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. However. a remarkable interaction. maeuctosphere is
However, a remarkable interaction is
Figure 2. gives a schematic view. beginning al the time of peak accretion rate. of what might be expected in terms of the light curves for the jet power (before allowance for beaming and radiative efficiency) and the thermal luminosity.
Figure \ref{fig:L-t} gives a schematic view, beginning at the time of peak accretion rate, of what might be expected in terms of the light curves for the jet power (before allowance for beaming and radiative efficiency) and the thermal luminosity.
For the parameter values chosen (μυ=10. all other scalingparameters unity). Zj4 Falls to the level of Lic at almost the same time. /21/4. às μα enters the sub-Edcdington regime and also begins to decline.
For the parameter values chosen $M_{BH,6} = 10$, all other scalingparameters unity), $L_{\rm jet}$ falls to the level of $L_{\rm therm}$ at almost the same time, $t \simeq 7 t_0$, as $L_{\rm therm}$ enters the sub-Eddington regime and also begins to decline.
From that time to /230/4. both fall together. maintaining similar power levels.
From that time to $t \simeq 30 t_0$, both fall together, maintaining similar power levels.
Finally. after /230/4 (i.e.. a time larger by jj?c4 than the time at which the thermal luminosity begins to decline). the jet luminosity stabilizes. while {ο continues to fall.
Finally, after $t \simeq 30t_0$ (i.e., a time larger by $\eta^{-3/5} \simeq 4$ than the time at which the thermal luminosity begins to decline), the jet luminosity stabilizes, while $L_{\rm therm}$ continues to fall.
The ratio Ligjet/thermLiga as a [unetion of time for fixed black hole mass can be described much more simply.
The ratio $L_{\rm jet}/L_{\rm therm}$ as a function of time for fixed black hole mass can be described much more simply.
Ii rough terms. it is just where ία} is the intrinsic (1.0.. without photon trapping) radiative efficiency [or a Given spin parameter.
In rough terms, it is just where $\eta(a/M)$ is the intrinsic (i.e., without photon trapping) radiative efficiency for a given spin parameter.
At high accretion rate. the ratio is xgrin: in the transition range where photon (rapping is marginal. the ratio may change relatively slowly: al low accretion rale. (he ratio is oi.+.
At high accretion rate, the ratio is $\propto q\dot m$; in the transition range where photon trapping is marginal, the ratio may change relatively slowly; at low accretion rate, the ratio is $\propto \dot m^{-1}$.
In any particular event. r2 rises rapidly (on a timescale ~fy) ad first. but then declines slowly.
In any particular event, $\dot m$ rises rapidly (on a timescale $\sim t_0$ ) at first, but then declines slowly.
The ratio ofobserved jet luminosity to thermal luminosity follows the same trend. modulated by any evolution of qBija.
The ratio of jet luminosity to thermal luminosity follows the same trend, modulated by any evolution of $q{\cal B}\eta_{\rm jet}$.
Eventually. the aceretion rate falls so low that the disk is no longer radiation-dominatecd. and our estimate for the pressure in the inner disk is no longer valid.
Eventually, the accretion rate falls so low that the disk is no longer radiation-dominated, and our estimate for the pressure in the inner disk is no longer valid.
Assuming that this occurs when the gas pressure becomes comparable to the radiation pressure αἱ rI0r,. the critical accretion rate is iic0.0507/0.1)(0/0.1)!Les"Mya
Assuming that this occurs when the gas pressure becomes comparable to the radiation pressure at $r \simeq 10r_g$, the critical accretion rate is $\dot m \simeq 0.05 (\eta/0.1)^{-1}(\alpha/0.1)^{-1/8} M_{BH,6}^{-1/8}$.
Η the accretion rate declines as (L/19). 77. it happens at a time After (his time. although the thermal Inminosity continues to decline in proportion to
If the accretion rate declines as $(t/t_0)^{-5/3}$ , it happens at a time After this time, although the thermal luminosity continues to decline in proportion to
underlving stellar absorption on nebula helium emission lines (hat is poorly constrained.
underlying stellar absorption on nebula helium emission lines that is poorly constrained.
Our analvsis is along the line of Peimbert οἱ al. (
Our analysis is along the line of Peimbert et al. (
2002) and Olive and Skillman (2004: hereinafter OS04). who introduced the helium absorption strength as a free parameter. although ours are somewhat more conservative.
2002) and Olive and Skillman (2004; hereinafter OS04), who introduced the helium absorption strength as a free parameter, although ours are somewhat more conservative.
OS04 ancl Peimbert οἱ al. (
OS04 and Peimbert et al. (
2000: 2002) presented an analvsis in which plasma temperature is also determined by (he helium emission lines alone.
2000; 2002) presented an analysis in which plasma temperature is also determined by the helium emission lines alone.
However. (his. in principle proper approach given accurate data. induces laree errors in (he resulting helium abundance with the present accuracy. of the available data for distant LIL regions. and a trend that might be brought about with the inclusion of stellar absorption is buried in (he noise.
However, this, in principle proper approach given accurate data, induces large errors in the resulting helium abundance with the present accuracy of the available data for distant HII regions, and a trend that might be brought about with the inclusion of stellar absorption is buried in the noise.
Since we do not see a compelling reason that plasma temperatures from helium and oxveen are significantlv dillerent. we take the approach (hat plasma. temperature is determined by the ratio of oxvgen emission lines. as was done in most of the work including ITO4. and study the effect of stellar absorption by introducing it as a [ree parameter.
Since we do not see a compelling reason that plasma temperatures from helium and oxygen are significantly different, we take the approach that plasma temperature is determined by the ratio of oxygen emission lines, as was done in most of the work including IT04, and study the effect of stellar absorption by introducing it as a free parameter.
We show thatY,and dY/dZ ave very sensitive to the introduction of the underlying stellar absorption of the helium lines.
We show that$Y_p$and $dY/dZ$ are very sensitive to the introduction of the underlying stellar absorption of the helium lines.
We consider 30 of the 33 IL IL regions given in A4026 A4363 AM959.5007. Ha. IL2. I5 Ho. I(AJ/F(IL3). F(A) W(À) αμι f(A)eg4 111. 143889. (1))
We consider 30 of the 33 H II regions given in $\lambda$ $\lambda$ $\lambda\lambda$ $\alpha$ $\beta$ $\gamma$ $\delta$ $I(\lambda)/I({\rm H}\beta)$ $F(\lambda)$ $W(\lambda)$ $a_{\rm HI}$ $f(\lambda)c_{{\rm H}\beta}$ $\beta$ $\lambda$ \ref{eq:Hemis})
forcing a fit to galaxies that truly have slowly decreasing power-law profiles will clearly create ersatz nuclei.
forcing a fit to galaxies that truly have slowly decreasing power-law profiles will clearly create ersatz nuclei.
Again. we see uo physical or even empirical justification to prefer the + nucleus uiodel. let aloue any demoustration strong enough to show that tlie Nuker law-basecl interpretation is uuteuable.
Again, we see no physical or even empirical justification to prefer the $+$ nucleus model, let alone any demonstration strong enough to show that the Nuker law-based interpretation is untenable.
The Nuker law. of course. has uo physical justification either. however. we are not using it to extrapolate bevouc the domain of the fit: it serves in this coutext as a smooth representation of the data.
The Nuker law, of course, has no physical justification either, however, we are not using it to extrapolate beyond the domain of the fit; it serves in this context as a smooth representation of the data.
Likewise. the use of models is interesting for the portious of the envelope for which they are adequate fits.
Likewise, the use of models is interesting for the portions of the envelope for which they are adequate fits.
Neither should be used to extrapolate to radii considerably sinaller tla those that are well fitted by their forms — this is why we emphasize the use of 2. which is always a local measure. in prefereuce to 2. which itself is the slope only realized as r—0. Iu this context it is interesting to revisit tlie uou-parametrically derived space density. profiles in Figure 6..
Neither should be used to extrapolate to radii considerably smaller than those that are well fitted by their forms — this is why we emphasize the use of $\gamma',$ which is always a local measure, in preference to $\gamma,$ which itself is the slope only realized as $r\rightarrow0.$ In this context it is interesting to revisit the non-parametrically derived space density profiles in Figure \ref{fig:den_pro}.
The stroug impression of bimodality iu this figure is concordant. with the parametric analysis based ou the limiting projected profile slopes provided by the Nuker law.
The strong impression of bimodality in this figure is concordant with the parametric analysis based on the limiting projected profile slopes provided by the Nuker law.
Under the VCS interpretation. however. the cleau separation of the two bundles of profiles iu the figure would be iuterpreted as due to nuclear compouents iu the upper buudle. aud the composite plot of "true? ealaxy density. profiles could ouly be constructed with reference to the VC'S parametric models.
Under the VCS interpretation, however, the clean separation of the two bundles of profiles in the figure would be interpreted as due to nuclear components in the upper bundle, and the composite plot of “true” galaxy density profiles could only be constructed with reference to the VCS parametric models.
Iu our analysis of WEPCTI data (Laueretal.1995) or WEPC?2 data (Laueretal.2005).. we icentilied nuclei by looking for upturus above a power-law cusp as r—0. These are often obvious in core galaxies. as cau be seen in some of the examples in Figure 11.. but for power-law galaxies the evidence for a possible nucleus is often just a subtle increase in the profile slope as the resolutiou ünit is approached.
In our analysis of WFPC1 data \citep{l95} or WFPC2 data \citep{l05}, we identified nuclei by looking for upturns above a power-law cusp as $r\rightarrow0.$ These are often obvious in core galaxies, as can be seen in some of the examples in Figure \ref{fig:acscomp1}, but for power-law galaxies the evidence for a possible nucleus is often just a subtle increase in the profile slope as the resolution limit is approached.
There are no strongupieerd breaks in auy of the galaxies discussed in thiW. section that would make detection of a nucleus unambiguous.
There are no strong breaks in any of the galaxies discussed in this section that would make detection of a nucleus unambiguous.
At the same time. Restetal.(2001 sresent decouvolved WEPC2 observatious of NGC L171 aud LIs2. two galaxies that are plotted iu Figure 8. with widely differing 5 values. that do have clearly defined nuclei. but again ones more uodest than those implied by the VCS moclels.
At the same time, \citet{rest} present deconvolved WFPC2 observations of NGC 4474 and 4482, two galaxies that are plotted in Figure \ref{fig:gam_diff} with widely differing $\gamma'$ values, that do have clearly defined nuclei, but again ones more modest than those implied by the VCS models.
We explore the non-uniqueness of the + wucleus model in further detail lor NGC 11253. in whieh we plot the Laueretal.(2005) data for this galaxy exteucled to large radii by the addition of the B band data of Jedrzejewski(1987). (Figure 11)).
We explore the non-uniqueness of the $+$ nucleus model in further detail for NGC 4458, in which we plot the \citet{l05} data for this galaxy extended to large radii by the addition of the $B$ band data of \citet{jed} (Figure \ref{fig:n4458}) ).
The Nuker law is fitted to r«125". or 2.8 decades iu radius. a portiou of the galaxy that Cotéetal.(2006) consider to be a bright and extended nucleus.
The Nuker law is fitted to $r<15'',$ or 2.8 decades in radius, a portion of the galaxy that \citet{cote} consider to be a bright and extended nucleus.
The Ferrareseetal.(2006) fit in contrast is valid over only I<r«20". a little more than a single decade in radius. but is then extrapolated inwards by 1.6 decades to the radius at which Ferrareseetal.(2006) report 5 The profile of this object is obviously complex aud the Nuker residuals shown in show a sinusoidal pattern. associated with au increase in prolile slope at rzz1". Perhaps by our criterion. this could be interpreted to be the onset of a nucleus.
The \citet{lf} fit in contrast is valid over only $4''<r<50'',$ a little more than a single decade in radius, but is then extrapolated inwards by 1.6 decades to the radius at which \citet{lf} report $\gamma'.$ The profile of this object is obviously complex and the Nuker residuals shown in \citet{l05} show a sinusoidal pattern, associated with an increase in profile slope at $r\approx1''.$ Perhaps by our criterion, this could be interpreted to be the onset of a nucleus.
Even so. the Nuker law fitted to just r>1” would clearly model this region with less curvature than implied by the moclel. again giving a less luminous nucleus.
Even so, the Nuker law fitted to just $r>1''$ would clearly model this region with less curvature than implied by the model, again giving a less luminous nucleus.
Yet another tuterpretation. however. is that NGC [1255 is a dwarf 50 galaxy. in which the Nuker law appropriately describes the bulge while the law
Yet another interpretation, however, is that NGC 4458 is a dwarf S0 galaxy, in which the Nuker law appropriately describes the bulge while the law
constraining the interior structure of low and high-mass RV exoplanets, respectively.
constraining the interior structure of low and high-mass RV exoplanets, respectively.
We would like to conclude by presenting a list of possibilities for determination of physical properties of planets from observations of orbital parameters.
We would like to conclude by presenting a list of possibilities for determination of physical properties of planets from observations of orbital parameters.
The compiled flow-chart is presented as Figure 7.
The compiled flow-chart is presented as Figure 7.
Let us summarize: if a newly discovered system harbors only a single tansiting hot Jupiter, the interior structure can be derived from monitoring of orbital precession (Ragozzine Wolf 2009).
Let us summarize: if a newly discovered system harbors only a single tansiting hot Jupiter, the interior structure can be derived from monitoring of orbital precession (Ragozzine Wolf 2009).
Alternatively, although observationally challenging, the rotational and tidal bulges can be deduced directly from the shape of the light-curve (Carter Winn 2010, Leconte et al 2011).
Alternatively, although observationally challenging, the rotational and tidal bulges can be deduced directly from the shape of the light-curve (Carter Winn 2010, Leconte et al 2011).
If two planets are present and reside at a fixed point, the situation becomes more advantageous.
If two planets are present and reside at a fixed point, the situation becomes more advantageous.
If tidal precession plays an important role, and the inner planet transits, the Love number can be derived from a single snap-shot observation of the orbital state (Batygin Bodenheimer Laughlin 2009).
If tidal precession plays an important role, and the inner planet transits, the Love number can be derived from a single snap-shot observation of the orbital state (Batygin Bodenheimer Laughlin 2009).
If the inner planet does not transit, its exact mass can be derived spectroscopically (Snellen et al and kyR? can be computed.
If the inner planet does not transit, its exact mass can be derived spectroscopically (Snellen et al 2010) and $k_2 R^5$ can be computed.
On the other hand, if GR. 2010)overwhelms tidal precession, sin(/) degeneracy of the system can be resolved.
On the other hand, if GR overwhelms tidal precession, $\sin(I)$ degeneracy of the system can be resolved.
If the system is tidally relaxed but is not co-planar, orbital evolution will follow a limit cycle rather than a fixed point (Mardling 2010).
If the system is tidally relaxed but is not co-planar, orbital evolution will follow a limit cycle rather than a fixed point (Mardling 2010).
In this case, precise modeling can yield constraints on the mutual inclination between planets.
In this case, precise modeling can yield constraints on the mutual inclination between planets.
If three or more planets are present in the system, the solution simplifies to one that is similar to the two-planet case if the system is at a fixed point.
If three or more planets are present in the system, the solution simplifies to one that is similar to the two-planet case if the system is at a fixed point.
Otherwise, the situation is considerably more complex and should be treated on a case-by-case basis.
Otherwise, the situation is considerably more complex and should be treated on a case-by-case basis.
Finally, it is always important to keep in mind that measurement of flux-excess during secondary eclipse can yield the tidal luminosity of a planet (e.g. Laughlin et al 2009), and thus its tidal Q. We are grateful to Y. Wu, D. J. Stevenson, J. A. Johnson and M. E. Brown for carefully reviewing the manuscript and for useful discussions.
Finally, it is always important to keep in mind that measurement of flux-excess during secondary eclipse can yield the tidal luminosity of a planet (e.g. Laughlin et al 2009), and thus its tidal Q. We are grateful to Y. Wu, D. J. Stevenson, J. A. Johnson and M. E. Brown for carefully reviewing the manuscript and for useful discussions.
We thank the anonymous referee for useful suggestions.
We thank the anonymous referee for useful suggestions.
This work was funded by NASA grant NNX08AY38A and NASA/Spitzer/JPL grant 1368434 to GL.
This work was funded by NASA grant NNX08AY38A and NASA/Spitzer/JPL grant 1368434 to GL.
Alagnetic white dwarfs olfer an important glimpse into the roles that magnetism may play in the formation anc evolution of stars with moclerate mass.
Magnetic white dwarfs offer an important glimpse into the roles that magnetism may play in the formation and evolution of stars with moderate mass.
At the same time. thes provide unique laboratories for studying the behavior of matter in Lields lar stronger than can be obtainec terrestriallv.
At the same time, they provide unique laboratories for studying the behavior of matter in fields far stronger than can be obtained terrestrially.
More than 5 dozen examples have been fou with field strengths. between ~310 G and 10" C. and the [ist of atomic ancl molecular species. representec includes virtually every substance seen among white cwarls in general. including HI. He. Na. Mg. Ca. €». and acdcditiona molecules that are as vet unidentified.
More than 5 dozen examples have been found with field strengths between $\sim$$3\times10^4$ G and $10^9$ G, and the list of atomic and molecular species represented includes virtually every substance seen among white dwarfs in general, including H, He, Na, Mg, Ca, $_2$, and additional molecules that are as yet unidentified.
Alodeling of spectroscopic and spectropolarimetric data on magnetic stars is à. powerful. technique for eainine information into the Ποια distributions over the stellar surfaces. particularly for the objects in which the observations can be phase-resolvecl over a rotational evcle.
Modeling of spectroscopic and spectropolarimetric data on magnetic stars is a powerful technique for gaining information into the field distributions over the stellar surfaces, particularly for the objects in which the observations can be phase-resolved over a rotational cycle.
This information is crucial for evaluating alternatives for the origin ancl evolution of the fields. ancl for relating magnetic structures found among one class of star to other stages of evolution.
This information is crucial for evaluating alternatives for the origin and evolution of the fields, and for relating magnetic structures found among one class of star to other stages of evolution.
Unfortunately. a lack of thorough observational material has traditionally handicapped studies of white ciwarfs in the southern hemisphere.
Unfortunately, a lack of thorough observational material has traditionally handicapped studies of white dwarfs in the southern hemisphere.
During the course of a spectropolarimetric survey for magnetic fields among southern white dwarfs. special attention was pald to several known or proposed magnetic examples.
During the course of a spectropolarimetric survey for magnetic fields among southern white dwarfs, special attention was paid to several known or proposed magnetic examples.
This paper reports the results on 9 objects which emerged from. the
This paper reports the results on 9 objects which emerged from the
In summary, analysis of the Fe K line profile provides evidence for a velocity-broadened emission line at a rest energy consistent with the principal resonance transition of FeXXV.
In summary, analysis of the Fe K line profile provides evidence for a velocity-broadened emission line at a rest energy consistent with the principal resonance transition of FeXXV.
As FeXXV is also identified as the ionisation state in the highly ionised absorber, it is reasonable to interpret the emission component in the PCygni profile with the same outflow.
As FeXXV is also identified as the ionisation state in the highly ionised absorber, it is reasonable to interpret the emission component in the PCygni profile with the same outflow.
We note that this conclusion, including the emission line broadening, is also consistent with the description of the broad band X-ray spectrum of in Section 4.
We note that this conclusion, including the emission line broadening, is also consistent with the description of the broad band X-ray spectrum of in Section 4.
The unfolded spectrum in figure 5 suggests that discrete spectral features might also be visible in the soft X-ray band.
The unfolded spectrum in figure 5 suggests that discrete spectral features might also be visible in the soft X-ray band.
If so, the higher resolution of the RRGS could provide a further constraint on the broadening of emission lines from the highly ionised outflow, as H-like ions of O and Ne will co-exist with He-Like FeXXV.
If so, the higher resolution of the RGS could provide a further constraint on the broadening of emission lines from the highly ionised outflow, as H-like ions of O and Ne will co-exist with He-Like FeXXV.
To check this possibility the spectra from all four RGS observations were stacked in the same way as for the EPIC data, and the ratio derived of the background-subtracted data to a best-fit power law (we found [~2.9, in agreement with the po2 component in Table 1) over the 14-28 Angstrom band.
To check this possibility the spectra from all four RGS observations were stacked in the same way as for the EPIC data, and the ratio derived of the background-subtracted data to a best-fit power law (we found $\Gamma$$\sim$ 2.9, in agreement with the po2 component in Table 1) over the 14-28 Angstrom band.
The data were then re-grouped in 9-channel bins to reduce random noise, giving an effective spectral resolution of ~0.1 Angstrom.
The data were then re-grouped in 9-channel bins to reduce random noise, giving an effective spectral resolution of $\sim$ 0.1 Angstrom.
Figure 10 shows the resulting RGS data:continuum spectral ratio and marks the rest wavelengths of the principal emission lines of OVII and OVIII, together with the edge energies of the recombination continua of OVII and NVI.
Figure 10 shows the resulting RGS data:continuum spectral ratio and marks the rest wavelengths of the principal emission lines of OVII and OVIII, together with the edge energies of the recombination continua of OVII and NVI.
As with the Fe line profile, Gaussians were fitted to the 3 most obvious emissionK lines, with wavelength, width and amplitude as free parameters.
As with the Fe K line profile, Gaussians were fitted to the 3 most obvious emission lines, with wavelength, width and amplitude as free parameters.
Of particular interest is a well-defined - and strong - OVIII Lyman-a line, as predicted in figure 5.
Of particular interest is a well-defined - and strong - OVIII $\alpha$ line, as predicted in figure 5.
The Gaussian fitting finds a wavelength of 20.48+0.08 Angstrom (18.95+0.08 Angstrom at the redshift of PG1211+143)), with a line width of c=0.42+0.08 Angstrom.
The Gaussian fitting finds a wavelength of $\pm$ 0.08 Angstrom $\pm$ 0.08 Angstrom at the redshift of ), with a line width of $\sigma$ $\pm$ 0.08 Angstrom.
Interpreted in terms of velocity broadening, the line width corresponds to ~ 14000+5500 km s! (FWHM).
Interpreted in terms of velocity broadening, the line width corresponds to $\sim$ $\pm$ 5500 km $^{-1}$ (FWHM).
While significantly lower than the value found from fitting the FeXXV emission line in the EPIC data, the higher intrinsic resolution of the RGS does hint at a narrower core and broader wings than modelled by the simple Gaussian line.
While significantly lower than the value found from fitting the FeXXV emission line in the EPIC data, the higher intrinsic resolution of the RGS does hint at a narrower core and broader wings than modelled by the simple Gaussian line.
Reference to figure 5 suggests that the narrow core might be due to a contribution from the lower ionisation, lower velocity gas.
Reference to figure 5 suggests that the narrow core might be due to a contribution from the lower ionisation, lower velocity gas.
The OVII (19-20) resonance line is also clearly detected in the stacked RGS data, at 23.22+0.06 Angstrom (21.48+0.05 Angstrom), but is significantly less wide than the higher ionisation OVIII line, with o=0.16+0.05 Angstrom.
The OVII (1s-2p) resonance line is also clearly detected in the stacked RGS data, at $\pm$ 0.06 Angstrom $\pm$ 0.05 Angstrom), but is significantly less wide than the higher ionisation OVIII line, with $\sigma$ $\pm$ 0.05 Angstrom.
Again, this result is consistent with the narrower Gaussian smoothing factor required for emission from the less ionised gas in the model of figure 5.
Again, this result is consistent with the narrower Gaussian smoothing factor required for emission from the less ionised gas in the model of figure 5.
Also seen in figure 10 is an unresolved line very close to the rest wavelength of the forbidden line in the OVII 1s-2p triplet.
Also seen in figure 10 is an unresolved line very close to the rest wavelength of the forbidden line in the OVII 1s-2p triplet.
We surmise that this emission arises from a low density component of the outflow, presumably at a substantially larger radial distance than the velocity-broadened lines.
We surmise that this emission arises from a low density component of the outflow, presumably at a substantially larger radial distance than the velocity-broadened lines.
Two other spectral features in figure 10 are identified with radiative recombination continua (RRC) of OVII and
Two other spectral features in figure 10 are identified with radiative recombination continua (RRC) of OVII and
Mop/Afay is basically > 1. independently of the tracer.
$M_{\rm CD}/M_{\rm vir}$ is basically $>$ 1, independently of the tracer.
It is worth stressing that the values of Afey obtained by Tlofuer et al. (
It is worth stressing that the values of $M_{\rm CD}$ obtained by Hofner et al. (
2000) from CO are less affected by πουταμαΊος on the abundance. which is much better established for C1*O than forCU.
2000) from $^{17}$ O are less affected by uncertainties on the abundance, which is much better established for $^{17}$ O than for.
oT. Iun conclusion. we favour the hvpothesis that the discrepancy between ορ aud AM is veal.
In conclusion, we favour the hypothesis that the discrepancy between $M_{\rm CD}$ and $M_{\rm vir}$ is real.
In this case AR'DMasl secus to indicate that the chimps are unstable against eravitational collapse.
In this case $M_{\rm CD}/M_{\rm vir}>1$ seems to indicate that the clumps are unstable against gravitational collapse.
If thermal pressure aud turbulence are the ouly nieans of support against gravitational collapse. iudeed. Mgy>Mag naplies collapse of the clips ou a free-fall time: for deusities of order 109 ? the latter is equal to —104 vx. an order of maguitude less than the estimated. Ποιο of the UC iregious enmibedded in the cbuups (Wood Churchwell 1989bj.
If thermal pressure and turbulence are the only means of support against gravitational collapse, indeed $M_{\rm CD}>M_{\rm vir}$ implies collapse of the clumps on a free-fall time: for densities of order $10^6$ $^{-3}$ the latter is equal to $\sim$$10^4$ yr, an order of magnitude less than the estimated lifetime of the UC regions embedded in the clumps (Wood Churchwell 1989b).
This sugecsts that magnetic ficlds wieght plav a role in stabilising the cloud against gravitational collapse.
This suggests that magnetic fields might play a role in stabilising the cloud against gravitational collapse.
From the virial theorem one can estimate the strength of the magnetic field. B. required to this purpose: following Alel&ee et al. (
From the virial theorem one can estimate the strength of the magnetic field, $B$, required to this purpose: following McKee et al. (
1993) and ucelecting the surface pressure ter. the expression for virial equilibrium can be written as where ο aud b are two factors of order munity that take iuto account the cloud ecometry aud the topology of the magnetic field.
1993) and neglecting the surface pressure term, the expression for virial equilibrium can be written as where $a$ and $b$ are two factors of order unity that take into account the cloud geometry and the topology of the magnetic field.
The equilibrium value of 57 is hence given by Asstuning ¢=L.17 sud 20.3 (Melxee et al.
The equilibrium value of $B^2$ is hence given by Assuming $a$ =1.17 and $b$ =0.3 (McKee et al.
1993) and posug AL=Afeyy we can compute the values of DB required to support our clumps: these are a few mC. Such values are comparable to those obtained by Lai ct al. (
1993) and posing $M=M_{\rm CD}$ we can compute the values of $B$ required to support our clumps: these are a few mG. Such values are comparable to those obtained by Lai et al. (
2001) who ucasured the magnetic field iu molecular clouds with densities similar to those of our clumps usiug interferometric polarisation maps.
2001) who measured the magnetic field in molecular clouds with densities similar to those of our clumps using interferometric polarisation maps.
We thus propose a scenario in which the clumps are mareinally stable due to the coutribution of the magnetic field.
We thus propose a scenario in which the clumps are marginally stable due to the contribution of the magnetic field.
In this case the clump will coutract ou the timescale fap οσαπιο: bv aimbipolar diffusion.
In this case the clump will contract on the timescale $t_{\rm AD}$ determined by ambipolar diffusion.
This can be related to the free-fall time. fg. bw Leads of Eq. (
This can be related to the free-fall time, $t_{\rm ff}$, by means of Eq. (
51) of Meee ct al. (
51) of McKee et al. (
1993): fap=Ste. thus obtaimine fAp(ovr)=2.910%[usGn72]0.
1993): $t_{\rm AD}\simeq8.5\,t_{\rm ff}$, thus obtaining $t_{\rm AD}({\rm yr})=2.9~10^8~[n_{\rm H_2}({\rm cm^{-3}})]^{-0.5}$.
The mass accretion rate onto the cunbedded stars can be hence computed from he ratio HM=Mop/fap auc plotted as à function of he source Iuniuosity. as done iu Fig. 7:
The mass accretion rate onto the embedded stars can be hence computed from the ratio $\dot{M}_{\rm acc}=M_{\rm CD}/t_{\rm AD}$ and plotted as a function of the source luminosity, as done in Fig. \ref{fratlum}:
iu this figure we wave also reported the estimates obtained from the C*O data of Hofner et al. (
in this figure we have also reported the estimates obtained from the $^{17}$ O data of Hofner et al. (
2000).
2000).