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The radio »ower Pisos. the radio largest linear size (LLS). aud ie N-rav hunuinositv (Ly) are in agreement with the TodELS aud PiwoeLy relations known for 1ο other halos in clusters. | The radio power $P_{\rm 1400 MHz}$, the radio largest linear size $LLS$ ), and the X-ray luminosity $L_X$ ), are in agreement with the $P_{\rm 1400 MHz}-LLS$ and $P_{\rm 1400 MHz}-L_X$ relations known for the other halos in clusters. |
The peripheral watch alone as a flux deusitv ~15.5+0.5 ταν. | The peripheral patch alone has a flux density $\simeq$ $\pm$ 0.5 mJy. |
Thus. if we consider 1e radio halo separated by the peripheral patch it results oe va flux density of 220.54!5 mJy. | Thus, if we consider the radio halo separated by the peripheral patch it results in a flux density of $\simeq$ $\pm$ 5 mJy. |
This value correspond o a radio power Pyouvttte—54.107 NN |ο still iu agreenent with the PijueLLS and ProsLx relations known iu the literature (see e.g. Cüovanuini et al. | This value correspond to a radio power $P_{\rm 1400 MHz} = 5.9\times10^{24}$ W $^{-1}$, still in agreement with the $P_{\rm 1400 MHz}-LLS$ and $P_{\rm 1400 MHz}-L_X$ relations known in the literature (see e.g. Giovannini et al. |
209). | 2009). |
Tιο flux deusitfies were calculated. after the primary 201111 correction. by inteeraine the total intensity surface xiehtuess. down to the 30 level. | The flux densities were calculated, after the primary beam correction, by integrating the total intensity surface brightness, down to the $\sigma$ level. |
However. we note tha he residual fiux density assmclated with tie diffuse cluster enissjon iust be interpreed with caution because of a possible variation iu the discrete sources flux ceusity. he slightly differcut frequerev of the two daa-scts, ale auv absolute calibration οiror between the two data-sets could cause ii an ouπο. Or OVOY subtraction of Hux. | However, we note that the residual flux density associated with the diffuse cluster emission must be interpreted with caution because of a possible variation in the discrete sources flux density, the slightly different frequency of the two data-sets, and any absolute calibration error between the two data-sets could cause in an under or over subtraction of flux. |
Iu addition. due to the short exposure tine of he archival observations. πε1ue diffuse ciussion could be nissed. | In addition, due to the short exposure time of the archival observations, some diffuse emission could be missed. |
Therefore. a deep ollow-up investigation woule ο necessary to eusure to 1'ecover all the radio flux ane o unauubieuouslv separate the emission of the diffuse Cluission from that of the uwelated discrete sources. | Therefore, a deep follow-up investigation would be necessary to ensure to recover all the radio flux and to unambiguously separate the emission of the diffuse emission from that of the unrelated discrete sources. |
we have ¢>7, also $>1. | we have $\phi > \eta$, also $\phi\gg 1$. |
For overdensities (6>0), the limit applied to Eq. (13)) | For overdensities $\delta > 0$ ), the limit applied to Eq. \ref{form:delta lim}) ) |
gives djim—+00. | gives $\delta_\mathrm{lim}\to+\infty$. |
Thus we can focus only on Formula (11)) for 6. | Thus we can focus only on Formula \ref{form:delta fi eta}) ) for $\delta$. |
From Eq. (11)) | From Eq. \ref{form:delta fi eta}) ) |
we see that in order to keep 6 finite (though arbitrarily large), also ¢ should tend to infinity. | we see that in order to keep $\delta$ finite (though arbitrarily large), also $\phi$ should tend to infinity. |
In other words, if 7>>1, then also ¢>>1, both for voids and overdensities. | In other words, if $\eta\gg 1$, then also $\phi\gg 1$, both for voids and overdensities. |
Hence, still from Equation (11)), we get, up to the leading order, and up to the second order Equivalently, Applying this formula in Equation (17)) and using the large-7 limit of the function f(1) (Eq. 25)) | Hence, still from Equation \ref{form:delta fi eta}) ), we get, up to the leading order, and up to the second order Equivalently, Applying this formula in Equation \ref{form:teta open}) ) and using the $\eta$ limit of the function $f(\eta)$ (Eq. \ref{form:f
eta big}) ) |
we obtain where In the limit Q—0 the second term in Equation (32)) vanishes, hence This is exactly the same relation as forthe linear regime (where |ó|< 1). | we obtain where In the limit $\Omega\to 0$ the second term in Equation \ref{form:tetafal2}) ) vanishes, hence This is exactly the same relation as forthe linear regime (where $|\delta| \ll 1$ ). |
However, here the density contrast can have an arbitrary value. | However, here the density contrast can have an arbitrary value. |
Thus, the formula of B92 (27)) does describe the dynamics of perturbations in the limit 2—0. | Thus, the formula of \citet{B92}~ \ref{form:Bernard
Teta}) ) does describe the dynamics of perturbations in the limit $\Omega\to 0$. |
The relation (34)), being very simple, is a non-trivial result. | The relation \ref{eq:linear theory}) ), being very simple, is a non-trivial result. |
When €? tends to 0, then alsothe scaled) velocity divergence ϐ-0 (peculiar velocities vanish with diminishing (2). | When $\Omega$ tends to 0, then alsothe scaled) velocity divergence $\theta\to 0$ (peculiar velocities vanish with diminishing $\Omega$ ). |
However, the quantity O, as introduced by Eq. (28)), | However, the quantity $\Theta$, as introduced by Eq. \ref{form:Teta}) ), |
converges to a non-zero value for 2.—0, due to the presence of the factor f(Q), approximated by (26)) for small Q. | converges to a non-zero value for $\Omega\to 0$, due to the presence of the factor $f(\Omega)$, approximated by \ref{form:f Omega small}) ) for small $\Omega$. |
The normalisation used here leads to ©=6 in the linear theory. | The normalisation used here leads to $\Theta=\delta$ in the linear theory. |
Why for very small values of Q this relation holds also in the non-linear regime? | Why for very small values of $\Omega$ this relation holds also in the non-linear regime? |
It turns out that this is a general result of dynamics in a low-density universe, and does not rely on any symmetry. | It turns out that this is a general result of dynamics in a low-density universe, and does not rely on any symmetry. |
The derivation is presented in Appendix A.. | The derivation is presented in Appendix \ref{app:empty}. |
For large but finite values of 7, Formula (32)) can be applied. | For large but finite values of $\eta$, Formula \ref{form:tetafal2}) ) can be applied. |
Specifically, it can be used for 7 significantly greater than 3 (Q significantly smaller than 0.2), which falls well below the presently accepted value of the cosmic density parameter. | Specifically, it can be used for $\eta$ significantly greater than 3 $\Omega$ significantly smaller than $0.2$ ), which falls well below the presently accepted value of the cosmic density parameter. |
Therefore, the approximation (32)) is of no practical importance; we have to continue our search for relevant relation. | Therefore, the approximation \ref{form:tetafal2}) ) is of no practical importance; we have to continue our search for a relevant relation. |
Just for illustrative purposes, on Figure 3 awe plot the exact relation, the B92 approximation, and the approximation (32)) for an exemplary value of Q=107? (7~ 13). | Just for illustrative purposes, on Figure \ref{fig:Theta small Om} we plot the exact relation, the \citet{B92} approximation, and the approximation \ref{form:tetafal2}) ), for an exemplary value of $\Omega=10^{-5}$ $\eta\simeq13$ ). |
We see that although for this value of Qthe relation is still non-linear, the B92 approximation drastically overestimates the degree of non-linearity. | We see that although for this value of $\Omega$the relation is still non-linear, the \citet{B92} approximation drastically overestimates the degree of non-linearity. |
As we will understand any underdense perturbations, i.e. those for which ó<0. | As we will understand any underdense perturbations, i.e. those for which $\delta<0$. |
In this section we examine the behaviour of the velocity divergence vs. the density contrast for such inhomogeneities. | In this section we examine the behaviour of the velocity divergence vs. the density contrast for such inhomogeneities. |
When considering overdense perturbations (with 6> 0), the regime of 6~1 is usually called (or at most mildly)) linear. | When considering overdense perturbations (with $\delta>0$ ), the regime of $\delta\simeq1$ is usually called (or at most ) non-linear. |
It may thus seem that it should be similarly for the limit ó=—1 (cf. Martel 1991)). | It may thus seem that it should be similarly for the limit $\delta\ga -1$ (cf. \citealt{Mar}) ). |
However, if we analyse Equation (11)), which is valid both for voids and for open overdensities, we can see that for finite values of η (which correspond to non-zero €?), the condition 6——1 mayonly be satisfied for 6—+00. | However, if we analyse Equation \ref{form:delta fi eta}) ), which is valid both for voids and for open overdensities, we can see that for finite values of $\eta$ (which correspond to non-zero $\Omega$ ), the condition $\delta\to -1$ mayonly be satisfied for $\phi\to+\infty$. |
Hence, the evolution of such perturbation is non-linear when the density contrast approachesa its minimum value. | Hence, the evolution of such a perturbation is non-linear when the density contrast approaches its minimum value. |
The scaled velocity divergence O, as defined in Eq. (28)), | The scaled velocity divergence $\Theta$ , as defined in Eq. \ref{form:Teta}) ), |
is a monotonically increasing function of 6 (for 7, or €), treated as a fixed parameter). | is a monotonically increasing function of $\delta$ (for $\eta$, or $\Omega$ , treated as a fixed parameter). |
Its minimum value is Omin=O(—1) (dependent on 7), obtained easily by calculating the limit ¢—--oo in (15)): For 7—0, equivalent to ()—1 (the Einstein-de Sitter model of the universe), we get the value of Omin=—1.5, which can also be calculated The opposite limit of Ω—0 (7— +00)leads to Oii;——1; this can be equally deduced from (34)). | Its minimum value is $\Theta_\mathrm{min}\equiv\Theta(-1)$ (dependent on $\eta$ ), obtained easily by calculating the limit $\phi\to+\infty$ in \ref{form:teta fi eta}) ): For $\eta\to0$, equivalent to $\Omega\to1$ (the Einstein–de Sitter model of the universe), we get the value of $\Theta_\mathrm{min}=-1.5$, which can also be calculated The opposite limit of $\Omega\to0$ $\eta\to+\infty$ )leads to $\Theta_\mathrm{min}\to-1$; this can be equally deduced from \ref{eq:linear theory}) ). |
If we adopt the currently accepted value of Qo~0.25 (ηο~ 2.63), we obtain O(—1)~ —1.43. | If we adopt the currently accepted value of $\Omega_0\simeq0.25$ $\eta_0\simeq2.63$ ), we obtain $\Theta(-1)\simeq-1.43$ . |
Thus, the B92 approximation (27)), which gives O(—1)=—1.5 independently of ©, has a relative error of approx. | Thus, the \citet{B92} approximation \ref{form:Bernard Teta}) ), which gives $\Theta(-1)=-1.5$ independently of $\Omega$ , has a relative error of approx. |
in this limit for such Qo. | in this limit for such $\Omega_0$ . |
We would now like tofind an (approximate)relation O—ó for the whole range ó€ [—1,0]. | We would now like tofind an (approximate)relation $\Theta$ $\delta$ for the whole range $\delta \in [-1,0]$ . |
B92 derived his formula expanding the relation around 6= 0. We adopt a different approach: we expand the relation around 6= —1. ( | \citet{B92} derived his formula expanding the relation around $\delta = 0$ We adopt a different approach: we expand the relation around $\delta = -1$ . ( |
That is, at a first step we | That is, at a first step we |
{Bahcall2003) (Efstathiou2001). Cruzetal.(2005) ~107. αι Tajian.Souradeep.&Cornish(2005). | \citep{bahcall:2003} \citep{efstathiou:2004} \citet{de Oliveira-Costa:2004} \citet{vielva:2004} \citet{cruz:2005} $\sim 10^{\circ}$ \citep{eriksen:2004a,hansen:2004a,hansen:2004b}. \cite{hajian:2005}. |
. has provided the motivation to investigate anisotropic cosinological models. | has provided the motivation to investigate anisotropic cosmological models. |
Following Bun.Ferreira.&Silk(1996). and Noeutetal.(1997).. we focus on a specific class of models Diauchi type VIL, (Barrowctal.J955). | Following \cite{bunn:1996} and \cite{kogut:1997}, we focus on a specific class of models -- Bianchi type $_h$ \citep{barrow:1985}. |
. Such models were previously compared to the COBE--DMR data in Iogutetal.(1997).. where lianits oithe shear (47),<10" and vorticity Gr),«6«10 were established. | Such models were previously compared to the -DMR data in \cite{kogut:1997}, where limits on the shear $\left (\frac{\sigma}{H} \right )_0 < 10^{-9}$ and vorticity $\left (\frac{\omega}{H}\right )_0 < 6\times10^{-8}$ were established. |
We consider that the observed anisotropy is the su of two contributions an Clósotroye term which is connected to variations in the deusiv aud gravitational potential. and a tenu from the anisotropic metric. | We consider that the observed anisotropy is the sum of two contributions – an isotropic' term which is connected to variations in the density and gravitational potential, and a term from the anisotropic metric. |
A nmechanisu to generate the isotropic fluctuations is required. particularly on simall auguar scales where the Bianchi contribution is ueglieible. but this need not be inflationary. | A mechanism to generate the isotropic fluctuations is required, particularly on small angular scales where the Bianchi contribution is negligible, but this need not be inflationary. |
In our analysis we smooth the data to probe oulv the low-( reeinic. aud find that xcsults are practically insensitive to the choice of spectruii for the isotropic component on Iurege-augular scales. | In our analysis we smooth the data to probe only the $\ell$ regime, and find that results are practically insensitive to the choice of spectrum for the isotropic component on large-angular scales. |
Remarkably. we fud ao statistically significaut correlation between oue of these iioclels and the data. | Remarkably, we find a statistically significant correlation between one of these models and the data. |
Such a result mav help to resolve some of the more usual observed features of the microwave sly. albeit at the introduction of a new coudtn the large-scale anisotropy is described at least in peut bv a low clensity Bianchi model whereas the sialler scalefluctuations are consistent with a cosmological constant dominated. critical density model ii an inflationary SCCLLALIO. | Such a result may help to resolve some of the more unusual observed features of the microwave sky, albeit at the introduction of a new conundrum – the large-scale anisotropy is described at least in part by a low density Bianchi model, whereas the smaller scalefluctuations are consistent with a cosmological constant dominated, critical density model in an inflationary scenario. |
Tn this analysis. we utilize the first-vear | In this analysis, we utilize the first-year |
(Marsh2001).. Cha | \citep{mar01}, \citet{cha35}. |
ndrasekhar(1935). (Provencaletal1998) (Marsh2000).. (Horne2002) 5 5 5 5 5 Agol(2002):: |43R60]7. Re=GMwp/cMyp a Rwp. ~Ry Rwp>Ae. Mwp. a) Rwp«Re. Mwp. a). (Agol2003).. Εςwp Ryis 7609/4, O (ug~0.1 ΙΔ]~107. Rwp~Re107Rys. | \citep{pro98} \citep{mar00}, \citep{bor97}
\citep{hor02} $\S$ $\S$ $\S$ $\S$ $\S$ \citet{ago02}; $R_{\rm{E}}=[4R_G a]^{1/2}$ $R_G=GM_{\rm{WD}}/c^2$$M_{\rm{WD}}$ $a$ $R_{\rm{WD}}$ $\sim R_{\rm{E}}$ $R_{\rm{WD}} \gg R_{\rm{E}}$ $M_{\rm{WD}}$ $a$ $R_{\rm{WD}} \ll R_{\rm{E}}$ $M_{\rm{WD}}$ $a$ \citep{ago03}, $F_{\rm{MS,WD}}$ $R_{\rm{MS}}$ $r$ $I(r)/\langle I\rangle$ $\Theta$ $a \sim 0.1$ $|\Delta f_1| \sim 10^{-4}$ $R_{\rm{WD}} \sim R_{\rm{E}} \sim 10^{-2} R_{\rm{MS}}$ |
uminosity of the ionizing source. | luminosity of the ionizing source. |
In this model. knowledge of the turnover frequency. 44. can be used to estimate the rina separation. e. which can then be compared with inclependenthy-known values. (Table 3). | In this model, knowledge of the turnover frequency, $\nu_{\rm t}$, can be used to estimate the binary separation, $a$, which can then be compared with independently-known values (Table 3). |
For à range in X covering two orders of magnitude. the binary separation (within a factor of 2) is (Seaquist Tavlor 1990): where 5, is the optically thin flux near the turnover. and d is the cistance. | For a range in $X$ covering two orders of magnitude, the binary separation (within a factor of 2) is (Seaquist Taylor 1990): where $S_{\rm t}$ is the optically thin flux near the turnover, and $d$ is the distance. |
Form=27 GGIIz and οι~12.6 mmy. we find eu,~AO0(d/kpe)AU. | For$\nu_{\rm t} = 27$ GHz and $S_{\rm t} \sim
12.6$ mJy, we find $a_{\rm radio} \sim 40 (d/\rm kpc)$. |
.. A comparison with the binary separation derived from spectroscopic orbit solution. ft,~2.2 (Ixenvon et 11991) shows that the observed turnoverfrequency over-estimates the binary separation by a [actor of ~30 for d~ 2kkpc. | A comparison with the binary separation derived from spectroscopic orbit solution, $a_{\rm sp} \sim 2.2$ (Kenyon et 1991) shows that the observed turnoverfrequency over-estimates the binary separation by a factor of $\sim 30$ for $d \sim 2$ kpc. |
The STB model apparently does not account satisfactorily for the racio emission from CI Cvg. | The STB model apparently does not account satisfactorily for the radio emission from CI Cyg. |
Vhere are also other. inconsistencies between the observed spectrum of CIE Cvg and the STD model. | There are also other inconsistencies between the observed spectrum of CI Cyg and the STB model. |
We have alreacky mentioned (see 833 above) the serious disagreement between the Lyman continuum luminosity. derived. from the optically thin radio emission and that estimated. from the UV continuumand. emission-line studies. | We have already mentioned (see 3 above) the serious disagreement between the Lyman continuum luminosity derived from the optically thin radio emission and that estimated from the UV continuumand emission-line studies. |
In. addition. the observed. optically thick spectral index (oο 10.6) immediately implies .Xz/4 in the STD model. | In addition, the observed optically thick spectral index $\alpha>+0.6$ ) immediately implies $X
< \pi/4$ in the STB model. |
Since Cl Cve is à welbstuclicc eclipsing svstem we know that our radio observations were mace when the system was viewed. along the binary axiswith the hot star in [ront tthe viewing angle. as defined in STD. 6= 07). | Since CI Cyg is a well-studied eclipsing system we know that our radio observations were made when the system was viewed along the binary axiswith the hot star in front the viewing angle, as defined in STB, $\theta \approx 0^{\circ}$ ). |
Thus a=[0.96 indicates Vox0.7 Pig. | Thus $\alpha = +0.96$ indicates $X \approx 0.7$ Fig. |
3 of Seaquist ‘Tavlor 1984). | 3 of Seaquist Taylor 1984). |
The nebula in Cl €vg should thus be radiation bounded. | The nebula in CI Cyg should thus be radiation bounded. |
This is inconsistent with its observed. forbidden-line spectrum. | This is inconsistent with its observed forbidden-line spectrum. |
In particular. after 1984 the only strong lines have been those with high excitation vil]. Nev]] and Megv]D while the intermediates and low-excitation lines have been very faint (O1u]]. Neiu]] or absent ul]. Su] suggesting that the nebula is density bounded. CY 1). | In particular, after 1984 the only strong lines have been those with high excitation ], ] and ]) while the intermediate- and low-excitation lines have been very faint ], ]) or absent ], ]) suggesting that the nebula is density bounded $X > 1$ ). |
Furtherinsight into the geometry of the nebular region(s) of Cl Cvg is provided by the apparent lack of Raman-scattered lines atAAGS25.7082. | Furtherinsight into the geometry of the nebular region(s) of CI Cyg is provided by the apparent lack of Raman-scattered lines at$\lambda\lambda 6825, 7082$. |
These lines. commonly observed in high-excitation svmbiotic svstems. havenever been detected in CL νο even at the epoch when the high- lines were very strong. | These lines, commonly observed in high-excitation symbiotic systems, have been detected in CI Cyg, even at the epoch when the high-ionization lines were very strong. |
X plausible. explanation seers to be a lack of sulicient neutral HI scattervs. which also implies a high valueτος X. (ο10). | A plausible explanation seems to be a lack of sufficient neutral $^0$ scatterers, which also implies a high value of $X$, $\ga 10$ ). |
There are several pausible explanations for t1e failure of the SPB model in the case of CI Cvg. | There are several plausible explanations for the failure of the STB model in the case of CI Cyg. |
Above all. CL Cwvg is one of the few symbiotic binaries in which the cool giant fills or nearly fills its Roche lobe (c.g. Mikolajewska 1996. and references therein). | Above all, CI Cyg is one of the few symbiotic binaries in which the cool giant fills or nearly fills its Roche lobe (e.g. ajewska 1996, and references therein). |
“Phis has two important. implications: first. the size of the giant. fills a Large fraction of the binary separation (~0.470 lor q=ΔιΛιν~ 3) and for XoS1/3 the ionisation front impinges on its photosphere: second. ancl perhaps most important. mass loss from the giant is stronely concentrated in a stream Uowing through the inner langrangian point (54) towards the hot component (as opposed to the spherically svnimetric wind assumed in the STB model). | This has two important implications: first, the size of the giant fills a large fraction of the binary separation $\sim 0.47a$ for $q \equiv
M_{\rm g}/M_{\rm h} \sim 3$ ) and for $X \la 1/3$ the ionisation front impinges on its photosphere; second, and perhaps most important, mass loss from the giant is strongly concentrated in a stream flowing through the inner langrangian point $L_1$ ) towards the hot component (as opposed to the spherically symmetric wind assumed in the STB model). |
The result is a complex density. cistribution. not the simple ~r distribution in the STD model. | The result is a complex density distribution, not the simple $\sim r^{-2}$ distribution in the STB model. |
In particular. the density should vary roughly as + along the stream. possibly in addition to a more symmetric component with much lower density — an order of magnitude or more lower that that in the stream LLubov Shu 1975). | In particular, the density should vary roughly as $r^{-1}$ along the stream, possibly in addition to a more symmetric component with much lower density – an order of magnitude or more lower that that in the stream Lubov Shu 1975). |
Thus the simple geometry assumed. for the SPB mock| is incompatible with the conditions in the cireumbinary environment of CI (να. | Thus the simple geometry assumed for the STB model is incompatible with the conditions in the circumbinary environment of CI Cyg. |
The fact that the giant component of Cl Cye fills its tidal lobe also implies that the interacting wind model (assuming spherically svmumetrie winds from. both components) cannot be a good match to the true conditions the stream should: result. in the formation of a clisk of material orbiting the companion. | The fact that the giant component of CI Cyg fills its tidal lobe also implies that the interacting wind model (assuming spherically symmetric winds from both components) cannot be a good match to the true conditions – the stream should result in the formation of a disk of material orbiting the companion. |
Any wind. from the companion willthus be bipolar rather than spherically svmiumetric. | Any wind from the companion willthus be bipolar rather than spherically symmetric. |
Radio continuum spectra of collimated ionisecstellar winds have been calculated. by Reynolds (1986). showing that unresolved: sources can have partially opaque spectra with spectral indices between |2 and 0.1. | Radio continuum spectra of collimated ionisedstellar winds have been calculated by Reynolds (1986) showing that unresolved sources can have partially opaque spectra with spectral indices between $+2$ and $-0.1$. |
These models assume the thermal material appears at afinite radius. ro. where the jet half-width is wy. | These models assume the thermal material appears at afinite radius, $r_{\rm 0}$ , where the jet half-width is $w_{\rm
0}$. |
Power-law dependencies of quantities on jet length. rare also assumed: in particular. the jet half-wicth. temperature. velocity. density and ionised fraction are assumed to vary as fro to powers ofe. qv. dv. (u. anl qu. respectively. | Power-law dependencies of quantities on jet length, $r$, are also assumed; in particular, the jet half-width, temperature, velocity, density and ionised fraction are assumed to vary as $r/r_{\rm 0}$ to powers of $\epsilon$ , $q_{\rm T}$ , $q_{\rm v}$ , $q_{\rm n}$ , and $q_{\rm x}$ , respectively. |
The models are defined by values oc. qe. and qu: theother gradients are derived from. these. | The models are defined by values of $\epsilon$ , $q_{\rm v}$ , and $q_{\rm x}$ ; theother gradients are derived from these. |
In particular. a spectrum with à= 1|0.95. as observed. for | In particular, a spectrum with $\alpha = +0.95$ , as observed for |
We computed the stellar structure for a large range of masses (from A=1 to 6.5 M.) and metallicities (Z-—0.0001. 0.004. 0.008 and 0.02) starting from the zero-age main sequence up throughout many thermal pulses during the AGB phase using the Mount Stromlo Stellar Siructure Program (Wood&Zarro1981:FrostLattanzio1996). | We computed the stellar structure for a large range of masses (from $M$ =1 to 6.5 ) and metallicities $Z$ =0.0001, 0.004, 0.008 and 0.02) starting from the zero-age main sequence up throughout many thermal pulses during the AGB phase using the Mount Stromlo Stellar Structure Program \citep{wood:81,frost:96}. |
. Mass loss is modelled on ihe AGB phase following the prescription of Vassiliaclis&Wood(1993).. which accounts for a [malsuperwind phase. | Mass loss is modelled on the AGB phase following the prescription of \citet{vassiliadis:93}, which accounts for a final phase. |
Using the prescription for unstable convective/radiative boundaries described in detail by Lattanzio(1986) we find the third dredge up to occur sell-consistentlyfor masses above 2.25 aab Z=0.02. above 1.5 and Z=0.008. above 1.25 aat Z=0.004 and for all the computed masses al ΖΞ- 0001. | Using the prescription for unstable convective/radiative boundaries described in detail by \citet{lattanzio:86} we find the third dredge up to occur self-consistentlyfor masses above 2.25 at $Z$ =0.02, above 1.5 at $Z$ =0.008, above 1.25 at $Z$ =0.004 and for all the computed masses at $Z$ =0.0001. |
More details reearcling these caleulations can be found in Ixarakas(2003) ane for the 3 Z = 0.02imodelin Lugearoetal.(2003). | More details regarding these calculations can be found in \citet{karakas:03} and for the 3 $Z$ =0.02 model in \citet{lugaro:03}. |
. To caleulate (he nucleosvuthesis in detail we have used a postprocessing code that caleulates abundance changes due to convective mixing and nuclear reactions (Cannon1993). | To calculate the nucleosynthesis in detail we have used a postprocessing code that calculates abundance changes due to convective mixing and nuclear reactions \citep{cannon:93}. |
. The stellar structure inputs. such as temperature. density. extent of convective zones. mixing length and mixing velocity as functions of mass and model number. are taken [rom the stellar evolutionary computations. | The stellar structure inputs, such as temperature, density, extent of convective zones, mixing length and mixing velocity as functions of mass and model number, are taken from the stellar evolutionary computations. |
Detween evolution models (he postprocessing code creates ils own lass mesh. resolving regions undergoing rapid changes in composition and using a combination of Lagrangian and non-Lagrangian points. | Between evolution models the postprocessing code creates its own mass mesh, resolving regions undergoing rapid changes in composition and using a combination of Lagrangian and non-Lagrangian points. |
Convective mixing is done time dependently. with no assumptions of instantaneous mixing. | Convective mixing is done time dependently, with no assumptions of instantaneous mixing. |
To model (his. a "donor cell scheme is adopted in which each nuclear species is stored as (wo variables representing (wo streams. one moving upward and one moving downward. | To model this, a “donor cell” scheme is adopted in which each nuclear species is stored as two variables representing two streams, one moving upward and one moving downward. |
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