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13b we have plotted the positions of all the orbits for the time interval of Fig.
13b we have plotted the positions of all the orbits for the time interval of Fig.
13a.
13a.
The color of each point shows the corresponding velocity value on the rotation plane.
The color of each point shows the corresponding velocity value on the rotation plane.
The color scale is the same as for the densities (see Fig.
The color scale is the same as for the densities (see Fig.
1) which means that blue color corresponds to the minima and red color to the maxima of the velocity values.
1) which means that blue color corresponds to the minima and red color to the maxima of the velocity values.
We observe that the density maxima are well correlated with the areas of small velocity values (dark to light blue colors in Fig.
We observe that the density maxima are well correlated with the areas of small velocity values (dark to light blue colors in Fig.
13b).
13b).
Figures 13c,d are similar to Figs.
Figures 13c,d are similar to Figs.
12b,c. We observe that the pericentres of the orbits (Fig.
12b,c. We observe that the pericentres of the orbits (Fig.
13c) form a slightly more closed spiral structure than that of the real particles (black density contours).
13c) form a slightly more closed spiral structure than that of the real particles (black density contours).
On the other hand the apocentres of the orbits (Fig.
On the other hand the apocentres of the orbits (Fig.
13d) fit well only the density contours of the bar and the innermost parts of the spiral structure that originate from the end of the bar.
13d) fit well only the density contours of the bar and the innermost parts of the spiral structure that originate from the end of the bar.
In Fig.
In Fig.
13e we plot the density distribution of the loci of the local velocity minima.
13e we plot the density distribution of the loci of the local velocity minima.
We notice that this distribution matches better the distribution of the apocentres in what concerns the bar and the distribution of the pericentres in what concerns the spiral structure.
We notice that this distribution matches better the distribution of the apocentres in what concerns the bar and the distribution of the pericentres in what concerns the spiral structure.
The 2:1 (orσιafterthenomenclatureofContopoulos&Papayannopoulos1980) family is generally considered responsible for the formation and the robustness of the bar.
The 2:1 \citep[or $x_1$ after the nomenclature of][]{b13} family is generally considered responsible for the formation and the robustness of the bar.
This is due to its morphology, together with the fact that this family is usually stable for low values of the Jacobi constant.
This is due to its morphology, together with the fact that this family is usually stable for low values of the Jacobi constant.
According to this point of view the bar should end not beyond the point where the x; family turns from stable to unstable.
According to this point of view the bar should end not beyond the point where the $x_1$ family turns from stable to unstable.
Here we point out the usefulness of the unstable part of this family which supports the spiral structure.
Here we point out the usefulness of the unstable part of this family which supports the spiral structure.
Figure 14a,b is similar to Fig.
Figure 14a,b is similar to Fig.
13a,b but for the zi family and for the same Jacobi constant value.
13a,b but for the $x_1$ family and for the same Jacobi constant value.
We observe that the density of the orbits starting close to the x1 periodic orbit is similar to the density of the orbits with initial conditions near the 3:1 periodic orbit.
We observe that the density of the orbits starting close to the $x_1$ periodic orbit is similar to the density of the orbits with initial conditions near the 3:1 periodic orbit.
Their density maxima support the morphological structures (bar and spiral) of the real particles for the same Jacobi constant value (Fig.
Their density maxima support the morphological structures (bar and spiral) of the real particles for the same Jacobi constant value (Fig.
14a).
14a).
These maxima lie near the areas corresponding to low values of plane velocities vy; (Fig.
These maxima lie near the areas corresponding to low values of plane velocities $v_{yz}$ (Fig.
14b).
14b).
Figure 15 is similar to Fig.
Figure 15 is similar to Fig.
14 but for the unstable periodic orbits PL1,2 which are located near corotation and for the same Jacobi constant value.
14 but for the unstable periodic orbits $PL_{1,2}$ which are located near corotation and for the same Jacobi constant value.
In this case we establish the same behavior (as for the cases 3:1 and 21) for the orbits initiating close to the symmetric periodic orbits PLi;.
In this case we establish the same behavior (as for the cases 3:1 and $x_1$ ) for the orbits initiating close to the symmetric periodic orbits $PL_{1,2}$.
The orbits starting near the periodic orbits 3:1, 2:1, PLi,2 follow the unstable directions of the asymptotic manifolds originating from these periodic orbits.
The orbits starting near the periodic orbits 3:1, 2:1, $PL_{1,2}$ follow the unstable directions of the asymptotic manifolds originating from these periodic orbits.
For the same Jacobi constant value these manifolds cannot intersect each other, and this means that these manifolds are parallel in the phase space.
For the same Jacobi constant value these manifolds cannot intersect each other, and this means that these manifolds are parallel in the phase space.
Thus, the orbits along the unstable directions of the various manifolds follow parallel paths and present a similar behavior in the configuration space.
Thus, the orbits along the unstable directions of the various manifolds follow parallel paths and present a similar behavior in the configuration space.
The major difference between the different sets of orbits starting near the different unstable periodic orbits (3:1, 2:1, PLi,2) is the diffusion rate (see section 5), which increases towards higher resonance orders (2:153:1—2 o0:1PL).
The major difference between the different sets of orbits starting near the different unstable periodic orbits (3:1, 2:1, $PL_{1,2}$ ) is the diffusion rate (see section 5), which increases towards higher resonance orders $(2:1\rightarrow 3:1\rightarrow \infty:1\equiv PL_{1,2})$ .
mass history (shown in the upper panel of Fig. 1))
mass history (shown in the upper panel of Fig. \ref{varfis}) )
and the SFR do not follow the same trend and seem to be in contradictioi in the latter 3 or 4 Gyr. when the aceretion diminishes while the SFR increases abruptly.
and the SFR do not follow the same trend and seem to be in contradiction in the latter 3 or 4 Gyr, when the accretion diminishes while the SFR increases abruptly.
It should be considerec however that the SFR should not follow the gas accretior closely as this accretion is only one of the mechanisms for increasing the SFR.
It should be considered however that the SFR should not follow the gas accretion closely as this accretion is only one of the mechanisms for increasing the SFR.
On large scales. the formation of stars is controlled by an interplay between self-gravity anc supersonic turbulence. operating on the gas already accreted.
On large scales, the formation of stars is controlled by an interplay between self-gravity and supersonic turbulence, operating on the gas already accreted.
It is not clear how star formation bursts are triggered in dwarf galaxies but. for 66822. Gouliermis et al. (
It is not clear how star formation bursts are triggered in dwarf galaxies but, for 6822, Gouliermis et al. (
2010) suggest that turbulence on kpe scales is the major agent regulating star formation.
2010) suggest that turbulence on kpc scales is the major agent regulating star formation.
Several mechanisms have been proposed as able to produce turbulence in large scales.
Several mechanisms have been proposed as able to produce turbulence in large scales.
In particular. for 66822. a possible mechanism. that could have triggered at least the increase in the SFR during the last 100-200 Myr. has been found in the presence of an apparently independent stellar structure called the “northwestern” companion. which ts considered to be currently interacting with the main body of NGC 6822 and causing the tidal arms in the southeast of the galaxy (de Block Walter 2000. 2003).
In particular, for 6822, a possible mechanism, that could have triggered at least the increase in the SFR during the last 100-200 Myr, has been found in the presence of an apparently independent stellar structure called the “northwestern” companion, which is considered to be currently interacting with the main body of NGC 6822 and causing the tidal arms in the southeast of the galaxy (de Block Walter 2000, 2003).
If such an interactior occurred in the past (which is possible if the northwestert companion is a satellite nearby NGC 6822) it could have been the mechanism for triggering different starbursts i1 66822.
If such an interaction occurred in the past (which is possible if the northwestern companion is a satellite nearby NGC 6822) it could have been the mechanism for triggering different starbursts in 6822.
3) We use the initial mass function (IMF) of Kroupa et al. (
3) We use the initial mass function (IMF) of Kroupa et al. (
1993). in the 7.5—M,, mmass range for Z«107? and in the 0.1—Μι mmass range for Z>1075.
1993), in the $7.5 - M_{up}$ mass range for $Z < 10^{-5}$ and in the $0.1 - M_{up}$ mass range for $Z > 10^{-5}$.
My is a free parameter adjusted to reproduce the observed O/H abundance ratio.
$M_{up}$ is a free parameter adjusted to reproduce the observed O/H abundance ratio.
4) We assume different stellar yields. dependent on initial stellar mass (71) and on initial stellar metallicity Z;. provided by different authors.
4) We assume different stellar yields, dependent on initial stellar mass $m$ ) and on initial stellar metallicity $Z_i$, provided by different authors.
However they do not cover all the mass range.
However they do not cover all the mass range.
In the case of LIMS. we have a complete library from ΜΜ. to MM.. and for MS. the mass range covered goes from MM. to 80 M...
In the case of LIMS, we have a complete library from $_\odot$ to $_\odot$ and for MS, the mass range covered goes from $_\odot$ to 80 $_\odot$.
In order to fill the mass gap (from MM.. to9 MMO). we proceeded as follows: for the 6Η/Μ.€7.5mass range we assigned the stellar yield values given by mass fraction (p;) of the MM.. star.
In order to fill the mass gap (from $_\odot$ to $\odot$ ), we proceeded as follows: for the $6 < m/M_\odot \leq 7.5 $mass range we assigned the stellar yield values given by mass fraction $p_i$ ) of the $_\odot$ star.
In the same way. for the 7.5«Η/Μ.«9 mass range we assigned the p; values of the MM. star.
In the same way, for the $7.5 < m/M_\odot < 9$ mass range we assigned the $p_i$ values of the $_\odot$ star.
Specifically. lem 4.1) For LIMS we adopt the stellar yields by Karakas Lattanzio (2007). and the integrated yields used by our model are given by: The results for ten elements. five initial stellar metallicities. and two different M,,, values are presented in Tables 4 and 5.
Specifically, 1cm 4.1) For LIMS we adopt the stellar yields by Karakas Lattanzio (2007), and the integrated yields used by our model are given by: The results for ten elements, five initial stellar metallicities, and two different $M_{up}$ values are presented in Tables 4 and 5.
lem 4.2) For MS. we consider the stellar yields obtained from models for the pre-SN stage and the SN stage.
1cm 4.2) For MS, we consider the stellar yields obtained from models for the pre-SN stage and the SN stage.
The pre-SN yields are taken from the work of the Geneva group (Maeder 1992: Meynet Maeder 2002: Hirschi et al.
The pre-SN yields are taken from the work of the Geneva group (Maeder 1992; Meynet Maeder 2002; Hirschi et al.
2005: Hirschi 2007).
2005; Hirschi 2007).
The SN yields are taken from Woosley Weaver (1995) adopting their models B for the 12 30MM. range and their models C. for the 35 - 40MM. range.
The SN yields are taken from Woosley Weaver (1995) adopting their models B for the 12 - $_\odot$ range and their models C, for the 35 - $_\odot$ range.
We combine the Geneva group vields with the Woosley Weaver yields using the prescription proposed by Carigi Hernandez (2008) where they connect the mass of the carbon-oxygen cores (Mca) from the Geneva group to Μου from Woosley Weaver. using the prescription given by Portinari et al. (
We combine the Geneva group yields with the Woosley Weaver yields using the prescription proposed by Carigi Hernandez (2008) where they connect the mass of the carbon-oxygen cores $_{CO}$ ) from the Geneva group to $_{CO}$ from Woosley Weaver, using the prescription given by Portinari et al. (
1998).
1998).
Under these assumptions the He. C. N. and O yields are equal to the pre-SN ones. but for heavier elements the yields are similar to the SN ones.
Under these assumptions the He, C, N, and O yields are equal to the pre-SN ones, but for heavier elements the yields are similar to the SN ones.
Form>40 tthe adopted yields for the heavier elements are similar to those given for m=40 Μ.
For $m > 40$ the adopted yields for the heavier elements are similar to those given for $m = 40$ .
... The chemical contribution of MS is in IRA. and the integrated yields are given by:
The chemical contribution of MS is in IRA, and the integrated yields are given by:
within nearborders.consideralsogalaxiesthatlocated2" because the correct. estimation of Voronoi cell volume is not possible in this case.
consider also galaxies that located within } near borders, because the correct estimation of Voronoi cell volume is not possible in this case.
Ο volunie-limited sample. is complete up to 17.7" but contains also about LOO more fainter galaxies.
Our volume-limited sample is complete up to $17.7^{m}$ but contains also about 100 more fainter galaxies.
Final number of galaxies in the sample is 6186.
Final number of galaxies in the sample is 6786.
We applied the second-order 3D. Voronoi tessellation to our sample 6786 galaxies and obtained 2196 eeometric pairs and 2394 single galaxies galaxies of whole sample are in pairs and are singles).
We applied the second-order 3D Voronoi tessellation to our sample 6786 galaxies and obtained 2196 geometric pairs and 2394 single galaxies galaxies of whole sample are in pairs and are singles).
We divided our samples of geometric pairs and singles on four equal parts by the parameter of isolation p and s. respectively.
We divided our samples of geometric pairs and singles on four equal parts by the parameter of isolation $p$ and $s$, respectively.
A quater of each sample with the highest isolation degree we called as (549 pairs and 598 singles).
A quater of each sample with the highest isolation degree we called as (549 pairs and 598 singles).
It means that the isolated. pairs and singles havep>Qs and s«(Qj. respectively. Q5 is third quartile and Qy is the first quartile.
It means that the isolated pairs and singles have $p > Q_{3}$ and $s < Q_{1}$, respectively, $Q_{3}$ is third quartile and $Q_{1}$ is the first quartile.
See values of quartiles in Table 1..
See values of quartiles in Table \ref{tab1d}.
Fig.
Fig.
3 shows the distributions of neighbouring galaxies number for galaxies that are members of pairs and singles.
\ref{1} shows the distributions of neighbouring galaxies number for galaxies that are members of pairs and singles.
We can see from Fig.
We can see from Fig.
3. that number of neighbours is varricel through range from 4 to 30 galaxies.
\ref{1} that number of neighbours is varried through range from 4 to 30 galaxies.
Isolated. galaxies have more neighbours than galaxies in other samples in average.
Isolated galaxies have more neighbours than galaxies in other samples in average.
lt is a feature of the second-order Voronoi tessellation (see above).
It is a feature of the second-order Voronoi tessellation (see above).
Galaxies in isolated pairs have approximately less by half neighbours than isolated. galaxies because of the pair's neighbours distribute among two members.
Galaxies in isolated pairs have approximately less by half neighbours than isolated galaxies because of the pair's neighbours distribute among two members.
Independently we applved the thirc-order 3D. Voronoi tessellation to our galaxy sample and obtained 1153 ecometric triplets of whole sample).
Independently we applyed the third-order 3D Voronoi tessellation to our galaxy sample and obtained 1182 geometric triplets of whole sample).
The/ quater (297)n of triplet sample with the highest isolation degree />(Q5 we called asisolated.
The quater (297) of triplet sample with the highest isolation degree $t>Q_{3}$ we called as.
.. Values of all quartiles for triplets can be found in Table 1..
Values of all quartiles for triplets can be found in Table \ref{tab1d}.
The distribution. of number of neighbouring triplets is drawn in Vig. 4..
The distribution of number of neighbouring triplets is drawn in Fig. \ref{t1}.
As can be seen. this picture looks the same as for distribution of neighbouring galaxies number in case of the second-order Voronol tesscllation (Fig. 3)).
As can be seen, this picture looks the same as for distribution of neighbouring galaxies number in case of the second-order Voronoi tessellation (Fig. \ref{1}) ).
We cross-correlatecl our results with other samples.
We cross-correlated our results with other samples.
In the first order we compared. pairs and triplets of our sample with “Tago et al. (
In the first order we compared pairs and triplets of our sample with Tago et al. (
2008) groups selected by. modified friencs- method using the same release of SDSS.
2008) groups selected by modified friends-of-friends method using the same release of SDSS.
From 965
From 965
lations that anv flight requiring a delav longer than one vear would have to be undertaken with a TAUVEX serformineg as originally planned.
nations that any flight requiring a delay longer than one year would have to be undertaken with a TAUVEX performing as originally planned.
Since the mirrors had con singled as the likely source of degradation. they would have to be recoated.
Since the mirrors had been singled as the likely source of degradation, they would have to be recoated.
This, fortunately, could be done in India and would not require reshipping the wiVload to Israel. then back to Iudia.
This, fortunately, could be done in India and would not require reshipping the payload to Israel, then back to India.
The prolonged TAUVEN saga described above bees a 111111ver of conclusions reearding the structure of the TAUVEN project managed in Ixacl.
The prolonged TAUVEX saga described above begs a number of conclusions regarding the structure of the TAUVEX project managed in Israel.
The first deals with ondssons bv the Isracli side: it was a iudstake ou je part of the science team to agree to continue the xoject after the national satellite and launcheLael pronised by ISA in the original call for proposals becaue unavailable.
The first deals with omissions by the Israeli side; it was a mistake on the part of the science team to agree to continue the project after the national satellite and launcher promised by ISA in the original call for proposals became unavailable.
This naive approach. that provided 10 exit. strateeies throughout the duration of the project. is uxerstandable ou the part of scientists, but ultinately did not pay off.
This naive approach, that provided no exit strategies throughout the duration of the project, is understandable on the part of scientists, but ultimately did not pay off.
The second imistake on the part of he TAUVEX Priicipal Duvestieators was to allow ISA to take full courol of the midget and of the final decisions regarding tlie conduct of the project at ELOp. xwule relegating themselves to an advisory role.
The second mistake on the part of the TAUVEX Principal Investigators was to allow ISA to take full control of the budget and of the final decisions regarding the conduct of the project at El-Op, while relegating themselves to an advisory role.
Duriug he long vears of this projec this caused the relaxatio1 of the tasks the Prime Contractor (ELOp) was require to perform. such as the iistallation of contamination inonitoring devices within TAUWVEN.
During the long years of this project this caused the relaxation of the tasks the Prime Contractor (El-Op) was required to perform, such as the installation of contamination monitoring devices within TAUVEX.
Similarly. uo insisting on a thorough iwestieation of the implicaions of the lone-term storage of the completed TAUVEN OU Was a uistake and the improper storage caused the throughput reduction presumably by degrading the nunror coatings.
Similarly, not insisting on a thorough investigation of the implications of the long-term storage of the completed TAUVEX OU was a mistake and the improper storage caused the throughput reduction presumably by degrading the mirror coatings.
ISA also relaxed the requirement to inaliain full doctuuentation for the project: the conclusion is that now there is no wav to know what was doje with the flight model. when, or dy whom.
ISA also relaxed the requirement to maintain full documentation for the project; the conclusion is that now there is no way to know what was done with the flight model, when, or by whom.
On he Indian side. ISRO carries significant lane since it entered into an agreement with ISA to launch TAUVEN on-board GSAT-1 but was rot able to fulfil it.
On the Indian side, ISRO carries significant blame since it entered into an agreement with ISA to launch TAUVEX on-board GSAT-4 but was not able to fulfil it.
ISA couk not enforce the launch :vereclnents with either RIXA «x ISRO because no punitive consequences were include Lin the launch aerecmens,
ISA could not enforce the launch agreements with either RKA or ISRO because no punitive consequences were included in the launch agreements.
ISRO inisled, willingly or 1uwillinely both science teanis. Tuclian aud Ixacli, as to he status of the GSLV laaucher aud of the GSAT-I sateHite.
ISRO misled, willingly or unwillingly, both science teams, Indian and Israeli, as to the status of the GSLV launcher and of the GSAT-4 satellite.
The delavs certainly did not help the state of the TAUVEN iiirrors and catsed uinecessary and significaif expenses to the Israeli side.
The delays certainly did not help the state of the TAUVEX mirrors and caused unnecessary and significant expenses to the Israeli side.
If the one-vear delay (2008-2009) in the integrajon would have been known in advance, it is possible twat ELOp would have had time to consider refurbishing the TAUVEN optics to recover the original respouse instead of seeping TAUVEN i1 the clean room of ISRO.
If the one-year delay (2008-2009) in the integration would have been known in advance, it is possible that El-Op would have had time to consider refurbishing the TAUVEX optics to recover the original response instead of keeping TAUVEX in the clean room of ISRO.
Ilowever. one should also meution here t10 STICCCSSCS 6the project. in particular (a) the built-in flexibility of the pavload that allowed a relatively easv shift from SRG to GSAT-I. and (b) the stric adherence of the Prine) Contractor (ELOp) to the differeiut schedules imposed. by the two satellites.
However, one should also mention here the successes of the project, in particular (a) the built-in flexibility of the payload that allowed a relatively easy shift from SRG to GSAT-4, and (b) the strict adherence of the Prime Contractor (El-Op) to the different schedules imposed by the two satellites.