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1996). | 1996). |
Upon investigation indeed halfofthe forciieutioned narrow enission Bue stars in Mazzali et al. | Upon investigation indeed half of the forementioned narrow emission line stars in Mazzali et al. |
lio within regious of pronounced. HIL. | lie within regions of pronounced HII. |
After correction for the effects of the snarounding ΠΤΙ cumission we claim that only 6 stars of their sample ave in fact Be stars. | After correction for the effects of the surrounding HII emission we claim that only 6 stars of their sample are in fact Be stars. |
Table 2. sunnunrises our current kuowledee of the euission status of bright MS members of NGC 330. | Table \ref{tbl-2}
summarises our current knowledge of the emission status of bright MS members of NGC 330. |
D29. identified bv Feast aid Black (1980) aud Carney et al. ( | B29, identified by Feast and Black (1980) and Carney et al. ( |
1985) as an A superejantzl without emission. shows siguificauto eissiou il our sπαν, | 1985) as an A supergiant without emission, shows significant emission in our study. |
I should be noted that the previous studies have focused on the blue portion of the spectrum where. as ποσα in figure L.. no eunission is evideut. | It should be noted that the previous studies have focused on the blue portion of the spectrum where, as seen in figure \ref{specsfig}, no emission is evident. |
The forementioned studies judee B29 as a field. A supereiaw on the basis of its radial veloc‘ity. | The forementioned studies judge B29 as a field A supergiant on the basis of its radial velocity. |
Let Us LOW discuss our results in he lieht of the assertio1i of Mazzal ct al. ( | Let us now discuss our results in the light of the assertion of Mazzali et al. ( |
1996). namely that we sec, in the case of NGC 330 a common aliguineu of Be star rotation axes. | 1996), namely that we see, in the case of NGC 330 a common alignment of Be star rotation axes. |
The argument of Mazzali ο al. | The argument of Mazzali et al. |
is laid out in detail. however it may be stummarised as ollows: (à) there are no rapidly rotating stars with weak οnuission. nor (bh) slow rotating stars with strongro ΠΕΓΗ in their sample. | is laid out in detail, however it may be summarised as follows: (a) there are no rapidly rotating stars with weak emission, nor (b) slow rotating stars with strong emission in their sample. |
They arene.Oo in the case of (a] hat the stars in their sample could be stars observed edge ou but this would eive double caked profiles which are not observed iu their saiple. | They argue, in the case of (a) that the stars in their sample could be stars observed edge on but this would give double peaked profiles which are not observed in their sample. |
Iu he case of (b) all slowly rotating stars are observed to ο weak enmütters aud this could 0 taken that we are observing stars with siia l«isks pole on. | In the case of (b) all slowly rotating stars are observed to be weak emitters and this could be taken that we are observing stars with small disks pole on. |
But since the xobabilitv of sectic all such stars pole ou is sinall. Mazzali eha | But since the probability of seeing all such stars pole on is small, Mazzali et al. ( |
dtA parieti seroaler ο wi Alae sale sni between the limits of (a) aud (0) (approx a+). | 1996) claim we must see all the stars at roughly the same $sin\:i$ between the limits of (a) and (b) (approx $\frac{\pi}{4}$ ). |
It ollows from this that there must be a correlation between 0 28d Wha) (the latter being| essentially| a incazure of| the disks size) The perceived. correlation appears fo arise from 201. nufortuitous selection of. sample stars. | It follows from this that there must be a correlation between $v$ and $\alpha$ ) (the latter being essentially a measure of the disk size) The perceived correlation appears to arise from an unfortuitous selection of sample stars. |
Our Observations show that double peak profiles 4ο Όσσα i NGC 330. for example. that of D31 shown 12. figmre L.. | Our observations show that double peak profiles do occur in NGC 330, for example, that of B31 shown in figure \ref{figure3}. |
Typical red to violet peak separations for double peaked profiles in the present. suuple are ~ orless | Typical red to violet peak separations for double peaked profiles in the present sample are $\sim$ $\:$ or less. |
Thema jorityof Matzalictal4!9 | The majority of Mazzali et al. ( |
096) sobservcat | 1996)'s observations were made with a resolution of $\:$ and so such double peaked profiles would have been undetectable. |
i | Mazzali et al. |
onswere | made additional higher resolution ) observations of 2 strong Be stars and no double peaks were found. |
in | It turns out that the choice of two strong emitters for closer examination was unfortuitous. |
null | As Dachs et al. \cite{dachs}) ) ( |
null | their figure 7) have shown, such emitters are unlikely to show double peak profiles. |
Our results (solid points ou figure 3)) span a large range of Wa) and esi» aud iu coutrast ο Mazzali et al. ( | Our results (solid points on figure \ref{figure1}) ) span a large range of $\alpha$ ) and $v\,sin\:i$ and in contrast to Mazzali et al. ( |
1996) (their feure 7) show uo correlatio1i between e;síni and equivalent width is present. | 1996) (their figure 7) show no correlation between $v, sin\:i$ and equivalent width is present. |
This iidicates that we are observing a sample of stars with c.so/ aud dise size as randomly distributed properties. | This indicates that we are observing a sample of stars with $v, sin\:i$ and disc size as randomly distributed properties. |
There is uo sign of a prefereutial alguinent of rotational axes ror a depeudence of disk size on ce. | There is no sign of a preferential alignment of rotational axes nor a dependence of disk size on $v$. |
We have presented the results of our spectroscopic observations of a sample of bright cluster 1ieiibers aud iu particular those of à ummber of bright Be stars. | We have presented the results of our spectroscopic observations of a sample of bright cluster members and in particular those of a number of bright Be stars. |
We find | We find |
During the gravitational collapse (hat forms star/disk systems. magnetic fields are dragged in from the interstellar medium (e.g.. Galli et al. | During the gravitational collapse that forms star/disk systems, magnetic fields are dragged in from the interstellar medium (e.g., Galli et al. |
2006: Shu et al. | 2006; Shu et al. |
2006). | 2006). |
Additional fields can be generated by the central star. | Additional fields can be generated by the central star. |
Consideration of mean field magnetolvdrocdyvnamics (MIID) in these disks shows that magnetic effects. produce substantial departures. [rom keplerian rotation curves through both magnetic pressure and magnetic tension (Shiu οἱ al. | Consideration of mean field magnetohydrodynamics (MHD) in these disks shows that magnetic effects produce substantial departures from keplerian rotation curves through both magnetic pressure and magnetic tension (Shu et al. |
2007. herealter 507). | 2007, hereafter S07). |
On the other hand. conservation of angular momentum implies (hat most of the material that eventually accretes onto the forming star initially lands on the disk (Cassen Aloosman 1981). | On the other hand, conservation of angular momentum implies that most of the material that eventually accretes onto the forming star initially lands on the disk (Cassen Moosman 1981). |
As a result. disk surface densities can be high enough to support gravitational instability. | As a result, disk surface densities can be high enough to support gravitational instability. |
In (he limit of axisvnunetric perturbations. the criterion for exavitational instability is determined by the value of the parameter Q. QjC where &=zcου is the epievclie frequency. Q is the angular rotation rale. « is (he sound speed. and X is the surface density (Ioomre 1964). | In the limit of axisymmetric perturbations, the criterion for gravitational instability is determined by the value of the parameter $Q_T$, Q_T, where $\kappa=\varpi^{-1} [\partial(\varpi^2\Omega)^2/\partial\varpi]^{1/2}$ is the epicyclic frequency, $\Omega$ is the angular rotation rate, $a$ is the sound speed, and $\Sigma$ is the surface density (Toomre 1964). |
In (he presence of maenetic fields. however. (he conditions required [or eravitational instability are modified. | In the presence of magnetic fields, however, the conditions required for gravitational instability are modified. |
The principal goal of (his paper is togeneralize the criterion of equation (1-1)) to include the effects of magnetic fields. | The principal goal of this paper is togeneralize the criterion of equation \ref{qtoomre}) ) to include the effects of magnetic fields. |
More specifically. we derive a generalized stability parameter Qu; Uhat characterizes magnetized disks. | More specifically, we derive a generalized stability parameter $Q_M$ that characterizes magnetized disks. |
We note that gravitational instability can play (wo important roles in circumstellar disks during the star formation process. | We note that gravitational instability can play two important roles in circumstellar disks during the star formation process. |
If the instabilities grow into the nonlinear regime. they can produce secondary bodies within the disk. such as brown clwarls aud giant planets. | If the instabilities grow into the nonlinear regime, they can produce secondary bodies within the disk, such as brown dwarfs and giant planets. |
If the growing perturbations saturate. (he gravitational torques can lead to redistribution οἱ angular momentum and disk accretion. | If the growing perturbations saturate, the gravitational torques can lead to redistribution of angular momentum and disk accretion. |
Both processes require the onset of gravitational instability. which is determined by (he parameter Q4, derived in this paper. | Both processes require the onset of gravitational instability, which is determined by the parameter $Q_M$ derived in this paper. |
The properties and evolution of magnetized disks also depend on (he dimensionless mass-to-fhix ratio A. defined by | The properties and evolution of magnetized disks also depend on the dimensionless mass-to-flux ratio $\lambda$ , defined by. |
For example. gravitational collapse requires A>1. | For example, gravitational collapse requires $\lambda > 1$. |
As found by S07 and discussed herein. for realistic magnetic field strengths. (his constraint inhibits the Formation of eiant planets by eravitational instability in circumnstellar disks. | As found by S07 and discussed herein, for realistic magnetic field strengths, this constraint inhibits the formation of giant planets by gravitational instability in circumstellar disks. |
In addition. (he generalized stability parameter Qa, derived in (his paper must be a functionof A. | In addition, the generalized stability parameter $Q_M$ derived in this paper must be a functionof $\lambda$ . |
which have the best S/N ratio. aud using the formalism by Bowellοἱal.(1989). with a slope parameter of G—0.15. we obtained a nucleus absolute magnitude of //221.340.3. | which have the best S/N ratio, and using the formalism by \cite{Bowell89} with a slope parameter of $G$ =0.15, we obtained a nucleus absolute magnitude of $H$ $\pm$ 0.3. |
Hence. a nucleus diameter of D=220+40 m can be determined. assuming a bulk albedo of p=0.11. tvpical of à S-type asteroid. | Hence, a nucleus diameter of $D$ $\pm$ 40 m can be determined, assuming a bulk albedo of $p$ =0.11, typical of a S-type asteroid. |
This assumption is based on (he [act that the S-tvpe asteroids are (he most common objects in the inner Main. Asteroid Delt (e.g.Dus&Dinzel2002). | This assumption is based on the fact that the S-type asteroids are the most common objects in the inner Main Asteroid Belt \citep[e.g.][]{Bus02}. |
. The combined images from GTC and WIT obtained on the 17th and 21st January show the best S/N ratio (see Fig. | The combined images from GTC and WHT obtained on the 17th and 21st January show the best S/N ratio (see Fig. |
1). ancl were selected for a more detailed analysis. | 1), and were selected for a more detailed analysis. |
To carry out the analvsis in terms of dust (ail models an additional rebinning was made of the images. | To carry out the analysis in terms of dust tail models an additional rebinning was made of the images. |
The WHT image was rebinned to 4 pixels. giving a spatial resolution of 772.4 km pixel|. while the GTC image was rebinned to 3 pixels to give a resolution of 576.3 km pixel!. | The WHT image was rebinned to 4 pixels, giving a spatial resolution of 772.4 km $^{-1}$, while the GTC image was rebinned to 3 pixels to give a resolution of 576.3 km $^{-1}$. |
Finally. the rebinned images were rotated to the (CN.M) coordinate svstem. where M is the extended radius vector from the Sun. aud is perpendicular to M. aud directed opposite to the objeet's motion along its orbit (Finson&Probstein1963). | Finally, the rebinned images were rotated to the $(N,M)$ coordinate system, where $M$ is the extended radius vector from the Sun, and $N$ is perpendicular to $M$ and directed opposite to the object's motion along its orbit \citep{Fin68}. |
. We have performed an analvsis of both the WIT and GTC images by the inverse Monte Carlo dust tail fitting code (e.g.Morenoetal.2004:2009).. which is based on the sanie procedures as that developed by Fulle (e.g.Fulle1989.2004). | We have performed an analysis of both the WHT and GTC images by the inverse Monte Carlo dust tail fitting code \citep[e.g.][]{Moreno04,
Moreno09}, which is based on the same procedures as that developed by Fulle \citep[e.g.][]{Fulle89, Fulle04}. |
. Brielly. a large amount of particles (typically 10*) of a selected size range are released from the surface of the object in a given time interval. with an assumed velocity law. which may be a function of time and particle size. | Briefly, a large amount of particles (typically $^7$ ) of a selected size range are released from the surface of the object in a given time interval, with an assumed velocity law, which may be a function of time and particle size. |
The particles are (hen submitted to (the radiation pressure and gravity field of the Sun. and their Keplerian orbits are computed. | The particles are then submitted to the radiation pressure and gravity field of the Sun, and their Keplerian orbits are computed. |
The ratio of the lorce exerted by (he solar radiation pressure and the solar gravity is given by 2. which can be expressed as j— CoQyQOpr). where C,,—1.19x * kg 7. and pis the particle density. | The ratio of the force exerted by the solar radiation pressure and the solar gravity is given by $\beta$ , which can be expressed as $\beta =
C_{pr}Q_{pr}/(2\rho r)$ , where $C_{pr}$ $\times$ $^{-3}$ kg $^{-2}$, and $\rho$ is the particle density. |
For particle radii r> 0.25 jun. the radiation pressure coefficient is (Q,,~ 1 (Burnsetal.1979). | For particle radii $r >$ 0.25 $\mu$ m, the radiation pressure coefficient is $Q_{pr}
\sim$ 1 \citep{Burns79}. |
. The inverse method involves the inversion of the overdetermined svstem of equations AF=I. where ο is the kernel matrix containing the dust tail model. ie.. the surface densitv of the sample of particles integrated over time and 3. F is the output. vector which contains the time-dependent distribution of 2. and J is the brightness of the input image in the selected region of the photographic (CV.M )-plane. | The inverse method involves the inversion of the overdetermined system of equations $AF=I$, where $A$ is the kernel matrix containing the dust tail model, i.e., the surface density of the sample of particles integrated over time and $\beta$, $F$ is the output vector which contains the time-dependent distribution of $\beta$, and $I$ is the brightness of the input image in the selected region of the photographic $(N,M)$ -plane. |
The physical appearance of the tail. detached [rom the nucleus ancl sun-ward oriented (see Figures 1 and 2). suggests that most of the dust was already ejected sometime well before the date of the observation. ancl should be composed of relatively large particles. otherwise they would have been blown away bv radiation pressure. | The physical appearance of the tail, detached from the nucleus and sun-ward oriented (see Figures 1 and 2), suggests that most of the dust was already ejected sometime well before the date of the observation, and should be composed of relatively large particles, otherwise they would have been blown away by radiation pressure. |
This is clearly demonstratedin Figure 2. where the combined WIIT image is shown along with the svnehrones | This is clearly demonstratedin Figure 2, where the combined WHT image is shown along with the synchrones |
metallicity disc or a disc with grain sizes ranging between millimetre and centimetre sizes which is realistic given | metallicity disc or a disc with grain sizes ranging between millimetre and centimetre sizes which is realistic given current observations \citep{Calvet_etal_cm_grains,Testi_etal_cm_grains,Rodman_etal_mm_grains,Lommen_etal_mm_grains}. |
We can see from Figure 8 that the disc with 0.1x interstellar opacity values is slightly cooler than the case with interstellar opacities, but is still unable to cool rapidly enough to maintain a state of thermal equilibrium with its boundary. | We can see from Figure \ref{fig:Q_Qmin0.75_0.01IS} that the disc with $0.1 \times$ interstellar opacity values is slightly cooler than the case with interstellar opacities, but is still unable to cool rapidly enough to maintain a state of thermal equilibrium with its boundary. |
However, the disc with 0.01x interstellar opacity | However, the disc with $0.01 \times$ interstellar opacity |
secure Data from RC3 (deVaucouleursal.1991) were then obtained for each of these galaxies, in order to isolate galaxies which were SO had axis ratios €2.0. ( | secure Data from RC3 \citep{rc3} were then obtained for each of these galaxies, in order to isolate galaxies which were S0 had axis ratios $\leq 2.0$. ( |
NGC 4733 is classified as “E+” in RC3 but has an SBO classification in NED and clearly hosts a strong bar, so we included it in the sample.) | NGC 4733 is classified as “E+” in RC3 but has an SB0 classification in NED and clearly hosts a strong bar, so we included it in the sample.) |
We then checked each galaxy for distance measurements. | We then checked each galaxy for distance measurements. |
This showed that NGC 4600 had a surface-brightness fluctuation distance of ~7 Mpc (Tonryetal.2001),, indicating that is a foreground object; we transferred it to the field sample. | This showed that NGC 4600 had a surface-brightness fluctuation distance of $\sim 7$ Mpc \citep{tonry01}, indicating that is a foreground object; we transferred it to the field sample. |
Several other galaxies were rejected because they overlapped with bright neighbors or very bright stars, had significantly distorted outer isophotes, were clearly edge-on, or were not actual SO galaxies. | Several other galaxies were rejected because they overlapped with bright neighbors or very bright stars, had significantly distorted outer isophotes, were clearly edge-on, or were not actual S0 galaxies. |
Finally, we restricted ourselves to galaxies with Mp< —17; this limit approximates the traditional boundaries between dwarf and giant galaxies, and corresponds to stellar masses >10??M. (assuming a typical SO B—V of ~0.8 and the color-based mass-to-light ratios of ZZibetti et 22009). | Finally, we restricted ourselves to galaxies with $M_B < -17$ ; this limit approximates the traditional boundaries between dwarf and giant galaxies, and corresponds to stellar masses $\gtrsim 10^{9.5} \Msun$ (assuming a typical S0 $B
- V$ of $\sim 0.8$ and the color-based mass-to-light ratios of \nocite{zibetti09}Z Zibetti et 2009). |
The result was a set of 24 Virgo Cluster S0 galaxies. | The result was a set of 24 Virgo Cluster S0 galaxies. |
The field sample was designed to have the same absolute magnitude limit and a distance limit of ~30 Mpc. | The field sample was designed to have the same absolute magnitude limit and a distance limit of $\sim 30$ Mpc. |
The starting point was a combined set of barred and unbarred galaxies, whose surface-brightness profiles were presented in Erwinetal.(2008) and Gutiérrezetal.(2011),, respectively (many of the Virgo S0 galaxies were also included in those studies). | The starting point was a combined set of barred and unbarred galaxies, whose surface-brightness profiles were presented in \citet{erwin08} and \citet{gutierrez11}, respectively (many of the Virgo S0 galaxies were also included in those studies). |
However, those samples were diameter-limited (Dos> 2.0’) and therefore tended to exclude more compact galaxies and galaxies at larger distances. | However, those samples were diameter-limited $D_{25} \geq 2.0\arcmin$ ) and therefore tended to exclude more compact galaxies and galaxies at larger distances. |
To better match the Virgo sample, we defined the field sample as follows: all galaxies from HyperLeda with Hubble types —4€T<0, Mp« —17, declination 6>—10°, and redshifts (corrected for Virgocentric <2000s~'. | To better match the Virgo sample, we defined the field sample as follows: all galaxies from HyperLeda with Hubble types $-4 \leq T \leq 0$, $M_{B} < -17$ , declination $\delta >
-10\arcdeg$, and redshifts (corrected for Virgocentric infall) $< 2000$. |
. Galaxies which were VCC members infall)were excluded only exception being NGC 4600; see above). | Galaxies which were VCC members were excluded (the only exception being NGC 4600; see above). |
As in the (theVirgo Cluster sample, RC3 measurements were then used to identify SO galaxies with axis ratios <2.0. | As in the Virgo Cluster sample, RC3 measurements were then used to identify S0 galaxies with axis ratios $\leq 2.0$. |
After closer inspection, nine galaxies were rejected for having been misclassified (e.g., NGC 2853 is classified as SBO°, but is clearly an spiral), interacting or overlapping with neighboring galaxies or bright stars, or being too highly inclined despite the published axis ratio. | After closer inspection, nine galaxies were rejected for having been misclassified (e.g., NGC 2853 is classified as $0^{0}$, but is clearly an spiral), interacting or overlapping with neighboring galaxies or bright stars, or being too highly inclined despite the published axis ratio. |
The resulting (nominal) field sample has a total of 55 SO galaxies; however, suitable images are not available for all. | The resulting (nominal) field sample has a total of 55 S0 galaxies; however, suitable images are not available for all. |
Since images from the Sloan Digital Sky Survey Yorketal. have proven more than adequate(SDSS; for outer-disk2000) profile work (seePohlen&Tru-jillo2006;Erwinetal. 2008),, we decided to use Data Release 7 Abazajianetal. as our primary image source. | Since images from the Sloan Digital Sky Survey \citep[SDSS;][]{york00} have proven more than adequate for outer-disk profile work \citep[see][]{pt06,erwin08}, we decided to use Data Release 7 \citep[DR7][]{abazajian09} as our primary image source. |
(DR7This encompasses the2009) entire Virgo Cluster and much of the nearby northern field; 43 of the field SO galaxies have DR7 images. | This encompasses the entire Virgo Cluster and much of the nearby northern field; 43 of the field S0 galaxies have DR7 images. |
An additional seven SO galaxies outside DR7 have already been analyzed using other image sources by Erwinetal.(2008) and Gutiérrezetal.(2011). | An additional seven S0 galaxies outside DR7 have already been analyzed using other image sources by \citet{erwin08} and \citet{gutierrez11}. |
. We include these in our final sample in order to increase the field-galaxy numbers. | We include these in our final sample in order to increase the field-galaxy numbers. |
Doing so does, however, introduce a slight bias in favor of brighter galaxies in the field sample, since the galaxies in the Erwin et al./Gutierrez et al. | Doing so does, however, introduce a slight bias in favor of brighter galaxies in the field sample, since the galaxies in the Erwin et al./Gutierrez et al. |
samples were selected to have Dg;>2.0’. | samples were selected to have $D_{25} \geq 2.0\arcmin$. |
Therefore, we check all our results by using both the full field sample (50 SO galaxies) and a “DR7-only” subsample, restricted to the 43 field SO galaxies covered by DR7. | Therefore, we check all our results by using both the full field sample (50 S0 galaxies) and a “DR7-only” subsample, restricted to the 43 field S0 galaxies covered by DR7. |
We use the term “field” somewhat loosely, since we did not attempt to distinguish between groups and genuinely isolated galaxies. | We use the term “field” somewhat loosely, since we did not attempt to distinguish between groups and genuinely isolated galaxies. |
However, we believe that there is à clear difference between the Virgo Cluster and field samples: the latter does not include any truly high-mass groups comparable to Virgo. | However, we believe that there is a clear difference between the Virgo Cluster and field samples: the latter does not include any truly high-mass groups comparable to Virgo. |
In the Nearby Optical Galaxy Groups (NOGG) catalogs (Giuricinetal. 2000), the largest group within 2500 in redshift and with 6>-—10? than the Virgo Cluster is the Ursa Major “Cluster” (Tullyetal.1996),, which has three of our field SOs. | In the Nearby Optical Galaxy Groups (NOGG) catalogs \citep{giurucin00}, the largest group within 2500 in redshift and with $\delta > -10\arcdeg$ than the Virgo Cluster is the Ursa Major “Cluster” \citep{tully96}, which has three of our field S0s. |
This spiral-dominated group has a velocity dispersion of only 148!, compared with 715 for the Virgo Cluster (Tully 1987). | This spiral-dominated group has a velocity dispersion of only 148, compared with 715 for the Virgo Cluster \citep{tully87}. |
. Twelve field S0s have no group assignment in the NOGG catalogs at all and are therefore plausible isolated galaxies. | Twelve field S0s have no group assignment in the NOGG catalogs at all and are therefore plausible isolated galaxies. |
The field sample is thus a mixture of low-mass groups and isolated galaxies, providing a strong contrast with the Virgo Cluster sample. | The field sample is thus a mixture of low-mass groups and isolated galaxies, providing a strong contrast with the Virgo Cluster sample. |
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