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Iu the huit of broad PDFs of the coluunu density he peak streneth reaches asviuptotically a value which is independent| on the main| panparameters of the screen. he mean extinction Gly} and standard deviation of he log-norimal function σε. | In the limit of broad PDFs of the column density the peak strength reaches asymptotically a value which is independent on the main parameters of the screen, the mean extinction $\left<A_V\right>$ and standard deviation of the log-normal function $\sigma_{\ln \xi}$. |
It solely depends ou the critical column density LVp]ags aud allows therefore a first estimate of the possible effect caused by the additional destruction ou the peak strength. | It solely depends on the critical column density $[N_{\rm H}]_{\rm crit}$ and allows therefore a first estimate of the possible effect caused by the additional destruction on the peak strength. |
The asviuptotic havior is analyzed in App. A.2.. | The asymptotic behavior is analyzed in App. \ref{app2}. |
. For the critical column density assunied in Fig. | For the critical column density assumed in Fig. |
3. the asvauptotic value is of. the intrinsic⋅⋅⋅ peak streugth. | \ref{fig_peakstrengtharr} the asymptotic value is of the intrinsic peak strength. |
As shown in. App. | As shown in App. |
A..wo ordto tical‘ ∪↥⋅⋪∐⋅∩⊾↸∖↥⋅↸⊳↥⋅↕∐⋈↧↸⊳≺⊔∐⊔∐∩∖∐↴∖↴↕↕↸∖↴∖↴↓↸∖⋪↧↴∖↴↖↽∐∩∪↕↸⊳↖↽⋪⊓∐∖col leusifies t acvnmptonetoti vi of the peak strength decreases strongly as 7,77€ Where 7i=KysolMujerir. | \ref{app2} for larger critical column densities the asymptotic value of the peak strength decreases strongly as $\tau_1^{-3/2}\,e^{-\tau_1}$ where $\tau_1=\kappa_{0.22}^{(1)}[N_{\rm H}]_{\rm crit}$. |
For critical cohuun densities well below [Miles=1PPcu7 the asymptotic peak strength reaches the value of 6854 caused by the turbulence in the lit of broad PDFs as discussed above. | For critical column densities well below $[N_{\rm H}]_{\rm crit}=10^{21}~{\rm cm^{-2}}$ the asymptotic peak strength reaches the value of $68\%$ caused by the turbulence in the limit of broad PDFs as discussed above. |
The effect of the critical column density on the peak strength is more accurately derived in Fie. L. | The effect of the critical column density on the peak strength is more accurately derived in Fig. \ref{fig_critcol}. |
The figure shows the critical column density needed to reduce the peak streueth to aud of the iutrinsic value. | The figure shows the critical column density needed to reduce the peak strength to and of the intrinsic value. |
To produce a peak of strengthturbulent sereeus with og,>1 and (ly)<10nag by more than 50% the critical column deusitvH needs to be at least ὃν.E10297σαD2, | To produce a peak strength of turbulent screens with $\sigma_{\ln\xi}>1$ and $\left<A_V\right><10~{\rm mag}$ by more than $50\%$ the critical column density needs to be at least $\sim 3\times 10^{20}~{\rm cm^{-2}}$. |
ToJj decrease in: the same paraicter range of the screen the peak streneth to of its intriusie value the critical colui: density needs to be at least ~2«1073cm 7. | To decrease in the same parameter range of the screen the peak strength to of its intrinsic value the critical column density needs to be at least $\sim 2\times 10^{21}~{\rm cm^{-2}}$ . |
As the figure shows the critical column density cannot be considerably Βαλ]: than 1025cur7 to produce peak streugtlis as low as 10. | As the figure shows the critical column density cannot be considerably smaller than $10^{21}~{\rm cm^{-2}}$ to produce peak strengths as low as . |
For esuuple. a critical colin deusity of 6<1073cui? | For example, a critical column density of $6\times 10^{21}~{\rm cm^{-2}}$ |
We define an X"Y"Z" whose Y"Z" plane coincides with the sky plane and the X" axis represents the line-of-sight. | We define an X”Y”Z” whose Y”Z” plane coincides with the sky plane and the X” axis represents the line-of-sight. |
The HI distribution is assumed to lie on the XY plane of a in a set of concentric, circular rings. | The HI distribution is assumed to lie on the XY plane of a in a set of concentric, circular rings. |
The two sistems are inclined by the angles i and ¢ (see Figure A1)), that are the inclination and the azimuth of the line of sight with respect to XYZ. | The two sistems are inclined by the angles $i$ and $\phi$ (see Figure \ref{geom1}) ), that are the inclination and the azimuth of the line of sight with respect to XYZ. |
The relation between the coordinates of the two systems is described by the rotation matrix R, as discussed in Galletta (1983): Each ring, labeled n, may be independent from the others and is inclined with respect to the galaxy reference plane by the angles 6, and αμ, shown in Figure A.1. | The relation between the coordinates of the two systems is described by the rotation matrix R, as discussed in Galletta (1983): Each ring, labeled n, may be independent from the others and is inclined with respect to the galaxy reference plane by the angles $\delta_n$ and $\alpha_n$, shown in Figure A.1. |
The change in 6, represent the warping of the gas plane, while the change in a, is the ring twisting, if present. | The change in $\delta_n$ represent the warping of the gas plane, while the change in $\alpha_n$ is the ring twisting, if present. |
The coordinate system of each ring is then The values of the coefficients Rjjn(i,6,On,αι) are listed in Arnaboldi Galletta (1993) and each ring is described by its radius r, and by an angle 0?«xBx360°. | The coordinate system of each ring is then The values of the coefficients $_{ijn}(i,\phi,\delta_n,\alpha_n)$ are listed in Arnaboldi Galletta (1993) and each ring is described by its radius $_n$ and by an angle $0^\circ\le\beta\le360^\circ$. |
To extract a simulated rotation curve, we calculate the couples of value on the sky traced along a fixed P.A. according to the relation: where K=tan(90+P.A.). | To extract a simulated rotation curve, we calculate the couples of value on the sky traced along a fixed P.A. according to the relation: where K=tan(90+P.A.). |
With this assumption, and the definition of the ring plane (equation A3)) the equation A2 becomes: | With this assumption, and the definition of the ring plane (equation \ref{planes}) ) the equation \ref{matrix} becomes: |
About sixty sources were isolated from the FIR maps shown in Fig. | About sixty sources were isolated from the FIR maps shown in Fig. |
1. | 1. |
This number ts large enough to allow statistical studies for the FIR properties of extragalactic star-forming regions. | This number is large enough to allow statistical studies for the FIR properties of extragalactic star-forming regions. |
Aperture photometry was done for these sources. with aperture diameters between ffor small regions. up to ffor the giant star-forming region 6604. | Aperture photometry was done for these sources, with aperture diameters between for small regions, up to for the giant star-forming region 604. |
Since in. the crowded areas the diffuse emission. from 333 cannot be unambigously determined. and since the introduction. of a model for this component would be rather subjective and lead to arbitrary results. the photometry is performed without a subtraction of the diffuse emission. | Since in the crowded areas the diffuse emission from 33 cannot be unambigously determined, and since the introduction of a model for this component would be rather subjective and lead to arbitrary results, the photometry is performed without a subtraction of the diffuse emission. |
From IRAS maps of 333. Rice et al. ( | From IRAS maps of 33, Rice et al. ( |
1990) localized a number of complexes and derived flux densities at 60 and 100m. Their 602m flux densities (Table 1) are in reasonable agreement with ours. while their 1OOgm data are generally higher. probably due to the inferior spatial resolution of IRAS. | 1990) localized a number of complexes and derived flux densities at 60 and $\mu$ m. Their $\mu$ m flux densities (Table 1) are in reasonable agreement with ours, while their $\mu$ m data are generally higher, probably due to the inferior spatial resolution of IRAS. |
Fig. | Fig. |
3 depicts the SEDs as derived from the photometry for a number of selected areas. | 3 depicts the SEDs as derived from the photometry for a number of selected areas. |
In the cases of the total galaxy and of 6604 and 5595 the IRAS (Rice et al. | In the cases of the total galaxy and of 604 and 595 the IRAS (Rice et al. |
1990) points are overplotted. | 1990) points are overplotted. |
The COBE/DIRBE (Odenwald et al. | The COBE/DIRBE (Odenwald et al. |
1998) "Sata overplotted in the SED for the total galaxy are somewhat lower. | 1998) data overplotted in the SED for the total galaxy are somewhat lower. |
The explanation for this difference is that M33 is situated in a small hole in the cirrus foreground. and the off-galaxy background measured by COBE/DIRBE with its large beam in the neighbourhood is probably too high. leading to lower flux densities for the galaxy. | The explanation for this difference is that M33 is situated in a small hole in the cirrus foreground, and the off-galaxy background measured by COBE/DIRBE with its large beam in the neighbourhood is probably too high, leading to lower flux densities for the galaxy. |
In all cases 33) it is obvious from the distribution of the three FIR data points that the SEDs cannot be represented by a single blackbody. but need a combination of two blackbody emission components. | In all cases 3) it is obvious from the distribution of the three FIR data points that the SEDs cannot be represented by a single blackbody, but need a combination of two blackbody emission components. |
We associate these two emissions with the two main morphological components measured directly im this paper. namely the localised (mainly warm) and the diffuse (mainly cold) component. | We associate these two emissions with the two main morphological components measured directly in this paper, namely the localised (mainly warm) and the diffuse (mainly cold) component. |
Two blackbodies have four degrees of freedom and as there are only three data points. no unique combination can be derived. | Two blackbodies have four degrees of freedom and as there are only three data points, no unique combination can be derived. |
In the cases of 333(total) and 6604 however. the IRAS data point at 254m puts an upper limit to the temperature of the warm blackbody component. | In the cases of 33(total) and 604 however, the IRAS data point at $\mu$ m puts an upper limit to the temperature of the warm blackbody component. |
At the long wavelength end Chini et al. ( | At the long wavelength end Chini et al. ( |
1986) found for Sb and Se type galaxies observed by IRAS an average ratio Si200un/Sodum~0.034. with a scatter of a factor 2.5. | 1986) found for Sb and Sc type galaxies observed by IRAS an average ratio $_{1200{\mu}m}/$ $_{60{\mu}m}\sim 0.034$, with a scatter of a factor 2.5. |
Adopting the same ratio for M33 we insert a 1200 rm data point into the M33 SED. | Adopting the same ratio for M33 we insert a $\mu$ m data point into the M33 SED. |
Attributing 30% of the signal at 254mm to hot dust. the fit with two modified blackbody functions (assuming an emissivity of Bo 7) to the four data points between 25 and pm yields Ti,=46.040.6 ΚΚ. and T,= KK. As seen in the plot the cold blackbody curve comes very close to the 1200umy point estimated above. | Attributing $\%$ of the signal at $\mu$ m to hot dust, the fit with two modified blackbody functions (assuming an emissivity of $\beta \propto \lambda^{-2}$ ) to the four data points between 25 and $\mu$ m yields $_{warm}=46.0\pm0.8$ K, and $_{cold}=16.7\pm0.5$ K. As seen in the plot the cold blackbody curve comes very close to the $\mu$ m point estimated above. |
Adopting the temperature of the warm component to be rather constant over the galaxy. we keep T,,,,,= 46KK fixed for fitting the cold component in the other areas. | Adopting the temperature of the warm component to be rather constant over the galaxy, we keep $_{warm}=46$ K fixed for fitting the cold component in the other areas. |
The resulting Τι varies only slightly. taking values between 15.3 and KK. as demonstrated in the figure. with error bars of typically +0.5 KK. This indicates that (coincidentially) the temperature of the diffuse cold dust component is rather close to the temperature of the localised cold dust component. | The resulting $_{cold}$ varies only slightly, taking values between 15.3 and K, as demonstrated in the figure, with error bars of typically $\pm0.5$ K. This indicates that (coincidentially) the temperature of the diffuse cold dust component is rather close to the temperature of the localised cold dust component. |
If one does the same forB«27!. one would get Tí,=52.5+ IL.OKK. and Tj;=19.4+0.7 KK for M33,,,. with à submm value a factor of 3 above the adopted one (dotted curve). while the variation of T; was again rather small over the field. | If one does the same for $\beta \propto \lambda^{-1}$, one would get $_{warm}=52.5\pm1.0$ K, and $_{cold}=19.4\pm0.7$ K for $_{total}$, with a submm value a factor of 3 above the adopted one (dotted curve), while the variation of $_{cold}$ was again rather small over the field. |
Therefore. we interpret the spatial variation. of the flux density ratio. FusΓιο as being due to a variation of their amplitudes. rather than being due to a change of their temperatures. which seem to remain almost constant over the | Therefore, we interpret the spatial variation of the flux density ratio $F_{warm}/F_{cold}$ as being due to a variation of their amplitudes, rather than being due to a change of their temperatures, which seem to remain almost constant over the |
this phase although our caleulatious assume that is does. | this phase although our calculations assume that is does. |
This rapid expansion of the str[ace may also affect the rate oL trausfer from the primary to he rest o‘the system. at least near tje start of πο transfer. | This rapid expansion of the surface may also affect the rate of transfer from the primary to the rest of the system, at least near the start of mass transfer. |
Another interesting feature is the distributio of the |uniuoslty ou the stellar su‘face. | Another interesting feature is the distribution of the luminosity on the stellar surface. |
The surfaces of consta| temperature are all exteucec in the clirection of the secoudary sé) that he cdirection of racdiaive cifrou is away from the line between the «enters of the two components. | The surfaces of constant temperature are all extended in the direction of the secondary so that the direction of radiative diffusion is away from the line between the centers of the two components. |
Thus. the radial ix. drops siguilicantly as one ayproaches the su‘face [rom the interior in that cdirection. | Thus, the radial flux drops significantly as one approaches the surface from the interior in that direction. |
The racial [lux drops in the opposite direction or the salue reason. but to a much slnaler extent. | The radial flux drops in the opposite direction for the same reason, but to a much smaller extent. |
Tis can be see iin Fig. 19.. | This can be seen in Fig. \ref{fig9}, |
. a pot of the local >uminositv. defined to be the area of a spherical surface multiplied by the local dial flux. as a [uuction of 0. | a plot of the local “luminosity", defined to be the area of a spherical surface multiplied by the local radial flux, as a function of $\theta$. |
We present this ininosity al a ralal clistauce ayout hallway from he mode center to the surface |ithe direction ward the companjon and at the surface. | We present this luminosity at a radial distance about halfway from the model center to the surface in the direction toward the companion and at the surface. |
The treud inentiojecl is present at tlie deeper location. iis quite prouotuiced at the surace. | The trend mentioned is present at the deeper location, but is quite pronounced at the surface. |
The small scale varjationus in the surface unmiuosity are ILOC|iced. by the surface changiug is radial zone number oi this particular tiue step. | The small scale variations in the surface luminosity are produced by the surface changing its radial zone number on this particular time step. |
The total ]milosity emitted hrough both surfaces is uealv the same. with the small ¢illerence produced Nw the OXyausion of the outer layers of the model. | The total luminosity emitted through both surfaces is nearly the same, with the small difference produced by the expansion of the outer layers of the model. |
The enlarge Sulace area produced by the elongation of the model towa‘ds the companion jas the effect of rediciug the average effective teiiperatWe. as seel iu the evolutionary tracks for a spherical model aid the iuodel with the largest separatio in Fig. 20.. | The enlarged surface area produced by the elongation of the model towards the companion has the effect of reducing the average effective temperature, as seen in the evolutionary tracks for a spherical model and the model with the largest separation in Fig. \ref{fig10}. |
This is somewhat illusiouary. lowever. lor it ig10)» tli the shine of the comyALLO iof the secondary onto the surface of the onnary aid the fTEl hat the observed effective temperaure now becomes a function of the location of he observer with "eSyect to the system geometry. | This is somewhat illusionary, however, for it ignores both the shine of the companion of the secondary onto the surface of the primary and the fact that the observed effective temperature now becomes a function of the location of the observer with respect to the system geometry. |
In all tlis work we have assumed that the secoudary may be treated by a point1 source potential. | In all this work we have assumed that the secondary may be treated by a point source potential. |
It is of xne interest to see Low signilicaut this assumptjon is. | It is of some interest to see how significant this assumption is. |
Therefore we c:€ulculated the ZANIS model of secondary assumiug the primary was the point source companio. | Therefore we calculated the ZAMS model of the secondary assuming the primary was the point source companion. |
This is uot completely self cousistent. but it sliould be adequate to determine some level of crecijlity. [or ος ui | This is not completely self consistent, but it should be adequate to determine some level of credibility for the assumption. |
We nuc that the self gravity of the SM... ZAMS model with the SAL. coupauion olla spherica surface just exterior to the largest surface radius varies by about 0.6 per cei on that surface. | We find that the self gravity of the $\Msun$ ZAMS model with the $\Msun$ companion on a spherical surface just exterior to the largest surface radius varies by about 0.6 per cent on that surface. |
We have performec 2D stellar evolution sequeices of the primary member of a binary syste. | We have performed 2D stellar evolution sequences of the primary member of a binary system. |
These sequences were carried through core hydroge1i burning up to the time of Roche lobe overflow. | These sequences were carried through core hydrogen burning up to the time of Roche lobe overflow. |
The interior stellar evolution characteristics were alterecl from the single star evoution ouly on the fraction of a percent level even for the smallest sej)»arations. | The interior stellar evolution characteristics were altered from the single star evolution only on the fraction of a percent level even for the smallest separations. |
The mass of the coivective core as a [uuction of time is also unchanged. although tlie convective core bouudary is no louger a completely spherical surface. | The mass of the convective core as a function of time is also unchanged, although the convective core boundary is no longer a completely spherical surface. |
Thus. the approximation that tje interior structure and evolution is the same | Thus, the approximation that the interior structure and evolution is the same |
times over this period. | times over this period. |
Ixurtz et al. ( | Kurtz et al. ( |
2000) show that the number of papers in their Bigs journals(Αρ... ApJL.ApJS..AGA... AAS... MNRAS... aand PASP)) increased at approximately a vealv rate between 1976 and 1998. | 2000) show that the number of papers in their Big8 journals, ApJL, and ) increased at approximately a yearly rate between 1976 and 1998. |
TIe astronotuical literature has doubled beween 1952 and 1999. the years covered in our studs. | The astronomical literature has doubled between 1982 and 1999, the years covered in our study. |
Has the electronic clistribution of preprints aid journal articles changed the ciation history ol papers? | Has the electronic distribution of preprints and journal articles changed the citation history of papers? |
To examine tlis ¢iestion. we divided the CEHT papers iu two groups: thiose published between LOS Land 1991. axl those publislied betwee11992 and 1999. | To examine this question, we divided the CFHT papers in two groups: those published between 1984 and 1991, and those published between 1992 and 1999. |
There were [28 aul 522 papers iu these two groups. | There were 428 and 522 papers in these two groups. |
In Fieure 2 tlie average citatioi rate for these two periods is shown alor& with the fit of a simple expone1le moclel lor each period. | In Figure 2 the average citation rate for these two periods is shown along with the fit of a simple exponential model for each period. |
The citation rate for tle lLewel yapers clearly decliles Wore apidly tha1 ilat of the older papers. | The citation rate for the newer papers clearly declines more rapidly than that of the older papers. |
The half-life of the older papers is T.ll7.1 years while the half-life for the lewer papers is 2.77 years. | The half-life of the older papers is 7.11 years while the half-life for the newer papers is 2.77 years. |
We believe that if οιe were able to sunuple cltatiou rates uouthly. the citations lor au average paper iu the more receib dataset. would peak less than two years after ptblication. | We believe that if one were able to sample citation rates monthly, the citations for an average paper in the more recent dataset would peak less than two years after publication. |
This is the result of more rapid dissemination of results by tLe electronic cist‘bution of pre-priuts (astro-ph) aud journal articles. | This is the result of more rapid dissemination of results by the electronic distribution of pre-prints (astro-ph) and journal articles. |
The [aser decline in citations for 1je recent subset. also indicate that new results supersede earlier results more quickly than iu the past. | The faster decline in citations for the recent subset also indicate that new results supersede earlier results more quickly than in the past. |
Comparing the citatjon nunbers for papers piblished in diflfereuo years ds difficult siice the uumbe ‘ol citations toa paper 1ncreases with time. | Comparing the citation numbers for papers published in different years is difficult since the number of citations to a paper increases with time. |
\Ve Lave establis1ος La method [or estimatiug the total number of citatious hat :| paper can be expeced to achieve ate “a suitably loug periol. | We have established a method for estimating the total number of citations that a paper can be expected to achieve after a suitably long period. |
How do we compare yApeLs piblisled over almost (weny vears. elven he natural growth in ciations with tiue? | How do we compare papers published over almost twenty years, given the natural growth in citations with time? |
Welave used the average citaion histo‘y of all CFHT λαyers to define a growth curve for citatious (Figure 3). | We have used the average citation history of all CFHT papers to define a growth curve for citations (Figure 3). |
Tus curve shows the percertage of the fina liunber of citations. delined as the number eielieen vears alte: publication. for au average paper veSus the years since publication. | This curve shows the percentage of the final number of citations, defined as the number eighteen years after publication, for an average paper versus the years since publication. |
Usine this curve we cau estimate the final citation count (FCC) or each paper given a citation count and the number of years since publication. | Using this curve we can estimate the final citation count (FCC) for each paper given a citation count and the number of years since publication. |
The first CFHT paper was submitted in May 1980 and. was published in Aueust of tha year (vandenBereh1980). | The first CFHT paper was submitted in May 1980 and was published in August of that year \citep{vdb80}. |
. CFHT’s productivity (Figure I) rose more or less contiuously through the 1980s until it reached a fairly coustaut. level of around seveuty-five paders per year beweell 1991 to 1997. | CFHT's productivity (Figure 4) rose more or less continuously through the 1980s until it reached a fairly constant level of around seventy-five papers per year between 1991 to 1997. |
It took approximately teu vears for CEHT to hit its stride aid reac La consistently high level of paper production. | It took approximately ten years for CFHT to hit its stride and reach a consistently high level of paper production. |
A telescope's productivity in aly one year is linked ο many factors such as weather. competitiveness of the available tustruments. aud the reliability oL iustruments auc the telescope. all in the several years before the year of publication. | A telescope's productivity in any one year is linked to many factors such as weather, competitiveness of the available instruments, and the reliability of instruments and the telescope, all in the several years before the year of publication. |
We attribite the increase | We attribute the increase |
We must remark that the light evlinder radius ©=1 satisfving equation (23)) is not the fast-magnetosonic point. | We must remark that the light cylinder radius $x=1$ satisfying equation \ref{position}) ) is not the fast-magnetosonic point. |
In spite of the existence of such a redundant solution. we use (his concise fom. (23)) For mathematical simplicity. | In spite of the existence of such a redundant solution, we use this concise form \ref{position}) ) for mathematical simplicity. |
In fact. equation (23)) is helpful for calculating the partial differentiation of equation (21)) with respect to 2 along a fixed field line at the fast-magnetosonic point. and we can straightlorwarcdly check that the terms involving 0€/Or automatically cancel out in the derivative OL,/Or at this critical point. and the critical condition for the value of the partial derivative of B, holds. respective of anv choice of €. ( | In fact, equation \ref{position}) ) is helpful for calculating the partial differentiation of equation \ref{bp}) ) with respect to $x$ along a fixed field line at the fast-magnetosonic point, and we can straightforwardly check that the terms involving $\partial\xi/\partial x$ automatically cancel out in the derivative $\partial B_{p}/\partial x$ at this critical point, and the critical condition for the value of the partial derivative of $B_{p}$ holds, irrespective of any choice of $\xi$. ( |
If the derivative ὃς/0.7 diverges at the [ast-magnetosonie point. the critical condition for 0D,/Ox is not satisfied. | If the derivative $\partial\xi/\partial x$ diverges at the fast-magnetosonic point, the critical condition for $\partial B_{p}/\partial x$ is not satisfied. |
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