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However. the large scale field generated possesses magnetic helicity aud. since for closed or periodic boundaries the magnetic helicitv can change ouly resistively. the erowthof the large scale field is slowed down as the magnetic Revuolds nuuber increases. | However, the large scale field generated possesses magnetic helicity and, since for closed or periodic boundaries the magnetic helicity can change only resistively, the growth of the large scale field is slowed down as the magnetic Reynolds number increases. |
This translates inevitably to a magnetice-Bevuolds-uuniber dependent a effect auc turbulent magnetic diffusivity. as sugeestedao by Vainshtein Cattaneo (1992)). | This translates inevitably to a magnetic-Reynolds-number dependent $\alpha$ effect and turbulent magnetic diffusivity, as suggested by Vainshtein Cattaneo \cite{vainshtein92}) ). |
The arguneut of Vaiushtein Cattaneo is however only phenomenological. not based upon the fundamental concept of magnetic lelicity couscrvation. and lence their conclusion that stroug large-scale fields are impossible is uot borne out bv the simulations of Brandenburg (2001)). | The argument of Vainshtein Cattaneo is however only phenomenological, not based upon the fundamental concept of magnetic helicity conservation, and hence their conclusion that strong large-scale fields are impossible is not borne out by the simulations of Brandenburg \cite{brandenburg00}) ). |
Purthermore. in that paper it was shown that the a obtained bv nuposing a maguetic field is indeed ai approximation to⋅⋅ the à that results naturally t if uo field is imposed. | Furthermore, in that paper it was shown that the $\alpha$ obtained by imposing a magnetic field is indeed a reasonable approximation to the $\alpha$ that results naturally even if no field is imposed. |
where Iu the preseut simulations we do not caleulate box dynamos. but rather conccutrate on the dynamo coctiicients that occur in meau-ficld theory. | In the present simulations we do not calculate box dynamos, but rather concentrate on the dynamo coefficients that occur in mean-field theory. |
Therefore. all simulations are performedwith an imposed maguctic field, and the maguctic Revuolds number is chosen subcritical, so that the magnetic field is not κο]«καλος, | Therefore, all simulations are performed with an imposed magnetic field, and the magnetic Reynolds number is chosen subcritical, so that the magnetic field is not self-sustained. |
We think that progress in stellar dvnamo theory can be made through a combination of exact MIID simulation and mean-field dynamo theory. | We think that progress in stellar dynamo theory can be made through a combination of exact MHD simulation and mean-field dynamo theory. |
Furthermore. the existence of svstelmatic. large-scale magnetic ficlds aud stellar evcles with periods far in excess of convective time scales suggestsOO that a iieau-ficld description is possible iu some orm. | Furthermore, the existence of systematic, large-scale magnetic fields and stellar cycles with periods far in excess of convective time scales suggests that a mean-field description is possible in some form. |
Also. we argue that mean-field theory (in the wide sense that includes the above-mentioned models such as Leightou’s) is the oulv current model that reproduces arge-scale magnetic fields and cycles. iucliding such an outstanding feature as the solar butterfly diagram. even rough the diverse approximations mace for calculating je cvnaimo cocficicuts may uot be valid uncer stellar conditions. | Also, we argue that mean-field theory (in the wide sense that includes the above-mentioned models such as Leighton's) is the only current model that reproduces large-scale magnetic fields and cycles, including such an outstanding feature as the solar butterfly diagram, even though the diverse approximations made for calculating the dynamo coefficients may not be valid under stellar conditions. |
The case of sclbexcited dvuame action would of course be very interesting too. especially in view of ie question. of. whether a-quenching. depeuds ou the naguctic Revnolds uuuboer. as suggested by Vainshtein Cattaneo (1992)). | The case of self-excited dynamo action would of course be very interesting too, especially in view of the question of whether $\alpha$ -quenching depends on the magnetic Reynolds number, as suggested by Vainshtein Cattaneo \cite{vainshtein92}) ). |
Towever. we postpone this uutil a later y.παν. partly because the measurement of the dviiuo coefficients iu the presence of a large-scale feld that is different from the imposed oue is less straightforward. | However, we postpone this until a later study, partly because the measurement of the dynamo coefficients in the presence of a large-scale field that is different from the imposed one is less straightforward. |
The present investigation is linited to the regime where the coefficients are determined directly by the flow. and we do not address the question of whether the large-scale magnetic field of late-tvpe stars is iu fact eeuerated by such an ordinary 6 effect in the convection zone. or by a magnetic instability in au underlviug stably stratified laver (e.g. Draudeuburg Schuütt 1998)). | The present investigation is limited to the regime where the coefficients are determined directly by the flow, and we do not address the question of whether the large-scale magnetic field of late-type stars is in fact generated by such an ordinary $\alpha$ effect in the convection zone, or by a magnetic instability in an underlying stably stratified layer (e.g., Brandenburg Schmitt \cite{brandenburg98}) ). |
We cdo include a stably stratified laver with overshooting convection. but its main purpose here is to provide realistic conditions for the dow in the unstable region. | We do include a stably stratified layer with overshooting convection, but its main purpose here is to provide realistic conditions for the flow in the unstable region. |
Iu most ruus. the streneth of the imposed field is set to a value which amounts to typically 2% of the equipartition field with respect to the |inetic cncrev density. | In most runs, the strength of the imposed field is set to a value which amounts to typically $2\%$ of the equipartition field with respect to the kinetic energy density. |
During the subsequenta evolution the field strength also remains simall compared to the equipartitiou value. | During the subsequent evolution the field strength also remains small compared to the equipartition value. |
Furthermore we shall explore the influence of the iauposed maguetic field bv inercasing its strength up to values somewhat i excess οἳ the equipartition value. | Furthermore we shall explore the influence of the imposed magnetic field by increasing its strength up to values somewhat in excess of the equipartition value. |
Therefore the results may lave relevance for the solar convection zone. where the imaenetico field is no stronecro than the equipartition value. | Therefore the results may have relevance for the solar convection zone, where the magnetic field is no stronger than the equipartition value. |
The α effect produced in the ealactic eas by supernova explosious has been calculated by Ziceler et al. (1996)). | The $\alpha$ effect produced in the galactic gas by supernova explosions has been calculated by Ziegler et al. \cite{ziegler96}) ), |
i a similar spirit as in the present work. | in a similar spirit as in the present work. |
The relevance of the transport cocficicuts for mean- dynamo theory becomes clear from the equation for the moeau maeuetic field. (B5 is the mean maguctic field. (U5 is the incau flow. w=U(Uj is the fluctuating component of the flow. and αν—bj is a contribution to the mean electric field. soimietines. referred to as thef | The relevance of the transport coefficients for mean-field dynamo theory becomes clear from the equation for the mean magnetic field, where $\lb\vec{B}\rb$ is the mean magnetic field, $\lb\vec{U}\rb$ is the mean flow, $\vec{u}=\vec{U}-\lb\vec{U}\rb$ is the fluctuating component of the flow, and $\lb\vec{u}\ti\vec{b}\rb$ is a contribution to the mean electric field, sometimes referred to as the. |
orce, The dynamo coefficients appear in au expansion of this eau electric field in terms of spatial derivatives of the niean maguctic field. | The dynamo coefficients appear in an expansion of this mean electric field in terms of spatial derivatives of the mean magnetic field. |
In general they can be represented ἂν kernelsof an integral equation (Brandcuburg Sokoloff (20013). | In general they can be represented as kernels of an integral equation (Brandenburg Sokoloff \cite{brandenburg99}) ). |
In the simplest case. the cocfficicuts are treated as local teusors. which leads to The first term du the expansion is the à effect. | In the simplest case, the coefficients are treated as local tensors, which leads to The first term in the expansion is the $\alpha$ effect. |
The alpha tensor is a pseudo tensor that exists only in non mürror-svnuuetric flows. as they occur in stellar convection. | The alpha tensor is a pseudo tensor that exists only in non mirror-symmetric flows, as they occur in stellar convection. |
For the solar dvwuaimo. the main siguificauce of the à effect lies in generating the poloidal mean imaeuetic field. which is achieved predominautlv by a... | For the solar dynamo, the main significance of the $\alpha$ effect lies in generating the poloidal mean magnetic field, which is achieved predominantly by $\alpha_{\phi\phi}$. |
Toroidal fields are generated by the strong differential rotation that exists in the near the base of the solar convection zoue. | Toroidal fields are generated by the strong differential rotation that exists in the near the base of the solar convection zone. |
In other sohu-tvpe stars and fully convective stars though. differcutial rotation could be weak (Ixükker Stix 2001)). so that the dvnaimo becomes of. the » a--type. | In other solar-type stars and fully convective stars though, differential rotation could be weak (Kükker Stix \cite{kueker00}) ), so that the dynamo becomes of the $\alpha^2$ -type. |
Inthat case. other components of. tle alpha tensor. such as o,,. are oeuportaut for maintainime the oroidal magnetic Ποιά, | In that case, other components of the alpha tensor, such as $\alpha_{rr}$, are important for maintaining the toroidal magnetic field. |
The remainder of the paper is structured as follows. | The remainder of the paper is structured as follows. |
After introducing the model aud the equations. we focus ou the dependence of α on rotation. | After introducing the model and the equations, we focus on the dependence of $\alpha$ on rotation. |
Iu the following section. effects of the strength and onentation of the imposed field are studied. | In the following section, effects of the strength and orientation of the imposed field are studied. |
In the &ual section. a discussion of the results is presented. | In the final section, a discussion of the results is presented. |
words. we achieved good sensitivity in the most promising clusters. | words, we achieved good sensitivity in the most promising clusters. |
As clisctssecl in relfsec:survey.. we are confident that our limiting flux densities are accurate unless there are pulsars in extremely. tight. binaries. | As discussed in \\ref{sec:survey}, we are confident that our limiting flux densities are accurate unless there are pulsars in extremely tight binaries. |
Lowever. since used the same search procedure as we have. they suffered from the same bias. so we do not believe this is a good explanation for the lack of pulsars in our sample. | However, since used the same search procedure as we have, they suffered from the same bias, so we do not believe this is a good explanation for the lack of pulsars in our sample. |
While it is possible that some of the pulsars could have a sleeper spectral index (han the assumed. value of —1.7. we would also expect sonie to have flatter spectra. making them easier to detect at 2Gllz. | While it is possible that some of the pulsars could have a steeper spectral index than the assumed value of $-1.7$, we would also expect some to have flatter spectra, making them easier to detect at $2\; \GHz$. |
It therefore seems likely that most of the clusters we searched lack a bright MSP. | It therefore seems likely that most of the clusters we searched lack a bright MSP. |
We now turn {ο the theoretical results of(2008).. who preclict the number of neutron stars in different twpes of GC's through Monte Carlo simulations. | We now turn to the theoretical results of, who predict the number of neutron stars in different types of GCs through Monte Carlo simulations. |
They simulated a variety of clusters. including those with log(p./pe.7)=3.4.5.6. | They simulated a variety of clusters, including those with $\log{(\rho\rmsub{c}/\pcubpc)} = 3, 4, 5, 6$. |
We began by empirically filling a simple exponential to the results of of the form with «=0.041 and b=—0.82. and where n4;1 is (he number of pulsars formed. per 2xLO?M. (as per the simulations). | We began by empirically fitting a simple exponential to the results of of the form with $a = 0.041$ and $b = -0.82$, and where $n\rmsub{psrs}$ is the number of pulsars formed per $2 \times 10^{5}\; \Msun$ (as per the simulations). |
We explored other functional forms but chose this one for its goocuess of fit and simplicitv. | We explored other functional forms but chose this one for its goodness of fit and simplicity. |
We then calculated the expected number of pulsars in our clusters based upon their central densities andmasses?. | We then calculated the expected number of pulsars in our clusters based upon their central densities and. |
. Next. we calculated. how many pulsars would lie above our limiting flux densities (at 2ms). given a power-law distribution. dN(L)xLdL. | Next, we calculated how many pulsars would lie above our limiting flux densities (at $2\; \ms$ ), given a power-law distribution, $dN(L)
\propto L^{-1}\, dL$. |
We assumed a maximum luminosity equal to the brightest cluster pulsars. (about 250mJyκρο at 2 Giz) and a minimum luminosity of 0.16mJykpe? (obtained by scaling the twpically assumed lower limit of 0.3mJvkpe? at 1.4Gllz to 2 Gllz). | We assumed a maximum luminosity equal to the brightest cluster pulsars, (about $250\; \mJy\, \kpc^2$ at $2\; \GHz$ ) and a minimum luminosity of $0.16\; \mJy\, \kpc^2$ (obtained by scaling the typically assumed lower limit of $0.3\; \mJy\, \kpc^2$ at $1.4\; \GHz$ to $2\; \GHz$ ). |
We caleulated upper and lower estimates in the same war. fitting to the maxinmun and minimun expected pulsars as defined by the errors quoted in(2008). | We calculated upper and lower estimates in the same way, fitting to the maximum and minimum expected pulsars as defined by the errors quoted in. |
Based on these calculations. we expect that about nine pulsars should have been detected in our sample. with upper and lower estimates of 16 and (hree pulsars. respectively, | Based on these calculations, we expect that about nine pulsars should have been detected in our sample, with upper and lower estimates of 16 and three pulsars, respectively. |
Our results are not very sensitive to our choices of L4; and Lyin since our limiting luminosities are above the Lyi, cutolE. | Our results are not very sensitive to our choices of $L\rmsub{max}$ and $L\rmsub{min}$ since our limiting luminosities are above the $L\rmsub{min}$ cutoff. |
Choosing a latter slope for the Iuminosity distribution only increases ihe number of potentially observable pulsars. | Choosing a flatter slope for the luminosity distribution only increases the number of potentially observable pulsars. |
As a check on our method. we performed the sane analvsis using all the clusters searched byHRSO0T. | As a check on our method, we performed the same analysis using all the clusters searched by. |
. MID (a dense. massive cluster with eight known pulsars) was an outlier in these calculations. with far more pulsars predicted than are observed: when it is excluded from the analysis. we predict G.I? observable pulsars | M15 (a dense, massive cluster with eight known pulsars) was an outlier in these calculations, with far more pulsars predicted than are observed; when it is excluded from the analysis, we predict $6^{+15}_{-6}$ observable pulsars |
a minimum median value of about 0.72 in July. and. [air uring December and February. | a minimum median value of about 0.72 in July, and fair during December and February. |
In addition. we calculated he quartiles of [(clear) as a function of hour of day using 10 complete cata set: good conditions are more common in 1e mornings. [(clear) is highest before noon and decreases owards the afternoon. | In addition, we calculated the quartiles of f(clear) as a function of hour of day using the complete data set: good conditions are more common in the mornings, f(clear) is highest before noon and decreases towards the afternoon. |
We also carried out the same analysis ( που. of day for the seasons subset. | We also carried out the same analysis of hour of day for the seasons subset. |
Lt is apparent. that he conditions are very stable for all the seasons except in he summer when there is more variability. | It is apparent that the conditions are very stable for all the seasons except in the summer when there is more variability. |
To summarise our results we created. a grey. level plot. where f(elear) is represented by the grey intensity. indicating the median fraction of clear time for each month and hour of dav: clear conclitions exist in the colder ancl drier months. [rom October o June while cloudy weather is present in the afternoons of he summer months. | To summarise our results we created a grey level plot, where f(clear) is represented by the grey intensity, indicating the median fraction of clear time for each month and hour of day: clear conditions exist in the colder and drier months, from October to June while cloudy weather is present in the afternoons of the summer months. |
The fit to the histograms of c developed. by Carrascoal.(2009). for Sierra Negra also reproduced. the SPM data showing that this method. might be generalized. to other observatory sites. | The fit to the histograms of $\psi$ developed by \citet{Carrasco09} for Sierra Negra also reproduced the SPM data showing that this method might be generalized to other observatory sites. |
Furthermore. the consistency of our results with those obtained by other authors shows the great potential of our method as cloud cover is a crucial parameter for astronomical characterization of any site and. can be estimated from in situ measurements. | Furthermore, the consistency of our results with those obtained by other authors shows the great potential of our method as cloud cover is a crucial parameter for astronomical characterization of any site and can be estimated from in situ measurements. |
The authors acknowledge the kindness of the TM site-testing group. | The authors acknowledge the kindness of the TMT site-testing group. |
The authors also thank €. Sanders. Ci. Djorgovski. A. Walker ancl AL Sehoeck and for. their permission to use the results from the Erasmus&VanStaden(2002) report for SPAL | The authors also thank G. Sanders, G. Djorgovski, A. Walker and M. Schöcck and for their permission to use the results from the \citet{Erasmus02} report for SPM. |
This. work was partially supported. by CONACLP and. PAPIET. through grants number 58291 and INI07109. respectively. | This work was partially supported by CONACyT and PAPIIT through grants number 58291 and IN107109, respectively. |
(107?sZr£10% s) observed for a good fraction of bursts detected by the Swift satellite. | $10^{2.5}\;{\rm s}\lesssim t\lesssim 10^4\;$ s) observed for a good fraction of bursts detected by the Swift satellite. |
The distribution at low uv0.1 is obtained by observations of supernovae Ic that are associated with GRBs. | The distribution at low $u\sim0.1$ is obtained by observations of supernovae Ic that are associated with GRBs. |
In the intermediate regime of |<uv30 the shape of the distribution function dE/dInu is very uncertain, but we argue that it is likely to be at least flat or slowly rising in this range. | In the intermediate regime of $1\lesssim
u\lesssim 30$ the shape of the distribution function $dE/d\ln u$ is very uncertain, but we argue that it is likely to be at least flat or slowly rising in this range. |
A prediction of this model for the shallow decline of X-ray light-curve, that is based on a deviation (at carly times) from the constant energy Blandford-McKce self-similar solution, is that we should see a roughly similar shallow decline in the optical band over the same time interval as in the X-ray data. | A prediction of this model for the shallow decline of X-ray light-curve, that is based on a deviation (at early times) from the constant energy Blandford-McKee self-similar solution, is that we should see a roughly similar shallow decline in the optical band over the same time interval as in the X-ray data. |
Since the optical and the X-ray bands in general lie in different segments of the synchrotron spectrum, and because the energy added to the forward shock by slower moving ejecta should be accompanied by a mildly relativistic reverse shock that could provide some added flux to the optical lightcurve, the rate of decline for the X-ray and optical lighteurves should be similar but not identical in this A highly magnetized outflow could significantly weaken the reverse shock (or even eliminate it altogether) and thus suppress its emission. | Since the optical and the X-ray bands in general lie in different segments of the synchrotron spectrum, and because the energy added to the forward shock by slower moving ejecta should be accompanied by a mildly relativistic reverse shock that could provide some added flux to the optical lightcurve, the rate of decline for the X-ray and optical lightcurves should be similar but not identical in this A highly magnetized outflow could significantly weaken the reverse shock (or even eliminate it altogether) and thus suppress its emission. |
The alternative explanation of a viewing angle slightly outside the edge of the jet would lead to a gradual steepening of the afterglow lighteurve (i.c. a gradual increase in o, as the beaming cone of the afterglow emission gradually approaches and eventually encompasses the line of sight), while a steeper break in the light curve is possible (and arguably, might also be expected) in the model described in this work, when the stage of energy injection into the afterglow shock ends. | The alternative explanation of a viewing angle slightly outside the edge of the jet would lead to a gradual steepening of the afterglow lightcurve (i.e. a gradual increase in $\alpha$, as the beaming cone of the afterglow emission gradually approaches and eventually encompasses the line of sight), while a steeper break in the light curve is possible (and arguably, might also be expected) in the model described in this work, when the stage of energy injection into the afterglow shock ends. |
The challenge posed for GRB/SNe models is to understand what physical processes give rise to dc2 and why the LF distribution of the ejecta peaks at a value roughly Ij~30—50. | The challenge posed for GRB/SNe models is to understand what physical processes give rise to $a\sim 2$ and why the LF distribution of the ejecta peaks at a value roughly $\Gamma_{\rm peak}\sim 30-50$. |
Understanding these results should help illuminate the processes operating during the period in which the central engine of gamma-ray burst is active and the interaction of the relativistic outflow with the collapsing star and its immediate surroundings. | Understanding these results should help illuminate the processes operating during the period in which the central engine of gamma-ray burst is active and the interaction of the relativistic outflow with the collapsing star and its immediate surroundings. |
We thank Stan Woosley for useful discussion. | We thank Stan Woosley for useful discussion. |
This work is supported in part by grants from NASA and NSF (AST-0406878) to PK and by the US Department of Energy under contract number DE-ACO3-76SE00515 (J. G.). | This work is supported in part by grants from NASA and NSF (AST-0406878) to PK and by the US Department of Energy under contract number DE-AC03-76SF00515 (J. G.). |
We have analyzed the effect of the additional destruction of a turbulent distant screen on the absorption feature by cousidering the effective peak streugth AAGS,/E(B whereσ]ησγο AAsος dsd the» difference of: theν effective extinction at peak frequeney of the complete model aud a model where the lump has been removed frou νο intrinsic extinction curve. | We have analyzed the effect of the additional destruction of a turbulent distant screen on the absorption feature by considering the effective peak strength $\Delta A_{\rm 0.22}^{\rm eff}/E(B-V)^{\rm eff}$ where $\Delta A_{0.22}^{\rm eff}$ is the difference of the effective extinction at peak frequency of the complete model and a model where the bump has been removed from the intrinsic extinction curve. |
To uuderstaud the tuaportauce of additional destruction we also considered a screen where uo further destruction has occurred. | To understand the importance of additional destruction we also considered a screen where no further destruction has occurred. |
As found in paper III the effective extinction curves of the turbulent screen are well determined by the effective absolute-to-relative extinction A. | As found in paper III the effective extinction curves of the turbulent screen are well determined by the effective absolute-to-relative extinction $R_V$. |
For given Ry--valuc we therefore. expect a certain. streugth of. the peak. | For given $R_V$ -value we therefore expect a certain strength of the peak. |
As Fie. | As Fig. |
⋅∙3 shows. iu case of probability distribution fictions (PDFs) of the cohuun densities with ej;<1 this behavior is quite accurate. | \ref{fig_peakstrengtharr} shows, in case of probability distribution functions (PDFs) of the column densities with $\sigma_{\ln \xi}\ll 1$ this behavior is quite accurate. |
For wide PDFs and high extinction values the Ry--valuc ouly provides au approximation of the correct atteuuation curves. | For wide PDFs and high extinction values the $R_V$ -value only provides an approximation of the correct attenuation curves. |
For example. if we consider a certain Ay--value the peak strength increases for broader PDFs. | For example, if we consider a certain $R_V$ -value the peak strength increases for broader PDFs. |
But still. for σιµε<2 the effect is in the order of ouly a few percent. | But still, for $\sigma_{\ln \xi}<2$ the effect is in the order of only a few percent. |
Turbulence not ouly flattens the extinction⋅⋅ curve but also reduces the peak ποιο as we have seen in the former section. | Turbulence not only flattens the extinction curve but also reduces the peak strength as we have seen in the former section. |
The effects are strouger in more optically thick media but. as Fig. | The effects are stronger in more optically thick media but, as Fig. |
3 shows. do not simply increase towards wider PDFs of the column deusitv. | \ref{fig_peakstrengtharr} shows, do not simply increase towards wider PDFs of the column density. |
This behavior is only true for media which are optically thin and for optically thick media with not extremely wide PDFs. | This behavior is only true for media which are optically thin and for optically thick media with not extremely wide PDFs. |
As shown in App. | As shown in App. |
A.2. in the limit of infinitely broad PDFs the Ry-value and the pcak streneth of the effective extinction curve become independent on the inean extinction (ly) and the standard deviation of the cohuunu density σιµε. | \ref{app2} in the limit of infinitely broad PDFs the $R_V$ -value and the peak strength of the effective extinction curve become independent on the mean extinction $\left<A_V\right>$ and the standard deviation of the column density $\sigma_{\ln\xi}$. |
The asvinptotic absolute-to-relative extinction. is. given. bv RoHE=VRVRE|EVR) | The asymptotic absolute-to-relative extinction is given by $R_V^{\rm eff}=\sqrt{R_V}/(\sqrt{R_V+1}-\sqrt{R_V})$. |
For Ry=3.1 we have RYEx6.67. | For $R_V=3.1$ we have $R_V^{\rm eff}\approx 6.67$. |
Likewise. we have a limit of the peak streugth given byG8%. | Likewise, we have a limit of the peak strength given by. |
. For media which are optically thick the asviuptotie value does not provide the strongest effect on the flatucss and peaks streneth. | For media which are optically thick the asymptotic value does not provide the strongest effect on the flatness and peaks strength. |
But still. for the considered parameter range the peak strength: is quite strone with >50%. | But still, for the considered parameter range the peak strength is quite strong with $>50\%$. |
Turbulence alone is therefore not able to produce the low peak strength of the Calzetti curve. | Turbulence alone is therefore not able to produce the low peak strength of the Calzetti curve. |
As a special example to analyze the effect caused by the additional destructionof the carriers of the peaks on its strength we considered again a critical column deusity of [Via=1Plau7. | As a special example to analyze the effect caused by the additional destructionof the carriers of the peak on its strength we considered again a critical column density of $[N_{\rm H}]_{\rm crit}=10^{21}~{\rm cm^{-2}}$. |
Fie. | Fig. |
3 shows a strong reduction of the peak streneth even for less broad PDFs. | \ref{fig_peakstrengtharr} shows a strong reduction of the peak strength even for less broad PDFs. |
Formean column deusities well above the critical coluun deusities the peak streneth weakeus strongly in case of more turbulentfa media. | Formean column densities well above the critical column densities the peak strength weakens strongly in case of more turbulent media. |
. For Gly)<;10mag aud oy,¢>2 the peak strength is lower than relative to the iufrinsie value. | For $\left<A_V\right><10~{\rm mag}$ and $\sigma_{\ln \xi}>2$ the peak strength is lower than relative to the intrinsic value. |
The nupact of the destruction on the carriers wealkenus for higher extinction values Cj. | The impact of the destruction on the carriers weakens for higher extinction values $\left<A_V\right>$. |
Iu case of: turbulent screens with: lean coluun deusities well below the critical colum deusity turbulence syoduces regions of high cohuun deusities where the μη] of the peak cau survive. | In case of turbulent screens with mean column densities well below the critical column density turbulence produces regions of high column densities where the carriers of the peak can survive. |
Ax the mass is conmressed £o yiore opaque clouds in higher turbulent media the peak stroneth increases with oj,c. | As the mass is compressed to more opaque clouds in higher turbulent media the peak strength increases with $\sigma_{\ln \xi}$. |
For iutermecdiate mean cobuun densities turbulence cads to au increase at low ej; but to a decrease of the soak strength at high oy,¢. | For intermediate mean column densities turbulence leads to an increase at low $\sigma_{\ln \xi}$ but to a decrease of the peak strength at high $\sigma_{\ln \xi}$. |
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