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6). | 6). |
Using their equation 9 Fig. | Using their equation 9 Fig. |
4 (but. baring in mind. the dilference in primary mass) ancl the observed: O parameter in V1405 Aql (Table 2). we can derive a weak upper limit on its mass ratio of qZ50.08. | 4 (but baring in mind the difference in primary mass) and the observed $\phi$ parameter in V1405 Aql (Table 2), we can derive a weak upper limit on its mass ratio of $q\la0.08$. |
For à primary neutron star at the Chanclrasckhar limit. this implies an upper limit on the mass of the secondary Alo&O.L2AL.. which is presumably a helium white clwart. | For a primary neutron star at the Chandrasekhar limit, this implies an upper limit on the mass of the secondary – $M_{2}\la0.12M_{\odot}$, which is presumably a helium white dwarf. |
The [act that binary svstems with very cilleren configurations (CVs α hyedrogen-rich white cwarl and a rec companion: XM CVn two degenerate helium white dvarfs and V1405 Aql à neutron star and a helium white dwarl) obey the relation presented in Fig. | The fact that binary systems with very different configurations (CVs – a hydrogen-rich white dwarf and a red companion; AM CVn – two degenerate helium white dwarfs and V1405 Aql – a neutron star and a helium white dwarf) obey the relation presented in Fig. |
5 is quite surprising. | 5 is quite surprising. |
I might be a coincidence. or it may. suggest. that ó indee depends on the orbital period ancl not on the mass ratio. | It might be a coincidence, or it may suggest that $\phi$ indeed depends on the orbital period and not on the mass ratio. |
Further determinations of this parameter in more permanen superhump svstems are required to study this issue. | Further determinations of this parameter in more permanent superhump systems are required to study this issue. |
The mechanism which places the negative superhump signal into the X-ray light curve is unclear. but changing vertical disc structure seems a promising candidate. | The mechanism which places the negative superhump signal into the X-ray light curve is unclear, but changing vertical disc structure seems a promising candidate. |
Lt is clear that »ositive superhumps coincide with increased dise thickness Allington et al. | It is clear that positive superhumps coincide with increased disc thickness (Billington et al. |
1996). the evidence being consistent with he idea that the area of the dise involved. in. producing he superhump light thickens at the time of the increased dissipation. | 1996), the evidence being consistent with the idea that the area of the disc involved in producing the superhump light thickens at the time of the increased dissipation. |
In the nodal precession model. Wood. et. al. ( | In the nodal precession model, Wood et al. ( |
2000) showed how the passage of the secondary star past each of the two halves of the disc out of the midplane increases the dissipation in that hall. | 2000) showed how the passage of the secondary star past each of the two halves of the disc out of the midplane increases the dissipation in that half. |
They. also required ju the side of the disc closest to the orbital plane is the most. cüsrupted. | They also required that the side of the disc closest to the orbital plane is the most disrupted. |
LL by analogy with positive superhunips. js disruption increases the vertical extent of the. disc. jen it will increase the obscuration of the X-ray. source. | If, by analogy with positive superhumps, this disruption increases the vertical extent of the disc, then it will increase the obscuration of the X-ray source. |
As the disc precesses. the timing of the obscuration will hange with phase. producing the required. modulation at 10 negative superhump period. | As the disc precesses, the timing of the obscuration will change with phase, producing the required modulation at the negative superhump period. |
The lack of structure and aree range in phase of the negative superhump modulation implies that both the clise structure and occulted region are arge. the latter presumably. being the inner aceretion disc or à corona. | The lack of structure and large range in phase of the negative superhump modulation implies that both the disc structure and occulted region are large, the latter presumably being the inner accretion disc or a corona. |
This scenario can also explain why negative superhump signals have not been observed. so far in the rav light. curves of low inclination svstenis. | This scenario can also explain why negative superhump signals have not been observed so far in the X-ray light curves of low inclination systems. |
Laswell ct al. ( | Haswell et al. ( |
2001). pointed. out that the dissipation of energy in the disc. which is believed. to be responsible for the positive superhump mechanism in CVs in the optical. cannot be applied to LAINRBs. | 2001) pointed out that the dissipation of energy in the disc, which is believed to be responsible for the positive superhump mechanism in CVs in the optical, cannot be applied to LMXRBs. |
They suggested that instead the disc area is changing with the superhump period. and thus preclieted that superhumps would appear mainly in low inclination systems. | They suggested that instead the disc area is changing with the superhump period, and thus predicted that superhumps would appear mainly in low inclination systems. |
Figs. | Figs. |
1 2 show that the X-ray data is modulated: with the positive superhump (£5). | 1 2 show that the X-ray data is modulated with the positive superhump $_{2}$ ). |
However. when the dips are rejected from the light curve. this peak disappears. | However, when the dips are rejected from the light curve, this peak disappears. |
Thus in. V1405. Aql only. the dips show the positive superhump. presumably since their amplitude and or phase vary with the apsicdal precession period. | Thus in V1405 Aql only the dips show the positive superhump, presumably since their amplitude and / or phase vary with the apsidal precession period. |
Note | Note |
calculations. it’s plausible that disk-like structures like those reported in this paper will continue to appear in future experiments. | calculations, it's plausible that disk-like structures like those reported in this paper will continue to appear in future experiments. |
Direct and. retrograde versions of à. close. passage are compared in Figure L.. | Direct and retrograde versions of a close passage are compared in Figure \ref{fig01}. |
Encounter DLR. 1:1 C (top) resembles direct. encounters. described. in other studies (Barnes llernquist. 1991. 1996: Mihos. Lernguist 1994. 1996). | Encounter DIR 1:1 C (top) resembles direct encounters described in other studies (Barnes Hernquist 1991, 1996; Mihos Hernquist 1994, 1996). |
Although the disks interpenetrate. only a modest fraction of the gas actually collides with gas from the other disk. | Although the disks interpenetrate, only a modest fraction of the gas actually collides with gas from the other disk. |
The stellar ancl gaseous components both respond to the tidal [orces by developing extended bridges and tails Cloomre 'Toomre 1972). | The stellar and gaseous components both respond to the tidal forces by developing extended bridges and tails (Toomre Toomre 1972). |
In the aftermath of such passages. much of the gas is rapidly driven into the central regions: these inllows are driven by gravitational torque between the stellar and gaseous bars formed in tidally perturbed disks (Combes. Dupraz. Corin 1990: Barnes llerneuist. 1991: Mihos Lernquist 1996). | In the aftermath of such passages, much of the gas is rapidly driven into the central regions; these inflows are driven by gravitational torque between the stellar and gaseous bars formed in tidally perturbed disks (Combes, Dupraz, Gerin 1990; Barnes Hernquist 1991; Mihos Hernquist 1996). |
Encounter RET Ll € (bottom) illustrates a violent interaction. | Encounter RET 1:1 C (bottom) illustrates a violent interaction. |
The geometry. of this collision insures that a large fraction of the gas sulfers strong shocks as the galaxies intersect. | The geometry of this collision insures that a large fraction of the gas suffers strong shocks as the galaxies intersect. |
By time /=1.25 (middle). much of the eas in these disks has been swept toward their centers. | By time $t = 1.25$ (middle), much of the gas in these disks has been swept toward their centers. |
These inflows are not driven by gravitational torques — the stellar disks are far less perturbed. than the gas. and incapable of exerting strong gravitational torques. | These inflows are not driven by gravitational torques – the stellar disks are far less perturbed than the gas, and incapable of exerting strong gravitational torques. |
Instead. they are driven by hydrodynamic forces: the gas loses its spin angular momentum bv colliding directly with gas in the other galaxy. | Instead, they are driven by hydrodynamic forces; the gas loses its spin angular momentum by colliding directly with gas in the other galaxy. |
Gas which escapes being swept in forms a plume connecting the two galaxies: such structures may. have been observed in some deeply interpenetrating encounters (c.g. Condon et al. | Gas which escapes being swept in forms a plume connecting the two galaxies; such structures may have been observed in some deeply interpenetrating encounters (e.g. Condon et al. |
1993: TFsuchiva. Ixorchagin. Wada 1998). | 1993; Tsuchiya, Korchagin, Wada 1998). |
To illustrate the range of evolutionary histories in this sample of encounters. Figure 2 concisely sunimarizes two rather dillerent experiments. | To illustrate the range of evolutionary histories in this sample of encounters, Figure \ref{fig02} concisely summarizes two rather different experiments. |
In these plots. {ρω is the total energy lost to radiative processes. while p is the gas density. | In these plots, $E_{\rm rad}$ is the total energy lost to radiative processes, while $\rho$ is the gas density. |
As one might. &uess from the discussion above. encounter UZE Ld € ds the most dissipative of those studied: here: net radiative losses amount to 20 percent of the initial inding energy of the entire svstem. | As one might guess from the discussion above, encounter RET 1:1 C is the most dissipative of those studied here; net radiative losses amount to $\sim 20$ percent of the initial binding energy of the entire system. |
These losses occur in arge-scale shocks as the two galaxies plow into each other ad fom1. fall back together at £273. and merge at /24.3. | These losses occur in large-scale shocks as the two galaxies plow into each other at $t \simeq 1$, fall back together at $t \simeq 3.7$, and merge at $t \simeq 4.3$. |
Gas densities increase. with cach burst. of dissipation: by he end of the simulation 90 percent of the gas lies in a barcly-resolved disk at the center of the merger remnant. | Gas densities increase with each burst of dissipation; by the end of the simulation $\sim 90$ percent of the gas lies in a barely-resolved disk at the center of the merger remnant. |
In contrast. encounter POL 3:1 is the least clissipative. losing only ~5 percent of its initial binding οποιον. | In contrast, encounter POL 3:1 is the least dissipative, losing only $\sim 5$ percent of its initial binding energy. |
The first passage at /21l. while close enough to produce definite tidal features. barely registers in the traces of Ly, and. p. | The first passage at $t \simeq 1$, while close enough to produce definite tidal features, barely registers in the traces of $E_{\rm rad}$ and $\rho$ . |
The next passage. at /&5.0. is more clramatic. ancl the final merger at /26.3 drives about half of the eas into the central regions: the rest of the gas eventually settles into a warpecd clisk. | The next passage, at $t \simeq 5.0$, is more dramatic, and the final merger at $t \simeq 6.3$ drives about half of the gas into the central regions; the rest of the gas eventually settles into a warped disk. |
Disk formation need not wait until the merger process is completed: reaccretion [rom tidal bridges anc tails can feed high angular momentum eas back into galaxies. after any reasonably direct. passage. | Disk formation need not wait until the merger process is completed; reaccretion from tidal bridges and tails can feed high angular momentum gas back into galaxies after any reasonably direct passage. |
An example is illustrated in Figure 3.. | An example is illustrated in Figure \ref{fig03}. |
Here the upper row shows eas in the larger disk of encounter DIR 3:1 responding after the direct. passage of its iehter companion: note the pronounced bar typically formed in such. passages. | Here the upper row shows gas in the larger disk of encounter DIR 3:1 responding after the direct passage of its lighter companion; note the pronounced bar typically formed in such passages. |
The lower row shows where shocks occur w rendering each particle with intensity proportional to the ocal dissipation rate A. | The lower row shows where shocks occur by rendering each particle with intensity proportional to the local dissipation rate $\dot{u}$. |
While the central bar is prominent in 10 lower images. shocks also develop in the disk surrounding 1ο bar. | While the central bar is prominent in the lower images, shocks also develop in the disk surrounding the bar. |
Some of these shocks form where gas falling back rom the tidal tail ancl bridge impinges on the disk: others occur within the disk. perhaps in response to forcing by je central bar. | Some of these shocks form where gas falling back from the tidal tail and bridge impinges on the disk; others occur within the disk, perhaps in response to forcing by the central bar. |
Between times /=L875 and /=3.0 the reaceretecl eas nearly doubles the size of the disk. | Between times $t =
1.875$ and $t = 3.0$ the reaccreted gas nearly doubles the size of the disk. |
]teaccretion of gas [rom tidal tails is evident in a recent study o£ NGC 4088/9 (Llibbared et al. | Reaccretion of gas from tidal tails is evident in a recent study of NGC 4038/9 (Hibbard et al. |
2001). | 2001). |
Relative to the systemic velocity. most of the tail associated with 1e northern disk (NGC 4088) is moving away from us. but we gas at the base of the tail has the opposite sense of =notion. | Relative to the systemic velocity, most of the tail associated with the northern disk (NGC 4038) is moving away from us, but the gas at the base of the tail has the opposite sense of motion. |
This indicates that the material at the base has dready attained apocenter and is now falling back onto the disk. | This indicates that the material at the base has already attained apocenter and is now falling back onto the disk. |
This reaccretecl gas may be fueling the ring of star formation in the disk of NCC 4038. | This reaccreted gas may be fueling the ring of star formation in the disk of NGC 4038. |
One consequence ofthis disk rebuilding is that the | One consequence ofthis disk rebuilding is that the |
The generalized Tohuan-Oppeuheimer-Volkov (ΤΟΝΟ equation Is Let ux write the metric coefficient. g,4. as where. b(r) is the shape function of the wormhole structure which can casily be recoguized ax mass function (LaudauandLifshitz1959). | The generalized Tolman-Oppenheimer-Volkov (TOV) equation is Let us write the metric coefficient $g_{rr}$ as where, $b(r)$ is the shape function of the wormhole structure which can easily be recognized as mass function \citep{Landau1959}. |
. Tere. the above shape fuuctiou. bv the use of the Eqs. ( | Here, the above shape function, by the use of the Eqs. ( |
6) aud (8). cau be expressed as From the field Eqs. ( | 6) and (8), can be expressed as From the field Eqs. ( |
8) and (9). via the ansatz (5). we ect which readily gives Now we cousider several tov models for the preseut case of worlholes. | 8) and (9), via the ansatz (5), we get which readily gives Now we consider several toy models for the present case of wormholes. |
Consider the specific formu: of shape function as where ry corresponds to the wormhole throat aud à js an arbitrary constant. | Consider the specific form of shape function as where $r_0$ corresponds to the wormhole throat and $\alpha$ is an arbitrary constant. |
Usine the above shape function (16) iu the field equations. we get the following expressious of the piarineters where Since the spacetime is asvinptotically flat. we demand inteeration constant to bo unity. | Using the above shape function (16) in the field equations, we get the following expressions of the parameters where Since the spacetime is asymptotically flat, we demand integration constant to be unity. |
One can note that. bir) »ÜOasoar >ox nmuplies a«1l. | One can note that, $\frac{b(r)}{r} ~\longrightarrow 0$ as $r
\longrightarrow \infty$ implies $\alpha<1$. |
Also. Πάνοο coudition. which cau be found out bv taking the derivative of the shape function b(r) afr—ry ie. V(rg)<1 gives. a<i. | Also, flare-out condition, which can be found out by taking the derivative of the shape function $b(r)$ at $r=r_0$ i.e. $b^\prime(r_0) < 1$ gives, $\alpha<1$. |
Let us consider the energy deusityv function as Tere. ry is the wormhole throat and py>0 corresponds to the cuerey density at the throat and dds an arbitrary constant. | Let us consider the energy density function as Here, $r_0$ is the wormhole throat and $\rho_0 >0$ corresponds to the energy density at the throat and $\beta$ is an arbitrary constant. |
Using the above cuerey density fiction (23). one can eet the solutious of the parameters characterized the wormlole as | Using the above energy density function (23), one can get the solutions of the parameters characterized the wormhole as |
The radio 1s0-contours at 1100 ΑΠ of the “Alain”. "Middle aud “East” cluster «X the system are shown iu the top panel of Fig. 2.. | The radio iso-contours at 1400 MHz of the ”Main”, “Middle” and “East” cluster of the system are shown in the top panel of Fig. \ref{radio}. |
This image has been obtained with the VLA in D coufiguratikn aud has à FWOAL beam of «LL8"7.. | This image has been obtained with the VLA in D configuration and has a FWHM beam of $\times$. |
In order to conare radio ane Nouv cluster eniissio1. the radio 1504'outours are overlaid on the NMM-Nowtou nuage preseuted in Fie. l.. | In order to compare radio and X-ray cluster emission, the radio iso-contours are overlaid on the XMM-Newton image presented in Fig. \ref{xmm}. |
We fiid that 10 ceutral region of the "Main cluster is permeatect by ithse low-surtace brightuess enussion which we cassified radio halo. | We find that the central region of the “Main” cluster is permeated by diffuse low-surface brightness emission which we classified as a radio halo. |
The radio halo appears to be liused xiehter peripheral patch previously fouud by Veuti . ( | The radio halo appears to be linked to the brighter peripheral patch previously found by Venturi et al. ( |
2008). | 2008). |
I1 addition. the diffuse radio ciissio iof “Main” cluster is elongated toward the "Subcluster | In addition, the diffuse radio emission of the “Main” cluster is elongated toward the “Subcluster”. |
-reastred fom the 3-7 radio isophote. the overall ditt wission has a raneular extensiou of about (2 Lak the custer distaucce). | As measured from the $\sigma$ radio isophote, the overall diffuse emission has an angular extension of about $\simeq 1.8$ Mpc at the cluster distance). |
To separate the diffuse radio enuission from discrete ποιαον we produced images at higher resolution. | To separate the diffuse radio emission from discrete sources we produced images at higher resolution. |
Iu muddle pancl of Fig. | In the middle panel of Fig. |
2. we present the radio iso-contours of A7al. taken with the VLÀ iu € configuration. | \ref{radio} we present the radio iso-contours of A781, taken with the VLA in C configuration. |
This inage has a EWIIM beam of «16.5".. | This image has a FWHM beam of $\times$. |
Athough ie relativev hieh resolution of this image is not daricularly suitable to detect diffuse cluster ciuission. the peripheral patch o: diffuse enission is clearly visible in he C array data-set too. | Although the relatively high resolution of this image is not particularly suitable to detect diffuse cluster emission, the peripheral patch of diffuse emission is clearly visible in the C array data-set too. |
The discrete sour‘es are labelled in tje figure aud their position and fix densities are given in Table 2.. | The discrete sources are labelled in the figure and their position and flux densities are given in Table \ref{tab2}. |
All of them show au ootical counterpart i1i the Sloan Digital Sky Survey (see bottom left panel of Fig. 3)). | All of them show an optical counterpart in the Sloan Digital Sky Survey (see bottom left panel of Fig. \ref{radio_sub}) ). |
The ouly exception is source D.3. which may be a background radio galaxy. | The only exception is source B, which may be a background radio galaxy. |
Source D. swich is located about west to the N-rav peak of the “Main” cluster. is the brightest radio source iu the field. | Source D, which is located about west to the X-ray peak of the “Main” cluster, is the brightest radio source in the field. |
Its fractional polarization is ~. | Its fractional polarization is $\simeq$. |
The other discrete soiPCOS eiibedaed in the halo have a fractional polarization below the 3-0 noise level. | The other discrete sources embedded in the halo have a fractional polarization below the $\sigma$ noise level. |
The oxipheral diffuse cussion apscars unpolarized too aud eiven that its surface brightucs sis 20.5 Παιν 1 . aud he seusitivity (1-0) of the lijiear polarization iniage is ~O.08 miJw ο, we can just set a loose 3-0 upper iuit to the fractional polarization of < cousistcut with the values fouud for other relic sources. | The peripheral diffuse emission appears unpolarized too and given that its surface brightness is $\simeq$ 0.5 mJy $^{-1}$ , and the sensitivity $\sigma$ ) of the linear polarization image is $\simeq$ 0.08 mJy $^{-1}$, we can just set a loose $\sigma$ upper limit to the fractional polarization of $<$, consistent with the values found for other relic sources. |
The image obtained with t16 VLA in A configuration vas a EWIIM beam of «1.47 and. in agreement with the € μα.” configuraion. confrius that just a few discrete sources are preset iu the field. | The image obtained with the VLA in A configuration has a FWHM beam of $\times$ and, in agreement with the C array configuration, confirms that just a few discrete sources are present in the field. |
ο the discrete sources. those Iabellec with A. D. C and D (shown in the bottom panel of Fig. 2) ) | Among the discrete sources, those labelled with A, B, C and D (shown in the bottom panel of Fig. \ref{radio}) ) |
are extended. | are extended. |
While À. C. and D show the typical 110rpholoev of “head-tail” radio sources in cluster. source B shows a straight “naked-jet™ morpholoey. | While A, C, and D show the typical morphology of “head-tail” radio sources in cluster, source B shows a straight “naked-jet” morphology. |
Tje total flux deusitv in the region of the “Alain” aud “Subcluster” is z 119-4 uJv. | The total flux density in the region of the “Main” and “Subcluster” is $\simeq$ $\pm$ 4 mJy. |
By subtracting the fiux density of the embedded discrete sources €. D. aud E as derived in the C configuraion data-set (see Table 2)). a flux density of ~ 3645 uJv appears to be associated with he low brightuess diffuse emission. | By subtracting the flux density of the embedded discrete sources C, D, and E as derived in the C configuration data-set (see Table \ref{tab2}) ), a flux density of $\simeq$ $\pm$ 5 mJy appears to be associated with the low brightness diffuse emission. |
This flix deusity value corresponds to a radio. power Pjou=41.0«425107" W | This flux density value corresponds to a radio power $P_{\rm 1400 MHz} = 1.0\times10^{25}$ W $^{-1}$. |
ATSL is part of he ROSAT Briel:est Cluster sample bv Ebeliug et al. ( | A781 is part of the ROSAT Brightest Cluster sample by Ebeling et al. ( |
908). | 1998). |
Its Νταν hο in re 01-2.1. keV. band is 1.1l«10% ore/sec. | Its X-ray luminosity in the 0.1-2.4 keV band is $1.1\times 10^{45}$ erg/sec. |
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