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The same figures also illustrate how the timescale of the sinusoidal variation changes as a [function of rji; with shorter time scales corresponding to faster orbital motion of the closer Lares.
The same figures also illustrate how the timescale of the sinusoidal variation changes as a function of $r_{flare}$ with shorter time scales corresponding to faster orbital motion of the closer flares.
ote how the structures on the reverberation map change Or à very close [lare (rg;=3m: see Fig.
Note how the structures on the reverberation map change for a very close flare $r_{flare}=3m$; see Fig.
SN).
8).
There is no triple maximum on the left hand. side of the A-shaped eature. but the maximum due to focusing emerges on the opposite side.
There is no triple maximum on the left hand side of the $\Lambda$ -shaped feature, but the maximum due to focusing emerges on the opposite side.
This is also shown on Fig.
This is also shown on Fig.
12 where three maxima are visible but. unlike in the case of more distant lares. in this case the lowermost and. micelle maxima are due to gravitational focusing.
12 where three maxima are visible but, unlike in the case of more distant flares, in this case the lowermost and middle maxima are due to gravitational focusing.
The lack of the uppermost and middle maxima on the Ieft hand side of this feature is related to the very large overall gravitational and transverse Doppler redshift.
The lack of the uppermost and middle maxima on the left hand side of this feature is related to the very large overall gravitational and transverse Doppler redshift.
Lt is also caused. by. the faster motion of the Hare (and thus the main flux maximum) combined with the relatively slow propagation of signals slowed. by he Shapiro delay in the vicinity of the black hole.
It is also caused by the faster motion of the flare (and thus the main flux maximum) combined with the relatively slow propagation of signals slowed by the Shapiro delay in the vicinity of the black hole.
In other words. the ratio between the time it takes for the [are o complete a half of one full revolution around. the black role to the signal crossing time decreases with decreasing distance of the Dare from the centre.
In other words, the ratio between the time it takes for the flare to complete a half of one full revolution around the black hole to the signal crossing time decreases with decreasing distance of the flare from the centre.
Phe above effects contribute to the swamping of these two maxima hy the main bright We have demonstrated that the very complex behaviour of the lines is predicted. by a relatively simple. moclel of the orbiting Dare.
The above effects contribute to the swamping of these two maxima by the main bright We have demonstrated that the very complex behaviour of the lines is predicted by a relatively simple model of the orbiting flare.
Our results can be applied. to future observations mace with XMM and particularly Constcllation-X and may help to understand: various processes operating in the vicinity of black holes.
Our results can be applied to future observations made with XMM and particularly Constellation-X and may help to understand various processes operating in the vicinity of black holes.
Fhese results can be used to put. constraints on their masses and spin parameters. the &cometry of the emitting region and test general relativity in the strong gravity regime.
These results can be used to put constraints on their masses and spin parameters, the geometry of the emitting region and test general relativity in the strong gravity regime.
Particularly interesting features seen on our cliagrams are the triple maxima in the temporary iron line profiles.
Particularly interesting features seen on our diagrams are the triple maxima in the temporary iron line profiles.
The micelle maximum is a consequence of strong light bending by the extreme eravitational fields very close to the central black hole and is thus a prediction of general relativity.
The middle maximum is a consequence of strong light bending by the extreme gravitational fields very close to the central black hole and is thus a prediction of general relativity.
Εις mav indicate that a complicated temporal behaviour of the iron line profiles seen in future data may not necessary imply a complicated model but could be explained for example in the framework of the orbiting Ware model.
This may indicate that a complicated temporal behaviour of the iron line profiles seen in future data may not necessary imply a complicated model but could be explained for example in the framework of the orbiting flare model.
AIR. acknowledges support from an Lxternal Research Studentship of Trinity College. Cambridge: an ORS award: and the Stefan. Batory Foundation.
MR acknowledges support from an External Research Studentship of Trinity College, Cambridge; an ORS award; and the Stefan Batory Foundation.
MIX thanks Andrew Fabian and Andrew: Young for discussions.
MR thanks Andrew Fabian and Andrew Young for discussions.
research was performed within projectPHY -Couvection in Stars” of the Austrian Fouds zur Forrderung der lichen Forschuug.
research was performed within project “Convection in Stars” of the Austrian Fonds zur Förrderung der lichen Forschung.
including several rotation periods.
including several rotation periods.
The observations were obtained on ~30 nights between 3 Nov 2001 and 3 March 2002 with a 1024x 1024 Photometries CCD attached to the 0.6m telescope al Van Vleck Observatory. located on the campus of Weslevan University.
The observations were obtained on $\sim$ 30 nights between 8 Nov 2001 and 8 March 2002 with a $\times$ 1024 Photometrics CCD attached to the 0.6m telescope at Van Vleck Observatory, located on the campus of Wesleyan University.
The field of view is 10.2" on a side ancl the size of a pixel is 0.6".
The field of view is $\arcmin$ on a side and the size of a pixel is $\arcsec$.
Four fields (designated A. D. C and D) were chosen to include the largest number of MDM 12À members possible [rom the list of twelve given bv Lulman(2001).
Four fields (designated A, B, C and D) were chosen to include the largest number of MBM 12A members possible from the list of twelve given by \citet{l01}.
. On each clear night. a sequence of 5 one-minute exposures was taken through the Cousins7 filter for each field. as well as twilight flats. bias Iranmies. ancl clark frames.
On each clear night, a sequence of 5 one-minute exposures was taken through the Cousins filter for each field, as well as twilight flats, bias frames, and dark frames.
These were combined into an image of effectively 5 minutes duration but with a ereater dynamic range than would have been possible with a single exposure.
These were combined into an image of effectively 5 minutes duration but with a greater dynamic range than would have been possible with a single exposure.
Also. any effects of non-uniform tracking by the telescope are removed by (his procedure.
Also, any effects of non-uniform tracking by the telescope are removed by this procedure.
Preliminary reductions were done with standard URAF tasks.
Preliminary reductions were done with standard IRAF tasks.
Aperture photometry was performed on all unerowded stars clearly visible on the images using the APPIIOT package in IRAF.
Aperture photometry was performed on all uncrowded stars clearly visible on the images using the APPHOT package in IRAF.
An aperture radius of 7.5 pixels was adopted and an annulus with inner and outer radii of 10 and 15 pixels respectively was used to determine the sky level.
An aperture radius of 7.5 pixels was adopted and an annulus with inner and outer radii of 10 and 15 pixels respectively was used to determine the sky level.
Differential magnitudes on the instrumental svstem. which is close to Cousins I but was nol iranslormed to il (since we had no color data) were computed for all stars by identifving a group of non-variable comparison stars.
Differential magnitudes on the instrumental system, which is close to Cousins I but was not transformed to it (since we had no color data) were computed for all stars by identifying a group of non-variable comparison stars.
This was done by simply. choosing the brightest few stars and averaging (heir magnitudes. taking care not to include any. known association members or field variable stars.
This was done by simply choosing the brightest few stars and averaging their magnitudes, taking care not to include any known association members or field variable stars.
Variables reveal themselves bv their larger than expected scatter relative to the comparison sel during this process and may easily be weeded out.
Variables reveal themselves by their larger than expected scatter relative to the comparison set during this process and may easily be weeded out.
Only one such star was found in our four fields.
Only one such star was found in our four fields.
Using this technique we found that the average error of a single photometric measurement was about 0.005 mag for
Using this technique we found that the average error of a single photometric measurement was about 0.005 mag for
cllects are opposite so that we may expect. o(AMa) to evolve little as far as pure haloes are concerned.
effects are opposite so that we may expect $\sigma$ $M_{\rm vir}$ ) to evolve little as far as pure haloes are concerned.
Let. us consider this quantitatively using a simple mocoel.
Let us consider this quantitatively using a simple model.
Without dissipational galaxv formation. the evolution of the central velocity. dispersion. would. be primarily determined. by. the evolutions of the virial mass CA). the virial radius (rà) and the concentration (ον).
Without dissipational galaxy formation, the evolution of the central velocity dispersion would be primarily determined by the evolutions of the virial mass $\Mvir$ ),the virial radius $\rvir$ ) and the concentration $\cvir$ ).
The velocity dispersion. is expected to increase. (decrease. increase) i£ Au (Gro. 6o) increases while the other two parameters are held constant.
The velocity dispersion is expected to increase (decrease, increase) if $\Mvir$ $\rvir$, $\cvir$ ) increases while the other two parameters are held constant.
Cosmological |N-bods simulations. predict. that all three parameters Moi. ro and e) increase às cosmic time evolves forward.
Cosmological $N$ -body simulations predict that all three parameters $\Mvir$ , $\rvir$ and $\cvir$ ) increase as cosmic time evolves forward.
Suppose στvir(νιrra) where 0 is the velocity dispersion in the central region waithin 0.01 ad. Cus=VCMray ds the circular velocity at the virial raclius. ΕΕr/rsi) is a model-dependent factor relating the two.
Suppose $\sigma = \vvir f(\cvir,r/\rvir)$ where $\sigma$ is the velocity dispersion in the central region within $0.01\rvir$ ), $\vvir=\sqrt{G \Mvir/\rvir}$ is the circular velocity at the virial radius, and $f(\cvir,r/\rvir)$ is a model-dependent factor relating the two.
N-body simulations show that A. reir and eall increase roughly by a factor of 2 [rom 2= 1100 (see. e.g... Wechslerctal. 2002)).
$N$ -body simulations show that $\Mvir$ , $\rvir$ and $\cvir$all increase roughly by a factor of $2$ from $z=1$ to $0$ (see, e.g., \citealt{Wec02}) ).
Then. (i stavs roughly constant and f(es.r£ra) increases by about from >= 1to 0 for an isotropic NEW model (see Lokas&Mammon 2001)).
Then, $\vvir$ stays roughly constant and $f(\cvir,r/\rvir)$ increases by about from $z=1$ to $0$ for an isotropic NFW model (see \citealt{LM01}) ).
Llence we expect some enhancement in the velocity dispersion aa positive coevolution) in the course of the ierarchical growth of a pure dark halo from z=1 to 0.
Hence we expect some enhancement in the velocity dispersion a positive coevolution) in the course of the hierarchical growth of a pure dark halo from $z=1$ to $0$ .
For realistic haloes hosting (clissipationally formed) ealaxies hwdrodynamic simulations can be used to oedict. the evolution of a( Ady).
For realistic haloes hosting (dissipationally formed) galaxies hydrodynamic simulations can be used to predict the evolution of $\sigma$ $\Mvir$ ).
Unfortunately. current ivdrodsnamic simulations co not predict. robustlv the xwvonic elleets on halo structures citealtBlus6.CneO4.Xba09.Pis 0.FeL10)).
Unfortunately, current hydrodynamic simulations do not predict robustly the baryonic effects on halo structures \\citealt{Blu86,Gne04,Aba09,Tis10,Fel10}) ).
Specifically. recent ivdrodsnamic simulations overpredict σ at a given AM citealtTis 10.LoL10)).
Specifically, recent hydrodynamic simulations overpredict $\sigma$ at a given $\Mvir$ \\citealt{Tis10,Fel10}) ).
The finding that the AZuu-o relation does not evolve for QOxz1. ollers new insights into galaxy formation and evolution.
The finding that the $\Mvir$ $\sigma$ relation does not evolve for $0 \le z \le 1$ offers new insights into galaxy formation and evolution.
Lt implies that the dynamical property of the central galaxy of a halo has little to do with its history but is dictated by the final halo virial mass at least since 1.
It implies that the dynamical property of the central galaxy of a halo has little to do with its history but is dictated by the final halo virial mass at least since $z=1$ .
Remarkably. this is the case for all halocs probed. (with a2100kms +).
Remarkably, this is the case for all haloes probed (with $\sigma \ga 100 \kms$ ).
Implications of this linding are discussed below in the context of the coevolution of Mo. σ and Ad,.
Implications of this finding are discussed below in the context of the coevolution of $\Mvir$, $\sigma$ and $\Mstars$.
relation: Tho. Al,-o relation at 2=O shows a power-law relation M,-xaM with a varving power-law index say ranging from 2.9. 44) for AL,LOOM. 160 2.02.9] for AL<1027 ML...
The $\Mstars$ $\sigma$ relation at $z=0$ shows a power-law relation $\Mstars \propto \sigma^{\gamma_{\rm SM}}$ with a varying power-law index $\gamma_{\rm SM}$ ranging from [2.9, 4.4] for $\Mstars > 10^{11.5} \Msun$ to [2.0,2.9] for $\Mstars < 10^{10.5} \Msun$ .
Let us compare the Ad.-o relation with power- correlations between luminosity and. internal velocity parameter. namely the Tullv-Fisher relation for the late-tvpe population and the Faber-Jackson. relation for the carly-tvpe population.
Let us compare the $\Mstars$ $\sigma$ relation with power-law correlations between luminosity and internal velocity parameter, namely the Tully-Fisher relation for the late-type population and the Faber-Jackson relation for the early-type population.
“Phe observed. Tullv-Fisher. relation exponent spp Lies between 2.5 and 3.5 (see 82.3 or Pizagno 2007)).
The observed Tully-Fisher relation exponent $\gamma_{\rm TF}$ lies between 2.5 and 3.5 (see 2.3 or \citealt{Piz07}) ).
The traditional value for the Faber-Jackson exponent συ for earlv-tvpe. galaxies is =4.
The traditional value for the Faber-Jackson exponent $\gamma_{\rm FJ}$ for early-type galaxies is $\approx 4$.
However. an extensive analysis of SDSS DRS carly-type galaxies reveals that 5p varies systematically from 2.7+0.2 at L, to 4.6+04 at the upper luminosity end (Choictal. 2007: see also Desrochesetal. 2007)).
However, an extensive analysis of SDSS DR5 early-type galaxies reveals that $\gamma_{\rm FJ}$ varies systematically from $2.7 \pm 0.2$ at $L_*$ to $4.6 \pm 0.4$ at the upper luminosity end \citealt{Cho07}; see also \citealt{Des07}) ).
The abundance matching M,-e relation for all galaxies can match well these Faber-Jackson/Tully-Fisher relations in conjunction. with measured AL,/L ratios citealt Dol03)).
The abundance matching $\Mstars$ $\sigma$ relation for all galaxies can match well these Faber-Jackson/Tully-Fisher relations in conjunction with measured $\Mstars/L$ ratios \\citealt{Bel03}) ).
In Fig.
In Fig.
7 the AL- relation at z—1 is compared with that at >=0 based on two VDEs and two SMES that are meant to encompass the current range of observations.
\ref{MstarV} the $\Mstars$ $\sigma$ relation at $z=1$ is compared with that at $z=0$ based on two VDFs and two SMFs that are meant to encompass the current range of observations.
As can be seen in the figure. the implied. evolution depends sensitively on the adopted SALE and to a less degree on the adopted. VDE.
As can be seen in the figure, the implied evolution depends sensitively on the adopted SMF and to a less degree on the adopted VDF.
The relation based on the COSMOS SME is consistent with zero evolution in &(M,) between s=1 and 0.
The relation based on the COSMOS SMF is consistent with zero evolution in $\sigma(\Mstars)$ between $z=1$ and $0$.
On the other hand. the relation based on the Spitzer SME (a ἱνρίσα downsizing SAIL) implies a dilferential evolution in ofAl,): for AM,1044A1. 1e implied. evolution in σ with redshift at fixed. AZ, is negative while it is positive for ALοML.s
On the other hand, the relation based on the Spitzer SMF (a typical downsizing SMF) implies a differential evolution in $\sigma(\Mstars)$: for $\Mstars \ga 10^{11} M_{\odot}$ the implied evolution in $\sigma$ with redshift at fixed $\Mstars$ is negative while it is positive for $\Mstars \la 10^{11} M_{\odot}$.
‘This means that based on the downsizing SME a galaxy at 2=1 would have a gashallower (steeper) mass profile than the local counterpart of the same stellar mass for AL,101AJ. (AL,101ALL).
This means that based on the downsizing SMF a galaxy at $z=1$ would have a shallower (steeper) mass profile than the local counterpart of the same stellar mass for $\Mstars \ga 10^{11} M_{\odot}$ $\Mstars \la 10^{11} M_{\odot}$ ).
llow the above results on the evolution in ald.) are compared. with other independent results on the structural evolutions of galaxies?
How the above results on the evolution in $\sigma(\Mstars)$ are compared with other independent results on the structural evolutions of galaxies?
First of all. we find little evolution in c(z) at M,=104M. for OxcS from a careful analysis of the data in the literature (see Fig. 8)).
First of all, we find little evolution in $\sigma(z)$ at $\Mstars=10^{11}\Msun$ for $0 \la z \la 1.8$ from a careful analysis of the data in the literature (see Fig. \ref{Vzevol}) ).
This is in excellent agreement with the above abundance matching results.
This is in excellent agreement with the above abundance matching results.
However. it cannot unfortunately distinguish. the abundance matching results because AZ,=101AL. happens to be the critical mass for the downsizing SME at which the evolution changes the sign.
However, it cannot unfortunately distinguish the abundance matching results because $\Mstars= 10^{11} \Msun$ happens to be the critical mass for the downsizing SMF at which the evolution changes the sign.
Second. many observational studies find a negative size evolution of galaxies with redshift implving a more steeply declining stellar mass profile at a higher 2 citealtEruQT.veW OS.CimOS.vanDOS)).
Second, many observational studies find a negative size evolution of galaxies with redshift implying a more steeply declining stellar mass profile at a higher $z$ \\citealt{Tru07,vdW08,Cim08,vanD08}) ).
However. more recent studies find that stellar mass density. profiles of the inner regions up to several kilo-parsees are consistent with no evolution for massive galaxies with AZ,10A4. (Llopkins 2009)).
However, more recent studies find that stellar mass density profiles of the inner regions up to several kilo-parsecs are consistent with no evolution for massive galaxies with $\Mstars \ga 10^{11} M_{\odot}$ \citealt{Hop09,Bez09}) ).
According to these stuclies. however. it is not clear whether stellar mass density profiles evolve bevond the inner regions.
According to these studies, however, it is not clear whether stellar mass density profiles evolve beyond the inner regions.
Whatever the case these results can only imply a similar or larger e at fixed AZ, at a higher redshift contradicting the abundance matching results based on the downsizing SME.
Whatever the case these results can only imply a similar or larger $\sigma$ at fixed $\Mstars$ at a higher redshift contradicting the abundance matching results based on the downsizing SMF.
What do hvdrodynamic simulations predict. on the evolution of the relation between AZ, and σι Llopk
What do hydrodynamic simulations predict on the evolution of the relation between $\Mstars$ and $\sigma$?
insetal.(2000b) combine galaxy merging with hvedrodynamic simulation to find a little evolution of & with z at fixed M, for anv 10M.xAL,=QM.
\citet{Hop09b} combine galaxy merging with hydrodynamic simulation to find a little evolution of $\sigma$ with $z$ at fixed $\Mstars$ for any $10^9\Msun \le \Mstars \le 10^{12} \Msun$.
In particular. Hopkinsetal.(2009b) explicitly. predict that the Al,-o relation evolves little between z=1 and 0.
In particular, \citet{Hop09b} explicitly predict that the $\Mstars$ $\sigma$ relation evolves little between $z=1$ and $0$.
Hopkinsetal.(2010). take into account a number of possible cllects in their cosmological simulations and [find slow evolutions of σ with z.
\citet{Hop10} take into account a number of possible effects in their cosmological simulations and find slow evolutions of $\sigma$ with $z$ .
These results are consistent with the evolution in &6(CAL)with 5 based on the COSMOS SME but not with the cdownsizing SME.
These results are consistent with the evolution in $\sigma(\Mstars)$with $z$ based on the COSMOS SMF but not with the downsizing SMF.
evolutions? We have already. compared the evolving. VDE with the evolving HIME and the evolving SME.
We have already compared the evolving VDF with the evolving HMF and the evolving SMF.
We find that he evolutions of the HILME. the VDE and the SME appear concordant. but that the downsizing SAIF is. disfavoured cause its implied. structural evolutions are unlikely.
We find that the evolutions of the HMF, the VDF and the SMF appear concordant, but that the downsizing SMF is disfavoured because its implied structural evolutions are unlikely.
Lt is clearly worthwhile to put the VDE evolution. in a xoader context of recent) cosmological observations on ealaxy evolutions.
It is clearly worthwhile to put the VDF evolution in a broader context of recent cosmological observations on galaxy evolutions.
The lensing constrained WDE evolutions show that he number density of massive carly-tvpe galaxies (σ ) not only evolves significantly.see but also shows a cillerentialevolution (see Fig. 1)):
The lensing constrained VDF evolutions show that the number density of massive early-type galaxies $ \sigma \ga 220 \kms$ ) not only evolves significantly but also shows a differentialevolution (see Fig. \ref{VDFs}) ):
the higher the velocity dispersion. the faster the number density evolution (the
the higher the velocity dispersion, the faster the number density evolution (the
entropy cores approach one another through shocked gas, they are continuously stripped as long as the ram pressure exceeds the thermal pressure within the cores, 4) stripping continues until all the gas beyond the core radius of the dark matter distribution has been stripped and then the remainder of the is stripped in bulk due to the nearly constant binding gasenergy per unit mass of the core gas, 5) for off-axis mergers, the cores can survive beyond the point of closest approach, after which ram pressure stripping becomes less efficient and the surviving cores expands 6) the chaotic entropy distribution of the mergedadiabatically, cluster drives large scale convection and some of the the shock energy that was deposited in the cluster outskirts is transported into the core gas, 7) eventually the two dark matter halos merge, and the lowest entropy gas settles into the minimum of the gravitational potential.
entropy cores approach one another through shocked gas, they are continuously stripped as long as the ram pressure exceeds the thermal pressure within the cores, 4) stripping continues until all the gas beyond the core radius of the dark matter distribution has been stripped and then the remainder of the gas is stripped in bulk due to the nearly constant binding energy per unit mass of the core gas, 5) for off-axis mergers, the cores can survive beyond the point of closest approach, after which ram pressure stripping becomes less efficient and the surviving cores expands adiabatically, 6) the chaotic entropy distribution of the merged cluster drives large scale convection and some of the the shock energy that was deposited in the cluster outskirts is transported into the core gas, 7) eventually the two dark matter halos merge, and the lowest entropy gas settles into the minimum of the gravitational potential.
The contours, hardness ratio map, and surface brightness X-rayprofiles of A1758N are consistent with a scenario in which the NW subcluster is presently moving toward the north and the SE subcluster is presently moving toward the SE (i.e., 5 above).
The X-ray contours, hardness ratio map, and surface brightness profiles of A1758N are consistent with a scenario in which the NW subcluster is presently moving toward the north and the SE subcluster is presently moving toward the SE (i.e., stage 5 above).
The NW subcluster has been stripped down to its stageinner 80 kpc and the SE subcluster to its central 115 kpc.
The NW subcluster has been stripped down to its inner 80 kpc and the SE subcluster to its central 115 kpc.
The survival of the two cores indicates that the core radii of the dark matter distributions in the merging systems are less than about 100 kpc.
The survival of the two cores indicates that the core radii of the dark matter distributions in the merging systems are less than about 100 kpc.
This is consistent with estimates deduced from Chandra observations of relaxed clusters (David et 22001, Arabadjis, Bautz, Garmire 2002, Allen, Schmidt, Fabian 2002).
This is consistent with estimates deduced from Chandra observations of relaxed clusters (David et 2001, Arabadjis, Bautz, Garmire 2002, Allen, Schmidt, Fabian 2002).
Based on the central densities and temperatures derived above, the central gas entropies are 120 and 110 keV cm? for the SE and NW subclusters.
Based on the central densities and temperatures derived above, the central gas entropies are 120 and 110 keV $^2$ for the SE and NW subclusters.
These values are consistent with the central regions of relaxed clusters (e.g., Lloyd-Davies, Ponman, Cannon 2000) and show that this gas was not strongly shocked during the merger.
These values are consistent with the central regions of relaxed clusters (e.g., Lloyd-Davies, Ponman, Cannon 2000) and show that this gas was not strongly shocked during the merger.
The hardness ratio map shows that the emission from the gas in the wakes is also soft, indicating that this was without being shocked.
The hardness ratio map shows that the emission from the gas in the wakes is also soft, indicating that this gas was stripped without being strongly shocked.
The detached gasnature of the strippedwake in the SE stronglysubcluster, as evident in Fig. 5,,
The detached nature of the wake in the SE subcluster, as evident in Fig. \ref{fig:adapt},
indicates that ram pressure stripping is lessening, as it should after the point of closest approach.
indicates that ram pressure stripping is lessening, as it should after the point of closest approach.
Combining the derived density and temperature jumps across the NW edge gives a pressure jump of 1.4+0.3 (lo error).
Combining the derived density and temperature jumps across the NW edge gives a pressure jump of $1.4 \pm 0.3$ $1 \sigma$ error).
The pressure in the core should be greater than that in the ambient medium due to ram pressure; however, the error on the pressure jump limits the relative between the two subclusters to be less than approximately velocity1600 km !.
The pressure in the core should be greater than that in the ambient medium due to ram pressure; however, the error on the pressure jump limits the relative velocity between the two subclusters to be less than approximately 1600 km $^{-1}$.
The curved shape of the wakes in A1758N shows that the collision of the two systems was not head-on.
The curved shape of the wakes in A1758N shows that the collision of the two systems was not head-on.
The SE subcluster to have been deflected from a NE trajectory towards the SE, appearswhile the NE cluster appears to have been deflected from a western trajectory towards the north.
The SE subcluster appears to have been deflected from a NE trajectory towards the SE, while the NE cluster appears to have been deflected from a western trajectory towards the north.
While we cannot determine the detailed merger kinematics without a high resolution temperature map, which would require significantly better photon statistics, we can check the validity of our proposed scheme by simply integrating the equations of motion backward for the two systems from their present positions.
While we cannot determine the detailed merger kinematics without a high resolution temperature map, which would require significantly better photon statistics, we can check the validity of our proposed scheme by simply integrating the equations of motion backward for the two systems from their present positions.
To do this we assume: 1) the SE subcluster is presently moving toward the SE and the NW subcluster is presently moving north, 2) the two subclusters can be represented masses with masses to the virial mass of a 7 keVby pointcluster (using the scaling equalrelations in Bryan Norman 1998), and 3) the orbits are in the plane of the sky.
To do this we assume: 1) the SE subcluster is presently moving toward the SE and the NW subcluster is presently moving north, 2) the two subclusters can be represented by point masses with masses equal to the virial mass of a 7 keV cluster (using the scaling relations in Bryan Norman 1998), and 3) the orbits are in the plane of the sky.
Figure 9 shows the resulting trajectories assuming present velocities for the NW and SE subclusters of 500 or 1000 km s! in the plane of the sky.
Figure \ref{fig:orbit} shows the resulting trajectories assuming present velocities for the NW and SE subclusters of 500 or 1000 km $^{-1}$ in the plane of the sky.
While this is a highly idealized calculation, both sets of trajectories have similar curvatures as the wakes in Fig. 5..
While this is a highly idealized calculation, both sets of trajectories have similar curvatures as the wakes in Fig. \ref{fig:adapt}.
Of course, the extended mass distribution in the clusters would soften the deflection angle near pericenter.
Of course, the extended mass distribution in the clusters would soften the deflection angle near pericenter.
Fig.
Fig.
5 shows that the wake of the SE subcluster is brightest where the curvature is the greatest which occurs at pericenter where ram pressure stripping is the strongest.
\ref{fig:adapt} shows that the wake of the SE subcluster is brightest where the curvature is the greatest which occurs at pericenter where ram pressure stripping is the strongest.