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In Section 2 a description of the RAIC method and the oocedure to test its validity are given. while in Section 3 he method is applied to analyze an observed H1D. Lye spectrum. | In Section 2 a description of the RMC method and the procedure to test its validity are given, while in Section 3 the method is applied to analyze an observed H+D $\alpha$ spectrum. |
The results obtained are summarized in Section EN | The results obtained are summarized in Section 4. |
The ΗΛΙΟ method. belongs to the class. of stochastic optimization algorithms developed: to solve optimization problems with a very large number of free. parameters. | The RMC method belongs to the class of stochastic optimization algorithms developed to solve optimization problems with a very large number of free parameters. |
Contrary to the standard Monte-Carlo procedure in which random configurations of a given physical svstem are eenerated to estimate its average characteristies. the RAC takes an experimentally determined. set of data and searches fora parameter configuration which reproduces the observational cata. | Contrary to the standard Monte-Carlo procedure in which random configurations of a given physical system are generated to estimate its average characteristics, the RMC takes an experimentally determined set of data and searches for a parameter configuration which reproduces the observational data. |
The inverse problem is always an optimization problem in which an objective function is minimized. | The inverse problem is always an optimization problem in which an objective function is minimized. |
The objective function defined. over a space of very Lage dimension is known to have many local minima. | The objective function defined over a space of very large dimension is known to have many local minima. |
Therefore optimization moethocs based on the choice of minimization direction (so-called. gracient methods) may. fail because of the possibility of being trapped in one of such minima. | Therefore optimization methods based on the choice of `minimization direction' (so-called gradient methods) may fail because of the possibility of being trapped in one of such minima. |
The RALC approach allows to overcome this problem. | The RMC approach allows to overcome this problem. |
It can get over the local minima because i does not use any concept of "direction. | It can get over the local minima because it does not use any concept of `direction'. |
Applied to the analysis of absorption spectra. the RALC method mav be formulated as follows. | Applied to the analysis of absorption spectra, the RMC method may be formulated as follows. |
The total parameter space consisting of the physical parameters (like IN.μι ete.) | The total parameter space consisting of the physical parameters (like $N, T_{kin},$ etc.) |
and the velocity components p; parallel to the line of sight at the individual positions 5j. is divided into two subspaces. | and the velocity components $v_j$ parallel to the line of sight at the individual positions $s_j$, is divided into two subspaces. |
Let O=[6] represent the subspace of physical parameters [N.LerorfenL/h. | Let $\Theta = \{\hat \theta\}$ represent the subspace of physical parameters $N, T_{kin}, \sigma_t/v_{th}, L/l$. |
For the special case of I}D Lye that we want to investigate. ὁ has to have one additional component D/II.— the ratio of the DI to Ill column densities. | For the special case of H+D $\alpha$ that we want to investigate, ${\hat \theta}$ has to have one additional component D/H – the ratio of the DI to HI column densities. |
Let further (6)=frye...Uy) be the veetor of the velocity components parallel to the line of sight at the spatial | Let further $\{{\hat v}\} = \{v_1, v_2, \ldots, v_{k}\}$ be the vector of the velocity components parallel to the line of sight at the spatial |
Montreal (Michaud et al. | Montreal (Michaud et al. |
2004). Padova (Yadav et al. | 2004), Padova (Yadav et al. |
2008). Teramo (Bellini et al. | 2008), Teramo (Bellini et al. |
2010). Victoria (VandenBerg et al. | 2010), Victoria (VandenBerg et al. |
2007). or Yale-Yonsei (Yadav et al.) | 2007), or Yale-Yonsei (Yadav et al.) |
isochrones. favour an age of 1.00.3 Gyr. | isochrones, favour an age of $4.0\pm 0.3$ Gyr. |
Moreover. Bellini et al. | Moreover, Bellini et al. |
have recently found that the age obtained from the cluster white dwarfs is fully consistent with the aforementioned turnoff age. | have recently found that the age obtained from the cluster white dwarfs is fully consistent with the aforementioned turnoff age. |
However. higher ages cannot yet be completely excluded (see examples provided by Yadav et al. | However, higher ages cannot yet be completely excluded (see examples provided by Yadav et al. |
and Magic et al.). | and Magic et al.). |
We note that the solar age is within the 20 error bar of M67's age. | We note that the solar age is within the $2\sigma$ error bar of M67's age. |
Our main finding. illustrated in Fig. 7.. | Our main finding, illustrated in Fig. \ref{fig:diff}, |
is that M67-1194 is indeed more similar to the Sun than most of the nearby solar twins in the field. | is that M67-1194 is indeed more similar to the Sun than most of the nearby solar twins in the field. |
This is interesting in view of the possible explanations for the systematic departures of the field twin from the Sun in abundances with condensation temperature. found and discussed by Melénndez et al. ( | This is interesting in view of the possible explanations for the systematic departures of the field twin from the Sun in abundances with condensation temperature, found and discussed by Melénndez et al. ( |
2009. see also Gustafsson et 22010). | 2009, see also Gustafsson et 2010). |
Basically. three possible explanations were discussed: (1) The solar proto-planetary gas disk was sufficiently long-lived. after the gas had been depleted in refractories by the formation of planetesimals and planets. for the solar convection zone to become so thin that the accreted gas could give visible traces in the solar spectrum. | Basically, three possible explanations were discussed: (1) The solar proto-planetary gas disk was sufficiently long-lived, after the gas had been depleted in refractories by the formation of planetesimals and planets, for the solar convection zone to become so thin that the accreted gas could give visible traces in the solar spectrum. |
The field twins. however. in general accreted their gas disks much earlier. ( | The field twins, however, in general accreted their gas disks much earlier. ( |
2) The solar outer convection zone never reached deep enough to encompass most of the solar mass. and was therefore much more easily polluted by the rarified infalling disk. | 2) The solar outer convection zone never reached deep enough to encompass most of the solar mass, and was therefore much more easily polluted by the rarified infalling disk. |
This property of the Sun. presumably reflecting the initial conditions of the cloud to later form the Sun and the Solar System or the details of the more or less episodic accretion history of the Sun (cf. | This property of the Sun, presumably reflecting the initial conditions of the cloud to later form the Sun and the Solar System or the details of the more or less episodic accretion history of the Sun (cf. |
Baraffe Chabrier 2010). was not usual among solar-type stars and is thus not shared by most twins. ( | Baraffe Chabrier 2010), was not usual among solar-type stars and is thus not shared by most twins. ( |
3) The proto-solar cloud was cleansed by radiation fields from massive stars. pushing dust grains out of the cloud. | 3) The proto-solar cloud was cleansed by radiation fields from massive stars, pushing dust grains out of the cloud. |
These effects must then have been greater for the solar cloud than for most of the twins. | These effects must then have been greater for the solar cloud than for most of the twins. |
If the tendency found here for our M67 twin is representative for the cluster. it speaks against the first explanation above. | If the tendency found here for our M67 twin is representative for the cluster, it speaks against the first explanation above. |
We see no reason why the gas disks around stars in a cluster should have longer life-times than those in the field. | We see no reason why the gas disks around stars in a cluster should have longer life-times than those in the field. |
It might be that the initial conditions of star formation are different in a cluster than in the field. and that this might couple to the evolution of the stellar convection zones. but this is only speculation. | It might be that the initial conditions of star formation are different in a cluster than in the field, and that this might couple to the evolution of the stellar convection zones, but this is only speculation. |
Maybe. à more episodic accretion history. gradually building stars from quite small entities. 15 more characteristic of cluster environment. | Maybe, a more episodic accretion history, gradually building stars from quite small entities, is more characteristic of cluster environment. |
In any case. there is independent evidence from radioisotopic abundances in the solar system that the Sun was born in a cluster (Looney et al. | In any case, there is independent evidence from radioisotopic abundances in the solar system that the Sun was born in a cluster (Looney et al. |
2006. see also Portegies Zwart. 2009) containing relatively close supernovae or massive AGB stars (Trigo-Rodrigguez et al. | 2006, see also Portegies Zwart, 2009) containing relatively close supernovae or massive AGB stars (Trigo-Rodrígguez et al. |
2009). | 2009). |
The similarity of the age and overall composition of the Sun with the corresponding data of M67. and in particular the agreement of the detailed chemical composition of the Sun with that of M67-1194. could suggest that the Sun has formed in this very cluster. | The similarity of the age and overall composition of the Sun with the corresponding data of M67, and in particular the agreement of the detailed chemical composition of the Sun with that of M67-1194, could suggest that the Sun has formed in this very cluster. |
According to the numerical simulations by Hurley et al. ( | According to the numerical simulations by Hurley et al. ( |
2005) the cluster has lost more than of its stars by tidal interaction with the Galaxy. m particular when passing the Galactic plane. and the Sun might be one of those. | 2005) the cluster has lost more than of its stars by tidal interaction with the Galaxy, in particular when passing the Galactic plane, and the Sun might be one of those. |
We note that the orbit of the cluster encloses. within its apocentre and pericentre. the solar orbit. | We note that the orbit of the cluster encloses, within its apocentre and pericentre, the solar orbit. |
However. the | However, the |
of the new abundances. | of the new abundances. |
The case of 3.2.. tthe one with full consideration of diffusion. was§ also extended by iucliding overshooting in the tracks for AIG7. | The case of \ref{s:calib}, the one with full consideration of diffusion, was also extended by including overshooting in the tracks for M67. |
We refrain frou showing the result here. as for both mixtures the convective core. as expected. persisted. but the overall fit got worse. | We refrain from showing the result here, as for both mixtures the convective core, as expected, persisted, but the overall fit got worse. |
This coincides with the isochrone fit shown by Pietriuferuietal.(200 1).. where the CMD could be better reproduced if overshooting was completely ignored. | This coincides with the isochrone fit shown by \citet{pietr:04}, where the CMD could be better reproduced if overshooting was completely ignored. |
It agrees also with Michaud.etal.(2001).. who neither found auv necessity for overshooting. and who. too. did iuclude diffision in their models. | It agrees also with \citet{mrrv:2004}, who neither found any necessity for overshooting, and who, too, did include diffusion in their models. |
As mentioned above. the nuclear reaction rates of the CNO-cevele are equally important for the occurrence of a convective core as is the abuucdanuce of CNO-uuclei. | As mentioned above, the nuclear reaction rates of the CNO-cycle are equally important for the occurrence of a convective core as is the abundance of CNO-nuclei. |
So fay we have prescuted models cuploving the NACRE-library reaction rates for these reactions. | So far we have presented models employing the NACRE-library reaction rates for these reactions. |
The bottleneck reaction of the CNO-cvcle. LINGp.51Ο. that determines the overall evele rate; has been measured at stellar energies in the laboratory by the LUNA collaboration (Formucolaetal.2001:Marta2008)... and was found to be lower bv about with respect to the NACRE rate. | The bottleneck reaction of the CNO-cycle, $\Iso{14}{N}(p,\gamma)\Iso{15}{O}$, that determines the overall cycle rate, has been measured at stellar energies in the laboratory by the LUNA collaboration \citep{lunan14:04,mfn14:2008}, and was found to be lower by about with respect to the NACRE rate. |
The consequences for elobular cluster age deteriiuations aud for some seusitive phases of low- aud interimediate-nass star evolution has been investigated by Tuibrianietal.(2001) and Weissetal.(2005). | The consequences for globular cluster age determinations and for some sensitive phases of low- and intermediate-mass star evolution has been investigated by \citet{icfbb:04} and \citet{wskschcd:2005}. |
. The rate being lower. we expect that the transition mass to harboriug a convective core increases; | The rate being lower, we expect that the transition mass to harboring a convective core increases. |
Therefore isochroucs using the lower CNO-abundauces of the AGSO5 nüxtures will be even less Likely to show the TO hook. | Therefore isochrones using the lower CNO-abundances of the AGS05 mixtures will be even less likely to show the TO hook. |
We repeated the case of 3.1 Henorie diffusion completely) with the updated aud most likely more accurate rate by Martaetal.(2008). | We repeated the case of \ref{s:repro} ignoring diffusion completely) with the updated and most likely more accurate rate by \citet{mfn14:2008}. |
. The resulting CMD for M67. using again our standard distance modulus aud reddening is shown in Figure |... | The resulting CMD for M67, using again our standard distance modulus and reddening is shown in Figure \ref{f:vg07n14}. |
Tn agreement with hubrianietal.(2001). the isochrone age had to be increased (by. 0.3 Cr for both mixtures) and Adee. iucreased bv =OOSM. du both cases, | In agreement with \citet{icfbb:04} the isochrone age had to be increased (by 0.3 Gyr for both mixtures) and $M_\mathrm{ccc}$ increased by $\approx
0.08\,M_\odot$ in both cases. |
As a consequence also the (1905 case now lacks the characteristic hook. | As a consequence also the GS98 case now lacks the characteristic hook. |
We add briefiv that the inclusion of overshooting docs not alter this result because the ecolctric cutoff is restrictive enough that the convective reeion formed at the cud of the preanuain sequence phase can not be maintained during the maim sequence evolution. | We add briefly that the inclusion of overshooting does not alter this result because the geometric cutoff is restrictive enough that the convective region formed at the end of the pre-main sequence phase can not be maintained during the main sequence evolution. |
The values for Af... ave 1.215 (CS98) and 1.258 (AGSO5). those at the TO 1.202 11.196 AL... | The values for $M_\mathrm{ccc}$ are 1.215 (GS98) and 1.258 (AGS05), those at the TO 1.202 1.196 $M_\odot$. |
This illustrates the fundamental problem with such tests: Tagine we would assume that the GS98 solar composition is the correct one. but we want to test which reaction rate is to be preferred. | This illustrates the fundamental problem with such tests: Imagine we would assume that the GS98 solar composition is the correct one, but we want to test which reaction rate is to be preferred. |
From Figures. | From Figures. |
d aud we would clearly conclude that the older oue is to be preferred! | \ref{f:vgrep} and \ref{f:vg07n14} we would clearly conclude that the older one is to be preferred! |
We now repeat the computation of 3.2.. tthe case with diffusion included. but with the§ newer aud lower UN(p.-YO reaction rate. | We now repeat the computation of \ref{s:calib}, the case with diffusion included, but with the newer and lower $\Iso{14}{N}(p,\gamma)
\Iso{15}{O}$ reaction rate. |
Iu this case we recognize that with the older solar composition a siall couvective core is present Mí = 1.211/1.172). which is completely absent in the ACGS05 case (L.201/1.2 AL). | In this case we recognize that with the older solar composition a small convective core is present $M_\mathrm{ccc}$ = 1.214/1.172), which is completely absent in the AGS05 case (1.201/1.241 $M_\odot$ ). |
While the CMD fit is not very good even with the CS98 isochrone. it can be improved by includiug overshootiug. | While the CMD fit is not very good even with the GS98 isochrone, it can be improved by including overshooting. |
The results. iucliding overshooting with the geometric | The results, including overshooting with the geometric |
PrayDd ds about 6. | $\nu_{ran}\ge 4$ is about $6$. |
The existence of intrinsic alignments enhances the average number of false peaks. | The existence of intrinsic alignments enhances the average number of false peaks. |
If the 48 dark peaks are all false ones and the number is +lo [rom the average ΠΠΟΥ of false peaks. we need the average number to be IN,42. | If the $48$ dark peaks are all false ones and the number is $+1\sigma$ from the average number of false peaks, we need the average number to be $N_{peak}\sim 42$. |
Then we have to have σοι.Tamanv39% Vo get such a high number of false peaks. | Then we have to have $\sigma^2_{0corr}/\sigma^2_{0ran}\sim 35\%$ to get such a high number of false peaks. |
For the redshift distribution of source galaxies. Schirmer et al. ( | For the redshift distribution of source galaxies, Schirmer et al. ( |
2007) give a=2. 2=1.5 and z;=0.4 for shallow survevs. | 2007) give $\alpha=2$, $\beta=1.5$ and $z_s=0.4$ for shallow surveys. |
The surface number density i5 n,~12arcimin?. and o,~0.48 (Schirmer et al. | The surface number density is $n_g\sim 12\hbox{ arcmin}^{-2}$, and $\sigma_{\epsilon}\sim 0.48$ (Schirmer et al. |
2007). | 2007). |
We then estimate o7,Oran~0.0015. | We then estimate $\sigma^2_{0ran}\sim 0.0015$. |
Thus the ralio στΟσο)fotOranc35%. requires the parameter «1 to be A~32. which is much higher than the constraint 4<1.29 from SDSS. | Thus the ratio $\sigma^2_{0corr}/\sigma^2_{0ran}\sim 35\%$ requires the parameter $A$ to be $A\sim 32$, which is much higher than the constraint $A\le 1.29$ from SDSS. |
Therefore 1 15 verv unlikely that (he 48 dark peaks are all false ones [rom intrinsic ellipticitlies of background galaxies. | Therefore it is very unlikely that the $48$ dark peaks are all false ones from intrinsic ellipticities of background galaxies. |
As we discussed previously and also in Schirmer et al. ( | As we discussed previously and also in Schirmer et al. ( |
2007). the joint effects of small mass chuups and the intrinsic ellipticities could contribute significantly (o (he mmuber of dark peaks with hieh significance. | 2007), the joint effects of small mass clumps and the intrinsic ellipticities could contribute significantly to the number of dark peaks with high significance. |
It should be pointed out that the Muectional form and the scale of the filtering hanction adopted by Sehirmer et al. ( | It should be pointed out that the functional form and the scale of the filtering function adopted by Schirmer et al. ( |
2007) are optimized to detect clusters with NEW clensity profiles. | 2007) are optimized to detect clusters with NFW density profiles. |
With Gaussian smoothings. (he number of peaks and their properties may change quantitatively, | With Gaussian smoothings, the number of peaks and their properties may change quantitatively. |
It is therefore desirable (ο analyze the observations wilh Gaussian smoothines so (hat we can perform detailed aualvses on the statistics of false peaks. | It is therefore desirable to analyze the observations with Gaussian smoothings so that we can perform detailed analyses on the statistics of false peaks. |
On (he other hand. it is also worthwhile investigating the noise properties and the associated statistics of false peaks under different smoothing schemes. | On the other hand, it is also worthwhile investigating the noise properties and the associated statistics of false peaks under different smoothing schemes. |
As the catalog of Schirmer et al. ( | As the catalog of Schirmer et al. ( |
2007) is the largest one so Eur. from many aspects careful observational ancl theoretical studies on (hese dark peaks are highly valuable. | 2007) is the largest one so far, from many aspects careful observational and theoretical studies on these dark peaks are highly valuable. |
Future survevs wilh larger areas will result many more peaks. | Future surveys with larger areas will result many more peaks. |
If a large number of false peaks from intrinsic ellipticities can be securely identified. we can put tight constraints on the level of intrinsic alignments. | If a large number of false peaks from intrinsic ellipticities can be securely identified, we can put tight constraints on the level of intrinsic alignments. |
Considering Poisson fIncetuations. we can estimate. as follows. how well the quantity =05,,,./06,,, Con be constrained from NV false peaks with vg,71. | Considering Poisson fluctuations, we can estimate, as follows, how well the quantity $x=\sigma^2_{0corr}/\sigma^2_{0ran}$ can be constrained from $N$ false peaks with $\nu_{ran}\ge \nu_0$. |
With the average cunnuative number of peaks IN,Xvexp(—v7/2) lor v> 3. where v is the true significance (e.g.. van Waerbeke 2000). we have. lor the central value of 2. denoted by ass where .N,,,, is (he average number of false peaks expected in (he field without considering intrinsic alignments. | With the average cumulative number of peaks $N_{peak}\propto \nu \exp(-\nu^2/2)$ for $\nu\ge 3$ , where $\nu$ is the true significance (e.g., van Waerbeke 2000), we have, for the central value of $x$, denoted by $x_c$ , where $N_{ran}$ is the average number of false peaks expected in the field without considering intrinsic alignments. |
The tle constraints on ο can then beobtained by | The $\pm 1\sigma$ constraints on $x$ can then beobtained by |
an exact shift (a circular penuutation). the uunerical dissipation has to decrease as the timestep increases. | an exact shift (a circular permutation), the numerical dissipation has to decrease as the timestep increases. |
We show in this section the validity of the modified rausport algorithui when applied to the interaction of a Jupiter sized protoplanet with a nmnuüninmun mass xotoplanetarv disk in which it is cibeccled. | We show in this section the validity of the modified transport algorithm when applied to the interaction of a Jupiter sized protoplanet with a minimum mass protoplanetary disk in which it is embedded. |
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