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Balmer-Dominated Spectra of Nonradiative Shocks in the Cygnus Loop, RCW 86 and Tycho Supern

Balmer-Dominated Spectra of Nonradiative Shocks in the Cygnus Loop, RCW 86 and Tycho Supern
Balmer-Dominated Spectra of Nonradiative Shocks in the Cygnus Loop, RCW 86 and Tycho Supern

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Balmer-Dominated Spectra of Nonradiative Shocks in the Cygnus Loop,RCW 86and Tycho Supernova Remnants Parviz Ghavamian 1,3,5,John Raymond 2,R.Chris Smith 4and Patrick Hartigan 1Received Accepted by the Astrophysical Journal

ABSTRACT

We present an observational and theoretical study of the optical emission from nonradiative shocks in three supernova remnants:the Cygnus Loop,RCW86and Tycho.The spectra of these shocks are dominated by collisionally excited hydrogen Balmer lines which have both a broad component caused by proton-neutral charge exchange and a narrow component caused by excitation of cold neutrals entering the shock.In each remnant we have obtained the broad to narrow?ux ratios of the Hαand Hβlines and measured the Hαbroad component width.

A new numerical shock code computes the broad and narrow Balmer line emission from nonradiative shocks in partially neutral gas.The Balmer line?uxes are sensitive to Lyman line trapping and the degree of electron-proton temperature equilibration. The code calculates the density,temperature and size of the postshock ionization layer and uses a Monte Carlo simulation to compute narrow Balmer line enhancement from Lyman line trapping.The initial fraction of the shock energy allocated to the electrons and protons(the equilibration)is a free parameter.Our models show that variations in electron-proton temperature equilibration and Lyman line trapping can reproduce the observed range of broad to narrow ratios.The results give80%?100% equilibration in nonradiative portions of the NE Cygnus Loop(v S~300km s?1), 40%?50%equilibration in nonradiative portions of RCW86(v S~600km s?1)and ~<20%equilibration in Tycho(v S~2000km s?1).Our results suggest an inverse correlation between magnetosonic Mach number and equilibration in the observed remnants.

Subject headings:ISM:supernova remnants:shock waves,radiative transfer

1.INTRODUCTION

Supernova explosions produce some of the strongest shocks in nature.During the event,the outer layers of a star are ejected at speeds as high as30,000km s?1.The dense ejecta behave like a highly supersonic piston,producing a strong shock wave in the ISM ahead of the piston (commonly known as the forward shock).When the mass swept up by the forward shock begins to exceed the ejecta mass,the supernova remnant(SNR)enters the blast wave(Sedov-Taylor)phase of evolution(Hamilton&Sarazin1984,Truelove&McKee1999).From the genesis of the SNR through the blast wave stage the forward shock is nonradiative,meaning that it loses a negligible fraction of its internal energy to radiative cooling.

Due to the low density(n~<1cm?3)and high Mach number(M~>200)of the forward shock,the heated interstellar gas behaves like a collisionless plasma(Draine&McKee1993). According to the strong shock jump conditions,electrons and protons are heated to temperatures in a minimum ratio T e/T p=m e/m p(~1/2000).However,plasma waves and MHD turbulence at the shock front may transfer energy from protons to electrons(Tidman&Krall1971,Kennel 1985,Cargill&Papadapoulos1988),further equilibrating the two particle temperatures.Since the electrons and protons are a?ected by a di?erent range of plasma waves and the Coulomb equilibration time downstream often exceeds the age of the remnant,the two particle temperatures can remain unequal throughout the shock.The types of plasma waves excited at the shock transition(and hence the amount of collisionless heating)depend strongly on parameters such as the magnetosonic Mach number M S and magnetic?eld orientation.Due to this complicated dependence and the extreme di?culty of creating high Mach number collisionless shocks in the laboratory,the properties of collisionless shocks remain poorly understood.

In a cold(~<104K),partially ionized medium,the charged and neutral distributions respond very di?erently to the passage of a collisionless shock.The cold neutrals are initially una?ected by the shock transition,while charged particles are compressed by a factor of four and strongly heated.Some of the cold neutrals entering the shock are collisionally excited before being destroyed by collisional ionization or charge transfer.Radiative decay by these excited neutrals

produces narrow component Balmer emission with a line width given by the preshock temperature. In contrast,charge exchange between cold neutrals and protons produces fast neutrals having the velocity distribution of the postshock protons.Collisional excitation of the fast neutrals produces broad Balmer line emission(Chevalier&Raymond1978,Chevalier,Kirshner&Raymond1980 (hereafter CKR80)).While the low temperatures in radiative shocks favor the emission of strong forbidden lines such as[O II],[O III],[N II]and[S II],the high temperatures behind nonradiative shocks produce hydrogen Balmer line emission far more e?ciently.Balmer-dominated shocks have been detected in Tycho(Kirshner,Winkler&Chevalier1987(hereafter KWC87),Smith et al. 1991,Ghavamian et al.2000),SN1006(KWC87,Smith et al.1991,Winkler&Long1997), RCW86(Long&Blair1990,Smith1997),Kepler(Blair,Long&Vancura1991),portions of the Cygnus Loop(Raymond et al.1983(hereafter RBFG83),Fesen&Itoh1985,Hester,Raymond& Blair1994(hereafter HRB94)),four remnants in the LMC(Tuohy et al.1982,Smith et al.1991, 1994)and the bow shock surrounding the pulsar PSR1957+20(Aldcroft,Romani&Cordes1992).

The optically emitting layer behind a nonradiative shock is extremely thin(~<10?3pc),so the proton temperature very close to the shock front can be measured from the width of a broad Balmer line.The proton temperature in turn depends on the shock velocity through the jump conditions,making the broad line pro?le a powerful diagnostic for probing the global kinematics of young SNRs.The broad to narrow?ux ratio is another important diagnostic because it also depends on the shock velocity(CKR80,Smith et al.1991).Proper motion measurements of Balmer-dominated?laments have been combined with shock velocity estimates from the broad component to estimate distances to several young SNRs(for example see Long,Blair&van den Bergh1988for SN1006,and Hesser&van den Bergh1981for Tycho).

Balmer-dominated spectra can be di?cult to interpret because the broad component width and broad to narrow ratio yield di?erent shock velocities depending on the assumed electron-proton equilibration.Since the equilibration is not known a priori,spectroscopic observations in the past have only yielded a range of shock velocities v S from the Balmer line pro?les:a minimum v S(min) for no equilibration and a maximum v S(max)for full equilibration.In addition,collisional

excitation behind the shock generates both Lyman line photons and Balmer line photons.Lyman line trapping by slow neutrals partially converts Lyβand higher Lyman photons into Balmer line photons;this enhances the Balmer line?ux in the narrow component and complicates the diagnostic interpretation of the broad to narrow ratio(CKR80,Smith et al.1991,Ghavamian 1999)).Moreover,since the Lyβoptical depth is larger than that of Lyγ,the Hαbroad to narrow ratio is more strongly a?ected than the Hβbroad to narrow ratio.The Lyman line optical depth behind the shock typically lies between0and1,so that neither Case A nor Case B conditions apply.It is clear that disentangling the combined e?ects of Lyman line trapping and equilibration on a Balmer-dominated spectrum requires(1)the acquisition of high S/N line pro?les in both Hαand Hβ,and(2)careful modeling of the atomic physics and radiative transfer.

In§2of this paper,we present high S/N spectra of three nonradiative shocks which resolve the broad and narrow components of both Hαand Hβ.In§3,we present measurements of the Hαbroad component width and broad to narrow ratios in Hαand Hβ.We describe numerical models of nonradiative shocks in§4,including calculations of ionization structures for a range of equilibrations and Monte Carlo simulations of Lyβand Lyγtrapping.In§5we compare the observed broad to narrow ratios with model predictions and simultaneously determine both the shock velocity and equilibration for the observed SNRs.In§6we discuss our results and in§7we present our conclusions.

2.SPECTROSCOPIC OBSER V ATIONS

The spectroscopic datasets presented here were acquired over a one year period between October1997and September1998.We chose the instrumental setup for each observation to simultaneously maximize the number of detected photons and provide enough spectral resolution to separate the broad Balmer lines from the narrow Balmer lines.A log of our spectroscopic observations appears in Table1.The telescope and spectrograph con?gurations used for the observations are described below.

2.1.Cygnus Loop and Tycho

Our spectroscopic observations of NE Cygnus and Tycho were performed on the nights of October7-10,1997(UT),using the1.5meter Tillinghast re?ector telescope at the Fred Lawrence Whipple Observatory.The Schmidt camera CCD was a Loral512×2688pixel chip,with an unbinned plate scale of0.6′′per15μm pixel.To reduce readout noise during these observations, we binned the CCD chip by4pixels along the spatial direction.The spectrograph was equipped with a1200l mm?1grating blazed at5700?A,providing a dispersion of0.38?A pixel?1and spectral coverage of1000?A.With this setup,only one Balmer line could be?t on the CCD chip, so we performed the Hαand Hβobservations at di?erent times.Our target in NE Cygnus Loop was?lament P7from the list of positions observed by the Hopkins Ultraviolet Telescope during the Astro-2mission.We used a1.1′′×3′slit for Hα,yielding a resolution of1.4?A.To obtain the Hβline pro?le,we observed Cygnus P7again on the night of September26,1998(UT).In this case,we used a3′′×3′slit with the1200l mm?1grating,yielding a resolution of1.5?A.A POSS image of the Cygnus P7?lament appears in Figure1,along with the two-dimensional FAST spectrum.The one-dimensional Hαand Hβpro?les appear in Figure2.From the Hαline,we?nd a broad component width of262±32km s?1,with no evidence of forbidden line emission.The shift between the broad and narror component line centers is less than the uncertainty in broad component width,indicating a nearly edge-on viewing geometry.

The1997Tycho observations focused on the bright nonradiative shock Knot g.In these observations,we used the300l mm?1grating with a3′′slit,centered on5545?A(4000?A coverage).This convenient combination put both Hαand Hβon the CCD chip and allowed simultaneous detection of the Hαand Hβbroad components.As in the previous observations,we binned the CCD chip by4pixels.The resolution for this setup was275km s?1(6?A at Hα).It is evident from the two-dimensional spectrum(Figure3)that the Hαsurface brightness and broad component width vary with position along the Knot g?lament,re?ecting variations in preshock density,shock velocity and viewing angle.The extraction aperture shown in Figure3was centered on the upper part of Knot g,where the broad component is brightest and its width most nearly

constant(hereafter labeled Knot g(1)).The extracted Hαand Hβline pro?les appear in Figure 4.Knot g(1)is the brightest portion of the?lament(broad component FWHM of1765±110 km s?1),while the lower part Knot g(2)is fainter(broad FWHM of2105±130km s?1).The broad component center of Knot g(1)is redshifted132±35km s?1from the center of the narrow component,indicating that the plane of the shock is tilted slightly into the plane of the sky.

In the1997Tycho spectra,we detected faint di?use Hαemission above Knot g.We did not subtract the1-D di?use spectrum directly from that of Knot g(1)because then the resulting1-D spectrum becomes too noisy to detect the Hβbroad component.Instead,we measured the Hαsurface brightnesses of Knot g and the di?use emission separately,using FAST spectra acquired in1998(using the same detector setup as the1997observations,see Ghavamian et al.2000). From the1998data,we found that the Di?use Hαemission contributes approximately12%of the narrow?ux from Knot g(1).We have used this information to correct the Hαbroad to narrow ratio of Knot g(1).The di?use Hβemission is very faint and is almost lost in the noise,so we have not corrected the Hβbroad to narrow ratio.In a separate paper(Ghavamian et al.2000),we show that the di?use emission is associated with a photoionization precursor from the supernova blast wave.Since the width of the broad Hbeta line and its shift from zero velocity must be the same as from the high S/N Hαmeasurement,we hold these quantities?xed while simultaneously ?tting the broad and narrow Hβlines.Constraining the?t in this manner is useful because the S/N of the Hβbroad component is signifcantly lower than that of Hα.

Prior to our observations,the most recent spectroscopic study of Knot g was that of Smith et al.(1991),who found a broad FWHM of1900±300in Hα.This value was obtained by averaging the broad component width over the length of Knot g.We note that this velocity lies roughly midway between our separately measured broad component widths for sections(1)and (2).In addition,the average Hαbroad to narrow ratio of sections(1)and(2)lies within the range quoted by Smith et al.(1991).However,in our spectra we?nd a signi?cantly smaller shift in the broad component line center than Smith et al.(1991).This may be due to the strong variations in shock viewing angle along the length of the?lament.In Table2we present our observational

results for Knot g side by side with those of earlier papers.

Since the Hαand Hβlines were recorded simultaneously,we were able to measure the broad and narrow component Balmer decrements I Hα/I Hβseparately for Knot g(1).Although the S/N of the broad Hβline is signi?cantly lower than that of the broad Hαline,we were able to estimate the broad Hβ?ux by setting the width and center of this line equal to that of Hαduring?tting. The Balmer decrements are shown in Table3for the broad and narrow components of Tycho Knot g(1).For comparison,we have computed I Hα/I Hβfor both upper and lower limits of the visual extinction parameter(1.6≤A V≤2.6)determined by CKR80.It is evident that the narrow Balmer decrement is considerably larger than the broad Balmer decrement.Interestingly,using A V=1.6yields a broad Balmer decrement of3.67,consistent with pure collisional excitation in a high temperature(~>106K)gas.Adopting the smaller value of A V also results in better agreement between observations and models of the photoionization precursor(Ghavamian et al.2000).

2.2.RCW86

We observed the galactic SNR RCW86on April5-8,1998(UT),using the RC Spectrograph at the f/7.8focus of the CTIO4meter telescope.The RC Spectrograph features a Loral3k CCD with15μm pixels connected to a Blue Air Schmidt camera.This combination gives a plate scale of 0.5′′pixel?1.A decker allows for an adjustable slit length,with a maximum unvignetted slit size of 5′.Our observations targeted4positions around the remnant,and included moderate resolution spectra of the Hαand Hβlines.In the Hαobservations,we used the CTIO1200l mm?1grating (0.5?A pixel?1,blazed at8000?A)with a?lter inserted to exclude higher order emission lines. With a3′′slit,the spectral resolution of the Hαobservations was2.2?A,with spectral coverage of1565?A.To obtain the Hβline pro?les,we used the860l mm?1grating in2nd order(0.34?A pixel?1,blazed at5500?A),with?lter bg39to exclude higher order emission https://www.doczj.com/doc/be1624537.html,bined with a slit size of3′′,the resolution of the Hβsetup was1.4?A,with spectral coverage of1135?A.

The brightest nonradiative shocks in RCW86are located in the southwestern corner of the

remnant,?anking the bright radiative shocks(Figure5).From the two-dimensional spectrum

of SW RCW86,it is evident that some of the shocks at this location have become radiative (marked by the absence of broad Balmer emission and the presence of[N II]λλ6548,6583and [S II]λλ6716,6731lines).We centered the extraction aperture as shown in Figure5to avoid the radiative emission above and bright stellar continuum below the aperture.Both optical(Leibowitz &Danziger1983,Rosado et al.1996,Smith1997))and X-ray(Kaastra et al.1992,Smith1997, Vink,Kaastra&Bleeker1998,Petruk1999)observations have shown that the radiative emission arises from a dense cloud overrun by the supernova blast wave.The high neutral density is also responsible for the brightness of the broad and narrow Hαlines in the one-dimensional spectrum (Figure6).

We reduced all spectroscopic data using standard routines in IRAF6.After applying overscan, bias,?at?eld,response and dark count corrections to all two-dimensional spectra,we corrected for the slit function in the two-dimensional spectra using twilight sky?ights.Finally,we untilted the emission lines using wavelength solutions from calibration lamp spectra,then subtracted the sky background using night sky emission adjacent to each target object.

The spectra presented in this paper were acquired under varying photometric conditions. Skies where non-photometric during the1997observations,so we only applied a sensitivity correction to the Cygnus Loop and Tycho data.Throughout the1998observations,however, conditions at Mt.Hopkins were nearly https://www.doczj.com/doc/be1624537.html,parison of the spectra from standard stars Hiltner102,LB1240,HD192281and BD284211with one another indicates that the1998 Cygnus Loop spectrum is photometrically accurate to within20%.The Hαobservations of RCW 86were performed under nearly photometric conditions,while the Hβobservations were performed under partial cirrus.From an examination of spectra from standard stars LTT3218,LTT7379 and LTT7987,we estimate that the Hα?ux shown in Figure6is accurate to within10%.

3.Line Pro?le Fits

To extract the broad and narrow component?uxes and measure the width of the

broad component,we?t each Balmer line pro?le with two independent Gaussians plus a linear https://www.doczj.com/doc/be1624537.html,ing the IRAF deblending task SPLOT and self-written routines forχ2minimization ?tting,we obtained quantitative estimates of the line?ux,width and center of the broad and narrow Balmer lines.Since the position of the zero level background a?ects the estimated?ux of the broad component,this baseline uncertainty is the dominant source of nonrandom error in cases where the broad component is very wide and faint(as in Tycho,for example).Both the baseline uncertainty and statistical uncertainty have been included in the quoted broad to narrow ratios.

We measured the broad component widths from the Hαline pro?les,then corrected for the instrumental response by subtracting the narrow component width in quadrature from the broad component width.In each case,the narrow component widths were equal to the instrumental resolution(they were unresolved).The broad and narrow components are most tightly blended in the Cygnus P7line pro?les.The error bars on the Hαand Hβbroad to narrow ratios are correspondingly larger.

4.The Numerical Shock Models

The goal of the numerical models is to calculate the Hαand Hβbroad to narrow ratios for arbitrary shock speed,equilibration and preshock neutral https://www.doczj.com/doc/be1624537.html,paring the predicted broad to narrow ratios with the observed values should then allow us to constrain the shock velocity and equilibration of the observed SNRs.To compute the Balmer line?ux from a nonradiative shock, we have computed the density and temperature of the postshock gas as a function of position.We have used the results of these calculations to compute the Lyβand Lyγoptical depths behind the shock.The Lyman optical depth behind the shock typically lies between0and1,meaning that neither Case A nor Case B conditions apply.

4.1.Cross Sections

We have consulted the following sources for collision cross sections and strengths:

Collisional Ionization and Charge Exchange:In the shock models we use the polynomial?t to the electron-hydrogen ionization cross section from Janev et al.(1987).The proton ionization cross section is from a numerical?t by Janev et al.that reproduces the experimental data of Shah et al.(1998),Shah,Elliott&Gilbody(1987)and Shah&Gilbody(1981)to within their uncertainties.The H?H+charge exchange rate used in the shock code has been taken from the analytic?t of Freeman&Jones(1974).

Collisional Excitation:For electron temperatures below5×105K,we use the polynomial

?ts of Giovanardi,Natta&Palla(1987)to the3s,p,d and4s,p,d,f collision strengths.Above 5×105K,we compute the collision rates directly using the modi?ed Born approximation cross sections of Whelan(1986).The available data on proton excitation is relatively sparse in the literature,and theoretical cross sections to n=3and4have only recently become available. The close-coupling calculations by Mart′?n(1999)include cross sections to?ne structure levels

of n=3and4for proton energies above40keV.The calculations of Mart′?n include charge exchange into excited states,a process which contributes as much as20%to the Balmer line?ux at high shock velocities(v S~>1500km s?1).The theoretical values agree reasonably well with the experimental measurements of Detle?sen et al.(1994),which covered proton energies in the range 40keV≤E≤800keV.The shock code utilizes the cross sections of Mart′?n(1999)and uses the calculations of McLaughlin et al.(1998)to estimate excitation cross sections between10and40 keV.

4.2.Ionization Structures

The shock structure calculation is initiated by using the jump conditions to set the temperature and density at the?rst time step.The equations describing the number densities of slow neutrals,fast neutrals,electrons and protons form a set of coupled,linear di?erential

equations which can be solved together to calculate the density of each species behind the shock. Assuming a pure H plasma(n e=n p),the equation for the slow neutrals is

dn H0(s)

v S(CKR80,Smith et al.

4

1991).Slow neutrals can also encounter an anisotropic electron distribution if the plasma is

far from temperature equilibrium and the postshock bulk velocity is comparable to the electron thermal speed.

Another important complication occurs when the temperatures of the electrons and fast neutrals are unequal.For the case T e=T p(equilibrated plasma),the electron thermal speed is43 times higher than the fast neutral thermal speed(=proton thermal speed).The fast neutrals are e?ectively at rest relative to the electrons,and the ionization rate integral is simple to evaluate. However,for an unequilibrated case,the collision rate integral involves the distribution functions of both electrons and fast neutrals,and becomes a complicated6-dimensional integral over the velocities of both species(Smith et al.1991).Fortunately,the electron-fast neutral collision rate integrals can be reduced to one-dimensional form involving the relative speed of the two particle species(Bandiera,1998;Weisheit,1998).Throughout the shock code,we have computed the electron-fast neutral and electron-slow neutral rates using the reduced integral.

As mentioned earlier,electrons and protons behind a nonradiative shock can be heated to very di?erent fractions of the bulk?ow energy.The total thermal energy E tot acquired by the postshock gas is,however,constant:

E tot=3

16

m p v2S(5)

The initial fraction of this energy going into electrons and protons is controlled by collisionless heating at the shock front,and is therefore a free parameter.Let us de?ne the parameter f eq such that f eq=0for no initial electron-proton equilibration and f eq=1for full initial electron-proton equilibration.The postshock temperatures for arbitrary f eq are then

T p=T0p+1

16

(m e f eq+(2?f eq)m p)

v2S

2

3

k

(7)

where T0p,e are the preshock proton and electron temperatures,respectively.For the extreme cases of no equilibration and full equilibration,

T p,e=T0p,e+3

k

v2S(f eq=0)(8)

and

T p,e=T0p,e+1

16

(m e+m p)

2

3

k

v2S(f eq=1)(9)

The temperature of the preshock medium is generally low enough so that T0p=T0e(=T0).The initial ratio of T e/T p behind the shock can be obtained by dividing Equations7and6.Assuming that T0p and T0e are small enough to ignore,

T e

2?f eq

(10) where terms involving m e/m p have been dropped.A diagram showing the dependence of T e and T p on v S and f eq appears in Figure7.

To illustrate the dependence of postshock ionization structures on the shock velocity and equilibration,we now describe four numerical models(assuming preshock parameters n0=1 cm?3,f H0=0.5,T0=5,000K):

250and500km s?1:The postshock electron and proton temperatures equilibrate rapidly in the250km s?1model,even when f eq=0.The protons are too cold to appreciably ionize H,so charge transfer and electron collisions dominate the ionization balance of the postshock gas.The slow and fast neutral densities are shown as a function of position behind the shock in Figure8. Coulomb collisions in the500km s?1,f eq=0model only produce30%equilibration by the time the neutrals fully ionize,and once again charge exchange is the dominant interaction between protons and neutral atoms.In this model,the broad and narrow Balmer emission is produced well before equilibration is complete.Note that the ionization zones for both250km s?1and500 km s?1models are more extended for low equilibration than for high equilibration.At higher equilibrations the electrons are hotter,ionizing the gas more e?ciently and reducing the thickness of the postshock neutral layer.At?xed equilibration,the size of the neutral layer is proportional to the shock velocity.Therefore,the faster the?ow,the larger the neutral layer.

1500and2500km s?1:There are two important di?erences between these models and those at lower shock velocity.First,T p in a high velocity f eq=0shock starts o?so much higher than T e that electron-proton equilibration is only a few percent complete by the time all the neutrals

disappear and all the Balmer emission is produced.Second,the proton ionization rate is now comparable to the electron ionization rate,and a sizable fraction of the Balmer line emission

is produced by proton excitation.At these shock velocities,the proton-slow neutral collision rate is a factor of2or more higher than the proton-fast neutral collision rate,due to the bulk velocity-shifted proton distribution encountered by the slow neutrals.At?xed shock velocity, the size of the postshock ionization layer is larger for high equilibration than low equilibration (Figure8),the opposite of the250and500km s?1models.

4.3.Calculation of Broad FWHM vs.Shock Velocity

To make the best use of the observational data,we have used the broad component Hαwidths in each SNR to bracket the range of possible shock velocities.For a given broad component width, no equilibration(f eq=0)yields the smallest shock velocity v S(min),while full equilibration (f eq=1)yields the largest shock velocity v max(CKR80,Smith1991).Intermediate equilibrations yield intermediate v S.For each observed shock,we ran numerical models sampling a range of

f eq between0and1,with each value of f eq mappin

g onto a unique v S.We then compared the output Hαand Hβbroad to narrow ratios wit

h the observed values.In this manner,our models self consistently utilized all of the relevant observables from each Balmer line spectrum.

For a given broad FWHM,the map between f eq and v S is the line pro?le functionφ(v x) (Smith et al.1991,CKR80).For a plane parallel shock viewed edgewise,φ(v x)is de?ned as the number of fast neutrals with velocity v x along the line of sight:

l3p

φ(v x)=

v S is the bulk velocity of

4

the shocked gas,taken to be along the z axis.We have computedφ(v x)numerically for a range of f eq and v S.In Figure9we present plots of the expected FWHM vs.shock velocity for four equilibrations.We have used these results to estimate v S for the observed nonradiative shocks,

listed in Table4for the limits of no equilibration and full equilibration.

4.4.Monte Carlo Models of Lyβand LyγTrapping

With the densities and temperatures of di?erent particle species known for a given v S and f eq,we can now quantitatively estimate the contribution of Lyman line trapping to the Hαand Hβlines.Since Lyman photons are emitted with Doppler shifts randomly distributed over the line pro?le,it is possible for a Lyman photon generated near line center of a fast neutral to be absorbed by a slow neutral,and vice versa.The conversion of Lyman line photons to Balmer line photons depends on the likelihood of absorption.Due to the3

the shock according to the emissivity.If a given excitation produces a Lyman photon,the photon is followed along a randomly oriented ray until it is either converted into a Balmer photon or escapes from the grid.After10,000excitations,the number of accumulated broad and narrow Balmer photons is divided to obtain the broad to narrow intensity ratio.

Before we compare our models with the observations,we note that our predicted broad to narrow ratios o?er a number of improvements over previous calculations(such as those of HRB94). The current models utilize more recent atomic rates and compute the broad to narrow ratios for both Hαand Hβ.Our new models also include direct collisional excitation of hydrogen by protons. Finally,by arranging our models into a grid we have been able to predict broad to narrow ratios for a single set of models covering a wide range of shock velocities and equilibrations.

https://www.doczj.com/doc/be1624537.html,parison of Models and Observations

With the numerical models available,we can now estimate v S and f eq for Cygnus P7,SW RCW86and Tycho Knot g(1).There is observational evidence that the temperature ahead

of nonradiative shocks can be as high as40,000K(Ghavamian et al.2000,Smith et al.1994, HRB94).The model predictions are rather insensitive to the preshock temperature(the Lyman optical depth at line center∝T?1/2),so in the following sections we have set T0=5,000K in all models.It should also be noted that since the preshock neutral density is equal to the neutral fraction times the total preshock density(n H0=f H0n0),predicted broad to narrow ratios from models with high f H0and low n H0are similar to models with low f H0and high n0.The reasons for this property are that(1)the total preshock density scales out of the ratio of the broad to narrow Lyman line optical depths,and(2)the equilibration,ionization and charge exchange times behind the shock scale as1/n0,o?setting the in?uence of varying n0on the excitation/ionization rates.Along with v S and f eq,the preshock neutral fraction f H0is the most important quantity a?ecting the broad to narrow ratios.For this reason,we set n0=1cm?3in the models which follow.

5.1.Cygnus Loop P7

To interpret our results we ran numerical shock models using the fractional equilibrations f eq=0,0.03,0.05,0.2,0.5,0.8and1.0,along with their corresponding shock velocities of265,268, 270,273,296,332and365km s?1.The predicted Hαand Hβbroad to narrow ratios are shown in Figure10vs.equilibration for preshock ionization fractions of0.1,0.5and0.9.In these models, the total preshock density is1cm?3.Each curve in the?gure corresponds to a di?erent preshock neutral fraction f H0.Each point along a given curve corresponds to a di?erent equilibration and maps to a di?erent shock velocity.An outstanding feature of the models is that the broad to narrow ratios reach a maximum at low equilibration.The peak occurs because the broad to narrow ratios are proportional to the ratio of the charge exchange rate to the collisional ionization rate.In these models the ratio peaks in the range0.03~

Although variations in f H0do a?ect the shape and position of the broad to narrow curves, the most conspicuous feature in Figure10is that the broad to narrow ratios are predominantly sensitive to f eq(and hence v S).The?gure shows that the higher equilibration models match the observations best.In Hα,the predicted broad to narrow ratios fall slightly above the observed values.The best match occurs for full equilibration,where the model value lies~10%above the upper error bar of the observations.However,the Hβbroad to narrow ratio does agree with observations,favoring f eq≈0.8?1.0(T e/T p=0.7?1.0from Equation10).Excluding the uncertainty in broad FWHM,the implied range of shock velocities is300?365km s?1.

The disagreement between the observed and predicted Hαbroad to narrow ratios may be due to the excitation cross sections utilized in the models.In the range of shock velocities implied by the observations,the thermal energy of the postshock electrons is~<15Rydbergs(1Rydberg= 13.6eV).At these energies,the collisional excitation cross sections are not as well determined as the cross sections at higher energies.This uncertainty is translated directly into the calculated broad to narrow ratios.

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(3)踩地脚轻轻蹬地,然后收到滑板上,放在滑板的后部,这时,整个身体和滑板就开始向前滑动。 下滑板时: (1)当滑板没有完全停下来,还在向前滑行时,将重心放在前脚上然后像起落架一样把后脚放在地上。 (2)后脚落地后,重心随即转移到后脚,然后抬起前脚,让两脚都落在滑板的一侧。当能自如地上、下滑板时,你就应该试着让前后脚位置换一下,熟悉反向滑行的姿势。 2、练习滑行每五人一组,进行五次练习,其它人进行观看。 组织教法要求: 1、通过教师讲解,使学生了解并掌握护具的穿带。 2、教师讲解示范的时候,学生要注意认真听讲。 3、教师要及时纠正学生的错误动作。 4、对学习进行安全教育防止伤害事故。 三、结束部分 1、由教师领做放松练习。 2、总结本次课的学习情况,指出学生在练习中的不足。 3、宣布下课,师生再见。 第二课时 活动内容: 惯性滑行 活动目标:

1、学习惯性滑行的动作要点,并完整练习惯性滑行的动作。 2、积极参加滑板活动,有敢于克服困难的勇气。 活动过程: 一、准备部分 1、学生穿戴好护具,整队。 2、活动身体各关节。 二、基本部分 1、讲解惯性滑行法: 将右脚踏在滑板的中前部靠右。左脚踩在地上,重心集中在右脚。用左脚蹬地,使滑板向前滑动,然后把左脚收上来踩在滑板尾部,保持站立的平衡,滑行一段,再用左脚蹬地,重复动作。 2、练习滑行每五人一组,进行五次练习,其它人进行观看。 3、做较长距离的滑行(10m、20m,)。 4、反复练习到可以轻松熟练地加速滑行为止。 三、游戏:警察和小偷 四、收拾场地,活动结束。 第三课时 活动内容: 障碍滑 活动目标: 1、初步学习障碍滑。

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报告目录 第一章企业全国市场开拓策略概述 (8) 第一节研究报告简介 (8) 第二节研究原则与方法 (9) 一、研究原则 (9) 二、研究方法 (9) 第三节研究企业全国市场开拓策略的重要性及意义 (11) 第二章市场调研:2019-2020年中国智能电动滑板车行业市场深度调研 (12) 第一节智能电动滑板车概述 (12) 第二节我国智能电动滑板车行业监管体制与发展特征 (12) 一、智能电动滑板车所处行业的基本情况 (13) 二、行业主管部门及监管体制 (13) 三、行业的主要法律法规、标准及产业政策 (13) (一)法律法规 (14) (1)境内法律法规 (14) (2)境外法律法规 (16) (二)行业标准 (22) (三)产业政策 (24) 四、各项法律法规、和产业政策对行业发展的影响 (26) (1)交通安全法规 (26) (2)产业政策 (26) 第二节我国智能电动滑板车行业监管体制与发展特征 (27) 一、行业技术水平及技术特点 (27) (1)广泛采用先进技术 (27) (2)强调工业设计的重要性 (27) (3)高性能电池技术有待提升 (27) 二、行业经营模式 (28) (1)生产模式 (28) (2)销售模式 (28) 三、行业的周期性、区域性和季节性特征 (28) (1)周期性 (28) (2)区域性 (29) (3)季节性 (29) 四、行业上下游产业的关联性 (30) (1)与上游行业的关系 (30) (2)下游行业发展情况对本行业的影响 (30) 第三节2019-2020年中国智能电动滑板车行业发展情况分析 (31) 一、人均消费能力提升为行业发展提供市场基础 (31) 二、多领域的市场需求驱动 (32) 三、共享出行市场快速发展带来巨大市场机遇 (32) 四、智能短交通产品符合节能减排、“绿色出行”的国家政策 (33) 第四节2019-2020年我国智能电动滑板车行业竞争格局分析 (33)

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9) 主螺钉那根用来将桥轴与基座结合(结合处有PU垫)的螺钉。 10) 主架桥的主要部分,做5050等动作时用来滑的部分。 11) 枢轴即主架前端与基座的结合处,其中有塑料的PU垫。 12) 桥垫即放于基座与版面间起缓冲作用的塑料或其他物质做的垫片。 13) 砂即置于版面用于加大摩擦力的砂。一般为黑色,不过也有带图案的砂。 14) 轴承即置于轮内用以支持滑行的东西。有双封与全封两种,双封对于滑友来说应是更好的选择。

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