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We describe how the marked point bootstrap can be used with the two- and three-point correlation function estimators. and by extension to estimators of N-point correlation functions. | We describe how the marked point bootstrap can be used with the two- and three-point correlation function estimators, and by extension to estimators of $N$ -point correlation functions. |
In Section d. we present results of a simulation study using simple point process models comparing the empirical coverage of confidence intervals obtained using parametric bootstrap and using normal approximations with Poisson errors. | In Section \ref{sect:simstudy} we present results of a simulation study using simple point process models comparing the empirical coverage of confidence intervals obtained using non-parametric bootstrap and using normal approximations with Poisson errors. |
In this paper. we restrict ourselves to constructing nominal confidence intervals. ie. (hese confidence intervals are supposed to contain the (rue value ol the time. | In this paper, we restrict ourselves to constructing nominal confidence intervals, i.e. these confidence intervals are supposed to contain the true value of the time. |
The empirical coverage of the confidence intervals is the actual confidence level achieved by the confidence intervals. | The empirical coverage of the confidence intervals is the actual confidence level achieved by the confidence intervals. |
In a simulation study with a known model. the empirical coverage can be obtained by finding the number of confidence intervals that contain the true value ancl then compared with the nominal level. | In a simulation study with a known model, the empirical coverage can be obtained by finding the number of confidence intervals that contain the true value and then compared with the nominal level. |
It is desirable. of course. Dor the empirical coverage to be close to the nominal level. | It is desirable, of course, for the empirical coverage to be close to the nominal level. |
Furthermore. it is olten better for the empirical coverage to be higher instead of lower (han the nominal level. so that the procedure Is Conservative. | Furthermore, it is often better for the empirical coverage to be higher instead of lower than the nominal level, so that the procedure is conservative. |
Bootstrap is a computationally intensive procedure. | Bootstrap is a computationally intensive procedure. |
With the large datasets now common in aslrononiv. even computing (he N-point correlation functions pose computational challenges. | With the large datasets now common in astronomy, even computing the $N$ -point correlation functions pose computational challenges. |
For example. Eisensteinetal.(2005) avoided using the jackknile procedure for error estimation because of the size of the data (μον used. | For example, \citet{eisenstein05} avoided using the jackknife procedure for error estimation because of the size of the data they used. |
The way the marked point bootstrap is formulated. however. makes it much [aster than subsampling (a generalization of the jackknile) and the block bootstrap. so that applying the procedure to large datasets is leasible as long as computing (he actual estimates is leasible. | The way the marked point bootstrap is formulated, however, makes it much faster than subsampling (a generalization of the jackknife) and the block bootstrap, so that applying the procedure to large datasets is feasible as long as computing the actual estimates is feasible. |
In Section 4 we provide some (ime measurements of the procedure used in our simulation stud. | In Section \ref{sect:simstudy} we provide some time measurements of the procedure used in our simulation study. |
The non-parametric bootstrap was originally developed for independent data Tibshirani 1994). | The non-parametric bootstrap was originally developed for independent data \citep{efron94}. |
. The main idea is to draw new samples from (he actual data by sampling with replacement a data point al a time. | The main idea is to draw new samples from the actual data by sampling with replacement a data point at a time. |
Bootstrap estimates of (he same statistic are computed from the bootstrap samples. | Bootstrap estimates of the same statistic are computed from the bootstrap samples. |
With these bootstrap estimates. confidence intervals. for example. can then be constructed. | With these bootstrap estimates, confidence intervals, for example, can then be constructed. |
This can be done in a variety of wavs. | This can be done in a variety of ways. |
Suppose A. IN and Ng—]....D are respectively the quantity of interest. the estimate of A. computed from the data ancl the bootstrap estimates. with D equal to the number of bootstrap samples. | Suppose $K$, $\hat{K}$ and $\hat{K}^*_i, i=1, \ldots B$ are respectively the quantity of interest, the estimate of $K$ computed from the data and the bootstrap estimates, with $B$ equal to the number of bootstrap samples. |
hird spectruu published iu the PRC shows the rotation of eas at a position angle of 132. which is intermediate )etween the two rings and reveals the complex kinematical structure of ESO. 17L-C26. | third spectrum published in the PRC shows the rotation of gas at a position angle of $^{\circ}$, which is intermediate between the two rings and reveals the complex kinematical structure of ESO 474-G26. |
The observed maxima rotation velocity of the galaxy is Vinee 7110 lau bat kpzm5" along PA=-3° (PRC). | The observed maximum rotation velocity of the galaxy is $_{max}\approx$ 140 km $^{-1}$ at $r\approx5''$ along $^{\rm o}$ (PRC). |
The apparent axial ratio of this ring is (5/0;=0.64.1. | The apparent axial ratio of this ring is $\langle b/a \rangle = 0.6 \pm 0.1$. |
Asstuuing that the cuission lines beloug to the arge rie. aud that this rine is intrinsically circular. we can estimate its Inclination as /=ποnu.47°. | Assuming that the emission lines belong to the large ring, and that this ring is intrinsically circular, we can estimate its inclination as $i=53^{\circ} \pm 7^{\circ}$. |
Therefore. corrected for the inclination. the 1iaxiunua rotation velocity at kr=5"5 kpeis V8. πα +. | Therefore, corrected for the inclination, the maximum rotation velocity at $r=5''=5$ kpc is $_{max}^0\approx$ 175 km $^{-1}$. |
The ΟΡ ratio is AD/Lpir<5")z1 Eo. a value that is unusual for carly-type galaxies and more typical of spirals with active star formation. | The mass to luminosity ratio is $L_B(r\leq 5'') \approx 1$ $_{\odot}$ $L_{\odot,B}$, a value that is unusual for early-type galaxies and more typical of spirals with active star formation. |
Duc o the highly uncertain geometry of the galaxy. the above estimates of ων and ΑΕΕ are tentative only. | Due to the highly uncertain geometry of the galaxy, the above estimates of $_{max}$ and $L_B$ are tentative only. |
The major axis position ange of the first (simaller) rine is 917. and its diameter is ~--37” or 37 kpc. | The major axis position angle of the first (smaller) ring is $^{\circ}$ , and its diameter is $\approx37''$ or 37 kpc. |
The seco1c (larger) ving has axd dianeter of 58" (58 kpc}. | The second (larger) ring has $^{\circ}$ and diameter of $''$ (58 kpc). |
Iu projection. the angle betwen the two rings is 767 | In projection, the angle between the two rings is $^{\circ}$. |
The optical colors of t1 rings were determine through a LO” diameter circilay aperture placed on the brightest parts of the riugs aloug its major axes. | The optical colors of the rings were determined through a $''$ diameter circular aperture placed on the brightest parts of the rings along its major axes. |
In the lareeoO rinec» we fouud the folloxving colors at the imdicate positions with respectto the | In the large ring we found the following colors at the indicated positions with respectto the |
spectrum aud bispectrum. | spectrum and bispectrum. |
Section L contaius our results on the SZ-ealaxy cross correlation aud the method to extract the redshift distribution of the SZ ellect. | Section \ref{sec:cross} contains our results on the SZ-galaxy cross correlation and the method to extract the redshift distribution of the SZ effect. |
The elect of nou-gravitatioual heating aud the method to extract it from overall gas pressure power spectrum are discussed iu section 5.. | The effect of non-gravitational heating and the method to extract it from overall gas pressure power spectrum are discussed in section \ref{sec:NGheating}. |
We discuss the potential inaccuracies arising [rom the approxiuiations in section 6.. | We discuss the potential inaccuracies arising from the approximations in section \ref{sec:discussion}. |
The paper couclicdes with sectiou 7.. | The paper concludes with section \ref{sec:conclusion}. |
The temperature distortion caused by the SZ ellect (ZelclovichaudSuuyaev1900) is: where n is the direction ou the sky. =fv(Το). aud the scattering function 5r)—1 when or<I (Rayleiel-Jeaus tail). | The temperature distortion caused by the SZ effect \citep{Zeldovich69}
is: where $\hat{n}$ is the direction on the sky, $x=h\nu/(kT_{CMB})$, and the scattering function $S(x)\rightarrow 1$ when $x \ll 1$ (Rayleigh-Jeans tail). |
Iu this limit the SZ ellect results in an apparent cooling of the CMB background. | In this limit the SZ effect results in an apparent cooling of the CMB background. |
Om The 7 parameter is defined as Here. Tj aud n, are the temperature and munber density of [ree electrons. respectively. | The $y$ ” parameter is defined as Here, $T_g$ and $n_e$ are the temperature and number density of free electrons, respectively. |
2. is the gas pressure. | $P_e$ is the gas pressure. |
yy=L/P.(14+0,)04/T, aud T,=(004)1,5 is the gas density weighted mean temperature. | $y_p=P_e/\bar{P_e}=(1+\delta_g) T_g/\bar{T_g}$ and $\bar{T_g}\equiv\langle(1+\delta_g)T_g\rangle$ is the gas density weighted mean temperature. |
d!=ασ)(λες is the proper distance. afc) is the scale factor. ;c(z) is the comoving distance. describes the geometric effect of the curved universe. A.=—1.0.1 for open. flat aud. closed uuiverses respectively. aud f=ποια—Qu)E? is the curvature radius. | $dl=a(z) C(x) dx$ is the proper distance, $a(z)$ is the scale factor, $x(z)$ is the comoving distance, describes the geometric effect of the curved universe, $K=-1,0,1$ for open, flat and closed universes respectively, and $R_0=\frac{c}{H_0} (1-\Omega_0)^{-1/2}$ is the curvature radius. |
ΟΕ present cosmological matter density. | $\rho_0=\rho_c \Omega_0$ is the present cosmological matter density. |
Pen(1999) showed that the intergalactic medium bas most likely been. preheated by sources to 1I keV per uucleon in order to be cousistent with the observed upper bounds from the X-ray. background. | \citet{Pen99} showed that the intergalactic medium has most likely been preheated by non-gravitational sources to $\sim 1$ keV per nucleon in order to be consistent with the observed upper bounds from the X-ray background. |
We adopt the iuodel of (Pen1990) to express the gas distribution as a convolution of the matter distribution: This equation expresses gas as beiug less clumped than dark matter. partly due to the required preheating. | We adopt the model of \citep{Pen99} to express the gas distribution as a convolution of the matter distribution: This equation expresses gas as being less clumped than dark matter, partly due to the required preheating. |
The effective radius in the top-hatwindow function. which is the gas heating radius. las the typical value ~1h+ Mpe from the X-ray. background coustraint (Pen 1999).. | The effective radius in the top-hatwindow function, which is the gas heating radius, has the typical value $\sim 1 h^{-1}$ Mpc from the X-ray background constraint \citep{Pen99}. . |
For simplicity. we adopt the Gaussian⋅ window⋅ Wj(r)⇁∣=exp(—r7∣Diy/2r;)/(v2nrq)Wyfy3o, (rgc9"nL/3h INpe: corresponds | For simplicity, we adopt the Gaussian window $W_g(r)=
\exp(-r^2/2r_g^2)/(\sqrt{2\pi}r_g)^3$ $r_g
\sim 1/3 h^{-1}$ Mpc corresponds |
For simplicity. we adopt the Gaussian⋅ window⋅ Wj(r)⇁∣=exp(—r7∣Diy/2r;)/(v2nrq)Wyfy3o, (rgc9"nL/3h INpe: corresponds: | For simplicity, we adopt the Gaussian window $W_g(r)=
\exp(-r^2/2r_g^2)/(\sqrt{2\pi}r_g)^3$ $r_g
\sim 1/3 h^{-1}$ Mpc corresponds |
where J—2|OL.iat is the Jacobi's integral ancl ]t is easy to see that the DEs obtained by equation (41)). for the cases m3. could be negative in some regions of the phase space corresponding to the physical domain. | where $J=\varepsilon+\Omega L_{z}-\begin{matrix} \frac{1}{2}
\end{matrix}\Omega^{2}a^{2}$ is the Jacobi's integral and It is easy to see that the DFs obtained by equation \ref{dfsnew2}) ), for the cases $m\geq3$, could be negative in some regions of the phase space corresponding to the physical domain. |
To avoid this inconvenient. it is necessary to impose a stronger condition for the constants D,. in order to obtain well-defined distribution functions. | To avoid this inconvenient, it is necessary to impose a stronger condition for the constants $B_1$, in order to obtain well-defined distribution functions. |
To do this. we formulate the Following equations (in a similar fashion as in subsection τηλ): Relation (44)) imposes thecondition that the DF has a minimum at D,=Di, and 2=Rua. while through the relation (45)). we demand that its value at such critical point vanishes. | To do this, we formulate the following equations (in a similar fashion as in subsection \ref{sec:correctionB}) ): Relation \ref{sist1}) ) imposes thecondition that the DF has a minimum at $B_1=B'_{1\mathrm{min}}$ and $R=R_{\mathrm{min}}$, while through the relation \ref{sist2}) ), we demand that its value at such critical point vanishes. |
The numeric solution to these equations give us the values shown in table 3.. for the models with m=3.4.5. | The numeric solution to these equations give us the values shown in table \ref{tablabp}, for the models with $m=3,4,5$. |
So. taking this values as a lower limit for Dj. the DE's given by (41)) become positive-defined in the physical domain of the phase space. | So, taking this values as a lower limit for $B_1$, the DFs given by \ref{dfsnew2}) ) become positive-defined in the physical domain of the phase space. |
The figure 10. shows the graphics ofthe DEs as Functions of the Jacobi's integral. with different values of 2). | The figure \ref{fig:DFJAC} shows the graphics of the DFs as functions of the Jacobi's integral, with different values of $B_1$. |
In general. we can observe that the probability is maximum for small values of J. and tends to a constant as J increases. | In general, we can observe that the probability is maximum for small values of $J$, and tends to a constant as $J$ increases. |
Moreover. in the cases m=3 we can see that for values of D, near to Di, the probability has a minimum at 8Jug. and it 2.is zero for⋅ D,=∕ al J=Ain. in. agreement with equations (44)) and (45)). | Moreover, in the cases $m\geq3$ we can see that for values of $B_1$ near to $B'_{1\mathrm{min}}$, the probability has a minimum at $J\approx J_{\mathrm{min}}$, and it is zero for $B_1=B'_{1\mathrm{min}}$ at $J=
J_{\mathrm{min}}$, in agreement with equations \ref{sist1}) ) and \ref{sist2}) ). |
On the other hand. it is convenient to derive a new kind of DE's. corresponding to more probable rotational states. | On the other hand, it is convenient to derive a new kind of DFs, corresponding to more probable rotational states. |
As it was shown by Dejonghe(1986).. it is possible to obtain Ds obeving the maximum entropy principle. through the equation where fi, is the even part of (41)). | As it was shown by \cite{dej}, it is possible to obtain DFs obeying the maximum entropy principle, through the equation where $f_{m+}$ is the even part of \ref{dfsnew2}) ). |
The figure 11 shows the behavior of the Ds given by (46)). | The figure \ref{fig:PedDF1}
shows the behavior of the DFs given by \ref{dfsnew3}) ). |
In (a) and (b) are plotted the contours corresponding to the model m=2. with different values of parameter a. | In (a) and (b) are plotted the contours corresponding to the model $m=2$, with different values of parameter $\alpha$. |
As it can be seen. a determines a particular rotational state in the stellar svstem. | As it can be seen, $\alpha$ determines a particular rotational state in the stellar system. |
As o increases. the probability to find a star with positive L. increases as well. | As $\alpha$ increases, the probability to find a star with positive $L_{z}$ increases as well. |
A similar result can be obtained for o<Q. when the probability to find a star with negative £L. decreases as à decreases. and the corresponding plots would be analogous to figure 11.. after a rellection about £L.=0. | A similar result can be obtained for $\alpha<0$ , when the probability to find a star with negative $L_{z}$ decreases as $\alpha$ decreases, and the corresponding plots would be analogous to figure \ref{fig:PedDF1}, after a reflection about $L_{z}=0$. |
In (c) and (d) are plotted the contours of model m=3 with D,πεDias for the same values of a. | In (c) and (d) are plotted the contours of model $m=3$ with $B_1\approx
B'_{1\mathrm{min}}$ for the same values of $\alpha$. |
The behavior of the Dis for the remaining cases is pretty similar to the shown in these figures: when £2,79D. the contours are similar to (a) and (b). while i£ D,zDu. the contours are similar to (c) and (d). in agreement with figure 10.. | The behavior of the DFs for the remaining cases is pretty similar to the shown in these figures: when $B_1\gg B'_{1\mathrm{min}}$, the contours are similar to (a) and (b), while if $B_1\approx B'_{1\mathrm{min}}$, the contours are similar to (c) and (d), in agreement with figure \ref{fig:DFJAC}. |
We have obtained a set of mocdels for axisvmmetric Jat galaxies. by superposing members belonging to the eeneralized. Ixalnajs dises family. | We have obtained a set of models for axisymmetric flat galaxies, by superposing members belonging to the generalized Kalnajs discs family. |
Phe mass distribution of each model (labeled through the parameter m=2.3....). described by (10)). is maximum at the center and vanishes at the edge. in concordance with a great. variety of galaxies. | The mass distribution of each model (labeled through the parameter $m=2,3,\ldots$ ), described by \ref{dennew}) ), is maximum at the center and vanishes at the edge, in concordance with a great variety of galaxies. |
Aloreover. the mass density can be expressed as a function of the gravitational potential (see equation. (22))). which makes possible to derive. analvticallv. the equilibrium DEs escribing the statistical features of the mocels. | Moreover, the mass density can be expressed as a function of the gravitational potential (see equation \ref{dennew2}) )), which makes possible to derive, analytically, the equilibrium DFs describing the statistical features of the models. |
These models have also interesting features concerning with the interior kinematical behavior. | These models have also interesting features concerning with the interior kinematical behavior. |
On one hand. we garowed that for some values of D,. the circular. velocity has a behavior very similar to that seen in many discoidal ealaxies. | On one hand, we showed that for some values of $B_{1}$, the circular velocity has a behavior very similar to that seen in many discoidal galaxies. |
This is a very relevant fact. which suggests that it ds not always necessary to introduce the hypothesis of ark matter halos (or MOND theories) in order to describe adequately ᾱ- variety of. rotational curves. | This is a very relevant fact, which suggests that it is not always necessary to introduce the hypothesis of dark matter halos (or MOND theories) in order to describe adequately a variety of rotational curves. |
On the other hand. the analysis of cpicvclic and: vertical frequencies. associated to quasi-cireular orbits. reveals that the mocdels are stable uncer radial. perturbations but unstable. under vertical disturbances. | On the other hand, the analysis of epicyclic and vertical frequencies, associated to quasi-circular orbits, reveals that the models are stable under radial perturbations but unstable under vertical disturbances. |
With regard to the motion of test xwticles around the models formulated here. we found that he behavior of cisc-crossing orbits is similar to that seen in he generalized. Ixalnajs family. | With regard to the motion of test particles around the models formulated here, we found that the behavior of disc-crossing orbits is similar to that seen in the generalized Kalnajs family. |
However. for certain values of the parameter D. the Poincaré surface of section reveals hat one can suggest the existence ofa (non analytical) third integral of motion. | However, for certain values of the parameter $B_{1}$, the Poincaré surface of section reveals that one can suggest the existence of a (non analytical) third integral of motion. |
On the other hand. we find two kinds of equilibrium DES or the models. | On the other hand, we find two kinds of equilibrium DFs for the models. |
Such two-integral DES can be formulated. ab first. as functionals of the Jacobi's integral. as it was sketched in the formalism. developed. by Ixalnajs.(1976). | Such two-integral DFs can be formulated, at first, as functionals of the Jacobi's integral, as it was sketched in the formalism developed by \cite{kal}. |
This class of DEs essentially describes systems which rotational state. in average. behaves as a rigid body. | This class of DFs essentially describes systems which rotational state, in average, behaves as a rigid body. |
Then. we use the procedure introduced. by Dejonghe (1986).. obtaining Ds which represents svstems with a mean rotational state consistent with the maximuni entropy principle and. therefore. more probable than the firstones. | Then, we use the procedure introduced by \cite{dej}, , obtaining DFs which represents systems with a mean rotational state consistent with the maximum entropy principle and, therefore, more probable than the firstones. |
The statements exposed. above suggest. that. the family presented here. can be considered as a set of realistic models that clescribes satisfactorily a great. variety of galaxies. | The statements exposed above suggest that the family presented here, can be considered as a set of realistic models that describes satisfactorily a great variety of galaxies. |
The aforementioned. isochrone fits provide the average UGD star we target with another 20 Myr on the RGB. | The aforementioned isochrone fits provide the average RGB star we target with another 20 Myr on the RGB. |
Assuming mass loss on the LB itself is negligible. this ranslates to an average mass-loss rate of * M. vet over he remainder of the RGB. | Assuming mass loss on the HB itself is negligible, this translates to an average mass-loss rate of $^{-8}$ $_\odot$ $^{-1}$ over the remainder of the RGB. |
In concurrence with previous relations (Catclan20092... ancl references. therein).-- this is rather higher than the average Reimers’ Law rate (Reimers1975) of 1.9.10° M. 1 (assuming. Reimers. η= 0.5). | In concurrence with previous relations \citealt{Catelan09a}, and references therein), this is rather higher than the average Reimers' Law mass-loss rate \citep{Reimers75} of $1.9 \times 10^{-9}$ $_\odot$ $^{-1}$ (assuming Reimers' $\eta = 0.5$ ). |
Lt is towards the higher end of the observed. range of mass-loss rates estimated from chromospheric line profiles citealtDS800:: Vievtesetal.2011) . suggesting that stronger miatss loss at the RGB tip is -- | It is towards the higher end of the observed range of mass-loss rates estimated from chromospheric line profiles \\citealt{DSS09}; \citealt{VMC+11}) ), suggesting that stronger mass loss at the RGB tip is important. |
One can also use the white cwarl mass to estimate that there is only 0.09 4 0.05 AL. of material for the star to lose during the ~9 Myr it spends in its (post-)AGB phases: also vielding an average mass-loss rate of 10.7 5. | One can also use the white dwarf mass to estimate that there is only 0.09 $\pm$ 0.05 $_\odot$ of material for the star to lose during the $\sim$ 9 Myr it spends in its (post-)AGB phases: also yielding an average mass-loss rate of $^{-8}$ $_\odot$ $^{-1}$. |
Chromospherie mass loss appears continuous on the AGB and can reach —6 «107 M. (Dupreeοἱal. 2009).. while the cluster also has several dust-producing stars. which typically M10 " M. for 10" (M|09: MeDonaldetseranal.20110) | Chromospheric mass loss appears continuous on the AGB and can reach $\sim$ 6 $\times 10^{-8}$ $_\odot$ $^{-1}$ \citep{DSS09}, while the cluster also has several dust-producing stars, which typically sustain $\sim$ $^{-6}$ $_\odot$ $^{-1}$ for $\sim$ $^5$ yr (M+09; \citealt{MvLS+11}) ). |
The combination of these processes Nilay mean Chat niulv stars lose their entire envelope before they reach the postACD. phase. perhaps even becoming ACGD-manqué stars Clailed AGB stars: e.g. O'Connell 19993). | The combination of these processes may mean that many stars lose their entire envelope before they reach the post-AGB phase, perhaps even becoming AGB-manqué stars (`failed' AGB stars; e.g. \citealt{OConnell99}) ). |
This would explain the surprisingly-LIow (L — 1500 L. ) of & Con's known post-ACB stars: LELD MM10"mj ... star) and 32029 (V1) (AleDonalel | This would explain the surprisingly-low luminosity (L $\sim$ 1500 $_\odot$ ) of $\omega$ Cen's known post-AGB stars: LEID 16018 (Fehrenbach's star) and 32029 (V1) \citealt{MvLS+11}) ). |
etal.n "mm the cillerential RGD/eAXGD mass in w Cen. and confirmed. it against existing models. it now becomes possible to repeat the study in other clusters where the models are less certain. | Having measured the differential RGB/eAGB mass in $\omega$ Cen, and confirmed it against existing models, it now becomes possible to repeat the study in other clusters where the models are less certain. |
In. particular. this technique will be useful in those clusters with higher metallicities and higher envelope masses. where the temperature of LLB stars is less sensitive to stellar mass. | In particular, this technique will be useful in those clusters with higher metallicities and higher envelope masses, where the temperature of HB stars is less sensitive to stellar mass. |
Our current observations do not allow us to relate metallicity. initial mass. or initial abundance to ROB mass loss. | Our current observations do not allow us to relate metallicity, initial mass, or initial abundance to RGB mass loss. |
For that. we need these observations repeated in other clusters. | For that, we need these observations repeated in other clusters. |
While other clusters are less populous than c Cen. we are limited. here by the existence of spectra. not. by the number of stars. | While other clusters are less populous than $\omega$ Cen, we are limited here by the existence of spectra, not by the number of stars. |
Bespoke targetting of stars (particularly on the ολ). and a selection of spectral range with more eravity-sensitive lines. would allow this study to be repeated to higher accuracy. even in much-smaller clusters. | Bespoke targetting of stars (particularly on the eAGB), and a selection of spectral range with more gravity-sensitive lines, would allow this study to be repeated to higher accuracy, even in much-smaller clusters. |
We have spectroscopically determined. surface gravitics or 66 central RGB and 21 ολ stars in w Cen. and combined these with photometric temperature. and uminositv measurements to calculate the dillerence in mass oween the two populations. | We have spectroscopically determined surface gravities for 66 central RGB and 21 eAGB stars in $\omega$ Cen, and combined these with photometric temperature and luminosity measurements to calculate the difference in mass between the two populations. |
We find that 26 - of their mass is lost. between these evolutionary phases. corresponding to 0.21 zc 0.05 M. for an initial mass of 83 M.. | We find that 26 $\pm$ of their mass is lost between these evolutionary phases, corresponding to 0.21 $\pm$ 0.03 $_\odot$ for an initial mass of 0.83 $_\odot$. |
By implication. this limits the mass lost on the AGB to some 0.09 + 0.05 M... which may. lead to early ermination of the AGB ancl of AGB manqué stars. | By implication, this limits the mass lost on the AGB to some 0.09 $\pm$ 0.05 $_\odot$, which may lead to early termination of the AGB and formation of AGB manqué stars. |
Our derived LED. masses hichof0.62 + modd0.04 AL. compares very well with LLB models. predict. LIB masses of 1.61 0.63 M. for appropriate (Y20.24. α ο = |0.3. οΗ] 1.62) models. | Our derived HB masses of 0.62 $\pm$ 0.04 $_\odot$ compares very well with HB models, which predict HB masses of 0.61 – 0.63 $_\odot$ for appropriate $Y \approx 0.24$, $\alpha$ /Fe] $\approx$ +0.3, [Fe/H] $\approx$ –1.62) models. |
This method has the potential to provide physical constraints on currenthy-uneertain regimes in modelling horizontal branch stars. | This method has the potential to provide physical constraints on currently-uncertain regimes in modelling horizontal branch stars. |
This material uses work supported " thes ational Science Foundation under award No. | This material uses work supported by the National Science Foundation under award No. |
AST-LO03201help to CLI. | AST-1003201 to CIJ. |
We thank the referee and Olivia Jones for comments. | We thank the referee and Olivia Jones for helpful comments. |
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