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The luminosity of our reference model described above, of the order 1074Lgaq is substantially lower than the luminosities (of the order 3x10-?-10-3Zgaq) inferred for the observed sources to which we want to apply the model. | The luminosity of our reference model described above, of the order $10^{-4}L_{\rm Edd}$ is substantially lower than the luminosities (of the order $3\times 10^{-2}$ $10^{-3}L_{\rm Edd}$ ) inferred for the observed sources to which we want to apply the model. |
This is a consequence of the flow model in DSO5 that is the basis of our analysis. | This is a consequence of the flow model in DS05 that is the basis of our analysis. |
In it, the surface density of the hot layer is governed by the physics of the Coulomb interaction of the hot ions penetrating through it, and its temperature by the energy balance between it and the underlying disk. | In it, the surface density of the hot layer is governed by the physics of the Coulomb interaction of the hot ions penetrating through it, and its temperature by the energy balance between it and the underlying disk. |
With temperature and surface density constrained in this way, the mass flux then depends only on the radial drift speed, i.e. the viscosity parameter, o. | With temperature and surface density constrained in this way, the mass flux then depends only on the radial drift speed, i.e. the viscosity parameter, $\alpha$. |
The actual mass flux is low because the temperature of the layer is only about 80keV. This suggests that the current model is incomplete, and we discuss a possible solution in sect. ??.. | The actual mass flux is low because the temperature of the layer is only about 80keV. This suggests that the current model is incomplete, and we discuss a possible solution in sect. \ref{sec:discussion}. |
In this paper, however, we solve this problem by introducing a parameter, C, by which the accretion rate (or equivalently the energy output of each component of the flow) is increased. | In this paper, however, we solve this problem by introducing a parameter, $C$, by which the accretion rate (or equivalently the energy output of each component of the flow) is increased. |
This makes the implicit assumption that increasing the accretion rate causes the energy output in each component to increase, but the relative contribution of each component to the overall energy budget and geometric configuration of the flow to stay constant. | This makes the implicit assumption that increasing the accretion rate causes the energy output in each component to increase, but the relative contribution of each component to the overall energy budget and geometric configuration of the flow to stay constant. |
Scaling the accretion rate in this way increases the luminosity in all components, which thus causes an increase in temperature for the cool disk at a fixed truncation radius. | Scaling the accretion rate in this way increases the luminosity in all components, which thus causes an increase in temperature for the cool disk at a fixed truncation radius. |
With the introduction of the parameters C and Z our model loses its predictive power, but the goal of this paper is to present a model that is plausible rather than precise in its details. | With the introduction of the parameters $C$ and $\zeta$ our model loses its predictive power, but the goal of this paper is to present a model that is plausible rather than precise in its details. |
In the next section we compare our spectra to the best fits from observations, and show that for reasonable values of the hot layer and inner ring and accretion rate, we can reproduce the Observed soft excesses using a significantly truncated accretion disk. | In the next section we compare our spectra to the best fits from observations, and show that for reasonable values of the hot layer and inner ring and accretion rate, we can reproduce the observed soft excesses using a significantly truncated accretion disk. |
To illustrate how our model can be made consistent with Observed soft excesses, we perform a qualitative comparison between the soft excesses observed in SWIFT J1753.5-0127 (?) and GX 339-4 (?) and our model. | To illustrate how our model can be made consistent with observed soft excesses, we perform a qualitative comparison between the soft excesses observed in SWIFT J1753.5-0127 \citep{2006ApJ...652L.113M}
and GX 339-4 \citep{2006ApJ...653..525M} and our model. |
For each object we use the estimates for black hole mass, inclination and distance to source presented in those two papers and take a=0.2 as a standard value for the viscosity parameter. | For each object we use the estimates for black hole mass, inclination and distance to source presented in those two papers and take $\alpha =
0.2$ as a standard value for the viscosity parameter. |
We then assume a moderate truncation radius and find a solution for energy and surface density as was discussed in sect. ??,, | We then assume a moderate truncation radius and find a solution for energy and surface density as was discussed in sect. \ref{sec:model}, |
and calculate the spectrum. | and calculate the spectrum. |
We change C (the accretion rate) and Z (the ratio between seed photons in the hot layer and inner ring) in order to match the luminosity and spectral index of the best fit to the observed spectrum, and compare our soft excess to the observed one. | We change $C$ (the accretion rate) and $\zeta$ (the ratio between seed photons in the hot layer and inner ring) in order to match the luminosity and spectral index of the best fit to the observed spectrum, and compare our soft excess to the observed one. |
If necessary we also change the amount of interstellar absorption, although for both the cases we consider we do not need to change it very much. | If necessary we also change the amount of interstellar absorption, although for both the cases we consider we do not need to change it very much. |
Given the systematic uncertainties in our model, a more statistical comparison to the data is not possible; our goal is instead to demonstrate that we are able to reproduce the observed spectra with physically reasonably parameters. | Given the systematic uncertainties in our model, a more statistical comparison to the data is not possible; our goal is instead to demonstrate that we are able to reproduce the observed spectra with physically reasonably parameters. |
The non-dimensional resolution A/.No~12(A/(H/r))CN,/384) where Ao=2x/V,,. is marginal even lor our highest resolution simulation. | The non-dimensional resolution $\lambda/\Delta\phi \simeq 12
(\lambda/(H/r)) (N_{x_1}/384)$ where $\Delta\phi = 2\pi/N_{x_3}$, is marginal even for our highest resolution simulation. |
For 5. the correlation length of the hiehest resolution is smaller (han (hat for any other variable. | For $b$, the correlation length of the highest resolution is smaller than that for any other variable. |
The magnetic field structure is underresolved. | The magnetic field structure is underresolved. |
Figure 14. plots correlation length: against resolution al the ISCO [or the same variables as in Figure 13: here red is the hard polar boundary. and black is the soft polar boundary. | Figure \ref{correlation_res} plots correlation length against resolution at the ISCO for the same variables as in Figure \ref{correlation}; here red is the hard polar boundary and black is the soft polar boundary. |
The dotted lines show how the correlation length would vary if it were fixed at 2.5 and 10 grid zones. | The dotted lines show how the correlation length would vary if it were fixed at $2, 5$ and $10$ grid zones. |
For p. u. and 8, (the nonmagnetic variables) the correlation length is ~5 grid zones for the two lowest resolution simulations. | For $\rho$, $u$ , and $\theta_e$ (the nonmagnetic variables) the correlation length is $\sim 5$ grid zones for the two lowest resolution simulations. |
At higher resolution|. γι=192 and 384 the correlation length increases to 210 grid zones. aud the slope of the change in correlation length with resolution decreases. | At higher resolution– $N_{x_1} = 192$ and $384$ – the correlation length increases to $> 10$ grid zones, and the slope of the change in correlation length with resolution decreases. |
This suggests that for the two highest resolution runs some structures in the turbulence are beginning (o be resolved. | This suggests that for the two highest resolution runs some structures in the turbulence are beginning to be resolved. |
For b. on the other hand. the correlation length decreases nearly proportional to the grid scale. with the correlation length fixed at around 5 grid zones per correlation length. | For $b$, on the other hand, the correlation length decreases nearly proportional to the grid scale, with the correlation length fixed at around $5$ grid zones per correlation length. |
There are small signs of an increase at the highest resolution. but in light of run-to-run variations the significance of this increase is marginal al best. | There are small signs of an increase at the highest resolution, but in light of run-to-run variations the significance of this increase is marginal at best. |
The outer scale for the magnetic field is nol resolved. | The outer scale for the magnetic field is not resolved. |
For all variables the correlation lengths for hard aud soft boundary polar conditions are consistent. | For all variables the correlation lengths for hard and soft boundary polar conditions are consistent. |
Evidently the polar boundary does not influence (he structure of turbulence in (he equatorial disk. | Evidently the polar boundary does not influence the structure of turbulence in the equatorial disk. |
llow do these correlation lengths correspond to those found in local model simulations? | How do these correlation lengths correspond to those found in local model simulations? |
Guanetal.(2009) [ound in their unstratified shearing box model that the three dimensional correlation Iunction was a (riaxial ellipsoid elongated in the azimuthal direction aad tilted into trailing orientation. | \cite{Guan09} found in their unstratified shearing box model that the three dimensional correlation function was a triaxial ellipsoid elongated in the azimuthal direction and tilted into trailing orientation. |
The relationship between our azimuthal correlation length. A, ancl ihe Guanetal.(2009) results is where 06,5,L5deg is the tilt angle of the correlation ellipse. and À,,,;. À,,5, are the major and minor axis of magnetic correlation lengths. | The relationship between our azimuthal correlation length $\lambda_b$ and the \citet{Guan09} results is where $\theta_{tilt} \approx 15\,\rm deg$ is the tilt angle of the correlation ellipse, and $\lambda_{maj}$, $\lambda_{min}$ are the major and minor axis of magnetic correlation lengths. |
For the best resolved net azimuthal field model in Guanetal.(2009). (v256b. which like our global models saturates ad o]2 20). (his implies A(0.1144c0.05rad. ox 0.016zrad. | For the best resolved net azimuthal field model in \citet{Guan09} (y256b, which like our global models saturates at $\beta \simeq 20$ ), this implies $\lambda
\simeq 0.17 H \simeq 0.05\,\rm rad$, or $0.016\pi\, \rm rad$. |
Therefore. it is surprising (hat correlation length as large as20.3rad.~II are measured in our model for the nonmagnetic variables. | Therefore, it is surprising that correlation length as large as$\simeq 0.3\, \rm rad\,\sim H$ are measured in our model for the nonmagnetic variables. |
Davisetal.(2010). have computed correlation lengths in stratified. isothermal models | \cite{Davi10} have computed correlation lengths in stratified, isothermal models |
theeories. | eories. |
. sttars. | tars. |
1.3mm. | 1.3 mm. |
moleculaar core. | ar core. |
appeaar too high. | ar too high. |
that value is obtained through the detailed results of HMM05 (displaying the wind composition as a function of time - or of mass left). | that value is obtained through the detailed results of HMM05 (displaying the wind composition as a function of time - or of mass left). |
Comparing the results of LC06 and HMMO05 one sees that rotation increases the mass loss llarger in HMM05), thus leaving the star with a smaller mass at explosion ssmaller in HMMO5). | Comparing the results of LC06 and HMM05 one sees that rotation increases the mass loss larger in HMM05), thus leaving the star with a smaller mass at explosion smaller in HMM05). |
Rotation also increases the size of nuclearly processed regions llarger in HMM05), since matter is rotationally mixed outwards to larger distances than achieved through convection. | Rotation also increases the size of nuclearly processed regions larger in HMM05), since matter is rotationally mixed outwards to larger distances than achieved through convection. |
In turn, this leads to larger amounts of processed material ffor the HMM05 models. | In turn, this leads to larger amounts of processed material for the HMM05 models. |
The aforementioned features of rotating vs non-rotating models, which are explained in detail in e.g. Maeder and Meynet (2000) are crucial in understanding the differences in the corresponding wind yields of the stars. | The aforementioned features of rotating vs non-rotating models, which are explained in detail in e.g. Maeder and Meynet (2000) are crucial in understanding the differences in the corresponding wind yields of the stars. |
LC06 provided (private communication) y; of all stable nuclear species, from H to Ge, included in their models and ejected through the winds of the stars, up to the moment of the explosion. | LC06 provided (private communication) $y_i$ of all stable nuclear species, from H to Ge, included in their models and ejected through the winds of the stars, up to the moment of the explosion. |
HMM05 provide (Table 3 in their paper) theyields y,,,; of the winds of their models for stable species from ?He to ??Na, from which the yields can be recovered through where the adopted solar values Xo, are displayed in Table 1 of HMM05. | HMM05 provide (Table 3 in their paper) the $y_{n,i}$ of the winds of their models for stable species from $^3$ He to $^{23}$ Na, from which the yields can be recovered through where the adopted solar values $_{\odot,i}$ are displayed in Table 1 of HMM05. |
The wind yields of a few selected species appear in Fig. 3,, | The wind yields of a few selected species appear in Fig. \ref{Fig:windmasses}, |
for the non-rotating models of LC06 and for both the non-rotating and the rotating models of HMM05. | for the non-rotating models of LC06 and for both the non-rotating and the rotating models of HMM05. |
It can be seen that, in general, there is excellent agreement between the results for non-rotating models of LC06 and ΗΜΜΟΡ, for stars up to 40Mo. | It can be seen that, in general, there is excellent agreement between the results for non-rotating models of LC06 and HMM05, for stars up to 40. |
. Their results differ only for the 60 mmodel (and presumably for higher masses as well) and only for the cases of the He-burning products !?C, 16Ο and ??Ne. | Their results differ only for the 60 model (and presumably for higher masses as well) and only for the cases of the He-burning products $^{12}$ C, $^{16}$ O and $^{22}$ Ne. |
Since both HMMO05 and LC06 use the same prescriptions for mass loss, the reason of that discrepancy could be the use of a small amount of overshooting in the case of HMMO05. | Since both HMM05 and LC06 use the same prescriptions for mass loss, the reason of that discrepancy could be the use of a small amount of overshooting in the case of HMM05. |
Rotation has a twofold effect on stellar yields: it increases the size of the nuclearly processed layers (since it mixes material further than convection alone) and reduces the escape velocity in the stellar equator, allowing larger amounts of mass to be ejected in the wind. | Rotation has a twofold effect on stellar yields: it increases the size of the nuclearly processed layers (since it mixes material further than convection alone) and reduces the escape velocity in the stellar equator, allowing larger amounts of mass to be ejected in the wind. |
Both effects enhance the wind yields up to some mass limit; above it, the wind has removed so much mass, that less material is left in the star to be processed in subsequent stages of the evolution, thus reducing the corresponding yields. | Both effects enhance the wind yields up to some mass limit; above it, the wind has removed so much mass, that less material is left in the star to be processed in subsequent stages of the evolution, thus reducing the corresponding yields. |
This is the case, for instance, with the He-burning products aand??7Ne,, the yields of which decrease above ~60 iin the rotating HMM05 models (see Fig. | This is the case, for instance, with the He-burning products and, the yields of which decrease above $\sim$ 60 in the rotating HMM05 models (see Fig. |
3 and HMMO05 for details). | \ref{Fig:windmasses} and HMM05 for details). |
In the following we assume that the wind interaction with the ISM has not substantially changed the wind stratification: the forward shock will first encounter the innermost wind layers, containing processed material in the case of the most massive stars; later it will encounter the outer wind layers (containing mostly the initial composition), before running into the ISM. | In the following we assume that the wind interaction with the ISM has not substantially changed the wind stratification: the forward shock will first encounter the innermost wind layers, containing processed material in the case of the most massive stars; later it will encounter the outer wind layers (containing mostly the initial composition), before running into the ISM. |
Fig. | Fig. |
4 displays thewind (for a few key metals), as encountered by the forward shock, moving outwards fromMg;,,, in the case of two rotating model stars of 25 aand 60 ((from HMMO05). | 4 displays the (for a few key metals), as encountered by the forward shock, moving outwards from, in the case of two rotating model stars of 25 and 60 (from HMM05). |
The quantity is displayed as a function of mass coordinate M, Xwind,i(M) being the mass fraction of isotope i in the wind of star of massM. | The quantity is displayed as a function of mass coordinate $M$, $_{wind,i}(M)$ being the mass fraction of isotope $i$ in the wind of star of mass. |
.. Obviously, one has m;(Mzzp))=0. | Obviously, one has $m_i$ )=0. |
and m4(M.))—yi(M.)), i.e. at crossing the last (outermost) wind layer, the forward shock has encountered the totality of the yield y; (M..)). | and $m_i$ $y_i$ ), i.e. at crossing the last (outermost) wind layer, the forward shock has encountered the totality of the yield $y_i$ ). |
will eive rise to detectable image separations for a subhalo of this mass. | will give rise to detectable image separations for a subhalo of this mass. |
Iu its original form. the NEW xofle gives X(«AR) lower than X, at these radii. whereas the truucated. version leads to “(<Rj) above he threshold. | In its original form, the NFW profile gives $\bar{\Sigma}(<R)$ lower than $\Sigma_\mathrm{c}$ at these radii, whereas the truncated version leads to $\bar{\Sigma}(<R)$ above the threshold. |
Both the 03 and I&0£ subhalo models. which should be far more realistic than amy sharp ruucation. do however predict X(A) smaller than that of an unidisturbed NEW halo of the same mass. | Both the H03 and K04 subhalo models, which should be far more realistic than any sharp truncation, do however predict $\bar{\Sigma}(R)$ smaller than that of an undisturbed NFW halo of the same mass. |
The NOL xofile (Gu both its original. stripped aud truucated form) also ends up below the threshold. due to its fiuite-deusitv core. | The N04 profile (in both its original, stripped and truncated form) also ends up below the threshold, due to its finite-density core. |
The effects of truucatiou versus gradual stripping are qualitatively simular for the NEW. NOL and M99 jndos a sharp truncation mereases the Einstein radius whereas— a gradual stripping decreases it relative to the Einstein radius produced bv the original profile. | The effects of truncation versus gradual stripping are qualitatively similar for the NFW, N04 and M99 halos – a sharp truncation increases the Einstein radius whereas a gradual stripping decreases it relative to the Einstein radius produced by the original profile. |
This indicates that previous investigations based on sharp outer truncations are likely to have Iu Fig. 2.. | This indicates that previous investigations based on sharp outer truncations are likely to have In Fig. \ref{fig2}, |
we plot the image separations predicted for 104 LottAL. subbalos against the angular resolution of a uunuber of plauned or existing observational facilities. operating at a wide range of wavelengths. | we plot the image separations predicted for $10^4$ $10^{11}\ M_\odot$ subhalos against the angular resolution of a number of planned or existing observational facilities, operating at a wide range of wavelengths. |
These include he proposed MANIAL pathfinder iu N-ravs":: VLTI with he proposed VSI instrament (Malbetetal.92006).. he planned and SIM satellites in he optical/uear-imfrared: the currently availableEVN?..IISAS.. arrays plus the planned ALMAP..EVLA... arrays. aud also space-VLBI with the damned satellite at radio wavelenetlis. | These include the proposed MAXIM pathfinder in ; VLTI with the proposed VSI instrument \citep{Malbet et al.}, the planned and SIM satellites in the optical/near-infrared; the currently available, arrays plus the planned, arrays, and also space-VLBI with the planned satellite at radio wavelengths. |
Please rote that here we consider ouly the best resolution iuits attaimable with these telescopes. whereas the resolution at the wavelengths that maximize the nuuber of observable high-redshift sources may be considerably Worse. | Please note that here we consider only the best resolution limits attainable with these telescopes, whereas the resolution at the wavelengths that maximize the number of observable high-redshift sources may be considerably worse. |
It is inumediately evicleaut from Fig. | It is immediately evident from Fig. |
2. that there aro large differences between the nuage separation predictions of the various halo models. | \ref{fig2} that there are large differences between the image separation predictions of the various halo models. |
As the discrepaney. between the nuuber deusities of luminous ealaxies aud dark matter halos does not start to become severe until the halo iuaSS rops below <1019AL, (c.g.Verdeetal.2002:vaudeuBosch2003).. subhalos at masses below this linut need to produce neasurable image separations (02lL.107 arcsec for VSOP-2. which has the best theoretical resolution among he telescopes included in Fie. 2)) | As the discrepancy between the number densities of luminous galaxies and dark matter halos does not start to become severe until the halo mass drops below $\lesssim 10^{10} \ M_\odot$ \citep[e.g.][]{Verde et al., van den Bosch et al. a}, subhalos at masses below this limit need to produce measurable image separations $\theta \gtrsim 4\times 10^{-5}$ arcsec for VSOP-2, which has the best theoretical resolution among the telescopes included in Fig. \ref{fig2}) ) |
iu order for dark ealaxies to be detectable twoueh dnage-splitting effects. | in order for dark galaxies to be detectable through image-splitting effects. |
Qut of the halo iuodels tested. ouly two actually mect lis criterion without adlding to sharp truucations: the SIS aud the M99 halos. | Out of the halo models tested, only two actually meet this criterion without adhering to sharp truncations: the SIS and the M99 halos. |
T1e Π0ῦ and IKO1 profiles both eive lage separations snaller than 10Ü ayesec for all he halo masses considere and are therefore completely outside the plotted region. | The H03 and K04 profiles both give image separations smaller than $10^{-6}$ arcsec for all the halo masses considered and are therefore completely outside the plotted region. |
Even in the optimistic case of an M99 halo (in either its original or stripped form. whereas the sharp truncalon. as discussed: previously. is not considered realistic). the image separations are a factor of z 37 smaller than those predicted. for a SIS (and z30 60 times simaller than those of a truncated SIS). rendering only the few nost massive subhalos (~LOMAL. or slightly higher) detectable at ~0.01" resolution. (GATA. SIM αιxl ALATA). | Even in the optimistic case of an M99 halo (in either its original or stripped form, whereas the sharp truncation, as discussed previously, is not considered realistic), the image separations are a factor of $\approx 3$ –7 smaller than those predicted for a SIS (and $\approx30$ –60 times smaller than those of a truncated SIS), rendering only the few most massive subhalos $\sim 10^{10} \ M_\odot$ or slightly higher) detectable at $\sim 0.01\arcsec$ resolution (GAIA, SIM and ALMA). |
At milliarcsecoud resolution (VLTI aud SIA). dark ogalaxies with masses Z109AL. may become detectable. | At milliarcsecond resolution (VLTI and SKA), dark galaxies with masses $\gtrsim10^9 \ M_\odot$ may become detectable. |
To probe further dowu the subhalo mass function. subiuilliaresecoud-aresolutiou facilities (ATANTAD pathfider. TISA. EVN. VLBA or VSOP-2) will be required. | To probe further down the subhalo mass function, submilliarcsecond-resolution facilities (MAXIM pathfinder, HSA, EVN, VLBA or VSOP-2) will be required. |
These nuage separatiois have been computed for fiducial leus aud source reshifts of :4=0.5 aud ος=2.0. but the overall picturedoes not change substantially for other realistic choices of these parameters. | These image separations have been computed for fiducial lens and source redshifts of $z_\mathrm{l}=0.5$ and $z_\mathrm{s}=2.0$, but the overall picturedoes not change substantially for other realistic choices of these parameters. |
A higher 2. lunplies a lower critical surface mass density Se for certain τν Which for a fixedsubhalo density profile | A higher $z_\mathrm{s}$ implies a lower critical surface mass density $\Sigma_\mathrm{c}$ for certain $z_\mathrm{l}$ , which for a fixedsubhalo density profile |
l.? between +=2 aud 2=L5. | $1.7$ between $z=2$ and $z=4.5$. |
This merease could be consistent with the dependence of the MIR effect on z. Ou upper lit on Εν at :=2 implies an upper limit ouT, at:=Oo0f Lx10sec1 | This increase could be consistent with the dependence of the MR effect on z. Our upper limit on $\Gamma_\nu$ at $z=2$ implies an upper limit on $\Gamma_\nu$ at $z=0$ of $4\times10^{-13}\,{\rm sec} ^{-1}$. |
Since the decay pbotons have an enerev close to the Lyman Πατ this iouisation rate converts to a photon flux by using the photoionisation cross-section. at this. limit.∙∙ which∙ is. 6⋅«,101Ncui. | Since the decay photons have an energy close to the Lyman limit this ionisation rate converts to a photon flux by using the photoionisation cross-section at this limit, which is $6\times10^{-18}\,{\rm cm}^2$. |
D Hence one obtains F(O)€7∖↓∩↓↸⊳↕⊔−↴∖↴↸∖↸⊳↽⋅≻ l which is not essentially differeut from the upper lit ~I0*en.που1 derived by Vogel et al (1995) aud by Donaline. Aldering Stocke (1995). the precise value of which in fact depends ou the uncertain shapes of the iutergalactie clouds which thev observed. | Hence one obtains $F(0)\le 7\times 10^4{\rm cm}^{-2}{\rm sec}^{-1}$ , which is not essentially different from the upper limit $\sim 10^5 {\rm cm}^{-2}{\rm sec} ^{-1}$ derived by Vogel et al (1995) and by Donahue, Aldering Stocke (1995), the precise value of which in fact depends on the uncertain shapes of the intergalactic clouds which they observed. |
We now show that the receuth derived Comu-Petersou optical depth in Well at 2~3. rope (Zheng et al 1995). in conjuction with the known upper lt on rcipbpy. leads to a lower limit on P at :~3. | We now show that the recently derived Gunn-Peterson optical depth in HeII at $z\sim3$, $\tau_{{\rm GP,HeII}}$ (Zheng et al 1998), in conjunction with the known upper limit on $\tau_{{\rm GP,HI}}$, leads to a lower limit on $\Gamma$ at $z\sim 3$. |
It turus out that this lower lait is close to the wpper lint estimated iu Sec. | It turns out that this lower limit is close to the upper limit estimated in Sec. |
3.2. | 3.2. |
There now exist a nuuber of observatious of ΠΟ absorption at :~2 to 3 in the spectra of QSOs (Jakobsen et al 19914. Tytler et al 1995. Jakobsen 1996. Davidsen. Kriss Zheug 1996. Toean. Anderson Rogers 1997. Reimers et al 1997). | There now exist a number of observations of HeII absorption at $z\sim 2$ to $3$ in the spectra of QSOs (Jakobsen et al 1994, Tytler et al 1995, Jakobsen 1996, Davidsen, Kriss Zheng 1996, Hogan, Anderson Rogers 1997, Reimers et al 1997). |
There has been considerable discussion in these aud other papers (Madan Alciksin 1991. Fardal. Cüroux Shull 1998) as to whether this absorption is cutirely due to the Πο in Lyinan a clouds.or whether part of it must be attributed to the CGunu-Petersou effect arising in an csseutially diffuse intergalactic medium. | There has been considerable discussion in these and other papers (Madau Meiksin 1994, Fardal, Giroux Shull 1998) as to whether this absorption is entirely due to the HeII in Lyman $\alpha$ clouds,or whether part of it must be attributed to the Gunn-Peterson effect arising in an essentially diffuse intergalactic medium. |
We here follow the calculations of Zheug. Davidseu I&riss (1998). which lead to a definite value of Topπω=1 for this effect at +=3. | We here follow the calculations of Zheng, Davidsen Kriss (1998), which lead to a definite value of $\tau_{{\rm GP,HeII}}=1$ for this effect at $z=3$. |
This would iuple that Πιο)=Lsio1? 7. | This would imply that $n_{\rm HeII}(3)= 4\times 10^{-10}$ $^{-3}$ . |
To see whether lis result is reasonable we derive frou it the iupliecd value of the total diffuse iutergalactie gas deusitv 2(3) at 2=X using estimates for the HeILionismug flux due o QSO radiation filtered through the absorbing Πουαι of Lyiiu à clouds and Lyinan luat svstems (IBbuuxlt Aladau 1996. Fardal. Ciroux Shull 1998). aud the value OUS for he WeI umber ratio. | To see whether this result is reasonable we derive from it the implied value of the total diffuse intergalactic gas density $n(3)$ at $z=3$, using estimates for the HeII-ionising flux due to QSO radiation filtered through the absorbing medium of Lyman $\alpha$ clouds and Lyman limit systems (Haardt Madau 1996, Fardal, Giroux Shull 1998), and the value 0.08 for the He/H number ratio. |
Using Τη=6«10D7 + one obtains 4(3)=l6x109 cn | Using $\Gamma_{\rm HeII}=6 \times 10^{-15}$ $^{-1}$ one obtains $n(3)= 4.7\times 10^{-6}$ $^{-3}$. |
Comparing lis with the higher of the two competing values for he tota barvon density 0409). based on measurements of the deuterum abundance aud the theory of big bang incleosvuthesis (Schramun Turner 1998). one finds that ο)μμ)=0.36. | Comparing this with the higher of the two competing values for the total baryon density $n_b(3)$ , based on measurements of the deuterium abundance and the theory of big bang nucleosynthesis (Schramm Turner 1998), one finds that $n(3)/n_b(3)=0.36$. |
This result is compatible with the somewhat dependent estimate of Ot,(3) made by Caallougo. nna Madau (1997). | This result is compatible with the somewhat model-dependent estimate of $\Omega_{\rm Ly\alpha}(3)$ made by Giallongo, na Madau (1997). |
These authors found that at z~3 about half of 55 could be attributed to gas in Lya clouds. leaving abou half for the IGAL (since the contribution frou, galaxies can here be neglected. (Persic Salucci 19923). | These authors found that at $z\sim 3$ about half of $n_b$ could be attributed to gas in $\alpha$ clouds, leaving about half for the IGM (since the contribution from galaxies can here be neglected (Persic Salucci 1992)). |
Cüven the uucertiiuties. this fraction of 1/2 is conrpatible with our derived value of 0.36. | Given the uncertainties, this fraction of 1/2 is compatible with our derived value of 0.36. |
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