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X-ray, Radio, and Optical Observations of the Putative Pulsar in the Supernova Remnant CTA

a r X i v :a s t r o -p h /0404312v 1 15 A p r 2004Submitted to The Astrophysical Journal

X-ray,Radio,and Optical Observations of the Putative Pulsar in the

Supernova Remnant CTA 1

J.P.Halpern,E.V.Gotthelf,F.Camilo,D.J.Helfand

Columbia Astrophysics Laboratory,Columbia University,550West 120th Street,New York,NY 10027-6601jules@https://www.doczj.com/doc/f43252445.html, S.M.Ransom Department of Physics,McGill University,Montreal,QC H3A 2T8,Canada ABSTRACT A Chandra image of the central X-ray source RX J0007.0+7303in the supernova remnant CTA 1reveals a point source,a compact nebula,and a bent jet,all of which are characteristic of energetic,rotation-powered https://www.doczj.com/doc/f43252445.html,ing the MDM 2.4m tele-scope we obtain upper limits in the optical at the position of the point source,(J2000)00h 07m 01.s 56,+73?03′08.′′1,determined to an accuracy of 0.′′1,of B >25.4,V >24.8,R >25.1,and I >23.7;these correspond to an X-ray-to-optical ?ux ratio 100.Neither a VLA image at 1425MHz,nor a deep pulsar search at 820MHz using the NRAO Green Bank Telescope,reveal a radio pulsar counterpart to an equivalent lu-minosity limit at 1400MHz of 0.02mJy kpc 2,which is equal to the lowest luminosity known for any radio pulsar.The Chandra point source accounts for ≈30%of the ?ux of RX J0007.0+7303,while its compact nebula plus jet comprise ≈70%.The X-ray spectrum of the point source is ?tted with a power-law plus blackbody model

with Γ=1.6±0.6,kT ∞=0.13±0.05keV,and R ∞=0.37km,values typical of

a young pulsar.An upper limit of T ∞e

<6.6×105K to the e?ective temperature of the entire neutron star surface is derived,which is one of the most constraining

data points on cooling models.The 0.5–10keV luminosity of RX J0007.0+7303is

≈4×1031(d/1.4kpc)2ergs s ?1,but the larger (～18′diameter)synchrotron nebula in

which it is embedded is two orders of magnitude more luminous.These properties allow

us to estimate,albeit crudely,that the spin-down luminosity of the underlying pulsar

is in the range 1036?1037ergs s ?1,and support the identi?cation of the high-energy

γ-ray source 3EG J0010+7309as a pulsar even though its spin parameters have not yet

been determined.

Subject headings:ISM:individual (CTA 1)—stars:individual (RX J0007.0+7303,

3EG J0010+7309)—stars:neutron —supernova remnants

1.Introduction

The supernova remnant CTA1(G119.5+10.2)is a radio shell with a diameter of≈1.?8(Seward, Schmidt,&Slane1995)and a center-?lled X-ray morphology.It has a kinematic distance of d=1.4±0.3kpc derived from an associated H I shell(Pineault et al.1993),and the remnant age from a Sedov analysis is t S≈1.3×104yr(Slane et al.2004).A detailed X-ray spectral study of the SNR using ASCA data showed that the large-scale extended emission is likely of a synchrotron origin;its total luminosity is5.6×1033(d/1.4kpc)2ergs s?1in the0.5–10keV band(Slane et al. 1997).The compact ROSAT PSPC source RX J0007.0+7303is located in the brightest part of the synchrotron nebula(Seward et al.1995;Slane et al.1997;Brazier et al.1998).RX J0007.0+7303 has the requisite properties for a rotation-powered pulsar.Its X-ray luminosity in the0.1–2.4keV band is4.3×1031(d/1.4kpc)2ergs s?1(Slane et al.1997),typical of young pulsars,but atypically small compared to the total luminosity of the large synchrotron nebula in CTA1.Appealing to an empirical relation between X-ray luminosity and spin-down power˙E,Slane et al.(1997)argued that the current spin-down power of the pulsar,required to account for the present nonthermal emission from the entire synchrotron nebula,is˙E=1.7×1036ergs s?https://www.doczj.com/doc/f43252445.html,bining this with the Sedov age predicts a rotation period P 0.17s and a dipolar surface magnetic?eld strength B p 6×1012G.

Within the boundary of CTA1lies3EG J0010+7309,one of the brighter unidenti?ed EGRET sources.With a95%con?dence localization diameter of only28′and an intermediate Galactic latitude of+10.?2,this EGRET/SNR coincidence is one of the most convincing among the unproven identi?cations(Brazier et al.1998),especially because of the likely pulsar in RX J0007.0+7303. Theγ-ray source itself has all of the characteristics of the known pulsars.It is not variable;other γ-ray pulsars show little if any change in?ux while most blazars,the other major class of EGRET source,are often dramatically variable.Its photon spectral index of1.85±0.10(Hartman et al. 1999)(1.58±0.18between70MeV and2GeV,Brazier et al.1998),is similar to other EGRET pulsars,and?atter than that of most blazars.The estimated values of d,t S,˙E,and P are all typical of what one would expect for a youngγ-ray pulsar.In particular,the distance to CTA1is typical for the predicted EGRET pulsar population(e.g.,Halpern&Ruderman1993;Kaaret&Cottam 1996;Romani&Yadigaroglu1995;Yadigaroglu&Romani1995,1997),and the inferred energetics are comparable to those of the Vela pulsar and other sources with similar values of˙E.

Recent observations with XMM-Newton resolved RX J0007.0+7303into a point source and a di?use nebula,and found a two-component(blackbody plus power-law)spectral?t that is consistent with a young pulsar(Slane et al.2004).Here,we present a higher resolution Chandra observation of these features that further resolves out a prominent jet-like structure and possible evidence of a torus,features typical of pulsar wind nebulae(PWNe)found around the most energetic of pulsars. In§2we present our Chandra imaging and spectroscopic results,in§3the optical observations, and in§4new radio imaging and deep radio search for pulsations from RX J0007.0+7303.In§5 we discuss the constraints on˙E for the putative pulsar in CTA1based on its X-ray and(likely)γ-ray luminosities.Throughout this paper,for clarity,we refer to the small-scale nebula resolved

by Chandra within RX J0007.0+7303as the PWN,as distinct from the large synchrotron nebula, which is also likely wind fed.

2.Chandra Observation of RX J0007.0+7303

The central region of CTA1was observered on2003April13with the Advanced CCD Imag-ing Spectrometer(ACIS;Burke et al.1997)onboard the Chandra X-ray Observatory(Weisskopf, O’Dell,&van Speybroeck1996).The source RX J0007.0+7303was positioned at the default lo-cation on the back-illuminated S3chip of the ACIS-S array.The standard TIMED readout with a frame time of3.2s was used,and the data were collected in VFAINT mode.A total of50139s of on-time was accumulated,while the e?ective exposure live-time was49484s.All data reduction and analysis were performed using the CIAO(V3.0.1),FTOOLS(V5.2),and XSPEC(V11.2)X-ray analysis software packages.No time?ltering was necessary as the background rate was stable over the course of the observation.Photon pile-up was not a consideration as the total count rate in the point source of interest was<0.01s?1.

We used the standard processed and?ltered event data with the latest aspect alignments, with the exception that the0.5pixel(0.′′25)randomization that is ordinarily applied to the photon positions was reversed,restoring slightly sharper images.The0.′′5ACIS pixels slightly undersample the on-axis point spread function of the Chandra mirrors in the restored images,as the radius encircling50%of the energy is≈0.′′5.However,the spacecraft dithering and time-dependent aspect solution preclude the need for additional randomization,which degrades a study of faint point sources embedded in di?use emission.

2.1.ACIS Image

In Figure1we compare the Chandra ACIS image of RX J0007.0+7303from2003April13 with the combined MOS1and MOS2image from the XMM-Newton observation of2002February 21,originally reported by Slane et al.(2004).In the Chandra image,187photons(after background subtraction)are found within1′′of the source maximum;most are attributable to a point source. Figure2shows the radial pro?le of the Chandra source,with a simulated point-spread-function (PSF)scaled to the detected counts in the central pixel.There is also a compact surrounding nebulosity with136photons within a radius of3′′(the PWN),as well as a jet that extends16′′to the south,with a≈50?bend to the southwest at12′′from the point source.There is also a possible faint extension of the jet for an additional8′′to the southwest,although the latter may be part of a general expansion of the jet into a large,low-surface brightness nebulosity extending to the west and northwest.The total number of photons in the jet is45after background subtraction. From the Vela pulsar,similar di?use emission apparently supplied by its jet has been observed (Kargaltsev et al.2003;Pavlov et al.2003).

In view of Chandra’s unique ability to reveal graphic evidence of a rotation-powered neutron star,we refer in this paper to“the pulsar”in RX J0007.0+7303rather than the customary cir-cumlocution“candidate pulsar.”The ACIS frame time of3.2s does not permit a search for X-ray pulsations in this observation.From the XMM-Newton EPIC pn data taken with6ms time reso-lution,Slane et al.(2004)derive an upper limit of61%sinusoidal pulsed fraction for frequencies up to83Hz.Nevertheless,we regard it as appropriate in cases such as this one to classify an X-ray source as a pulsar even though its spin parameters are not yet known.The position of the pulsar is(J2000)00h07m01.s56,+73?03′08.′′1(see§3for a description of the astrometry).

While the similarity between the jets of RX J0007.0+7303and Vela is striking,it is curious that the prominent torus structure of Vela is so much weaker in RX J0007.0+7303,if it is present at all.The compact PWN surrounding the pulsar appears to be elongated at an angle perpendicular to the inner jet,which by analogy with Vela may plausibly be interpreted as an equatorial torus with the jet emerging along the rotation axis.Figure3shows the Chandra image in two di?erent energy bands,soft(0.2–2.0keV)and hard(2–8keV).The PWN is more prominent in the hard band,while the pulsar itself is brighter in the soft band,presumably due to the contribution of surface thermal emission from the neutron star(see§2.2.2),which has a softer spectrum than the synchrotron nebulosity.Apparent spectral di?erences exist along the length of the jet.The hardest regions of the jet are closest to the pulsar,while the softest part of the jet is farther away,below the bend.

The features of the lower-resolution XMM-Newton image are roughly consistent with what one would expect from the Chandra image,although the part of the jet past the bend is not obvious with XMM-Newton.It is possible that the structure of the jet has changed markedly in the14 months between the two observations.Such behavior would be consistent with the rapid changes seen in the jet of the Vela pulsar(Kargaltsev et al.2003;Pavlov et al.2003),which moves with speeds in the range0.3?0.7c,even in directions transverse to its length.Velocities comparable to c were also seen in Chandra observations of G11.2–0.3(Roberts et al.2003).At the1.4kpc distance of CTA1,the16′′length of the jet corresponds to3.4×1017cm,or130light days.The length of the Vela pulsar’s jet is almost the same,≈4.3×1017(d/300pc)cm,which may suggest that the two sources have similar spin-down luminosities.The bending and termination of the jet can plausibly be explained by its impact against the larger synchrotron nebula.In addition,if the pulsar is traveling toward the southeast,the low surface brightness di?use emission to the west and northwest of the pulsar may be due to jet material dumping its energy and dispersing it into the larger nebula,as suggested by Pavlov et al.(2003)in the case of Vela.

2.2.X-ray Spectral Fitting

Source and background spectra were extracted using the CIAO script psextract to generate the photon energy histograms and appropriate response matrices for analysis of three spatial regions: the pulsar(r=1′′),the PWN(1′′

served as background for the pulsar spectrum,while a larger annular background region(11′′< r<15′′)was extracted for use with the PWN and the jet spectra.All spectra were grouped with

a minimum of20counts per bin.

2.2.1.The PWN and its Intervening Column Density

We?rst?tted the136background-subtracted counts obtained from the PWN region to an absorbed power-law model.This produced a rather unconstrained?t with N H=3.5(0.0?8.9)×1021cm?2andΓ=1.0(0.3?1.4),where the1σrange is given in parentheses.The unabsorbed ?ux in the0.5?10keV band is6.6×10?14ergs cm?2s?1after adding a presumed contribution, scaled by area,from within the pulsar region(r=1′′).We note that the best?tted value of N H=3.5×1021cm?2is somewhat larger than expected based on the total Galactic optical extinction in the direction of CTA1.According to the100μm IRAS/COBE maps(Schlegel, Finkbeiner,&Davis1998),E(B?V)=0.414mag,corresponding to A V=1.37,which can be considered an upper limit on the extinction to CTA1.The Predehl&Schmitt(1995)relation N H/A V=1.8×1021cm?2mag?1then implies N H=2.5×1021cm?2.The latter value is close to that derived by Slane et al.(1997)from joint?ts to ROSAT PSPC and ASCA spectra,which gave N H=2.8(2.3?3.4)×1021cm?2.Given the distance and intermediate Galactic latitude of CTA1(+10.?2),it is plausible that the source lies above the bulk of the dust layer,since 1400sin(10.?2)≈250pc.Therefore,we adopt a?xed value of N H=2.8×1021cm?2in all further spectral?ts,the results of which are listed in Table1.

The0.5–10keV luminosity of the compact PWN region in RX J0007.0+7303is1.8×1031ergs s?1. In comparison,the0.1–10keV luminosity of the Vela nebula within a radius of53′′(2.4×1017cm) is(5?6)×1032ergs s?1(Helfand,Gotthelf,&Halpern2001;Pavlov et al.2003),a di?erence that is manifest in the relative prominence of the toroidal features of the Vela nebula.

2.2.2.The Pulsar

We next?tted the pulsar spectrum,consisting of187background-subtracted counts,to a two-component absorbed power-law plus blackbody model,to allow for non-thermal magnetospheric emission and thermal emission from the neutron star surface,respectively.The column density was held?xed at N H=2.8×1021cm?2.The best?tted parameters areΓ=1.6(1.1?2.2)and kT∞= 0.13(0.08?0.18)keV,with unabsorbed?uxes in the0.5?10keV band of4.0×10?14ergs cm?2s?1 and8.2×10?15ergs cm?2s?1,for the power-law and blackbody components,respectively.The small e?ective radius of the blackbody component,R∞=0.37km,is similar to the value R∞=0.63km from the XMM-Newton analysis(Slane et al.2004),and might be evidence of a hot polar cap heated by back?ow of energetic particles.On the other hand,Slane et al.(2004)also?tted a light-element atmosphere model with a larger?xed radius of10km,enabling a lower temperature

to be derived.Such systematic ambiguities are always present in thermal modeling of neutron star spectra.

Independent of this spectral?t to the pulsar,we also derive an upper limit to the e?ective blackbody temperature of the entire neutron star surface.Assuming d=1.4kpc,N H=2.8×1021cm?2,and a radius at in?nity of12km,we compared simulated blackbody spectra of increasing temperature with the data until the predicted spectrum exceeded the observered counts in the lowest energy bin by3σ,or nearly a factor of2.The resulting upper limit is T∞e<6.6×105K. In Figure4,we compare this value with a range of cooling models that include both standard and “exotic”processes(see also Page&Applegate1992;Tsuruta et al.2002,and the reviews of neutron star cooling by Tsuruta1998and Yakovlev&Pethick2004).Recent calculations show that the temperatures or upper limits on all cooling neutron stars,such as Vela,Geminga,3C58(PSR J0205+6449),and RX J0007.0+7303,can be?tted with models that include proton and neutron super?uidity,and masses<1.5M⊙(Kaminker,Yakovlev,&Gnedin2002;Yakovlev et al.2002), as shown in Figure4.Here,the direct Urca process is operating in the more massive neutron stars. Cooling can also be enhanced in a super?uid neutron star by Cooper-pairing neutrino emission, which was modeled most recently by Gusakov et al.(2004)and Page et al.(2004).

2.2.

3.The Jet

For the jet we created a polygonal region which encompassed and followed the contour of the jet from2.′′5to22′′from the pulsar.A?t to the45background-subtracted photons with an absorbed power-law model,with N H again?xed to the ASCA value,yieldedΓ=1.26(0.86?1.69) and an unabsorbed?ux of3.1×10?14ergs cm?2s?1.While there are probably changes in spectral index along the jet that are related to the apparent di?erences in the soft and hard images(Fig.

3),there are too few photons to?t spectra to multiple regions.The0.5–10keV luminosity of the jet,7.3×1030ergs s?1,is almost identical to that of the main(inner plus outer)jet of the Vela pulsar,which has L X(1?8keV)≈6×1030ergs s?1(Pavlov et al.2003).Within the range of uncertainty and variability,these two sources have jets of equal length and luminosity,which is in curious contrast to the relative dominance of the toroids in Vela.

3.Optical Observations of RX J0007.0+7303

We obtained multiple CCD images of the?eld of RX J0007.0+7303using the2.4m Hiltner telescope of the MDM Observatory on2002August26-30.A thinned,back-illuminated SITe 2048×2048CCD with a spatial scale of0.′′275per24μm pixel was used to cover a9.′4×9.′4 area.The sky conditions were usually photometric enough to calibrate the BV RI images with Landolt(1992)standard stars,although moonlight prevented us from reaching the deepest possible limiting magnitudes.Total integration times were100,72,120,and75minutes in B,V,R,and I,

respectively.The seeing in the?nal,summed images,shown in Figure5,ranged from a best of0.′′8 in I to a worst of1.′′2in V.

We were able to con?rm and re?ne the astrometric accuracy of the Chandra X-ray image relative to the optical reference frame of the USNO-A2.0catalog(Monet et al.1998)by identifying the counterparts of several X-ray sources in the vicinity of RX J0007.0+7303.X-ray positions and counts from the standard data processing,and optical positions and magnitudes from our CCD images,are listed in Table2.The X-ray centroids and source counts are calculated within the 80%enclosed energy contour of the local point-spread function.All of the optical counterparts in Table2appear point-like except the?rst entry,CXOU J000647.2+730109,which is evidently a compact galaxy,and perhaps the very faint CXOU J000739.2+730404,whose structure is not clear.The?ve neighboring sources had mean X-ray–optical o?sets of only?0.′′11in right ascension and+0.′′06in declination,and rms scatter of0.′′28in right ascension and0.′′14in declination.The rms scatter is consistent with the statistical accuracies of the individual optical and X-ray source positions,while the mean o?set is well within the Chandra systematic90%con?dence accuracy of 0.′′6.Accordingly,we corrected the Chandra coordinates of the RX J0007.0+7303point source by the small mean o?sets,obtaining a?nal position of(J2000)00h07m01.s56,+73?03′08.′′1,which we expect is accurate to≈0.′′1relative to the optical reference frame.

Limiting(3σ)magnitudes at the position of the Chandra point source are B>25.4,V>24.8, R>25.1,and I>23.7.The extinction-corrected limits using the Schlegel et al.(1998)values of A B=1.79,A V=1.37,A R=1.11,and A I=0.80,are B>23.6,V>23.4,R>24.0,and I>22.9.This corresponds to f X/f V>300,or>83after correction for extinction.Similar values are obtained in the other bands,and are consistent with an isolated neutron star at the distance of CTA1.No extended optical emission is seen associated with the X-ray jet.

4.Radio Observations of RX J0007.0+7303

4.1.VLA Image

The?eld of RX J0007.0+7303was imaged at1425MHz using the AB con?guration of the VLA on2002May27,which gave a beam FWHM of5.′′9×4.′′4.An exposure time of1hour achieved a 1σnoise level of31μJy and a non-detection at the precise Chandra position of the pulsar.This is equivalent to a3σ?ux density upper limit of0.09mJy.The relevant part of the image in shown in Figure6.

4.2.Radio Pulsar Search at GBT

CTA1was searched for pulsations by Nice&Sayer(1997)at radio frequencies of370MHz and 1390MHz.The sensitivity of those observations,translated to a standard frequency of1400MHz

using a spectral indexα=?1.6(the median for all pulsars;Lorimer et al.1995),was～0.2mJy and～0.6mJy,respectively.Also,Lorimer,Lyne,&Camilo(1998)reached a limit S1400～0.2mJy in their search at600MHz.Our VLA upper limit,S1400 0.1mJy,implies a luminosity L1400≡S1400d2 0.2mJy kpc2.While this is a stringent limit(the least luminous young radio pulsar known,in SNR3C58,has about twice this luminosity;Camilo et al.2002c),there are weaker pulsars known.We therefore used the extremely sensitive Green Bank Telescope(GBT),where CTA1is a circumpolar source,to improve on this limit.

We observed the Chandra position of the pulsar for a total of19.60hr on2003October11.We used the Berkeley-Caltech Pulsar Machine(BCPM;Backer et al.1997),an analog/digital?lter-bank with96channels for each of two polarizations,to record a48MHz-wide band centered at a sky frequency of820MHz.After summing in hardware the signals from the two polarizations, removing the mean and scaling,the power levels from each frequency channel were recorded with 4-bit precision to disk every72μs,for a total of980million time samples.[See Camilo et al.(2002c) for more details of a similar observation at the GBT using the BCPM.]

We analyzed the data using standard methods as implemented in the software package PRESTO (Ransom2001).This involved identi?cation and removal of the worst radio-frequency interference (much of it generated at the observatory),time-shifting the96frequency channels to compensate for dispersive interstellar propagation prior to summing the respective samples(doing this once for each assumed value of dispersion measure,the integrated column density of free electrons), performing a Fast-Fourier Transform of the resulting one-dimensional time series for each trial DM after transformation to the solar-system barycenter,and sifting the resulting spectrum for statisti-cally signi?cant peaks.The last stage included searching for narrow pulse shapes by summing up to eight harmonics of the spectrum;and also searching for moderately accelerated signals,as might be expected from a pulsar in a binary system,or a young one with a large period derivative.

At a distance of1.4kpc,both the Taylor&Cordes(1993)and Cordes&Lazio(2002)electron density models predict DM≈25cm?3pc for the putative radio pulsar in CTA1.However,the X-ray-measured N H≈2.8×1021cm?2would predict DM≈90cm?3pc,assuming an average ratio n e/n H≈0.1.Also,the maximum Galactic dispersion in the direction of CTA1predicted by the Cordes&Lazio model is200cm?3pc,so we searched up to this DM.Although the expected period for the pulsar in CTA1is P～0.1s,and almost certainly not less than～20ms,we chose to analyze our data with much higher time resolution in order to retain serendipitous sensitivity to any pulsars located within the15′-diameter GBT beam.In order to simplify the onerous reduction task,we?rst rebinned the data four-fold to a time resolution of0.288ms,which we kept for the ?rst240trial DMs,each separated by0.5cm?3pc.The e?ective time resolution at the upper end of this range,limited by dispersive smearing within one frequency channel,is about1ms.We then further halved the time resolution,doubled the DM step,and searched a further80time series. In the end,we examined≈100signi?cant signals that appeared at more than one DM,but none showed a true interstellar dispersion pattern that would qualify it as a good pulsar candidate.

We now estimate the?ux density limit of our observation.The ideal rms noise of the observa-tion isσ≡T G?1(nBt)?1/2,where T≈35K includes the system temperature on cold sky as well as a～7K contribution from Galactic synchrotron emission and～3K from CTA1;G=2K Jy?1is the telescope gain;n=2polarizations;B is the bandwidth;and t is the integration time.With our parameters,σ≈7μJy.Including a～20%factor accounting for losses due to hardware limitations and a threshold signal-to-noise ratio of8,we obtain an estimated sensitivity for a sinusoidal pulse shape of～65μJy.For a pulse with duty cycle w=0.1P,this limit is further improved by a factor of～3.Translating this to1400MHz withα≈?1.6,we obtain S1400 30μJy for a sinusoidal pulse shape or S1400 10μJy for w=10%.Strictly,these limits apply to relatively long pulse periods;for P 50ms the limits are somewhat worse,the more so as DM/P increases.

Taking10μJy as the?ux density limit at1400MHz for the pulsar in CTA1implies L1400 0.02 mJy kpc2.This is equal to the lowest luminosity known for a radio pulsar,and is a factor of≈20 below the least-luminous pulsar known with an age of less than1Myr.If the pulsar in CTA1 emits radio waves that intersect the Earth,its luminosity is lower than that of any detected radio pulsar;perhaps more likely,if it is a radio pulsar at all,its beam does not intersect the Earth.

5.Discussion:What is the Pulsar˙E?

The most important unknown property of RX J0007.0+7303is its spin-down luminosity.Pre-dictions of˙E typically make use of correlations between L X and˙E among known pulsars(e.g., Seward&Wang1988;Possenti et al.2002),but this method is fraught with uncertainty,as well as special di?culties in the case of RX J0007.0+7303.The0.5–10keV luminosity of RX J0007.0+7303 that we measure with Chandra,including the point and di?use components,is4.0×1031ergs s?1. This is slightly smaller than the value of5.4×1031ergs s?1measured by Slane et al.(2004)using XMM-Newton,the di?erence probably attributable to an additional contribution of di?use emis-sion contained in the larger XMM-Newton extraction region.The spin-down luminosity predicted by Slane et al.(2004)using the Seward&Wang(1988)relation is then˙E≈5×1034ergs s?1,com-parable to the values found for olderγ-ray pulsars such as Geminga,which has an˙E=3.3×1034 ergs s?1.This interpretation is troubling in its neglect of the large synchrotron nebula,for which there is no proposed power source other than the pulsar.It is impossible to measure the entire syn-chrotron nebula of CTA1with Chandra because of its large size,low surface brightness,and lack of a clear boundary.But since the total synchrotron emission seen by ASCA exceeds the compact source luminosity by more than two orders of magnitude,consideration of the total energy budget would favor a minimum value of˙E≈1.7×1036ergs s?1,as originally proposed by Slane et al. (1997).

We may also look to more detailed X-ray studies of pulsars with PWNe to estimate the spin-down power of CTA1.From an empirical perspective,bright PWNe are found only around pulsars

with˙E>3×1036ergs s?1(Gotthelf2004).1Above this threshold,PWN emission typically exceeds the pulsar point-source luminosity by an order of magnitude.Furthermore,the spectral index of the pulsar in the2–10keV band correlates with˙E according to the Gotthelf(2003)relation

,where˙E38is the spin-down power in units of1038ergs s?1Applying this ΓPSR=2.08?0.29˙E?1/2

to CTA1for whichΓPSR=(1.1?2.2)suggests that˙E 6×1036ergs s?1,allowing for scatter in the relation.

Further indication that˙E is in this higher range is suggested by theγ-ray luminosity of 3EG J0010+7309,which provides a lower-limit on the spin-down power.At d=1.4kpc,theγ-ray ?ux integrated above100MeV corresponds to Lγ=6×1034ergs s?1if isotropic,or5×1033 ergs s?1if beamed into1steradian as is often(but arbitrarily)assumed.Thus,a prediction of ˙E≈5×1034ergs s?1is incompatible with isotropicγ-ray emission,and requires a substantial degree of beaming.On the other hand,if˙E≈6×1036ergs s?1,then the ratio Lγ/˙E is only0.01in the isotropic case,which is similar to Vela,whose˙E=6.9×1036ergs s?1.Note that this argument is independent of whether the X-ray spectrum of RX J0007.0+7303can be extrapolated over four orders of magnitude in energy to join theγ-ray spectrum.Such a connection was suggested by Slane et al.(2004),but it is impossible to verify,as well as unnecessary for associating the sources. The0.5?10keV power law of the Geminga pulsar clearly does not connect with itsγ-ray spectrum (Jackson et al.2002);rather,they are separate spectral components arising from di?erent emission mechanisms.

6.Conclusions

The resemblance of the X-ray morphology of RX J0007.0+7303to the PWN and jets seen in Chandra images of the Crab(Weisskopf et al.2000),Vela(Helfand et al.2001;Pavlov et al. 2001,2003),PSR B1509–58(Gaensler et al.2002),and other newly discovered young pulsars (Halpern et al.2001;Lu et al.2002;Camilo et al.2002a;Hessels et al.2004),enables us to point con?dently to“the pulsar”in the SNR CTA1even though its spin parameters have not yet been determined.Similar conclusions were drawn from Chandra observations of supernova remnants G0.9+0.1(Gaensler,Pivovaro?,&Garmire2001),IC443(Olbert et al.2001),3C396(Olbert et al.2003),and another unidenti?ed EGRET source,GeV J1809–2327(Braje et al.2002).Using clues gathered from its X-ray luminosity,morphology,spectrum,and likely identi?cation with 3EG J0010+7309,we predict that the spin-down power of the pulsar in RX J0007.0+7303is in the range1036?1037ergs s?1.

The upper limit of T∞e<6.6×105K that we derive on the e?ective temperature of the full neutron star surface in CTA1is more constraining of cooling models than nearly all other cases.

As described by Yakovlev et al.(2002),X-ray observations do not yet require exotic phases of matter such as pion and kaon condensates,or free quarks.However,it is necessary to allow a range of neutron star masses if the measured temperatures and ages are to be accommodated by a single equation of state and theory of super?uid properties(Gusakov et al.2004).In this sense, the neutron star in CTA1is cooler for its age than most others,and similar to Vela and Geminga in requiring a mass>1.42M⊙.If so,it may become an issue to understand why single neutron stars often have inferred masses greater than the precise values that are measured in binary radio pulsars,which cluster tightly around1.35M⊙(Thorsett&Chakrabarty1999;Stairs et al.2002; Lyne et al.2004;Weisberg&Taylor2003).Discussion of that potential problem is beyond the scope of this paper.

Energetic pulsars are being discovered with extremely small radio luminosities;whether this is intrinsic or due to beaming remains unclear.Recent examples include PSR J2229+6114coincident with3EG J2227+6122(Halpern et al.2001),PSR J1930+1852in G54.1+0.3(Lu et al.2002; Camilo et al.2002a),PSR J1124–5916in G292.0+1.8(Hughes et al.2001;Camilo et al.2002b), and PSR J0205+6449in3C58(Murray et al.2002;Camilo et al.2002c).All of these pulsars have ˙E=(1?3)×1037ergs s?1and luminosities at1400MHz of≈1mJy kpc2.Such radio luminosities are less than those of≈95%of all pulsars,and less than every other pulsar younger than2×104yr (Camilo et al.2002b).In comparison,the luminosity upper limit for RX J0007.0+7303is only ≈0.02mJy kpc2,which makes it fainter in the radio than all pulsars except the nearby Geminga and perhaps the putative pulsar powering3EG J1835+5918(Mirabal et al.2000;Mirabal&Halpern 2001;Halpern et al.2002).If due to unfavorable orientation with respect to the radio beam,the likely existence of a radio-quietγ-ray pulsar in CTA1tends to support the outer-gap model,in which theγ-rays arise from regions far out in the magnetosphere and are emitted into a wide fan beam,illuminating a much larger fraction of the sky than does the narrow radio beam.

We thank Don Backer for making the BCPM available to the GBT user community.This is work was supported by SAO grant GO3-4064X.

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Fig.1.—XMM-Newton and Chandra images of the central source RX J0007.0+7303in CTA1in the0.5?8keV band,at two di?erent display scales.North is up and east is to the left.Top panels are256′′×256′′.Bottom panels are64′′×64′′.Left:Combined XMM-Newton MOS1and MOS2 images,smoothed with a Gaussian ofσ=1′′.Right:Chandra ACIS-S3image,smoothed with a Gaussian ofσ=0.′′5.The position of the point source is(J2000)00h07m01.s56,+73?03′08.′′1.[A color version of this?gure is available from the author.]

Fig. 2.—Chandra radial pro?le of RX J0007.0+7303(histogram)compared to the PSF(dashed line),which is calculated for the observed spectral distribution.The PSF is scaled to match the detected counts in the central pixel and the background measured in the annulus25′′

A clear excess is seen corresponding to the faint nebulosity at r<3′′,and additional enhancement

at3′′

Fig. 3.—Chandra images of the central source RX J0007.0+7303in CTA1in di?erent energy bands and smoothed with a Gaussian ofσ=0.′′5.North is up and east is to the left.Left:Soft (0.2–2.0keV).Right:Hard(2–8keV).Top panels are64′′×64′′.Bottom panels are32′′×32′′.[A color version of this?gure is available from the author.]

-------

CTA 1

Fig.4.—Left:Upper limit on the surface temperature of the neutron star in CTA1,in comparison with cooling models of Page(1998).The horizontal line denotes a possible age range of(1?3)×104yr.This?gure is reproduced from Slane,Helfand,&Murray(2002),and includes their upper limit on3C58.Right:This?gure is taken from Yakovlev et al.(2002),and includes cooling models calculated assuming strong proton super?uidity and weak neutron super?uidity.Here,the direct

Urca process is not completely suppressed,and operates in the more massive neutron stars.

Fig. 5.—CCD images at the location of the central X-ray source RX J0007.0+7303in CTA1 obtained with the2.4m Hiltner telescope.North is up,and east is to the left.Each panel is70′′on a side.Seeing ranges from0.′′8in I to1.′′2in V.Interference fringes in the I-band image are artifacts.Limiting(3σ)magnitudes at the position of the Chandra point source,(J2000) 00h07m01.s56,+73?03′08.′′1as indicated by the crosses,are B>25.4,V>24.8,R>25.1,and I>23.7.[A higher resolution version of this?gure is available from the author.]

-- ---- --

Fig. 6.—VLA image of the central region of CTA 1at 1425MHz,taken in AB con?guration with a beam FWHM of 5.′′9×4.′′4.The cross marks the Chandra location of the neutron star in RX J0007.0+7303.The 1σnoise level is 31μJy per beam at this position.For comparison,the point source marked “S”has a ?ux density of 180μJy.The large-scale periodic noise in the image is an artifact.

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X射线数字成像检测系统郑金泉.doc

实用标准文档 X射线数字成像检测系统

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小学三年级数学《简单的时间计算》教案范文三篇时间计算是继二十四时计时法的学习之后安排的一个内容。下面就是小编给大家带来的小学三年级数学《简单的时间计算》教案范文，欢迎大家阅读! 教学目标： 1、利用已学的24时记时法和生活中对经过时间的感受，探索简单的时间计算方法。 2、在运用不同方法计算时间的过程中，体会简单的时间计算在生活中的应用，建立时间观念，养成珍惜时间的好习惯。 3、进一步培养课外阅读的兴趣和多渠收集信息的能力。教学重点：计算经过时间的思路与方法。教学难点：计算从几时几十分到几时几十分经过了多少分钟的问题。教学过程：一、创设情景，激趣导入 1、谈话：小朋友你们喜欢过星期天吗?老师相信我们的星期天都过得很快乐!明明也有一个愉快的星期天，让我们一起来看看明明的一天，好吗? 2、小黑板出示明明星期天的时间安排。 7：10-7：30 起床、刷牙、洗脸; 7：40-8：20 早锻炼; 8：30-9：00 吃早饭; 9：00-11：00 看书、做作业 …… 3、看了刚才明明星期天的时间安排，你知道了什么?你是怎么知道的?你还想知道什么?

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X射线数字成像检测系统

X射线数字成像检测系统X射线数字成像检测系统

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射线数字成像技术发展

射线数字成像技术发展摘要：射线数字成像是一种先进辐射成像技术，是辐射成像技术的重要发展方向，该技术利用射线观察物体内部的技术。这种技术可以在不破坏物体的情况下获得物体内部的结构和密度等信息，并且通过计算机进行图像处理和判定。目前已经广泛应用于医疗卫生、国民经济、科学究等领域。关键词：辐射成像射线数字成像 1引言自德国物理学家伦琴1895年发现X射线以来，射线无损探伤作为一种常规的无损检测方法在工业领域应用已有近百年的历史，人们一直使用胶片记录X（γ）射线穿过被检物件后的影像，其中60多年来，则一直使用增感屏配合胶片来获取高品质的影像，曝光过后的胶片经过化学处理，产生可视的影像后，在观片灯上显示出来以供读取、分析及判断。胶片-增感屏系统可使射线检测人员实现对影像的采集、显示和存储。这种方法操作简单，产生的图像质量优异，功能效用全面，因此该技术在包括核工业在内的工业、医疗领域一直被广泛使用。胶片照相法的不足在于检测周期长，因为需要暗室处理，检测周期在3～20个小时不等；大量底片造成保存上的困难，查阅不便；胶片成本高；曝光时间长；在大量的检测工作面前，需要大量人力资源；底片难以共享，某些焊缝底片在需要专家共同研讨评定时，该弊端特别明显；不利于环境保护等。无法满足目前工业化生产和竞争日益激烈的需要。随着科学技术和设备制造能力的进步，例如电子技术、光电子技术、数字图像处理技术的发展；高亮度高分辨率显示器的诞生；高性能计算机/工作站的广泛应用；计算机海量存储、宽带互联网的发展，使得数字成像技术挑战传统胶片成像方式在技术上形成可能。以射线DR、CR和CT为代表的数字射线成像技术，结合远程评定技术将是无损检测技术领域的一次革命。数字射线照相技术具有检测速度快，图像保存方便，容易实现远程分析和判断，是未来射线检测发展的方向[1]。

X射线数字成像检测系统(郑金泉)

X射线数字成像检测系统

目录一、目的意义 (3) 二、系统介绍 (3) 2.1 CR技术与DR技术的共同点 (4) 2.2 CR技术与DR技术的不同点 (4) 2.3对比分析 (5) 2.4 系统组成 (5) 2.5 X射线数字平板探测器 (6) 2.6 X射线源 (7) 2.7 图像处理系统 (8) 2.8成像板扫描仪 (9) 2.9IP成像板 (9) 三、DR检测案例 (10) 3.1 广西220kV振林变 (10) 3.2 广西220kV水南变 (11) 3.3 温州220kV白沙变 (13) 3.4 广西110kV城东变 (15) 3.5 广西乐滩水电站 (16) 四、CR检测案例 (18) 4.1百色茗雅220kV变电站 (18)

一、目的意义气体绝缘全封闭组合电器（GIS）设备结构复杂，由断路器、隔离开关、接地开关、互感器、避雷器、母线、连接件和出线终端等组成，内部充有SF6绝缘气体，给解体检修工作带来很大的困难，且检修工作技术含量高，耗时长，停电所造成的损失大。通过对GIS设备事故的分析发现，大部分严重事故，未能通过现有的检测手段在缺陷发展初期被发现，导致击穿、烧损等严重事故的发生。通过GIS设备局放监测，结合专家数据库和现场经验，可大致判断GIS设备局放类型，进行大致的定位，但无法明确GIS设备内部的具体故障。结合X射线数字成像检测系统，对GIS设备进行多方位透视成像，配合专用的图像处理与判读技术，实现其内部结构的“可视化”与质量状态快速诊断，极大地提高GIS 设备故障定位与判别的准确性，提高故障诊断效率，为整个设备的运行安全与质量监控提供一种全新的检测手段。对GIS设备局放可能造成的危害及其影响范围和程度，提出相应策略，采取相应的措施，对电网的安全、稳定、经济运行具有重要意义。二、系统介绍按照读出方式（即X射线曝光到图像显示过程）不同，可分为： ◆数字射线成像（DR-Digital Radiography ） ◆计算机射线成像（CR-Computed Radiography）图1-1检测原理图

古代时间的计算方法

中国古代时间的计算方法（1）现时每昼夜为二十四小时，在古时则为十二个时辰。当年西方机械钟表传入中国，人们将中西时点，分别称为“大时”和“小时”。随着钟表的普及，人们将“大时”忘淡，而“小时”沿用至今。古时的时（大时）不以一二三四来算，而用子丑寅卯作标，又分别用鼠牛虎兔等动物作代，以为易记。具体划分如下：子（鼠）时是十一到一点，以十二点为正点；丑（牛）时是一点到三点，以两点为正点；寅（虎）时是三点到五点，以四点为正点；卯（兔）时是五点到七点，以六点为正点；辰（龙）时是七点到九点，以八点为正点；巳（蛇）时是九点到十一点，以十点为正点；午（马）时是十一点到一点，以十二点为正点；未（羊）时是一点到三点，以两点为正点；申（猴）时是三点到五点，以四点为正点；酉（鸡）时是五点到七点，以六点为正点；戌（狗）时是七点到九点，以八点为正点；亥（猪）时是九点到十一点，以十点为正点。古人说时间，白天与黑夜各不相同，白天说“钟”，黑夜说“更”或“鼓”。又有“晨钟暮鼓”之说，古时城镇多设钟鼓楼，晨起（辰时，今之七点）撞钟报时，所以白天说“几点钟”；暮起（酉时，今之十九点）鼓报时，故夜晚又说是几鼓天。夜晚说时间又有用“更”的，这是由于巡夜人，边巡行边打击梆子，以点数报时。全夜分五个更，第三更是子时，所以又有“三更半夜”之说。时以下的计量单位为“刻”，一个时辰分作八刻，每刻等于现时的十五分钟。旧小说有“午时三刻开斩”之说，意即，在午时三刻钟（差十五分钟到正午）时开刀问斩，此时阳气最盛，阴气即时消散，此罪大恶极之犯，应该“连鬼都不得做”，以示严惩。阴阳家说的阳气最盛，与现代天文学的说法不同，并非是正午最盛，而是在午时三刻。古代行斩刑是分时辰开斩的，亦即是斩刑有轻重。一般斩刑是正午

excel表格日期计算

竭诚为您提供优质文档/双击可除 excel表格日期计算篇一：excel中几个时间计算公式假设b2为生日 =datedif(b2,today(),"y") datediF函数，除excel2000中在帮助文档有描述外，其他版本的excel在帮助文档中都没有说明，并且在所有版本的函数向导中也都找不到此函数。但该函数在电子表格中确实存在，并且用来计算两个日期之间的天数、月数或年数很方便。微软称，提供此函数是为了与lotus1-2-3兼容。该函数的用法为 “datediF(start_date,end_date,unit)”，其中start_date 为一个日期，它代表时间段内的第一个日期或起始日期。end_date为一个日期，它代表时间段内的最后一个日期或结束日期。unit为所需信息的返回类型。 “y”为时间段中的整年数，“m”为时间段中的整月数，“d”时间段中的天数。“md”为start_date与end_date日期中天数的差，可忽略日期中的月和年。“ym”为start_date 与end_date日期中月数的差，可忽略日期中的日和年。“yd”

为start_date与end_date日期中天数的差，可忽略日期中的年。比如，b2单元格中存放的是出生日期（输入年月日时，用斜线或短横线隔开），在c2单元格中输入 “=datedif(b2,today(),"y")”（c2单元格的格式为常规），按回车键后，c2单元格中的数值就是计算后的年龄。此函数在计算时，只有在两日期相差满12个月，才算为一年，假如生日是20xx年2月27日，今天是20xx年2月28日，用此函数计算的年龄则为0岁，这样算出的年龄其实是最公平的。身份证号提取年龄 =datediF(--text((len(a1)=15)*19”即可获得当时的日期时间； 2、使用公式：用=now()而非=date()，=date()只有日期，然后进行菜单“工具->选项”，选择“重新计算”页，选中“人工重算”，勾不勾选“保存前自动重算”看自己的需要和想法了，如果勾选了，那日期时间那总是最后一次保存的日期时间，不勾选的话，如果你的表格中有公式记得准备存前按F9 篇二：excel中如何计算两个日期之间的月数 excel中如何计算两个日期之间的月数

射线数字成像技术的应用样本

射线数字成像技术的应用在管道建设工程中, 射线检测是确保焊接质量的主要无损检测手段, 直接关系到工程建设质量、健康环境、施工效率、建设成本以及管线的安全运行。长期以来, 射线检测主要采用X射线或γ射线的胶片成像技术, 检测劳动强度大, 工作效率较低, 常常影响施工进度。近年来随着计算机数字图像处理技术及数字平板射线探测技术的发展, X射线数字成像检测正逐渐运用于容器制造和管道建设工程中。数字图像便于储存, 检索、统计快速方便, 易于实现远程图像传输、专家评审, 结合GPS系统可对每道焊口进行精确定位, 便于工程质量监督。同时, 由于没有了底片暗室处理环节, 消除了化学药剂对环境以及人员健康的影响。过大量的工程实践与应用, 对管道焊缝射线数字化检测与评估系统进行了应用研究分析探索。 1 射线数字成像技术的应用背景随着中国经济的快速发展, 对能源的需求越来越大, 输油输气管道建设工程也越来越多, 众多的能源基础设施建设促进了金属材料焊接技术及检测技术的进步。当前, 在管道建设工程中, 管道焊接基本实现了自动化和半自动化, 而与之配套的射线检测主要采用胶片成像技术, 检测周期长、效率低下。”十二五”期间, 将有更多的油气管道建设工程相继启动, 如何将一种可靠的、快速的、”绿色”的射线数字检测技术应用于工程建设中, 以替代传统射线胶片检测技术已成为当前管道焊缝射线检测领域亟需解决的问题。 2 国内外管道焊缝数字化检测的现状 2.1 几种主要的射线数字检测技术 1) CCD型射线成像( 影像增强器) 2) 光激励磷光体型射线成像( CR)

3) 线阵探测器( LDA) 成像系统 4) 平板探测器( FPD) 成像系统几种技术各有特点, 当前适用于管道工程检测的是CR和FPD, 但CR不能实时出具检测结果, 且操作环节较繁琐、成本较高, 因此平板探测器成像系统成为射线数字检测的主要发展方向。 2.2 国内研发情况国内当前从事管道焊缝射线数字化检测系统研发的机构主要有几家射线仪器公司, 但其产品主要用于钢管生产厂的螺旋焊缝检测。经过实践应用比较, 研究应用电子学研究所研发的基于平板探测器的管道焊接射线数字化检测与评估系统已能够满足管道工程检测需要, 并经过了科技成果鉴定。 2.3 国外研发情况国外对数字化射线图像信息获取和无损检测方面的实验室研究工作开展较早, 并进行了深入的研究, 国外文献对数字X射线平板探测系统的工作原理、典型结构、参数优化、应用领域等诸多方面有少量的公开资料报道, 其中美国、日本等国对该技术的研究已比较成熟, 有些技术还申请了专利保护, 并已有实用产品用于实际领域的报道, 但关键制造技术则未见详细报道。 3 数字成像系统的的工程应用可行性 3.1 系统主要组成 RDEES系统主要由数字平板探测器( FPD) 、 X射线源( 或爬行器) 、工装夹具、系统软件、便携式计算机、 GPS定位器等部分组成。 3.2 检测布置根据不同管道环焊缝特点可选择源在外的双壁透照方式或源在内的中心透照方式。

时间计算公式

高中地理计算公式一、时间的计算 1、求时区：时区数＝已知经度／15°（商四舍五入取整数，即为时区数） 2、求区时：所求区时＝已知区时±时区差（东加西减） 3、求地方时：所求地方时＝已知地方时±4分钟／度×经度差（东加西减）二、太阳高度的计算 1、求正午太阳高度： H＝90°－︱纬度差︱（纬度差指当地纬度与太阳直射纬度之间的差） 2、求子夜太阳高度： H＝︱纬度和︱－90°（纬度和指当地纬度与太阳直射纬度之间的和） 3、求南北两楼的楼间距： L＝h?cotH (h为楼高，H为该地一年中最小的正午太阳高度) 三、昼夜长短的计算 1、求昼长：（1）昼长＝昼弧∕15° （2）昼长＝日落时间－日出时间（3）昼长＝24－夜长（4）昼长＝（12－日出地方时）×2 （5）昼长＝（日落地方时－12） 2、求夜长（1）夜长＝夜弧∕15° （2）夜长＝24－昼长（3）夜长＝（24－日落地方时）×2 （4）北半球某纬度的夜长＝南半球同纬度的昼长四、日出、日落时刻的计算１、求日出时刻：（1）日出时刻＝当地纬线与晨线交点的时刻（2）日出时刻＝12－昼长∕2 2、求日落时刻：（1）日落时刻＝当地纬线与昏线交点的时刻（2）日落时刻＝12＋昼长∕2 五、球面距离的计算（1）赤道和经线上的距离111Km×度数（2）纬线上的距离＝111Km×度数?COSθ(θ为当地的纬度) （3）对趾点的计算:经度互补,一东一西；纬度相等,一南一北。六、比例尺的计算（1）比例尺＝图上距离∕实地距离（2）缩放图幅面积＝原图幅面积×比例尺缩放的平方七、相对高度的计算（1）陡崖相对高度：（n－1）d≤H＜(n＋1)d (n为等高线条数，d为等高距) （2）H＝T∕6°×1000米 (H为两地相对高度,T为两地温差)

日期计算器

程序设计与算法课程设计

课程设计评语对课程设计的评语: 平时成绩：课程设计成绩：总成绩：评阅人签名：注：1、无评阅人签名成绩无效； 2、必须用钢笔或圆珠笔批阅，用铅笔阅卷无效； 3、如有平时成绩，必须在上面评分表中标出，并计算入总成绩。

目录课程设计评语 (2) 目录 (3) 1．课程论文题目.............................................................................................. 错误！未定义书签。2．程序设计思路.. (4) 3．功能模块图 (4) 4．数据结构设计 (5) 5．算法设计 (5) 6．程序代码 (6) 7．程序运行结果 (7) 8．编程中遇到的困难及解决方法.................................................................. 错误！未定义书签。9．总结及建议.................................................................................................. 错误！未定义书签。10．致谢. (8)

1.课程设计题目：日期计算器【要求】功能：计算输入日期是当年中的第几天系统要求实现以下功能： 1. 由用户分别输入：年、月、日 2. 计算该日期是当年中的第几天 3. 输出计算出的天数分步实施： 1、首先设计Dater对象构造器 2、判断此年是否为闰年。 3、计算从此年年初到此日的一共多少天 4、输入输出处理。【提示】需求分析：使用Dater对象构造器,用1判断为闰年,,0判断为不是闰年,使用累加的方法计算年初到此日共有多少天,进行输入输出处理. （1）主函数设计主函数提供输入，处理，输出部分的函数调用。（2）功能模块设计模块：由用户自己录入年，月，日，、。计算该日期为一年的中德第几天。输出计算出的天数，返回主菜单。 3. 功能模块图（1）输入模块由用户分别输入：年、月、日

射线数字成像检测系统

X射线数字成像检测系统 This manuscript was revised by the office on December 10, 2020.

X射线数字成像检测系统X射线数字成像检测系统

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