cult to ful?l simultaneously.Obviously,it appears impossible to decide between these models simply on the basis of pro?le width https://www.wendangku.net/doc/9417412658.html,ing additional timing data,we can only set an upper limit on the size of the emission region,but the data are in fact con-sistent with a single emission altitude(see also Phillips&Wolszczan1992and Kramer et al.1997). Blaskiewicz,Cordes&Wasserman(1991)and von Hoensbroech&Xilouris(1997)have tried to determine any dependence of the emission height on frequency by analysing polarization data of normal pulsars including relativistic corrections to the rotating-vector-model(Radhakrishnan& Cooke1969).Although this method yields negative emission heights for5out of36sources(Blask-iewicz et al.1991,von Hoensbroech&Xilouris1997),and although most of the results are,within the(often large)uncertainties,consistent with a constant emission altitude,there is an interesting trend visible in the data.According to the interpretation of the Blaskiewicz et al.model,this trend suggests a weak but non-zero RFM.However,any evidence has yet to be obtained and a single emission altitude is still consistent with the data.The pulsar width data of MSPs presented here at least indicate a very weak or even non-existing RFM for these sources,but this may not be surprising given the compactness of their magnetospheres—even if RFM is present in normal pulsars.

6.3.De-polarization and pro?le width

As mentioned before,the occurrence of orthogonal polarization modes is a natural consequence of the birefringence model.An overlap of orthogonal modes leads generally to a de-polarization of the average pulse pro?le.The emission of normal pulsars is in fact well known to exhibit a strong de-polarization with frequency(e.g.Manchester,Taylor&Huguenin1975)and observations at very high radio frequencies(i.e.32GHz)suggest that all pulsars become de-polarized at su?ciently high frequencies(Xilouris et al.1996).Among other models(see e.g.Xilouris et al.1994for a summary), it was therefore suggested that an increased occurrence of orthogonal modes at high frequencies may be responsible for the observed de-polarization(Stinebring et al.1984).McKinnon(1997)?nally linked the decreasing pro?le width and the increasing de-polarization as a function of frequency to the same birefringence model.

Our polarimetric pro?les of MSPs discussed in this work suggest that we observe an essentially complete de-polarization of MSPs already at frequencies around5GHz–at least for the limited sample with polarization data up to this frequency.At the same time,even though very little is known about single pulse polarimetry of MSPs(see e.g.Sallmen1998),it is clear that orthogonal polarization modes are present in the emission of MSPs(e.g.Thorsett&Stinebring1990,Paper II, Sallmen1998,Stairs et al.1999).However,the pro?les of MSPs show a strikingly constant width across the observed frequencies.In other words,the de-polarization of MSP emission appears to be

de-coupled from the e?ect of pro?le narrowing.Since MSPs and normal pulsars appear to share the same emission mechanism(cf.Sect.1),we are therefore led to the conclusion that these phenomena are unrelated for normal pulsars as well,at least to zero order.

6.4.Flux density spectra

The apparent simplicity of the observed?ux density spectra may also point to a small size of the emission region,perhaps embedded in a dipolar structure of the magnetic?eld.One could expect that a di?erent?eld geometry or at least a signi?cant change in emission height also alters the e?ciency of the emission process,e.g.due to a change in magnetic?eld strength,curvature radius or plasma densities(see e.g.Kuzmin et al.1986).It is therefore interesting that we very often observe a steepening in the?ux density spectra of normal pulsars but apparently not for MSPs.In fact,at least55%of all45normal pulsars studied by Malofeev et al.(1994)exhibit a break in their power law spectra with a mean break frequency of2.2±0.4GHz.From the twelve MSPs with?ux measurements up to5GHz,only PSR J0437?4715shows a clear steepening in its spectrum above1GHz,while PSRs J1713+0747and J2145?0750are likely cases.Assuming that the fraction of pulsars with double power law spectra is the same for MSPs and normal pulsars,we could expect about six MSPs in our sample to exhibit a steepening spectrum.It is important to note that the statistical signi?cance for this di?erence being real may be still low as indicated by aχ2-test which yields only a60%probability that both samples are di?erent.However,treating those spectra which are consistent with a straight power law as such with a break frequency at zero Hz,we can compare the spectral break frequency distribution of normal pulsars and MSPs.

A Kolmogorov-Smirnov test then yields the result,that both samples are drawn from the same mother distribution with a probability of only2.2%.It is also interesting to compare the mean spectral index derived for MSPs detected at4.9GHz to those of108normal pulsars between1.4 and4.9GHz which were measured with the same observing system by Kijak et al.(1998).The MSP spectral index of?1.6±0.1is somewhat?atter than that of normal pulsars for which the mean spectral index is?1.9±0.2above1.4GHz,although we did not apply any spectral criterion when selecting our sources.

An interesting spectral behaviour was already indicated by the early work of Foster et al.(1991) who studied the spectra of PSRs B1620?26,B1821?24,B1855+09and B1937+21.Their analysis including also low frequency measurements(cf.Fig.1)revealed simple straight power laws from very low frequencies up to a few GHz,without indications of any low-frequency turn-over.In fact, according to Erickson&Mahoney(1985),there is not any indication of a maximum or turn-over in the spectrum of PSR B1937+21above10MHz.The?ux measurement at102MHz for PSR J2145?0750by Kuzmin&Losovsky(1996)shown in Fig.1establishes this trend for yet another source.However,more low frequency?ux measurements are of utmost importance to investigate this question further.

6.5.Pro?le evolution–Cones&Cores

We have reviewed in Paper I that the large number of pre-and post-cursors and interpulses in MSP pro?les is a very signi?cant di?erence to the emission properties of normal pulsars.In Paper II we revealed similarly di?erences in the pro?le evolution of MSPs and normal pulsars.These ?ndings are con?rmed in this work covering a larger frequency range.

The pro?le evolution re?ects the spectral behaviour of individual pro?le components.In the case of normal pulsars,we observe a very clear dependence of the component spectral index on the distance to the magnetic axis(Rankin1983,Lyne&Manchester1988or Kramer et al.1994). Although central components in normal pulsar pro?les can be often associated with so-called“core”components(Rankin1983;Lyne&Manchester1988),the usually steeper spectral index can also be found for some central components which are certainly so-called“conal”components(Lyne& Manchester1988;Kramer et al.1994).Although we can distinguish core and conal components also by their polarisation properties(see Rankin1983)even in the case of MSPs(see Paper II), one should obviously be reluctant to simply identify such obvious di?erences in emission properties directly with di?erent emission processes.Other explanations for the steeper spectrum like a geometrical origin are equally likely(Kramer et al.1994,Sieber1997).Whatever is responsible for the observed patterns in emission properties of normal pulsars,it is clear from the pro?le developments discussed in Paper II and in this work that the canonical picture of strong central components at low and strong outer components at high frequencies does not simply apply to MSPs.Although some examples for this trend can be even found among the sample of MSPs (e.g.PSRs J0751+1807and B1913+16),for many sources this is not true and leads either to no pro?le development at all(e.g.PSRs J0621?1002and J1744?1134)or to one which was classi?ed as“abnormal”(relative to our expectations originating from studies of normal pulsars)in Paper II (e.g.PSRs J0437?4715or J2145?0750).

In some cases where we consider the pro?le development as abnormal,we might have been mislead to this classi?cation by the possibility that we observe a pro?le type which would be classi?ed as“partial cone”,following the terms of Lyne&Manchester(1988;see their Table4).In such a case,like for the normal pulsar PSR B0355+54,only the leading(or trailing)part of the full emission cone is active,so that a core component is located at the trailing(or leading)outer edge of the visible pro?le.As a consequence,this apparent outer(but truly central)component would generally show a steeper?ux density spectrum.Pulsar J0613?0200is almost certainly such a case, since the polarization pro?les suggest that the trailing component is a core,which also shows by far the steepest spectrum(see Sallmen1998and Stairs et al.1999).Therefore,the study of the pro?le development of MSPs shows that un?lled emission beams are certainly present.This fact may help to solve the problems of the undersized emission beams discussed in detail in Paper I and the overall?at position angles which were?rst noted in Paper II(see Sallmen1998).However, we are still left with the fact,that typical patterns in pro?le development are hardly observed for MSPs.

The lack of clear trends visible in the pro?le evolution of MSPs(with frequency)is a good indication that either the emission structures are not as regular as for normal pulsars(e.g.due to un?lled emission beams),or that the formation of recognisable patterns is only possible if the emission region provides enough space.Again,the compactness of the magnetosphere might thus prevent the formation of pro?le components with distinct emission properties.The presence of disturbing e?ects like swept-back magnetic?elds or magnetic multi-poles is still possible but less likely given the good alignment of the pulse pro?les across the frequencies.Under the presumption that the emission mechanism of MSPs and normal pulsars is the same,as supported by the results of Paper I&II and also Jenet et al.(1998),this study of MSPs suggests that the di?erent char-acteristics of core and conal components found for normal pulsars are in fact due to di?erences in emission heights or size of the emission region or due to geometrical or propagation e?ects in the magnetosphere,but not due to a fundamentally di?erent emission process.This conclusion is in agreement with that of Lyne&Manchester(1988)which recently found new support by the work of Manchester et al.(1998),who presented a large number of polarization pro?les of normal pulsars, where“typical”core polarization properties can be sometimes observed in cone components.

7.Conclusions

Considering the frequency independence of the pro?le width and the observed de-polarization of the radiation,MSP emission properties tend to resemble those of normal pulsars only shifted towards higher frequencies.This trend is also consistent with the early termination of the pro?le development in frequency.All these characteristics may be understood in the context of a very compact magnetosphere existing for MSPs which possibly contains only a extremely small emission region.Most likely,these regions are too small to allow for timing irregularities or a signi?cant change in pro?le shape or width or perhaps?ux density spectrum.

While the pro?le width and component separation appear remarkably constant for all frequen-cies,we cannot ultimately decide in favour or against a RFM,which would be certainly weak for MSPs.However,polarization observations for a few sources up to5GHz suggest that the decrease in pro?le width and de-polarization of pulsar emission are not directly related.

We?nd weak indications that the spectra of MSPs may not show the spectral break as often observed for normal pulsars around a few GHz.At the same time,we cannot observe a clear dependence of spectral index of individual pulse components on distance to the pro?le midpoint (and presumably magnetic axis).Nevertheless,features like partial cones as known from normal pulsars seem also to be present for some MSPs.A combination of all available MSP data with the previously shown fact that the radiation of MSPs and normal pulsars is obviously created by the same emission mechanism,leads us to conclude that there is a no direct evidence for a fundamentally di?erent emission process of so-called core and conal components.

Finally,this study demonstrates that for a number of MSPs regular observations at frequencies

above2GHz are easily possible with a wide bandwidth system.Besides studying emission proper-ties,such measurements can provide a useful tool for high precision timing by a determination of disturbing e?ects due to the interstellar weather(Backer&Wong1998).

During this work we made extensive use of the European Pulsar Network data archive.We are thus indebted to all authors who generously contributed their measurements to the database.MK acknowledges the receipt of the Otto-Hahn Prize,during whose tenure this paper was written,and the warm hospitality of the Astronomy Department at UC Berkeley.The authors also bene?ted from stimulating discussions with J.Arons,J.Hibschman,A.Melatos,S.Sallmen,A.Somer,and A.Spitkovsky.Arecibo Observatory is operated by Cornell University under cooperative agreement with the National Science Foundation.

REFERENCES

Alpar M.A.,Cheng A.F.,Ruderman M.A.,Shaham J.,1982,Nature,300,728

Arzoumanian Z.,Cordes J.M.,Wasserman I.,1999,Astrophys.J.,in press(astro-ph/9811323)

Backer D.,Wong T.,1998,in Pulsar Timing,General Relativity,and the Internal Structure of Neutron Stars,eds.Z.Arzoumanian,E.van den Heuvel,J.and van Paradis,North Holland, Amsterdam,in press

Backer D.C.,1995,J.Astrophys.Astr.,16,165

Backer D.C.,Kulkarni S.R.,Heiles C.,Davis M.M.,Goss W.M.,1982,Nature,300,615

Backer D.C.,Dexter M.R.,Zepka A.,Ng D.,Werthimer D.J.,Ray P.S.,Foster R.S.,1997,Publ.

Astr.Soc.Paci?c,109,61

Bailes M.et al.,1997,Astrophys.J.,481,386

Barnard J.J.,Arons J.,1986,Astrophys.J.,302,138

Bell J.F.,Bailes M.,Manchester R.N.,Lyne A.G.,Camilo F.,Sandhu J.S.,1997,Mon.Not.R.

astr.Soc.,286,463

Beskin V.S.,Gurevich A.V.,Istomin Y.N.,1993,Physics of the Pulsar Magnetosphere.Cambridge University Press

Blaskiewicz M.,Cordes J.M.,Wasserman I.,1991,Astrophys.J.,370,643

Camilo F.,1995,PhD thesis,Princeton University

Camilo F.,Nice D.J.,Shrauner J.A.,Taylor J.H.,1996,Astrophys.J.,469,819

高二《甜美纯净的女声独唱》教案

高二《甜美纯净的女声独唱》教案 一、基本说明 教学内容 1）教学内容所属模块：歌唱 2）年级：高二 3）所用教材出版单位：湖南文艺出版社 4）所属的章节：第三单元第一节 5）学时数： 45 分钟 二、教学设计 1、教学目标： ①、在欣赏互动中感受女声的音域及演唱风格，体验女声的音色特点。 ②、在欣赏互动中，掌握美声、民族、通俗三种唱法的特点，体验其魅力。 ③、让学生能够尝试用不同演唱风格表现同一首歌。 ④、通过学唱歌曲培养学生热爱祖国、热爱生活的激情。 2、教学重点： ①、掌握女高音、女中音的音域和演唱特点。 ②、掌握美声、民族、通俗三种方法演唱风格。 3、教学难点： ①、学生归纳不同唱法的特点与风格。

②、学生尝试用不同演唱风格表现同一首歌。 3、设计思路 《普通高中音乐课程标准》指出：“音乐课的教学过程就是音乐的艺术实践过程。”《甜美纯净的女声独唱》作为《魅力四射的独唱舞台》单元的第一课，是让学生在丰富多彩的歌唱艺术形式中感受出女声独唱以其优美纯净的声音特点而散发出独特的魅力。为此，本课从身边熟悉的人物和情景入手，激发学生学习兴趣，把教学重心放在艺术实践中，让学生在欣赏、学习不同的歌唱风格中，培养自己的综合欣赏能力及歌唱水平。在教学过程中让学生体会不同风格的甜美纯净女声的内涵，感知优美纯净的声音特点而散发出的独特魅力，学会多听、多唱，掌握一定的歌唱技巧，提高自己的演唱水平。为实现以上目标，本人将新课标“过程与方法”中的“体验、比较、探究、合作”四个具体目标贯穿全课，注重学生的个人感受和独特见解，鼓励学生的自我意识与创新精神，强调探究、强调实践，将教学过程变为整合、转化间接经验为学生直接经验的过程，让学生亲身去感悟、去演唱，并力求改变现在高中学生普遍只关注流行歌曲的现状，让学生自己确定最适合自己演唱的方法，自我发现、自我欣赏，充分展示自己的的声音魅力。 三、教学过程 教学环节及时间教师活动学生活动设计意图

The way常见用法

The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because

适合女生KTV唱的100首好听的歌

适合女生KTV唱的100首好听的歌别吝色你的嗓音很好学 1、偏爱----张芸京 2、阴天----莫文蔚 3、眼泪----范晓萱 4、我要我们在一起---=范晓萱 5、无底洞----蔡健雅 6、呼吸----蔡健雅 7、原点----蔡健雅&孙燕姿 8、我怀念的----孙燕姿 9、不是真的爱我----孙燕姿 10、我也很想他----孙燕姿 11、一直很安静----阿桑 12、让我爱----阿桑 13、错过----梁咏琪 14、爱得起----梁咏琪 15、蓝天----张惠妹 16、记得----张惠妹 17、简爱----张惠妹 18、趁早----张惠妹 19、一念之间----戴佩妮 20、两难----戴佩妮 21、怎样----戴佩妮 22、一颗心的距离----范玮琪 23、我们的纪念日----范玮琪 24、启程----范玮琪 25、最初的梦想----范玮琪 26、是非题----范玮琪 27、你是答案----范玮琪 28、没那么爱他----范玮琪 29、可不可以不勇敢----范玮琪 30、一个像夏天一个像秋天----范玮琪 31、听，是谁在唱歌----刘若英 32、城里的月光----许美静 33、女人何苦为难女人----辛晓琪 34、他不爱我----莫文蔚 35、你是爱我的----张惠妹 36、同类----孙燕姿 37、漩涡----孙燕姿 38、爱上你等于爱上寂寞----那英 39、梦醒了----那英 40、出卖----那英 41、梦一场----那英 42、愿赌服输----那英

43、蔷薇----萧亚轩 44、你是我心中一句惊叹----萧亚轩 45、突然想起你----萧亚轩 46、类似爱情----萧亚轩 47、Honey----萧亚轩 48、他和他的故事----萧亚轩 49、一个人的精彩----萧亚轩 50、最熟悉的陌生人----萧亚轩 51、想你零点零一分----张靓颖 52、如果爱下去----张靓颖 53、我想我是你的女人----尚雯婕 54、爱恨恢恢----周迅 55、不在乎他----张惠妹 56、雪地----张惠妹 57、喜欢两个人----彭佳慧 58、相见恨晚----彭佳慧 59、囚鸟----彭羚 60、听说爱情回来过----彭佳慧 61、我也不想这样----王菲 62、打错了----王菲 63、催眠----王菲 64、执迷不悔----王菲 65、阳宝----王菲 66、我爱你----王菲 67、闷----王菲 68、蝴蝶----王菲 69、其实很爱你----张韶涵 70、爱情旅程----张韶涵 71、舍得----郑秀文 72、值得----郑秀文 73、如果云知道----许茹芸 74、爱我的人和我爱的人----裘海正 75、谢谢你让我这么爱你----柯以敏 76、陪我看日出----蔡淳佳 77、那年夏天----许飞 78、我真的受伤了----王菀之 79、值得一辈子去爱----纪如璟 80、太委屈----陶晶莹 81、那年的情书----江美琪 82、梦醒时分----陈淑桦 83、我很快乐----刘惜君 84、留爱给最相爱的人----倪睿思 85、下一个天亮----郭静 86、心墙----郭静

The way的用法及其含义(二)

The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中

(完整版)the的用法

定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...

2019-2020年高一音乐 甜美纯净的女声独唱教案

2019-2020年高一音乐甜美纯净的女声独唱教案 一、教学目标 1、认知目标：初步了解民族唱法、美声唱法、通俗唱法三种唱法的风格。 2、能力目标：通过欣赏部分女声独唱作品，学生能归纳总结出她们的演唱 风格和特点，并同时用三种不同风格演唱同一首歌曲。 3、情感目标：通过欣赏比较，对独唱舞台有更多元化的审美意识。 二、教学重点：学生能用三种不同风格演唱形式演唱同一首歌。 三、教学难点：通过欣赏部分女声独唱作品，学生能归纳总结出她们的演唱 风格和特点。 四、教学过程： （一）导入 1、播放第十三界全国青年歌手大奖赛预告片 （师）问：同学们对预告片中的歌手认识吗 （生）答： （师）问：在预告片中提出了几种唱法？ （生）答：有民族、美声、通俗以及原生态四种唱法，今天以女声独唱歌曲重点欣赏民族、美声、通俗唱法，希望通过欣赏同学们能总结出三种唱法的风格和特点。 （二）、音乐欣赏

1、通俗唱法 ①(师)问：同学们平常最喜欢唱那些女歌手的歌呢？能唱唱吗？ （可让学生演唱几句喜欢的歌，并鼓励） ②欣赏几首通俗音乐 视频一：毛阿敏《绿叶对根的情谊》片段、谭晶《在那东山顶上》片段、韩红《天路》片段、刘若英《后来》片段 视频二：超女《想唱就唱唱得响亮》 ①由学生总结出通俗音乐的特点 ②师总结并板书通俗音乐的特点：通俗唱法是在演唱通俗歌曲的基础上发展起来的，又称“流行唱法”。通俗歌曲是以通俗易懂、易唱易记、娱乐性强、便于流行而见长，它没有统一的规格和演唱技法的要求，比较强调歌唱者本人的自然嗓音和情绪的渲染，重视歌曲感情的表达。演唱上要求吐字清晰，音调流畅，表情真挚，带有口语化。 ③指出通俗音乐尚未形成系统的发声训练体系。其中用沙哑、干枯的音色“狂唱”和用娇柔、做作的姿态“嗲唱”，不属于声乐艺术的正道之物，应予以摒弃。 2、民族唱法 ①俗话说民族的才是世界的那么民族唱法的特点是什么呢？ ②欣赏彭丽媛《万里春色满人间》片段 鉴赏提示：这首歌是剧种女主角田玉梅即将走上刑场时的一段难度较大的咏叹调。

“the way+从句”结构的意义及用法

“tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法

不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.

way 用法

表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法

女生唱的歌曲欢快甜美

女生唱的歌曲欢快甜美 美妙的歌曲能令我们陶醉其中而无法自拨，最激烈的歌曲能令我们的身体不由自主的跟着手舞足蹈起来，下面是小编整理的欢快甜美的歌曲的内容，希望能够帮到您。 欢快甜美的歌曲 1. Talking - 2. 羽毛- 劲歌金曲 3. 为你- 黑龙 4. 我的小时候- 罗艺达 5. 听说爱情回来过 6. 那个男人 7. 夫妻观灯_韩再芬、李迎春- 中国民歌宝典二 8. 往生- 镀飞爱在阳光空气中- 区瑞强- 音乐合辑 9. 说中国- 班- 华语群星 10. 第十八封信- Kent王健 11. 那一夜你喝了酒- 傅薇 12. 最近比较烦- 周华健/李宗盛/品冠- 滚石群星 13. 告白- 张娜拉 14. Talking VIII - 15. my love - 网友精选曲 16. 音乐人民- 音乐合辑 17. 深深深深- 徐誉滕 18. Honkytonk U - Toby Keith 19. 征服- 阿强 20. 我总会感动你- 沙宝亮欢快甜美的歌曲 1. 一千步的距离- 高桐 2. fleeing star - 音乐合辑 3. My Life - 李威杰 4. 小妹听我说- 金久哲 5. 上海滩- 梁玉嵘- 华语群星 6. 爱我多爱一些- 黎姿 7. 恋人未满- 8. 玛奇朵飘浮- 音乐听吧 9. 風- 音乐听吧 10. 七月- 小鸣 11. 滚滚红尘- 罗大佑 12. 张震岳—想要- 华语群星 13. 有梦有朋友- 14. 童年- 拜尔娜 15. 洪湖水，浪打浪- 宋祖英 16. 只爱到一半- 魏晨 17. 风雨人生路- 何静 18. 居家男人- 回音哥如果当时- 许嵩 19. 那个男人的谎言Tae In - 非主流音乐

The way的用法及其含义(一)

The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.

适合女生唱的各种难度的歌

【适合女生唱的各种难度的歌】以后点歌的时候记得挑战一下自己（哈哈，今天心情高兴，在微博整理下的小东西和大家分享） 1.我不知道--唐笑（特别喜欢的一首歌） 2.那个--文筱芮（特别伤的歌，真的可以听到心里去） 3.一半--丁当（喜欢喜欢，但没能力唱） 4.指望--郁可唯（本来不喜欢她，但她唱歌挺有水平） 5.路人--江美琪（推荐，好听又挺好唱的） 6.过敏--杨丞琳（听听就知道了） 7.大女人--张亚飞（没什么名气的超级女生，这歌挺棒的） 8.一个人的星光--许静岚（绿光森林的主题曲） 9.不要说爱我--许紫涵（高潮真的挺好听，我爱单曲循环，但这歌还没腻） 10.为你我受冷风吹--林忆莲（没那么简单，都是很喜欢的老歌，偶尔听听老歌感觉特别好） 11.一秒也好--卓文萱（她的（爱我好吗）也不错，最近挺喜欢她的歌） 12.你在哪里--张婧（不被太多人知道的歌手） 13.你的背包--莫艳琳（在校内看到一个女孩唱的，觉得挺好听的） 14.原来爱情那么难--泳儿（好听好听，没什么难度，就是在ktv不太好找） 15.在你眼里--同恩（也是到副歌特别吸引人的一首）

16.很久很久以后--梁文音（爱她的歌，她的很多歌都特别好听） 17.知道我们不会有结果--金莎（听着特别有感觉，那些喜欢听悲伤歌的都是因为这种感觉吧） 18.指尖的星光--钟汶（不太好唱的，我就只有听的份了） 19.放不下--龚诗嘉（挺简单的一首，调调挺平的，她的（远远在一起）也不错） 20.灰色的彩虹--范玮琪 21.现在才明白--萧贺硕（不被太多人知道的歌手，有些歌真的很好听，只是需要慢慢挖掘） 22.终点--关心妍（这首歌大多都听过，自己感觉吧） 23.遇到--王蓝茵（旋律让人感觉特舒服的，很爱的一首） 24.一个人--蔡依（她的毅力不是一般人能做到的） 25.婴儿--陈倩倩（这首歌真的凄凉到有点甚人的感觉。“喜欢一个人的心情”--江语晨，因为这歌的词）26.那又怎么样呢--张玉华（我爱听音乐，但一定要是伤感的，虽然不会听到泪流满面，但是那种感觉真的很好） 27.还爱你--景甜（像这样好听，又不被大家熟悉的歌还有很多吧）

way 的用法

way 的用法 【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗？ 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。 【归纳总结】 ●way作“方法，方式”讲时，如表示“以……方式”，前面常加介词in。如例1； ●way作“方法，方式”讲时，其后可接不定式to do sth.，也可接of doing sth. 作定语，表示做某事的方法。如例2，例3；

适合女生KTV唱的100首好听的歌

分享适合女生KTV唱的100首好听的歌别吝色你的嗓音很好学 1、偏爱----张芸京 2、阴天----莫文蔚 3、眼泪----范晓萱 4、我要我们在一起---=范晓萱 5、无底洞----蔡健雅 6、呼吸----蔡健雅 7、原点----蔡健雅&孙燕姿 8、我怀念的----孙燕姿 9、不是真的爱我----孙燕姿 10、我也很想他----孙燕姿 11、一直很安静----阿桑 12、让我爱----阿桑 13、错过----梁咏琪 14、爱得起----梁咏琪 15、蓝天----张惠妹 16、记得----张惠妹 17、简爱----张惠妹 18、趁早----张惠妹 19、一念之间----戴佩妮 20、两难----戴佩妮 21、怎样----戴佩妮 22、一颗心的距离----范玮琪 23、我们的纪念日----范玮琪 24、启程----范玮琪 25、最初的梦想----范玮琪 26、是非题----范玮琪 27、你是答案----范玮琪 28、没那么爱他----范玮琪 29、可不可以不勇敢----范玮琪 30、一个像夏天一个像秋天----范玮琪 31、听，是谁在唱歌----刘若英 32、城里的月光----许美静 33、女人何苦为难女人----辛晓琪 34、他不爱我----莫文蔚 35、你是爱我的----张惠妹 36、同类----孙燕姿 37、漩涡----孙燕姿 38、爱上你等于爱上寂寞----那英 39、梦醒了----那英 40、出卖----那英 41、梦一场----那英 42、愿赌服输----那英

43、蔷薇----萧亚轩 44、你是我心中一句惊叹----萧亚轩 45、突然想起你----萧亚轩 46、类似爱情----萧亚轩 47、Honey----萧亚轩 48、他和他的故事----萧亚轩 49、一个人的精彩----萧亚轩 50、最熟悉的陌生人----萧亚轩 51、想你零点零一分----张靓颖 52、如果爱下去----张靓颖 53、我想我是你的女人----尚雯婕 54、爱恨恢恢----周迅 55、不在乎他----张惠妹 56、雪地----张惠妹 57、喜欢两个人----彭佳慧 58、相见恨晚----彭佳慧 59、囚鸟----彭羚 60、听说爱情回来过----彭佳慧 61、我也不想这样----王菲 62、打错了----王菲 63、催眠----王菲 64、执迷不悔----王菲 65、阳宝----王菲 66、我爱你----王菲 67、闷----王菲 68、蝴蝶----王菲 69、其实很爱你----张韶涵 70、爱情旅程----张韶涵 71、舍得----郑秀文 72、值得----郑秀文 73、如果云知道----许茹芸 74、爱我的人和我爱的人----裘海正 75、谢谢你让我这么爱你----柯以敏 76、陪我看日出----蔡淳佳 77、那年夏天----许飞 78、我真的受伤了----王菀之 79、值得一辈子去爱----纪如璟 80、太委屈----陶晶莹 81、那年的情书----江美琪 82、梦醒时分----陈淑桦 83、我很快乐----刘惜君 84、留爱给最相爱的人----倪睿思 85、下一个天亮----郭静 86、心墙----郭静

100首适合女人唱的歌,不要吝惜自己的嗓子

1、偏爱----张芸京 2、阴天----莫文蔚 3、眼泪----范晓萱 4、我要我们在一起---=范晓萱 5、无底洞----蔡健雅 6、呼吸----蔡健雅 7、原点----蔡健雅&孙燕姿 8、我怀念的----孙燕姿 9、不是真的爱我----孙燕姿 10、我也很想他----孙燕姿 11、一直很安静----阿桑 12、让我爱----阿桑 13、错过----梁咏琪 14、爱得起----梁咏琪 15、蓝天----张惠妹 16、记得----张惠妹 17、简爱----张惠妹 18、趁早----张惠妹 19、一念之间----戴佩妮 20、两难----戴佩妮 21、怎样----戴佩妮 22、一颗心的距离----范玮琪 23、我们的纪念日----范玮琪 24、启程----范玮琪 25、最初的梦想----范玮琪 26、是非题----范玮琪 27、你是答案----范玮琪 28、没那么爱他----范玮琪 29、可不可以不勇敢----范玮琪 30、一个像夏天一个像秋天----范玮琪 31、听，是谁在唱歌----刘若英 32、城里的月光----许美静 33、女人何苦为难女人----辛晓琪 34、他不爱我----莫文蔚 35、你是爱我的----张惠妹 36、同类----孙燕姿 37、漩涡----孙燕姿 38、爱上你等于爱上寂寞----那英 39、梦醒了----那英 40、出卖----那英 41、梦一场----那英 42、愿赌服输----那英 43、蔷薇----萧亚轩 44、你是我心中一句惊叹----萧亚轩

45、突然想起你----萧亚轩 46、类似爱情----萧亚轩 47、Honey----萧亚轩 48、他和他的故事----萧亚轩 49、一个人的精彩----萧亚轩 50、最熟悉的陌生人----萧亚轩 51、想你零点零一分----张靓颖 52、如果爱下去----张靓颖 53、我想我是你的女人----尚雯婕 54、爱恨恢恢----周迅 55、不在乎他----张惠妹 56、雪地----张惠妹 57、喜欢两个人----彭佳慧 58、相见恨晚----彭佳慧 59、囚鸟----彭羚 60、听说爱情回来过----彭佳慧 61、我也不想这样----王菲 62、打错了----王菲 63、催眠----王菲 64、执迷不悔----王菲 65、阳宝----王菲 66、我爱你----王菲 67、闷----王菲 68、蝴蝶----王菲 69、其实很爱你----张韶涵 70、爱情旅程----张韶涵 71、舍得----郑秀文 72、值得----郑秀文 73、如果云知道----许茹芸 74、爱我的人和我爱的人----裘海正 75、谢谢你让我这么爱你----柯以敏 76、陪我看日出----蔡淳佳 77、那年夏天----许飞 78、我真的受伤了----王菀之 79、值得一辈子去爱----纪如璟 80、太委屈----陶晶莹 81、那年的情书----江美琪 82、梦醒时分----陈淑桦 83、我很快乐----刘惜君 84、留爱给最相爱的人----倪睿思 85、下一个天亮----郭静 86、心墙----郭静 87、那片海----韩红 88、美丽心情----RURU

the-way-的用法讲解学习

t h e-w a y-的用法

The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.

适合女生唱的各种难度的歌

婴儿——陈倩倩 这首歌真的凄凉到有点儿甚人的感觉。“喜欢一个人的心情”——江语晨，因为这歌的词。 那又怎么样呢——张玉华 我爱听音乐，但一定要是伤感的，虽然不会听到泪流满面，但是那种感觉真的很好 还爱你——景甜 你可以爱我很久吗——游艾迪 夜夜夜夜——原唱齐秦 爱一直存在——梁文音 有人想找男生唱的，真不常听男生的歌，不过有几首觉得挺不错的。 初雪的忧伤——赵子浩 爱你，离开你——南拳妈妈 说谎——林宥嘉 三人游、爱爱爱——方大同 分开以后——唐禹哲 突然好想你——五月天 还是男生的， 寂寞的季节、暗恋——陶喆 情歌两三首——郭顶 掌纹——曹格 需要人陪——王力宏 王妃——箫敬腾（除了这首，其他几首都是比较安静抒情的。） 挥之不去——殷悦 别再哭了——罗忆诗 前段时间特别喜欢这首歌，听的快吐了，真的挺好听。 热气球——黄淑惠 很特别，超级好听，强烈推荐。 你是爱我的——张惠妹 她的嗓音让我着迷，超级喜欢。 问——粱静茹 老歌了，不过很喜欢。

忽略——萧萧 握不住的他，看到萧萧还是会第一个想起这首。 趁早——张惠妹 她有点儿沙哑的声音让我着迷。 幸运草——丁当 早点儿的歌了，喜欢丁当。 哭了——范晓萱 越听越喜欢，。 氧气——范晓萱 小时候喜欢听她的歌，不过随着年龄的增长，喜欢的类型也变了。 温柔的慈悲——阿桑 喜欢她的歌，只是她的声音不能再更新了。 礼物——刘力扬 罗美玲的也还好。。 洋葱——丁当杨宗纬（两个不一样的感觉） 挺难的唱不好，不过喜欢听。 眼泪知道——温岚 喜欢，唱出来特别有激情哈。

类似爱情——萧亚轩 不难又有感觉。 第三者——梁静茹 还好，喜欢这首歌的歌词。 心墙——郭静 “我不想忘记你”，“不药而愈”，“每一天都不同”，都好听喜欢她的歌。 我知道你很难过——蔡依林 唱起来有感觉也不难唱，推荐。 夏伤——SARA 感觉很特别，喜欢。 那天——蓝又时 喜欢她的歌，她的调调，强烈推荐。“秘密”也不错。 礼物——罗美玲 好听有感觉，不过不太好唱。 我比想象中爱你——JS 老歌了一直很喜欢，唱起来有感觉。

高一音乐 甜美纯净的女声独唱教案

魅力四射的独唱舞台 ——甜美纯净的女声独唱 一、教学目标 1、认知目标：初步了解民族唱法、美声唱法、通俗唱法三种唱法的风格。 2、能力目标：通过欣赏部分女声独唱作品，学生能归纳总结出她们的演唱 风格和特点，并同时用三种不同风格演唱同一首歌曲。 3、情感目标：通过欣赏比较，对独唱舞台有更多元化的审美意识。 二、教学重点：学生能用三种不同风格演唱形式演唱同一首歌。 三、教学难点：通过欣赏部分女声独唱作品，学生能归纳总结出她们的演唱 风格和特点。 四、教学过程： （一）导入 1、播放第十三界全国青年歌手大奖赛预告片 （师）问：同学们对预告片中的歌手认识吗 （生）答： （师）问：在预告片中提出了几种唱法？ （生）答：有民族、美声、通俗以及原生态四种唱法，今天以女声独唱歌曲重点欣赏民族、美声、通俗唱法，希望通过欣赏同学们能总结出三种唱法的风格和特点。

（二）、音乐欣赏 1、通俗唱法 ①(师)问：同学们平常最喜欢唱那些女歌手的歌呢？能唱唱吗？ （可让学生演唱几句喜欢的歌，并鼓励） ②欣赏几首通俗音乐 视频一：毛阿敏《绿叶对根的情谊》片段、谭晶《在那东山顶上》片段、韩红《天路》片段、刘若英《后来》片段 视频二：超女《想唱就唱唱得响亮》 ①由学生总结出通俗音乐的特点 ②师总结并板书通俗音乐的特点：通俗唱法是在演唱通俗歌曲的基础上发展起来的，又称“流行唱法”。通俗歌曲是以通俗易懂、易唱易记、娱乐性强、便于流行而见长，它没有统一的规格和演唱技法的要求，比较强调歌唱者本人的自然嗓音和情绪的渲染，重视歌曲感情的表达。演唱上要求吐字清晰，音调流畅，表情真挚，带有口语化。 ③指出通俗音乐尚未形成系统的发声训练体系。其中用沙哑、干枯的音色“狂唱”和用娇柔、做作的姿态“嗲唱”，不属于声乐艺术的正道之物，应予以摒弃。 2、民族唱法 ①俗话说民族的才是世界的那么民族唱法的特点是什么呢？ ②欣赏彭丽媛《万里春色满人间》片段 鉴赏提示：这首歌是剧种女主角田玉梅即将走上刑场时的一段难度较大的咏叹调。

way的用法总结大全

way的用法总结大全 way的用法你知道多少，今天给大家带来way的用法，希望能够帮助到大家，下面就和大家分享，来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地，大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。

way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句

适合女生唱的100首好听的歌

适合女生唱的100首好听的歌 1、偏爱----张芸京 2、阴天----莫文蔚味道很难把握 3、眼泪----范晓萱还好，张学友版本适合男生 4、我要我们在一起---范晓萱A段超级难唱的，拍子和口气都不好抓 5、无底洞----蔡健雅听起来简单，唱起来很难——这首是典型的例子 6、呼吸----蔡健雅 7、原点----蔡健雅&孙燕姿到哪里找两个好听的女中音呢？ 8、我怀念的----孙燕姿 9、不是真的爱我----孙燕姿 10、我也很想他----孙燕姿 11、一直很安静----阿桑 12、让我爱----阿桑 13、错过----梁咏琪 14、爱得起----梁咏琪为什么没有洗脸？剪发？胆小鬼？ 15、蓝天----张惠妹 16、记得----张惠妹 17、简爱----张惠妹是剪爱吧？ 18、趁早----张惠妹男生可以试试张宇的版本 19、一念之间----戴佩妮 20、两难----戴佩妮 21、怎样----戴佩妮 22、一颗心的距离----范玮琪 23、我们的纪念日----范玮琪 24、启程----范玮琪 25、最初的梦想----范玮琪 26、是非题----范玮琪 27、你是答案----范玮琪 28、没那么爱他----范玮琪 29、可不可以不勇敢----范玮琪 30、一个像夏天一个像秋天----范玮琪范范的歌这么多啊。。。 31、听，是谁在唱歌----刘若英 32、城里的月光----许美静 33、女人何苦为难女人----辛晓琪我一直在找这个歌曲的粤语版，却找不到

34、他不爱我----莫文蔚 35、你是爱我的----张惠妹 36、同类----孙燕姿 37、漩涡----孙燕姿 38、爱上你等于爱上寂寞----那英在KTV点这个歌曲的MTV不是会很尴尬吗？ 39、梦醒了----那英 40、出卖----那英 41、梦一场----那英 42、愿赌服输----那英没有征服？也许是太大众了吧。 43、蔷薇----萧亚轩 44、你是我心中一句惊叹----萧亚轩 45、突然想起你----萧亚轩 46、类似爱情----萧亚轩 47、Honey----萧亚轩 48、他和他的故事----萧亚轩 49、一个人的精彩----萧亚轩 50、最熟悉的陌生人----萧亚轩还记得她第一张专籍里面最喜欢那首《没有人》 51、想你零点零一分----张靓颖 52、如果爱下去----张靓颖 53、我想我是你的女人----尚雯婕 54、爱恨恢恢----周迅 55、不在乎他----张惠妹 56、雪地----张惠妹 57、喜欢两个人----彭佳慧 58、相见恨晚----彭佳慧 59、囚鸟----彭羚 60、听说爱情回来过----彭佳慧 61、我也不想这样----王菲 62、打错了----王菲 63、催眠----王菲 64、执迷不悔----王菲 65、阳宝----王菲 66、我爱你----王菲 67、闷----王菲