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Within 1e uncertainties. the distances [from the Sun of Sh2-252A. C. E. Itusscil | Within the uncertainties, the distances from the Sun of Sh2-252A, C, E, \citealt{Russeil03}) |
The processes which precipitated the steep decline in the co-moving density of luminous quasars since the epoch z~2 remain poorly understood. | The processes which precipitated the steep decline in the co-moving density of luminous quasars since the epoch $z\sim 2$ remain poorly understood. |
One observational approach to the problem. proceeds through the study. of the emission-line gas extending tens of kiloparsees from the quasar. | One observational approach to the problem proceeds through the study of the emission-line gas extending tens of kiloparsecs from the quasar. |
This material is the only visible tracer of the quasars immediate environment. and as such its kinematies and ionization state may vield clues to the mechanisms which have driven the cosmological evolution of the population as a whole. as well as the early stages of galaxy. formation more generally. | This material is the only visible tracer of the quasar's immediate environment, and as such its kinematics and ionization state may yield clues to the mechanisms which have driven the cosmological evolution of the population as a whole, as well as the early stages of galaxy formation more generally. |
There are numerous indications that at redshift 2>05 powerful radio sources inhabit environments simiar to the rich clusters found locally around the luminous FR LE sources Cygnus A and 3€295. | There are numerous indications that at redshift $z>0.5$ powerful radio sources inhabit environments similar to the rich clusters found locally around the luminous FR II sources Cygnus A and 3C295. |
Phe radio source properties. alone demand a certain tvpe of environment: a confining medium 'apable of acting as a working surface for the formation of Leepespectrum radio lobes is a basic requirement. | The radio source properties alone demand a certain type of environment: a confining medium capable of acting as a working surface for the formation of steep-spectrum radio lobes is a basic requirement. |
Faraday epolarization asvmmetrv. (Carrington Conway 1901). distorted/compressed.: radio source morphologies at. high redsult (Llintzen et al. | Faraday depolarization asymmetry (Garrington Conway 1991), distorted/compressed radio source morphologies at high redshift (Hintzen et al. |
1983: Barthel Aliley LOSS) and the ciscovery of sources with very high. Faraday. rotation measures (Carilli et al. | 1983; Barthel Miley 1988) and the discovery of sources with very high Faraday rotation measures (Carilli et al. |
1994. 1997) suggest that the medium is cleunpy ancl dense. | 1994, 1997) suggest that the medium is clumpy and dense. |
OF particular interest is the ποcaller "alignment effect. whereby the radio and extended optical/UV. emission of z20.6 radio galaxies are seen to be coincident (CNcCarthy et al. | Of particular interest is the so-called `alignment effect', whereby the radio and extended optical/UV emission of $z>0.6$ radio galaxies are seen to be coincident (McCarthy et al. |
LOST: Chambers et al. | 1987; Chambers et al. |
LOST): recent work bv Lacy ct al. ( | 1987); recent work by Lacy et al. ( |
1999) suggests that cilferent pwsical mechanisms are responsible for its manifestation on clillerent spatial scales. | 1999) suggests that different physical mechanisms are responsible for its manifestation on different spatial scales. |
Similarly. Best οἱ al. ( | Similarly, Best et al. ( |
2000a.b) have studied the emission-line properties of a large sample of ο~1 radio galaxies: they conclude that in small racli sources (x150 in size) the kinematics and. ionizatic ate of the linc-emitting clouds are dominated by the effec of the bow shock associated with the expansion of the racli source through a confining medium: photoionization of t eas by the nuclear source is more important in larger raci SOULCOS. | 2000a,b) have studied the emission-line properties of a large sample of $z\sim1$ radio galaxies: they conclude that in small radio sources $\leq 150$ in size) the kinematics and ionization state of the line-emitting clouds are dominated by the effects of the bow shock associated with the expansion of the radio source through a confining medium; photoionization of the gas by the nuclear source is more important in larger radio sources. |
To study the environments. of radio-loud quasars in corresponding detail is technically more cillicult. as the bright unresolved nucleus tends to overwhelm surrounding structure. | To study the environments of radio-loud quasars in corresponding detail is technically more difficult, as the bright unresolved nucleus tends to overwhelm surrounding structure. |
Over the last decade or more. however. we have pioneered the use of optical long-slit: spectroscopy to probe the extended emission-line regions around radio-loud quasars oul to redshift z1 (Fabian et al. | Over the last decade or more, however, we have pioneered the use of optical long-slit spectroscopy to probe the extended emission-line regions around radio-loud quasars out to redshift $z\sim1$ (Fabian et al. |
LOSS: Crawford Fabian 1989: Forbes et al. | 1988; Crawford Fabian 1989; Forbes et al. |
1990: Bremer et al. | 1990; Bremer et al. |
1992). | 1992). |
Where the emission line ratio OLILJA5007 OLLA3727 can be nieasured for the extended gas. it can be used in conjunction with photoionization models to deduce the gas pressure. | Where the emission line ratio $\lambda5007$ $\lambda3727$ can be measured for the extended gas, it can be used in conjunction with photoionization models to deduce the gas pressure. |
The latter is found to be consistently high (n1~5101.10 | The latter is found to be consistently high $nT \sim 5 \times 10^{5} - 1 \times 10^{7}$ |
(2011).. who report 2, based on stellar radius 2... the orbital period P. and the estimated 7; and surface eravily log οἱ the host star. | , who report $R_p$ based on stellar radius $R_*$, the orbital period $P$, and the estimated $T_e$ and surface gravity $\log g$ of the host star. |
Stellar parameters are based on (the multi-passband photometry and Bayesian analysis of the ορίου Input. Catalog (IXIC) Brownetal.(2011). | Stellar parameters are based on the multi-passband photometry and Bayesian analysis of the Kepler Input Catalog (KIC) \citet{Brown2011}. |
. We consider only. putative dwarl stars with 4«logg4.9. | We consider only putative dwarf stars with $4 < \log g < 4.9$. |
We choose a T, range that includes a substantial number of stars from each sample and maximizes (he similarity in the temperature distributions as assaved by (he Ixolmogorov-5uirnov (Ix-9) statistic. | We choose a $T_e$ range that includes a substantial number of stars from each sample and maximizes the similarity in the temperature distributions as assayed by the Kolmogorov-Smirnov (K-S) statistic. |
For an interval of 1000 Ix. that range is 3660-4660 Ix. (IX-8 probability =4.7x10. 7). | For an interval of 1000 K, that range is 3660-4660 K (K-S probability $= 4.7 \times 10^{-3}$ ). |
This includes 150 MIN stars (1202 measurenienis) and 10.013.Aepler target stars. the latter having 138 candidate planets. ancl excludes the 410 very coolestAepler target stars ancl 6 hotter M2IN stars. | This includes 150 M2K stars (1202 measurements) and 10,018 target stars, the latter having 138 candidate planets, and excludes the 410 very coolest target stars and 6 hotter M2K stars. |
The mean effective temperatures of the M2Ix. and.Aepler subsamples are 4230 Ix and 4200 Ix. respectively. | The mean effective temperatures of the M2K and subsamples are 4230 K and 4200 K, respectively. |
The low Ίντο probablity reflects the narrower distribution of M2IN. stars within (hiis range ol 7; compared to theKepler sample (Figure 2)). | The low K-S probablity reflects the narrower distribution of M2K stars within this range of $T_e$ compared to the sample (Figure \ref{fig.teff}) ). |
We speculate on the possible impact of this difference on our analvsis in Section 6.. | We speculate on the possible impact of this difference on our analysis in Section \ref{sec.discussion}. |
The expected Irequency of the ‘th planet candidate in theAepler survey is οι where s;=M;pijqij. pj; is the geometric probability of a transiting orbit around the jth star. and q;; is the probability of detection if the planet is on a transiting orbit. | The expected frequency of the $i$ th planet candidate in the survey is $1/s_i$, where $s_i = \Sigma_j
p_{ij}q_{ij}$, $p_{ij}$ is the geometric probability of a transiting orbit around the $j$ th star, and $q_{ij}$ is the probability of detection if the planet is on a transiting orbit. |
s; is the expected nunber of stars around which a planet would be detected. if every star had this planet on its particular orbit. | $s_i$ is the expected number of stars around which a planet would be detected, if every star had this planet on its particular orbit. |
For example. a planet (hat could have been detected around 100 stars. but has been found once. has a most likely occurence rate of1. | For example, a planet that could have been detected around 100 stars, but has been found once, has a most likely occurence rate of. |
. For planets that are small compared to their host stars aid on nearly circular orbits. the (transit probability is: | For planets that are small compared to their host stars and on nearly circular orbits, the transit probability is: |
In the framework of the discussed model an important relation can be established between (he slopes of the intrinsic 5-rav spectrum and (he highest energv. part of the secondary svinchrotron components. | In the framework of the discussed model an important relation can be established between the slopes of the intrinsic $\gamma$ -ray spectrum and the highest energy part of the secondary synchrotron components. |
This part of the svnchrotron spectrum is produced bv electron-positron pairs which are created significantly above the threshold of the 55 interaction. (hus it is possible to use the asvuiplotic limit of (he cross section. | This part of the synchrotron spectrum is produced by electron-positron pairs which are created significantly above the threshold of the $\gamma\gamma$ interaction, thus it is possible to use the asymptotic limit of the cross section. |
Since one of the secondary. electrons receives almost the all parent 5-rav energy. the cross section can be approximated as Then. the spectrum of the secondary. pairs. which is determined by (he intrinsic spectrum of VIIE 5-ravs. is: ∐↥↕↽≻≀↧↴↕⋅∐≺∢∏↥≀↧↴↕⋅⋅∐⋟⊔∐↲↕∐∏⋅↕∐⋟∖⊽↕≺∢↶↵−↕⋅≀↕∶∖↽⋟∖⊽↕↽≻≼↲≺∢⊔⋅∏∐↓↕⋟∖⊽≀↧↴↕↽≻∪∖∖⊽≼↲↕⋅↥≀↧↴∖∖⇁↕∐⊔∐⋟∖⊽≼↲∐≼↲↕⋅≸↽↔↴⋡∖↽∣↽⋯↴∐≼⇂⋅∖∖⇁↕⊔↥ a photon index s. (hen. since the dominant cooling mechanism is svnchrotron radiation. the energy distribution of the secondary leptons is a power law with the index s+2 and the hieh energy part of the svnchrotron spectrum is described by a power law with photon index (s4-3)/2. | Since one of the secondary electrons receives almost the all parent $\gamma$ -ray energy, the cross section can be approximated as Then, the spectrum of the secondary pairs, which is determined by the intrinsic spectrum of VHE $\gamma$ -rays, is: In particular, if the intrinsic $\gamma$ -ray spectrum is a power law in this energy band, with a photon index $s$, then, since the dominant cooling mechanism is synchrotron radiation, the energy distribution of the secondary leptons is a power law with the index $s+2$ and the high energy part of the synchrotron spectrum is described by a power law with photon index $(s+3)/2$. |
We note that even for a very hard intrinsic y-ray spectrum of s~1.5. the svuchrotron emission of secondary. pairs will be characterized by a photon index ~2.25. | We note that even for a very hard intrinsic $\gamma$ -ray spectrum of $s\sim 1.5$, the synchrotron emission of secondary pairs will be characterized by a photon index $\sim
2.25$. |
such behavior is expected al energies For numerical calculations. we assumed the blob to be homogeneous. | Such behavior is expected at energies For numerical calculations, we assumed the blob to be homogeneous. |
The pair production kernel. i.e. (he energy distribution of secondary electrons produced by a 5-rav of a certain energy. was calculated using anisotropic differential pair production cross section convolved with boosted Planckian distribution and averaged over the initial 5-rav | The pair production kernel, i.e. the energy distribution of secondary electrons produced by a $\gamma$ -ray of a certain energy, was calculated using anisotropic differential pair production cross section convolved with boosted Planckian distribution and averaged over the initial $\gamma$ -ray |
O.Struecm O.Struecm O.Struecm O.Struecm O.Struecm O.Struecm | 0.5truecm 0.5truecm 0.5truecm 0.5truecm 0.5truecm 0.5truecm |
tidal feld. | tidal field. |
However. studies of disc-subhalo. interactions using the Aquarius haloes (Lowing et al. | However, studies of disc-subhalo interactions using the Aquarius haloes (Lowing et al. |
in prep) support our assumption that the subhalo population (in the regime relevant to lensing) is only mareinally alfected by the presence of a realistic stellar disc. | in prep) support our assumption that the subhalo population (in the regime relevant to lensing) is only marginally affected by the presence of a realistic stellar disc. |
Disc shocking (e.g. 2?)) mav also reduce the inner substructure abundance. which would. further aggravate the problem of explaining the observed lensing anomalies. | Disc shocking (e.g. \citealt{Kazantzidis2009,
OnghiaSpringle2009DiskShocking}) ) may also reduce the inner substructure abundance, which would further aggravate the problem of explaining the observed lensing anomalies. |
In ?.. the dark matter-only Aquarius simulations were used to study Che relation between dark matter substructure abundance and lensing Hux-ratio anomalies. in. particular the cusp-caustic violations observed. for multiply: imaged quasars. | In \citet{Dandan09AquI}, the dark matter-only Aquarius simulations were used to study the relation between dark matter substructure abundance and lensing flux-ratio anomalies, in particular the cusp-caustic violations observed for multiply imaged quasars. |
We found that the dark substructures intrinsic to a typical galaxy-scale lensing halo were not sullicicnt to explain the observed [frequency of cusp-caustic violations. | We found that the dark substructures intrinsic to a typical galaxy-scale lensing halo were not sufficient to explain the observed frequency of cusp-caustic violations. |
1n this work. we have considered. whether this expectation changes when satellite galaxies in subhaloes are. taken into account. or when the lensing halo ijs assumed to contain a MW-like globular cluster population that is not associated with surviving dark matter substructures. | In this work, we have considered whether this expectation changes when satellite galaxies in subhaloes are taken into account, or when the lensing halo is assumed to contain a MW-like globular cluster population that is not associated with surviving dark matter substructures. |
We have also considered: streams of dark matter identified. in the Aquarius simulations. in order to estimate the lensing cllect of irregularities in the halo itself. | We have also considered streams of dark matter identified in the Aquarius simulations, in order to estimate the lensing effect of irregularities in the halo itself. |
.. We conclude that the abundance of intrinsic substructures. dark or bright. bound. or dilfuse. cannot fully account. for. the observed cusp-violation frequency. | We conclude that the abundance of intrinsic substructures, dark or bright, bound or diffuse, cannot fully account for the observed cusp-violation frequency. |
Taken at face value. this lack of substructure suggests à serious problem for the CDM model. | Taken at face value, this lack of substructure suggests a serious problem for the CDM model. |
Warm dark matter mocoels. which could reduce the satellite abundance and may help to bring the dwarf galaxy. LE into agreement with observations without invoking strong cedhack or photoionization elfects. (oe. 7)) would. only make this problemi worse. | Warm dark matter models, which could reduce the satellite abundance and may help to bring the dwarf galaxy LF into agreement with observations without invoking strong feedback or photoionization effects, (e.g. \citealt{SavalaWhite2010}) ) would only make this problem worse. |
However. it is possible that the observed frequeney of Dux anomalies are strongly biased by he small number statistics of CLASS. | However, it is possible that the observed frequency of flux anomalies are strongly biased by the small number statistics of CLASS. |
Previous studies have shown that intergalactic haloes (AJο A1.) projected along the line of sight can cause surface density [uctuations at the level of 1-10. per cent. making them a probable source of lensing Lux anomalies (?7?777). | Previous studies have shown that intergalactic haloes $M \lesssim
10^{10} M_{\odot}$ ) projected along the line of sight can cause surface density fluctuations at the level of 1-10 per cent, making them a probable source of lensing flux anomalies \citep{Chen2003, Wambsganss2005, Metcalf2005a,
Metcalf2005b,Miranda2007}. |
. In future work. we will examine the contribution of his large-scale structure to observations of the cusp-caustic violation rate. using high-resolution. cosmological volume simulations. which self-consistentlv. model the halo. mass function and clustering along the line of sight (e.g.?).. | In future work, we will examine the contribution of this large-scale structure to observations of the cusp-caustic violation rate, using high-resolution cosmological volume simulations, which self-consistently model the halo mass function and clustering along the line of sight \citep[e.g.][]{PunchweinHilbert2009}. |
We thank lan Browne. Neal Jackson and Simon White for useful cliseussions and the referee for their comments. | We thank Ian Browne, Neal Jackson and Simon White for useful discussions and the referee for their comments. |
DDN has been supported. by a Dorothy Hocdgkin fellowship for her postgraduate studies. | DDX has been supported by a Dorothy Hodgkin fellowship for her postgraduate studies. |
LG acknowledges; support from a STEC advanced fellowship. one-huncdred-talents program of the Chinese Academy of Sciences (CAS)} and the National Basic Research Program of China (973 program under erant No. | LG acknowledges support from a STFC advanced fellowship, one-hundred-talents program of the Chinese Academy of Sciences (CAS) and the National Basic Research Program of China (973 program under grant No. |
2000€B24901). | 2009CB24901). |
CSE acknowledges a Itoval Society Wolfson Research Merit. award. | CSF acknowledges a Royal Society Wolfson Research Merit award. |
APC is supported. by an SPEC postspostgraduate studentship. | APC is supported by an STFC postgraduate studentship. |
Ι The simulations for the AquariusἹ Projectj were carried out at the Leibniz Computingputing Contre. Garching. Germany: at the Computing Centre of the Max Planck Society in Garching: at. the Institute for Computational Cosmology in. Durham: and on the STELLA’ supercomputer of the LOPAL. experiment at the University of Groningen, | The simulations for the Aquarius Project were carried out at the Leibniz Computing Centre, Garching, Germany; at the Computing Centre of the Max Planck Society in Garching; at the Institute for Computational Cosmology in Durham; and on the `STELLA' supercomputer of the LOFAR experiment at the University of Groningen. |
and A will vary in tandem. so that they have only a effect on the A(Ile|41) ratio. | and $K$ will vary in tandem, so that they have only a second-order effect on the $K/({\rm H}\epsilon + H)$ ratio. |
One of the most important. considerations when using the calcium line as a classification criterion is the reduced metallicity of the SAIC. | One of the most important considerations when using the calcium line as a classification criterion is the reduced metallicity of the SMC. |
One approach to the metallicity issue is given in 2.. where the spectral types of a sample of SAIC A-type supergiants were adjusted in the light of mocdel-atmosphere analysis. | One approach to the metallicity issue is given in \citet{venn99}, where the spectral types of a sample of SMC A-type supergiants were adjusted in the light of model-atmosphere analysis. |
Our approach to the issues regarding classification that arise [rom this ancl other stucies were discussed in Section 2.. | Our approach to the issues regarding classification that arise from this and other studies were discussed in Section \ref{principles}. |
In the current context of classifving the 2d sample. the criteria in ‘Table 3 are applied: on the basis that they are themorphological counterparts of Galactic criteria. with the explicit understanding there may not be a correspondence inphysical properties. between Galactic ancl SMC stars. | In the current context of classifying the 2dF sample, the criteria in Table \ref{aclass} are applied on the basis that they are the counterparts of Galactic criteria, with the explicit understanding there may not be a correspondence in properties between Galactic and SMC stars. |
The influence of. rotational broadening on X-stars classification has been discussed. bv. 2... | The influence of rotational broadening on A-stars classification has been discussed by \citet{gg87}. |
They. defined: low and high standards on the basis that. broadening of the A line in rapid rotators may allect the classification process. | They defined low and high standards on the basis that broadening of the $K$ line in rapid rotators may affect the classification process. |
? subsequently concluded that at tvpe A5 and Later this elect is reduced. such that the AI ratio can be safely used for rapid. rotators. | \citet{gg89b}
subsequently concluded that at type A5 and later this effect is reduced, such that the $\;K$ $\epsilon$ ratio can be safely used for rapid rotators. |
This is not of direct concern in the 2dE dataset because of the distance (ie. luminosity) selection.ellect. | This is not of direct concern in the 2dF dataset because of the distance (i.e., luminosity) selectioneffect. |
. Fvpical rotational velocities for X-tvpe supergiants are low (of order 2030tsCg... 27)). so rotation is not a significant issue. | Typical rotational velocities for A-type supergiants are low (of order 20–30;, \citealt{am95, venn95}) ), so rotation is not a significant issue. |
For comparison. the “high” stars referred to w ? have velocities in the range of 150275 (with uminosity types ranging from LLL to V). | For comparison, the “high” stars referred to by \citet{gg87} have velocities in the range of 150–275 (with luminosity types ranging from III to V). |
In principle there could. be a svstematic dillerence in he rotational velocity distributions between the Galaxy and the SMC. as discussed by ο in reference to B-type stars. | In principle there could be a systematic difference in the rotational velocity distributions between the Galaxy and the SMC, as discussed by \citet{mgm99} in reference to B-type stars. |
Rotation could also have an indirect. elfect. through he Galactic stars. used here to describe the classification ramework. | Rotation could also have an indirect effect through the Galactic stars used here to describe the classification framework. |
Where available. rotational velocities from ? are eiven in Table 1. for our Galactic targets. | Where available, rotational velocities from \citet{am95} are given in Table \ref{atargets} for our Galactic targets. |
Phe majority of the Galactic stars have relatively low velocities. and those with aster rotation are not particularly. discrepant in Figure 4.. sugeesting that rotational effects. are unlikely to play a significant role in the current work. | The majority of the Galactic stars have relatively low velocities, and those with faster rotation are not particularly discrepant in Figure \ref{ca}, suggesting that rotational effects are unlikely to play a significant $\hat{\rm o}$ le in the current work. |
The AL ratio is useful for distinguishing between A spectral subtypes. even in data of moderate to poor quality. but is not a sullicient criterion to distinguish late-B [roni early-A. nor earlv-E. from late-A stars. | The $K/{\rm H}\epsilon$ ratio is useful for distinguishing between A spectral subtypes, even in data of moderate to poor quality, but is not a sufficient criterion to distinguish late-B from early-A, nor early-F from late-A stars. |
The D stars. are. straighforwarelly identified by. the presence of helium lines (e.g.2).. while the 100 supergiants with spectral types later than FO observed in the 2dE sample (as à result of photometric errors in the input catalogue) were classified. using the INTE data as a point of reference. in combination with the criteria given by 2... | The B stars are straighforwardly identified by the presence of helium lines \citep[e.g.][]{djl}, while the $\sim$ 100 supergiants with spectral types later than F0 observed in the 2dF sample (as a result of photometric errors in the input catalogue) were classified using the INT data as a point of reference, in combination with the criteria given by \citet{jj90}. . |
Essentially. ]E-tvpe stars are characterized by increasingly strong metal | Essentially, F-type stars are characterized by increasingly strong metal |
we considered the Following cases. | we considered the following cases. |
First (cases 1.3] in Figs. | First (cases [1,3] in Figs. |
2. and 3)). all clusters were assumed. to be 1 Gr old and located at the same galactocentric distance of D=0.7 kpe. | \ref{powerlaw.fig} and \ref{lognormal.fig}) ), all clusters were assumed to be 1 Gyr old and located at the same galactocentric distance of $D = 0.7$ kpc. |
Consequently. they are all characterized: by the same ambient density (pauc2.5 AL. I). ane thus by the same disruption time-scale. | Consequently, they are all characterized by the same ambient density $\rho_{\rm amb} \simeq 2.5$ $_\odot$ $^{-3}$ ), and thus by the same disruption time-scale. |
Secondly (case 2 in Figs. | Secondly (case [2] in Figs. |
2. and 3)). we considered the case of a cluster system characterized by uniform distributions in age aux ealactocentric distance. | \ref{powerlaw.fig} and \ref{lognormal.fig}) ), we considered the case of a cluster system characterized by uniform distributions in age and galactocentric distance. |
Following our definition of the burs of cluster formation. (see Fig. 1)). | Following our definition of the burst of cluster formation (see Fig. \ref{turnover.fig}) ), |
the lower and upper limits of the age distribution are log(//vr)=S.7 sux 9.2. respectively, | the lower and upper limits of the age distribution are $\log(t/{\rm yr}) = 8.7$ and 9.2, respectively. |
As for the spatial distribution. clusters were assumed to be distributed uniformly in galactocentric distance across the region (0.4<(D/kpe) 1.0). the raclia extent of MS2 D. In this case. the cluster system: probes a range of ambient. densities and. therefore. of characteristic disruption time-scales. | As for the spatial distribution, clusters were assumed to be distributed uniformly in galactocentric distance across the region $0.4 \le (D/{\rm kpc}) \le 1.0$ ), the radial extent of M82 B. In this case, the cluster system probes a range of ambient densities and, therefore, of characteristic disruption time-scales. |
We assume that the radial profile of the ambient density is that of a singular isothermal sphere. PoulXD= and that pau—0Tkpe)22.5 M. pe7. | We assume that the radial profile of the ambient density is that of a singular isothermal sphere, $\rho_{\rm amb} \propto D^{-2}$, and that $\rho_{\rm amb}(D=0.7\,{\rm kpc})=2.5$ $_\odot$ $^{-3}$. |
The initial power-law CALF is characterised. by a slope of 2 (see de Cuijs et al. | The initial power-law CMF is characterised by a slope of $-2$ (see de Grijs et al. |
2003€ for a review). | 2003c for a review). |
Vig. | Fig. |
2 shows the corresponding evolved. mass distributions. using both the disruption time-scale determined by de Cirijs ct al. ( | \ref{powerlaw.fig} shows the corresponding evolved mass distributions, using both the disruption time-scale determined by de Grijs et al. ( |
2003a: case 3]). and the —16. longer time-scale suggestec by Baumegardt Alakino’s (2003) N-body simulations (ease 1). | 2003a; case [3]), and the $\sim 16 \times$ longer time-scale suggested by Baumgardt Makino's (2003) $N$ -body simulations (case [1]). |
We also show the small differences between a coeval (exactly) 1 Cyr-old. cluster population. located a a galactocentric distance of (exactly) 0.7. kpe (case 1]). and the scenario in which the clusters show a uniform age spread over 8.7xlog(Xge/sr)9.2 and are distributer uniformly. across the region (0.4<(D/kpe) 1.0). | We also show the small differences between a coeval (exactly) 1 Gyr-old cluster population, located at a galactocentric distance of (exactly) 0.7 kpc (case [1]), and the scenario in which the clusters show a uniform age spread over $8.7 \le \log( {\rm Age/yr} ) \le 9.2$ and are distributed uniformly across the region $0.4 \le (D/{\rm kpc}) \le 1.0$ ). |
This uniform cistribution in galactocentrie distance corresponds to a number density profile scaling as 2)7. | This uniform distribution in galactocentric distance corresponds to a number density profile scaling as $D^{-2}$. |
We checked tha the dilferences caused by assuming radial density profiles Following a fairly arbitrary (ancl shallow) profile x2LN as well as a much steeper number density. distribution such as that of GC's in the Galactic halo. xD.°° (ce. Zinn 1985). result in identical evolved mass distributions. within the uncertainties. | We checked that the differences caused by assuming radial density profiles following a fairly arbitrary (and shallow) profile $\propto D^{-0.5}$, as well as a much steeper number density distribution such as that of GCs in the Galactic halo, $\propto D^{-3.5}$ (e.g., Zinn 1985), result in identical evolved mass distributions, within the uncertainties. |
Phe assumed. spatial distribution of the clusters allects our results negligibly. which is a natural consequence of the small radial extent of MS82 D. In view of the region's disturbed appearance and unique star (cluster) formation history. neither a uniform nor à stronely raciiallv dependent initial density distribution can be ruled. outpriori. | The assumed spatial distribution of the clusters affects our results negligibly, which is a natural consequence of the small radial extent of M82 B. In view of the region's disturbed appearance and unique star (cluster) formation history, neither a uniform nor a strongly radially dependent initial density distribution can be ruled out. |
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