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Mapping the Galactic Halo III. Simulated Observations of Tidal Streams

Mapping the Galactic Halo III. Simulated Observations of Tidal Streams
Mapping the Galactic Halo III. Simulated Observations of Tidal Streams

a r X i v :a s t r o -p h /0012307v 1 14 D e c 2000Mapping the Galactic Halo III.Simulated Observations of Tidal Streams

Paul Harding

Steward Observatory,University of Arizona,Tucson,Arizona 85726

electronic mail:harding@https://www.doczj.com/doc/b29100456.html,

Heather L.Morrison 1Department of Astronomy 2,Case Western Reserve University,Cleveland OH 44106-7215electronic mail:heather@https://www.doczj.com/doc/b29100456.html, Edward W.Olszewski Steward Observatory,University of Arizona,Tucson,AZ 85721electronic mail:edo@https://www.doczj.com/doc/b29100456.html, John Arabadjis,Mario Mateo and R.C.Dohm-Palmer Department of Astronomy,University of Michigan,821Dennison Bldg.,Ann Arbor,MI 48109–1090electronic mail:jsa@https://www.doczj.com/doc/b29100456.html,,mateo@https://www.doczj.com/doc/b29100456.html,,rdpalmer@https://www.doczj.com/doc/b29100456.html, Kenneth C.Freeman and John E.Norris Research School of Astronomy &Astrophysics,The Australian National University,Private Bag,Weston Creek PO,2611Canberra,ACT,Australia electronic mail:kcf@https://www.doczj.com/doc/b29100456.html,.au,jen@https://www.doczj.com/doc/b29100456.html,.au ABSTRACT

We have simulated the evolution of tidal debris in the Galactic halo in order to

guide our ongoing survey to determine the fraction of halo mass accreted via satellite infall.Contrary to naive expectations that the satellite debris will produce a single narrow velocity peak on a smooth distribution,there are many di?erent signatures of substructure,including multiple peaks and broad but asymmetrical velocity distribu-tions.Observations of the simulations show that there is a high probability of detecting the presence of tidal debris with a pencil beam survey of 100square degrees.In the limiting case of a single 107M ⊙satellite contributing 1%of the luminous halo mass the detection probability is a few percent using just the velocities of 100halo stars in a single 1deg 2?eld.The detection probabilities scale with the accreted fraction of the halo and the number of ?elds surveyed.There is also surprisingly little dependence of the detection probabilities on the time since the satellite became tidally disrupted,or on the initial orbit of the satellite,except for the time spent in the survey volume.

Subject headings:Galaxy:halo—Galaxy:formation—Galaxy:kinematics and dy-

namics

1.Introduction

Studies of our Galaxy’s halo have an important role to play in understanding the process of galaxy formation.Classical scenarios of halo formation such as that of Eggen et al.(1962) have given way to a more mature view of galaxy formation in the context of the formation of structure in the universe(Steinmetz and Mueller1994;White and Sprigel2000).These ideas were foreshadowed by Searle and Zinn(1978)from an observational perspective.Hierarchical structure formation models now have the resolution that allows them to make predictions on scales as small as the Local Group.There are some puzzling early results:the recent simulations of Klypin et al. (1999)and Moore et al.(1999)predict that there should be many more dwarf satellites at z=0in the Local Group than are currently seen(if the dark halos in their simulations can be associated with dwarf galaxies).Were these satellites torn apart to form the stellar halo?If so,some of them should still be visible as tidal streams.In fact,we now have strong evidence that the halo was formed at least in part by the recent accretion of one or more satellites.Earlier papers in this series (Morrison et al.2000a;Dohm-Palmer et al.2000)have reviewed the evidence from both kinematics and star counts for substructure in the halo.It is clear that further studies of the halo of the Milky Way and its satellites are needed to clarify these discrepancies.

To date,theoretical investigations have focused on the accretion and destruction of a limited range of satellite orbits.In this paper we concentrate on estimating the detectability of tidal debris from a large range of initial satellite orbits—in other words,our focus is more statistical and observational.Our aim is to estimate the probability of detecting kinematic substructure using currently feasible observational strategies.We hope to provide a bridge for observers from more theoretical papers on satellite destruction and phase mixing(Helmi and White1999;Tremaine 1999)to?nd the optimum observational techniques to detect kinematic substructure in the halo.

Dynamical models are not only helpful in tracing the history of the debris,but can also be used to plan the survey strategy and to help interpret results.For example,the early detection of kinematic substructure at the NGP by Majewski et al.(1994)was puzzling because of its large velocity spread(σ?100km/s in each component of the proper motions).This is now understand-able in terms of multiple wraps of a single orbit(Helmi et al.1999).A more recent puzzle is the discovery of the Sloan over-density along30degrees of their equatorial strip(Ivezic et al.2000; Yanny et al.2000).Was this just a fortunate coincidence that a narrow tidal feature was aligned with the celestial equator,or is the feature in fact more spatially extended?

In this paper we assemble the tools for using our survey data to measure the fraction of the halo that has been accreted.In Section2we begin by outlining the procedure used to create the Galaxy model,satellite model and tidal streams.Section3shows the results from six satellite orbits to highlight properties of the spatial and velocity evolution of the debris.We then illustrate how these results map into observable coordinates.In section4we discuss how we“observe”the models to determine their detection probability using our survey strategy.We then discuss the factors that determine the detection of the debris on di?erent orbits at di?erent times.Section 5looks at how sensitive the detection probabilities are to speci?c observing procedures.We note how the properties of currently available instrumentation?gure into these constraints.Section6 discusses implications of these results for detecting substructure in the halo,in particular which new methods need to be developed to e?ciently trace detected substructure.

2.Simulating the Galaxy’s Halo

We have created model stellar halos from a mix of a“lumpy”and smooth components.The lumpy component represents debris from satellite accretions which still retains information about its origin.The smooth component represents the portion of the halo which is so well-mixed that its velocity distribution can be approximated by a velocity ellipsoid.We created the lumpy component by evolving satellites on a range of initial orbits in the Galaxy’s potential.(We describe in Section 2.2our library of initial satellite orbits.)We then sample from the remains of the satellites at various times during their destruction.Two versions of the smooth component have been created. One has a radially extended velocity ellipsoid similar to the underlying distribution from which the satellite orbits were chosen.The second used an isotropic velocity ellipsoid.

Many realizations of the model halos need to be created so that we can become familiar with the range of accretion signatures likely to be present in our observational data.We wish also to quantify the detection probability as a function of the initial satellite orbit,its time since destruction,the galactic coordinates(l,b)of the?elds surveyed,and how the detection probabilities scale with the accreted fraction of the halo.

In order to maximize the number of di?erent satellite orbits available to select from in the creation of our model halos,we have made a number of simpli?cations to reduce the computation time required to a reasonable level.We have used a?xed potential for the Galaxy and have neglected the self-gravity of the satellites as we destroy them to make tidal debris.As a general principle we have attempted to match the observed properties of the Galactic halo wherever possible in our choice of parameters.Details of the models are given in the following sections.

2.1.The Potential

We have followed the prescription of Johnston et al.(1995)for the Milky Way’s potential, which provides a good match to the rotation curve of the Galaxy.The potential consists of three components.The disk is described by a Miyamoto-Nagai potential(Miyamoto&Nagai1975),

GM disk

Φdisk=?

R2+(a+

;

r+c

and the dark halo by a logarithmic potential:

Φhalo=v2halo ln(r2+d2).

Here M disk=1.0×1011M⊙,M spher=3.4×1010M⊙,v halo=128km/s,and lengths a=6.5 kpc,b=0.26kpc,c=0.7kpc,and d=12.0kpc.The adoption of a?xed potential should not have a signi?cant in?uence on our results,since the mass of the stellar halo(~109M⊙,Morrison1996) is only a small fraction of the total mass of the Galaxy(~1012M⊙,Zaritsky et al.1989).

TheΛ-dominated cosmology predicts that most of the Galaxy’s mass was assembled in the ?rst5Gyr(in contrast to the?=1CDM cosmology(Navarro et al1995)where assembly happens later),and therefore a?xed potential is a good approximation for the next10Gyr.The growth of the Galaxy’s potential,provided it happens on time-scales longer than the satellite orbital period should not be signi?cant in changing the outcome of these simulations(Zhao et al.1999).

2.2.Orbit selection

The Galaxy’s visible halo is extremely centrally concentrated,with densityρ∝r?3or even r?3.5(Saha1985;Zinn1993;Preston et al.1994;Morrison et al.2000a).Yanny et al.(2000)have also shown that,if the excess of BHB stars associated with the Sloan stream are excluded,then the density of BHB stars in their survey falls as r?3.1.To create a density distribution this steep there needs to be a signi?cant fraction of orbits with small mean radii.It is impossible to make a halo steeper than r?3with only radial orbits with large apocenters with this potential,since the time spent traversing a segment of the orbit always decreases faster than the volume element at that radius.

First we constructed an equilibrium distribution of orbits in the Galaxy’s potential.They were chosen to have an r?3.0density distribution,and radially anisotropic velocity ellipsoid of (σr,σφ,σθ)=(150,110,100)km/s,similar to the values determined by Chiba&Yoshii(1998).

This selection3produces a range of orbital energies and angular momenta allowed by the potential, weighted towards more radial orbits.The satellite orbits have a distribution of eccentricities similar to those predicted by the high resolution structure formation models(Ghigna et al.1998;van den Bosch,Lewis,Lake and Stadel1999).

A subset of180orbits were sampled from this distribution,to have pericenters between0.4 and26kpc and mean radii4greater than8kpc.These orbits will serve as center-of-mass orbits for the satellites whose destruction we will study below.The properties of the selected orbits are summarized in Figure1.In the following sections we will refer to orbits by their mean radius.(The approximate apocenter in kpc and orbital period in Gyr can be estimated by scaling the mean radius of the orbit by1.4and0.02respectively.)

These selection criteria allow us to focus our computational resources on the orbits of interest without introducing any signi?cant statistical biases.Orbits with pericenter less than0.5kpc disperse in phase space within a few orbits.Thus they are more appropriately treated as part of the smooth component of the halo.Orbits with pericenter greater than27kpc can never fall into our survey volume.Our survey has a magnitude limit of V<20(Morrison et al.2000a),which translates into a maximum distance of R⊙<20kpc for dwarf stars near the turno?.Dwarfs are the only halo tracer population where it is possible to e?ciently obtain a sample of?100velocities within a small area of the sky,due to the rarity of luminous halo stars(Morrison et al.2000a). Turno?stars are the most luminous tracers for which this is possible.Orbits with mean radii less than8kpc,whatever their pericenter,are also assumed to be part of the smooth component of the models.They were presumably accreted early in the Galaxy’s history and their kinematics will have lost any measurable information about their origin due to phase mixing.Early on,violent relaxation may also have contributed to the loss of information.

How can a satellite be accreted from outside the Milky Way and have a very small mean radius? This is only possible via dynamical friction.However,recently accreted satellites will not have had time to sink to small mean radii—the time-scale for dynamical friction is too long(Colpi et al. 1999).Only satellites more massive than1011M⊙would decay su?ciently rapidly to have mean radii10kpc or less.However,satellites this massive,if they remained predominantly intact,would cause signi?cant heating of the old thin disk,which is not observed(Walker et al.1996;Edvardssen et al.1993).

2.3.Evolution of satellites into tidal streams

The satellites representing small dwarf galaxies were created using a tidally truncated Plummer model(Binney and Tremaine1987)of107M⊙,populated with200,000particles.The satellites are chosen to have properties similar to the Milky Way dwarf spheroidals(Mateo1998),with a core radius of0.1kpc and a tidal radius of2.0kpc.(The chosen core radius is at the small end of the range of the dSphs to compensate partially for the lack of self-gravity in our simulations.See the discussion below of the potential gradient across the satellite.)The projected central velocity dispersion of the satellite is8km/s and the velocity dispersion of all particles in the satellite is6.5 km/s.

With200,000particles per satellite and a model composed of100destroyed satellites,the density of particles in the model approximately matches the density of halo turno?stars seen in our survey.This near one-to-one relationship between particles and stars is important because the velocity signature of kinematic substructure may be due to the presence of only a few satellite stars in a?eld.If these stars occur at high velocities(as might be expected for a plunging orbit crossing our survey volume)then their presence in the wings of the velocity distribution leads to a statistically signi?cant detection.Under-sampling the number of tracers in our simulations would introduce biases in the detection probabilities.

Rather than use an N-body method to model the interaction of satellite particles,we neglect the self-gravity of the satellite,and assume that each satellite is disrupted at its?rst pericenter passage.Thus each simulation was started with the satellite at pericenter.While it is not physical that all the satellites modeled would have become unbound on their?rst perigalactic passage,it is a reasonable simplifying approximation to make for this study.Our aim is not a detailed investigation of the tidal disruption of satellites and the resultant tidal streams(eg Johnston et al.1996;Helmi and White1999),or to make a detailed model such as has been done for the Sagittarius dwarf (Johnston et al.1995;Helmi and White2000;Jiang and Binney2000).Our aim is rather to study the observability of tidal streams in a statistical sense.

In reality,satellite destruction depends strongly on the initial conditions,particularly the structure of the dwarf galaxy and the distribution of stars,gas,and dark matter within it.Un-fortunately we have little information on primordial dwarf galaxies.The properties and orbits of existing dwarfs around the Milky Way may be special in allowing them to survive,thus telling us little about the initial properties of the destroyed satellites.For gas-rich satellites the loss of their gas during disk plane crossing could lead to much of their stellar mass becoming unbound.Our simulations are closer to this case than to pure tidal stripping where stars are lost over a number of perigalactic passages.In the tidal stripping case the gradient of the potential across the tidal diameter dominates the energy distribution of the unbound stars and the subsequent evolution of the tidal stream.This is because stars at the tidal boundary have close to zero velocity relative to the satellite’s center of mass.(Tremaine1993;Johnston et al.1998).In our models the disruptive e?ect of the Galaxy’s tidal force is aided by the satellite’s lack of self-gravity.Thus the energy

spread of the particles should be somewhat larger than in the purely tidal case where the spatial dispersion of the satellite correspondingly more rapid.

Streams of tidal debris were created by evolving a satellite whose center of mass is initially along each of the180orbits.The evolution of the particles in each satellite was followed for1010 years,and the results were saved every5×108years.The resulting library contains3600snapshots of satellite destruction which can be sampled to create halos.A7th order Runge-Kutta integrator was used for the orbit calculations.Typical energy conservation per particle was0.01%or better over the10Gyr.

https://www.doczj.com/doc/b29100456.html,parison with N-body models

If we are to have con?dence in our method,it is important that we understand how the neglect of the self-gravity of each satellite a?ects the observed spatial and kinematic distribution of particles.The orbital binding energy is U orb=M satΦgal,while the self-gravitating binding energy U bind,for the spherical Plummer model,is given by

U bind=1

GM2sat

32

of the meridional plane includes the zero-velocity surface for the dynamical center of the satellite system to aid in the comparison.Figure3shows the V z and V y projections for each model.The distributions resulting from the two treatments of self-gravity are essentially indistinguishable for the low J models(1039and1250).The morphology of the debris in simulation3117is similar in the two treatments,although the particle density along the tidal stream is lower in the self-gravity case.The self-gravitating model1213populates a much smaller volume of the phase space available compared to its non-self-gravitating counterpart.

The ability of a satellite to?ll the available phase space depends upon the rate at which the satellite disrupts.Figure4shows the time evolution of the bound fraction of each satellite.The low J simulations1039and1250pass within~3kpc of the Galactic center,where the tidal?eld is strongest,and disrupt very rapidly,thereby spending most of the duration evolving as would the non-self-gravitating models.Model3117sheds about40%of its mass in10Gyr,resulting in a tidal stream density that is correspondingly lower than the non-self-gravitating model(except x,y,z=?15,2,?21kpc,where the bound particles and the most recent escapers still aggregate). Model1213still contains almost3/4of its original membership after10Gyr,and so di?ers most from the initial total dispersal approximation of the non-self-gravity model.Note that the outer ?fth of each system begins the simulation unbound because the tidal radius used to construct each truncated Plummer system is set to2kpc,regardless of the orbital parameters.

The validity of our approximation depends upon the particular dwarf galaxy orbit.It is clear that the approximation is valid for low J orbits.In the case of high J orbits,we have a problem in that the models may overestimate the density of stars along the tidal debris stream,especially for high J,E orbits.However,since the sampling density of orbital parameters for the dwarf ensemble is lowest toward high E and high J systems(see the bottom panel of Figure1),the problem is reduced somewhat.In addition,the presence of moderate amounts of gas in each primordial dwarf can signi?cantly shorten its disruption time,since gravitating gas would be stripped in short order, further mitigating the problem.In any case,our ignorance of the initial state of each dwarf renders the uncertainty in satellite disruption times of a small subset of these dwarfs a second-order problem to which we will return in a subsequent study.

3.Views of the models

3.1.Views from a theoretical perspective

The evolution of a satellite on three orbits with large apocenters is shown in Figure5.The left two panels of each row show the XY and ZY spatial projections of each orbit.The heavy black locus of points shows the satellite after1Gyr of evolution subsequent to its?rst perigalactic passage.The lighter points show the results after10Gyr.The right hand panel shows the radial component of velocity and distance with respect to the Galactic center.The three di?erent simulations are chosen to have an orbital pericenters between8(top)and2(bottom)kpc.The latter reaches regions where

the potential gradient is greater.The orbital period is smaller for the bottom simulation,leading to more frequent perigalactic passages.This orbit also spends more time closer to the in?uence of the disk.All these factors contribute to the increased dispersal of the satellite.

Figure6shows three satellites on orbits with smaller apocenters at the same two stages of evolution as Figure5.For these orbits,spatial structure is rapidly dispersed and little remains after only a few Gyr.However,the velocity structure remains visible in the right-hand panels of both Figures.While it is possible to directly associate each wrap of the orbit seen in the spatial projections on the left with the loops in phase space on the right of Figure5,it is seen that this is not possible in Figure6as most of the spatial information has been lost.

The power of searches in velocity space to detect older accretion events is clearly seen.The reason for the persistence of structure in the velocity vs.Galactocentric distance diagram is that we are plotting conserved or nearly conserved quantities.The apocenter of the orbit re?ects the par-ticle’s total energy,and pericenter is dominated by the particle’s total angular momentum.While only the z component of angular momentum is strictly conserved for an axisymmetric potential, the dispersion in total angular momentum of satellite particles is relatively small if their orbits remain outside the disk region.The spread in total angular momentum for the particles in Figure 5is approximately20%larger than their initial spread.This would be larger if the halo potential was signi?cantly?attened.

3.2.Views from an observational perspective

Our perspective as observers is limited to the view of the Galaxy from the Sun.In theory, if distances were known accurately and proper motions were available,we could transform back to the Galactocentric perspective.However,distances based on broad band photometry of halo turno?stars are at best accurate to50%due to their near vertical evolution in the color magnitude diagram.These stars are also too faint and distant to have currently measurable proper motions of useful accuracy5.In this paper we will thus concentrate on radial velocity measurements alone.

Figures7and8show the same satellite orbits as Figures5and6,but plotted against observable quantities to illustrate the e?ects of projection on the appearance of the orbits.(At this stage,we do not add the e?ect of observational error on distance and velocity.)

The left panel shows the distribution of the disrupting satellites over the sky in l and b.The center panel shows the relation between R⊙and longitude,and the right panel the heliocentric

radial velocities versus distance from the Sun.Even the three relatively simple debris streams seen in Figure5become more di?cult to interpret with the shift in perspective from galactocentric to heliocentric.

This is further complicated by the distance limit of any velocity survey,optimistically set here at30kpc which corresponds to approximately V=21.5for halo turno?stars.For orbits with large mean radii,only the portion of the orbit near pericenter is visible causing the streams of tidal debris to appear as isolated islands.The density of particles is also reduced due to the relatively small fraction of the orbital period that particles spend near pericenter.However,the velocity substructure signal remains clear in the right hand panel of Figure7,especially for those particles more than approximately10kpc from the Sun.

For the orbits with smaller mean radii,we have the advantage that most of the orbit remains within the survey volume,but this is o?set by the more rapid mixing of the satellite particles.Orbit 1082,seen in the lower panel of Figure8,represents a particularly extreme case where no velocity substructure information apparently remains to isolate the satellite debris.The other two orbits in Figure8show more promise for detection via velocities.The individual wraps of the orbit are no longer clearly separated as was seen in the right hand panel of Figure5.This is because projection e?ects due to our observing perspective from the Sun are larger than the separation between wraps. However,the satellite particles still occupy a relatively narrow region of phase space.

4.Pencil-Beam Surveys

As we shall see below,observations in discrete?elds,such as those from pencil beam surveys, can recover more of the information contained in phase space than appears likely from the right hand panel of Figure8.In this panel,two of the three spatial coordinates have been summed over, obscuring the correlations of radial velocity with spatial structure seen in the other two panels. This holds true even for orbits such as1082after it has mixed for10Gyrs.We will show below that the observed velocity distributions,even in such well-mixed cases,can vary signi?cantly from those expected from a smooth halo.

Now we consider observations in individual?elds.Figure9shows the spatial and velocity distribution of the particles from satellite1082seen at age1Gyr.The bulk of the satellite particles in this?gure are distributed between two consecutive apocenter passages of their orbit.In order of decreasing energy(and increasing l),particles are distributed from an apocenter of28kpc near l=310,through pericenter at l=10to an apocenter19kpc at l=150.The rest of the particles with higher and lower energy spread over an additional two wraps of the orbit but are few in number as they originate in the outer,low density regions of the satellite.

In the lower section of Figure9the velocity histograms are shown for three lines of sight.Most of the observations of this satellite will show a larger velocity spread than in the original satellite. This is because most lines of sight will intersect a signi?cant fraction of the orbit since its apocenter

is small.The two histograms on the right are broadened due to observing particles near apocenter, both coming and going.The histogram on the left shows one of the few sections of the orbit where a narrow velocity dispersion is seen.However,this case,a low energy satellite observed at only1 Gyr after?rst passage,is less relevant to our question of late halo building because satellites with such small mean radii were most likely accreted very early in the Galaxy’s history,before most of its mass was acquired.

When the majority of the satellite has not spread much beyond a single orbital wrap it is relatively easy to trace the relationship of the features seen on the sky to the velocities,for example, in Figures9and11,for satellites1082and1197respectively.However,when the debris have wrapped many times around the orbit(as will be the case for debris that spends most of its time near the solar circle)this is no longer possible.Satellite1082is shown in Figure10after10Gyr of evolution.The satellite debris still traces a fairly narrow path across the sky but at each position there is a large range of velocities(and distances)present.Despite the fact that the particles have wrapped13times around the orbit,the velocity histograms here are distinctly non-Gaussian. Velocity structure remains,despite the very smooth spatial appearance.In reality,small e?ects such as scattering o?spiral structure and molecular clouds in the disk will add further to the smearing in velocity space.

We are using these satellites as examples because their con?nement to a narrow band of b on the sky makes it easier to produce an understandable two-dimensional?gure.However,it is somewhat misleading,in that only for orbits in the plane of the disk are the debris con?ned to such a small volume.In general the orbital plane will precess and thus the debris will spread over many orbital wraps and will eventually?ll a torus-like volume(as can be seen in Figure4of Helmi and White(1999)).It is then much less likely that a narrow line of sight will intersect multiple wraps of the same satellite and hence the observed velocity distributions will be narrower and mono-modal.

A velocity-distance plot,made possible with high accuracy proper motions and parallaxes from Hipparcos(Helmi et al.1999),is then more illuminating.

In Figure11,which shows satellite1197with apocenter100kpc,it can be seen that once a tidal feature is detected in a single?eld,it will be possible to trace it on the sky in other?elds,as there will be a clear correlation of velocities with position on the sky(and distance,as can be seen in Figures7and8).Even with limited distance information it should be possible to constrain the orbit of the satellite with only the radial component of the velocities measured.Figure12shows the satellite particles after10Gyr of evolution.The more complicated spatial and velocity structure is due to the particles having wrapped?ve times around the orbit—most of the particles on each wrap are more than30kpc from the Sun and are thus not plotted.Along many lines of sight, particles on di?erent wraps of the orbit are seen with signi?cantly di?erent velocities.However, it will be possible but more di?cult to trace it on the sky by following the run of velocities with position and distance.

In summary,despite di?culties introduced by the Sun’s position relative to the stream and our

survey distance limits,velocity structure remains.Pencil-beam surveys can detect this structure even if the spatial density of the stream is signi?cantly reduced by its evolution in phase space,and the situation is further confused by the appearance of multiple wraps of the stream along the line of sight.

5.Observing single strands against a smooth halo.

We have been considering the properties of tidal debris from individual satellites in isolation. However,we know that in the solar neighborhood there is a well-mixed component of the halo (as can be seen in Helmi et al.1999)which will complicate our detection of satellite debris.It is possible that the outer halo,where few?eld stars are known,is dominated by tidal debris,but this part of the Galaxy needs to be surveyed using the more luminous but rarer red giants and so a di?erent detection strategy will be needed.

We will,thus,consider the case of detecting the debris from a single satellite seen against a smooth well-mixed halo.The advantage of this approach is that we can represent the kinematics of the well-mixed component using a velocity ellipsoid,rather than having to evolve the orbits for each particle.The observed distribution of radial velocities along a given line of sight is close to Gaussian even for a non-isotropic velocity ellipsoid as long as the halo does not have signi?cant net rotation(Carney and Latham1986;Norris1986;Beers et al.2000).Thus the null hypothesis which we test against(Gaussian shape)is well-de?ned,and there already exist e?cient statistical tests.We have assumed that the contributions of the thin and thick disk populations to the velocity distributions can be ignored.This is true for our survey,where the photometric accuracy of the photometry combined with the color and magnitude range used to de?ne the main sequence turno?region minimizes any contamination by disk stars Morrison et al.(2000a);Dohm-Palmer et al. (2000);Morrison et al.(2000b).However in the case for studies based on photographic photometry (eg Gilmore,Wyse and Jones1995)the larger photometric errors will lead to signi?cant disk contamination.

We populate the smooth halo along each line of sight according to an r?3density distribution. The normalization is set to match the density of halo turno?stars seen in the solar neighborhood (Bahcall and Casertano1986;Morrison et al.2000a).Although there is increasing evidence for a moderate?attening in the inner halo(Kinman,Wirtanen and Janes1965;Preston et al.1991),we have chosen for simplicity to use a spherical model.The spherical halo model over-estimates the number of stars at the pole,and underestimates the numbers towards the anticenter compared to the observed?attened halo.A moderately?attened halo would not produce signi?cantly di?erent answers in what follows.The velocity ellipsoid used,from which the observed radial velocities of the smooth halo particles are sampled has(σr,σφ,σθ)=(161,115,108)(Chiba&Yoshii1998). We also use an isotropic velocity ellipsoid with(σr,σφ,σθ)=(115,115,115);closer to the values measured in more distant halo?elds.Both models have a mean rotational velocity of zero.(The exact underlying distribution is known in our models,but there are currently few observational

constraints on the true distribution of halo velocities away from the solar neighborhood.Even the mean rotational velocity is subject to some dispute(Majewski1992).)

We use a grid of61?elds with30

We are interested in what makes an orbit detectable,not the accidents of viewing geometry. Therefore we will average the detection probabilities of each strand over100realizations of obser-vations.These randomizations also minimize any sampling biases caused by a?xed grid of?elds and increase the volume of phase space occupied by the orbits.The following parameters are varied for each observation:

(i)Viewing orientation of the strand is altered by selecting at random the azimuthal position of

the Sun in the X-Y plane through0?360?.There is nothing special about the azimuthal position of the Sun with respect to a satellite’s orbit.The relative orientation of Sun and particle orbit alters which particles are included in the survey volume and how the components of their space velocity are projected into their observed radial velocity.

(ii)The galactocentric radius of the Sun is varied randomly from8-9kpc.This modi?es the line of sight through debris,particularly those particles that pass close to the Sun.

(iii)The actual?eld center used is o?set at random by one degree on the sky.This alters the line of sight through more distant orbits and minimizes the possibility of chance alignments of the limited sample of orbits with the grid of?eld positions,which would bias our results.

(iv)The orbits of the particles are re?ected randomly about the Galactic plane.This ensures our ?elds are representive of both Galactic hemispheres.

(v)The orbital direction of the particles are reversed randomly.This ensures velocity symmetry.

In most cases few,if any,particles from a single strand are present in a given?eld due to the small?lling factor of the debris.The variation in the distribution over the sky of the debris was seen in Figures10and12where two strands with orbital periods of0.26and1.1Gyr respectively are shown.It can be seen that the shorter period orbit satellite particles are almost completely disrupted and have a relatively large?lling factor,occupying most of the volume that its precession traces out.

If?ve or more particles are present in a?eld,we test for their detection6.Because we do not want results dominated by random e?ects,we construct25realizations of a smooth halo in that direction and add to each the strand particles from the?eld.A20km/s Gaussian velocity error is also added to the particle velocities to match our observational errors.

5.1.Statistical Tests for Substructure

The velocity distributions of the smooth component of the halo appear close to Gaussian for both the isotropic and radially elongated velocity ellipsoids.In the latter case the line of sight projection of the three components of the velocity ellipsoid varies with distance—the radial component becoming dominant at large distances(see Woolley1978,for a derivation).The standard deviations range from120to160km/s depending on the Galactic coordinates of the?eld.

We will show below that,contrary to naive expectations that the satellite debris will produce a single narrow velocity peak on a smooth distribution,there are many di?erent signatures of substructure,including multiple peaks and broad but asymmetrical velocity distributions.The statistical test we use must accommodate a large range of deviations from Gaussian shape,and should not be focussed too narrowly on a particular velocity signature.

We use Shapiro and Wilk’s W-statistic to test for substructure in the combined velocity his-tograms because of its omnibus behavior—it is sensitive to many di?erent deviations from Gaussian shape.The W-statistic is a sensitive and well-established test for departures from Gaussian shape (Shapiro and Wilk1965),which is based on a useful technique of exploratory data analysis,the normal probability plot.This plot transforms the cumulative distribution function(CDF)of a gaussian to a straight line so that deviations from gaussian shape are immediately noticeable.The W-statistic can be viewed as the square of the correlation coe?cient of the points in the probability plot:the closer the data approach a straight line on the probability plot the closer the W-statistic is to1.The con?dence level that the distribution is non-Gaussian(P-value)can then be calculated based on the W-statistic.Royston(1995)7provides an algorithm for evaluating the W-test,and estimating its P-value for any n in the range3≤n≤5000.

D’Agostino and Stephens(1986)give a critical summary of goodness of?t tests and comment on the e?ciency of the Shapiro-Wilk W-test:the test is a good compromise between tests requiring too many assumptions about the distribution and overly general tests which have little power.Examples of the former include tests based on detailed knowledge of the moments of the distribution,and the latter,the Kolmogorov-Smirnov test.

The W-statistic responds to the minor deviations from Gaussian shape in the smooth distri-bution caused by the non-isotropic velocity ellipsoid.This results in a small bias in the P-values which varies little from?eld to?eld.At the99%con?dence level there is a failure rate of0–1% more than the1%that would be expected for a pure Gaussian distribution.This bias is small compared to the e?ect of the small?lling factor of the debris and will be left uncorrected.Smooth halo models were also run with an isotropic velocity ellipsoid and there was little change in the detection probabilities(see below).

In our analysis of the simulated velocity distributions we de?ne a detection to be a rejection of Gaussian distribution of velocities at the99%con?dence level(P-value<0.01),when there are ?ve or more satellite particles present in the?eld.

5.2.Detections of tidal debris against the underlying halo

Before compiling the overall detection probability of satellite debris,it is worthwhile to develop an empirical understanding of the range of velocity distributions that can lead to a detection. Earlier sections looked only at the behavior of satellite debris in isolation,without the presence of the underlying smooth halo particles and observational errors;also there were no selection criteria which correspond to real observational situations such as pencil-beam surveys.

Examples of velocity histograms that pass our detection criteria are shown in the lower half of Figure14.Each of the four columns show data from a satellite detected in di?erent?elds on the sky.The unshaded histogram gives the combined distribution of satellite and smooth halo particle velocities observed in the?eld.The shaded histogram shows the velocities of the satellite particles. The(l,b)coordinates of the?eld are shown on the upper left of each velocity histogram and the P-value of the detection on the upper right.The upper half of Figure14shows the magnitude distributions of the same particles.The(l,b)coordinates of the?eld are again given at top left, and the age of the satellite debris in Gyr at top right.The velocities include an observational error of20km/s and the observed magnitudes include a sigma of0.35mag,corresponding to the scatter in absolute magnitude of halo turno?stars within the color range of our survey(Morrison et al. 2000a).

The velocities of the satellite particles show a broad range of properties.Orbit1197is the simplest to interpret—the four histograms each show a single peak in velocity far away from the mean of the smooth halo for the satellite particles due to a single intersection of the orbit of debris and the line of sight.In this case the detection probability depends strongly on the number of stars in the wings of the velocity distribution.The detection at(135,30)is marginal because there are only6satellite stars in the?eld.With a mean orbital radius of63kpc,the debris are outside the survey volume90%of the time,minimizing the chance of multiple wraps being seen in a?eld.This panel is typical of the detections of other satellites on orbits with large mean radii.

Orbit6866(180,80)shows a di?erent detection situation:the satellite particles have a velocity

close to the mean but the large number of satellite particles in the peak leads to a symmetric but very non-Gaussian velocity distribution.Thus the hypothesis of Gaussian shape is rejected with very high con?dence.

Column4of Figure14shows another unusual case:a polar orbit similar to that proposed for the Sgr dwarf(Helmi and White2000).Because of its polar orbit it has remained con?ned to a plane and the probability of detection of satellite particles on multiple wraps is proportionately higher.

The histograms of the right-hand three orbits of Figure14show multiple peaks in the velocity distribution of satellite particles.This is due to the line of sight intersecting multiple wraps of the debris.Each peak in the velocities of orbits6866and1031are from particles on a single wrap.However,interpretation is more complex for orbit1082:particles on each wrap of the orbit contribute to each of the peaks.This is due to the apocenter of the orbit(22kpc)falling within the survey volume.

Figure15illustrates this situation by showing the relationship of total energy to Galactocentric radial velocity:energy changes slowly and almost monotonically along a single wrap.The sorting in energy of the particles due to phase space conservation is clearly visible.The crosses show where particles seen within the?eld originate in overall energy distribution of the debris particles.In orbit1082,the particles come predominantly from two wraps,but because the apocenter of this orbit is only22kpc,we see particles over most of the orbit in a single?eld(both“coming”and “going”).In order to have enough particles from this di?use stream to trigger a detection in the velocity histogram,orientations where streams are lined up close to the line of sight are needed.

The debris on orbit1082mixes rapidly,leading to approximately13wraps of the debris after 10Gyr.The velocities of satellite particles tend to be closer to the underlying distribution of halo velocities and hence more particles are usually required for a detection.The detection shown in Figure14at9Gyr for this satellite is close to the limiting detection threshold of1%despite the presence of50satellite particles.

After we have detected substructure,a natural next step is to attempt to determine the orbits of the particles and then to reconstruct the properties of the satellite from the debris(eg Helmi and White2000).In extreme cases it is clear which particles in the combined distribution belong to the satellite(for example orbit1197).However,this is not the case for most of the detections. The combined velocity distributions are often clearly non-Gaussian to the eye,but it is not easy to accurately identify the contribution of the satellite particles from either the velocity or magnitude distributions alone.While in a single?eld it is not possible to uniquely identify which stars are from an accreted satellite,it is possible to make statistical allocations.We are exploring the use of mixture modeling on the velocity distributions of each?eld to quantify the components present in the distribution(Sun et al.2001).

The fraction of the halo that has been accreted can be estimated using the fraction of?elds that show kinematic substructure.This can be modeled by extending our simulations of model

halos to those composed of varying mixes of smooth component and debris from multiple satellites. The accreted fraction can be estimated more directly,once the kinematic and spatial distribution of stars in each stream is su?ciently well quanti?ed to allow an estimate of the properties of the progenitors(eg Helmi and White2000).

It is tempting to think that observations made with higher velocity accuracy would simplify the task of identifying the satellite particles.This would be true if our line of sight was nearly normal to a stream that is well phase-mixed(Helmi and White2000)in which case the velocity variation along the stream would only be detectable with proper motions.However,that situation is geometrically rare,and the number of observable stars from the satellite within a?eld will usually be too small to trigger a detection based on the velocities.In fact,there is a bias towards detecting streams of debris that obliquely cross the line of sight due to the higher projected density of satellite particles.In this case the width of the observed velocity distribution from a single wrap will usually be dominated by the velocity variation along the stream.This can be clearly seen in the middle right panel of Figure15.

Combining velocity data with even inaccurate distance information is helpful.This is seen in the upper panel of Figure15for both satellites.The clear correlation of velocity with distance seen in the middle panel of Figure15for both satellites remains when the distances are transformed to magnitudes(including the absolute magnitude distribution)and20km/s errors added to the velocities.The linear dependence of velocity on distance can still be seen in the upper panel. (Deriving distances from observed magnitudes and colors leads to~50%distance errors.)

5.3.Detection probabilities

We are now in a position to combine the above work into quantitative estimates of detection probabilities of debris.Our aim is to determine the probability of detecting velocity substructure from the debris from a single satellite on a given initial orbit when we observe velocities for a sample of halo turno?stars in a single?eld.We consider the example of a single night’s observing with a multi-object?ber spectrograph on a single?eld of a preselected sample of halo turno?stars(uncontaminated by thin or thick disk stars).The detection probabilities derived below are representative of the likelihood that these observations would show substructure in the velocities. Such an observation would typically return from50to several hundred halo turno?star velocities, depending on the telescope/instrument combination.

There are two major contributions to the detection probability:?rst there need to be satellite particles in the?eld observed,and the probability of this is quite small.Second,if particles do exist in the?eld,we calculate the probability that they are detected in a velocity histogram.

In the following subsections we will look at how the detection probabilities vary with the properties of the telescope and instrumentation used for the velocity measurements.In particular we consider the in?uence of the number of stars observed per?eld,the limiting magnitude,velocity

accuracy and location of the?elds observed on the substructure detection probabilities.

5.3.1.Velocities obtained for all halo turno?stars

With instruments such as the Anglo-Australian telescope’s2df system or the Sloan?ber spec-trograph,there are su?cient?bers to observe almost all halo turno?stars in a?eld of size one square degree.(Numbers of turno?stars per square degree brighter than V=20will vary from 100to500depending on Galactic latitude and longitude(Morrison et al.2000a).)In this case the typical detection probability of a single strand is?1%.Figure16summarizes the contributions to detection probability for each of the180satellite orbits in the library if they were to be observed 6.5Gyr after?rst pericenter passage.The number of times that?ve or more particles are“found”in the?eld is dominated by the fraction of the orbit accessible within the survey volume,as seen by a comparison of the upper two panels.The small?lling factor on the sky,particularly of orbits with large mean radius,causes this percentage to be low.The third panel shows the probability, given that?ve or more stars are in the?eld,that the strand is detected in the velocity histogram. The bottom panel shows the total detection probability plotted against the mean radius of the satellite orbit.This is obtained by multiplying the probability that satellite particles are present by the probability that if particles are present,they are detected.Thus the detection probability in the bottom panel is the product of the probabilities in the two panels above.

A general decrease in detection probability for mean radii above15kpc is seen.This is primarily due to the small fraction of time such satellite debris spend in the survey volume.Once particles from the satellite are found in the?eld,the detection probability is relatively high for all orbits except the innermost ones.The particles with orbits of large mean radius are relatively close to pericenter when detected,and thus their large radial velocities are easier to detect against the smooth halo velocity distribution,even when few particles are present,as can be seen in Figure14. The detection probability drops rapidly for orbits with mean radii below15kpc for three reasons. These orbits have shorter periods and thus disperse more rapidly.Thus although particles on such orbits pass through the survey?elds frequently,~30%of the time,the detection probability is low since there are usually too few particles present in a?eld for a signi?cant detection.Also their velocities are on average less extreme and so harder to detect against the underlying distribution of velocities.Orbits with mean radii below10kpc have dispersed su?ciently that the probability of?ve or more particles occurring in a?eld is low.

The orbits that are con?ned close the plane have low detection probabilities as we have no ?elds below30degrees.There was no pre-selection made against these orbits in our simulations since in reality it becomes increasingly di?cult to detect halo stars reliably in?elds with high stellar density and variable reddening.

5.3.2.Time dependence of detection probabilities

We now explore the dependence of detection probability on time since satellite dispersion. Figure17shows the detection probabilities at ages1.5,4,6.5and9Gyr.In order to show the general trends the detection probability for each satellite has been averaged over a2.5Gyr period. It is striking how little the detection probabilities vary with time.As the strands evolve,the mean densities along the strands decrease by factors of100to1000.The competing e?ects of spatial spreading,which increases the probability of?nding particles from a strand in a?eld,and the decreasing mean number of particles found in a?eld approximately balance.The general trend is that more tightly bound orbits become more di?cult to detect with time,due to their more rapid spatial dispersion decreasing the number of stars per?eld below a level that triggers a detection. Conversely,the orbits with large mean radii become easier to detect at later times.

This behavior is seen in Figure18where the“found”and detection probabilities are shown at each time step for the debris from six satellites.For example orbit6866shows the trend clearly with a steady increase in the“found”probability reaching35%at10Gyr as the debris disperse spatially.However,the fraction of the“founds”that result in a detection decreases from55%at 1Gyr to8%at10Gyr.The broad peak in the detection probabilities is the result of these two e?ects.As the mean radii of the orbits increase,the peak in the detection probabilities moves to later times and broadens.Orbits with mean radii beyond35kpc have detection probabilities that on average remain constant.The main source of variation in their detection probabilities seen in the upper three panels of Figure18is caused by the presence of densest parts of the tidal debris in the sample volume.

5.3.3.Detection probabilities with smaller samples of halo turno?stars

For systems like the NOAO Hydra spectrographs with98or132?bers it is only possible to obtain velocities for50-100halo turno?stars in a single?eld with an exposure time of6-8hours. Also,unless observing conditions are perfect it is impossible to obtain accurate velocities for the more distant candidates in the sample.

To test the e?ect of these observational constraints the velocities in each?eld were sub-sampled by randomly selecting the required number of velocities from the combined sample of satellite and smooth halo velocities.A new subsample was created for each of25realizations of the smooth halo.As before this was only done when5or more satellite particles were present in the full data set for the?eld.An added constraint was that four or more satellite stars had to remain in the velocity subsample before the W-test was run(because the number of satellite stars varied in each subsample).

A comparison of the detection probabilities averaged over all ages for the cases where velocities

of all8halo stars detected in the?eld,or100,or50halo stars are obtained within each?eld is shown in Figure19.It can be seen that the overall shape of the relationship between detection probability and mean radius of the orbit remains basically unchanged,but the detection probabilities scale roughly with the number of velocities obtained.This general behavior is true at all of the ages sampled.Both the number of?elds with satellite particles found and the probability of detection if such particles exist scale down in approximately the same way.

In summary the detection probabilities show a linear decrease with the number of stars observed per?eld,falling to~0.25%(for debris on orbits with mean radius above30kpc)when only50halo turno?stars.It is important to obtain velocities of as many halo turno?stars as possible within the?eld to maximize the detection probability.

5.3.4.Detection probabilities at brighter limiting magnitude

Another series of observations of the models were made with the survey radius reduced to12 kpc,corresponding to a magnitude limit of approximately V=19.This represents the current magnitude limit achievable with Hydra on the WIYN telescope in6hours of exposure for20km/s velocity accuracy on halo turno?stars with M V?4

Figure20shows the detection probabilities averaged over all ages for the three cases where all,100,and50velocities are obtained within each?eld.These probabilities should be compared to those in Figure19.It is seen that the upper envelope of detection probabilities has decreased by factor of2–3,comparable to the factor of2.7reduction in the volume surveyed.The25orbits with pericenters greater than17kpc are no longer detected.

5.3.5.Dependence of detections on l,b

For the?elds studied there is no strong dependence of the detection probability with l,b coordinates except for orbits with pericenters near the survey radius.These orbits can only be detected in the?elds towards the anticenter that probe larger Galactocentric distances.The?elds closer to the Galactic center do not sample as large Galactocentric distances as the anticenter?elds. Thus on average,orbits with larger pericenters are less likely to be detected in these?elds because of the distance limit of the survey.However,they have an increased detection probability for orbits at intermediate Galactocentric distances.This is because it is possible to survey a larger volume at Galactocentric distances close to the solar radius on the opposite side of the Galactic center.

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议程2:

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┊┊┊┊┊┊┊┊┊┊┊┊┊装┊┊┊┊┊订┊┊┊┊┊线┊┊┊┊┊┊┊┊┊┊┊┊┊序号(学号):241140402 长春大学 毕业设计(论文) 浅谈碧昂丝《halo》的演唱技巧及演唱风格 姓名陈圆圆 学院音乐学院 专业音乐表演(歌舞) 班级2411404 指导教师王熠娜 2014 年12 月15 日

┊ ┊┊┊┊┊┊┊┊┊┊┊┊装┊┊┊┊┊订┊┊┊┊┊线┊┊┊┊┊┊┊┊┊┊┊┊┊ 浅谈碧昂丝《halo》的演唱技巧及演唱风格 摘要:每一个人对于歌曲的感觉或许已经不是那么陌生了,每一首歌曲会给大家带来怎么样的听觉感受都是我们对于评定一首歌曲好坏的重要标准,也是衡量一个歌手对于歌唱技巧的掌握程度的好坏。而对于《halo》这样一首非常火并且韵律又比较经典的一首英文歌我想每一个都会哼唱那么几句。无论是原唱碧昂丝还是后来翻唱的吉克隽逸都是我们广为知晓的明星,所以本篇论文就是借用了碧昂丝的《halo》为主要的研究对象,针对一些流行歌曲以及经典歌曲的演唱技巧以及演唱风格进行描写,并且在针对这样的描写可以找到所有流行音乐的共同点,从中找到一个适合未来流行音乐发展的演唱技巧以及演唱风格,并且引起所有的歌唱爱好者的关注。其实,对于一首好歌的演唱技巧是歌曲是否能红起来的关键问题所在,因此在论文的创作中会着重的描述歌手对于歌曲的演唱技巧的描写。 关键词:流行歌曲歌唱技巧歌唱风格

┊┊┊┊┊┊┊┊┊┊┊┊┊装┊┊┊┊┊订┊┊┊┊┊线┊┊┊┊┊┊┊┊┊┊┊┊┊ Abstract Each individual for the feel of the song may not be so strange, each song will bring you what are we hearing feeling for the important criteria for the assessment of a song is good or bad, is a measure of the degree of mastering the singer singing skills quality. But for the "halo" such a very fire and rhythm and comparison of the classic song English song and I think every one would hum so few words. Both the original singer Beyonce and cover jikejuan escape we are widely known star, so this paper is borrowed from Beyonce's "halo" as the main object of study, in view of some pop songs, classical songs singing skills and singing style in description, and according to this description can be found in common to all pop music, find a suitable for the development of future pop music singing skills and singing style from, and cause all the singing lovers attention. In fact, for a good song singing skills is the key to the problem whether the song to red, so emphatically in the thesis creation described in the singer for song singing skills description. Keywords:The skill of singing style of singing popular songs

咖啡馆设计方案

咖啡馆设计方案 一、可行性分析 1.市场需求: ①对自由交流、氛围的追求——需要一个这样的咖啡馆! ②文化营地事实的缺失,和人们内心故有的追求——需要这样一个咖啡馆! ③选址在自然客流需求强的地段,如写字楼密集区或者高校附近,或居民聚居地——自然客流也需要这样一个短暂的约谈或休闲的咖啡馆! ④如本区域各种学校众多,当中的教职工和学生情侣也是潜在客源。 2.地理及商业环境: 待选位置毗邻朝阳大悦城商圈,诸多写字楼商场附近,临近居民生活区天鹅湾、星河湾等高档社区,该地段地铁5号线即将完工投入使用。 其他位置正在努力选址中,在确定投资股东后会拿出其他地址以供讨论确定。 3.行业发展趋势 ①网站70万会员的一个理想聚焦点——需要这样的一个咖啡馆! 网站调查数据显示: a、83.11%的会员对开咖啡馆持赞同并看好前景的意见,7.68%的理论上给予支持, 9.22%的对多股东合作形式表示不乐观。 b、71.96%的会员表示愿意加入咖啡馆的投资,23.53%的会员表示只关注不加入, 4.51%的表示不愿意加入或者不关心。 c、表示投资数额在5K到1万的,有72人;表示投资1到2万的,有80人;表示投资5到10万的,有27人;表示投资10万以上的有20人。 ②(1)咖啡消费市场发展迅速,已经成为城市消费一大潮流,市场前期造 就已经结束。雀巢、麦斯威尔、哥伦比亚等国际咖啡公司纷纷在中国设立分公司或工厂,根据一项在12个内陆城市的调查,32%的城市居民喝咖啡。过去一年内喝过速溶咖啡的人口比例在30%以上的地区除了上海之外,还有昆明、厦门、杭州和天津。 2)咖啡消费品位越来越高,文化的魅力就是市场的魅力。单纯速溶咖啡己远远不能满足请求了,消费者开端认知咖啡的品牌、作风和知道如何享受咖啡带来的乐趣。

公司部门及缩写中英对照

公司部门及缩写中英对照

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总公司HeadOffice 分公司Branch Office 营业部Business Office 人事部Personnel Department 人力资源部HumanResources Department总务部General Affairs Department 财务部General AccountingDepartment 销售部Sales Department促销部SalesPromotionDepartment国际部International Department出口部Export Department 进口部I mportDepartment?公共关系PublicRelations Department广告部Advertising Department 企划部Planning Department 产品开发部ProductDevelopment Department研发部Researc hand Development Department(R&D) 秘书室Secretarial Pool 采购部PurchasingDepartment 工程部EngineeringDepartment?行政部Admin.Department人力资源部HR Department市场部Marketing Department?技术部Technolog Department客服部Service Department 行政部: Administration?财务部FinancialDepartment 总经理室、Direcotor, or P resident 副总经理室、Deputy Director, or Vice president 总经办、General Deparment 采购部、Purchase & Order Department 工程部、Engineering Deparm ent 研发部、Research Deparment 生产部、ProductiveDepartment销售部、Sales Deparment?拓展部BusinessExpending Department 物供部、Supply Department B&Dbusinessand development 业务拓展部HR人力资源部Account会计部PRpeople relationship 公共关系部 OFC(Office,但不常见) / OMB =Officeof Management and Budget办公室Finance财务部?MKTG (Marketing) 市场部R&D (R esearch&Development)研发部MFG (Manufacturing) 产品部AdministrationDept. 管理部?Purchasing Dept 采购部Chair man/PresidentOffice //Gerneral Manageroffice or GM office 总经理办公室Monitor& Support Department监事会Strategy Research战略研究部?外销部: OverseasDepartme nt,International Sales Section,Export Section?财务科:Financial/F iscalDepartment?会议室:MeetingRoom/Hall/Auditorium,或C onferenceHall/Auditorium或直接Auditorium, 会客室:Reception Lounge/Room/House,或Meeting Room或Guest Room?质检科:Back-check Section/Department,Quality-inspection/QualityControl Department 内销部:DomesticSales Section/Department?厂长室:Miller/Director/President'Office( 这很取决于你们厂的类型和规模)?行政 科:AdministrationSection/Department,Service section 技术部:TechnologySection 档案室:Archives(Office) 生产科:Production/Processing Section

HALO 成就清单

HALO:Wars 战役模式:关卡 野猪兽屠夫Everything's Better with Bacon 战役第1关:用疣猪号冲撞50 名野猪兽沼气槽终结者Endless Fun 战役第2关:摧毁所有沼气槽 坠落的星盟Covenant "Hot Drop" 战役第3关:用光桥杀死至少5 个星盟单位 真正的赢家The Real Winner战役第4关:抢救亚当 劫持高手He's Got The Jack 战役第5关:劫持6 个星盟载具 犀牛保护者Rhino Hugger 战役第6关:成功保护所有犀牛号 直捣黄龙Micro Manager 战役第7关:不摧毁任何动力节点 巨象号步兵官Ramblin' Man 战役第8关:用巨象号训练100 队步兵 小憩片刻Sweet Naptime 战役第9关:同时让所有虫族聚落进入冬眠 慢条斯理The Procrastinator 战役第10关:干扰所有高压电塔的牵引光束 封住舱口Battened Down the Hatches 战役第11关:保护所有空气闸门 修理高手Handy with Tools 战役第12关:在 4 分钟内修复动力核心 圣甲虫号的骄傲Beaming with Pride 战役第13关:用圣甲虫号摧毁25 个单位 独立作战Didn't Get To Second Base 战役第14关:没有占领其它基地 按部就班Thinkin' about My Doorbell 战役第15关:依照顺序打开闸门 战役模式:秘密成就 会合佛吉军士Meet Sergeant Forge 以任何难度完成战役第1 关 冰雪战士Ice Warriors 以任何难度完成战役第1-3 关 波希之钥Key to Pirth以任何难度完成战役第4-7 关 丑陋的战争Ugly is only Skin Deep 以任何难度完成战役第8-11 关 漫漫长路No Way Home?以任何难度完成战役第12-15 关 战役模式:合作 相互扶持Backscratcher 合作完成任一战役任务 最佳拍档OMG BFF FTW 合作完成全部战役任务 战役模式:难度 神风烈士的判决Adjudicate the Arbiter完成英雄难度的战役游戏

英文加中文的网名

英文加中文的网名 英文加中文的网名 英文加中文的.网名 1、Feastaw离愁 2、Zing【生命力】 3、Guardianship相守 4、MySunshine我的阳光 5、〆゛丶yoyo 6、Hopeless(绝望) 7、DIE° 8、旧情话clot 9、Allure(诱惑) 10、▲角逐pursue 11、Shine(光芒) 12、傀儡Puppet▼ 13、shouldnot-溺宠(不该) 14、Overdoes【过分】 15、﹏Lostloveゝ 16、Monster怪兽 17、Sick°[病态] 18、eccentric°[怪人]

19、印象║Vicious 20、ERosIon腐朽 21、Despair(绝望) 22、Yoke(羁绊) 23、酷girl. 24、゛法式夕阳Romantic 25、◆◇sorrow°痕迹、 26、Enteral丶不朽 27、孽╮noone 28、Obsession【强迫症】 29、perpetual 30、Lonely孤独先生 31、Sunshine.? 32、baby公主 33、ゝxτяéмé° 34、Halo(光环) 35、分岛花音DeathSword* 36、乱祈°Amor▲ 37、disappear逃避 38、Winner(冠军) 39、Capital、魅魇 40、Devil(魔鬼)

41、simplelove[简单爱] 42、False.虚假 43、。Aliveㄣ 44、﹏heartbreaker° 45、Demonprincess(妖妃) 46、catastrophe浩劫。 47、Pull(难挽) 48、Pretext(借口) 49、_Edmundヾ 50、敷衍Continue\\\" 51、Schoolleave毕业生 52、Roselife(玫瑰人生) 53、Prevaricate(说谎) 54、Dislike(不喜) 55、aholic.(沉迷者) 56、Dear°心裂 57、call@ 58、温柔女Boss. 59、oo-┈→Danica℡~ 60、LuHan 61、Owetokiss 62、Moonlight月光

Halo Beyonce

【故事背景】 公元 2552 年,地球依然存在于银河系之中,但由于人口过剩的问题,让地球上的居民不得不前往开拓新的殖民地。当时超光速的飞行已经成为事实,让人们可以自由穿梭于星际之中,而地球上的联合政府也经由联合国太空指挥部 (the United Nations Space Command),将转移权力重心至新开发之殖民地区。将近百万的地球人离开了地球,居住于太阳系中其它适合居住的星球上。Reach行星的开发,是人类殖民历史中重要的里程碑,也因此进而发展出供百姓使用的殖民拓荒宇宙飞船舰,以及供联合国太空指挥部 (UNSC) 军队使用之太空军舰,不但拉近了与地球的距离,Reach行星区也成为科技发展以及军事活动的中心。 三十二年前,与外星殖民活动是不被重视的;一支军事部队曾经执行过勘查任务,但几乎被消灭,只有一艘损坏严重的船舰返回 Reach 行星。幸存的船员叙述着外星舰队的恐怖攻击,可以轻易地将我方舰队摧毁,难以抵抗的种种经历。 这是人类与星盟的的第一次接触,而星盟的组成,是由许多外星种族因共同的宗教信仰聚集而成的。星盟的宗教长老认为,人类对天神有侮辱轻蔑之意,因而与人类展开战争,以圣战之名来驱离地球之人类。在经历过许许多多的大小战役,UNSC 的海军上将普雷斯顿?柯尔 (Preston Cole) 拟定了「柯尔草案」:任何船舰不得将星盟引至地球。当被迫撤离时,不能使用以地球为导航之撤离路线,也就是说,一旦遇到了危险攻击而遭俘虏时,所有船舰必须启动自毁装置已顾全大局。在 Reach 星球上进行着一项军事机密研究,就是创造出一系列基因强化战士的重大新发现。斯巴达二号 (SPARTAN II) 的基因强化战士在与星盟对战的测试中,留下令人印象深刻的纪录,但是却无法扭转战争的局势。

图书馆咖啡厅设计方案

南岭校区图书馆咖啡厅 建设的设计方案 一、前言 学校图书馆历来都是学生看书、查阅资料、自习的理想场所。但是图书馆的环境好与坏会直接影响到学生学习的心情和效果。随着社会的发展,国民消费水平的提升,人们的消费观念也有了很大的改变,越来越多的人开始追求生活的品质与情调,大学生也是如此,一杯咖啡、一本书,在一种舒适、安静的环境下渡过一天的学习时光,是每一名学生的愿望。 二、具体设想 由我们承包南岭校区二楼阅览室,建设成面对服务学生的多功能咖啡厅,由我们负责向学生经营销售如咖啡、牛奶、饮料等饮品及其他辅助食品,并保证食品的卫生及安全,可随时接受图书馆的检查及管理。 我们将负责对新咖啡厅的设计、施工以及设备、设施购置。我们将会把整个咖啡厅将分割成咖啡厅、讨论区、影视区、休闲区四个主题服务区。每个服务区都是独立的,在讨论区,每张茶几上都会配置一台电脑,供学生查阅资料使用;在影视区,我们会选播一些有利于学生学习的影片,且每张座椅上都会配有单独的耳麦,使播放影片的时候不会影响到其他区域的同学。我们的最终目标是把咖啡厅建成南岭校区地标性场所。使之既达到空间布局合理,又满足了学生的需求,为学生创造出具有品质的、舒适的的学习环境。

三、前期投入 据我们保守估算整个施工加上设备、设施的购置,总共前期投入达30万元左右。其中各项配置情况初步打算如下: 装修:因图书馆是学校防火重点单位,在选材上要选择防火合格材料;施工期间要严格按照学校防火要求施工,保证安全。 设施:在讨论区每四张座椅、一张桌子为一套,打算安装10套;在影视区,打算安装30张座椅;在咖啡厅每四张椅子、一张桌子为一套,打算安装8套。在休闲区两张座椅、一张桌子为一套,打算安装12套。所有物品初步选择的品牌为千派(长春市比较知名),价格正在商谈中。物品外观如效果图中所显示一样,或按需要配置。具体安装数量要在施工完毕经现场测量结果而定。 设备:电视选择韩国三星品牌(因学生都是爱国青年,为避免不必要的麻烦,暂不考虑日本品牌),具体尺寸要看实际效果而定。投影仪选择索尼品牌(按实际需求选购)。 五、利润分配 根据学校的学生人数及扣学校放假等原因预算,咖啡厅年收入初步估算在8万元左右。由于前期投入的原因,我们建议在收回成本之前,我方与贵方在利润分配上为7:3分成,我方占7,贵方占3;待到收回成本后双方以5:5分成。我方可向贵方提供进货单、日销售表及月销售表以供随时查帐。 以上是我们的一些见意,请领导审查。

世界咖啡方案设计1.0

世界咖啡研讨方案设计 背景:著名的“WorldCafe”(世界咖啡)会议模式的主要精神就是“跨界(Crossover),世界咖啡不同专业背景、不同职务、不同部门的一群人,针对数个主题,发表各自的见解,互相意见碰撞,激发出意想不到的创新点子。世界咖啡让参与者从对个人风格、学习方式和情感智商所有这些我们惯用的评判人的方式的关注中解放出来,使人们能够用新的视角来看世界。在此基础上,逐渐领悟学习型组织的真谛,以饱含意义的汇谈,激荡出更多人内心的无尽智慧,真正建设起学习型组织。 方案设计 活动前准备: (预计是约10个组最好双数组,每个组约10人以下。分组的方法是进门时每人拿一张扑克牌,根据实际人数调整。) 议题从共青团日常工作中产生。(比如调研活动的开展,主题团日活动的开展等) 活动前准备:(道具:信封,事先准备好的研讨议题,草稿纸,大张展示纸,打印好的机票道具,印章,彩笔1盒/组,道具权杖1个/组、扑克牌、桌签,以及可以活动的圆桌,不能是教室。)活动中: 所有成员到齐后推举一个桌长,并设计自己的桌名。如果是前期已经有系列培训,可以延续用之前的名字。 由一个培训老师和几个助理控场,开始后老师先和大家分享世界

咖啡讨论的由来和应用,并讲解整个活动的流程。(有必要的情况下可以展示一下讨论成果的思维导图)请所有学员迅速进入到角色中。并分发本次议题以及相应的道具。(约15分钟) 助理分配到各组巡场,如果学员要提问或者帮助时,及时给予帮助。 讨论流程如下: PART1:活动形式:讨论 第一环节:各位成员按照分组就座,对该组的议题展开第一轮讨论,时间15-25分钟,并将讨论成果绘制成思维导图(并非要严格的思维导图,可以调低要求,可以展示就行)。小组成员需手持魔法棒轮流发言,在相应时间范围内(可以是老师控场或者音乐停止时)手拿魔法棒的同学需作出总结(2分钟左右) 第二环节:各位成员(除桌长外)根据机票的指引转移到和上一个议题不同的小组,桌长留守本桌负责向来访的新组员讲解上一轮的成果,并对来访的组员的贡献给予感谢和肯定并盖章。(每个客人都要发表意见桌长才给予盖章,多发表多盖章)。这一轮大约进行10分钟的自由讨论。 第三环节:继续第二轮的各位成员(除桌长外)根据机票的指引转移到和上一个议题不同的小组,桌长留守本桌负责向来访的新组员讲解上一轮的成果,并对来访的组员的贡献给予感谢和肯定并盖章。(每个客人都要发表意见桌长才给予盖章,多发表多盖章)。这一轮大约进行10分钟的自由讨论。

halo歌词

Beyonce - Halo 中英对照歌词 Remember those walls i built 还记得我一手搭建起的围墙吗? Well baby they're tumbling down 好了,孩子,现在它们开始坍塌了 And they didn't even put up a fight 它们甚至无力抵抗 They didn't even make a sound 它们甚至还来不及做声 I found a way to let you in 我找到了让你进来的路 But i never really had a doubt 但是,我真的从没怀疑过你 Standing in the light of your halo 站在你光环的照耀下 I got my angel now 我找到了方向 It's like i've been awakened 我感觉好像已经觉醒了 Every rule i had you breakin' 你打破了我所有的规则 It's the risk that i'm takin' 我正在顶着这个风险 I ain't never gonna shut you out 我永远不会将你置之不理!Everywhere i'm looking now 无论我的视线停留在哪 I'm surrounded by your embrace 都被你的光辉环抱着 Baby i can see your halo 孩子,我能看到你的光环 You know you're my saving grace 你知道你就是我的恩赐 You're everything i need and more 你超过我所需要的一切 It's written all over your face 这些都写在了你的脸上 Baby i can feel your halo 孩子,我能感觉到你的光环 Pray it won't fade away 祈祷它永不凋零吧 I can feel your halo (halo) halo 我能感觉你的光芒 I can see your halo (halo) halo 我能理解你的光芒 I can feel your halo (halo) halo 我能感觉你的光芒 I can see your halo (halo) halo 我能理解你的光芒 Hit me like a ray of sun 像一束阳光一样投向我吧 Burning through my darkest night 燃尽我最漆黑的夜晚 You're the only one that i want 你就是我唯一需要的人 Think i'm addicted to your light 我想我已被你的光芒折服 I swore i'd never fall again我曾发誓我不会再一次屈服 But this don't even feel like falling 但是,这一次感觉像是彻底崩塌了Gravity can't forget 重力并没忘记 To pull me to the ground again 将我再次拉回地面 Feels like i've been awakened 我感觉好像已经觉醒了 Every rule i had you breakin' 你打破了我所有的规则 The risk that i'm takin' 我正在顶着这个风险 I'm never gonna shut you out 我不会将你置之不理的 Everywhere i'm looking now 无论我的视线停留在哪 I'm surrounded by your embrace 都被你的光辉环抱着 Baby i can see your halo 孩子,我能看到你的光环 You know you're my saving grace 你知道你就是我的恩赐 You're everything i need and more 你超过我所需要的一切 It's written all over your face 这些都写在了你的脸上

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