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This field could be part of the confusion-Iimited survey. which will be certainly split in several smaller area surveys. | This field could be part of the confusion-limited survey which will be certainly split in several smaller area surveys. |
For the whole field of view of —1.75* 3.5. the current estimates of time needed to reach 50;,,,23 mdv is 1 hour (Albrecht Poglitsch. private communication). | For the whole field of view of $\sim$ 1.75' $\times$ 3.5', the current estimates of time needed to reach $\sigma_{inst}$ =3 mJy is 1 hour (Albrecht Poglitsch, private communication). |
At 75. 110 and 170 jun. the confusion limits are about 0.13. 0.89. and. 7.08 niJy. with quencing OF 8.9. S5 and 7.1 respectively. | At 75, 110 and 170 $\mu$ m, the confusion limits are about 0.13, 0.89, and 7.08 mJy, with $_{density}$ of 8.9, 8.7 and 7.1 respectively. |
To reach he confusion limit for one field of view. Le 50;,,,20.1. 0.9 and 7.1. we need 567. 11 and 0.18 hours at 75. 110 and 170 [im respectively. | To reach the confusion limit for one field of view, i.e $\sigma_{inst}$ =0.1, 0.9 and 7.1, we need 567, 11 and 0.18 hours at 75, 110 and 170 $\mu$ m respectively. |
Since forPACS the confusion limits and he time to reach those sensitivities are very cilferent at the hree wavelengths. three kinds of survevs could be done that. schematically. will probe the CLB in the three bands: These three surveys correspond. to about the same amount of time as theSPARE surveys. | Since for the confusion limits and the time to reach those sensitivities are very different at the three wavelengths, three kinds of surveys could be done that, schematically, will probe the CIB in the three bands: These three surveys correspond to about the same amount of time as the surveys. |
Obviously. thePACS surveys have to be done within the same areas as the SPIRE is observing simulaneously the 170 ancl 110. sam channels or the 170 and 75 yam channels. | Obviously, the surveys have to be done within the same areas as the is observing simulaneously the 170 and 110 $\mu$ m channels or the 170 and 75 $\mu$ m channels. |
Leeally a combination 75/110 yam and 75/170 pmi would have been preferable since the 170. ji observation in the deep and ultra-ceep surveys will not. bring new science compared to the [arge area survey. | Ideally a combination 75/110 $\mu$ m and 75/170 $\mu$ m would have been preferable since the 170 $\mu$ m observation in the deep and ultra-deep surveys will not bring new science compared to the large area survey. |
On the contrary. observing the shortest wavelengths in the shallow survey will detect the very luminous. hot and rare galaxies that may be missed in 10 deep ancl ultra-deep surveys. | On the contrary, observing the shortest wavelengths in the shallow survey will detect the very luminous, hot and rare galaxies that may be missed in the deep and ultra-deep surveys. |
The three surveys will detect thousane of sources ab zl (Fig. 20)) | The three surveys will detect thousand of sources at $\sim$ 1 (Fig. \ref{z-PACS}) ) |
and will probe most of the CID source population (they will resolve about 49. 77 and ὃν of the CIB at 75. 110 and 170 p/m respectively. see Table 6)). | and will probe most of the CIB source population (they will resolve about 49, 77 and $\%$ of the CIB at 75, 110 and 170 $\mu$ m respectively, see Table \ref{Sens_PACS}) ). |
At 170 jn. the shallow survey will give an unprecedent measurement of the evolution of the 10-1077 L. galaxies [rom z 0.25 to 1 and the evolution of the 1017-107? L. galaxies from z~ 0.5 to 3 (with enough objects to ensure «104 Poisson noise). | At 170 $\mu$ m, the shallow survey will give an unprecedent measurement of the evolution of the $^{11}$ $^{12}$ $_{\odot}$ galaxies from $\sim$ 0.25 to 1 and the evolution of the $^{12}$ $^{13}$ $_{\odot}$ galaxies from $\sim$ 0.5 to 3 (with enough objects to ensure $<$ $\%$ Poisson noise). |
Since half of the background is resolved into discrete sources at 170 jn. one complementary approach is to reduce the surface. of the shallow survey to have a better signal-to-noise ratio and thus study the uncerlving population. | Since half of the background is resolved into discrete sources at 170 $\mu$ m, one complementary approach is to reduce the surface of the shallow survey to have a better signal-to-noise ratio and thus study the underlying population. |
However. to study the correlation in the IR background. a minimum of 8S Sq. | However, to study the correlation in the IR background, a minimum of 8 Sq. |
Deg. | Deg. |
is required. | is required. |
A survey ab S,,5, = S mv. corresponding to 50;,,23.7 mJv. would take around. 128 days for S Sq. | A survey at $_{min}$ = 8 mJy, corresponding to $\sigma_{inst}$ =3.7 mJy, would take around 128 days for 8 Sq. |
Deg. | Deg. |
Such a survey would eive less statistics for the resolved sources but. would help in understanding the whole CLB population. | Such a survey would give less statistics for the resolved sources but would help in understanding the whole CIB population. |
With a SN Square Deg. | With a 8 Square Deg. |
field. the measure of the high luminosity source evolution would still be possible with a high degree of lo contusion.PACS will resolve about SOM of the CID around 100. yanCSZRUEF will resolve at most around 55% of the CIB at 70. fam and. 20% at 160. yam. Dole et al. | field, the measure of the high luminosity source evolution would still be possible with a high degree of In conlusion, will resolve about $\%$ of the CIB around 100 $\mu$ m will resolve at most around $\%$ of the CIB at 70 $\mu$ m and $\%$ at 160 $\mu$ m, Dole et al. |
2002). | 2002). |
Le will definitely resolve the question of the population =-xkine the CIB near its enission’s peak. | It will definitely resolve the question of the population making the CIB near its emission's peak. |
Lt will measure with unprecedented accuracy the history of the LR-tracec star formation up to ze1.5. | It will measure with unprecedented accuracy the history of the IR-traced star formation up to $\sim$ 1.5. |
For the higher redshifts. the informations will come mainly from theSPIRE surveys. | For the higher redshifts, the informations will come mainly from the surveys. |
AlthoughSPLRL will resolve less than 1054 of the CLB in the submum. it will bring an unprecedented. information on the evolution of galaxiesup to z~3 and also on the underlving population that will be very hard to detect from the ground due to the small area of the present surveys. | Although will resolve less than $\%$ of the CIB in the submm, it will bring an unprecedented information on the evolution of galaxiesup to $\sim$ 3 and also on the underlying population that will be very hard to detect from the ground due to the small area of the present surveys. |
The red giant branch bump (RGDD) and the red champ (RC) ave two observables of (he color-magnitude diagrams (CMBDs) of low and intermediate mass metal-rich populations which correspond (to specific post main-sequence phases of stellar evolution. | The red giant branch bump (RGBB) and the red clump (RC) are two observables of the color-magnitude diagrams (CMDs) of low and intermediate mass metal-rich populations which correspond to specific post main-sequence phases of stellar evolution. |
The RGDD occurs. first. curing ascent of the red. giant (RG) branch. | The RGBB occurs first, during ascent of the red giant (RG) branch. |
As the hydrogen burning shell expands. il eventually comes into contact with the convective envelope. which provides additional fuel. | As the hydrogen burning shell expands, it eventually comes into contact with the convective envelope, which provides additional fuel. |
The star then gets fainter until the extra [uel is consumed whence it begins brightening again. | The star then gets fainter until the extra fuel is consumed whence it begins brightening again. |
As the star crosses (he same Iuminositv region three times. there is an increase in (he number density of stars at that luminosity (Cassisi&Salaris1997). | As the star crosses the same luminosity region three times, there is an increase in the number density of stars at that luminosity \citep{1997MNRAS.285..593C}. |
. The RC occurs alter the degenerate helium core has accretecl enough mass for core helium burning induced by the helium flash. it is the horizontal branch of an old. metal-rich population (Girardi&Salaris2001).. | The RC occurs after the degenerate helium core has accreted enough mass for core helium burning induced by the helium flash, it is the horizontal branch of an old, metal-rich population \citep{2001MNRAS.323..109G}. |
The relative number counts anc brightness for these two populations are a function of their composition. | The relative number counts and brightness for these two populations are a function of their composition. |
In particular. the RGDD gets fainter relative to the RC as metallicity increases (Cassisi&Salaris1997;Zoccaliοἱal.1999:Rielloetal.2003:DiCeeceoοἱ 2010).. and the liletime of the RGDD decreases with increasing helium abundance (Bonoetal.2001:DiCeceo2010).. while that of the RC increases (Renzini1994).. | In particular, the RGBB gets fainter relative to the RC as metallicity increases \citep{1997MNRAS.285..593C,1999ApJ...518L..49Z,2003A&A...410..553R,2010ApJ...712..527D}, and the lifetime of the RGBB decreases with increasing helium abundance \citep{2001ApJ...546L.109B,2010ApJ...712..527D}, while that of the RC increases \citep{1994A&A...285L...5R}. |
Whereas the RC has had a vibrant historv. as a tracer of Galactic bulge redcdening (Stanek1996:Udalski2003:Stuni2004:Nishivamaetal.2009).. structure etal.2010:AleWilliam&Zoceali2010) ancl dynamics (Rattenburyetal. 2010).. there has been little study of the Galactic bulge RGBB. | Whereas the RC has had a vibrant history as a tracer of Galactic bulge reddening \citep{1996ApJ...460L..37S,2003ApJ...590..284U,2004MNRAS.349..193S,2009ApJ...696.1407N}, structure \citep{1997ApJ...477..163S,2005MNRAS.358.1309B,2007MNRAS.378.1064R,2008A&A...491..781C,2010ApJ...721L..28N,2010ApJ...724.1491M} and dynamics \citep{2007MNRAS.378.1165R,2010A&A...519A..77B}, there has been little study of the Galactic bulge RGBB. |
Indeed. we find only | Indeed, we find only |
host halo mass. and in 3.2 we investigate trends with halo environment. | host halo mass, and in \ref{sec:env} we investigate trends with halo environment. |
We then consider the distribution of the satellite number (83.3). | We then consider the distribution of the satellite number \ref{sec:pois}) ). |
Finally. we extend this analysis to include a more observationally relevant selection based on galaxy luminosities in 4. | Finally, we extend this analysis to include a more observationally relevant selection based on galaxy luminosities in \ref{sec:luminosities}. |
Because the mass resolution of the Bolshot simulation creates a halo catalog complete down to 50s7!.. roughly equivalent to the lower bound of the mass of the MCs (vander 2006).. we begin by measuring the probability distribution for halos hosting ssubhalos with Ving larger. than a given. value. | Because the mass resolution of the Bolshoi simulation creates a halo catalog complete down to 50, roughly equivalent to the lower bound of the mass of the MCs \citep{VanDerMarel02, Stanimirovic04,
Harris06}, we begin by measuring the probability distribution for halos hosting subhalos with $\vmax$ larger than a given value. |
This measurement is made by identifying the virial radius of all distinet (non-subhalo) MW mass halos and counting the number of objects internal to their virial radii. | This measurement is made by identifying the virial radius of all distinct (non-subhalo) MW mass halos and counting the number of objects internal to their virial radii. |
We take the virial mass of the Milky Way to be οσμήΜ.}Ξ0.12 (M4=1.2«107M ..). the mass measured in Bushaetal. (2010).. which i5 consistent with most results in the literature (Battagliaetal.2005:Dehnen2006:Smith2007;al. 2008). | We take the virial mass of the Milky Way to be $\log(\mvir/\msol) = 12.08 \pm 0.12$ $\mvir = 1.2
\times 10^{12} \msol$ ), the mass measured in \cite{Busha10c}, which is consistent with most results in the literature \citep{Battaglia05,
Dehnen06, Smith07, Xue08}. |
. This results in 36.000 MW analogs found in the Bolshoi volume. | This results in 36,000 MW analogs found in the Bolshoi volume. |
We present the resulting probability distribution of satellite counts as the colored points in the left panel of Figure |.. | We present the resulting probability distribution of satellite counts as the colored points in the left panel of Figure \ref{fig:vmax_comp}. |
Here. the different colors represent different thresholds for satellite vay: red. green. and blue represent all satellites with v4,> 50. 60. and 70κ. | Here, the different colors represent different thresholds for satellite $\vmax$: red, green, and blue represent all satellites with $\vmax > $ 50, 60, and 70. |
Error bars were calculated using the bootstrap method and represent confidence intervals. | Error bars were calculated using the bootstrap method and represent confidence intervals. |
From Figure l.. we can immediately see that the likelihood of hosting multiple satellites is somewhat low. | From Figure \ref{fig:vmax_comp}, we can immediately see that the likelihood of hosting multiple satellites is somewhat low. |
For satellites with Vinay greater than 50sh, roughly of simulated hosts contain one or more subhalos and just have two or more. | For satellites with $\vmax$ greater than 50, roughly of simulated hosts contain one or more subhalos and just have two or more. |
These numbers are in excellent agreement with the work of BKIO. who performed a similar analysis on the Aillennium IHE simulation. which was run using a different N-body code in à WMAPI cosmology and with a very different subhalo identification algorithm. | These numbers are in excellent agreement with the work of BK10, who performed a similar analysis on the Millennium II simulation, which was run using a different N-body code in a WMAP1 cosmology and with a very different subhalo identification algorithm. |
The probability of hosting nultiple satellites drops precipitously with increasing satellite nass: e.g.. the probability of a halo hosting two subhalos larger than vy,=70km is just1%. | The probability of hosting multiple satellites drops precipitously with increasing satellite mass; e.g., the probability of a halo hosting two subhalos larger than $\vmax =
70$ is just. |
.. For comparison. the black points in Figure | represent neasurements from Liuetal.(2010)... who measured the probability distribution for finding MC-luminosity satellites within 250 kpe around tsolated MW-luminosity galaxies (the mean virial radius of our sample). | For comparison, the black points in Figure \ref{fig:vmax_comp}
represent measurements from \cite{Liu10}, who measured the probability distribution for finding MC-luminosity satellites within 250 kpc around isolated MW-luminosity galaxies (the mean virial radius of our sample). |
We only plot these measurements out to == 3 because. for a 250 kpe aperture. uncertainties from their background subtraction become extremely large for higher (lower probability) values ofΛ | We only plot these measurements out to = 3 because, for a 250 kpc aperture, uncertainties from their background subtraction become extremely large for higher (lower probability) values of. |
ίμα Here. the agreement for satellites larger than 50 is striking. indicating that CDM can reproduce the statistics of MCs. | Here, the agreement for satellites larger than 50 is striking, indicating that CDM can reproduce the statistics of MCs. |
We must. however. be careful about over-interpreting this result. | We must, however, be careful about over-interpreting this result. |
In particular. their selection criteria are very different from our mass selection. | In particular, their selection criteria are very different from our mass selection. |
We will return to this in $4.4 where we make a comparison directly to similarly selected samples. | We will return to this in 4.4 where we make a comparison directly to similarly selected samples. |
By comparison with the Bolshoi simulation. the existence of two satellites with vyyay larger than mmakes the MW almost a 2c outher. | By comparison with the Bolshoi simulation, the existence of two satellites with $\vmax$ larger than makes the MW almost a $\sigma$ outlier. |
Understanding whether anything other than random chance is responsible for putting the MW in this slightly rare regime motivates further investigation into which other properties may correlate with satellite abundance. | Understanding whether anything other than random chance is responsible for putting the MW in this slightly rare regime motivates further investigation into which other properties may correlate with satellite abundance. |
In particular. we investigate the correlation of the number of subhalos with host mass and environment. | In particular, we investigate the correlation of the number of subhalos with host mass and environment. |
The correlation between subhalo abundance and host mass has been well studied (Zentner&Bullock2003:Diemand2010). | The correlation between subhalo abundance and host mass has been well studied \citep{Zentner03, Diemand04, Gao04, Zentner05, Klypin10}. |
. These studies have all found that. when scaled in units of 2Mus/My. larger halos contain more subhalos above a giveni µ than do smaller ones. | These studies have all found that, when scaled in units of $\mu =
M_{sub}/M_{host}$, larger halos contain more subhalos above a given $\mu$ than do smaller ones. |
This 15 the expected result from the hierarchical merging picture of CDM. in which larger objects grow through the merging of smaller objects and therefore form later (Blumenthaletal.1984;Lacey&Cole1993). | This is the expected result from the hierarchical merging picture of CDM, in which larger objects grow through the merging of smaller objects and therefore form later \citep{Blumenthal84,Lacey93}. |
. This later formation has a two-fold impact: it reduces the amount of time available to tidally strip a subhalo. and lowers the host concentration. further reducing the ability of a host to tidally strip its subhalos (Wechsleretal.2002:Bushaetal. 2007). | This later formation has a two-fold impact: it reduces the amount of time available to tidally strip a subhalo, and lowers the host concentration, further reducing the ability of a host to tidally strip its subhalos \citep{W02, Busha07}. |
. Motivated by this. we present the abundance of LMC and SMC-mass subhalos for the 27.000 Bolshot halos with M,=2.6+0.9«10M ... | Motivated by this, we present the abundance of LMC and SMC-mass subhalos for the 27,000 Bolshoi halos with $\mvir = 2.6\pm 0.9 \times
10^{12}\msol$ . |
The results can be seen in Figure |.. | The results can be seen in Figure \ref{fig:vmax_comp}. |
Here. the left panel shows the results for selecting hosts with My,=0.8—1.7«I07M... while the right panel shows a mass range Mj,=1.7—3.4«10M... | Here, the left panel shows the results for selecting hosts with $\mvir
= 0.8-1.7\times 10^{12}\msol$, while the right panel shows a mass range $\mvir = 1.7-3.4\times 10^{12}\msol$. |
For the more massive Ma~2.6«ΙΟΙΞΜ.. halos. the cumulative probability of hosting two or more 50 halos increases by a factor of3 compared to the 1.2«107M. objects (from to 26%)). while jumping by a factor of 6 for subhalos (from to nearly 6%)). | For the more massive $\mvir \sim 2.6 \times 10^{12} \msol$ halos, the cumulative probability of hosting two or more 50 halos increases by a factor of 3 compared to the $1.2\times 10^{12} \msol$ objects (from to ), while jumping by a factor of 6 for subhalos (from to nearly ). |
We emphasize that this is not a contradiction with the results of Bushaetal. (2010).. which found that a halo with exactly two MC-like subhalos was likely to have mass 1.2«10M... | We emphasize that this is not a contradiction with the results of \cite{Busha10c}, which found that a halo with exactly two MC-like subhalos was likely to have mass $1.2\times 10^{12} \msol$. |
While the fraction of more massive halos hosting two MC-like subhalos is larger. the steep slope of the mass function means that there are many more lower-mass halos. | While the fraction of more massive halos hosting two MC-like subhalos is larger, the steep slope of the mass function means that there are many more lower-mass halos. |
Additionally. aside from just considering Vijay. Bushaetal.(2010) selected halos with satellites like the MCs in terms of location and three-dimensional velocity. properties not considered in the present analysis. | Additionally, aside from just considering $\vmax$, \cite{Busha10c}
selected halos with satellites like the MCs in terms of location and three-dimensional velocity, properties not considered in the present analysis. |
Again. these results are in excellent agreement with the work of BKIO. | Again, these results are in excellent agreement with the work of BK10. |
While such an agreement is generally expected from pure collisionless N-body simulations. such agreement Is not as trivial as it may appear. | While such an agreement is generally expected from pure collisionless N-body simulations, such agreement is not as trivial as it may appear. |
While the present work uses results from the Bolshoi simulation. run using the adaptive refinement ART code and the BDM halo finder. BK10used the Millenntum-IHI simulation run with the TreePM code Gadget-2 with substructures identified using the Subfind algorithm (Springeletal. 2001). | While the present work uses results from the Bolshoi simulation, run using the adaptive refinement ART code and the BDM halo finder, BK10used the Millennium-II simulation run with the TreePM code Gadget-2 with substructures identified using the Subfind algorithm \citep{subfind}. . |
. Additionally. in both cases. we are concerned with subhalos close to the mass-limit for | Additionally, in both cases, we are concerned with subhalos close to the mass-limit for |
as that observed iu situ iu the bulee by MeWillimn Rich (1995)). an indication of a conunon orem for both populations. | as that observed in situ in the bulge by McWilliam Rich \cite{McWilliam}) ), an indication of a common origin for both populations. |
The ages are also heterogeneous with a rauge between 6 to 10 Cr (Fie. £0). | The ages are also heterogeneous with a range between 6 to 10 Gyr (Fig. \ref{fig:HR}) ). |
The @ anomaly has hence to be iuterpreted as a conuuon respouse of old stars to secular gravitational sollicitations rather than as a memory of initial coucditious. | The $\overline{u}$ anomaly has hence to be interpreted as a common response of old stars to secular gravitational sollicitations rather than as a memory of initial conditions. |
Tn this section we compare the observational features ueutioned above with the local kiucmiaties of old dise particles inferred from simulation with global selt-consistent 3-D nuuercal models of our Galaxy developed o» Fux (1997)). | In this section we compare the observational features mentioned above with the local kinematics of old disc particles inferred from simulation with global self-consistent 3-D numerical models of our Galaxy developed by Fux \cite{fux}) ). |
These models have a bar axis ratio bía=0.5x0.1 and a bar pattern speed ο0,=50t10 aus! corresponcdiue oa corotation radius of 1.3x0.5 spe. | These models have a bar axis ratio $b/a=0.5\pm0.1$ and a bar pattern speed $\Omega_{p}=50\pm10$ km $^{-1}$ corresponding to a corotation radius of $4.3\pm0.5$ kpc. |
The Fux model πα at £223.2 Cyr preseuts the best agreement with the different local aud global observational constraints considered by Fux. | The Fux model m08 at $t$ =3.2 Gyr presents the best agreement with the different local and global observational constraints considered by Fux. |
Tn this mi(08 simulation we follow the mean radial motion @ of particles wit. | In this m08 simulation we follow the mean radial motion $\overline{u}$ of particles w.r.t. |
the GC as a function of time. across a toroidal region of d kpc diameter at a distance R=Ry= WNpc from he GC. | the GC as a function of time, across a toroidal region of 1 kpc diameter at a distance $R=R_{0}=8$ Kpc from the GC. |
Tn the cousidered models. built with ouwtieules which essentially represcut the old clisc. the eloba deviation with respect to axisviunietry ix practically negligible before 2 xr (Fie. 5)). | In the considered models, built with particules which essentially represent the old disc, the global deviation with respect to axisymmetry is practically negligible before 2 Gyr (Fig. \ref{fig:ubphi}) ). |
The har. if i exists. could be at most confined to a very small reeion around the ceuter. | The bar, if it exists, could be at most confined to a very small region around the center. |
Some transitory spiral density waves are observed. but α is never very different from zero duving this carly period. | Some transitory spiral density waves are observed, but $\overline{u}$ is never very different from zero during this early period. |
However. as soon as the bar is stabilized (for f>2.9 Cir). 0 differs siguificautly from 0 aud depends on o. the angle between the bar aud the line Sun-ealactic center. | However, as soon as the bar is stabilized (for $t >
2.9$ Gyr), $\overline{u}$ differs significantly from 0 and depends on $\phi$ , the angle between the bar and the line Sun-galactic center. |
The bar produces a sine-like behaviour in o for the mean velocity @ (note that the streaming notion «d 1s zero when iutegrated over o for several bar rotational periods. even for stochastic orbits). | The bar produces a sine-like behaviour in $\phi$ for the mean velocity $\overline{u}$ (note that the streaming motion $\overline{u}$ is zero when integrated over $\phi$ for several bar rotational periods, even for stochastic orbits). |
The mean amplitude of πω) is ~17 km ft. dont [9| values as high ax 28 kins + are temporarily obtained. | The mean amplitude of $\overline{u}(\phi)$ is $\sim 17$ km $^{-1}$, but $|\overline{u}|$ values as high as 28 km $^{-1}$ are temporarily obtained. |
For example. around f£=1.53 Cor and o= which is the angle correspouding to the best statistical agrecinenut of the models with the COBE/DIRBE data). 7 of the order of 20 kin 1 aye obtained. in agreement with the observational results reported in Sect. | For example, around $t = 4.53$ Gyr and $\phi =$ (which is the angle corresponding to the best statistical agreement of the models with the COBE/DIRBE data), $\overline{u}$ of the order of 20 km $^{-1}$ are obtained, in agreement with the observational results reported in Sect. |
3. | 3. |
Figure 6 is a slice cutting of Fig. | Figure \ref{fig:ut} is a slice cutting of Fig. |
5. for o=307. | \ref{fig:ubphi} for $\phi = 30$. |
.. The values of 7 have been averaged within bius of 200 Myr width. | The values of $\overline{u}$ have been averaged within bins of 200 Myr width. |
One obtains a significantly positive value of 7 when the bar is stabilized. | One obtains a significantly positive value of $\overline{u}$ when the bar is stabilized. |
The presence of a bar in our Calaxy Προς characteristic orbital behaviours of stars | The presence of a bar in our Galaxy implies characteristic orbital behaviours of stars. |
Detailed discussions ou the kind of trajectories followed by stars in seltconsisteut barred potentials have been preseuted by Sparke Selhwood (1987)). Pfeuuiger Friedl (19913) and Kaufmann Coutopoulos (1996)). | Detailed discussions on the kind of trajectories followed by stars in self-consistent barred potentials have been presented by Sparke Sellwood \cite{sparke}) ), Pfenniger Friedli \cite{pfenniger}) ) and Kaufmann Contopoulos \cite{kaufmann}) ). |
Let us distinguish here two categories of orbits: 1) elougated orbits confines to the bar. trapped about the loug-axis wy family of> periodic orbits (bar particles). 2) “hot” orbits which esschtially cisplay a typical chaotic behaviour. erratically wandering between regions inside the bar aud outside corotation. | Let us distinguish here two categories of orbits: 1) elongated orbits confined to the bar, trapped about the long-axis $x_{1}$ family of periodic orbits (bar particles), 2) “hot” orbits which essentially display a typical chaotic behaviour, erratically wandering between regions inside the bar and outside corotation. |
Whereas orbits of kind 1) have an Wamiltoman II«Πο]. the "hot orbits have ff>FI(L4»). IT(E49) boiug the WTamiltonian at the Lagrange poiut Z4 and Ly for a zero velocity iu the rotating frame. | Whereas orbits of kind 1) have an Hamiltonian $H < H(L_{1,2})$, the “hot” orbits have $H > H(L_{1,2})$, $H(L_{1,2})$ being the Hamiltonian at the Lagrange point $L_{1}$ and $L_{2}$ for a zero velocity in the rotating frame. |
Examples of these kinds of orbits can be seen for ex. | Examples of these kinds of orbits can be seen for ex. |
in Fig. | in Fig. |
15 of Sparke Sellwood (1987)). | 15 of Sparke Sellwood \cite{sparke}) ). |
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