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Future observations and. modelling might put. interesting upper limits on the timescale over which the massive stars [ormed in the GC. and detail the structure and orbit of such a GMCC. | Future observations and modelling might put interesting upper limits on the timescale over which the massive stars formed in the GC, and detail the structure and orbit of such a GMC. |
analysis of the two stars. | analysis of the two stars. |
However. the temperatures adopted are supported by the Balmer lines. and we confirmed the assuned metallicity by computing svuthetic spectra near a few Fe lines with good gf values; | However, the temperatures adopted are supported by the Balmer lines, and we confirmed the assumed metallicity by computing synthetic spectra near a few Fe lines with good $gf$ values. |
We did not explicitly took into account au cnhhancement in Ie in the stellar atmospheres: however. the expected effect on irou abundauce determination is uceleible (seediscussiousinCarettactal.2006:Bra-eachactal.2010) ancl this is most probably true for the other elemeuts. | We did not explicitly took into account an enhancement in He in the stellar atmospheres; however, the expected effect on iron abundance determination is negligible \citep[see discussions in][]{carretta06,bragagliahe} and this is most probably true for the other elements. |
Although we did not do a detailed analysis of other heavy-clemeut species. we noted that lines of c.e.. Ti and Ca have approximately the same streneth iu both stars. | Although we did not do a detailed analysis of other heavy-element species, we noted that lines of e.g., Ti and Ca have approximately the same strength in both stars. |
None of the suggested pollution sources that contribute hydrogseu-burniug products to newly forming stars should contribute elements bevoud $i. | None of the suggested pollution sources that contribute hydrogen-burning products to newly forming stars should contribute elements beyond Si. |
Heasier à oor Fo-peak abuudances should be the same in all NCC 2808 stars. and our spectra do not coutracict this expectation. | Heavier $\alpha$ or Fe-peak abundances should be the same in all NGC 2808 stars, and our spectra do not contradict this expectation. |
Adopting the stellar parameters defined above. we used standard routines to compute svuthetic spectra for some particularly interesting Clements: N Grom the NIJ feature at 3360 A)). Al (from the 3961 rresonant line). Me (from the Mg b lines near 5180 À)). C (from the CII features in the C-band near 1300 Aj). and Na (from the 8183-01 ddoublet). | Adopting the stellar parameters defined above, we used standard routines to compute synthetic spectra for some particularly interesting elements: N (from the NH feature at 3360 ), Al (from the 3961 resonant line), Mg (from the Mg b lines near 5180 ), C (from the CH features in the G-band near 4300 ), and Na (from the 8183-94 doublet). |
The spectral svutheses shown in the figures were computed with the LTE spectroscopic analysis code ROSA (Οτο.1988) for the atomic lines (Al. Me. and Na) and MOOCG (Sueden1973). for the molecules (NIL CTL). | The spectral syntheses shown in the figures were computed with the LTE spectroscopic analysis code ROSA \citep{rosa} for the atomic lines (Al, Mg, and Na) and MOOG \citep{moog} for the molecules (NH, CH). |
However. all the svuthesis work was checked independently using both codes: results are in very good agreement. | However, all the synthesis work was checked independently using both codes; results are in very good agreement. |
Abundances for all eleiieuts are presented in Table 1. | Abundances for all elements are presented in Table \ref{info}. |
The derived values have conservative error estinates (anostlv due to the uncertain coutimmiun placement) of 0.1 dex for Na (and Fe). aud 0.2 dex for N. €. Ale. and Al. | The derived values have conservative error estimates (mostly due to the uncertain continuum placement) of 0.1 dex for Na (and Fe), and 0.2 dex for N, C, Mg, and Al. |
We stress however that the main result of our analysis les in the between the abundance patterns of the two stars. moro than in the absolute values for the chemical abundances. | We stress however that the main result of our analysis lies in the between the abundance patterns of the two stars, more than in the absolute values for the chemical abundances. |
We will show that the light-clemeut differcuces between rMS-star aud bMS-star exceed their uncertainties. | We will show that the light-element differences between rMS-star and bMS-star exceed their uncertainties. |
Comparison of observed and svuthetie spectra are shown Fie. | Comparison of observed and synthetic spectra are shown in Fig. |
2 for NTT. Ali. CIL and Ale features. | \ref{synth} for NH, Al, CH, and Mg features. |
Frou the closestin observed/svuthetic matches we estimated the abuudances that are given in Table 1.. | From the closest observed/synthetic matches we estimated the abundances that are given in Table \ref{info}. |
The expectations are that N and Al should be increased. and C aud Ale should be decreased i bMS-star with respect to he values for rMS-star (tle one of supposedly.normal. xumnordial composition). following what has been fouud or evolved RGB stars (e... Ivausetal.2001:Cohen2002:Ramirez&Cohen2003:Carrettaetal. 20 | The expectations are that N and Al should be increased, and C and Mg should be decreased in bMS-star with respect to the values for rMS-star (the one of supposedly, primordial composition), following what has been found for evolved RGB stars (e.g., \citealt{ivans01,cohen02,rc03,carretta09b}) ). |
095). | Fig. |
Fie. 2. demoustrates that the two stars have different ight-clement spectra. | \ref{synth} demonstrates that the two stars have different light-element spectra. |
This is most obvious for N: the NID absorption is mich stronger m bMS-star than iu rMS-star. | This is most obvious for N: the NH absorption is much stronger in bMS-star than in rMS-star. |
Neither details iu the spectimm normalization ror (πια) differences iu the atinosphlierie parameters cau account for this difference. | Neither details in the spectrum normalization nor (small) differences in the atmospheric parameters can account for this difference. |
The Al abundance was derived ouly from the 3961 rresonance line. since its doublet partner at 3011 jis a blend (Arpiguy&Magaiu 1983). | The Al abundance was derived only from the 3961 resonance line, since its doublet partner at 3944 is a blend \citep{arpigny83}. |
. The svuthesis was computed acopting the Ca abundance appropriate for NGC 2808 (|Ca/Fe|2|0.31. Carrettaetal.200953) to reproduce the Ca II EK lines. | The synthesis was computed adopting the Ca abundance appropriate for NGC 2808 ([Ca/Fe]=+0.34, \citealt{carretta09b}) ) to reproduce the Ca H K lines. |
The values for Al and Me given in Table 1 are corrected for NLTE effects according to (ιοποetal.(2001): the corrections are about |0.5 dex for Aland |0.06 dex for Me. respectively. cor both stars. | The values for Al and Mg given in Table \ref{info} are corrected for NLTE effects according to \cite{gehren04}; the corrections are about +0.5 dex for Al and +0.06 dex for Mg, respectively, for both stars. |
The huge abundance of N found for bDATS-stay (which also had decreased €) can be explained oulv with the ransformiation of (virtually) all oxvecn iuto nitrogen. | The huge abundance of N found for bMS-star (which also had decreased C) can be explained only with the transformation of (virtually) all oxygen into nitrogen. |
Our findines sccm to indicate that we are secing. iu he eas from which this star formed. the outcome of he complete CNO cvele. | Our findings seem to indicate that we are seeing, in the gas from which this star formed, the outcome of the complete CNO cycle. |
Actually. if we combine the C/Fe] and [N/Fo] values of Table 1. with the solar C. N. and O abuudances by Asplundetal.(2009) and with the maximum |O/Fe] ratio for RGB stars in NGC 2808 (Carrettaetal.2006)). even large depletions of O 'Fe|«1) cannot reproduce a coustaut sui of the(o CNO eleiieuts | Actually, if we combine the [C/Fe] and [N/Fe] values of Table \ref{info} with the solar C, N, and O abundances by \cite{asplund09} and with the maximum [O/Fe] ratio for RGB stars in NGC 2808 \citealt{carretta06}) ), even large depletions of O $<-1$ ) cannot reproduce a constant sum of the CNO elements. |
This would be reproduced by assuning [N/Fe|-1.1 for bMS-star. | This would be reproduced by assuming $\sim 1.4$ for bMS-star. |
We uote that a systematic offset of ~0.6 dex in N abunudauces from our analysis would produce a roughly solar scaled [N/Fe] ratio for rMS-stir. which would agree fairly well with the values usually asstuned for feld halo stars (Crattouetal. 2000)). | We note that a systematic offset of $\sim 0.6$ dex in N abundances from our analysis would produce a roughly solar scaled [N/Fe] ratio for rMS-star, which would agree fairly well with the values usually assumed for field halo stars \citealt{gratton00}) ). |
Ouce again. what is most important is the difference between the derived: abundauces. aud this is a sound result. | Once again, what is most important is the difference between the derived abundances, and this is a sound result. |
Unufortunatelv. it was not possihle to iueasure OQ abundances for these two stars. since the O triplet at τπτ]τπτ lis weak and falls in a waveleneth region where the sky subtraction is difficult for these very faint objects. | Unfortunately, it was not possible to measure O abundances for these two stars, since the O triplet at 7771-7774 is weak and falls in a wavelength region where the sky subtraction is difficult for these very faint objects. |
However. we were able to estimate the Na abundances. | However, we were able to estimate the Na abundances. |
Fie. | Fig. |
5 shows observed aud svuthetic spectra surroundiug the 5152-01 NNa lines. | \ref{na} shows observed and synthetic spectra surrounding the 8183-94 Na lines. |
We see in the figure that the Na lines are stronger iu bMS-star than in rMS-star and this is reflected iu the abundance ratios indicated im Table | | We see in the figure that the Na lines are stronger in bMS-star than in rMS-star and this is reflected in the abundance ratios indicated in Table \ref{info}. |
These abundances inclide NLTE corrections (about -0.1 dex) as reccomended by Crattonetal.(1999). | These abundances include NLTE corrections (about -0.1 dex) as reccomended by \cite{gratton99}. |
. The chief lanitation is the stroug telhwic-line contamination in this spectral region. | The chief limitation is the strong telluric-line contamination in this spectral region. |
The tellurics were climinated by division of the program star spectra with that of a hot. rapidly rotating star. using an IRAF routine for this task. | The tellurics were eliminated by division of the program star spectra with that of a hot, rapidly rotating star, using an IRAF routine for this task. |
The cleaning quality is much better for the bluest of the two lines. so that our Na abundances rest ou that suele feature. | The cleaning quality is much better for the bluest of the two lines, so that our Na abundances rest on that single feature. |
They are qualitatively confirmed by the other line and by the relative streneths of the Na D lues; | They are qualitatively confirmed by the other line and by the relative strengths of the Na D lines. |
Unfortunately. strong interstellar absorption aud sky enussion made the derivation of Na abundance from the D lines less secure. given the radial velocity at the time of observation and the moderate resolution of the N-shooter spectra. | Unfortunately, strong interstellar absorption and sky emission made the derivation of Na abundance from the D lines less secure, given the radial velocity at the time of observation and the moderate resolution of the X-shooter spectra. |
The present Al and Meg results are in good agreement with those found from high resohition UVES spectra of 12 red giauts im NGC 2808 bv Carrettaetal.(2009)b). | The present Al and Mg results are in good agreement with those found from high resolution UVES spectra of 12 red giants in NGC 2808 by \cite{carretta09b}. |
. Iu Fig. | In Fig. |
6 we plot the Me-Al auticorrelatiou for the RGB stars and the two MS stars analyzed here. | \ref{almg} we plot the Mg-Al anticorrelation for the RGB stars and the two MS stars analyzed here. |
Apart from a possible small zero-point effect due to the use of differeut lues. corrections for NLTE. ete.. | Apart from a possible small zero-point effect due to the use of different lines, corrections for NLTE, etc., |
the two AIS stars do uicely participate in the same treud defined by the giauts. | the two MS stars do nicely participate in the same trend defined by the giants. |
The £MS and the bMS star fall iu the Mevich/Al-poor and Me-poor/Alvich groups. respectively. | The rMS and the bMS star fall in the Mg-rich/Al-poor and Mg-poor/Al-rich groups, respectively. |
This result indicates that the extreme abundance pattern of the | This result indicates that the extreme abundance pattern of the |
when the Lorentz factor of the ejecta drops toκ1/8. the edge of the jet becomes visible. | when the Lorentz factor of the ejecta drops to$\gamma < 1/ \theta$, the edge of the jet becomes visible. |
Phus the light curve will steepen by £75, where f is the observed time. | Thus the light curve will steepen by $t^{-3/4}$ where $t$ is the observed time. |
This is called the edge ellect (Mésszárros Rees 1999). | This is called the edge effect (Mésszárros Rees 1999). |
Another ellect is called the lateral expansion effect. | Another effect is called the lateral expansion effect. |
1ο.joacls (1997. 19992. b) has shown that the lateral expansion (at sound speed) of a relativisticjet (5,2 2) will cause the blastwave to decelerate more quickly. leading to a sharp break in the afterglow light curve. | Rhoads (1997, 1999a, b) has shown that the lateral expansion (at sound speed) of a relativistic jet $\gamma \geq 2$ ) will cause the blastwave to decelerate more quickly, leading to a sharp break in the afterglow light curve. |
The breaking point is again determined by 5ον1/6. | The breaking point is again determined by $\gamma \sim 1/\theta$. |
The power law decay indices of afterglows from CGIUS 9080326 and 980519 are anomalously large. a~2.0 (Ciroot et al. | The power law decay indices of afterglows from GRB 980326 and 980519 are anomalously large, $\alpha \sim 2.0$ (Groot et al. |
1908: Owens et al. | 1998; Owens et al. |
1998: Halpern et al. | 1998; Halpern et al. |
1999). and optical light curves of GRB 990123 and 990510 even show obvious steepening at {51 2 d (Ixulkarni et al. | 1999), and optical light curves of GRB 990123 and 990510 even show obvious steepening at $t \geq 1$ — 2 d (Kulkarni et al. |
1999: Harrison et al. | 1999; Harrison et al. |
1999: C'astro-Tirado et al. | 1999; Castro-Tirado et al. |
1999). | 1999). |
Recently GRB 970228 was also reported to have a large index of à1.73 (Calama et al. | Recently GRB 970228 was also reported to have a large index of $\alpha \sim 1.73$ (Galama et al. |
1999b3. | 1999b). |
Phese phenomena have been widely regarded as evidence for relativistic jets (Sari. Piran Llalpern 1999). | These phenomena have been widely regarded as evidence for relativistic jets (Sari, Piran Halpern 1999). |
llowever. numerical studies of some other authors (Panaitescu Mésszárros 1998: Mocerski. Sikora Bulik 1999) have shown that due to the increased swept-up matter and the time delay of the large angle emission. the sidewavy expansion of the jet does not lead to an obvious cdimming of the afterglow. | However, numerical studies of some other authors (Panaitescu Mésszárros 1998; Moderski, Sikora Bulik 1999) have shown that due to the increased swept-up matter and the time delay of the large angle emission, the sideway expansion of the jet does not lead to an obvious dimming of the afterglow. |
Thus there are two opposite conclusions about the jet ellect: the analytical solution preclicts a sharp break. while the numerical calculation shows no such sharp breaks. | Thus there are two opposite conclusions about the jet effect: the analytical solution predicts a sharp break, while the numerical calculation shows no such sharp breaks. |
The condition is quite confusing. | The condition is quite confusing. |
We need to clarify this question urgently. | We need to clarify this question urgently. |
In a recent paper (lluang et al. | In a recent paper (Huang et al. |
1999c). we have developed a. refined: model to describe the evolution. of jetted GARB remnants. | 1999c), we have developed a refined model to describe the evolution of jetted GRB remnants. |
Due. to some crucial refinemoents in the dynamics. we can follow the overall evolution of a realistic jet till its expanding velocity is as small as ~10c. | Due to some crucial refinements in the dynamics, we can follow the overall evolution of a realistic jet till its expanding velocity is as small as $\sim 10^{-3} c$. |
Many new results were obtained in that paper. e.g.. (1) We found no obvious break in the optical light curve duringilself. ie. the time determined winc10 is not a breaking point. | Many new results were obtained in that paper, e.g., (i) We found no obvious break in the optical light curve during, i.e. the time determined by $\gamma \sim 1/\theta$ is not a breaking point. |
But in some cases. obvious breaks does appear at the relativistic-Newtonian ransition point. ( | But in some cases, obvious breaks does appear at the relativistic-Newtonian transition point. ( |
i) Cenerally speaking. the Newtonian hase of jet evolution is characterized by a sharp decay. of optical afterglows. with the power law timing index àcL8 2.1.. | ii) Generally speaking, the Newtonian phase of jet evolution is characterized by a sharp decay of optical afterglows, with the power law timing index $\alpha \geq 1.8$ — $2.1$. |
The most interesting finding may be that whether he relativistic-Newtonian break appears or not depends on £.. the parameter characterizing the energy. equipartition oetween electrons and protons. | The most interesting finding may be that whether the relativistic-Newtonian break appears or not depends on $\xi_{\rm e}$, the parameter characterizing the energy equipartition between electrons and protons. |
This has given strong hints on the solution to the confusing problem. mentioned just above: whether an obvious break appears or not may depend On parvanietCrs. | This has given strong hints on the solution to the confusing problem mentioned just above: whether an obvious break appears or not may depend on parameters. |
In this paper. we go further to investigate what impact will other parameters have on the optical light curves. based on the model developed. by Huang et al. ( | In this paper, we go further to investigate what impact will other parameters have on the optical light curves, based on the model developed by Huang et al. ( |
19996). | 1999c). |
The organization of the paper is as follows. | The organization of the paper is as follows. |
For completeness. the model is briellv. described in Section 2. | For completeness, the model is briefly described in Section 2. |
ln Section 3 we investigate various parameter effects. ancl present. our detailed numerical results. mainly in the form of optical light curves. | In Section 3 we investigate various parameter effects and present our detailed numerical results, mainly in the form of optical light curves. |
We find that the light curve break is really alfected by many other parameters. | We find that the light curve break is really affected by many other parameters. |
Section 4 is our final conclusion. and Section 5 is a brief discussion. | Section 4 is our final conclusion, and Section 5 is a brief discussion. |
We use the model developed by Luang ct al. ( | We use the model developed by Huang et al. ( |
19996). | 1999c). |
"Ehis model has the following advantages: (i) Lt is applicable to th radiative and acdiabatie blastwaves. and appropriate for roth ultra-relativistic and non-relativistic stages. | This model has the following advantages: (i) It is applicable to both radiative and adiabatic blastwaves, and appropriate for both ultra-relativistic and non-relativistic stages. |
“Phe mocel even allows the radiative ellicieney € to evolve with time. so hat it can trace the evolution of a realistic GRB remnant. which is believed to evolve from the highly raciative regime o the adiabatic one (Dai. Huang Lu 1999). ( | The model even allows the radiative efficiency $\epsilon$ to evolve with time, so that it can trace the evolution of a realistic GRB remnant, which is believed to evolve from the highly radiative regime to the adiabatic one (Dai, Huang Lu 1999). ( |
ii) Lt takes he lateral expansion of the jet into account. | ii) It takes the lateral expansion of the jet into account. |
The lateral speed is given by a reasonable expression. ( | The lateral speed is given by a reasonable expression. ( |
ii) Lt also akes many other ellects into account. for example. the cooling of electrons. ancl the equal arrival time surfaces. | iii) It also takes many other effects into account, for example, the cooling of electrons, and the equal arrival time surfaces. |
Vhe model is very convenient for numerical studies. | The model is very convenient for numerical studies. |
Llere. or completeness. we describe the model briellv. | Here, for completeness, we describe the model briefly. |
For details ease see Huang et al. ( | For details please see Huang et al. ( |
19996). | 1999c). |
Let & be the radial coordinate in the burster frame: / be the observer's time: συ and M. be the initial Lorentz factor and ejecta mass and ϐ the half opening angle of the ejecta. | Let $R$ be the radial coordinate in the burster frame; $t$ be the observer's time; $\gamma_0$ and $M_{\rm ej}$ be the initial Lorentz factor and ejecta mass and $\theta$ the half opening angle of the ejecta. |
The burst energy is Ly=59M. | The burst energy is $E_0 = \gamma_0 M_{\rm ej} c^2$. |
The evolution of radius (2). the swept-up mass (m). the half opening angle (0) and the Lorentz factor (5) is described by (Lluane et al. | The evolution of radius $R$ ), the swept-up mass $m$ ), the half opening angle $\theta$ ) and the Lorentz factor $\gamma$ ) is described by (Huang et al. |
19996): where 3=VERl/s. n is the number density of surrounding interstellar medium.(18M). my is the mass of proton. e is the co-moving lateral radius of the ejecta (Rhoacs 1999a: Moderski. Sikora Bulik 1999). ος is the co-moving sound speed. and ο is the radiative efficiency. | 1999c): where $\beta = \sqrt{\gamma^2-1}/\gamma$, $n$ is the number density of surrounding interstellar medium(ISM), $m_{\rm p}$ is the mass of proton, $a$ is the co-moving lateral radius of the ejecta (Rhoads 1999a; Moderski, Sikora Bulik 1999), $c_{\rm s}$ is the co-moving sound speed, and $\epsilon$ is the radiative efficiency. |
A reasonable expression for ὃς is where 4z(45|1)/(35) is the acliabatic index. | A reasonable expression for $c_{\rm s}$ is where $\hat{\gamma} \approx (4 \gamma + 1)/(3 \gamma)$ is the adiabatic index. |
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