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Thus. for the intermediate A.V state only odd partial waves are allowed. | Thus, for the intermediate $\Delta N$ state only odd partial waves are allowed. |
In contrast. in the pp—dx reaction both negative and positive parity states are allowed and formation of the intermediate S-wave AN state with J=2 leads to a perfect. resonance looping in the ο pp-partial wave in the respective Argand diagram |11].. | In contrast, in the $pp\to d\pi^+$ reaction both negative and positive parity states are allowed and formation of the intermediate S-wave $\Delta N$ state with $J^P=2^+$ leads to a perfect resonance looping in the $^1D_2$ $pp$ -partial wave in the respective Argand diagram \cite{arndt}. . |
Therefore. the relative contribution of the A-mechanisim to the reaction pp—Ípp]z" is expected to be suppressed as compared to the reaction pp—dz . | Therefore, the relative contribution of the $\Delta$ -mechanism to the reaction $pp\to \{pp\}_s\pi^0$ is expected to be suppressed as compared to the reaction $pp\to d\pi^+$. |
CDhis argument. was applied in Ref. | This argument was applied in Ref. |
[12]. to explain a very small ratio (less of few percents) of the spin-singlet to spin-triplet pn-pairs observed in the LAMPF data in the final state interaction regionof the reaction pp—pnz al proton beam energy 0.8 GeV. Furthermore. since A-type mechanisms are of long-range tvpe. reduction of their contribution would mean that other mechanisms. like |V-exehanges [0] which are more sensitive to short-range NN-dynanmies. could be more pronounced in the reaction as compared to the pp—dx reaction [U].. | \cite{uzwilk2001} to explain a very small ratio (less of few percents) of the spin-singlet to spin-triplet pn-pairs observed in the LAMPF data \cite{HGabitch}
in the final state interaction regionof the reaction $pp\to pn\pi^+$ at proton beam energy 0.8 GeV. Furthermore, since $\Delta-$ type mechanisms are of long-range type, reduction of their contribution would mean that other mechanisms, like $N^*$ -exchanges \cite{sharmamitra} which are more sensitive to short-range NN-dynamics, could be more pronounced in the reaction $pp\to \{pp\}_s\pi^0$ as compared to the $pp\to d\pi^+$ reaction \cite{ponting}. |
The cross section of the reaction pp—Ípp].z" was measured recently at energy. 0.8 GeV in Ref.[0) and at beam energies 0.5—2.0 GeV inRef. [3].. | The cross section of the reaction $pp\to \{pp\}_s\pi^0$ was measured recently at energy 0.8 GeV in \cite{dymov06} and at beam energies $0.5 - 2.0$ GeV inRef. \cite{kurbatov}. . |
At zero angle. the data show a broad maximum in the energy dependence of the cross section al 0.5—1.4 GeV. | At zero angle, the data \cite{kurbatov} show a broad maximum in the energy dependence of the cross section at $0.5 - 1.4$ GeV. |
universe is low: ο,0.2 - 0.5. aud os~ 1 (see references above). | universe is low: $\Omega_{m} \sim 0.2$ - 0.5, and $\sigma _{8} \sim$ 1 (see references above). |
However. the total uuuboer of clusters currently studied at high redshifts is still σα. and the model comparISOs are eeneralv based on the Press-Scliceiter (4971) approximation which. while surprisiely accurate. js kuowu to lave biases. | However, the total number of clusters currently studied at high redshifts is still small, and the model comparisons are generally based on the Press-Schechter (1974) approximation which, while surprisingly accurate, is known to have biases. |
Direct coiuparlisons with siulations have also been used. but hese are eenerallv too siual to find fie rare ueh-ludas οusters especially at large recshifts. | Direct comparisons with simulations have also been used, but these are generally too small to find the rare high-mass clusters, especially at large redshifts. |
Now observations are currently underway to cletermune more precisely the evolution of cluster anmudauce MSIE opical. N-ray. Suuvaev-Zel«ovich. aud eravitational leusiug surveys. | New observations are currently underway to determine more precisely the evolution of cluster abundance using optical, X-ray, Sunyaev-Zel'dovich, and gravitational lensing surveys. |
At f1C sale due. larger and more accurate cosmological sa.ulations are needed in order to accurately detertune the expected mass function of clusters of ealaxies and its evolution with time. in order to allow or proper coluparison with the upcoming observations. | At the same time, larger and more accurate cosmological simulations are needed in order to accurately determine the expected mass function of clusters of galaxies and its evolution with time, in order to allow for proper comparison with the upcoming observations. |
Iu this oper we prescut eieaparsec-scale siatious of four popular CDAL models which allow an accurate determinaion of the evolution of the cluster mass function from redshift +=3 tor.=0. including the rare ancl cosinologicallv powerful massive clusters. | In this paper we present gigaparsec-scale simulations of four popular CDM models which allow an accurate determination of the evolution of the cluster mass function from redshift $z=3$ to $z=0$, including the rare and cosmologically powerful massive clusters. |
The rapid increase of available computing power aid new algorithms which ruu cficicutly ou paralcl machines make possible a colmbination of large simulation volume and high resolution. | The rapid increase of available computing power and new algorithms which run efficiently on parallel machines make possible a combination of large simulation volume and high resolution. |
For comouwison. the models prescutec here are of a larger volune than the Covernatoeta.(1999). sinulations. aud attain considerably higher resolution than the Virgo “Hubble Volume” s«mnuatious (Evrard1998:Jenkiusctal.2000). | For comparison, the models presented here are of a larger volume than the \cite{GBQTBKL99} simulations, and attain considerably higher resolution than the Virgo “Hubble Volume” simulations \citep{Evrard98,JFWCCEY00}. |
. Furtheriuore. we are able to cover several different models. inchiding the first large voluuec. high resolfion. simulaion of tilted ο, as well as a quiutesseuce model. | Furthermore, we are able to cover several different models, including the first large volume, high resolution simulation of tilted $\Omega_{m}=1$ as well as a quintessence model. |
The aln of his paper is to provide the fouation for οςMuparisons with the 1pconiue observations. | The aim of this paper is to provide the foundation for comparisons with the upcoming observations. |
Thus the evolution of the dass fuuction 1s preseied n a qmanner tha cal be direcIv conpare with observations. using cluster lasses Within a variety of specific radii typically used in observations. rather than usine the not so casily observade virial mmass. | Thus the evolution of the mass function is presented in a manner that can be directly compared with observations, using cluster masses within a variety of specific radii typically used in observations, rather than using the not so easily observable virial mass. |
We discuss the siunulatious aud t1ο method of cluster selection iu 52.. | We discuss the simulations and the method of cluster selection in $\S$ \ref{seccreate}. . |
The evolution of the resulting cluster ias function is preseuted in οι, | The evolution of the resulting cluster mass function is presented in $\S$ \ref{secevol}. |
Comparison with the Press-Schecher ατομαο. 1s lade in ol. ancl effects of resolution are discussed in κκ85.. | Comparison with the Press-Schechter approximation is made in $\S$ \ref{secpscomp}, , and effects of resolution are discussed in $\S$ \ref{secreseff}. |
Comparisons with current observations are shown in 66.. and conclusions are sunmnauarized i Ότι, | Comparisons with current observations are shown in $\S$ \ref{secobscomp}, and conclusions are summarized in $\S$ \ref{secconcl}. |
Four currently favored variants of the CDM model were chosen. with parameters cousistet with mamerous observationa constraints (Balicalletal.1999). | Four currently favored variants of the CDM model were chosen, with parameters consistent with numerous observational constraints \citep{BOPS99}. |
. These observaions tend to favor a low deusity universe with 0,~0.3: in addition to spatially fat (LCDM) and οxm (OCDAL) inoels woe inelude a quintessence model (QCDAL. | These observations tend to favor a low density universe with $\om\simeq0.3$; in addition to spatially flat (LCDM) and open (OCDM) models we include a quintessence model (QCDM). |
Like LCDM. the QCDAI is iade spatialy flat by including a conrponeut witi negative pressire. but the Q component is vuauically evolving and spatially iuhoiiogeneous (CalcdaweLDaveVASteinhardt L998). | Like LCDM, the QCDM is made spatially flat by including a component with negative pressure, but the Q component is dynamically evolving and spatially inhomogeneous \citep{CDS98}. |
.. The equation of sate of he Q component. (e=2/3, was chosen to bο du the range favored by observations (Waneetal.2000). | The equation of state of the Q component, $w=-2/3$, was chosen to be in the range favored by observations \citep{WCOS00}. |
. A standard Q,,=1 CDM ueel was also run. wit ia stronely tilted power spectrum so as to avo overproduction of present-day clusters. | A standard $\om=1$ CDM model was also run, with a strongly tilted power spectrum so as to avoid overproduction of present-day clusters. |
All unoels are normalized (bv ox) to match the observe preseut-day cluster abundauce and be consisteat with the CODE microwave backeround normalization. | All models are normalized (by $\sigma_8$ ) to match the observed present-day cluster abundance and be consistent with the COBE microwave background normalization. |
The cosmological parameters for the ciffereut ταις are listed in Tade 1.. | The cosmological parameters for the different runs are listed in Table \ref{tblparams}. |
The ranster fiction for a oοiven model was computed àsine the CMDBFAST code (Seljak&Zaldarriaga 1996).. modified to haidle a clynamiical cherey coleut in the QCDM case (Caldwell.Dave.&Steinhardt 1998). | The transfer function for a given model was computed using the CMBFAST code \citep{SZ96}, modified to handle a dynamical energy component in the QCDM case \citep{CDS98}. |
. The resulting peAVCL spectrum was used to generate iitial concitloli by perturbing particles on a rectilinear grid: this step was performed with the COSMICS soTwure package (Mla&Bertschinecr1995:Bertsc11igor 1995). | The resulting power spectrum was used to generate initial conditions by perturbing particles on a rectilinear grid; this step was performed with the COSMICS software package \citep{MB95,Bert95}. |
. Eacji unmulatiou was beguu at a redshift when the RAIS deusity fluctuation was 15. | Each simulation was begun at a redshift when the RMS density fluctuation was . |
. For QCDAL the fluctuations in the ϱ compoveut are neeligible bv the time the simulation beelus (22 30). | For QCDM, the fluctuations in the Q component are negligible by the time the simulation begins $z\approx 30$ ). |
Thus. once the matter power spectrum is been computed. the Q component lias an eftect oulv through the overall expansion factor e(f). | Thus, once the matter power spectrum has been computed, the Q component has an effect only through the overall expansion factor $a(t)$. |
All four runs contained 512°151 uulion particles iu a periodic cube. | All four runs contained $512^3=134$ million particles in a periodic cube. |
For the £3,=0.3 rus the box leneth is 10007. 1Mpc: iu the SCDM runit is sunaller. such thatthe volume isrediiced o» a factor of 0.3 relative to the other niodels (sco Table 13). | For the $\om=0.3$ runs the box length is $ h^{-1}$ Mpc; in the SCDM runit is smaller, such thatthe volume isreduced by a factor of 0.3 relative to the other models (see Table \ref{tblparams}) ). |
With this choice of parameters | With this choice of parameters |
The <20kkeV X-ray spectrum of Cyg X-2. and of persistent bright NS LMXBs in general. has been usually described as the sum of a soft and a hard component. | The $<$ keV X-ray spectrum of Cyg X–2, and of persistent bright NS LMXBs in general, has been usually described as the sum of a soft and a hard component. |
The soft component is interpreted as emission from the accretion disc (Easternmodel.?) or originating at (or close to) the NS (Westernmodel.?) whereas the hard component is most likely formed due to Comptonization of NS and/or disc emission by a hot plasma (so-called “corona’) electrons. | The soft component is interpreted as emission from the accretion disc \citep[Eastern model, ][]{mitsuda84}
or originating at (or close to) the NS \citep[Western model, ][]{white86}
whereas the hard component is most likely formed due to Comptonization of NS and/or disc emission by a hot plasma (so-called "corona") electrons. |
These two models describe equally well the spectra of NS LMXBs below about kkeV. The first studies of the X-ray spectrum above ~20 kkeV were performed with detectors on balloons (?).. | These two models describe equally well the spectra of NS LMXBs below about keV. The first studies of the X-ray spectrum above $\sim20$ keV were performed with detectors on balloons \citep{peterson73}. |
Interestingly. an unexpected hardening was observed in the spectrum of tthat was fitted by a powerlaw (PL) with photon index of 2.8 (?) or 1.9 (?).. | Interestingly, an unexpected hardening was observed in the spectrum of that was fitted by a powerlaw (PL) with photon index of 2.8 \citep{maurer82} or 1.9 \citep{ling96}. |
It soon became clear that simultaneous broad band observations of the X-ray spectrum were needed to investigate the nature of this spectral flattening. | It soon became clear that simultaneous broad band observations of the X-ray spectrum were needed to investigate the nature of this spectral flattening. |
The advent of broad-band X-ray missions. such asINTEGRAL.. revealed that many such spectral hardenings (so-called "hard tails”) occur in Z sources: Cyg X-2 (?2).. GX | 2 (??).. GX | 2 (2).. Sco X-1 (2?).. GX 5-1 (22)... GX | 0 (?).. | The advent of broad-band X-ray missions, such as, revealed that many such spectral hardenings (so-called "hard tails") occur in Z sources: Cyg X–2 \citep{frontera98,disalvo02b}, GX $+$ 2 \citep{farinelli05,disalvo00}, GX $+$ 2 \citep{disalvo01}, Sco X–1 \citep{damico01,disalvo06}, GX 5–1 \citep{paizis05,asai94}, GX $+$ 0 \citep{lavagetto04}. |
Recently. a hard tal has also been discovered in the bright atoll source GX |1 (?.hereafterPOG).. | Recently, a hard tail has also been discovered in the bright atoll source GX $+1$ \citep[][hereafter P06]{p06}. |
The spectra of these sources and m particular the hard X-ray tails have been extensively studied and focused on a single source basis. and mainly in terms of phenomenological models (see??.forareviewonNSLMXBspectra).. | The spectra of these sources and in particular the hard X-ray tails have been extensively studied and focused on a single source basis, and mainly in terms of phenomenological models \citep[see][for a review on NS LMXB spectra]{barret01, disalvo02}. |
In the attempt to study these sources in terms of a in the less known domain above kkeV. Ρ06 studied the long term average hard X-ray (720 kkeV) spectra of a sample of twelve bright NS LMXBs (six Z and six atoll sources). using data from IBIS instrument on-board (?).. | In the attempt to study these sources in terms of a in the less known domain above keV, P06 studied the long term average hard X-ray $>$ keV) spectra of a sample of twelve bright NS LMXBs (six Z and six atoll sources), using data from IBIS instrument on-board \citep{winkler03}. |
Merging their results with those of ? for the atoll source (GX 354-0). Ρ06 identified four main spectral states for NS LMXBs (see Fig. | Merging their results with those of \cite{falanga06} for the atoll source (GX 354–0), P06 identified four main spectral states for NS LMXBs (see Fig. |
4 in POO): state 354-0)). sstate and 1608—55)). sstate (where the hard X-ray tail appears. e.g.. Cyg X-2. Sco X-1.5-1.. GX | 2) and sstate (e.g.. GX 3| I. GX 9| I. GX | 9). | 4 in P06): state ), state and ), state (where the hard X-ray tail appears, e.g., Cyg X–2, Sco X–1, GX $+$ 2) and state (e.g., GX $+$ 1, GX $+$ 1, GX $+$ 9). |
The different spectral states. including the hard tails. could be well fit in terms of the interplay of thermal and bulk Comptonization (TC and BC. respectively) using the mmodel inXSPEC. | The different spectral states, including the hard tails, could be well fit in terms of the interplay of thermal and bulk Comptonization (TC and BC, respectively) using the model in. |
. The relative contribution between the two Comptonization regimes (thermal versus bulk) is proposed to be drawn by the accretion rate AT. | The relative contribution between the two Comptonization regimes (thermal versus bulk) is proposed to be drawn by the accretion rate $\dot{M}$. |
Indeed (see POG). starting from the lowest level V. the sstate spectra. whose cut-off is below kKKeV.can be interpreted in terms of TC of soft photons off a hot (7-30 kkeV) electron population: at increasing 1. bulk Comptonization starts | Indeed (see P06), starting from the lowest level $\dot{M}$, the state spectra, whose cut-off is below keV,can be interpreted in terms of TC of soft photons off a hot $\sim$ keV) electron population; at increasing $\dot{M}$ bulk Comptonization starts |
and is allected intensely by extinction and metallicity (?).. | and is affected intensely by extinction and metallicity \citep{2006MNRAS.369..891M}. |
In the assumption of case D recombination. two-thirds of (he Lyman continuum photons are reprocessed asLvo. | In the assumption of case B recombination, two-thirds of the Lyman continuum photons are reprocessed as. |
. Therefor. voung starbursts should be easily detected by their emission. | Therefor, young starbursts should be easily detected by their emission. |
However. observations of nearby starbursts (e.g.??)| revealed in most starburst ealaxies a much weaker than predicted by simple models of galaxy formation. | However, observations of nearby starbursts \citep[e.g.][]{1988ApJ...326..101H,
1992ApJ...399L..39C} revealed in most starburst galaxies a much weaker than predicted by simple models of galaxy formation. |
To explain (his low flux. ? suggested that strong emission requires either a low abundance of dust or an AGN. | To explain this low flux, \citet{1993ApJ...415..580C} suggested that strong emission requires either a low abundance of dust or an AGN. |
However. ? clemonstrated that pure extinction could not explain the weak Iluxes. | However, \citet{1996ApJ...470..189G} demonstrated that pure extinction could not explain the weak fluxes. |
Results suggest that photons are decoupled from the continuum radiation resulting in a increased sensitivity to dust ?.. | Results suggest that photons are decoupled from the continuum radiation resulting in a increased sensitivity to dust \citet{1990ApJ...350..216N}. |
systems al z>5 are a very useful probe of the properties of very voung star-forming svslenms al the epoch after reionization. | systems at $z>5$ are a very useful probe of the properties of very young star-forming systems at the epoch after reionization. |
Unlortunately. the data obtained to the date are not sufficient to place strong constraints on the Pandamental properties. | Unfortunately, the data obtained to the date \citep[e.g. ][]{2003PASJ...55L..17K,2004AJ....127..563H,
2004ApJ...611...59R, 2005A&A...430L..21W, 2005PASJ...57..165T,
2006ApJ...638..596A,2006PASJ...58..313S} are not sufficient to place strong constraints on the fundamental properties. |
The line is not used commonly as à SER tracer. | The line is not used commonly as a SFR tracer. |
Resonant scattering of photons by neutral atomic hyerogen affects their relation with the SER in a galaxy (?).. | Resonant scattering of photons by neutral atomic hydrogen affects their relation with the SFR in a galaxy \citep{1993ApJ...415..580C}. . |
Narrow-band imaging produces approximately volume-Inmnitecd samples. since (he observed bands correspond to small windows in redshift space. | Narrow-band imaging produces approximately volume-limited samples, since the narrow-observed bands correspond to small windows in redshift space. |
The objects are selected with a well defined limit in equivalent width and the line flix can be transformed into Iuminosity with some simple assumptions. | The objects are selected with a well defined limit in equivalent width and the line flux can be transformed into luminosity with some simple assumptions. |
Narrow-band imagine thus provide lime humninosities Lor a volume-limited sample of emission line galaxies. | Narrow-band imaging thus provide line luminosities for a volume-limited sample of emission line galaxies. |
In the case of detecüng limes used as star. formation tracers. the sample would be directly. SFR-selected. except for the AGN contribution. | In the case of detecting lines used as star formation tracers, the sample would be directly SFR-selected, except for the AGN contribution. |
The problem with (his approach is that stars contzuninating (he sample or contributions from different emission lines cannot be separated only wilh narrow-bancl imaging. | The problem with this approach is that stars contaminating the sample or contributions from different emission lines cannot be separated only with narrow-band imaging. |
Additional assumptions (onthehuminositvfunctionsofELGs.e.g.2) or additional data (see.e.g..Checolor-colordiagramsof2). are needed (to complete the scenario. | Additional assumptions \citep[on the luminosity functions of ELGs,
e.g. ][]{2001ApJ...550..593J} or additional data \citep[see, e.g., the
color-color diagrams of][]{2003ApJ...586L.115F} are needed to complete the scenario. |
The aim of this work is to contribute to several aspects of the narrow-band imaging in order to optimize the results of the observations. | The aim of this work is to contribute to several aspects of the narrow-band imaging in order to optimize the results of the observations. |
Section 2. describes (he characterization of the fillers used through this work. | Section \ref{sec:description} describes the characterization of the filters used through this work. |
In Section 3. we deal with the different sources of contamination. either galactic or extragalactic that can be found in an narrow-band survey and. different. methods used to detect them. | In Section \ref{sec:contamination} we deal with the different sources of contamination, either galactic or extragalactic that can be found in an narrow-band survey and different methods used to detect them. |
Section 4. describes how to infer the line and continuum. fluxes. (ancl the corresponding equivalent width) from (the measured magnitudes in a variety of scenarios. including more than one broad-band. filler ancl more than one line inside the narrow-band filler. | Section \ref{sec:el} describes how to infer the line and continuum fluxes (and the corresponding equivalent width) from the measured magnitudes in a variety of scenarios, including more than one broad-band filter and more than one line inside the narrow-band filter. |
We study the method to select the candidates. based solely on broad and narrow-band colors in Sect. 5.. | We study the method to select the candidates, based solely on broad and narrow-band colors in Sect. \ref{sec:dispq}. |
We study in detail also the comoving volume covered bv a narrow-band selected sample. | We study in detail also the comoving volume covered by a narrow-band selected sample. |
Numeric examples with three filter set. includingbroad and narrow-haac | Numeric examples with three filter set, includingbroad and narrow-band |
Numeric examples with three filter set. includingbroad and narrow-haacl | Numeric examples with three filter set, includingbroad and narrow-band |
Since the distribution of e is svinmietric we cousicer only the absolute value of e. | Since the distribution of $v$ is symmetric we consider only the absolute value of $v$. |
At level z. for a eivoen- T. e ranges fromB 0 to ej=(57v)η. | At level $z$, for a given $T$, $v$ ranges from 0 to $v_{l} =
(S^{2} - w_{t}^{2})^{1/2}$. |
? The predicted distribution will be shown to be: where C is a coustant defined below. | The predicted distribution will be shown to be: where $C^{'}$ is a constant defined below. |
We define by ΑΝον0) the πα of objects at level + per unit of e aud of we. | We define by $N(v,w)$ the number of objects at level $z$ per unit of $v$ and of $w$. |
Equation 10. then follows from where. R?=ο42), we—(5? (2) and οο)2N(QLO)S/ZS2.—62. so that. € =(0.0)is the umimber per uut e and uut «at e =O.= 0at; — 0. | Equation \ref{eq:dvdv} then follows from where, $R^{2} = (S^{2} - w^{2})$, $w_{l}^{2} = (S^{2} - v^{2})$ , and $N(0,w)
= N(0,0)\;S/\sqrt{S^{2}-v^{2}}$, so that, where $C^{'} = N(0,0)$ is the number per unit $v$ and unit $w$ at $v=0$, $w=0$ at $z=0$. |
For low :-levels the distribution De)de is nearly flat up to e close to cj. | For low $z$ -levels the distribution $D(v)\;{\rm d}v$ is nearly flat up to $v$ close to $v_{l}$ . |
This is due to the fact that the secoud term in equation 10. becomes significant with respect to the first. constant term. ouly at high ce. | This is due to the fact that the second term in equation \ref{eq:dvdv} becomes significant with respect to the first, constant term, only at high $v$. |
For instance. for S=200 kua/sec aud T=20 Myr. at 0=000. the ratio between the second aud the first term near 2=0 is only 0.036. | For instance, for $S=200$ km/sec and $T=20$ Myr, at $v=0.9v_{l}$, the ratio between the second and the first term near $z=0$ is only 0.036. |
For high z-Ievels the distribution becomes less fiat. | For high $z$ -levels the distribution becomes less flat. |
Figure P. cdemoustrates this effect. | Figure \ref{fig:vlsim} demonstrates this effect. |
As we chose hieicr values of T. the nature of the curves for higher > becomes more siuilar to the oue for the lowest 2. | As we chose higher values of $T$, the nature of the curves for higher $z$ becomes more similar to the one for the lowest $z$. |
The truncated nature of Doe}. particularly at low 2. provides an important tool in estimating 9: the extreme observed value. 0; is an approximate nieasure of S virtually independent of the assume lite time T. | The truncated nature of $D(v)$, particularly at low $z$, provides an important tool in estimating $S$; the extreme observed value, $v_{l}$ is an approximate measure of $S$ virtually independent of the assumed life time $T$. |
We did a Monte Carlo simulation to generate a large nuuber of objects in the solar uciglhbourlhood (with initial value of «==0). keeping the surface density οςuistant. | We did a Monte Carlo simulation to generate a large number of objects in the solar neighbourhood (with initial value of $z$ =0), keeping the surface density constant. |
As mentioned in the previous sections. we assuned a simplistic model with all neutron stars being ejected out isotropically with a coustaut speed (9). | As mentioned in the previous sections, we assumed a simplistic model with all neutron stars being ejected out isotropically with a constant speed $S$ ). |
This assuniptiou corresponds to having initia velocities in the + direction ranging from zero to 5 with uniform probability. | This assumption corresponds to having initial velocities in the $z$ –direction ranging from zero to $S$ with uniform probability. |
We evolve thei in a assed local eravitational potential to ect their velocity aud spatial distributions. aud iu additiou we studied the distributions of their characteristic ages. | We evolve them in an assumed local gravitational potential to get their velocity and spatial distributions, and in addition we studied the distributions of their characteristic ages. |
Each object was assigned au age cliosen randomsv with uniform probability between zero auc T. | Each object was assigned an age chosen randomly with uniform probability between zero and $T$. |
Cüven the distribution of characteristic ages of known pulsars. we chose a value of Z7—50 Myr as an optimal choice in order to inclide a sufficicutly buro"e sunuple. aud at the same time describe the kinematics with our poteutial model. | Given the distribution of characteristic ages of known pulsars, we chose a value of $T=50$ Myr as an optimal choice in order to include a sufficiently large sample, and at the same time describe the kinematics with our potential model. |
The presence oft16 objects which turi over after reaching their axis anmnpltude of oscillation within their age are accounted for. | The presence of the objects which turn over after reaching their maximum $z$ –amplitude of oscillation within their age are accounted for. |
Tostudy the kinematics of the generated objectswe assumed the local gravitational poteutial function een by Rujken Cühuore (1989). | Tostudy the kinematics of the generated objectswe assumed the local gravitational potential function given by Kuijken Gilmore (1989). |
The vertical acceleration due to this poteutial is οἼναι by (Bhattacharva al) | The vertical acceleration due to this potential is given by (Bhattacharya ) |
Mirabel and. Roclrigues (2003) shows that the black holes whose projenitors have masses 74047. do not recieve a velocity kick at their birth. | Mirabel and Rodrigues (2003) shows that the black holes whose projenitors have masses $>40M_{\odot}$ do not recieve a velocity kick at their birth. |
Thus. the disc-born black holes are likely to remain embedded in the disc. | Thus, the disc-born black holes are likely to remain embedded in the disc. |
Once formed. the stellar-mass black holes will clramatically. allect the dvnamics of the AGN disc. | Once formed, the stellar-mass black holes will dramatically affect the dynamics of the AGN disc. |
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