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Hence. the additional energv available from converting hadronic to strange quark matter aud during accretion onto the QS seenis crucial in explaiuiug the nature of CRBs.
Hence, the additional energy available from converting hadronic to strange quark matter and during accretion onto the QS seems crucial in explaining the nature of GRBs.
Tn addition to au cnerectics point of view. the most inportaut benefits of our GRD 120del involving a QS stage are: (i) the QS offers an additional stage that allows for more enerev to be extracted from the conversion from NS to QS as well as from accretion.
In addition to an energetics point of view, the most important benefits of our GRB model involving a QS stage are: (i) the QS offers an additional stage that allows for more energy to be extracted from the conversion from NS to QS as well as from accretion.
Also. additional energy is released as the QS quickly evolves from a uou-aligned to au aligued rotator following its birth with up to 10/7 eres released iu a few seconds (Ouyed.ct 2006).
Also, additional energy is released as the QS quickly evolves from a non-aligned to an aligned rotator following its birth with up to $10^{47}$ ergs released in a few seconds \citep{ouyed_niebergal06}.
As such. the QS phase extends the cugine activity and so cau account for both the prompt ciission id inreenlar N-ray afterglow activity: Gi) a natural uplification of the NS maeuetic field to 104-1025. C during the transition to the QS (wazaki2005).
As such, the QS phase extends the engine activity and so can account for both the prompt emission and irregular X-ray afterglow activity; (ii) a natural amplification of the NS magnetic field to $10^{14}$ $10^{15}$ G during the transition to the QS \citep{iwazaki05}.
. Such lieh streneths eives the correct spin down timeto for the plateau: (ii) since QS in the CFL phase might not have a crust. the spin down cnerev will most likely be extracted as an ele fireball with verv little barvon contamination (seediscussioninNicherealetal.
Such high strengths gives the correct spin down timeto for the plateau; (iii) since QS in the CFL phase might not have a crust, the spin down energy will most likely be extracted as an $e^+e^-$ fireball with very little baryon contamination \citep[see discussion in][]{niebergal06}. .
2006).. Panaitescu(2007) favors a birvon free secondary outflow to explain the plateau.
\citet{panaitescu07} favors a baryon free secondary outflow to explain the plateau.
of the gap formation time scale is obtained in the zero viscosity limit.
of the gap formation time scale is obtained in the zero viscosity limit.
In this case, an analytic formulation is provided by Brydenetal.(1999) in the form where P is the orbital period, q=M,/M, and A=2Ry as defined above.
In this case, an analytic formulation is provided by \cite{br99} in the form where $P$ is the orbital period, $q=M_p/M_{\star}$ and $\Delta = 2R_H$ as defined above.
Assuming Keplerian rotation, we can rewrite the time scale for the gap formation as The upper panel of Figure 12 shows the calculated values of rA" for the stellar mass of DG Tau (0.3 Mo).
Assuming Keplerian rotation, we can rewrite the time scale for the gap formation as The upper panel of Figure \ref{fig:tau_delta} shows the calculated values of $\tau^{min}_\Delta$ for the stellar mass of DG Tau (0.3 $M_{\sun}$ ).
In the case of a planet with a mass between 0.3 and 0.5 M; orbiting at a radius larger than 40 AU, the minimum time scale for the gap formation is comparable with the age of the system (0.1 Myr).
In the case of a planet with a mass between 0.3 and 0.5 $_J$ orbiting at a radius larger than 40 AU, the minimum time scale for the gap formation is comparable with the age of the system (0.1 Myr).
For more massive planets, or for closer radii, the minimum gaps time scale is a small fraction of the age of the system.
For more massive planets, or for closer radii, the minimum gaps time scale is a small fraction of the age of the system.
We conclude that, for DG Tau, the observations lack the sensitivity and angular resolution required to investigate the presence of planets less massive than about 0.5 M, at any orbital radius.
We conclude that, for DG Tau, the observations lack the sensitivity and angular resolution required to investigate the presence of planets less massive than about 0.5 $_J$ at any orbital radius.
Our analysis indicates that no planets more massive than Jupiter are present between 5 and 50 AU, unless they are younger than 10 years.
Our analysis indicates that no planets more massive than Jupiter are present between 5 and 50 AU, unless they are younger than $10^4$ years.
The similarity solution for the disk surface density is characterized by y=—0.56+0.18 and R,~26—3 AU.
The similarity solution for the disk surface density is characterized by $\gamma= -0.56\pm0.18$ and $R_t\sim26\pm3$ AU.
As shown in Figure 9,, the surface density increases roughly as VR from the inner radius at 0.1 AU up to about 26 AU and then decreases exponentially outward.
As shown in Figure \ref{fig:sigma}, the surface density increases roughly as $\sqrt{R}$ from the inner radius at 0.1 AU up to about 26 AU and then decreases exponentially outward.
This supports the suggestion in Section 3 that the RY Tau inner disk might be partially dust depleted with respect to power law disk models.
This supports the suggestion in Section \ref{sec:morp} that the RY Tau inner disk might be partially dust depleted with respect to power law disk models.
We note that this surface density profile may provide an explanation for both the double peak intensity at 1.3 mm and the disk excess at infrared wavelengths.
We note that this surface density profile may provide an explanation for both the double peak intensity at 1.3 mm and the disk excess at infrared wavelengths.
Indeed, within 10 AU the model disk remains optically thick at optical and infrared wavelengths, exhibiting the infrared excess typical of classical disks.
Indeed, within 10 AU the model disk remains optically thick at optical and infrared wavelengths, exhibiting the infrared excess typical of classical disks.
At larger radii, the surface density in RY Tau disk decreases smoothly and the residuals calculated by subtracting the best fit models to the 1.3 mm dust emission map do not show any structure at more than 3c.
At larger radii, the surface density in RY Tau disk decreases smoothly and the residuals calculated by subtracting the best fit models to the 1.3 mm dust emission map do not show any structure at more than $\sigma$ .
This excludes strong deviations from an unperturbed viscous disk profile.
This excludes strong deviations from an unperturbed viscous disk profile.
The lower panel of Figure 11 shows the signal-to-noise ratio of the detection of a gap generated by planets of 1, 5 and 10 Jupiter masses as a function of the orbital radius.
The lower panel of Figure \ref{fig:planet_deviation} shows the signal-to-noise ratio of the detection of a gap generated by planets of 1, 5 and 10 Jupiter masses as a function of the orbital radius.
Dueto the higher
Dueto the higher
lt is now well established that all massive galaxies (AL.5ο0L. 1077 AL.) in the local Universe harbour central super-massive black holes (SMDIIS). with masses proportional to hose of their stellar spheroids (hereafter. bulge: citealt kormendy95::: 723).
It is now well established that all massive galaxies $M_* \approx 10^{10}$ $10^{12} \Msun$ ) in the local Universe harbour central super-massive black holes (SMBHs), with masses proportional to those of their stellar spheroids (hereafter, bulge; \\citealt{kormendy95}; \citealt{magorrian98}) ).
Comparisons between the SALBIL mass density in the local Universe and the total energy ooduced. by active galactic nuclei: CXGNs) across. cosmic ime have shown that these SMDBlIIS were primarily grown hrough mass-accretion events citealtsoltans2:: ?:: 2)).
Comparisons between the SMBH mass density in the local Universe and the total energy produced by active galactic nuclei (AGNs) across cosmic time have shown that these SMBHs were primarily grown through mass-accretion events \\citealt{soltan82}; \citealt{rees84}; \citealt{marconi04}) ).
The space density of high-Iuminosity AGNs appears to have peaked at higher redshifts than Lower-uminosity ACGNs. suggesting that the most massive SMDIIs (Mig2107 107 AL.) grew first. a result commonly referred to às “AGN cosmic downsizing citealteowie(ü3:: 2: 2: ?:: 72)).
The space density of high-luminosity AGNs appears to have peaked at higher redshifts than lower-luminosity AGNs, suggesting that the most massive SMBHs $\Mbh \approx 10^8$ $10^9 \Msun$ ) grew first, a result commonly referred to as `AGN cosmic downsizing' \\citealt{cowie03}; \citealt{ueda03}; \citealt{mclure04}; \citealt{hasinger05}; \citealt{alonso08}) ).
Extrapolation of these results imply that the most rapidly erowing SMDBlIS in the nearby Universe should. be of comparatively low mass (Albu107AL. ).
Extrapolation of these results imply that the most rapidly growing SMBHs in the nearby Universe should be of comparatively low mass $\Mbh \ll 10^{8} \Msun$ ).
To determine the characteristic masses of these growing SAIBLIs requires a complete census of ACGIN activity and SMDLLI masses in the local Universe.
To determine the characteristic masses of these growing SMBHs requires a complete census of AGN activity and SMBH masses in the local Universe.
Using data from the Sloan Digital Sky Survey (SDSS: in conjunction with the well established SMLstellar velocity dispersion relation. (hereafter. ay: eg. ?: ?)). 7T (2004: hereafter. 10141) deduced that relatively low mass SALDIIs (Mpg23.107M. ) residing in moderately niassive bulec-dominated galaxies host. the. majority. of. present- accretion onto SMDlIIs.
Using data from the Sloan Digital Sky Survey \citep[SDSS; ][] {sdss_tech} in conjunction with the well established SMBH–stellar velocity dispersion relation (hereafter, $\sigma_*$; e.g., \citealt{gebhardt00}; \citealt{tremaine02}) ), \citeauthor{heckman04} (2004; hereafter, H04) deduced that relatively low mass SMBHs $\Mbh \approx 3 \times 10^7 \Msun$ ) residing in moderately massive bulge-dominated galaxies host the majority of present-day accretion onto SMBHs.
However. the space density. of SALBUs derived from the σι relation in the optical survey
However, the space density of SMBHs derived from the $\sigma_*$ relation in the optical survey
and σι is in radians.
and $\sigma_{A}$ is in radians.
This approach excludes the uncertainties in the orbital period aux can therefore oulv vield the lower limit for the detection threshold.
This approach excludes the uncertainties in the orbital period and can therefore only yield the lower limit for the detection threshold.
Hence. ifEq. (6))
Hence, ifEq. \ref{amplitude}) )
does not hold. it will be impossible to detect the sigual.
does not hold, it will be impossible to detect the signal.
However. if it holds. the detectability of such a companion needs to be examined more closely * nunercal simulations aud by analysing the simulated ata using methods such as AICALC and Bayesian model selection criterion.
However, if it holds, the detectability of such a companion needs to be examined more closely by numerical simulations and by analysing the simulated data using methods such as MCMC and Bayesian model selection criterion.
To fully investigate the ability to detect planctary conrpanions. we must define when a positive detection has been made.
To fully investigate the ability to detect planetary companions, we must define when a positive detection has been made.
This question can be approached through Bayesian probabilities.
This question can be approached through Bayesian probabilities.
Let Ry be the model im Eq. (1))
Let $\vec{R}_{1}$ be the model in Eq. \ref{model}) )
with oue planctary companion (corresponding 12 paralucters in the RV and astrometrv models). aud Ry a inode without a planetary companion (5 parameters).
with one planetary companion (corresponding 12 parameters in the RV and astrometry models), and $\vec{R}_{0}$ a model without a planetary companion (5 parameters).
Iu general. let Ry be a model with & plaucts.
In general, let $\vec{R}_{k}$ be a model with $k$ planets.
Using the Bayes theorem. it can be seen that the conditional probability of iiodel Ry. represcuting the data (1) best. out of the p|1 alternatives to be tested. can be written as where the Bayes factor D; is defined as (e.g. Wass aud Raftery. 1995) and PUR,.) is the prior probability of the Ath model. here set equal for all A. because it is assuued that there is no prior information available.
Using the Bayes theorem, it can be seen that the conditional probability of model $\vec{R}_{k}$ representing the data $m$ ) best, out of the $p+1$ alternatives to be tested, can be written as where the Bayes factor $B_{k,j}$ is defined as (e.g. Kass and Raftery, 1995) and $P(\vec{R}_{k})$ is the prior probability of the $k$ th model, here set equal for all $k$, because it is assumed that there is no prior information available.
Here the likelihood Pon Ry). with paraucters ujCUy for the Ath model. is where ponr|e,.Rp) ds the parameter likelihood fuuction and pu;R,) the prior density.
Here the likelihood $P(m | \vec{R}_{k})$ , with parameters $\vec{u}_{k} \in U_{k}$ for the $k$ th model, is where $p(m | \vec{u}_{k}, \vec{R}_{k})$ is the parameter likelihood function and $p(\vec{u}_{k} | \vec{R}_{k})$ the prior density.
Since the model probability. defined iu this wav. automatically takes the Occamian principle of parsimony iuto account. the model with the smallest number of paramcters out of those having alinost equal probabilities will be selected.
Since the model probability, defined in this way, automatically takes the Occamian principle of parsimony into account, the model with the smallest number of parameters out of those having almost equal probabilities will be selected.
Hence. it can be said that a detection has been made if (Jeffreys 1961) This criterion is used throughout this article when deciding whether a statistically siguificaut detection has been made or not.
Hence, it can be said that a detection has been made if (Jeffreys 1961) This criterion is used throughout this article when deciding whether a statistically significant detection has been made or not.
The fitting was performed by requiring that the values of all the least-squares cost-fiuctious 5, (astrometric e). 5, (astrometric gy). Spy (RV). aud their suu be miunized siunltaueouslv.
The fitting was performed by requiring that the values of all the least-squares cost-functions $S_{x}$ (astrometric $x$ ), $S_{y}$ (astrometric $y$ ), $S_{RV}$ (RV), and their sum be minimized simultaneously.
This method. called iuultidata inversion. has been used successfully with astrometric and RV nieasurements when detecting stellar binaries (e.g. Torres 2007).
This method, called multidata inversion, has been used successfully with astrometric and RV measurements when detecting stellar binaries (e.g. Torres 2007).
See the discussion in Iaasalainen aud Loauberg (2006). where the multidata inversion was applied to asteroid observations.
See the discussion in Kaasalainen and Lamberg (2006), where the multidata inversion was applied to asteroid observations.
The models for astrometric position aud RV of the two-hody system of interest are non-linear. so an iterative method of fitting the model paramcters is needed.
The models for astrometric position and RV of the two-body system of interest are non-linear, so an iterative method of fitting the model parameters is needed.
The MCALC with Metropolis-IIastiues (AL-ID) aleorithiu was chosen because it is a elobal method (Metropolis ct al.
The MCMC with Metropolis-Hastings (M-H) algorithm was chosen because it is a global method (Metropolis et al.
1953: [astines 1970). it offers a direct estimate of the posterior probability density. aud )ecause It can be used to verify the existence and uniqueness of the solution.
1953; Hastings 1970), it offers a direct estimate of the posterior probability density, and because it can be used to verify the existence and uniqueness of the solution.
Since the probability densities eiven the measurements are available. AICAIC can be used to calculate realistical CLror estimates or the model parameters.
Since the probability densities given the measurements are available, MCMC can be used to calculate realistical error estimates for the model parameters.
These estimates are typically πιο larger than those calculated using traditional methods (c.c. Ford 2006). implying that MCAIC should )o preferred when assessing the parameter errors.
These estimates are typically much larger than those calculated using traditional methods (e.g. Ford 2006), implying that MCMC should be preferred when assessing the parameter errors.
Asstuuine Gaussian errors with zero mica. the likelihood. function of the paramcters with respect to RV lneasurelments can be written as When applying MCAIC. a parameter value (ay) is selected for the first member of the chain.
Assuming Gaussian errors with zero mean, the likelihood function of the parameters with respect to RV measurements can be written as When applying MCMC, a parameter value $\vec{u}_{0}$ ) is selected for the first member of the chain.
The next value wy). 38 fouud by randomly selecting a proposal in he vicinity of u;.
The next value $\vec{u}_{k+1}$ is found by randomly selecting a proposal in the vicinity of $\vec{u}_{k}$.
This is then accepted by comparing he likchhoods of the two paraimcter values.
This is then accepted by comparing the likelihoods of the two parameter values.
Proposed xmeuneter values αν Awith a ereater Bkelibood. than hat of aw; are always selected as the next chain member. mt values with a smaller likelihood cau also be selected according to the criterion of Hastings (1970).
Proposed parameter values $\vec{u}_{k+1}$  with a greater likelihood than that of $\vec{u}_{k}$ are always selected as the next chain member, but values with a smaller likelihood can also be selected according to the criterion of Hastings (1970).
Samples of at least LO? points were generated when sampling the waralucter space.
Samples of at least $10^{5}$ points were generated when sampling the parameter space.
For practical details ou AICAIC with astronomical data. see c.g. Gregory (2005).
For practical details on MCMC with astronomical data, see e.g. Gregory (2005).
The paramcter space C in this Neplerian two-body uodel has a comparatively small dimension (cant= 12). but iu some cases it already makes the sample colmputationally expensive.
The parameter space $U$ in this Keplerian two-body model has a comparatively small dimension $\dim U = 12$ ), but in some cases it already makes the sampling computationally expensive.
Especially when covariances )etxyeeen the parameters are large and of non-linear nature. he space of reasonable probability C5CU to be sampled can be verv narrow and. as a result. the next proposed value of parameter vector w in the Markov chain is ikelv to be outside this subspace and thus rejected. cousiderably increasing the time needed to generate a statistically representative chain.
Especially when covariances between the parameters are large and of non-linear nature, the space of reasonable probability $U_{R} \subset U$ to be sampled can be very narrow and, as a result, the next proposed value of parameter vector $\vec{u}$ in the Markov chain is likely to be outside this subspace and thus rejected, considerably increasing the time needed to generate a statistically representative chain.
For this reason. when musing a iuuitivariate Gaussian density as a proposal. the acceptance rates were low. approximately 0.1 iu the AMCALIC sanaplines.
For this reason, when using a multivariate Gaussian density as a proposal, the acceptance rates were low, approximately 0.1 in the MCMC samplings.
With more than one source of measurements available. it is possible to get more information from the «απο of interest than when relving ou any sinele observation method alone.
With more than one source of measurements available, it is possible to get more information from the system of interest than when relying on any single observation method alone.
This is aconsequence of Bayesian infercuce.
This is aconsequence of Bayesian inference.
Denoting the astrometric measuremeuts bv O0, and the RV ineasuremenuts by £,. the conditional probability
Denoting the astrometric measurements by $\vec{\Theta}_{o}$ and the RV measurements by $\dot{\vec{z}}_{o}$ , the conditional probability
In their kinetic simulations of DSA, Kang and Jones (hereafter KJ) evolve the standard time-dependent gasdynamic conservation laws with the CR pressure terms in Eulerian form for one-dimensional plane-parallel geometry 2007), where p=p(z,t) is the gas density, u=u(x,t) is the fluid velocity, P=P(z,t) is the gas (P,) or CR (P,) pressure (eq. 22))
In their kinetic simulations of DSA, Kang and Jones (hereafter KJ) evolve the standard time-dependent gasdynamic conservation laws with the CR pressure terms in Eulerian form for one-dimensional plane-parallel geometry \citep{kjg02,kj07}, , where $\rho=\rho(x,t)$ is the gas density, $u=u(x,t)$ is the fluid velocity, $P=P(x,t)$ is the gas $P_{g}$ ) or CR $P_{c}$ ) pressure (eq. \ref{xicr}) )
and y=5/3 is the gas adiabatic index.
and $\gamma= 5/3$ is the gas adiabatic index.
L(x,t) is the injection energy loss term, which accounts for the energy carried away by the suprathermal particles injected into the CR component at the subshock and is subtracted from the postshock gas immediately behind the subshock.
$\mathcal{L}(x,t)$ is the injection energy loss term, which accounts for the energy carried away by the suprathermal particles injected into the CR component at the subshock and is subtracted from the postshock gas immediately behind the subshock.
The gas heating due to the Alfvénn wave dissipation in the upstream region is modeled following McKenzie&Volk(1982) and is given by the term where v4(z,t)=Bo//4np(x, is the local Alfvénn speed and Bo is the magnetic field strength far upstream.
The gas heating due to the Alfvénn wave dissipation in the upstream region is modeled following \cite{mck-v82} and is given by the term where $v_A(x,t)= B_0/\sqrt{4\pi \rho(x,t)}$ is the local Alfvénn speed and $B_0$ is the magnetic field strength far upstream.
Here and in the following we will label with the subscript 0 quantities at upstream infinity, and with 1 and 2 quantities immediately upstream and downstream of the subshock, respectively.
Here and in the following we will label with the subscript 0 quantities at upstream infinity, and with 1 and 2 quantities immediately upstream and downstream of the subshock, respectively.
These equations can be used to describe parallel shocks, where the large-scale magnetic field is aligned with the shock normal and the pressure contribution from the turbulent magnetic fields can be neglected.
These equations can be used to describe parallel shocks, where the large-scale magnetic field is aligned with the shock normal and the pressure contribution from the turbulent magnetic fields can be neglected.
The CR population is evolved by solving the diffusion-convection equation for the angle-averaged (isotropic in momentum space) distribution function, f(z,p,t), in the form: where D(z,p) is thespatial diffusion coefficient (seee.g.|Skilling)|1975, and p is the scalar, momentum magnitude.
The CR population is evolved by solving the diffusion-convection equation for the pitch-angle-averaged (isotropic in momentum space) distribution function, $f(x,p,t)$, in the form: where $D(x,p)$ is thespatial diffusion coefficient \citep[see e.g.][for a derivation]{ski75} and $p$ is the scalar, momentum magnitude.
This equation is then usefully rewritten and
This equation is then usefully rewritten and
and Na-rich stars: although we derive the same Li abundance for the two populations, it is interesting to note that Na-rich stars have a larger scatter in Li with respect to Na-poor ones.
and Na-rich stars: although we derive the same Li abundance for the two populations, it is interesting to note that Na-rich stars have a larger scatter in Li with respect to Na-poor ones.
A one-tailed Fisher test returns a probability such that a difference can be obtained by chance.
A one-tailed Fisher test returns a probability such that a difference can be obtained by chance.
In fact, if a decrease in O of ~50%//60% occurred (as derived e.g. by Marino et al.
In fact, if a decrease in O of $\sim$ occurred (as derived e.g. by Marino et al.
2008 and Carretta et al.
2008 and Carretta et al.
2010), also Li must have been depleted.
2010), also Li must have been depleted.
In a recent work, D’Antona Ventura (2010) have presented the expected Li production as a function of the polluter mass (AGB stars) for metallicity Z=0.001.
In a recent work, D'Antona Ventura (2010) have presented the expected Li production as a function of the polluter mass (AGB stars) for metallicity $Z$ =0.001.
Looking at their Figure 5, one can see that a very low mass AGB polluter #4 Mo) can produce a moderate Li content with (ie.,values very close to the Li plateau (log n(Li)~2.2-2.3).
Looking at their Figure 5, one can see that a very low mass AGB polluter (i.e., $\approx$ 4 $M_\odot$ ) can produce a moderate Li content with values very close to the Li plateau $\log{n{\rm (Li)}}$$\sim$ 2.2-2.3).
After considering a depletion of a factor of ~20 at the 1DUP, this result agrees very well with our values log n(Li)~1.3-1.4).
After considering a depletion of a factor of $\sim$ 20 at the 1DUP, this result agrees very well with our values (i.e. $\log{n{\rm (Li)}}$$\sim$ 1.3-1.4).
As also briefly explained in the (ie.Section ?? widely discussed in Carretta et al.
As also briefly explained in the Section \ref{sec:intro} (and widely discussed in Carretta et al.
2010), there are (andfurther indications that only low-mass polluters could have contributed to the observed chemical pattern in M4: an almost “vertical” Na-O anticorrelation, with very (1)small oxygen variation (depletion); and (2) the lack of Mg—Altion, which in fact requires high mass polluters for the activation of higher temperature cycles (T ~65 MK; Prantzos Charbonnel 2006).
2010), there are further indications that only low-mass polluters could have contributed to the observed chemical pattern in M4: (1) an almost “vertical" $-$ O anticorrelation, with very small oxygen variation (depletion); and (2) the lack of $-$ Al, which in fact requires high mass polluters for the activation of higher temperature cycles $T\sim$ 65 MK; Prantzos Charbonnel 2006).
A similar case could have occurred for NGC 6397, where according to Pasquini et al.
A similar case could have occurred for NGC 6397, where according to Pasquini et al. (
two stars differ by —0.6 dex in O, but have the (2008),same “normal” Li (log n(Li)=2.2).
2008), two stars differ by $\sim$ 0.6 dex in O, but have the same “normal" Li $\log{n{\rm (Li)}}$ =2.2).
Also, in a recent work Lind et al. (
Also, in a recent work Lind et al. (
2009), based on a sample of ~100 MS and early SGB/stars, found no difference in Li abundances between Na-rich and Na-poor stars with only two stars driving a Li—Na anticorrelation.
2009), based on a sample of $\sim$ 100 MS and early SGB/stars, found no difference in Li abundances between Na-rich and Na-poor stars with only two stars driving a $-$ Na anticorrelation.
They concluded that Li content is independent of intra-cluster pollution; however the Na—O distribution points out to a certain small) degree of oxygen depletion and, as a consequence,(though of Li destruction as well.
They concluded that Li content is independent of intra-cluster pollution; however the $-$ O distribution points out to a certain (though small) degree of oxygen depletion and, as a consequence, of Li destruction as well.
Hence, if first and second generation stars share the same Li abundances, a Li production should also be required for this cluster.
Hence, if first and second generation stars share the same Li abundances, a Li production should also be required for this cluster.
Along with a difference in metallicity of ~0.9 dex, the two clusters, NGC 6397 and M 4, have both quite small integrated magnitudes (i.e., mass) with My«——6.63 and My«—— 7.20, respectively (Harris
Along with a difference in metallicity of $\sim$ 0.9 dex, the two clusters, NGC 6397 and M 4, have both quite small integrated magnitudes (i.e., mass) with $M_{\rm Vt}$ $-$ 6.63 and $M_{\rm Vt}$ $-$ 7.20, respectively (Harris 1996).
The similarity in masses between these two GCs also 1996).seems to suggest a similar “typical” polluter for both M4 and NGC 6397, with the requirement to have in both cases neither very high mass polluters (no extended MgAI/NaO anticorrelations, very little Hehancement?, and no Li—Na anticorrelation) nor low mass polluters (<4 Mo), otherwise the C--N--O is not constant and/or s-process variations should be present (see Ivans 1999; Yong et al.
The similarity in masses between these two GCs also seems to suggest a similar “typical" polluter for both M4 and NGC 6397, with the requirement to have in both cases neither very high mass polluters (no extended MgAl/NaO anticorrelations, very little He, and no $-$ Na anticorrelation) nor low mass polluters $\leq$ 4 $M_\odot$ ), otherwise the C+N+O is not constant and/or $s$ -process variations should be present (see Ivans 1999; Yong et al.
2008).
2008).
The more massive GC NGC 6752 (Myz=—7.73) could present a different behavior.
The more massive GC NGC 6752 $M_{\rm Vt}$ $-$ 7.73) could present a different behavior.
We might speculate that only a very low Li production from higher mass polluters of z:5—6Mo (see Figure 5 of D'Antona Ventura, 2010) does not erase Li—Na anticorrelation for thiscluster?.
We might speculate that only a very low Li production from higher mass polluters of $\approx$ $-$ $M_\odot$ (see Figure 5 of D'Antona Ventura, 2010) does not erase $-$ Na anticorrelation for this.
. Note in fact that NGC 6752 presents an extended Na—O anticorrelation and a large variation in Al (i.e., the MgAI chain was active in the polluter stars).
Note in fact that NGC 6752 presents an extended $-$ O anticorrelation and a large variation in Al (i.e., the MgAl chain was active in the polluter stars).
On the other hand, it seems very difficult to discriminate the nature of polluters and their properties for 47 Tuc: maybe this GC was similar to NGC 6752 but the intrinsic scatter in Li abundance, independent of intracluster pollution, washes out the fossil imprint by the previous generation of polluter stars (D'Orazi et al.
On the other hand, it seems very difficult to discriminate the nature of polluters and their properties for 47 Tuc: maybe this GC was similar to NGC 6752 but the intrinsic scatter in Li abundance, independent of intracluster pollution, washes out the fossil imprint by the previous generation of polluter stars (D'Orazi et al.
2010).
2010).
Given the large uncertainties linked to model predictions (cross sections, mass loss law, overshooting,
Given the large uncertainties linked to model predictions (cross sections, mass loss law, overshooting,
Urea process to be satislied αἱ lower densities due to the increased proton Traction (Prakash 1992).. and depending on their exact concentrations could potentially contribute to the fast cooling of the star throughAyperonie direct. Urea processes (Pageelal.2006)..
Urca process to be satisfied at lower densities due to the increased proton fraction \citep{1992ApJ...390L..77P}, and depending on their exact concentrations could potentially contribute to the fast cooling of the star through direct Urca processes \citep{Page:2005fq}.
These considerations would alter the balance between the curves in Fig.
These considerations would alter the balance between the curves in Fig.
9 and ultimately the results displaced in Fie.
9 and ultimately the results displaced in Fig.
8 in favor of the direct. Urea process. ie. smaller masses and hieher frequencies would be necessary (o close the fast cooling channel.
8 in favor of the direct Urca process, i.e. smaller masses and higher frequencies would be necessary to close the fast cooling channel.