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Gravitational collapse. turbulence aud maguetic field evolution are except for some idealized cases difficult to study analytically. because the svstem is hiehllv uou-near aud naturally three-dimensional.
Gravitational collapse, turbulence and magnetic field evolution are –except for some idealized cases– difficult to study analytically, because the system is highly non-linear and naturally three-dimensional.
Thus. we study the processes leading to turbulence aud magnetic field anmpliücation through eravitational collapse im ligh-resolution. MIID siuiulatious.
Thus, we study the processes leading to turbulence and magnetic field amplification through gravitational collapse in high-resolution MHD simulations.
We present results of a numerical experiment with a collapsing. maguetized. turbulent eas core (sec.Sur D..
We present results of a numerical experiment with a collapsing, magnetized, turbulent gas core \citep[see,][paper I]{SurEtAl2010}.
We focus on the eravitational collapse and inagnetie Ποια amplification of a dense eas cloud. using a simplified setup. where we assume an almost isothermal equation of state (effective D=dlogTf/dlogp|d= ll. with the temperature T and density p) and neglect nou-ideal MITID effects (discussed below).
We focus on the gravitational collapse and magnetic field amplification of a dense gas cloud, using a simplified setup, where we assume an almost isothermal equation of state (effective $\Gamma=d\log T/d\log\rho+1=1.1$ , with the temperature $T$ and density $\rho$ ) and neglect non-ideal MHD effects (discussed below).
The numerical simulations preseuted here were performed with the publicly available adaptiveanesht refinement (AMIR) code. FLASTI2.5 (Fryxelletal. 2000)..
The numerical simulations presented here were performed with the publicly available adaptive-mesh refinement (AMR) code, FLASH2.5 \citep{FryxellEtAl2000}. .
We solve the equations of ideal ΑΠΟ. including selt- with a refinement criterion euarautecing that the Jeans leneth. with the sound speed ος. gravitational constant G.
We solve the equations of ideal MHD, including self-gravity with a refinement criterion guaranteeing that the Jeans length, with the sound speed $c_{\mathrm s}$ , gravitational constant $G$ ,
the remnant masses from are larger except in the case of s25A. Model s25A was mapped to after 1x104 seconds of evolution inKEPLER.
the remnant masses from are larger except in the case of s25A. Model s25A was mapped to after $1 \times 10^4$ seconds of evolution in.
. Although this does not alter the final mixed state of the star, it does alter the amount of mass that accumulates at the inner boundary, since most of the infall occurs during the first 104 seconds, when the star was still being evolved forward with the Lagrangian codeKEPLER.
Although this does not alter the final mixed state of the star, it does alter the amount of mass that accumulates at the inner boundary, since most of the infall occurs during the first $10^4$ seconds, when the star was still being evolved forward with the Lagrangian code.
. Both 15 solar mass models are in good agreement with the results.
Both 15 solar mass models are in good agreement with the results.
z25D shows the most deviation, most likely because this model experienced the most fall back of any of the models studied here.
z25D shows the most deviation, most likely because this model experienced the most fall back of any of the models studied here.
We were unable to replicate the fine resolution employed by a one dimensional code, and that is almost certainly the reason for the enhanced infall mass.
We were unable to replicate the fine resolution employed by a one dimensional code, and that is almost certainly the reason for the enhanced infall mass.
The initial remnant mass in 2D was sufficiently larger than the ID remnant mass that the additional force it exerted on the surrounding material was large enough to cause additional infall.
The initial remnant mass in 2D was sufficiently larger than the 1D remnant mass that the additional force it exerted on the surrounding material was large enough to cause additional infall.
This led to a larger remnant, causing a mild runaway effect.
This led to a larger remnant, causing a mild runaway effect.
While the remnant mass obtained with for Model z25D is likely inaccurate, Rayleigh-Taylor mixing in this star has stopped by 2x104 seconds, at which point the remnant mass in the simulation was not significantly larger than that in the simulation.
While the remnant mass obtained with for Model z25D is likely inaccurate, Rayleigh-Taylor mixing in this star has stopped by $2 \times 10^4$ seconds, at which point the remnant mass in the simulation was not significantly larger than that in the simulation.
It is unlikely that increased infall has had significant impact on the evolution of the Rayleigh-Taylora instability, so the mixing results remain sound.
It is unlikely that increased infall has had a significant impact on the evolution of the Rayleigh-Taylor instability, so the mixing results remain sound.
Random perturbations of amplitude 0.596 and 296 of the original velocity profile were added to the initial model for the solar composition models, as described in2.
Random perturbations of amplitude $0.5\%$ and $2\%$ of the original velocity profile were added to the initial model for the solar composition models, as described in.
2.. Random perturbations of 2% were added to the zero-metal stars, and an additional simulation with an initial perturbation of 596 was performed for Model z25D. Perturbations of 0.596 produce an original size scale for the Rayleigh-Taylor instabilities that is about the same size asthose arising for the non-perturbed case, while the 296 perturbations result in a larger initial scale for the instability, implying that grid perturbations for these models are between 0.596 and 296, as shown in Figure 1..
Random perturbations of $2\%$ were added to the zero-metal stars, and an additional simulation with an initial perturbation of $5\%$ was performed for Model z25D. Perturbations of $0.5\%$ produce an original size scale for the Rayleigh-Taylor instabilities that is about the same size asthose arising for the non-perturbed case, while the $2\%$ perturbations result in a larger initial scale for the instability, implying that grid perturbations for these models are between $0.5\%$ and $2\%$, as shown in Figure \ref{s15A_pert}.
The Rayleigh-Taylor instabilities can grow for at least as long as the reverse shock takes to reach the origin.
The Rayleigh-Taylor instabilities can grow for at least as long as the reverse shock takes to reach the origin.
The instabilities in the solar metallicity stars can grow for many e—folding times, a long enough time to wash out the initial scale and spectrum of the instabilities.
The instabilities in the solar metallicity stars can grow for many $e-$ folding times, a long enough time to wash out the initial scale and spectrum of the instabilities.
The final states of the perturbed models appear essentially identical to the unperturbed models.
The final states of the perturbed models appear essentially identical to the unperturbed models.
The distribution of the isotopes in both velocity (Figures 16 and 17)) and and mass space (Figures 20 and 21)) has no systematic correlation with the magnitude of the initial perturbation for solar metallicity stars.
The distribution of the isotopes in both velocity (Figures \ref{s15_changevel} and \ref{s25_changevel}) ) and and mass space (Figures \ref{s15_changeel} and \ref{s25_changeel}) ) has no systematic correlation with the magnitude of the initial perturbation for solar metallicity stars.
The scale of the perturbations one would expect in a real star is set by the magnitude of the convective velocities, which are on the order of 0.5% of the total velocity.
The scale of the perturbations one would expect in a real star is set by the magnitude of the convective velocities, which are on the order of $0.5\%$ of the total velocity.
Perturbations for the zero-metallicity case have a greater effect on the final amount of mixing in these stars.
Perturbations for the zero-metallicity case have a greater effect on the final amount of mixing in these stars.
Larger perturbations lead to a larger size scale for the initial Rayleigh-Taylor fingers, which allows them to grow more quickly before the reverse shock passes them and the pressure gradient is no longer opposite the density gradient.
Larger perturbations lead to a larger size scale for the initial Rayleigh-Taylor fingers, which allows them to grow more quickly before the reverse shock passes them and the pressure gradient is no longer opposite the density gradient.
In these models, the Rayleigh-Taylor instabilities cannot grow for many e—folding times, and so the initial scale of the perturbations matters.
In these models, the Rayleigh-Taylor instabilities cannot grow for many $e-$ folding times, and so the initial scale of the perturbations matters.
This can be seen in Figures 18 and 19,, which show the final distribution of isotopes as a function of enclosed mass for different amounts of perturbation.
This can be seen in Figures \ref{z15_changeel} and \ref{z25_changeel}, which show the final distribution of isotopes as a function of enclosed mass for different amounts of perturbation.
The final amount of mixing is set by the size scale of the initial perturbation.
The final amount of mixing is set by the size scale of the initial perturbation.
The amount of mixing determines the distribution of isotopes with velocity, as well, as shown in Figures 14 and 15.
The amount of mixing determines the distribution of isotopes with velocity, as well, as shown in Figures \ref{z15_changevel} and \ref{z25_changevel}. .
aand aare the most affected.
and are the most affected.
The distance in mass space over which these isotopes are
The distance in mass space over which these isotopes are
stated total number of about 90 O stars within their sample space. a runaway fraction of 15/90— 16 per cent results.
stated total number of about 90 O stars within their sample space, a runaway fraction of 15/90= 16 per cent results.
Vhev further conclude that the true runaway [fraction of ο stars depends on the adopted: velocity eut-olf ancl may [ie in the range of 10)25 per cent.
They further conclude that the true runaway fraction of O stars depends on the adopted velocity cut-off and may lie in the range of 10–25 per cent.
? also found the binary fraction among runaway O stars in their sample to be about 10 per cent.
\citet{gies1986a} also found the binary fraction among runaway O stars in their sample to be about 10 per cent.
As explained above. O stars released in a supernova in an ejected massive binary result in field O stars which can not be traced back to their parent star clusters.
As explained above, O stars released in a supernova in an ejected massive binary result in field O stars which can not be traced back to their parent star clusters.
‘Thus. on the basis of the O-star runaway fraction and binary fraction of O-runaway data published by ? 12.5 per cent of O stars can not be traced back to the star cluster where they have form.
Thus, on the basis of the O-star runaway fraction and binary fraction of O-runaway data published by \citet{gies1986a} 1–2.5 per cent of O stars can not be traced back to the star cluster where they have form.
These O stars will appear to have formed in isolation. although they were born in an ordinary star cluster,
These O stars will appear to have formed in isolation, although they were born in an ordinary star cluster.
Phe different O-star runaway fractions in the literature have been unified by 7. by considering true space frequencies: The radial velocity. spectrum of O stars is. decomposed into two cillerent Gaussian velocity. distributions. which correspond. το two different Alaxwellian space velocity distributions.
The different O-star runaway fractions in the literature have been unified by \citet{stone1991a} by considering true space frequencies: The radial velocity spectrum of O stars is decomposed into two different Gaussian velocity distributions, which correspond to two different Maxwellian space velocity distributions.
The high velocity component has a number fraction of fH=46 per cent and a velocity distribution ol cQ —28.2 km s
The high velocity component has a number fraction of $f_\mathrm{H}$ =46 per cent and a velocity distribution of $\sigma_\mathrm{H}$ =28.2 km $^{-1}$.
ὃν transforming individual O star runaway studies. which are based on individual runaway definitions. to true space frequencies based. on bimodality in the velocity distribution of O stars. ?.— achieves. good agreement between the dillerent individual studies.
By transforming individual O star runaway studies, which are based on individual runaway definitions, to true space frequencies based on bimodality in the velocity distribution of O stars, \citet{stone1991a} achieves good agreement between the different individual studies.
From the runaway fraction of 46 per cent derived. by 7 it follows that a fraction of 4.6 per cent of O stars will apparently form in isolation. if the runaway binary fraction of 10 per cent by 2 is used.
From the runaway fraction of 46 per cent derived by \citet{stone1991a} it follows that a fraction of 4.6 per cent of O stars will apparently form in isolation, if the runaway binary fraction of 10 per cent by \citet{gies1986a} is used.
Thus. the two-step-cjection process predicts a fraction of O stars which have formed. apparently. in isolation in the range of 14.6 per cent.
Thus, the two-step-ejection process predicts a fraction of O stars which have formed apparently in isolation in the range of 1–4.6 per cent.
?? conclude. based. on the actually observed positions ancl velocities of O stars. that EE 2 per cent of O stars can be considered: as candidates of massive stars formed in isolation. because such stars can not be traced back to a voung star cluster.
\citet{dewit2004a,dewit2005a} conclude, based on the actually observed positions and velocities of O stars, that $\pm$ 2 per cent of O stars can be considered as candidates of massive stars formed in isolation, because such stars can not be traced back to a young star cluster.
Consequently. the process of two-step ejection can quantitatively account for the proposed. fraction of massive candidates formed. in isolation.
Consequently, the process of two-step ejection can quantitatively account for the proposed fraction of massive candidates formed in isolation.
The maximum possible velocity in the two-step-ejection process iS Cues=fr|te. Le. if the star is released in the moving direction of the previous binary.
The maximum possible velocity in the two-step-ejection process is $v_\mathrm{max}=v_\mathrm{r}+v_\mathrm{e}$, i.e. if the star is released in the moving direction of the previous binary.
Binaries can be ejected from star clusters due to dynamical interactions.
Binaries can be ejected from star clusters due to dynamical interactions.
Two common situations are the scattering of two binaries (D|DB) and the scattering of one binary and one single star (BIS).
Two common situations are the scattering of two binaries (B+B) and the scattering of one binary and one single star (B+S).
D|Beevents leac commonly tο two single runaway stars and one tight binary.
B+B-events lead commonly to two single runaway stars and one tight binary.
But also ügh velocity. binaries can be produced in roughly LO per cent of all cases (?)..
But also high velocity binaries can be produced in roughly 10 per cent of all cases \citep{mikkola1983a}.
In the BIS event. high velociv binaries must. be produced due to local conservation of linear momentum.
In the B+S event high velocity binaries must be produced due to local conservation of linear momentum.
The ejection velocity of the single star is tvpicallv of the order of the orbital velocity of the binary (2). 0s.
The ejection velocity of the single star is typically of the order of the orbital velocity of the binary \citep{heggie1980a}, , $v_\mathrm{o}$.
In the case of equal masses the ejection velocity of the binary. 6. is half of the ejection velocity of the single star. e.=47.
In the case of equal masses the ejection velocity of the binary, $v_\mathrm{e}$, is half of the ejection velocity of the single star, $v_\mathrm{e}=\frac{1}{2}\;v_\mathrm{o}$.
When the ejected binary. clisintegrates due to a supernova explosion then the maximum possible velocity of the released. star is ÜUuaax=Ü.
When the ejected binary disintegrates due to a supernova explosion then the maximum possible velocity of the released star is $v_\mathrm{max}=\frac{3}{2}\;v_\mathrm{o}$.
If on the other hand. the companion of the massive star is à low-mass star then the ejection velocity of the binary is equal to the ejection velocity of the single star. thus we have oe.=60.
If on the other hand, the companion of the massive star is a low-mass star then the ejection velocity of the binary is equal to the ejection velocity of the single star, thus we have $v_\mathrm{e}=v_\mathrm{o}$.
Phe maximum possible velocity of the released (less-massive companion) star after binary disintegration is of the order Musas=2eo.
The maximum possible velocity of the released (less-massive companion) star after binary disintegration is of the order $v_\mathrm{max}=2\;v_\mathrm{o}$.
dH might be expected that in the case ol binaries consisting of a hieh-mass and a low-mass star encountered by a high-mass star the low-mass star will be ected and an equal-mass binary will form.
It might be expected that in the case of binaries consisting of a high-mass and a low-mass star encountered by a high-mass star the low-mass star will be ejected and an equal-mass binary will form.
To what amount binaries with a large mass ratio will not suller an exchange has to be quantified numerically in further studies.
To what amount binaries with a large mass ratio will not suffer an exchange has to be quantified numerically in further studies.
Various theoretical and numerical studies exist on individual ection processes of massive stars. namely the dynamical ejection scenario and the supernova ejection scenario. but the combined elect of both scenarios for the distribution of massive stars in à gaaxy has not been considered vet.
Various theoretical and numerical studies exist on individual ejection processes of massive stars, namely the dynamical ejection scenario and the supernova ejection scenario, but the combined effect of both scenarios for the distribution of massive stars in a galaxy has not been considered yet.
In this paper we investigate for the first time the implications of the combination of the dynamical ancl the supernova ejection scenario for the O-sar population of the Galactic field.
In this paper we investigate for the first time the implications of the combination of the dynamical and the supernova ejection scenario for the O-star population of the Galactic field.
We call this combined. elfect. the process. of massive stars.
We call this combined effect the process of massive stars.
The main results are as follows: i) The compound velocity. eo. which is the vectorial sum of the ejection velocity. (0. of the binary from the star cluster and the release velocity. ey. with which a star is released: during a supernova. can be larger or smaller than the previous ejection velocity.
The main results are as follows: i) The compound velocity, $v_\mathrm{c}$, which is the vectorial sum of the ejection velocity, $v_\mathrm{e}$, of the binary from the star cluster and the release velocity, $v_\mathrm{r}$, with which a star is released during a supernova, can be larger or smaller than the previous ejection velocity.
Stars can be both. accelerated ancl decelerated.
Stars can be both, accelerated and decelerated.
ii) The mean compound velocity is always greater than each of the initial velocities. ος and (y (eq. 22)).
ii) The mean compound velocity is always greater than each of the initial velocities, $v_\mathrm{e}$ and $v_\mathrm{r}$ (eq. \ref{eq_mean_v}) ).
iii) Ht is very unlikely that the parent star cluster of a massive field star produced by the two-step-ejection scenario can be identified.
iii) It is very unlikely that the parent star cluster of a massive field star produced by the two-step-ejection scenario can be identified.
Lhe expected number fraction of such massive field stars which are formed apparently in isolation can account quantitatively for the number of candidates for isolated massive star formation derived in ?..
The expected number fraction of such massive field stars which are formed apparently in isolation can account quantitatively for the number of candidates for isolated massive star formation derived in \citet{dewit2005a}.
iv) Massive stars which are ejected via the two-step scenario can get higher maximum space velocities (up to 1.5 times higher for equal-mass binary components or2 times higher for significanth unequal-mass companion masses) than can be obtained by each process. (dynamical or supernova ejection) individually.
iv) Massive stars which are ejected via the two-step scenario can get higher maximum space velocities (up to 1.5 times higher for equal-mass binary components or2 times higher for significantly unequal-mass companion masses) than can be obtained by each process (dynamical or supernova ejection) individually.
only consider Lat cosmologies) the value of the galaxy-mass bias can be found from 3. which in turn. gives the value of the mass correlation function if the galaxy correlation function at z=0 is known. as shown below.
only consider flat cosmologies) the value of the galaxy-mass bias can be found from $\beta_{\rm g}$, which in turn gives the value of the mass correlation function if the galaxy correlation function at $z=0$ is known, as shown below.
The evolution in the mass correlation function can be calculated for this cosmology. and hence by comparing the z~1.4 to mass correlation. function to that of the QSOs. an estimate of the QSO bias factor can be obtained.
The evolution in the mass correlation function can be calculated for this cosmology, and hence by comparing the $z\sim1.4$ to mass correlation function to that of the QSOs, an estimate of the QSO bias factor can be obtained.
Finally. this can be used to derive an estimate of 3, as a function of cosmology.
Finally, this can be used to derive an estimate of $\beta_q$ as a function of cosmology.
One possible caveat with this technique is that we are comparing values of 4, and 3, that were measured using different estimators ane on clilferent scales.
One possible caveat with this technique is that we are comparing values of $\beta_g$ and $\beta_q$ that were measured using different estimators and on different scales.
To. minimise any possible svstematic cllects this analysis could be carried out self-consistently using the same method to determine 5, (Outram. Llovle Shanks 2000).
To minimise any possible systematic effects this analysis could be carried out self-consistently using the same method to determine $\beta_g$ (Outram, Hoyle Shanks 2000).
As the δα Galaxy Redshift Survey data is not vet available. we have chosen for simplicity to use a correlation function analysis.
As the 2dF Galaxy Redshift Survey data is not yet available, we have chosen for simplicity to use a correlation function analysis.
Rather than determining the value of the two-point correlation function at one particular point. we use the less noisy volume averaged two-point correlation function out to 20h tAIpe. £(20).
Rather than determining the value of the two-point correlation function at one particular point, we use the less noisy volume averaged two-point correlation function out to $20 h^{-1}$ Mpc, $\bar{\xi} (20)$.
Lo estimate the redshift. space. volume averaged two-point correlation function of galaxies. Sj. we assume that the galaxy correlation. function. can be approximated by a power law of the form £5;-—(s/6h *AMlpe)πλ.
To estimate the redshift space, volume averaged two-point correlation function of galaxies, $\bar{\xi}^s_g$, we assume that the galaxy correlation function can be approximated by a power law of the form $\xi^s_g=(s/6 h^{-1}$ $)^{-1.7}$.
‘Phe power law approximation is in very good agreement with early results. from the 2b Galaxy Redshift Survey two-point correlation function over the range of scales 2«s«20h *Alpe (Peder Norhere. private communication).
The power law approximation is in very good agreement with early results from the 2dF Galaxy Redshift Survey two-point correlation function over the range of scales $<s<$ $h^{-1}$ Mpc (Peder Norberg, private communication).
Once the 241 Galaxy Redshift Survey is completed. there will be no need to make this approximation.
Once the 2dF Galaxy Redshift Survey is completed, there will be no need to make this approximation.
£, Is then found. via ὃν integrating out to 205.! Mpe. the non-linear ellects on the volume averaged correlation. function. should. be small. and. are not considered. in this analwsis.
$\bar{\xi}_g$ is then found via By integrating out to $h^{-1}$ Mpc, the non-linear effects on the volume averaged correlation function should be small, and are not considered in this analysis.
liedshift measurement errors should only be a factor on small. 5h.iX pe. scales and so are also not considered.
Redshift measurement errors should only be a factor on small, $\la 5 h^{-1}$ Mpc, scales and so are also not considered.
For each cosmology.e» the bias between the ὃνgalaxies and the mass at 2=0. 5,,(0). can be found from The real space galaxy correlation function can be determined from. the redshift space ealaxy correlation funetion where the superscripts r and s indicate real and redshift space respectively.
For each cosmology, the bias between the galaxies and the mass at $z$ =0, $b_{g \rho}(0)$, can be found from The real space galaxy correlation function can be determined from the redshift space galaxy correlation function where the superscripts $r$ and $s$ indicate real and redshift space respectively.
Phe real space mass correlation function al 2=0 can now be found as The real space mass correlation. [function evolves according to linoar theory such that where ἐς). is the growth factor. which depends. on cosmology. found. from. the formula. of Carroll. Press "Turner (1992).
The real space mass correlation function at $z$ =0 can now be found as The real space mass correlation function evolves according to linear theory such that where $G(z)$ is the growth factor, which depends on cosmology, found from the formula of Carroll, Press Turner (1992).
When 04,21. G(s)—(11z).
When $\Omega_{\rm m}$ =1, $G(z) = (1 + z)$.
We now relate the correlation function of the mass at > measured in real space to the amplitude of the QSO clustering at ο. measured in redshift space as we wish to know S42). where the subseript q stands for QSO. as à function of £,,(0). £7(20)..
We now relate the correlation function of the mass at $z$ measured in real space to the amplitude of the QSO clustering at $z$, measured in redshift space as we wish to know $\beta_q(z)$, where the subscript $q$ stands for QSO, as a function of $\Omega_{\rm m}(0)$. $\bar{\xi}^s_q (20)$,
measured. over the redshift range O.3«z2.2. is determüned separately in cach cosmological model from the latest 2QZ results (see Croom et al. (
measured over the redshift range $0.3<z<2.2$, is determined separately in each cosmological model from the latest 2QZ results (see Croom et al. (
2001a) for details).
2001a) for details).
In this analysis we have not taken into account the effect. of redshift’ determination errors on the measurement of the QSO correlation function.
In this analysis we have not taken into account the effect of redshift determination errors on the measurement of the QSO correlation function.
This may leac to a slight svsteniatic overestimate of the QSO bias.
This may lead to a slight systematic overestimate of the QSO bias.
First we calculate 4,62) using (valid for Hat. cosmologies only).
First we calculate $\Omega_{\rm m}(z)$ using (valid for flat cosmologies only).
92,2) is then given by where 56,,02) ts defined by
$\beta_q(z)$ is then given by where $b_{q\rho}(z)$ is defined by
could be observed [rom high-: massive accreting black holes using the Atacama Large Millimeter/submillimeter Array (ALMA).
could be observed from $z$ massive accreting black holes using the Atacama Large Millimeter/submillimeter Array (ALMA).
Such observations could provide a diagnostic of (he radiation source: PDR or x-ray dominated region (XDI). for example.
Such observations could provide a diagnostic of the radiation source: PDR or x-ray dominated region (XDR), for example.
However. as the densities of such objects are tvpically 10° 7. collisions with the dominant species. I». will determine the CO rotational populations.
However, as the densities of such objects are typically $^5$ $^{-3}$, collisions with the dominant species, $_2$, will determine the CO rotational populations.
In Fig. 10..
In Fig. \ref{fig10},
the critical densities [or CO cue {ο para-II» collisions are plotted (neglecting optical depth effects) where the critical density of rotational level jo is defined as (e.g..Osterbrock&Ferland2006) and ονιν are the spontaneous transition probabilities for dipole transitions.
the critical densities for CO due to $_2$ collisions are plotted (neglecting optical depth effects) where the critical density of rotational level $j_2$ is defined as \citep[e.g.,][]{ost06} and $A_{j_2\rightarrow j_2'}$ are the spontaneous transition probabilities for dipole transitions.
Rotational levels joZ10 are seen to be clearly out of thermal equilibrium for a eas density of 10? "oE requiring a non-LTE analysis.
Rotational levels $j_2\gtrsim 10$ are seen to be clearly out of thermal equilibrium for a gas density of $^5$ $^{-3}$ requiring a non-LTE analysis.
As the LAMDA database incorporates the CO-IIs rate coefficients of Wernlietal.(2006). and Flower(2001) with extrapolations for para- and ortho-II» collisions above jo=29 and 20. respectively. the predicted CO line intensities of Spaanus&Meijerink(2008) [or emission from levels larger than jo=20 would likely be improved if the current rate coellicients are adopted.
As the LAMDA database incorporates the $_2$ rate coefficients of \citet{wern06} and \citet{flower01} with extrapolations for para- and $_2$ collisions above $j_2=29$ and 20, respectively, the predicted CO line intensities of \citet{spa08} for emission from levels larger than $j_2=20$ would likely be improved if the current rate coefficients are adopted.
Interestingly. their predicted CO SEDs peak at jo=10 and jo=25 for PDR and XDR environments. respectively.
Interestingly, their predicted CO SEDs peak at $j_2=10$ and $j_2=25$ for PDR and XDR environments, respectively.
The jo=645 and j-t-6lnes have been observed in the starburst galaxy NGC 253 (IIailev-Dunsheathοἱal.2008:Dradfordet2003).
The $j_2=6\rightarrow 5$ and $j_2=7\rightarrow 6$ lines have been observed in the starburst galaxy NGC 253 \citep{hai08,bra03}.
. Using à non-LTE analvsis. Dradfordetal.(2003) concluded that the cooling in the CO lines is so large Chatit must be balanced by a cosmic ταν heating rate ~SO0 times greater than that in the Alilky Way.
Using a non-LTE analysis, \citet{bra03} concluded that the cooling in the CO lines is so large thatit must be balanced by a cosmic ray heating rate $\sim$ 800 times greater than that in the Milky Way.
Previously. Krolik&Lepp(1989). suggested that highlv-excited jo lines (e.g... jo=16— 53) could be detectable [rom Sevlert galaxies eiving diagnostics of the internal pressure of the clust-obscurec torus.
Previously, \citet{kro89} suggested that highly-excited $j_2$ lines (e.g., $j_2=16-58$ ) could be detectable from Seyfert galaxies giving diagnostics of the internal pressure of the dust-obscured torus.
The Observatory studied a large variety of pre-main sequence objects
The studied a large variety of pre-main sequence objects
by the tidal threshing of more massive progenitors.
by the tidal threshing of more massive progenitors.