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As the core grows in mass. it approaches a spherical shape consistent with the dominance of self-gravity. | As the core grows in mass, it approaches a spherical shape consistent with the dominance of self-gravity. |
As we shall see. this behavior is consistent with the present observational picture. | As we shall see, this behavior is consistent with the present observational picture. |
We analyzed recent dust continuum (submillimeter) observations of dense cores in three prominent star-forming regions: Orion OMC-2 and 3 (Chini et 11997). p Ophiuchus (Motte. André., Neri 1998). and Orton B (Motte et 22001). | We analyzed recent dust continuum (submillimeter) observations of dense cores in three prominent star-forming regions: Orion OMC-2 and 3 (Chini et 1997), $\rho$ Ophiuchus (Motte, André,, Neri 1998), and Orion B (Motte et 2001). |
Collectively. we refer to these observations. which identified a total of 165 dense cores. as the "combined continuum dataset.” | Collectively, we refer to these observations, which identified a total of 165 dense cores, as the “combined continuum dataset.” |
The dust continuum data have at least two distinct advantages over molecular line measurements as a probe of core structure. | The dust continuum data have at least two distinct advantages over molecular line measurements as a probe of core structure. |
First. while molecular lines have a limited range of both column and number density sensitivity (a factor ~ 10-30) due to opacity and molecular freeze-out onto grains. thermal emission from dust is presumably optically thin. | First, while molecular lines have a limited range of both column and number density sensitivity (a factor $\sim$ 10–30) due to opacity and molecular freeze-out onto grains, thermal emission from dust is presumably optically thin. |
This means that column (or continuum flux) densities are bounded only from below by detector sensitivity. while the derived number densities vary inversely with beam resolution (beam-averaged H» column densities >107 em are typical: e.g.. Testi Sargent 1998). | This means that column (or continuum flux) densities are bounded only from below by detector sensitivity, while the derived number densities vary inversely with beam resolution (beam-averaged $_2$ column densities $\gae 10^{23}$ $^{-2}$ are typical; e.g., Testi Sargent 1998). |
Second. while there is in most cases a rough spatial coincidence between the peaks seen in the dust continuum surveys and those seen in dense molecular tracers. the continuum cores may in fact be more representative of the progenitors of stars. | Second, while there is in most cases a rough spatial coincidence between the peaks seen in the dust continuum surveys and those seen in dense molecular tracers, the continuum cores may in fact be more representative of the progenitors of stars. |
This is suggested by the remarkable agreement between the mass spectrum of the cores and the field star initial mass function (Testi Sargent 1998: Motte et 11998. 2001: Johnstone et 2000. 2001). | This is suggested by the remarkable agreement between the mass spectrum of the cores and the field star initial mass function (Testi Sargent 1998; Motte et 1998, 2001; Johnstone et 2000, 2001). |
Since we make extensive use of the Motte et ((2001) "Sataset (hereafter MOT). we note here some of Its properties used later in the analysis. | Since we make extensive use of the Motte et (2001) dataset (hereafter M01), we note here some of its properties used later in the analysis. |
The survey covered a 32«18’ region of Orion B. including the NGC 2068/2071 protoclusters. and identified 82 dense condensations. | The survey covered a $32\arcmin \times 18\arcmin$ region of Orion B, including the NGC 2068/2071 protoclusters, and identified 82 dense condensations. |
We analyzed the 850;:m"Sata. for which the half-power beam width is Rg~13”z5000 AU at the assumed distance of Orion B (400 pe). | We analyzed the $850 \micron$data, for which the half-power beam width is $R_B \simeq 13\arcsec
\approx 5000$ AU at the assumed distance of Orion B (400 pc). |
The one-sigma "ms noise within the beam is A7=22 mJy/beam. | The one-sigma rms noise within the beam is $\Delta I = 22$ mJy/beam. |
For a core with FWHM size R. the rms noise in the integrated (total) flux "Sensity S is AS=22 mly ουν(ΚΕΔΔΙ«2265 mly for R=5500 AU. the mean core size in the sample. | For a core with FWHM size $R$ , the rms noise in the integrated (total) flux density $S$ is $\Delta S \approx 22$ mJy $\times \sqrt{(R^2 +
R_B^2)/R_B^2}
\times 2 = 65$ mJy for $R \simeq 5500$ AU, the mean core size in the sample. |
The absolute calibration uncertainty of the measurements is ~20%.. | The absolute calibration uncertainty of the measurements is $\sim$. |
Only the total flux for each core was given in MOI: peak intensities ] (flux within a single beam) were obtained from the authors. | Only the total flux for each core was given in M01; peak intensities $I$ (flux within a single beam) were obtained from the authors. |
The total error in log / ranges between —0.22 and +0.14 over the range observed. | The total error in log $I$ ranges between $-0.22$ and $+0.14$ over the range observed. |
We take the error in log p to be 40.05. as determined from the precision of MOT's figures for the core major and minor axes (+200 AU). | We take the error in log $p$ to be $\pm 0.05$, as determined from the precision of M01's figures for the core major and minor axes $\pm 200$ AU). |
While several dust continuum surveys of other regions are now available. we have used only those for which both apparent major/minor axes and peak intensities were tabulated. | While several dust continuum surveys of other regions are now available, we have used only those for which both apparent major/minor axes and peak intensities were tabulated. |
The reason for this will become clear presently. | The reason for this will become clear presently. |
The frequency distribution. of the apparent axis ratio. p (apparent minor/major axis length =b’/a) is the only tool used thus far in efforts to deduce the intrinsic shapes ofmolecular cloud cores. | The frequency distribution of the apparent axis ratio $p$ (apparent minor/major axis length $\equiv b'/a'$ ) is the only tool used thus far in efforts to deduce the intrinsic shapes ofmolecular cloud cores. |
While prone to selection effects at both low and high ellipticity. the method can give some insight into. the constraints involved (see $1. for references). | While prone to selection effects at both low and high ellipticity, the method can give some insight into the constraints involved (see \ref{sec-intro} for references). |
The histogram in Figure Ia shows the distribution of core apparent axis ratios. using the combined continuum dataset. | The histogram in Figure $a$ shows the distribution of core apparent axis ratios, using the combined continuum dataset. |
The mean value is (pj=0.63 (median: 0.64). with a standard deviation of 0.20. | The mean value is $\lb p \rb = 0.63$ (median: 0.64), with a standard deviation of 0.20. |
This distribution is similar to that seen in the extensive and much more heterogeneous ammonia dataset of Jijina et (1999) (see Jones et 22001). | This distribution is similar to that seen in the extensive and much more heterogeneous ammonia dataset of Jijina et (1999) (see Jones et 2001). |
In particular. both distributions are skewed towards p=I: in Figure | there are more than twice as many objects with 0.8<px1 than with 0.]xpx:0.3. | In particular, both distributions are skewed towards $p=1$: in Figure 1 there are more than twice as many objects with $0.8 \leq p \leq 1$ than with $0.1 \leq p \leq 0.3$. |
This characteristic is particularly evident in the Chini et aand Motte et ((1998) samples. in which and of the cores. respectively. have p>0.5. | This characteristic is particularly evident in the Chini et and Motte et (1998) samples, in which and of the cores, respectively, have $p \geq 0.5$. |
Let the intrinsic frequency distribution of cores of intrinsic axis ratio g (intrinsic. minor/major axis length =b/a) be denoted by «(g). | Let the intrinsic frequency distribution of cores of intrinsic axis ratio $q$ (intrinsic minor/major axis length $\equiv b/a$ ) be denoted by $\psi (q)$. |
Then. if the cores are oriented randomly on the sky. the observed distribution © of apparent (projected) axis ratios p is given by (Noerdlinger 1979; Fall Frenk 1983): o(p)- AS qr-q Cg (oblate): -pΕπ ο... Cg (prolate). | Then, if the cores are oriented randomly on the sky, the observed distribution $\phi$ of apparent (projected) axis ratios $p$ is given by (Noerdlinger 1979; Fall Frenk 1983): (p) = p _0^p dq (p^2 - (q) ); = _0^p dq q^2 (p^2 - (q) ). |
The derivation of ο) from the observed o(p) has been attempted in a number of ways. | The derivation of $\psi (q)$ from the observed $\phi (p)$ has been attempted in a number of ways. |
For example. Ryden (1996) employed a nonparametric kernel estimator. while Jones et ((2001) used an analytic inversion method. | For example, Ryden (1996) employed a nonparametric kernel estimator, while Jones et (2001) used an analytic inversion method. |
Both replaced the observed distribution histogram with a smooth function before inverting to find (6). | Both replaced the observed distribution histogram with a smooth function before inverting to find $\psi (q)$. |
In the process. restrictions were placed on either the form of o(p) (an odd polynomial of degree 5; Jones et al.) | In the process, restrictions were placed on either the form of $\phi (p)$ (an odd polynomial of degree 5; Jones et al.) |
or its slope at the endpoints (do/dp=0; Ryden). | or its slope at the endpoints $d\phi/dp = 0$; Ryden). |
Despite the fact that this biases any comparison of the observed and theoretical distributions, the goodness-of-fit criteria in both studies rely upon the behavior near the endpoints. particularly at p—lI. | Despite the fact that this biases any comparison of the observed and theoretical distributions, the goodness-of-fit criteria in both studies rely upon the behavior near the endpoints, particularly at $p=1$. |
Thus. these authors’ finding that the probability distributions of spheroids become negative (for some samples) near p=| needs to be re-established in the absence of such restrictions. | Thus, these authors' finding that the probability distributions of spheroids become negative (for some samples) near $p=1$ needs to be re-established in the absence of such restrictions. |
While a direct inversion method. such as the type devised by Lucy (1974) (and applied in the galactic contextby Noerdlinger). would be the most robust means of deriving ο). our objective here is more modest. | While a direct inversion method, such as the type devised by Lucy (1974) (and applied in the galactic contextby Noerdlinger), would be the most robust means of deriving $\psi (q)$, our objective here is more modest. |
We seek merely to demonstrate that a reasonable distribution of randomly-oriented spheroids can reproduce the histogram of Figure lu. | We seek merely to demonstrate that a reasonable distribution of randomly-oriented spheroids can reproduce the histogram of Figure $a$. |
We let ο) equal a gaussian with mean value (gj and dispersion o. and generated o(p) from equations (1)) and (2)) for a range of values of these parameters. | We let $\psi (q)$ equal a gaussian with mean value $\lb q \rb$ and dispersion $\sigma$, and generated $\phi (p)$ from equations \ref{eq-obphi}) ) and \ref{eq-plphi}) ) for a range of values of these parameters. |
The resulting V7 minimization fits to the observed histogram (now shown as a probability density) are shown in Figure 15. | The resulting $\chi^2$ minimization fits to the observed histogram (now shown as a probability density) are shown in Figure $b$ . |
While neither prolate noroblate distributions give a completely satisfactory fit. the prolate distribution with (gj=0.54 and ao20.19 (4= 0.28) is clearly superior. | While neither prolate noroblate distributions give a completely satisfactory fit, the prolate distribution with $\lb q \rb = 0.54$ and $\sigma = 0.19$ $\chi^2 = 0.28$ ) is clearly superior. |
The fit in the oblate case is less satisfactory: (dg)=0.39 and 520.16 with V7 =0.51. | The fit in the oblate case is less satisfactory: $\lb q \rb =
0.39$ and $\sigma = 0.16$ with $\chi^2 = 0.51$ . |
In this case. while the observed o can be fit at low p. the peak | In this case, while the observed $\phi$ can be fit at low $p$ , the peak |
the eroup's ICAL or brightest eroup elliptical. are well consistent with the known £.-2 relation of clusters aud eroups of galaxies. ie. with the ICAL as counterpart. | the group's IGM or brightest group elliptical, are well consistent with the known $L_{\rm x}$ $T$ relation of clusters and groups of galaxies, i.e., with the IGM as counterpart. |
Further. the derived. Ly~31077 ere/s would be rather hnieh for au elliptical outside a rich cluster euvironineut (particularly for the observed (Stocke et al. | Further, the derived $L_{\rm x} \simeq 3\,10^{43}$ erg/s would be rather high for an elliptical outside a rich cluster environment (particularly for the observed (Stocke et al. |
1981) R-magnitude of ig = 15.1). but usual for the ICAL | 1984) R-magnitude of $m_{\rm R}$ = 15.1), but usual for the IGM. |
The IIRI position is iuteriuediate between the elliptical aud the quasar. and cousisteut with all three ideutificatious. | The HRI position is intermediate between the elliptical and the quasar, and consistent with all three identifications. |
ILlowever. there is evideuce that the source enission is extended. | However, there is evidence that the source emission is extended. |
lu sunniuv. if only oue euütter dominates the N-raw flux (instead of a contribution from poteutial counterparts. which would strongly complicate matters aut cannot be excluded) it seems that the available data (constancy iu source flux. high Ly. fit iuto L.-T relation. evidence for source extent) favour au identification with he ICM. of the nearby group at :—0.111. | In summary, if only one emitter dominates the X-ray flux (instead of a contribution from potential counterparts, which would strongly complicate matters but cannot be excluded) it seems that the available data (constancy in source flux, high $L_{\rm x}$, fit into $L_{\rm x}$ $T$ relation, evidence for source extent) favour an identification with the IGM of the nearby group at $z$ =0.111. |
. A deep high spatial resolution observationcentered on 00101 should fnally resolve the counterpart question. | A deep high spatial resolution observation on 0104 should finally resolve the counterpart question. |
We have presented a study of the X-ray properties of the 32382 eroup of galaxies. extending the work of T97. aud of the source 0010113135. | We have presented a study of the X-ray properties of the 383 group of galaxies, extending the work of T97, and of the source 0104+3135. |
The properties of the iutra-group medium derived from the PSPC observation are sunmnuiuuized in Tab. | The properties of the intra-group medium derived from the PSPC observation are summarized in Tab. |
3. | 3. |
The N-rav cussion of the ICAL can be traced out to about INE Mpc. which turus out to be about the virial radius of the eroup. | The X-ray emission of the IGM can be traced out to about $1 h_{50}^{-1}$ Mpc, which turns out to be about the virial radius of the group. |
Several lines of evidence were presented that he eroup inside this radius is quite relaxed. | Several lines of evidence were presented that the group inside this radius is quite relaxed. |
With the eiven depth of the PSPC observatious we can herefore characterize the cutive ealaxy svsteni as far as it has approached a dynamical equilibrium state. | With the given depth of the PSPC observations we can therefore characterize the entire galaxy system as far as it has approached a dynamical equilibrium state. |
For this out of the eroup we find a total mass of 61020. AM. and a gas nass fraction of. | For this part of the group we find a total mass of $6\,10^{13} h_{50}^{-1}$ $_{\odot}$ and a gas mass fraction of. |
The latter value is at he upper end of the distribution for eroups. | The latter value is at the upper end of the distribution for groups. |
The result nuples that the gravitational potential of the group is deep οποιο] to prevent a majour gas loss. iu contrast to ess Inassive eroups (Davis et al. | The result implies that the gravitational potential of the group is deep enough to prevent a majour gas loss, in contrast to less massive groups (Davis et al. |
1998). | 1998). |
The surface brightness profile is characterized bv a slope parzuueter Jj&0.1 which is shallower thau Or most of the galaxy clusters but a quite common value for eroups. | The surface brightness profile is characterized by a slope parameter $\beta \simeq 0.4$ which is shallower than for most of the galaxy clusters but a quite common value for groups. |
The temperature of 1.5 keV found for the IGA is well consistent with the £,.T relation OoeiviugC» further support to the picture that the eroup is a well relaxed aud normal πλΜΟΙ. | The temperature of $1.5$ keV found for the IGM is well consistent with the $L_x - T$ relation giving further support to the picture that the group is a well relaxed and normal system. |
With an estimated central cooling time larger than the IIubble iue no central cooling flow is expected aud no sienature for it is found neither iu the spatial aud spectral A-rav data nor in the optical spectrum. | With an estimated central cooling time larger than the Hubble time no central cooling flow is expected and no signature for it is found neither in the spatial and spectral X-ray data nor in the optical spectrum. |
We do not find any conspicuous spatial correlation of A-rav cluission and radio jet which might be partly due to the narrowness of the jet and the 2D view of the 3D source structure. | We do not find any conspicuous spatial correlation of X-ray emission and radio jet which might be partly due to the narrowness of the jet and the 2D view of the 3D source structure. |
We also discussed the X-ray properties of the wellstudied radio ealaxy 331 which is located near the center of the extended N-ray cussion. | We also discussed the X-ray properties of the well-studied radio galaxy 31 which is located near the center of the extended X-ray emission. |
If one wishes to avoid excessively depleted metal abundauces. the spectrun of 3231 is best described by a two-component model. consisting of a low-temperature rs component and a hard tail (pl or secoud rs). confirming T97. | If one wishes to avoid excessively depleted metal abundances, the spectrum of 31 is best described by a two-component model, consisting of a low-temperature rs component and a hard tail (pl or second rs), confirming T97. |
The soft component contributes with ~3104 ere/s to the total N-rav luminosity of £,~5101 cre/s (assuming metal abundances of «solar). | The soft component contributes with $\simeq3\,10^{41}$ erg/s to the total X-ray luminosity of $L_{\rm x} \simeq5\,10^{41}$ erg/s (assuming metal abundances of $\times$ solar). |
No temporal variability iu the N-ray flux is detected. | No temporal variability in the X-ray flux is detected. |
A-rav endsson from the direction of the interesting source 00101123135. by chance located in the field of view. was analyzed. | X-ray emission from the direction of the interesting source 0104+3135, by chance located in the field of view, was analyzed. |
One scenario (trausieut brightening of the :—2 BAL 00101123135 due to lensing during the earlier observation) turued out to be unlikely. | One scenario (transient brightening of the $z$ =2 BAL 0104+3135 due to lensing during the earlier observation) turned out to be unlikely. |
Besides an absorbed powerlaw. the spectrum of LEOOLOL can be described by a Bavinoud-Sumith ποσο] with AYx 2 keV resulting iu an intrinsic huuünositv of Lyc310% cre/s at :—0.111. | Besides an absorbed powerlaw, the spectrum of 0104 can be described by a Raymond-Smith model with $kT \simeq$ 2 keV resulting in an intrinsic luminosity of $L_{\rm x} \simeq 3\,10^{43}$ erg/s at $z$ =0.111. |
Although no potential counterpart (QSO. nearby elliptical galaxy. or ICM oftle sxinall eroup to which the elliptical belongs) cau be safely ruled out at prescut. there are several hiuts (coustancy in source flux. high Ly. consistency with [κα relation for eroups/clusters. evidence for source extent) for au identification of the N-rav source with the ICM of the nearby eroup of galaxies at :—0.111. | Although no potential counterpart (QSO, nearby elliptical galaxy or IGM of the small group to which the elliptical belongs) can be safely ruled out at present, there are several hints (constancy in source flux, high $L_{\rm x}$, consistency with $L_{\rm x}$ $T$ relation for groups/clusters, evidence for source extent) for an identification of the X-ray source with the IGM of the nearby group of galaxies at $z$ =0.111. |
where (CrGh.δρ). is the mean curvature of peaks with 6); and. Ap ancl iM(2).ὁpk} (j —13) are its associated dimensionless semiaxes A; scaled to the square root of the Laplacian. so that they satisfy AT|.Ü5|d;=1. | ), where $\xbra(\R,\delta\pk)$ is the mean curvature of peaks with $\delta\pk$ and $\R$ and $A\jpk(\R,\delta\pk)$ (j $=1\div 3$ ) are its associated dimensionless semiaxes $\lambda\jj$ scaled to the square root of the Laplacian, so that they satisfy $A\opk^2+A\tpk^2+A\zpk^2=1$ . |
These semiaxes depend on d). and Ze through (Cr in a well-known form calculated by BBINS. | These semiaxes depend on $\delta\pk$ and $\R$ through $\xbra$ in a well-known form calculated by BBKS. |
Thus. we can calculate them as well as the Curvature iir over the peak trajectory Pu(Z/) Leading to the halo with Af at / and invert equation (109)) by means of the same procedure as used for equation (872). | Thus, we can calculate them as well as the curvature $\xbra$ over the peak trajectory $\delta\pk(\R)$ leading to the halo with $M$ at $t$ and invert equation \ref{inv}) ) by means of the same procedure as used for equation \ref{Fred}) ). |
In addition. the integral on the left of equation (109)) can also be calculated from he known spherically averaged protohalo density contrast. profile. | In addition, the integral on the left of equation \ref{inv}) ) can also be calculated from the known spherically averaged protohalo density contrast profile. |
Thus. taking the ratios between the solutions for different j obtained [rom inversion of equation (109)). we can infer the eccentricity profiles for the seeds of typical haloes grown by PA. | Thus, taking the ratios between the solutions for different j obtained from inversion of equation \ref{inv}) ), we can infer the eccentricity profiles for the seeds of typical haloes grown by PA. |
Once the eccentricity. profiles. (6,)5(7,) and (0)pr). are known. the typical halo shape and kinematics can be inferred ollowing the steps described in Sections ?? and ??: 1) infer (through. eqs. 49]] | Once the eccentricity profiles, $(\ep)\p(r\p)$ and $(\es)\p(r\p)$, are known, the typical halo shape and kinematics can be inferred following the steps described in Sections \ref{eccentricity} and \ref{anisotropy}: 1) infer (through eqs. \ref{6th}] ] |
anc 72]]) the cecentricity profiles ο) and ο(ή) of the halo as a function of e(r): 2) determi16 from them the mean squared density [Ductuation profile for the halo (eq. 10]]) | and \ref{7th}] ]) the eccentricity profiles $\ep(r)$ and $\es(r)$ of the halo as a function of $\sigma(r)$; 2) determine from them the mean squared density fluctuation profile for the halo (eq. \ref{4th}] ]) |
as a function of ei): 3)2 infer the corresponding mean squared. potential HHuctuaion profile (eqs 14]] ancl 41] as a 'unction of e(r): 4) solve the generalise Jeans equation (86)) for the velocity dispersion prolile σι ancl 5)r determine (from eqs. 49]] | as a function of $\sigma(r)$; 3) infer the corresponding mean squared potential fluctuation profile (eqs \ref{D1}] ] and \ref{D3}] ]) as a function of $\sigma(r)$; 4) solve the generalise Jeans equation \ref{exJeq2}) ) for the velocity dispersion profile $\sigma(r)$; and 5) determine (from eqs. \ref{6th}] ] |
and. το} 10 typical eccentricity. profiles. ορ) and ei(e). now using the explici values of a(r). and the anisotropy »rolile jr) (eq. 14]] | and \ref{7th}] ]) the typical eccentricity profiles, $\ep(r)$ and $\es(r)$, now using the explicit values of $\sigma(r)$, and the anisotropy profile $\beta(r)$ (eq. \ref{00th}] ] |
after deriving the mean squared »otential Huctuation profile). | after deriving the mean squared potential fluctuation profile). |
Unfortunatelv. the accurate theoretical eccentriciies so inferred. could not be compared with the results of numerical simulations because there is so far no such tvpical profiles drawn from simulations. | Unfortunately, the accurate theoretical eccentricities so inferred could not be compared with the results of numerical simulations because there is so far no such typical profiles drawn from simulations. |
We just know some main trends of the vpical shape of haloes. | We just know some main trends of the typical shape of haloes. |
Thus. it is not worth at this stage to carry out such a complex derivation. | Thus, it is not worth at this stage to carry out such a complex derivation. |
In fact. the purpose of the esent paper is not to infer accurate eccentricity and. kinematic profiles for CDM haloes cirectly from the power-spectrum of 1ο concordance model but rather to verily the valiitv of the model and try to understand the origin of theuniversal trenes ga10wn by such halo properties in numerical simulations. | In fact, the purpose of the present paper is not to infer accurate eccentricity and kinematic profiles for CDM haloes directly from the power-spectrum of the concordance model but rather to verify the validity of the model and try to understand the origin of theuniversal trends shown by such halo properties in numerical simulations. |
And these two objectives are much better obtained. by means of the ollowing approximate procedure. | And these two objectives are much better obtained by means of the following approximate procedure. |
Peaks are triaxial with a rather prolate shape (BBS). | Peaks are triaxial with a rather prolate shape (BBKS). |
Xs mentioned. their cecentricitics depend on 9, and 2) through jeir curvature in such a wav that. the larger ur. the more spherical is the peak. | As mentioned, their eccentricities depend on $\delta\pk$ and $\R$ through their curvature $x$ in such a way that, the larger $x$, the more spherical is the peak. |
Phe quantity. Gr increases progressively =vith increasing Ay over typical peak trajectories. meaning that peaks become increasingly spherical over those tracks. very gaowly first and much more rapidly a he end. | The quantity $\xbra$ increases progressively with increasing $\R$ over typical peak trajectories, meaning that peaks become increasingly spherical over those tracks, very slowly first and much more rapidly at the end. |
Thus. the same trend must be found in protohaloes for increasing ry as well as in typical haloes for increasing r. ( | Thus, the same trend must be found in protohaloes for increasing $r\p$ as well as in typical haloes for increasing $r$. ( |
Lt is true that the relation between the eccentricities in the seed and the halo also depencds on ar). but this dependence can be neglected at small racic while at large radii the decrease with increasing rj of protohalo eccentricities is so marked that the dependence on e(r) cannot reverse it.) | It is true that the relation between the eccentricities in the seed and the halo also depends on $\sigma(r)$, but this dependence can be neglected at small radii, while at large radii the decrease with increasing $r\p$ of protohalo eccentricities is so marked that the dependence on $\sigma(r)$ cannot reverse it.) |
Therefore. according to the present model. haloes should be rather prolate and approximately homologous at small and intermediate radii and tend to become more spherical near the halo edge. | Therefore, according to the present model, haloes should be rather prolate and approximately homologous at small and intermediate radii and tend to become more spherical near the halo edge. |
This behaviour is fully consistent with the results of numerical simulations (e.g. 2006:Stadelctal. 2009)). | This behaviour is fully consistent with the results of numerical simulations (e.g. \citealt{JS02,bs05,All06,St09}) ). |
Moreover. we can have an idea on he overall values of halo eccentricities because. as mentioned. they are expected to be rather uniform except near the edge. | Moreover, we can have an idea on the overall values of halo eccentricities because, as mentioned, they are expected to be rather uniform except near the edge. |
T16 typical ratio between the major and minor axes (the major and intermediate axes) in peaks with low and moderate average curvature is 1.7 (~ 1.3) (BBISS). implying tvpical values of the eccentricities €, (ος) of ~0.51 (C 0.64). | The typical ratio between the major and minor axes (the major and intermediate axes) in peaks with low and moderate average curvature is $\sim 1.7$ $\sim 1.3$ ) (BBKS), implying typical values of the eccentricities $\ep$ $\es$ ) of $\sim 0.81$ $\sim 0.64$ ). |
Such typical vaues. independent of the filtering scale (they only show a mocderate dependence on the curvature) were derived by BBINS for pxks in the old standard CDM mocel (Le. in the Einstein-de Sitter cosmology). so they are valid for any CDM cosmology as al cosmologies converge for high enough redshifts as those corresponding to primordial peaks to the Einstein-cde Sittermodel. | Such typical values, independent of the filtering scale (they only show a moderate dependence on the curvature) were derived by BBKS for peaks in the old standard CDM model (i.e. in the Einstein-de Sitter cosmology), so they are valid for any CDM cosmology as all cosmologies converge for high enough redshifts as those corresponding to primordial peaks to the Einstein-de Sittermodel. |
As C(r) is close to one with a small bias towards two at small i. the expected. values o ey fe.) in haloes at small radii shoud be close to. perhaps a little larger than. those of peaks. sav. 0.0 (~ 0.8). | As $U(r)$ is close to one with a small bias towards two at small $r$ , the expected values of $\ep$ $\es$ ) in haloes at small radii should be close to, perhaps a little larger than, those of peaks, say, $\sim
0.9$ $\sim 0.8$ ). |
Τις is also consistent with the values found in numerical simulations | This is also consistent with the values found in numerical simulations |
)). | ). |
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