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This mdicates. therefore. that line contamination is negligible iu this object.
This indicates, therefore, that line contamination is negligible in this object.
The positious of the most important lines are marked in Fig.
The positions of the most important lines are marked in Fig.
3. where one can see that |SiIT[A33Ls. although very prominent im SNRs. does not coutribute significantly because it falls at a wavelength where IRAS was virtually blind.
\ref{iras_filt} where one can see that 34.8, although very prominent in SNRs, does not contribute significantly because it falls at a wavelength where IRAS was virtually blind.
The same applies to. [NeIITJALL5.6 which has an intensity comparable to [NeIT| but falls in the hole between the 12 and 25 The possible coutribution of [OTJAGG3.0 to the IRAS OO baud was already pointed out by Burton et al. (1990))
The same applies to 15.6 which has an intensity comparable to [NeII] but falls in the hole between the 12 and 25 The possible contribution of 63.0 to the IRAS 60 band was already pointed out by Burton et al. \cite{burton90}) )
who observed this line in the southern (vmolecular) rim of ICLI2 using a 337 aperture spectrometer on the NAO aud found Lue surface brightucsses a factor of ~2 larger than those measured bv IRAS.
who observed this line in the southern (“molecular”) rim of IC443 using a 33" aperture spectrometer on the KAO and found line surface brightnesses a factor of $\sim$ 2 larger than those measured by IRAS.
Ou the other haud. however. ISOTAVS iecasureimeuts of |OI[JA663.0 through a sa” aperture centered ou the optical filaments of WLE (Beach Rho 1996)) vield a line surface brightuess a factor of 22.5 lower than the IRAS 60 indicating. therefore. that the contamination by ΤΟΠ is relatively uniniportaut. at least iu this
On the other hand, however, ISO–LWS measurements of 63.0 through a $\oslash$ 80" aperture centered on the optical filaments of W44 (Reach Rho \cite{reach}) ) yield a line surface brightness a factor of $\simeq$ 2.5 than the IRAS 60 indicating, therefore, that the contamination by [OI] is relatively unimportant, at least in this
by eye all galaxies in the E/S0 sample with gradients 0.4—1.0; these numbered 1869 out of 70378.
by eye all galaxies in the E/S0 sample with gradients 0.4–1.0; these numbered 1869 out of 70378.
It was estimated that 108 of these were elliptical-elliptical mergers, 26 were mergers involving spirals, 98 were barred spirals, 142 were edge-on disks, 120 were other galaxies with visible spiral arms and 88 were confused with stars.
It was estimated that 108 of these were elliptical-elliptical mergers, 26 were mergers involving spirals, 98 were barred spirals, 142 were edge-on disks, 120 were other galaxies with visible spiral arms and 88 were confused with stars.
All of these except the elliptical mergers, 474 galaxies, were marked for exclusion.
All of these except the elliptical mergers, 474 galaxies, were marked for exclusion.
It should also be noted that many other high colour gradient galaxies were asymmetric or disturbed.
It should also be noted that many other high colour gradient galaxies were asymmetric or disturbed.
At lower colour gradients the proportion of face-on spirals decreases steeply (1396 at gradient >0.4, 5% at 0.3, 296 at 0.2) but less steeply for edge-on disks (896 at gradient >0.4, 8% at 0.3, 3% at 0.2).
At lower colour gradients the proportion of face-on spirals decreases steeply $13\%$ at gradient $>0.4$, $5\%$ at 0.3, $2\%$ at 0.2) but less steeply for edge-on disks $8\%$ at gradient $>0.4$, $8\%$ at 0.3, $3\%$ at 0.2).
However, the latter could easily be removed as they had axis ratios (from the r- de Vaucouleurs fits) of typically b/a~0.3 and always b/a« 0.4, whereas virtually all ellipticals had b/a>0.4.
However, the latter could easily be removed as they had axis ratios (from the $r$ -band de Vaucouleurs fits) of typically $b/a\simeq 0.3$ and always $b/a<0.4$ , whereas virtually all ellipticals had $b/a>0.4$.
We therefore exclude all galaxies with b/a«0.4, whatever their colour gradient.
We therefore exclude all galaxies with $b/a<0.4$, whatever their colour gradient.
Lastly, because of their very large scatter on Figure 7, we exclude all objects with r-band reyz smaller than 1.8 arcsec.
Lastly, because of their very large scatter on Figure 7, we exclude all objects with $r$ -band $r_{eff}$ smaller than 1.8 arcsec.
These exclusion criteria, for the purposes of colour gradient analysis, reduce the all E/SO sample to 37001, the M—r«—22.5 non-BCG sample to 13652, and the max-BCG sample to 4485 (we note that these exclusions make very little difference to the colour-magnitude relations of the respective samples, the main effect being increased error bars at the lowest luminosities).
These exclusion criteria, for the purposes of colour gradient analysis, reduce the all E/S0 sample to 37001, the $M-r<-22.5$ non-BCG sample to 13652, and the max-BCG sample to 4485 (we note that these exclusions make very little difference to the colour-magnitude relations of the respective samples, the main effect being increased error bars at the lowest luminosities).
After this filtering, for the whole E/SO sample the mean zu)—1 is 0.111152:0.00061 with a scatter 0.11724.
After this filtering, for the whole E/S0 sample the mean ${{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1$ is $0.11115\pm 0.00061$ with a scatter 0.11724.
From the relation on Figure 6 this corresponds to iruc—0.10 and so lies half-way between the mean gradient d(logd(g—T)r)...—0.071 measured for similarly selected E/S0s by La Barbera and Carvalho (2009) and the larger st=—0.14 found by Suh et al. (
From the relation on Figure 6 this corresponds to ${{d(g-r)}\over{d({\rm log~r)}}}\simeq -0.10$ and so lies half-way between the mean gradient ${{d(g-r)}\over{d({\rm log~r)}}}=-0.071$ measured for similarly selected E/S0s by La Barbera and Carvalho (2009) and the larger ${{d(g-r)}\over{d({\rm log~r)}}}=-0.14$ found by Suh et al. (
2010) for ‘red-cored’ morphological early-types after the exclusion of zero and inverted gradients.
2010) for `red-cored' morphological early-types after the exclusion of zero and inverted gradients.
For the M,«-—22.5 non-BCGs sample the mean gradient is similar, 0.105503-0.00098 with a scatter 0.11414.
For the $M_r<-22.5$ non-BCGs sample the mean gradient is similar, $0.10550\pm 0.00098$ with a scatter 0.11414.
But for the max-BCGs the mean gradient is significantly lower at 0.08142+0.00114 with scatter 0.07645.
But for the max-BCGs the mean gradient is significantly lower at $0.08142\pm 0.00114$ with scatter 0.07645.
Hence, we find evidence that BCGs have flatter colour gradients than other E/S0s; the difference is modest but with this large sample highly significant - the BCGs’ mean gradient is 22.8+1.896 less than for the M,<—22.5 non-BCGs and 26.7+1.8% less than for all E/SO.
Hence, we find evidence that BCGs have flatter colour gradients than other E/S0s; the difference is modest but with this large sample highly significant - the BCGs' mean gradient is $22.8\pm 1.8\%$ less than for the $M_r<-22.5$ non-BCGs and $26.7\pm 1.8\%$ less than for all E/S0.
Figure 8 shows the mean repf(g)f(r)—1 as a function of absolute magnitude M,..
Figure 8 shows the mean ${{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1$ as a function of absolute magnitude $M_r$.
The luminosityTep dependence is mild.
The luminosity dependence is mild.
There is a broad maximum at M,~—22, with a decrease of up to 20% to higher luminosity (BCGs excluded) and 24% to lower luminosities.
There is a broad maximum at $M_r\simeq -22$, with a decrease of up to $20\%$ to higher luminosity (BCGs excluded) and $24\%$ to lower luminosities.
BCGs have significantly lower mean colour gradient than other E/SOs aacross their range of luminosities.
BCGs have a significantly lower mean colour gradient than other E/S0s across their range of luminosities.
Figure 9 shows the mean —1 with the galaxies divided by velocity dispersion σ.
Figure 9 shows the mean ${{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1$ with the galaxies divided by velocity dispersion $\sigma$.
Colour gradient is maximum at low velocity dispersions of 100-150 km s! and decreases by almost 1/2 to o~300 km s!.
Colour gradient is maximum at low velocity dispersions of 100–150 km $\rm s^{-1}$ and decreases by almost 1/2 to $\sigma\simeq 300$ km $\rm s^{-1}$.
The BCGs have a lower colour gradient that non-BCGs in each c interval, although the gap between the two is narrower (~ 0.01) than with the galaxies in M, intervals (0.02-0.03).
The BCGs have a lower colour gradient that non-BCGs in each $\sigma$ interval, although the gap between the two is narrower $\sim 0.01$ ) than with the galaxies in $M_r$ intervals (0.02–0.03).
In the non-BCG sample, which has a sharp lower cutoff in luminosity, there is a steep increase in colour gradient at σ«180 km s!
In the non-BCG sample, which has a sharp lower cutoff in luminosity, there is a steep increase in colour gradient at $\sigma<180$ km $\rm s^{-1}$.
This reflects the finding in Paper I that a low c relative to luminosity is associated with a strong colour gradient.
This reflects the finding in Paper I that a low $\sigma$ relative to luminosity is associated with a strong colour gradient.
This is again seen on Figure 10 where the E/SO sample is divided by absolute magnitude.
This is again seen on Figure 10 where the E/S0 sample is divided by absolute magnitude.
Strong (> 0.15) colour gradients are a feature of galaxies with moderate or high luminosity of M.«—21 combined with log e<2.25 180 km s~').
Strong $>0.15$ ) colour gradients are a feature of galaxies with moderate or high luminosity of $M_r<-21$ combined with log $\sigma<2.25$ $\sigma<180$ km $\rm s^{-1}$ ).
Figure 11 shows colour gradient against effective radius.
Figure 11 shows colour gradient against effective radius.
For the E/S0s the mean (LS—1 almost doubles from the smallest radii up to reg— 8-10 kpc, and similarly for theM,<—22.5 non-BCGs, for which the gradient peaks at larger radii of 11-14 kpc (presumably because of the greater mean luminosity of this sample).
For the E/S0s the mean $({{{\rm r}_{eff}(g)}\over{{\rm r}_{eff}(r)}}-1$ almost doubles from the smallest radii up to $\rm r_{eff}=8$ –10 kpc, and similarly for the$M_r<-22.5$ non-BCGs, for which the gradient peaks at larger radii of 11–14 kpc (presumably because of the greater mean luminosity of this sample).
In both samples, mean gradient decreases at even larger radii.
In both samples, mean gradient decreases at even larger radii.
In BCGs the colour gradient shows a much weaker variation with radius and
In BCGs the colour gradient shows a much weaker variation with radius and
radial.
radial.
This is the configuration envisaged by Fabrika (1993) and it is not only plausible but is supported by evidence from P Cyent like absorption features observed on the blue side of (among others) Ha and He I emission.
This is the configuration envisaged by Fabrika (1993) and it is not only plausible but is supported by evidence from P Cygni like absorption features observed on the blue side of (among others) $\alpha$ and He I emission.
These absorption lines correspond to an equatorial outflow with a speed of ~ 200 km s, most visible when the accretion disk is edge on to the line of sight.
These absorption lines correspond to an equatorial outflow with a speed of $\sim$ 200 km $^{-1}$, most visible when the accretion disk is edge on to the line of sight.
The speed of outflow along the line of sight oscillates with the orbital period; Kopylov et al (1989) report for Πα a mean radial velocity of 2290 km s! with an amplitude of ~ 185 km s!: there is considerable scatter.
The speed of outflow along the line of sight oscillates with the orbital period; Kopylov et al (1989) report for $\alpha$ a mean radial velocity of $ -$ 290 km $^{-1}$ with an amplitude of $\sim$ 185 km $^{-1}$; there is considerable scatter.
They further suggest that the 13 day period oscillation is because the ejected gas slows down as it draws further away from the centre of mass of the binary.
They further suggest that the 13 day period oscillation is because the ejected gas slows down as it draws further away from the centre of mass of the binary.
The narrow Hw lines attributed to a circumbinary disk have a 13 day oscillation with an amplitude of no more than 25 km s. attributed in the model of section 5 to a slow fading of the emission with orbital phase.
The narrow $\alpha$ lines attributed to a circumbinary disk have a 13 day oscillation with an amplitude of no more than 25 km $^{-1}$, attributed in the model of section 5 to a slow fading of the emission with orbital phase.
The flow of gas from the companion to a compact object in à close binary hàs been modelled by Sawada et al (1986).
The flow of gas from the companion to a compact object in a close binary has been modelled by Sawada et al (1986).
These authors followed overflow gas as far as the L2 point and concluded that a substantial fraction of gas from the companion is discarded through the L2. point (but not through the L3 point).
These authors followed overflow gas as far as the L2 point and concluded that a substantial fraction of gas from the companion is discarded through the L2 point (but not through the L3 point).
| am not aware of any calculations exploring in detail its subsequent fate.
I am not aware of any calculations exploring in detail its subsequent fate.
Some insight can however be gained from a rather simple calculation.
Some insight can however be gained from a rather simple calculation.
The radius from the centre of mass of the binary of the L2 point is. as a fraction of the binary separationA. almost independent of the ratio of the mass of the compact object to that of the companion. q.
The radius from the centre of mass of the binary of the L2 point is, as a fraction of the binary separation, almost independent of the ratio of the mass of the compact object to that of the companion, .
It ranges from a value of 1.26A for g=0.35 to 1.20A for g= 1.
It ranges from a value of $1.26A$ for $q=0.35$ to $1.20A$ for $q=1$ .
The orbital speed of the L2 point is then given by a fraction 1.2€1+6) of the orbital velocity of the compact object and ts in all cases of interest a little smaller than the escape velocity from the L2 radius.
The orbital speed of the L2 point is then given by a fraction $1.2(1+q)$ of the orbital velocity of the compact object and is in all cases of interest a little smaller than the escape velocity from the L2 radius.
Thus one may expect some spillover from L2 to leave the binary system eventually and other material to fall back and either be captured or Join a stable circumbinary ring.
Thus one may expect some spillover from L2 to leave the binary system eventually and other material to fall back and either be captured or join a stable circumbinary ring.
It is simple to follow (at least approximately) the fate of material leaving the L2 point tangentially at just the escape velocity. along a parabolic orbit.
It is simple to follow (at least approximately) the fate of material leaving the L2 point tangentially at just the escape velocity, along a parabolic orbit.
It reaches the inner stable circumbinary radius (~ 2A) after 4 days. making an angle of approximately 45° and moving at 1.25 the speed of that orbit.
It reaches the inner stable circumbinary radius $\sim 2A$ ) after 4 days, making an angle of approximately $^{o}$ and moving at 1.25 the speed of that orbit.
Because of the rotation of the whole system. matter moving in the opposite direction to the material just leaving L2 was launched about 8 days earlier and has reached a radius of 3.44.
Because of the rotation of the whole system, matter moving in the opposite direction to the material just leaving L2 was launched about 8 days earlier and has reached a radius of $3.4A$.
At that distance itis now moving with half the speed of material leaving the L2 point tangentially.
At that distance it is now moving with half the speed of material leaving the L2 point tangentially.
Thus at orbital phase 0.75. when the L2 point is receding at naximum line of sight velocity. the approaching material on the far side of the spiral structure is moving. in the binary centre of mass. at half the L2 speed.
Thus at orbital phase 0.75, when the L2 point is receding at maximum line of sight velocity, the approaching material on the far side of the spiral structure is moving, in the binary centre of mass, at half the L2 speed.
It has also probably faded very considerably.
It has also probably faded very considerably.
If the two extreme components could be properly identified either of the two narrow Imes would oscillate with a period of 13 days and amplitude about one third of the mean Doppler speed.
If the two extreme components could be properly identified either of the two narrow lines would oscillate with a period of 13 days and amplitude about one third of the mean Doppler speed.
At least in the absence of a detailed model. it would not be possible to rule out an expanding spiral structure as the origin of the He I lines. but the above considerations do not seem consistent with the extreme stability of He.
At least in the absence of a detailed model, it would not be possible to rule out an expanding spiral structure as the origin of the He I lines, but the above considerations do not seem consistent with the extreme stability of $\alpha$.
The great stability of the narrow red and blue components of the stationary Ha line in the spectrum of SS 433 is easily understood in terms of an orbiting circumbinary ring. presumed to be the inner rim of a larger disk.
The great stability of the narrow red and blue components of the stationary $\alpha$ line in the spectrum of SS 433 is easily understood in terms of an orbiting circumbinary ring, presumed to be the inner rim of a larger disk.
This stability ts very much at odds with a source in an outward flow through the L2 point.
This stability is very much at odds with a source in an outward flow through the L2 point.
The more complicated behaviour of the He I lines is consistent with an origin in the eircumbinary disk. provided only that the more rapid fading can be accomodated.
The more complicated behaviour of the He I lines is consistent with an origin in the circumbinary disk, provided only that the more rapid fading can be accomodated.
Thus the very simple model in which radiation from the circumbinary disk decays exponentially behind a leading edge. convoluted with a Gaussian function. accounts astonishingly well for the narrow components found within the stationary Ha and He I lines.
Thus the very simple model in which radiation from the circumbinary disk decays exponentially behind a leading edge, convoluted with a Gaussian function, accounts astonishingly well for the narrow components found within the stationary $\alpha$ and He I lines.
Ha’ at least is contributed by radiation from the inner circumbinary disk. orbiting the binary at very approximately 250 km s.
$\alpha$ at least is contributed by radiation from the inner circumbinary disk, orbiting the binary at very approximately 250 km $^{-1}$.
The apparent systemic velocity of the ring is approximately 70 km s7!.
The apparent systemic velocity of the ring is approximately 70 km $^{-1}$.
He emission fades on a timescale of 14 days whereas He I has a fading time of about 4 days.
$\alpha$ emission fades on a timescale of 14 days whereas He I has a fading time of about 4 days.
In this simple model the leading edge of the Ha emission is found close to the passage of the compact object and its disk but the leading edge for He [ is perhaps a day or so earlier.
In this simple model the leading edge of the $\alpha$ emission is found close to the passage of the compact object and its disk but the leading edge for He I is perhaps a day or so earlier.
The irradiation of a given point on the circumbinary disk by the source of intense radiation in the vicinity of the compact object varies by a factor of almost three over the orbit. from geometric effects alone.
The irradiation of a given point on the circumbinary disk by the source of intense radiation in the vicinity of the compact object varies by a factor of almost three over the orbit, from geometric effects alone.
When the compact object is furthest from a point on the disk. additionally the companion eclipses that portion.
When the compact object is furthest from a point on the disk, additionally the companion eclipses that portion.
This suggests that intense radiation from the vicinity of the compact object periodically refreshes emission from the cireumbinary disk - the effect might be augmented by arrival of material from L2 - and a decay scale of about one period is not unreasonable.
This suggests that intense radiation from the vicinity of the compact object periodically refreshes emission from the circumbinary disk - the effect might be augmented by arrival of material from L2 - and a decay scale of about one period is not unreasonable.
It Is perhaps curious that the He I signal decays much faster than He and the hot spot is ahead of the compact object.
It is perhaps curious that the He I signal decays much faster than $\alpha$ and the hot spot is ahead of the compact object.
It seems entirely possible that some phases at least of the He I lines are dominated by radiation from the stream leaving the L2 point. which feeds the circumbinary disk and eventually the wider environment.
It seems entirely possible that some phases at least of the He I lines are dominated by radiation from the stream leaving the L2 point, which feeds the circumbinary disk and eventually the wider environment.
For the remainder of this paper I shall suppose that the eircumbinary disk is real and that the inner edge has at least approximately the orbital speed extracted from the model.
For the remainder of this paper I shall suppose that the circumbinary disk is real and that the inner edge has at least approximately the orbital speed extracted from the model.
The remaining uncertainty ας the radius at which the ring of fire orbits.
The remaining uncertainty is the radius at which the ring of fire orbits.
The rotational speed of the inner circumbinary disk provides an important constraint on the mass of the system and hence on the mass of the compact object.
The rotational speed of the inner circumbinary disk provides an important constraint on the mass of the system and hence on the mass of the compact object.
If the radius at which the material orbits with speed v 1s fA. A being the separation of the two members of the binary. then the mass of the system ts given by in units ofM. being specified in km s! [Eq.
If the radius at which the material orbits with speed $v$ is $fA$, $A$ being the separation of the two members of the binary, then the mass of the system is given by in units of, being specified in km $^{-1}$ [Eq.
3 of Blundell. Bowler & Schmidtobreick (2008)].
3 of Blundell, Bowler $\&$ Schmidtobreick (2008)].
The innermost stable orbit about the binary system corresponds tof approximately 2. estimates varying between 1.8 and 2.3.
The innermost stable orbit about the binary system corresponds to approximately 2, estimates varying between 1.8 and 2.3.
However. in à system such as SS 433 where material is almost certainly being added to the cireumbinary disk via the L2 point. the glowing inner rimmaybe within the innermost stable orbit. depending on the residence time and the rate at which matter
However, in a system such as SS 433 where material is almost certainly being added to the circumbinary disk via the L2 point, the glowing inner rimmaybe within the innermost stable orbit, depending on the residence time and the rate at which matter
less than 1013 g s-! in the propeller regime.
less than $10^{12}$ g $^{-1}$ in the propeller regime.
However, as a consequence of the centrifugal barrier, only a minor fraction (if any) of such mass rate would enter the Alfven radius.
However, as a consequence of the centrifugal barrier, only a minor fraction (if any) of such mass rate would enter the Alfven radius.
On the other hand, in the accretor regime, which is allowed only forvery low magnetic field values (smaller than a few 105 G !),
On the other hand, in the accretor regime, which is allowed only for low magnetic field values (smaller than a few $10^{8}$ G !),
we would expect an accretion rate smaller than ~5x107? g s-!.
we would expect an accretion rate smaller than $\sim5\times10^{10}$ g $^{-1}$.
In both the propeller and the accretor pictures, the accretion rate on the INS could yield a luminosity of ~10?! erg s!.
In both the propeller and the accretor pictures, the accretion rate on the INS could yield a luminosity of $\sim 10^{31}$ erg $^{-1}$.
This is about two order of magnitude smaller than the X-rayluminosity of the hot thermal component (~9x10?? erg s~+) seen in the X-ray spectrum of citepdeluca04.. Fig.3)
This is about two order of magnitude smaller than the X-rayluminosity of the hot thermal component $\sim9\times10^{32}$ erg $^{-1}$ ) seen in the X-ray spectrum of . \ref{limits})
This is about two order of magnitude smaller than the X-rayluminosity of the hot thermal component (~9x10?? erg s~+) seen in the X-ray spectrum of citepdeluca04.. Fig.3))
This is about two order of magnitude smaller than the X-rayluminosity of the hot thermal component $\sim9\times10^{32}$ erg $^{-1}$ ) seen in the X-ray spectrum of . \ref{limits})
This is about two order of magnitude smaller than the X-rayluminosity of the hot thermal component (~9x10?? erg s~+) seen in the X-ray spectrum of citepdeluca04.. Fig.3)),
This is about two order of magnitude smaller than the X-rayluminosity of the hot thermal component $\sim9\times10^{32}$ erg $^{-1}$ ) seen in the X-ray spectrum of . \ref{limits})
soll 5-rav repeaters (SGRs) are sources of recurrent. short (/~ 0.18). intense eres) bursts of 5-rav emission with a soft energy spectrum.
Soft $\gamma$ -ray repeaters (SGRs) are sources of recurrent, short $t \sim 0.1\,\mathrm{s}$ ), intense $L \sim 10^{44}~\rm{ergs}$ ) bursts of $\gamma$ -ray emission with a soft energy spectrum.
The normal pattern of SGRs are intense activitv. periods which can last weeks or months. separated by quiescent phases lasting vears or decades.
The normal pattern of SGRs are intense activity periods which can last weeks or months, separated by quiescent phases lasting years or decades.
The (tliree most intense SCI bursts ever recorded were the 5 March 1979 eiant flare of SGR 0526-66 (Mazets οἱ 11979). the similar 28 August 1998 ejant [lare of SGR 1900--14. and the 27 December 2004 burst (SCR. 1806-20).
The three most intense SGR bursts ever recorded were the 5 March 1979 giant flare of SGR 0526-66 (Mazets et 1979), the similar 28 August 1998 giant flare of SGR 1900+14 and the 27 December 2004 burst (SGR 1806-20).
ANPs are similar in nature but with a somewhat weaker intensity and no recurrent bursting.
AXPs are similar in nature but with a somewhat weaker intensity and no recurrent bursting.
Several
Several
times are loosely coupled to the eas aud have therefore hieh collision velocities.
times are loosely coupled to the gas and have therefore high collision velocities.
For this reason. the maximal particle mass proportional to the eas clensity.
For this reason, the maximum particle mass proportional to the gas density.
The comunon feature of these simulations is that the dust scale height for à=107 is always similar to the gas scale height (see Table 1)).
The common feature of these simulations is that the dust scale height for $\alpha=10^{-2}$ is always similar to the gas scale height (see Table \ref{table:sedi}) ).
Therefore. we conclude that the disk atinospheres can be kept dustv in sparse aud dense disks alike with suticicutly high turbulence values.
Therefore, we conclude that the disk atmospheres can be kept dusty in sparse and dense disks alike with sufficiently high turbulence values.
The Branusclaveig collisiou model is based on laboratory experiuenuts that used fractal dimension 3 ageregates[mm with an eulargemienut parameter typically between 7 aud 2.
The Braunschweig collision model is based on laboratory experiments that used fractal dimension 3 aggregates with an enlargement parameter typically between 7 and 2.
As seen iu Table 1.. the maxinnun culargement paraiaceter of the ageregatesOO can be several orders of magnitude lareer than the dust agereeatesCocoOo used in the laboratory.
As seen in Table \ref{table:sedi}, the maximum enlargement parameter of the aggregates can be several orders of magnitude larger than the dust aggregates used in the laboratory.
More specifically. the hit&sstick collision regine is followed by a collision type called sticking through surface effects (see Paper D) aud bouncing at higher collisional energies.
More specifically, the stick collision regime is followed by a collision type called sticking through surface effects (see Paper I) and bouncing at higher collisional energies.
Thus we asstune that the transition from fractal ageregates in he hit&sstick regime to fractal dimension 3 agerceatcsOO in bouncing is an iustautaucous one.
Thus we assume that the transition from fractal aggregates in the stick regime to fractal dimension 3 aggregates in bouncing is an instantaneous one.
Furtherinore. our »orositv anodel for bouncing is calibrated for dust cakes (enlareenmientzl parameter of 6). however the eulareeimoento xuanmeter at the cud of the hit&sstick plase is 2-3 orders of magnitude larger than the cularecment paraueter of he dust cakes (see Table 1)).
Furthermore, our porosity model for bouncing is calibrated for dust cakes (enlargement parameter of 6), however the enlargement parameter at the end of the stick phase is 2-3 orders of magnitude larger than the enlargement parameter of the dust cakes (see Table \ref{table:sedi}) ).