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We also. thank Orkan Umurhan for helpful discussions and the anonymous referee for helpful suggestions. | We also thank Orkan Umurhan for helpful discussions and the anonymous referee for helpful suggestions. |
C.W. is supported by the Science and Technology Facilities Council (STFC). | C.W. is supported by the Science and Technology Facilities Council (STFC). |
J.Y-K.C. is supported by NASA NNGO4GN82G and STFC PP/E001858/1 | J.Y-K.C. is supported by NASA NNG04GN82G and STFC PP/E001858/1 |
surface mass densities (/ and peo in the prescribed. -7 and η ranges. | surface mass densities $\mu^g$ and $\mu^s$ in the prescribed $\beta$ and $\eta$ ranges. |
For purpose of illustration. we present in Fig. | For purpose of illustration, we present in Fig. |
11 a few solution examples in terms of y=D7) as functions of ‘racial waventunber € for specilie parameters m=2.9 =L/S and 1/4.9=1/4.1l and 4 and η=1 and 5. | 11 a few solution examples in terms of $y\equiv D_s^2)$ as functions of `radial wavenumber' $\xi$ for specific parameters $m=2$, $\beta=-1/8$ and $1/4$, $\delta=1/4,\ 1$ and $4$ and $\eta=1$ and $5$. |
The analvsis presented in this paper is à generalization and extension of the previous work by Sver Tremaine (1996). Shu et al. ( | The analysis presented in this paper is a generalization and extension of the previous work by Syer Tremaine (1996), Shu et al. ( |
2000). Lou Shen (2003) and Shen Lou (2003). | 2000), Lou Shen (2003) and Shen Lou (2003). |
We have constructed. both aligned and. logarithmic spiral. scale-free. coplanar stationary »erturbation configurations in à composite svstem of two eravitationally coupled: discs. | We have constructed both aligned and logarithmic spiral, scale-free, coplanar stationary perturbation configurations in a composite system of two gravitationally coupled discs. |
While highly: idealized. we rave in münd. at least conceptually. is a system of spiral ealaxy consisting of one stellar disc and one gaseous clisc. with a barotropic equation of state. | While highly idealized, we have in mind, at least conceptually, is a system of spiral galaxy consisting of one stellar disc and one gaseous disc, with a barotropic equation of state. |
“Phis problem may hen have relevance to distributions of stellar mass ancl gas materials in a disc galaxy. | This problem may then have relevance to distributions of stellar mass and gas materials in a disc galaxy. |
Qualitativelv. the two branches of solutions derived in this paper suggest two possible coupled yerturbation modes. (not necessarily stationary: see Lou Fan 1998b) where surface mass density perturbations in the stellar disc and in the gaseous disc exhibit either in-phase or out-of-phase correlations. | Qualitatively, the two branches of solutions derived in this paper suggest two possible coupled perturbation modes (not necessarily stationary; see Lou Fan 1998b) where surface mass density perturbations in the stellar disc and in the gaseous disc exhibit either in-phase or out-of-phase correlations. |
These two distinctly different classes of perturbation modes are mathematically allowable. although there might be some kind of prevalence related to initial conditions or other uncertainties. | These two distinctly different classes of perturbation modes are mathematically allowable, although there might be some kind of prevalence related to initial conditions or other uncertainties. |
Lor observational diagnostics of disc galaxies. one can obtain non-axisvnimetric stellar structures in the optical band (c.g. Rix Zaritsky 1995) and derive. maps for the gaseous disc Component (e.g. Richter Sancisi 1994). | For observational diagnostics of disc galaxies, one can obtain non-axisymmetric stellar structures in the optical band (e.g. Rix Zaritsky 1995) and derive maps for the gaseous disc component (e.g. Richter Sancisi 1994). |
οσο wo maps in different wave bands may be compared. to see whether the stellar and. gaseous arms are roughly coincident or apparently. interlaced. | These two maps in different wave bands may be compared to see whether the stellar and gaseous arms are roughly coincident or apparently interlaced. |
The real situation may »v even more complicated than this. | The real situation may be even more complicated than this. |
Active star formation oocesses in the optical arms will further consumeLL gas and the places whereLL gas clumps will trigger. more star formation activities. | Active star formation processes in the optical arms will further consume gas and the places where gas clumps will trigger more star formation activities. |
Depending on the level of these interrelated: processes. a phase shift. between optical arms andHIE arms may not be easily interpreted in terms of the out-of-phase perturbation modes. | Depending on the level of these interrelated processes, a phase shift between optical arms and arms may not be easily interpreted in terms of the out-of-phase perturbation modes. |
Perhaps. the most cogent evidence for out-of-phase. density. perturbations would. be a lopsided disc galaxy where the gaseous and. stellar. disc components are comparable and the Iopsidednesses for the two components are opposite. | Perhaps, the most cogent evidence for out-of-phase density perturbations would be a lopsided disc galaxy where the gaseous and stellar disc components are comparable and the lopsidednesses for the two components are opposite. |
In a broader perspective. the ideal two-Iuid approach adopted here may be applicable to other two-component disc system where the two components can be treated. as ideal Εις with dillerent temperatures. eg. à composite disc system. of stars and. dusts or a composite disc system: composed of voung niassive stars and relatively old stars. or even to composite dise svstems with more components. | In a broader perspective, the ideal two-fluid approach adopted here may be applicable to other two-component disc system where the two components can be treated as ideal fluids with different temperatures, e.g., a composite disc system of stars and dusts or a composite disc system composed of young massive stars and relatively old stars, or even to composite disc systems with more components. |
These different "hot and "cold? [uid disc components are coupled in the overall dise dynamics and contribute to various structures in multi-band observations. | These different `hot' and `cold' fluid disc components are coupled in the overall disc dynamics and contribute to various structures in multi-band observations. |
In order to satisfv the seale-[ree conditions in our model. both the stellar and gaseous clises in an axisvmmetric equilibrium state have rotation curves exrr. and surface mass densities vNyxr1o28 with a /barotropic index n—(1|43)/(122) for the parameter regime of 33(1/4.1/2). | In order to satisfy the scale-free conditions in our model, both the stellar and gaseous discs in an axisymmetric equilibrium state have rotation curves $v\propto r^{-\beta}$ and surface mass densities $\Sigma_0\propto r^{-1-2\beta}$ with a barotropic index $n=(1+4\beta)/(1+2\beta)$ for the parameter regime of $\beta\in(-1/4,1/2)$ . |
For both cases of aligned. ancl logarithmic spiral perturbations. we derive sensible. values of 7. to support such neutral or stationary density wave modes in an inertial frame of reference. | For both cases of aligned and logarithmic spiral perturbations, we derive sensible values of $D_s^2$ to support such neutral or stationary density wave modes in an inertial frame of reference. |
There are two classes. of stationary density wave modes in à composite svstem of two coupled. disces in general: this is in contrast to one class of stationary density wave modes in a single cise svstem. | There are two classes of stationary density wave modes in a composite system of two coupled discs in general; this is in contrast to one class of stationary density wave modes in a single disc system. |
We now summarize our main results below. | We now summarize our main results below. |
(weighted at LO%)) and σο=500 km/s (weighted at )). | (weighted at ) and $\sigma_2 = 500$ km/s (weighted at ). |
Iereafter we refer to this distribution of kicks as the “Arzoumanian kick distribution". | Hereafter we refer to this distribution of kicks as the “Arzoumanian kick distribution”. |
The distinguishing characteristics of the other 9 models are described in Table 2.. | The distinguishing characteristics of the other 9 models are described in Table \ref{table:StartrackModels}. |
With this set of models we vary the values (within reasonable ranges) of a umber of stellar and binary evolution parameters that are known to affect DNS formation sguificautlv. | With this set of models we vary the values (within reasonable ranges) of a number of stellar and binary evolution parameters that are known to affect DNS formation significantly. |
For more information on the specific choices of values for both the standard aud these inodels. see DBelezvuskietal.(2002). | For more information on the specific choices of values for both the standard and these models, see \cite{BKB}. |
. As a possible explanation of the low ecceutricities. it has been suggested that a class of neutron stars forming in DNS systems that received simall-imacuitucdes kicks is responsible for the observed low eccentricitfies (seevauPfahletal.2002:Dewict 2005).. | As a possible explanation of the low eccentricities, it has been suggested that a class of neutron stars forming in DNS systems that received small-magnitudes kicks is responsible for the observed low eccentricities \citetext{see \citealp{vdH}, see also \citealp{Pods,PRPS,Dewi}}. |
To investigate this sugeestion statistically we created another 3 sets of models which cach adopt a differeut NS kick distribution (other than the Arzoumeamian kick distribution): (1) a set of (unplivsical in our opinion) models with zero NS kicks (all SN events are asstumed to be sviunetrie)s (4) a set with a sinele Maxwellian of σ10 Ἐν and (ila set with a sinele Maswellian of σ=5b0klauss |. | To investigate this suggestion statistically we created another 3 sets of models which each adopt a different NS kick distribution (other than the Arzoumanian kick distribution): (i) a set of (unphysical in our opinion) models with zero NS kicks (all SN events are assumed to be symmetric); (ii) a set with a single Maxwellian of $\sigma=10$ $^{-1}$; and (iii) a set with a single Maxwellian of $\sigma=50$ $^{-1}$. |
With hese choices we hope to examine the effect of zero or ow kick magnitudes on DNS orbital ecceutiicities. | With these choices we hope to examine the effect of zero or low kick magnitudes on DNS orbital eccentricities. |
Each of these three kick distributions are adopted for all ten nocels listed in Table 2.. | Each of these three kick distributions are adopted for all ten models listed in Table \ref{table:StartrackModels}. |
We note that the sugeestion im favor of low kicks mace w (vandenIHeuvel2001:Podsiadlowskietal.2001) is connected to NS forming from heliuniaich. progenitors with masses up to 223.5 MM. (ITaichi.progenitorsiuthe 2001). | We note that the suggestion in favor of low kicks made by \citep{vdH,Pods} is connected to NS forming from helium-rich progenitors with masses up to $\simeq 3.5$ $_\odot$ \citep[H-rich progenitors in the mass range $8-13$\,M$_\odot$; for details see][]{Pods}. |
Examination of the οαπο DNS progenitors in all our simulations reveals that the vast majority (typically above and in some cases close to 100543) have masses =23.5 MAL... | Examination of the helium-rich DNS progenitors in all our simulations reveals that the vast majority (typically above and in some cases close to ) have masses $\lesssim 3.5$ $_\odot$. |
Therefore our consideration of models with low kicks for all NS is consistent with the sugecstious by vandeuIeuvel(2001). aud Podsiadlowskietal. (2001). | Therefore our consideration of models with low kicks for all NS is consistent with the suggestions by \citet{vdH} and \citet{Pods}. |
.. Furthermore the models with perfectly sviunietrie explosions provide a clean case that allows us to track the qualitative behavior of DNS ecceutricitics to pre-SN properties. as discussed iu what follows. | Furthermore the models with perfectly symmetric explosions provide a clean case that allows us to track the qualitative behavior of DNS eccentricities to pre-SN properties, as discussed in what follows. |
From the large populations of binarics we evolve. we consider all of the DNS systems formed and focus on the resultant DNS eccentricity distrbution fictions. for each model. | From the large populations of binaries we evolve, we consider all of the DNS systems formed and focus on the resultant DNS eccentricity distrbution functions, for each model. |
We typically ecucrate ~30 DNS for every LO? primordial binaries evolved. though iu some eases 107 primordials will ouly produce a few relevant objects. | We typically generate $\sim30$ DNS for every $10^5$ primordial binaries evolved, though in some cases $10^5$ primordials will only produce a few relevant objects. |
Iu short. generating reliable statistics for a varietv of different models is computationally expeusive and requires mich time aud patience. | In short, generating reliable statistics for a variety of different models is computationally expensive and requires much time and patience. |
We make sure that for cach model considered here we typically have model siuuples of 2.000.3.000 DNS at birth aud at least ~200 DNS for models that have atypically low DNS formation rates (ee. L2. MI). | We make sure that for each model considered here we typically have model samples of $2,000-3,000$ DNS at birth and at least $\sim200$ DNS for models that have atypically low DNS formation rates (e.g., L2, M1). |
In Fies. | In Figs. |
dl and 2 wo present the eccentricity distribution fuuctious at DNS birth for three of the models cousidered i our study. aud for close iud wide DNS. respectively. | \ref{fig:ecoal} and \ref{fig:enon} we present the eccentricity distribution functions at DNS birth for three of the models considered in our study, and for close and wide DNS, respectively. |
Before we proceed with our statistical analysis and comparison to the observed sample. there are a nuniber of qualitative conclusions we cau draw from hese distributions. | Before we proceed with our statistical analysis and comparison to the observed sample, there are a number of qualitative conclusions we can draw from these distributions. |
Iu the case of coalescing DNS (Fie. 1)). | In the case of coalescing DNS (Fig. \ref{fig:ecoal}) ), |
we fud that he eccentricity distributions are clistiuctly different for he models with the Arzowmeaman (standard) kick distribution aud those with zero or low kicks. | we find that the eccentricity distributions are distinctly different for the models with the Arzoumanian (“standard”) kick distribution and those with zero or low kicks. |
In the first case the distribution covers the full range of values up o unity. and for most models it is almost flat across he range. | In the first case the distribution covers the full range of values up to unity, and for most models it is almost flat across the range. |
As kick magnitudes decrease the distributions appear to be restricted to a low range of values. most vpically below ο= (0.6. | As kick magnitudes decrease the distributions appear to be restricted to a low range of values, most typically below $e=0.6$ . |
This behavior appears to ο consistent across all ten binary evolution iuodels. independent of the specific model assuiptions. and it is consisteut with the suggestion made ly vandenHeuvel(2001). that verv siall NS kicks could be responsible for the low ecceutricities in the observed saluple. | This behavior appears to be consistent across all ten binary evolution models, independent of the specific model assumptions, and it is consistent with the suggestion made by \cite{vdH} that very small NS kicks could be responsible for the low eccentricities in the observed sample. |
When supernova explosions are perfectly syauiuetric or have vervsiall kicks (~10δηιν» 1) DNS | When supernova explosions are perfectly symmetric or have verysmall kicks $\sim 10-20$ $^{-1}$ ) DNS |
inhomogeneities on our abundance values. | inhomogeneities on our abundance values. |
The results are shown in Table [8]. | The results are shown in Table \ref{tab:3D}. |
The parameters of the 3D models are not exactly the same as our sample stars, but these calculations provide a rough estimate of the 3D-1D differences and some qualitative conclusions can be drawn: the corrections for the [SI] line seem to grow larger for higher temperatures, larger surface gravity and lower [Fe/H]. | The parameters of the 3D models are not exactly the same as our sample stars, but these calculations provide a rough estimate of the 3D-1D differences and some qualitative conclusions can be drawn: the corrections for the $[\ion{S}{i}] $ line seem to grow larger for higher temperatures, larger surface gravity and lower $\left[\mathrm{Fe}/\mathrm{H}\right]$. |
For our sample stars the 3D corrections for the sulphur abundances as derived from the [S1] line all seem to be around or below -0.1 dex. | For our sample stars the 3D corrections for the sulphur abundances as derived from the $[\ion{S}{i}] $ line all seem to be around or below -0.1 dex. |
The corrections for the triplet, on the other hand, are rather constant for the different 3D models and all seem to be around 40.2 dex. | The corrections for the triplet, on the other hand, are rather constant for the different 3D models and all seem to be around +0.2 dex. |
Our 3D analysis for these sulphur lines is the first for giants, but ? explored the 3D correction for the [S1] line in the Sun and ?? explored the 3D corrections for the 1045 nm triplet in the Sun, Procyon and four other dwarfs. | Our 3D analysis for these sulphur lines is the first for giants, but \cite{Caffau2007a} explored the 3D correction for the $[\ion{S}{i}]$ line in the Sun and \cite{Caffau2007b,Caffau2010} explored the 3D corrections for the 1045 nm triplet in the Sun, Procyon and four other dwarfs. |
All three works used CO?BOLD 3D hydrodynamical atmospheres for calculating the 3D effects. | All three works used $\mathrm{CO}^5\mathrm{BOLD}$ 3D hydrodynamical atmospheres for calculating the 3D effects. |
? found that the negative 3D-corrections for the [S1] line gets more significant (up to roughly —0.2 dex) for lower [Fe/H] and ? found positive 3D-corrections for the 1045 nm triplet more or less canceling the non-LTE corrections applied (+0.1 dex). | \cite{Caffau2007a} found that the negative 3D-corrections for the $[\ion{S}{i}]$ line gets more significant (up to roughly $-0.2$ dex) for lower $\left[\mathrm{Fe}/\mathrm{H}\right]$ and \cite{Caffau2010} found positive 3D-corrections for the 1045 nm triplet more or less canceling the non-LTE corrections applied $\sim+0.1$ dex). |
It is of course difficult to compare our models to the models used in ? and ?? because of the large difference in stellar parameters, but it can be noted, however, that all works predict a negative correction for the [S1] line and a positive for the triplet. | It is of course difficult to compare our models to the models used in \cite{Caffau2007a} and \cite{Caffau2007b, Caffau2010} because of the large difference in stellar parameters, but it can be noted, however, that all works predict a negative correction for the $[\ion{S}{i}] $ line and a positive for the triplet. |
We have also estimated corrections to the Fe abundances taken from the literature (see Sect. ??)), | We have also estimated corrections to the Fe abundances taken from the literature (see Sect. \ref{stellarparams}) ), |
and found values from -0.1 dex to -0.2 dex for Fe1 and from 40.05 dex to +0.1 dex for FeIl. | and found values from -0.1 dex to -0.2 dex for $\ion{Fe}{i}$ and from +0.05 dex to +0.1 dex for $\ion{Fe}{ii}$. |
The measured sulphur abundances and the applied non-LTE corrections from ? can be seen in Table 9]. | The measured sulphur abundances and the applied non-LTE corrections from \cite{Takeda2005} can be seen in Table \ref{tab:abund}. |
In this table we also list the difference between the LTE and non-LTE sulphur abundances derived from the 1045 nm triplet and those derived from the 1082 nm [S1] line. | In this table we also list the difference between the LTE and non-LTE sulphur abundances derived from the 1045 nm triplet and those derived from the 1082 nm $[\ion{S}{i}] $ line. |
The plot of [S/Fe] vs. [Fe/H] can be seen in Fig. | The plot of $\left[\mathrm{S}/\mathrm{Fe}\right]$ vs. $\left[\mathrm{Fe}/\mathrm{H}\right]$ can be seen in Fig. |
[6 and [7]. | \ref{fig:evo} and \ref{fig:Si_evo}. |
We have used a solar sulphur abundance of loge(S)o=7.12 (?) and all data in Fig. | We have used a solar sulphur abundance of $\log \epsilon(S)_{\odot}=7.12$ \citep{Asplund2009} and all data in Fig. |
[6] are put on this scale. | \ref{fig:evo} are put on this scale. |
A different choice of solar sulphur abundance would simply shift all data systematically by e.g., 0.04 dex using the value of ?.. | A different choice of solar sulphur abundance would simply shift all data systematically by e.g., 0.04 dex using the value of \citet{Caffau2010a}. |
In the Table 9] and Figs. | In the Table \ref{tab:abund} and Figs. |
- we have ignored 3D-corrections since we only have a coarse grid of models available for stars with parameters like our stars, but if they were to be applied they would work in the direction of lowering the sulphur abundances as determined from the [S1] line and adding to the abundances from the 1045 triplet. | \ref{fig:evo} - \ref{fig:Si_evo} we have ignored 3D-corrections since we only have a coarse grid of models available for stars with parameters like our stars, but if they were to be applied they would work in the direction of lowering the sulphur abundances as determined from the ] line and adding to the abundances from the 1045 triplet. |
In our narrow wavelength range there are few lines suitable for determining abundances for other a elements, but there are threeSi lines that can be used. | In our narrow wavelength range there are few lines suitable for determining abundances for other $\alpha$ elements, but there are three lines that can be used. |
The atomic data are taken from the NIST database and can be seen in ΤαΡΙΕΠΟΙ. | The atomic data are taken from the NIST database and can be seen in Table \ref{tab:si_data}. |
Equivalent widths for the Sir-lines used are found in Table [I1]. | Equivalent widths for the -lines used are found in Table \ref{tab:si_eqw}. |
For stars with no values given for the 1037.1 nm and 1084.4 nm lines, no observations were made and for the two stars with no values given for the 1088.3 nm line, the line was covered by a telluric line. | For stars with no values given for the 1037.1 nm and 1084.4 nm lines, no observations were made and for the two stars with no values given for the 1088.3 nm line, the line was covered by a telluric line. |
The derived silicon abundances are shown in Table we and the plot of [Si/Fe] vs. [Fe/H] in Fig. [7]. | The derived silicon abundances are shown in Table \ref{tab:si_abund}, and the plot of $\left[\mathrm{Si}/\mathrm{Fe}\right]$ vs. $\left[\mathrm{Fe}/\mathrm{H}\right]$ in Fig. \ref{fig:Si_evo}. |
We are not aware of any non-LTE calculations for these Sit-lines. | We are not aware of any non-LTE calculations for these }-lines. |
Until a decade ago, only few studies of sulphur abundances in Galactic halo stars (or, more correctly, for stars more metal-poor than [Fe/H]<—1), had been made, mainly due to the lack of suitable diagnostic lines. | Until a decade ago, only few studies of sulphur abundances in Galactic halo stars (or, more correctly, for stars more metal-poor than $<-1$ ), had been made, mainly due to the lack of suitable diagnostic lines. |
The weak doublet around 869 nm, a transition from a relatively high level at 7.9 eV, was used but these lines are increasingly difficult to measure as the metallicity decreases. | The weak doublet around 869 nm, a transition from a relatively high level at 7.9 eV, was used but these lines are increasingly difficult to measure as the metallicity decreases. |
However their formation is close to LTE conditions, and are therefore a recommended diagnostic when detactable (?).. | However their formation is close to LTE conditions, and are therefore a recommended diagnostic when detactable \citep{Takeda2005}. |
In 2004 Nissen et al. | In 2004 Nissen et al. |
and Ryde Lambert used the triplet lines around 923 nm (Yexe=6.5 eV) which are strong enough for determining sulphur abundances at high precision in halo stars, also for the metal-poor ones. | and Ryde Lambert used the triplet lines around 923 nm $\chi_{exc}=6.5$ eV) which are strong enough for determining sulphur abundances at high precision in halo stars, also for the metal-poor ones. |
The 923 nm triplet is heavily affected by telluric lines, but this can nicely be handled with an observation of a telluric standard star (??).. | The 923 nm triplet is heavily affected by telluric lines, but this can nicely be handled with an observation of a telluric standard star \citep{Ryde2004, Nissen2004}. |
A severe problem with these stronger lines has been that not all optical CCDs reach up to the wavelengths required. | A severe problem with these stronger lines has been that not all optical CCDs reach up to the wavelengths required. |
Also, the lines are presumably not formed in LTE (?).. | Also, the lines are presumably not formed in LTE \citep{Takeda2005}. |
Recently, the diagnostic power of new sulphur lines in the near IR, but beyond the reach of normal CCDs, have been explored by means of spectrometers like CRIRES at VLT and near-IR detector arrays (i.e.,??).. | Recently, the diagnostic power of new sulphur lines in the near IR, but beyond the reach of normal CCDs, have been explored by means of spectrometers like CRIRES at VLT and near-IR detector arrays \citep[i.e.,][]{Ryde2006,Nissen2007}. |
These lines are the 1082 nm [Si] line and 1045 nm triplet explored and used in this work. | These lines are the 1082 nm $\ion{S}{i}$ ] line and 1045 nm triplet explored and used in this work. |
The 1045 nm triplet has non-LTE corrections calculated by ? and the [S 1] line, being a forbidden line, is formed under close to LTE conditions, which is confirmed by non-LTE calculations by Korotin (private communication). | The 1045 nm triplet has non-LTE corrections calculated by \citet{Takeda2005} and the $\ion{S}{i}$ ] line, being a forbidden line, is formed under close to LTE conditions, which is confirmed by non-LTE calculations by Korotin (private communication). |
This makes analyses based on other sulphur lines than the 869 nm doublet or the 1082 nm [S 1] line rely on more or lessuncertaim], but necessary, LTE calculations. | This makes analyses based on other sulphur lines than the 869 nm doublet or the 1082 nm $\ion{S}{i}$ ] line rely on more or less, but necessary, non-LTE calculations. |
In this paper we have analyzed ten halo giants observed in the near-IR at high spectral resolution in order to determine the sulphur abundances from the near-IR triplet at 1045 and the forbidden line at 1082 nm. | In this paper we have analyzed ten halo giants observed in the near-IR at high spectral resolution in order to determine the sulphur abundances from the near-IR triplet at 1045 and the forbidden line at 1082 nm. |
We are able, for the first time, to analyse the 1082 nm [51] line for halo stars and show that it is indeed a useful diagnostic in giants down to at least [Fe/H] -2.3. | We are able, for the first time, to analyse the 1082 nm $\ion{S}{i}$ ] line for halo stars and show that it is indeed a useful diagnostic in giants down to at least $\left[\mathrm{Fe}/\mathrm{H}\right] \sim -2.3$ . |
This result is in agreement with our model predictions (see Fig. [T)) | This result is in agreement with our model predictions (see Fig. \ref{fig:SI_eqw}) ) |
showing that it should be usable even for lower [Fe/H] for cool stars with low surface gravity. | showing that it should be usable even for lower $\left[\mathrm{Fe}/\mathrm{H}\right]$ for cool stars with low surface gravity. |
Our model predictions also show that in dwarfs and subgiants this | Our model predictions also show that in dwarfs and subgiants this |
it (0) there is à prominent signal at 417 day. while after Lit (1) this signal is still present but it is no longer dominant and seems to be within the noise level. | fit (0) there is a prominent signal at 417 day, while after fit (1) this signal is still present but it is no longer dominant and seems to be within the noise level. |
This is similar to he behavior described in Sect. | This is similar to the behavior described in Sect. |
4.3. | 4.3. |
From Table 5 we see hat although Gt (1) is better than fit (0). the fit with a λαοί at 417 day is currently better. | From Table 5 we see that although fit (1) is better than fit (0), the fit with a planet at 417 day is currently better. |
As explained. above. his could be due to the short-observation timespan. or even due to the particular sampling of the radial velocity. data. | As explained above, this could be due to the short-observation timespan, or even due to the particular sampling of the radial velocity data. |
Aloreover. the fit with the planet introduces additional five ree parameters while Gt (1) introduces only one more free xwameter (a2) which could. also help explain why the Lit with the planet seems better than fit (1). | Moreover, the fit with the planet introduces additional five free parameters while fit (1) introduces only one more free parameter $\dot{\omega}_2$ ) which could also help explain why the fit with the planet seems better than fit (1). |
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