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As described in previous papers (Renzini da Costa 1997, Nonino 1998. hereafter paper D the main goals of the EIS project are to conduct an imaging survey suitable for finding "rare" objects for follow-up observations with the VLT and to lay down the groundwork for more ambitious wide-field digital. multicolor imaging surveys. | As described in previous papers (Renzini da Costa 1997, Nonino 1998, hereafter paper I) the main goals of the EIS project are to conduct an imaging survey suitable for finding “rare” objects for follow-up observations with the VLT and to lay down the groundwork for more ambitious wide-field digital, multicolor imaging surveys. |
The adopted strategy was designed to search for distant clusters of galaxies. quasars. high-redshift galaxies and to identify rare stellar types. | The adopted strategy was designed to search for distant clusters of galaxies, quasars, high-redshift galaxies and to identify rare stellar types. |
As part of EIS-wide. observations were obtained in three passbands (B.V and /) over an area of about 1.7 square degrees in a region near the South Galactic Pole (EIS-wide patch B). | As part of EIS-wide, observations were obtained in three passbands $B, V$ and $I$ ) over an area of about 1.7 square degrees in a region near the South Galactic Pole (EIS-wide patch B). |
The region was selected because of the high density of know1 intermediate red-shift quasars. | The region was selected because of the high density of known intermediate red-shift quasars. |
The multicolor data for patch B are now being released and in a separate paper the observations. calibration and the overall quality of the data are deseribec (Prandoni 1998. paper IID. | The multicolor data for patch B are now being released and in a separate paper the observations, calibration and the overall quality of the data are described (Prandoni 1998, paper III). |
In that paper. preliminary single passband catalogs were presented and evaluated by comparing the star- and galaxy-counts with models anc results from other surveys and the EIS patch A. presented i paper I. The good agreement found from these comparisons indicates that the available data. reductior procedures and object catalogs extracted in each of the passbands are reliable. | In that paper, preliminary single passband catalogs were presented and evaluated by comparing the star- and galaxy-counts with models and results from other surveys and the EIS patch A, presented in paper I. The good agreement found from these comparisons indicates that the available data, reduction procedures and object catalogs extracted in each of the passbands are reliable. |
Furthermore. comparison of the observed color distribution for point-like sources. derived from a preliminary version of a color catalog. with predictions of galactic models also shows reasonable agreement. | Furthermore, comparison of the observed color distribution for point-like sources, derived from a preliminary version of a color catalog, with predictions of galactic models also shows reasonable agreement. |
Although encouraging. the above results do not fully characterize the color catalog. in particular if it is to be used to identify different types of objects based on color selection criteria. | Although encouraging, the above results do not fully characterize the color catalog, in particular if it is to be used to identify different types of objects based on color selection criteria. |
Target selection based on the location of objects in color-color space. require a careful investigation of the performance of the pipeline since any problem may lead to objects with spurious colors. | Target selection based on the location of objects in color-color space, require a careful investigation of the performance of the pipeline since any problem may lead to objects with spurious colors. |
Colors are sensitive to a number of effects such as the observing conditions. the photometric and astrometric solutions in the different passbands and the | Colors are sensitive to a number of effects such as the observing conditions, the photometric and astrometric solutions in the different passbands and the |
the figwe points to the location where the “EIT wave" frout stopped. | the figure points to the location where the “EIT wave" front stopped. |
We cau see that it is indeed cospatial with the magnetic separatrix. | We can see that it is indeed cospatial with the magnetic separatrix. |
Tje coronal Moreton wave. front F1 in tle top pauel of Figure 2.. whic1 is [ast-inode wave iu lature. does not care the existence of the maguetic separatrix at the clistau'e of (rom the flare site. | The coronal Moreton wave, front F1 in the top panel of Figure \ref{fig2}, which is fast-mode wave in nature, does not care the existence of the magnetic separatrix at the distance of from the flare site. |
It. propagated across it. tiough its speed decreased. (die to weaker magnetic field) as inferred from its declined slope in the lop palel of Figure 2.. | It propagated across it, though its speed decreased (due to weaker magnetic field) as inferred from its declined slope in the top panel of Figure \ref{fig2}. |
However. oue feature that is not expected is the second fast wave front F2 i the top panel of Figure 2.. | However, one feature that is not expected is the second fast wave front F2 in the top panel of Figure \ref{fig2}. |
Aj»parently it emanated from tie bright. “EIT wave" [ront at 08:55:00 UT wheithe “EIT wave [roit was at a distance of ~920" (rom the flare site. | Apparently it emanated from the bright “EIT wave" front at 08:55:00 UT when the “EIT wave" front was at a distance of $\sim
220\arcsec$ from the flare site. |
Checking the EUV iuages in Figure 1.. we fine tha there is asi nall-sized coronal loop situated at such a distance. with a relatively stronger inagnetk: fielcl as mentioned1 in re[sect:res.. | Checking the EUV images in Figure \ref{fig1}, we find that there is a small-sized coronal loop situated at such a distance, with a relatively stronger magnetic field as mentioned in \\ref{sect:res}. |
Therefore. we hyyothesize that [rout F2 is die to the [ast-mode imagnetoacot*16 Wave uear the west side of the small coronal loop beiug diffractec to propagate to the eas. | Therefore, we hypothesize that front F2 is due to the fast-mode magnetoacoustic wave near the west side of the small coronal loop being diffracted to propagate to the east. |
This is reinforced by the movie dif.inpg) attached with Fiewe 1.. | This is reinforced by the movie ) attached with Figure \ref{fig1}. |
Along sice B. the bottou pauel of Figure 2. preset tsa bright front (FD+)) with a propagation speed of 170 aad anothe ‘faint [ront behixd (52) with a speed of 170. | Along slice B, the bottom panel of Figure \ref{fig2} presents a bright front (F3) with a propagation speed of 470 and another faint front behind (S2) with a speed of 170. |
. Apparently the faster wave seenis o be an orciuary “EIT wave intie sense that ain expatcling cimiming was 1iunediately following. | Apparently the faster wave seems to be an ordinary “EIT wave" in the sense that an expanding dimming was immediately following. |
However. we interpret it as lthe cornal Moretou wave. Le. a fas-mode wave. because it was moving ogether wit1 the coronal lOreto1 wave ou slice A. Besides. here isa very faint reflected. wave in the bottom parel of Figu [e whe1 the faster wave F2 aj»proacled the stall coronal loop at 081092:30 WT. whic lois a tyjlcal clara‘teristic of fast-mode waves. | However, we interpret it as the coronal Moreton wave, i.e., a fast-mode wave, because it was moving together with the coronal Moreton wave on slice A. Besides, there is a very faint reflected wave in the bottom panel of Figure \ref{fig2} when the faster wave F2 approached the small coronal loop at 08:52:30 UT, which is a typical characteristic of fast-mode waves. |
Àoreover. this faster wave las routs sharper tha1 “EIT waves. | Moreover, this faster wave has fronts sharper than “EIT waves". |
Tellue the nature of the sower [ront 52 is not straightforward sluce H was so weaz that it i5 evel 101 ¢iscernable from the dilerence images in Figure L.. | Telling the nature of the slower front S2 is not straightforward since it was so weak that it is even not discernable from the difference images in Figure \ref{fig1}. |
Since this rout had a typical speed for “EIT waves”. we tentatively expain it as an EIT wave. | Since this front had a typical speed for “EIT waves", we tentatively explain it as an EIT wave. |
It is seen that e EIT wave f“OL along sice B was 1wich weaker than that aloug slice A. The possible reason is at the magnelic ield lines overlying the eruption site were 1iainty oriented along the direction of ice A as illust‘ated by Figure 3.. | It is seen that the EIT wave front along slice B was much weaker than that along slice A. The possible reason is that the magnetic field lines overlying the eruption site were mainly oriented along the direction of slice A as illustrated by Figure \ref{fig3}. |
According to the fieldline sretching 1uodel ofJOD).. as these field lives are pushed to stretch up. compression would be formed at the lees of ese field lines. | According to the fieldline stretching model of, as these field lines are pushed to stretch up, compression would be formed at the legs of these field lines. |
Therefore. bright “EIT wave” [routs are visibe aloug slice A. The fast-moce wave. jowever. is always reracted toward the region with weak magnetic fieldLOGS).. and has iothiug to do with tle magnetic connectivity. | Therefore, bright “EIT wave" fronts are visible along slice A. The fast-mode wave, however, is always refracted toward the region with weak magnetic field, and has nothing to do with the magnetic connectivity. |
This is why the coronal Moreton wave is extremely isght along slice B (where the maguetic field is weak) ancl faint. along slice A. It is interesting o note that. either along slice A or slice B. the coronal Moreton wave was uoviug with a speed ~3 times higher than that of the following “EIT wave. cousistent with the »edicetiou of the fieldine stretching moclel of when semi-circular magnetic configuratiou is assumed. | This is why the coronal Moreton wave is extremely bright along slice B (where the magnetic field is weak) and faint along slice A. It is interesting to note that, either along slice A or slice B, the coronal Moreton wave was moving with a speed $\sim 3$ times higher than that of the following “EIT wave", consistent with the prediction of the fieldline stretching model of when semi-circular magnetic configuration is assumed. |
nodels by Querci et al. ( | models by Querci et al. ( |
1971) and Johuson (1971) with effective temperatures of 3800. 3600 and 3500 I& (warier hau the Tg values usually derived in C-N stars). eravity og g—L0. C/O=1.3 aud modelled three Li I lines. ranely the A6101.. AGTOS aud ASI26 lines. | 1974) and Johnson (1974) with effective temperatures of 3800, 3600 and 3500 K (warmer than the $\rm{_{eff}}$ values usually derived in C-N stars), gravity log $=1.0$, $=1.3$ and modelled three Li I lines, namely the $\lambda6104$, $\lambda6708$ and $\lambda8126$ lines. |
They also vied to model the impact of a chromosphere ou the ormnation of Lithimm lines usine the approach of (Tyaq) ou the bound-free transitions of lithiu. | They also tried to model the impact of a chromosphere on the formation of lithium lines using the approach of $_{\rm{rad}}$ ) on the bound-free transitions of lithium. |
Several aspects in their NLTE calculation differ from the preseut study: | Several aspects in their NLTE calculation differ from the present study: |
NNCOGCHI6G20. We acknowledee the significant contribution of Volker Spriusel for the simulations used in this work. | NNG06GH62G. We acknowledge the significant contribution of Volker Springel for the simulations used in this work. |
RON ds erateful for the hospitality of Institute for the Plhivsies and Matheiiaties of the Universe. The University of Tokwo. where part of this work was douce. | KN is grateful for the hospitality of Institute for the Physics and Mathematics of the Universe, The University of Tokyo, where part of this work was done. |
to distances of ~4 Alpe (e.g.Giovannini&Feretti 2004). | to distances of $\sim$ 4 Mpc \citep[e.g.][]{Giovannini04}. |
. Some of the known examples of relies which lio at distances bevond ~2 Mpe from the nearest cluster core. such as D0917|75 (Harris ct al. | Some of the known examples of relics which lie at distances beyond $\sim$ 2 Mpc from the nearest cluster core, such as B0917+75 (Harris et al. |
1993: Johnston-Laollitt 2003). are typically associated with structure larger than a single cluster. | 1993; Johnston-Hollitt 2003), are typically associated with structure larger than a single cluster. |
In the case of r-30017το it is the Rood 27 cluster group. | In the case of B0917+75 it is the Rood 27 cluster group. |
TFhis is similar to our situation. | This is similar to our situation. |
It is also relevant to. note jab the minor axis of the relic does not point towards either the WAT source or the cD galaxy. suggesting sub-structure in this large-scale structure. | It is also relevant to note that the minor axis of the relic does not point towards either the WAT source or the cD galaxy, suggesting sub-structure in this large-scale structure. |
Simulations of shock generation curing hierarchical mass assembly sugeest relies can be produced. over 8 Alpe from the cluster centre2009). | Simulations of shock generation during hierarchical mass assembly suggest relics can be produced over 8 Mpc from the cluster centre. |
. These aspects along with its racio structure and lack of an obvious optical identification make it very likely to be a radio relie. | These aspects along with its radio structure and lack of an obvious optical identification make it very likely to be a radio relic. |
One could eneuire whether this object might be a dying radio galaxy. | One could enquire whether this object might be a dying radio galaxy. |
The non-detection of an early-tvpe ealaxy associated with it suggests that this is unlikely to be the case. | The non-detection of an early-type galaxy associated with it suggests that this is unlikely to be the case. |
Phere are very [ow relies known beyond a redshift of —0.2 (ος.Ciovannini&Feretti2004).. which makes this finding a significant one. | There are very few relics known beyond a redshift of $\sim$ 0.2 \citep[e.g.][]{Giovannini04}, which makes this finding a significant one. |
The other interesting source in the field. is the FRI radio source. 91110. | The other interesting source in the field is the FRI radio source S1110. |
The radio emission from SILIO is svmimetric within ~SO kpe from the host ealaxv. SWIREAJ.J008306.30-431020.8. reminiscent | The radio emission from S1110 is symmetric within $\sim$ 80 kpc from the host galaxy, J003306.30-431029.8, reminiscent |
The observed instabilities can be compared with expectations from linear stability theory. | The observed instabilities can be compared with expectations from linear stability theory. |
To do this. we extract from the axisymmetric simulations the quantities that enter the stability conditions. and then compare the result with the evidence of non-axisymmetric instability in the corresponding 3D simulation. | To do this, we extract from the axisymmetric simulations the quantities that enter the stability conditions, and then compare the result with the evidence of non-axisymmetric instability in the corresponding 3D simulation. |
The available stability conditions apply only to steady or static configurations and have been derived either in the context of controlled fusion or cylindrical jets (??).. hence the comparison can only be indicative. | The available stability conditions apply only to steady or static configurations and have been derived either in the context of controlled fusion or cylindrical jets \citep{2000Appl,2000Lery}, hence the comparison can only be indicative. |
According to the Kruskal-Shafranov criterion. the longitudinal wavelength of an instability must be at least as high as the magnetic pitch on the unstable surface. defined to be the distance covered during one revolution of a helical field line about the central axis. | According to the Kruskal-Shafranov criterion, the longitudinal wavelength of an instability must be at least as high as the magnetic pitch on the unstable surface, defined to be the distance covered during one revolution of a helical field line about the central axis. |
Besides being the result of linear stability analyses in the context of controlled fusion. it can be derived heuristically from geometric arguments (?).. | Besides being the result of linear stability analyses in the context of controlled fusion, it can be derived heuristically from geometric arguments \citep{1958Johnson}. |
Therefore. it should give a convenient scale also in cases for which it was not originally intended. like the expanding jets studied here. | Therefore, it should give a convenient scale also in cases for which it was not originally intended, like the expanding jets studied here. |
Deviations can be expected e.g. from the effect of one-ended line-tying. which in some cases has been found to lead to mereased instability as opposed to a configuration without a free end (???).. | Deviations can be expected e.g. from the effect of one-ended line-tying, which in some cases has been found to lead to increased instability as opposed to a configuration without a free end \citep{2006Furno,2006Lapenta,2008Sun}. |
For a conical jet. the magnetic pitch is on the )=const surface. | For a conical jet, the magnetic pitch is on the $\vartheta=\const$ surface. |
See Appendix AppendixA: for a derivation of this expression. | See Appendix \ref{app:conicalpitch} for a derivation of this expression. |
In the simulations. /: decreases with + and settles to a constant value above the radius. see Fig. | In the simulations, $h$ decreases with $r$ and settles to a constant value above the radius, see Fig. |
5. (compare also Fig. 3)). | \ref{fig:pitch}
(compare also Fig. \ref{fig:flines}) ). |
The variation of the pitch with 2 depends on the kind of rotation imposed at the lower boundary. | The variation of the pitch with $\vartheta$ depends on the kind of rotation imposed at the lower boundary. |
In the Keplerian case. the dependence ts strong. with the asymptotic pitch being approximately 10 near the axis and 40 at the limb of the jet. | In the Keplerian case, the dependence is strong, with the asymptotic pitch being approximately $10$ near the axis and $40$ at the limb of the jet. |
In the rigid rotation case. /r=25 im all directions within the jet. | In the rigid rotation case, $h \approx 25$ in all directions within the jet. |
The crossing time in a conical. unaccelerated jet. defined as the time it takes an azimuthal wave to orbit the central axis. is given by where ¢=27 for a full revolution. v4.=const is the azimuthal speed and vp=v,sinP is the expansion velocity. | The crossing time in a conical, unaccelerated jet, defined as the time it takes an azimuthal wave to orbit the central axis, is given by where $\iota=2\pi$ for a full revolution, $\vAphi=\const$ is the azimuthal speed and $v_R = v_r \sin \vartheta$ is the expansion velocity. |
In the simulations. vaxconst above the radius. | In the simulations, $\vAphi \approx \const$ above the radius. |
This is as expected theoretically from conservation of mass and magnetic flux in à conically expanding. steady axisymmetric Jet. | This is as expected theoretically from conservation of mass and magnetic flux in a conically expanding, steady axisymmetric jet. |
το Is finite and physically meaningful only if the condition | $\tauc$ is finite and physically meaningful only if the condition |
As we show in (his paper. the inclusion of magnetic fields leads to competing effects. some of which inhibit and some of which enhance gravitational instability aud planet formation. | As we show in this paper, the inclusion of magnetic fields leads to competing effects, some of which inhibit and some of which enhance gravitational instability and planet formation. |
Ilowever. as outlined above. magnetic fields will be present within cireiumstellar disks. | However, as outlined above, magnetic fields will be present within circumstellar disks. |
As a result. in order (o understand disk physics. one must include the effects of magnetic fields. and the goal of this paper is to provide an assessment of these effects. | As a result, in order to understand disk physics, one must include the effects of magnetic fields, and the goal of this paper is to provide an assessment of these effects. |
This paper is organized as follows. | This paper is organized as follows. |
We specilv the equations of motion for magnetized disks in Section 2. and find (heir linearized counterparts in Section 3.. | We specify the equations of motion for magnetized disks in Section \ref{sec:basic} and find their linearized counterparts in Section \ref{sec:linear}. |
This procedure leads to the dispersion relation lor spiral density waves and (he generalized stability. parameter eM Qa. | This procedure leads to the dispersion relation for spiral density waves and the generalized stability parameter $Q_M$ . |
In Section 4 we present numerical examples and apply the results to the observed protostellar source Ceph A IIW2. | In Section \ref{sec:numerical}
we present numerical examples and apply the results to the observed protostellar source Ceph A HW2. |
The condition Qu;>1 is necessary for stability and implies a corresponding maximum disk mass. as shown in Section 5.. | The condition $Q_M > 1$ is necessary for stability and implies a corresponding maximum disk mass, as shown in Section \ref{sec:maxmass}. |
The onset of instability ancl the derivation of Qa, can be determined by setting the resistivity + = 0: however. realistic disks have 7740 and Section 6 outlines the corresponding effects of magnetic diffusion. | The onset of instability and the derivation of $Q_M$ can be determined by setting the resistivity $\eta$ = 0; however, realistic disks have $\eta \ne 0$ and Section \ref{sec:diffusion} outlines the corresponding effects of magnetic diffusion. |
We then consider giant planet formation in Section 7.. | We then consider giant planet formation in Section \ref{sec:pformation}. |
In addition to deriving modified constraints on planet formation via gravitational instability due to magnetic effects. we find that magnetic disks require an additional constraint: The need to remove magnetic flux places a lower bound on the electrical resistivity η. | In addition to deriving modified constraints on planet formation via gravitational instability due to magnetic effects, we find that magnetic disks require an additional constraint: The need to remove magnetic flux places a lower bound on the electrical resistivity $\eta$. |
Finally. we conclude in Section 8. wilh a summary and discussion of our results. | Finally, we conclude in Section \ref{sec:conclude} with a summary and discussion of our results. |
This section specifies (he equations of motion lor this problem. | This section specifies the equations of motion for this problem. |
We include the elfects of a poloidal magnetic field dragged into the disk during (he gravitational collapse of the the natal cloud that produces a newly born star/disk svstem. | We include the effects of a poloidal magnetic field dragged into the disk during the gravitational collapse of the the natal cloud that produces a newly born star/disk system. |
This field threads vertically through the circumstellar disk ancl is pinched racially inward by. viscous disk accretion. | This field threads vertically through the circumstellar disk and is pinched radially inward by viscous disk accretion. |
The accretion in these disks is believed (o occur via (he magneto-rotational instability (MIRI: see. e.g. (he review of Balbus Lawley 1993). | The accretion in these disks is believed to occur via the magneto-rotational instability (MRI; see, e.g., the review of Balbus Hawley 1998). |
In [act. an empirical formulation of the MBI viscosity in thin disks has been obtained by S07 using mixing length arguments. | In fact, an empirical formulation of the MRI viscosity in thin disks has been obtained by S07 using mixing length arguments. |
Consider the evolution of gas and magnetic field in a thinaxisvmmetric. viscously accreting disk of hall-thickness 2). surrounding a voung star with mass A, at the origin ol a evlindrical coordinate svstem (zc.:). | Consider the evolution of gas and magnetic field in a thinaxisymmetric, viscously accreting disk of half-thickness $z_0$, surrounding a young star with mass $M_\star$ at the origin of a cylindrical coordinate system $(\varpi, z)$. |
We denote the surface densitv of the disk by X. the radial velocity of accretion in the plane by 4. the azimuthal velocity about the z axis bv e. the component of the magnetic field threading vertically through the disk by D.. and the radial component of the magnetic Ποια just above the disk that responds to (he racial accretion flow by D... | We denote the surface density of the disk by $\Sigma$, the radial velocity of accretion in the plane by $u$, the azimuthal velocity about the $z$ axis by $v$, the component of the magnetic field threading vertically through the disk by $B_z$ , and the radial component of the magnetic field just above the disk that responds to the radial accretion flow by $B_\varpi^+$ . |
The component of the Lorentz force perunit area inthe plane of the | The component of the Lorentz force perunit area inthe plane of the |
dividing the sample by luminosity still produces relatively modest numbers of galaxies per bin. which vary significantly in their properties: these variations result in the noise apparent in the greyscale image. | dividing the sample by luminosity still produces relatively modest numbers of galaxies per bin, which vary significantly in their properties; these variations result in the noise apparent in the greyscale image. |
However. when the luminosity bins are all combined. this residual sampling notse is dramatically reduced. producing the reliable smooth total stellar phase space density distributions shown in the left-hand panels. | However, when the luminosity bins are all combined, this residual sampling noise is dramatically reduced, producing the reliable smooth total stellar phase space density distributions shown in the left-hand panels. |
Figure 3. also compares these results to the mean trends established by ?.. | Figure \ref{fig:MGCphase} also compares these results to the mean trends established by \citet{MaoMo98}. |
For the spheroidal component. there is good agreement between the two analyses on the upper cut-off in phase densities. | For the spheroidal component, there is good agreement between the two analyses on the upper cut-off in phase densities. |
The effective phase density derived by ? appears somewhat higher than a measure that one would infer from the greyscale. but the logarithmic nature of the plot is somewhat misleading. and it is notable that the value of this effective phase density does lie very close to the mode in the projection of the full distribution. | The effective phase density derived by \citet{MaoMo98} appears somewhat higher than a measure that one would infer from the greyscale, but the logarithmic nature of the plot is somewhat misleading, and it is notable that the value of this effective phase density does lie very close to the mode in the projection of the full distribution. |
The disk component reveals a similar phenomenon. with the effective phase density again lying very close to the peak of the distribution. | The disk component reveals a similar phenomenon, with the effective phase density again lying very close to the peak of the distribution. |
The central phase density of the disk is less informative. since. as noted in Sect. 2.2.. | The central phase density of the disk is less informative, since, as noted in Sect. \ref{sec:diskmodel}, |
it does not represent à maximum value. but rather the minimum value in the plane of the disk. | it does not represent a maximum value, but rather the minimum value in the plane of the disk. |
Of course. lower values of phase density can. be found away from the plane of the disk. so this local minimum value has little physical significance in the context of the total distribution of phase densities. | Of course, lower values of phase density can be found away from the plane of the disk, so this local minimum value has little physical significance in the context of the total distribution of phase densities. |
The difference between the ? disk relation and the observed phase density distribution at bright magnitudes 15 more interesting. but also has a relatively simple explanation. | The difference between the \citet{MaoMo98} disk relation and the observed phase density distribution at bright magnitudes is more interesting, but also has a relatively simple explanation. |
In their analysis. ? selected disk-dominated systems to derive this relation. so the total absolute magnitude on the abseissa when plotting their data corresponds quite closely to the disk luminosity. | In their analysis, \citet{MaoMo98} selected disk-dominated systems to derive this relation, so the total absolute magnitude on the abscissa when plotting their data corresponds quite closely to the disk luminosity. |
However. in the current analysis a random sample of galaxies from the local Universe has been selected. and at such bright magnitudes these systems are frequently spheroid-dominated. with relatively faint but oftei quite extended disk components. | However, in the current analysis a random sample of galaxies from the local Universe has been selected, and at such bright magnitudes these systems are frequently spheroid-dominated, with relatively faint but often quite extended disk components. |
These lower-luminosity disks produce the lower phase density of stars that we see in the disk-component distribution. | These lower-luminosity disks produce the lower phase density of stars that we see in the disk-component distribution. |
The net result of combining these components produces a total stellar phase density distribution in the local Universe that is quite similar to that found in a typical spiral galaxy (see Fig. 1)). | The net result of combining these components produces a total stellar phase density distribution in the local Universe that is quite similar to that found in a typical spiral galaxy (see Fig. \ref{fig:mwphase}) ), |
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