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50 [ar we have dealt with only a subset of our data. those galaxies near the very brightest.
So far we have dealt with only a subset of our data, those galaxies near the very brightest.
If we wish to make trulv general comparisons of peculiar velocities wilh luminous matter. as well as make use of a great deal of data painstakingly gathered. we should find a wav to look at all (he galaxies in the sample.
If we wish to make truly general comparisons of peculiar velocities with luminous matter, as well as make use of a great deal of data painstakingly gathered, we should find a way to look at all the galaxies in the sample.
For this we again make use of the dynamical vouth of the Local Volume. which allows us to compare apples with oranges.
For this we again make use of the dynamical youth of the Local Volume, which allows us to compare apples with oranges.
Assume that peculiar velocities are produced by fluetuations in the gravitational field which can be identified with galaxies.
Assume that peculiar velocities are produced by fluctuations in the gravitational field which can be identified with galaxies.
If the fluctuations are linear (as (hev are on much larger scales than we are looking al). the local gravitational acceleration and the local peculiar velocity should be proportional: plotting one against the other gives a straight line.
If the fluctuations are linear (as they are on much larger scales than we are looking at), the local gravitational acceleration and the local peculiar velocity should be proportional: plotting one against the other gives a straight line.
In the mildly nonlinear regime the line will become an S-shaped curve. as the effects of mass concentrations reinforce themselves.
In the mildly nonlinear regime the line will become an S-shaped curve, as the effects of mass concentrations reinforce themselves.
As some objects complete infall and pass to the other side of larger masses. the ends of the S will Irav: but as long as the system is not dvnamically relaxed there will be some cdisceriable relation between the gravity field and the peculiar velocity field: apples and oranges.
As some objects complete infall and pass to the other side of larger masses, the ends of the S will fray; but as long as the system is not dynamically relaxed there will be some discernable relation between the gravity field and the peculiar velocity field: apples and oranges.
If possible. we want to avoid the worst inaccuracies in this kind of cealeulation.
If possible, we want to avoid the worst inaccuracies in this kind of calculation.
Galaxies
Galaxies
varies roughly from 071 to 074.
varies roughly from $\farcs$ 1 to $\farcs$ 4.
We took all the sources inside the 95% (~ 2.4860) confidence X-ray error circle as the possible counterparts in optical band.
We took all the sources inside the $95\%$ $\sim$ $\sigma$ ) confidence X-ray error circle as the possible counterparts in optical band.
Their finding charts are listed in figure 5.
Their finding charts are listed in figure 5.
We first used the results of revised astrometry described above to search for probable ooptical counterparts. which are within the confidence position error circles of the XX-ray source positions.
We first used the results of revised astrometry described above to search for probable optical counterparts, which are within the confidence position error circles of the X-ray source positions.
For the case of multiple optical sources inside the error circle. we included all of them as possible counterparts.
For the case of multiple optical sources inside the error circle, we included all of them as possible counterparts.
Within the AACS field of view. there are five X-ray sources and each of them has 1-3 optical counterparts.
Within the ACS field of view, there are five X-ray sources and each of them has 1-3 optical counterparts.
We then calculated the probabilities of chance positional coincidences for the five X-ray sources and their possible optical counterparts.
We then calculated the probabilities of chance positional coincidences for the five X-ray sources and their possible optical counterparts.
We calculated the average number of sources within the error circles by computing the area ratios of the error circles to the field of view of the 5” \ 5" finding charts and also the total number of the sources inside the field of view of the 5” ΞΏΟ‚ 5” finding charts.
We calculated the average number of sources within the error circles by computing the area ratios of the error circles to the field of view of the $\arcsec$ $\times$ $\arcsec$ finding charts and also the total number of the sources inside the field of view of the $\arcsec$ $\times$ $\arcsec$ finding charts.
With the assumption of Poisson distribution. we obtained the probabilities of finding the number of observed sources or more sources inside the error circles and listed them (chance |) in Table 4.
With the assumption of Poisson distribution, we obtained the probabilities of finding the number of observed sources or more sources inside the error circles and listed them (chance 1) in Table 4.
Based on the probability. for CX1. CX3. and CXS. it is possible that all the optical sources inside the error circles are located there by chance and are not secure optical counterparts.
Based on the probability, for CX1, CX3, and CX5, it is possible that all the optical sources inside the error circles are located there by chance and are not secure optical counterparts.
For CX2. because of the low probability (~0.1%) of finding three or more sources inside the error circle. one of the three sources probably is the real optical counterpart.
For CX2, because of the low probability $\sim$ $\%$ ) of finding three or more sources inside the error circle, one of the three sources probably is the real optical counterpart.
CX4 is a marginal case and we cannot exclude the possibility that neither of the two sources within the error cirele is the real counterpart.
CX4 is a marginal case and we cannot exclude the possibility that neither of the two sources within the error circle is the real counterpart.
We further checked the number of false counterparts matches by shifting all the ppositions in four directions (north. south. east. and west) and 5” away from the sources.
We further checked the number of false counterparts matches by shifting all the positions in four directions (north, south, east, and west) and $\arcsec$ away from the sources.
We again calculated the average number of false matches and the probabilities of getting the number of observed sources or more sources inside the error circles with Poisson distribution (chance 2).
We again calculated the average number of false matches and the probabilities of getting the number of observed sources or more sources inside the error circles with Poisson distribution (chance 2).
We summarized the results in table 4.
We summarized the results in table 4.
The results are similar to the previously calculated probabilities and confirm them.
The results are similar to the previously calculated probabilities and confirm them.
Apart from checking the positional coincidences. we then checked whether these sources have special behavior in the optical CMDs.
Apart from checking the positional coincidences, we then checked whether these sources have special behavior in the optical CMDs.
For the optical candidate counterparts of the X-ray sources. We expect they will have unusual optical properties (e.g. the color of candidate counterparts) corresponding to different kinds of X-ray sources.
For the optical candidate counterparts of the X-ray sources, we expect they will have unusual optical properties (e.g. the color of candidate counterparts) corresponding to different kinds of X-ray sources.
Through inspecting the positions on the CMDs of the candidate counterparts. we can know more about their nature in the optical band which will help us identify the X-ray sources with higher confidence.
Through inspecting the positions on the CMDs of the candidate counterparts, we can know more about their nature in the optical band which will help us identify the X-ray sources with higher confidence.
Finally. we compared the optical characteristies with the X-ray properties and the X-ray to optical flux ratio fx/fopy (See table 3) to classify possible counterparts.
Finally, we compared the optical characteristics with the X-ray properties and the X-ray to optical flux ratio $f_\mathrm{X}$ $f_\mathrm{OPT}$ (See table 3) to classify possible counterparts.
CXI has the highest X-ray photon count rate and is the second most luminous source in the whole field. and it is the one at 0.3’ from the center of MI2 (in a field of view of 8.3 Β« 8.3).
CX1 has the highest X-ray photon count rate and is the second most luminous source in the whole field, and it is the one at $\arcmin$ from the center of M12 (in a field of view of $\arcmin$ $\times$ $\arcmin$ ).
The probability of one of the two brightest sources of MI2 occurring within the 0.3’ half-mass radius is only β€”0.866. and we conclude that CX1 is a secure member of M12 - independent on the optical identification.
The probability of one of the two brightest sources of M12 occurring within the $\arcmin$ half-mass radius is only $\sim$ $\%$, and we conclude that CX1 is a secure member of M12 - independent on the optical identification.
This implies an X-ray luminosity (See table 3) which ts typical for a CV. and rather too high for an AB of main-sequence stars.
This implies an X-ray luminosity (See table 3) which is typical for a CV, and rather too high for an AB of main-sequence stars.
If it were an AB. Figure 6 shows that 1t would be the most X-ray luminous AB so far detected in any globular cluster and 1t would be more than 100 times brighter than any AB at the same optical magnitude near the Sun (100 if the optical star is the counterpart. more than 100 if the optical counterpart is fainter).
If it were an AB, Figure 6 shows that it would be the most X-ray luminous AB so far detected in any globular cluster and it would be more than 100 times brighter than any AB at the same optical magnitude near the Sun (100 if the optical star is the counterpart, more than 100 if the optical counterpart is fainter).
We conclude that it is Γ  CV.
We conclude that it is a CV.
Its X-ray spectrum and its variability (Figure 3) on a time scale of an hour are compatible with this conclusion.
Its X-ray spectrum and its variability (Figure 3) on a time scale of an hour are compatible with this conclusion.
The possible optical counterpart of CX1 shows no special color or Ha emission in the AACS observation.
The possible optical counterpart of CX1 shows no special color or $\alpha$ emission in the ACS observation.
In the WFPC2 observation. no significant color change is detected.
In the WFPC2 observation, no significant color change is detected.
The optical counterpart shows no CV characteristics.
The optical counterpart shows no CV characteristics.
Therefore. it is possible that the optical source inside the eerror circle may not be the real counterpart of CX1.
Therefore, it is possible that the optical source inside the error circle may not be the real counterpart of CX1.
We included 3 optical counterpart candidates of CX2.
We included 3 optical counterpart candidates of CX2.
CX2 has relatively hard X-ray color.
CX2 has relatively hard X-ray color.
For the optical counterpart candidates. CX2b have a relatively low X-ray to optical flux ratio and is redder and below the subgiant branch of the CMDs.
For the optical counterpart candidates, CX2b have a relatively low X-ray to optical flux ratio and is redder and below the subgiant branch of the CMDs.
The position of CX2b on the CMD ts consistent with some identified sub-subgiants in other globular clusters (e.g. Mathieu et.
The position of CX2b on the CMD is consistent with some identified sub-subgiants in other globular clusters (e.g. Mathieu et.
al 2005: optical sources No.14 and No.43 in figure 9 of Edmonds et al.
al 2003; optical sources No.14 and No.43 in figure 9 of Edmonds et al.
2003a).
2003a).
The position of CX2b on figure 6 Is also consistent with an AB.
The position of CX2b on figure 6 is also consistent with an AB.
Therefore. we suggest that CX2b is an AB ff it is the optical counterpart.
Therefore, we suggest that CX2b is an AB if it is the optical counterpart.
In the case of CX2c. it is obvious bluer than the other two and has some Ha emission. so It Is a possible CV.
In the case of CX2c, it is obvious bluer than the other two and has some $\alpha$ emission, so it is a possible CV.
It is located above the line that represent
It is located above the line that represent
Most extra-solar planet. detections rely on measuring the xvcent stars wobble which is assumed to be caused by a jxanet.
Most extra-solar planet detections rely on measuring the parent star's wobble which is assumed to be caused by a planet.
However. other effects can cause stellar wobble thus it is important to study these in order to avoid. erroneous new planet announcements. as it already. happened in the ; ?7β‰»β‰Ίβ†§βŠ³βˆ–β†Ώβ†Ώβˆ–βˆ™βˆ™βˆ£β†΄β†¦
However, other effects can cause stellar wobble thus it is important to study these in order to avoid erroneous new planet announcements, as it already happened in the past \citep{Queloz2001A&A,Santos_etal2002A&A}.
β†“βŠ”β†“β‰»β†“β‹…βˆ’β‹…βˆ–β‹°β†“βˆͺβŠ”β‰±βˆ–β‹œβŠ”β‹…β†₯β‹ βŠ”βˆ™β‡‚βˆ’β‹…β‰±βˆ–β†Ώβˆ–β‡€βˆ™β†—β‡€βˆ™β†—βŠβ‹‘β‹‘βˆ–βˆ–β‡β‹–β‹…β‹‘βˆ–β‹―βˆβ‹―β‡‚β†₯⇂β†₯β‹–β‹…β‹‘βˆ–β†“β†•βˆͺβ†“β‹…β†Ώβˆ’βŠ“β‹…β†“β‹…βŠ”β†“ ellect of a binary system on a star's motion.
In previous articles \citep{Morais&Correia2008,Morais&Correia2011}, we studied the short-term effect of a binary system on a star's motion.
We saw that his could mimic a planet companion to the star under some circumstances.
We saw that this could mimic a planet companion to the star under some circumstances.
In these articles. we considered. moderately close binary systems (210 AU) in which the stars motion around the binarv's centre of mass had. periods of several decades.
In these articles, we considered moderately close binary systems $\ge 10$ AU) in which the star's motion around the binary's centre of mass had periods of several decades.
Moreover. we realistically assumed. that we had observationalvati data loror only⇁ a fractionvacti of thithis period.Ξ· and not severalEhe orbits.
Moreover, we realistically assumed that we had observational data for only a fraction of this period, and not several orbits.
llere. we will present another scenario that requires a dillerent. analvsis.
Here, we will present another scenario that requires a different analysis.
We consider a star with a close binary system (Β«5 AU) and we assume that the observational data covers a few periods of the star's motion around the binary svstem's centre of mass.
We consider a star with a close binary system $<5$ AU) and we assume that the observational data covers a few periods of the star's motion around the binary system's centre of mass.
We will show that. in this case. we rave to take into account secular effects which Head to slow oecession of the star's orbit.
We will show that, in this case, we have to take into account secular effects which lead to slow precession of the star's orbit.
In Sect.
In Sect.
2 we present the secular theory for hierarchical riple star svstems composed of a star and a nearby binary.
2 we present the secular theory for hierarchical triple star systems composed of a star and a nearby binary.
In Sect.
In Sect.
3 we show how we can measure the secular of. theβ‹… stars orbit.op from .radial velocity. datawhere . how we can predict the. binary system's. parametersMis β‹… .this measurement.
3 we show how we can measure the secular precession of the star's orbit from radial velocity data and how we can predict the binary system's parameters from this measurement.
. La Sect.
In Sect.
4. we apply the results Tyo rom previous Sections to fictitious hierarchical triple star systems.
4 we apply the results from previous Sections to fictitious hierarchical triple star systems.
In Sect.
In Sect.
5 we discuss the reported finding ofa planet in the binary. system Β£-Octantis.
5 we discuss the reported finding of a planet in the binary system $\nu$ -Octantis.
In Sect.
In Sect.
6 we present. our conclusions.
6 we present our conclusions.
: : βˆ–βˆ–βˆ’β‹…β‰Όβˆ™βˆͺβŠ”β‰±βˆ–βŠ”β‡‚β‹–β‹…β†“β‹…βˆ₯β‡‚β†“β‹…β†“β†“β‰»β†“β‹–βŠΎβŠ³βˆ–β†Ώβ‹œβŠ”β‹…βŠ³βˆ–βˆ™βˆ–β‡βŠ³βˆ–βˆ©β‹…βŠ”β†“β‰ΌβˆΌβˆͺβŠ”β†“β†“β‰»βˆͺβ‰±βˆ–β‹–β‹…βˆ β‡‚βˆͺβ‡‚β‹œβ‹―βˆͺβˆ£β‹‘β‰±βˆ–βˆ’β‹…β†“β‹…βˆ–β‡βˆ’βŠΎβˆ β‡‚; star. ms. and a nearby. binary of masses mo and mj.
We consider a triple star system composed of an observed star, $m_2$, and a nearby binary of masses $m_0$ and $m_1$ .
We use the Jacobi coordinates rj (clistance of mg to mo). and r (distance of me to the centre of mass of mo and. mj).
We use the Jacobi coordinates $\vec{r_1}$ (distance of $m_1$ to $m_0$ ), and $\vec{r_2} $ (distance of $m_2$ to the centre of mass of $m_0$ and $m_1$ ).
Aloreover. we assume that [|]«ο] (hierarchical triple system).
Moreover, we assume that $|\vec{r}_{1}| \ll |\vec{r}_{2}|$ (hierarchical triple system).
opHamiltonian is. (??) β€˜ where the 1st term describes the Ixeplerian motion of my with respect to mo (inner binary). the 2nd term describes the [xeplerian motion of mo with respect to the centre of mass of mo and my (outer binary). and Gis the gravitational constant. the distance of yrecession LO neo 19 and. and the distance of mΒ» to mj is
The Hamiltonian is \citep{Lee&Peale2003ApJ,Farago&Laskar2010} where the 1st term describes the Keplerian motion of $m_1$ with respect to $m_0$ (inner binary), the 2nd term describes the Keplerian motion of $m_2$ with respect to the centre of mass of $m_0$ and $m_1$ (outer binary), and where $G$is the gravitational constant, the distance of $m_2$ to $m_0$ is and the distance of $m_2$ to $m_1$ is
the flaring coniponent.
the flaring component.
The flaring is most likely related to a backflow/transverse shock resulting frou the putative collision between he jet and a cloud ~225 mas (370 pc) from the nucleus {Couway Schilizzi 200)).
The flaring is most likely related to a backflow/transverse shock resulting from the putative collision between the jet and a cloud $\sim 225$ mas (370 pc) from the nucleus (Conway Schilizzi \cite{conway}) ).
The ariu-lenehn ratios (the ratio Β«ft the distances from the nucleus to the extremitics of he components) of the inner and outer structure are quite. different.
The arm-length ratios (the ratio of the distances from the nucleus to the extremities of the components) of the inner and outer structure are quite different.
The eud Β’of the NW. componcu on the small scales is considerabv further from the nucleus han the eud of the SE compoucut. whereas ou he large angular scales. the reverse ds true.
The end of the NW component on the small scales is considerably further from the nucleus than the end of the SE component, whereas on the large angular scales, the reverse is true.
The ari-leeth raio for the large scale sruture ds ~1,0, defue as the distance of the SE hospe(X from the nucleus Β«ivied bv the distauce of the end of the NW. structure fro ut1ΞΏ nucleus.
The arm-length ratio for the large scale structure is $\sim 1.6$, defined as the distance of the SE hotspot from the nucleus divided by the distance of the end of the NW structure from the nucleus.
This Is all average arnrleusth ratio for giant radio galaxies (Sc10011users et al. 2000)).
This is an average arm-length ratio for giant radio galaxies (Schoenmakers et al. \cite{schoenmakers}) ).
Defined iu he same way. arua-leποτ ratio for he compac structure is ΞΏΞ½0.23.
Defined in the same way, the arm-length ratio for the compact structure is $\sim 0.3$.
The difference may reflect the fact that he large scale 1lcture ds shaped by the iuteractio το Ο„je jet with the oeiter-galactic median auk the sumall scale sructure by the 1teraction of the jet with the ISM.
The difference may reflect the fact that the large scale structure is shaped by the interaction of the jet with the inter-galactic medium and the small scale structure by the interaction of the jet with the ISM.
It is also intrigue tla the Alpe SE couuter-jet is consideradv longer aud beter coliuated than the NW ]ct.
It is also intriguing that the Mpc SE counter-jet is considerably longer and better collimated than the NW jet.
This suggestsCoco that t1e jet to the NW has eicountered a deuser galactic or intereaactic medi wYch has reduced its outward luoion.
This suggests that the jet to the NW has encountered a denser galactic or intergalactic medium which has reduced its outward motion.
T1e large scale zxii-leugth asviuuncetry cannot be due to ligit travel time effects (Longair Riley 1979)). αΌ©ΞΉ particilar since we conclude that the NW side is approachig.
The large scale arm-length asymmetry cannot be due to light travel time effects (Longair Riley \cite{longair}) ), in particular since we conclude that the NW side is approaching.
The fact that 30236 is so large aud has remained SO stable in overall oricutation argues that it resides in a relatively empty cnviromment.
The fact that 3C236 is so large and has remained so stable in overall orientation argues that it resides in a relatively empty environment.
AGN in more dense environueuts (ce.
AGN in more dense environments (eg.
Cyenuus Γ€) radiate more of their energy aud/or becole Wide Anele Tail sources. whereas more of the ereYev in objects like 30236 goes iuto outward expansion (ΞΏΟ‚,
Cygnus A) radiate more of their energy and/or become Wide Angle Tail sources, whereas more of the energy in objects like 3C236 goes into outward expansion (eg.
Barthel Arnoud 1996)).
Barthel Arnoud \cite{barthel2}) ).
The 92 cni nuage of 30236 (Fi
The 92 cm image of 3C236 (Fig.
e. 9 bottom) provides strong evidence that the jet to the SE has been on for most of the liὉ of the radio source.
\ref{Fig. 9} bottom) provides strong evidence that the jet to the SE has been on for most of the life of the radio source.
At the resolution of the liensurenienrs (15 arcsec). the jet appears to originate im the nucleus axd cotinue for β€”2.5 Mpc before terminating ina doubk! hotspo (Dirthele al. 1985)).
At the resolution of the measurements (45 arcsec), the jet appears to originate in the nucleus and continue for $\sim 2.5$ Mpc before terminating in a double hotspot (Barthel et al. \cite{barthel}) ).
The jet appears to broaden i the PAMSVCESC (irection as it moves further away frou f1ο uucleus. eventuallyal subteudiug au anele of ~107 wÜüch is considerably larger than the augle subtended by the separation of he hotspot at the uncle. 3°.
The jet appears to broaden in the transverse direction as it moves further away from the nucleus, eventually subtending an angle of $\sim 10\degr$ which is considerably larger than the angle subtended by the separation of the hotspot at the nucleus, $\degr$.
Barthe Let al. (1985))
Barthel et al. \cite{barthel}) )
show t the ridge line of he SE Sructure wigelesge over tΞΉΞΏ final 6tX0 kpe of its trajector so that the cone of opening a18oe 107 may well ) t envelope of the jet’s traISVOTSC lktion.
show that the ridge line of the SE structure wiggles over the final 600 kpc of its trajectory, so that the cone of opening angle $\degr$ may well be the envelope of the jet's transverse motion.
The jet riceo li oeji the 92 cni nuage 1s located :oue the southern edee of the conc| but curves sightly jorthliwaurd. before reaching +re doubk| hotspot.
The jet ridge line in the 92 cm image is located along the southern edge of the cone but curves slightly northward before reaching the double hotspot.
Ou average. the jet auc cotiter]et iections have remained very stable over the liteiue of the source
On average, the jet and counterjet directions have remained very stable over the lifetime of the source.
Close to the uucleus. the SE jet is apparently blockec due to a collision with a cloud (Conway Schilizzi 2000)) which has caused what looks like a transverse reverse shock back towards the nucleus.
Close to the nucleus, the SE jet is apparently blocked due to a collision with a cloud (Conway Schilizzi \cite{conway}) ) which has caused what looks like a transverse reverse shock back towards the nucleus.
This is prestunably of recent Β’xiein since the jet must re-start further out. as we SCO 1ithe 92 Β’u data.
This is presumably of recent origin since the jet must re-start further out, as we see in the 92 cm data.
The highest resolution data ou the large scale jet was published by Barthel et al. (10551)
The highest resolution data on the large scale jet was published by Barthel et al. \cite{barthel}) )
a 21 cin |mt does not have sufficient sensitivity to trace the jet iuc ose to the nucleus.
at 21 cm but does not have sufficient sensitivity to trace the jet in close to the nucleus.
σιperficially. the evidence from the large-scale joet to the SE is that activity iu 3€236 is continuous rather than recurrent.
Superficially, the evidence from the large-scale jet to the SE is that activity in 3C236 is $\it{continuous}$ rather than $\it{recurrent}$.