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As discussed 1n relsec.rilicalpoint..hinustbenegativeattlhecriticalpoint.
As discussed in \\ref{sec_criticalpoint}, $h$ must be negative at the critical point.
FEromE qure l..Efindthathisnegativefrom
From Figure \ref{fig_cak_h}, I find that $h$ is negative from the photospheric height to beyond 100 times the photospheric radius.
ltheph s
The sonic radius is assumed here to be equal to the photospheric radius.
ince
The maximum possible value for the critical point position, as constrained by $h(q)$ , can be determined by equations \ref{equ_isocak_q}) ) and \ref{equ_isocak_h}) ).
I am as
However, given the additional assumption that the sonic radius is equal to the photospheric radius, I do not expect the critical point to be beyond 100 times the photospheric radius.
suming an isothermal wind. it follows that at the critical point the nozzle function must be increasing with position |eq. (22))].
Since I am assuming an isothermal wind, it follows that at the critical point the nozzle function must be increasing with position [eq. \ref{equ_critical22na}) )].
show in Figure 2 the nozzle function. and find that the nozzle function is monotonically increasing [rom the photospheric height to bevond LOO times the photospheric height.
I show in Figure \ref{fig_cak_n} the nozzle function, and find that the nozzle function is monotonically increasing from the photospheric height to beyond 100 times the photospheric height.
Thus. the critical point conditions relsec,.riticalpoint))hold [orallspatialpointsbetiweenthephotospherieradiusandbeugondlOOtimesthisradius.
Thus, the critical point conditions \\ref{sec_criticalpoint}) ) hold for all spatial points between the photospheric radius and beyond 100 times this radius.
oL. and m.
In other words, for all these spatial points there are well defined, well determined values for $\omega_c$, $\omega'_c$, and $\dot{m}$.
The existence of local solutions in (he vicinity of each critical point can be determined through equation (26)).
The existence of local solutions in the vicinity of each critical point can be determined through equation \ref{equ_local4}) ).
The expressions 2 and 9” in equation (26)) depend on the critical point position through the condition w=uw: and 5 also depends on the critical point (Ας
The expressions $\beta'$ and $\beta''$ in equation \ref{equ_local4}) ) depend on the critical point position through the condition $\omega=\omega_c$; and $\dot{m}$ also depends on the critical point \ref{equ_critical20}) )].
Figure 3. shows that allthe spatial points up to 100 times the photospheric radius
Figure \ref{fig_cak_l} shows that allthe spatial points up to 100 times the photospheric radius
extracted from the [ongslit py arrays. and: corrected. for the emission from adjacent regions along the slit. length.
extracted from the longslit pv arrays and corrected for the emission from adjacent regions along the slit length.
The very high radial velocities of these features can cause contamination. from. nearby spectral lines.
The very high radial velocities of these features can cause contamination from nearby spectral lines.
The cillerent spectral lines cisplavecl for the two positions were chosen to avoid. this.
The different spectral lines displayed for the two positions were chosen to avoid this.
]t can be seen in the py array in Fig.
It can be seen in the pv array in Fig.
2 that the base of String 1 at A coincides closely with a remarkable spatially localised velocity feature that extends from Via=↖∖∪∪↓⋯↓⊳∖1 (at the bottom of⋅ the figure)⋅ toViv.
2 that the base of String 1 at A coincides closely with a remarkable spatially localised velocity feature that extends from $\vhel= -800~{\rm km~s^{-1}}$ (at the bottom of the figure) to.
.. ⊳↴⊀This ]Denarge rangeof ob[ velocitiosvelociti over indicatesindi‘ that᾿‘ the| regionE. ‘at which the string emerges from the inner shell of iis highly disturbed.
This large range of velocities over indicates that the region at which the string emerges from the inner shell of is highly disturbed.
The profiles from String 1 at positions C and D (Fig.
The profiles from String 1 at positions C and B (Fig.
3 a b) are easier to interpret.
3 a b) are easier to interpret.
Profile € is clearly split by τε 48 wwhile profile D seems to consist of two blended components of comparable separation.
Profile C is clearly split by $\approx$ 48 while profile B seems to consist of two blended components of comparable separation.
These imply that the string is expanding. at −24. »perpencdieularlv to the length of the string.
These imply that the string is expanding at 24 perpendicularly to the length of the string.
However. the centroid of the split. from. position B is shifted. bx GOO from wwhile that [rom position C is shifted hy S60.
However, the centroid of the split from position B is shifted by –600 from while that from position C is shifted by –860.
L. Positions D and € are at aand from rrespectively so a reasonably linear change of radial velocity along the length of String 1 is indicated.
Positions B and C are at and from respectively so a reasonably linear change of radial velocity along the length of String 1 is indicated.
Even with such aree shifts in radial velocity the widths (PFWILL) of the individual velocity components (corrected for the 12 instrumental resolution) are only =40kms+.
Even with such large shifts in radial velocity the widths (FWHM) of the individual velocity components (corrected for the 12 instrumental resolution) are only $\approx 40 \kms$.
Notethat there is an unresolved stcllar-like feature (at D in Fig.
Note that there is an unresolved stellar-like feature (at D in Fig.
1) and. although somewhat detached. it is in ine with String 1 andCarinac.
1) and, although somewhat detached, it is in line with String 1 and.
. Currie et (2000) lave used proper motion measurements to show that this is a bullet travelling at à higher velocity than the rest of he string and is likely to be physically associated with he string.
Currie et (2000b) have used proper motion measurements to show that this is a bullet travelling at a higher velocity than the rest of the string and is likely to be physically associated with the string.
Their astrometric measurements suggest. that he bullets are travelling at up to 3000kms.* Le. around of the speed of light.
Their astrometric measurements suggest that the bullets are travelling at up to $3000~{\rm km~s^{-1}}$ i.e. around $1\%$ of the speed of light.
The angle of the string to the plane of sky is determined by comparison of the astrometric velocity measurements with racial velocity nieasurements to be (Currie et 2000b).
The angle of the string to the plane of sky is determined by comparison of the astrometric velocity measurements with radial velocity measurements to be (Currie et 2000b).
This angle agrees with that estimated by. Weis et (1999).
This angle agrees with that estimated by Weis et (1999).
In this section. various possible explanations for the origin of the strings are considered in turn.
In this section, various possible explanations for the origin of the strings are considered in turn.
Garcta-Seguraetal.(1999). have shown that. for a planetary nebula medium in which the magnetic pressure. dominates the eas pressure. narrow collimated. jet like features with a velocity that increases along the jet can be produced.
\scite{garcia_segura.et.al99} have shown that, for a planetary nebula medium in which the magnetic pressure dominates the gas pressure, narrow collimated jet like features with a velocity that increases along the jet can be produced.
The calculations were two dimensional and they argued. that when extended to 3D. pinching instabilities could lead: to localised disturbances along the jet ancl possibly break up into clumps.
The calculations were two dimensional and they argued that when extended to 3D, pinching instabilities could lead to localised disturbances along the jet and possibly break up into clumps.
At first sight. this tvpe of model. suitably adaptec for the conditions in the η Carinae nebulosity. appears promising.
At first sight, this type of model, suitably adapted for the conditions in the $\eta$ Carinae nebulosity, appears promising.
A major problem is that a bipolar axis is require along which these structures will form.
A major problem is that a bipolar axis is required along which these structures will form.
In y Carinae there are at least 5 strings.
In $\eta$ Carinae there are at least 5 strings.
Vhere are likely to be more since the observed strings happen to fie at fortuitous positions anm ace-on and obscured strings will not be detected.
There are likely to be more since the observed strings happen to lie at fortuitous positions and face-on and obscured strings will not be detected.
Some kine of precessing axis also appears unlikely since the dvnamica of imesthe strings indicates that they were all ejected at the ime of the great outburst of the 1840s although a rapidly oecessing and tumbling axis cannot be ruled out.
Some kind of precessing axis also appears unlikely since the dynamical times of the strings indicates that they were all ejected at the time of the great outburst of the 1840s although a rapidly precessing and tumbling axis cannot be ruled out.
The number of strings is also a problem for a ivdrodynamical jet. interpretation for similar reasons to hose above.
The number of strings is also a problem for a hydrodynamical jet interpretation for similar reasons to those above.
Several collimating sources with cillering
Several collimating sources with differing
(he galaxies in this sample. about 10? M. with some galaxies having significantly stricter upper limits (Robertsetal.1991:Breeman.Loge.andRoberts1992).
the galaxies in this sample, about $^{8.5}$ $_{\odot}$, with some galaxies having significantly stricter upper limits \citep{roberts91,breg92}.
.. At à conduction rate of 107 NL, 4. this would lead to a lifetime for the cold gas reservoir of 105 vr. so the gas would have to be replenished every LO"] vr by the amount of gas found in galaxies about one-tenth the mass of the Milky Way.
At a conduction rate of $^{2.5}$ $_{\odot}$ $^{-1}$, this would lead to a lifetime for the cold gas reservoir of $^{6}$ yr, so the gas would have to be replenished every $^{6}$ yr by the amount of gas found in galaxies about one-tenth the mass of the Milky Way.
The orbital interaction time would be about 105 vr. so we should see many of these galaxies passing through the earlv-tvpe galaxy. which is nol the case.
The orbital interaction time would be about $^{8}$ yr, so we should see many of these galaxies passing through the early-type galaxy, which is not the case.
Consequently. it seems unlikely that conductive heating of gas could produce the lines that we observe.
Consequently, it seems unlikely that conductive heating of gas could produce the lines that we observe.
A final issue is whether the gas is undergoing simple radiativecooling or whether turbulent mixing lavers play a role (Slavin.Shull.anclBDegelnan1993).
A final issue is whether the gas is undergoing simple radiativecooling or whether turbulent mixing layers play a role \citep{slavin93}.
. In. this case. the mixing would be between the hot ambient mecdium and gas that has already cooled. and (his process can cause gas (o spend less time al a given temperature compared to the pure raciative model.
In this case, the mixing would be between the hot ambient medium and gas that has already cooled, and this process can cause gas to spend less time at a given temperature compared to the pure radiative model.
This has been suggested as a process within cluster cooling flows in order {ο remain consistent with the discrepancy between (he observed and predicted strength of the X-ray OVII line within the cooling flow model (Fabian οἱ al.
This has been suggested as a process within cluster cooling flows in order to remain consistent with the discrepancy between the observed and predicted strength of the X-ray OVII line within the cooling flow model (Fabian et al.
2001).
2001).
A similar discrepancy exists for NGC 4636. where the OVII line is weaker (han expected for gas cooling at the rate derived from the data (Xu οἱ al.
A similar discrepancy exists for NGC 4636, where the OVII line is weaker than expected for gas cooling at the rate derived from the data (Xu et al.
2003).
2003).
If tiubulent mixing causes gas to effectively junp over the OVII temperature region (~ LO’ IN). it could solve this issue. but it also makes the prediction that there will be emission trom the CIV A 1550 line at a Iuminosityv. greater than the OVI doublet.
If turbulent mixing causes gas to effectively jump over the OVII temperature region $\sim$ $^{6}$ K), it could solve this issue, but it also makes the prediction that there will be emission from the CIV $\lambda$ 1550 line at a luminosity greater than the OVI doublet.
Unfortunately. there is presently no instrument that can measure the CIV A 1550 line with the required sensitivity.
Unfortunately, there is presently no instrument that can measure the CIV $\lambda$ 1550 line with the required sensitivity.
The use of OVI emission has given a new insight into (he properties of the hot gas in earlv-tvpe galaxies. ancl (his study highlights the need for Burther investigations.
The use of OVI emission has given a new insight into the properties of the hot gas in early-type galaxies, and this study highlights the need for further investigations.
The greatest need is for a substantial increase in sensitivity. since most of the galaxies were nol detected and even the detections are tvpically at the 3-50 level.
The greatest need is for a substantial increase in sensitivity, since most of the galaxies were not detected and even the detections are typically at the $\sigma$ level.
For objects with short exposure limes (« 5 ksec). it should be possible to double or even triple the S/N with moderate inves(mentis of observing time ((his applies (ο six objects in (hie sample. four of which are detections or possible detections).
For objects with short exposure times $<$ 5 ksec), it should be possible to double or even triple the S/N with moderate investments of observing time (this applies to six objects in the sample, four of which are detections or possible detections).
The other objects generally have exposure times of ksec. requiring an additional 15-30 ksec per object (generally of night data) to double the S/N. For the objects with upper limits. improving the S/N by 2-3 will not make (hese objects secure detections even if there is a weak feature present.
The other objects generally have exposure times of 5-10 ksec, requiring an additional 15-30 ksec per object (generally of night data) to double the S/N. For the objects with upper limits, improving the S/N by 2-3 will not make these objects secure detections even if there is a weak feature present.
Improved studies of these objects. or of more distant sources will require a new instrument with al least an order of magnitude greater sensitivitv.
Improved studies of these objects, or of more distant sources will require a new instrument with at least an order of magnitude greater sensitivity.
This instrumental goal should be achievable as is a
This instrumental goal should be achievable as is a
combination considered that gives a reasonable represcutation of the observed colors of Αν clusters.
combination considered that gives a reasonable representation of the observed colors of M31's clusters.
Consideriug such shifts between models aud observations provides —an important— tool for— refining— SPS models.
Considering such shifts between models and observations provides an important tool for refining SPS models.
Such offsets should be considered when inferring the properties of elobular clusters and ealaxics from their integrated emission.
Such offsets should be considered when inferring the properties of globular clusters and galaxies from their integrated emission.
We would Like to thank Dr. Charlie Conroy for referecing this paper and for providing prompt cohunents. which were beneficial to the final version.
We would like to thank Dr. Charlie Conroy for refereeing this paper and for providing prompt comments, which were beneficial to the final version.
We would also like to thank Claudia Marastou for providing us with an advanced copy of her paper aud updated stellar population models.
We would also like to thank Claudia Maraston for providing us with an advanced copy of her paper and updated stellar population models.
NDP aud SEZ would like to acknowledge support from the NASA eraut NNAOSATOOG.
MBP and SEZ would like to acknowledge support from the NASA grant NNX08AJ60G.
NDP aud SEZ would like to acknowledge support from the NASA eraut NNAOSATOOG.,
MBP and SEZ would like to acknowledge support from the NASA grant NNX08AJ60G.
The formation of the first stars should in principle be simpler to understand than present-day star formation.
The formation of the first stars should in principle be simpler to understand than present-day star formation.
The usual prediction that the mass of the first stars O(100.—LOOOJAL. is attributable to dominance of H» cooling and consequent high temperature and accretion rate (Abel. Bryan and Norman 2002: Bromm. Coppi and Larson 2002).
The usual prediction that the mass of the first stars ${\mathcal{O}}(100-1000)\rm M_\odot$ is attributable to dominance of $_2$ cooling and consequent high temperature and accretion rate (Abel, Bryan and Norman 2002; Bromm, Coppi and Larson 2002).
It is appropriate to question this result. that only very massive stars formed. for at least four phenomenological reasons.
It is appropriate to question this result, that only very massive stars formed, for at least four phenomenological reasons.
Firstly. one finds solar mass stars at Fe]5.4.
Firstly, one finds solar mass stars at $\rm [Fe] \simlt -4$.
These may be contaminated by companion stars that exploded as hypernovae. whose ejecta are depleted in Fe relative to N and C and this interpretation is consistent with the measured abundance ratios for a handful of extreme metal-poor stars.
These may be contaminated by companion stars that exploded as hypernovae, whose ejecta are depleted in Fe relative to N and C and this interpretation is consistent with the measured abundance ratios for a handful of extreme metal-poor stars.
However not all metal poor halo stars display such anomalies. and a substantial fraction at the 107 solar level have abundance ratios that are consistent with conventional SNII precursors.
However not all metal poor halo stars display such anomalies, and a substantial fraction at the $10^{-4}$ solar level have abundance ratios that are consistent with conventional SNII precursors.
There are at least two halo stars known at ο5.
There are at least two halo stars known at $\rm [Fe] \simlt -5$.
HE 0107-5240 is a giant with [Fe/H] —-5.3. but enhanced nitrogen. carbon and oxygen: [N/H]= -3.0. [C/H]= 1.3 and [O/H]=-2.9 (Christlieb et al.
HE 0107-5240 is a giant with [Fe/H] =-5.3, but enhanced nitrogen, carbon and oxygen: [N/H]= -3.0, [C/H]= -1.3 and [O/H]=-2.9 (Christlieb et al.
2004).
2004).
HE 1327-2326 isa main sequence star (tor subgiant) with an iron abundance about a factor of 2 lower than HE 0107-5240.
HE 1327-2326 is a main sequence star (or subgiant) with an iron abundance about a factor of 2 lower than HE 0107-5240.
In this latter case. both nitrogen and carbon are enhanced relative to iron by about 4 dex. while there is only a comparable upper limit on oxygen (Frebel et al.
In this latter case, both nitrogen and carbon are enhanced relative to iron by about 4 dex, while there is only a comparable upper limit on oxygen (Frebel et al.
2005).
2005).
Appeal to preenrichment by a core collapse ~25M. supernova of Population III. abundance with fallback fits the abundance patterns well (Umeda and Nomoto 2003). although oxygen may possibly be overproduced in the case of HE 0107-5240 (Bessell. Christlieb and Gustafsson 2004).
Appeal to preenrichment by a core collapse $\sim 25 \rm\,M_\odot$ supernova of Population III abundance with fallback fits the abundance patterns well (Umeda and Nomoto 2003), although oxygen may possibly be overproduced in the case of HE 0107-5240 (Bessell, Christlieb and Gustafsson 2004).
The example of HE 1327-2326 eliminates any internal enrichment source (e.g. convective dredge-up). nor is there evidence for a binary companion in the case of HE 0107-524. thereby also suggesting that mass transfer from an AGB star is an unlikely explanation.
The example of HE 1327-2326 eliminates any internal enrichment source (e.g. convective dredge-up), nor is there evidence for a binary companion in the case of HE 0107-524, thereby also suggesting that mass transfer from an AGB star is an unlikely explanation.
The high CNO abundances argue for a common explanation involving enrichment of the primordial cloud by Type II supernovae of primordial abundance.
The high CNO abundances argue for a common explanation involving enrichment of the primordial cloud by Type II supernovae of primordial abundance.
Indeed. the abundance patterns in extremely metal poor halo stars suggest that enrichment was produced by Population III stars in the mass range 20-130 A7. (Umeda and Nomoto 2003).
Indeed, the abundance patterns in extremely metal poor halo stars suggest that enrichment was produced by Population III stars in the mass range 20-130 $M_\odot$ (Umeda and Nomoto 2005).
Secondly. the broad emission line regions of very high redshift quasars. reveal high elemental abundances that appear to have also been generated by conventional SNII precursors.
Secondly, the broad emission line regions of very high redshift quasars, reveal high elemental abundances that appear to have also been generated by conventional SNII precursors.
In particular. the nearly constant FeII/MgII emission line ratios over 0«&ο«5 requires intense SNIT activity at a redshift as high as 9 (Dietrich. Hamann. Appenzeller and Vestergaard 2003).
In particular, the nearly constant FeII/MgII emission line ratios over $0<z<5$ requires intense SNII activity at a redshift as high as 9 (Dietrich, Hamann, Appenzeller and Vestergaard 2003).
Thirdly. the chemical yield predictions from primordial very massive stars. when normalised to the inferred ionising photon output required to reionise the universe at high redshift. do not correspond to observed abundances in any primitive environments.
Thirdly, the chemical yield predictions from primordial very massive stars, when normalised to the inferred ionising photon output required to reionise the universe at high redshift, do not correspond to observed abundances in any primitive environments.
In particular, the pair-instability supernova nucleosynthetic signatures generated by stars with initial masses in the range 130 to 260 M. are not seen either in the intergalactic medium. including both Lyman alpha forest and damped Lyman alpha absorption systems. or in extremely metal-poor halo stars (Daigne et al.
In particular, the pair-instability supernova nucleosynthetic signatures generated by stars with initial masses in the range 130 to 260 $_\odot$ are not seen either in the intergalactic medium, including both Lyman alpha forest and damped Lyman alpha absorption systems, or in extremely metal-poor halo stars (Daigne et al.
2005).
2005).
Finally. from the theoretical perspective with regard to cooling. the primordial metal abundance pattern has profound consequences for the thermal balance and chemical composition of the gas. and hence for the equation of state of the parental cloud.
Finally, from the theoretical perspective with regard to cooling, the primordial metal abundance pattern has profound consequences for the thermal balance and chemical composition of the gas, and hence for the equation of state of the parental cloud.
Spaans and Silk (2005) tind that the polytropic index is soft for low oxygen abundance enhancements. 5. us appropriate for Population IIT. but stiffens to a polytropic index larger than unity for [O/H]LO= due to the large opacity in the CO and Π.Ο cooling lines.
Spaans and Silk (2005) find that the polytropic index is soft for low oxygen abundance enhancements, $<-3$, as appropriate for Population III, but stiffens to a polytropic index $\gamma$ larger than unity for $>10^{-2}$ due to the large opacity in the CO and $_2$ O cooling lines.
Hence Pop II star formation is efficient. especially before hypernova enrichment and associated oxygen enhancement has occurred.
Hence Pop III star formation is efficient, especially before hypernova enrichment and associated oxygen enhancement has occurred.
There should be no obstacle to forming stars over a wide range of masses even in the absence of significant fine-structure cooling.
There should be no obstacle to forming stars over a wide range of masses even in the absence of significant fine-structure cooling.
On the contrary. once the polytropic index
On the contrary, once the polytropic index
CGrant PB 19951132-02-01.
Grant PB 1995-1132-02-01.
"n Phe data reduction was carried out on the Oxford node using the ark software.
The data reduction was carried out on the Oxford Starlink node using the $\sc ark$ software.
case of the OH GC group, 19 clusters are of Rec>10 kpc and 6 are Rec>20 kpc, however, these samples are consistent with an isotropic parent distribution in and of trials respectively.
case of the OH GC group, 19 clusters are of $R_{GC} > 10$ kpc and 6 are $R_{GC} > 20$ kpc, however, these samples are consistent with an isotropic parent distribution in and of trials respectively.
In the case of the YH GC group, however, the hypothesis of a spatially isotropic parent distribution becomes increasingly unlikely as we restrict the sample to more distant objects.
In the case of the YH GC group, however, the hypothesis of a spatially isotropic parent distribution becomes increasingly unlikely as we restrict the sample to more distant objects.
As seen in the γ-ζ plane (Figure 2)) the YH GCs are increasingly located at larger y and G with increasing galactocentric distance.
As seen in the $\gamma$ $\zeta$ plane (Figure \ref{figure:gammazeta}) ) the YH GCs are increasingly located at larger $\gamma$ and $\zeta$ with increasing galactocentric distance.
This is indicative that the spherical distribution of the normal vectors to the best-fitting plane for the population is becoming increasingly confined to a preferred direction.
This is indicative that the spherical distribution of the normal vectors to the best-fitting plane for the population is becoming increasingly confined to a preferred direction.
That is to say, the YH GCs are seen to be increasingly confined to a planar alignment as we progress to larger galactocentric distances.
That is to say, the YH GCs are seen to be increasingly confined to a planar alignment as we progress to larger galactocentric distances.
In Table 1 we summarize our findings regarding the orientation and rms thickness of the plane that best matches to the observed sample.
In Table \ref{table:lsq} we summarize our findings regarding the orientation and rms thickness of the plane that best matches to the observed sample.