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In thisframework?.. angular differential imaging (ADI) can be applied to reduce the speckle noise further. | In this, angular differential imaging (ADI) can be applied to reduce the speckle noise further. |
Various codes have been written to perform ADI on real images (see Maroisetal. 2006)). | Various codes have been written to perform ADI on real images (see \citealt{Ma06a}) ). |
Here. we considered a variant of this method that we defined as azimuthal filtering Cazimuthal". meaning along ares at à constant radius). | Here, we considered a variant of this method that we defined as azimuthal filtering (”azimuthal”, meaning along arcs at a constant radius). |
This procedure is composed of the following steps: While this procedure does not completely eliminate the impact of static speckles. it also works well for quasi-static speckles. which are speckles having a lifetime longer than field rotation but shorter than the total exposure time. | This procedure is composed of the following steps: While this procedure does not completely eliminate the impact of static speckles, it also works well for quasi-static speckles, which are speckles having a lifetime longer than field rotation but shorter than the total exposure time. |
In this section. we review the most important. results obtained from our simulations. | In this section we review the most important results obtained from our simulations. |
As said in previous sections. We eXpect a significant improvement in the contrast using the MDI method compared to a simple S-SDI. when exploiting all of the many monochromatic images provided by an IPS. | As said in previous sections, we expect a significant improvement in the contrast using the MDI method compared to a simple S-SDI, when exploiting all of the many monochromatic images provided by an IFS. |
In particular we expect that the contrast scales with the square root of the number of independent single differences that we can realize when using the whole spectrum. | In particular we expect that the contrast scales with the square root of the number of independent single differences that we can realize when using the whole spectrum. |
Α΄ further | A further |
which was part of a entirely different object at each of a series of earlier redshifts. | which was part of a entirely different object at each of a series of earlier redshifts. |
We refer to this fraction as the “accreted fraction” and we then estimate the distribution of accreted fraction for the halos in each of our four mass ranges and for accretion since redshifts of 0.5, 1, 2 and 3. | We refer to this fraction as the “accreted fraction” and we then estimate the distribution of accreted fraction for the halos in each of our four mass ranges and for accretion since redshifts of 0.5, 1, 2 and 3. |
For the purposes of this calculation we define the “core” of each z0 halo to consist of the 100 most bound particles in its main subhalo. | For the purposes of this calculation we define the “core” of each $z=0$ halo to consist of the 100 most bound particles in its main subhalo. |
Each particle is considered to be part of a disjoint object at some earlier redshift (and thus part of the accreted fraction) if at that time it was more than 100h~'kpce (physical) from the centre of the largest progenitor of the core (defined by calculating the mutual gravitational potential of all 100 core particles and picking the particle with the lowest value). | Each particle is considered to be part of a disjoint object at some earlier redshift (and thus part of the accreted fraction) if at that time it was more than $100h^{-1}$ kpc (physical) from the centre of the largest progenitor of the core (defined by calculating the mutual gravitational potential of all 100 core particles and picking the particle with the lowest value). |
The results of this exercise are shown in Fig. 5.. | The results of this exercise are shown in Fig. \ref{fig:fig5}. |
Each panel refers to one of our ranges of halo mass and contains | Each panel refers to one of our ranges of halo mass and contains |
Whilst observations of powerful. racto-loud Active Galactic Nuelei (AGN) were an early. probe of the distant. Universe summary). starburst galaxies are three or more orders of magnitudes. less luminous at racio wavelengths and hence dillieult to observe at large distances. | Whilst observations of powerful, radio-loud Active Galactic Nuclei (AGN) were an early probe of the distant Universe , starburst galaxies are three or more orders of magnitudes less luminous at radio wavelengths and hence difficult to observe at large distances. |
However the deepest. radio surveys at GCOLIZz now reach an rms below 10μονete). | However the deepest radio surveys at GHz now reach an rms below $10\uJy$. |
These deep radio observations reveal a (very well characterised) up-turn in the [Euclidean normalised sources counts below mmy above that predicted from the extrapolation of the AGN counts measured at brighter [ux densities. | These deep radio observations reveal a (very well characterised) up-turn in the Euclidean normalised sources counts below mJy above that predicted from the extrapolation of the AGN counts measured at brighter flux densities. |
This up-turn has been attributed to the emergence of a star forming galaxy (SECO population. requiring strong evolution of the SEC radio luminosity function.2007).. although some authors argue that there is a significant. contribution due to relatively weak | This up-turn has been attributed to the emergence of a star forming galaxy (SFG) population, requiring strong evolution of the SFG radio luminosity function, although some authors argue that there is a significant contribution due to relatively weak |
Supermassive black holes have been couvincinely detected in the centers of some nearby galaxies (οποιον Richstone 1995). | Supermassive black holes have been convincingly detected in the centers of some nearby galaxies (Kormendy Richstone 1995). |
I&ormieudy: Gebhardt (2001. hereafter IKCG2001) eave a comprehleusive review of receut black hole discoveries made with theTelescope IST). | Kormendy Gebhardt (2001, hereafter KG2001) gave a comprehensive review of recent black hole discoveries made with the (HST). |
A tight correlation between black hole mass auc bulge velocity dispersion is confirmed. | A tight correlation between black hole mass and bulge velocity dispersion is confirmed. |
They noticed that black hole mass correlates with the luminosity of “pseudobulges” in disk ogalaxies. elliptical galaxies aud the bulges of disk. ealaxies. but is independent of the Iuuiuositv of galaxy disks. | They noticed that black hole mass correlates with the luminosity of “pseudobulges” in disk galaxies, elliptical galaxies and the bulges of disk galaxies, but is independent of the luminosity of galaxy disks. |
The correlation stronglv suggests a causal connection between t1e formation aud evolution of the black hole and the bulge but the nature of this connection τομας uuknowl. | The correlation strongly suggests a causal connection between the formation and evolution of the black hole and the bulge but the nature of this connection remains unknown. |
It is interesting to check whether this correlation still applies to both larger aud simaller spherical systems. | It is interesting to check whether this correlation still applies to both larger and smaller spherical systems. |
We may even speculate whether the correlation extends to systems with dispersion as ow as that of elobular clusters. since the elobular clusters are also sclferavitating splerical svsteus simular to galactic bulges. | We may even speculate whether the correlation extends to systems with dispersion as low as that of globular clusters, since the globular clusters are also self-gravitating spherical systems similar to galactic bulges. |
Using the AIpy 0 correlation. a crude estimate for the possible black hole mass in elolnlar clusters can be obtained. | Using the $_{BH}$ – $\sigma$ correlation, a crude estimate for the possible black hole mass in globular clusters can be obtained. |
For a typical massive globular cluster having a dispersion of the order of 10 l a black hole mass of about «10? NINE, is expected. | For a typical massive globular cluster having a dispersion of the order of 10 $^{-1}$, a black hole mass of about $\times\,10^3$ $_\odot$ is expected. |
In certain galaxies. the 1ack hole directly reveals itself through its associated accretion aud activity. | In certain galaxies, the black hole directly reveals itself through its associated accretion and activity. |
Such activity can hardly happen in elobulay clusters due to shortage of eas. | Such activity can hardly happen in globular clusters due to shortage of gas. |
However. receut. N-ray. observations of several starburst galaxies (6.9. M82. NGC 1038/39) reveal the existence of iutermiediate-niass black hole im starburst regions which are related to the formation of elolar clusters (INiuucet et al. | However, recent X-ray observations of several starburst galaxies (e.g. M82, NGC 4038/39) reveal the existence of intermediate-mass black hole in starburst regions which are related to the formation of globular clusters (Kaaret et al. |
2001: Matsiunioto et al. | 2001; Matsumoto et al. |
2001: Fabbiano. Zezas. Murray. 2001). | 2001; Fabbiano, Zezas, Murray 2001). |
The preseuce of a black hole iu à globular cluster affects the stellar deusity profile aud the central stellar ΠΕ | The presence of a black hole in a globular cluster affects the stellar density profile and the central stellar dynamics. |
With tιο dynamical detection sensitivity currently available. black hole mass as low as 1000 AL. can hardly be ideuti&ied (wan der Marel 2001). | With the dynamical detection sensitivity currently available, black hole mass as low as 1000 $_\odot$ can hardly be identified (van der Marel 2001). |
So far. the ouly example was presented by Ceblardt et al. ( | So far, the only example was presented by Gebhardt et al. ( |
2000) for MI5 wich Ίαν possibly host a black hole of the order of 10° ML... | 2000) for M15 which may possibly host a black hole of the order of $^3$ $_\odot$. |
rates in the universe (Per Fall 1995). | rates in the universe (Pei Fall 1995). |
LW the observed metallicities in QSO absorption systems are common. then their interpretation as galactic disks implies that substantial evolution has taken place since z~3. | If the observed metallicities in QSO absorption systems are common, then their interpretation as galactic disks implies that substantial evolution has taken place since $z\sim 3$. |
Lf the quantity of dust on cosmic scales also follows such a trend. then one niv expect the ellects of obscuration to high redshift to be reduced relative to non-evolving predictions. | If the quantity of dust on cosmic scales also follows such a trend, then one may expect the effects of obscuration to high redshift to be reduced relative to non-evolving predictions. |
In this paper. we continue to model the effects. of intervening galactic dust on the background. universe at optical wavelengths using a more generalised model where the dust. content evolves. | In this paper, we continue to model the effects of intervening galactic dust on the background universe at optical wavelengths using a more generalised model where the dust content evolves. |
We explore the effects of our predictions on quasar number counts in the optical and their implication for quasar evolution. | We explore the effects of our predictions on quasar number counts in the optical and their implication for quasar evolution. |
This paper is organised as follows: The next section briellv describes the generalised model and. assumptions. | This paper is organised as follows: The next section briefly describes the generalised model and assumptions. |
Section 3. describes the model parameters and their values assumed in our calculations. | Section \ref{mprev}
describes the model parameters and their values assumed in our calculations. |
Mocdel results are presented and analysed in Section 4.. | Model results are presented and analysed in Section \ref{rests}. |
Implications on quasar statistics and evolution are discussed in Section 5.. | Implications on quasar statistics and evolution are discussed in Section \ref{QSOev}. |
Other implications are discussed in Section G6 and. all results are summarised in Section 7.. | Other implications are discussed in Section \ref{evmodd} and all results are summarised in Section \ref{concfour}. |
Unless otherwise stated. all caleulations assume a Friedmann cosmology with qa=0.5. and Hubble parameter hoy=1 where Ly=50bs5kmsAlpe | Unless otherwise stated, all calculations assume a Friedmann cosmology with $q_{0}=0.5$, and Hubble parameter $h_{50}=1$ where $H_{0}=50h_{50}\, \rm km\,s^{-1}\,Mpc^{-1}$. |
We caleulate the probability distribution in total dust optical depth from model ealaxics along any random line-ol-sight as a function of redshift by following the method oesented in Masci Webster (1995). | We calculate the probability distribution in total dust optical depth from model galaxies along any random line-of-sight as a function of redshift by following the method presented in Masci Webster (1995). |
his was based on a method introduced by Wright (1986) which did not include any ellects of evolution with redshift. | This was based on a method introduced by Wright (1986) which did not include any effects of evolution with redshift. |
Llere we &eneralise his model by considering the possibility. of evolution. in he dust. properties of galaxies. | Here we generalise this model by considering the possibility of evolution in the dust properties of galaxies. |
In the discussion below zux unless otherwise indicated. by a subscript. we celine 7 to » the total optical depth encountered by emitted. photons and measured. in an (cllectively a À= 4400A)). | In the discussion below and unless otherwise indicated by a subscript, we define $\tau$ to be the total optical depth encountered by emitted photons and measured in an (effectively at $\lambda=4400$ ). |
We assume the following properties for individua absorbing galaxies. | We assume the following properties for individual absorbing galaxies. |
Following previous studies (eg. | Following previous studies (eg. |
Wrieh 1986. Leister Ostriker LOSS). we model galaxies as randomly. tilte exponential disks. where the optical depth through a [ace-on disk decreases exponentially with distance r from the center: ry ds à characteristic radius and. 7o( the value of τ through the center of the galaxy (r=0). | Wright 1986, Heisler Ostriker 1988), we model galaxies as randomly tilted exponential disks, where the optical depth through a face-on disk decreases exponentially with distance $r$ from the center: $r_{0}$ is a characteristic radius and $\tau_{0}(z)$, the value of $\tau$ through the center of the galaxy $(r=0)$. |
The redshift dependence o£ 7) is due to the increase in absorber rest fraume frequeney with redshift. | The redshift dependence of $\tau_{0}$ is due to the increase in absorber rest frame frequency with redshift. |
Since we wish to model the observed. B-band. optical depth to 286. we require an extinction law £(A)=rfTg that extends to wavelengths. of ~630.. | Since we wish to model the observed $B$ -band optical depth to $z\simlt6$, we require an extinction law $\xi(\lambda)\equiv\tau_{\lambda}/\tau_{B}$ that extends to wavelengths of $\sim630$. |
. We use the analytical fit for €(A) as derived by Pei (1992) for cilfuse galactic dust in the range 500ASAS25m. The optical depth in an observers frame through an absorber at redshift z (Tu(2) in equation 1)) can be written: where 7g is the D-band optical depth through the center of an individual galactic absorber. | We use the analytical fit for $\xi(\lambda)$ as derived by Pei (1992) for diffuse galactic dust in the range $500{\rm\AA}\simlt\lambda\simlt25\mu$ m. The optical depth in an observer's frame through an absorber at redshift $z$ $\tau_{0}(z)$ in equation \ref{expr}) ) can be written: where $\tau_{B}$ is the $B$ -band optical depth through the center of an individual galactic absorber. |
Equation (2)) must be mocified if the dust content in cach galaxy is assumed to evolve with cosmic time. | Equation \ref{tz}) ) must be modified if the dust content in each galaxy is assumed to evolve with cosmic time. |
The optical depth seen through the center of a single absorber at some redshift. τος). will depend on the quantity of dust. formed roni past stellar processes. | The optical depth seen through the center of a single absorber at some redshift, $\tau_{0}(z)$, will depend on the quantity of dust formed from past stellar processes. |
Por simplicity. we assume all galaxies form simultaneously. maintain a constant space clensity. and increase in dust content at a rate that is uniform hroughout. | For simplicity, we assume all galaxies form simultaneously, maintain a constant space density, and increase in dust content at a rate that is uniform throughout. |
We also assume no evolution in the dust. law £(A) with redshift. | We also assume no evolution in the dust law $\xi(\lambda)$ with redshift. |
Even though a lower mean metallicity at ugh redshift may suggest a dillerent wavelength dependence or the dust law. there is no evidence from local observations of the dilfuse ISM to support this view (eg. | Even though a lower mean metallicity at high redshift may suggest a different wavelength dependence for the dust law, there is no evidence from local observations of the diffuse ISM to support this view (eg. |
Whittet 1992). | Whittet 1992). |
We parameterise evolution in dust content by following simulations of the formation of heavy metals in the cold dark matter scenario. of. galaxy formation. by Blain Longair (1993a. 1993b). | We parameterise evolution in dust content by following simulations of the formation of heavy metals in the cold dark matter scenario of galaxy formation by Blain Longair (1993a, 1993b). |
These authors assume that galaxies orm bv the coalescence of gaseous. protocloucs through ucrarchical clustering as prescribed. by Press Schechter (1974). | These authors assume that galaxies form by the coalescence of gaseous protoclouds through hierarchical clustering as prescribed by Press Schechter (1974). |
A fixed fraction of the mass involved in each merger event is converted. into stars. leading to the formation of wavy metals and. dust. | A fixed fraction of the mass involved in each merger event is converted into stars, leading to the formation of heavy metals and dust. |
Lt was assumed that the energy iberateck through stellar. radiation. was absorbed by dus and. re-raciated into the far-infrared. | It was assumed that the energy liberated through stellar radiation was absorbed by dust and re-radiated into the far-infrared. |
“Phey found that such radiation can contribute substantially to the far-inlrarec vackerounc intensity from which they use to constrain a model for the formation of heavy metals as a function of cosmic time. | They found that such radiation can contribute substantially to the far-infrared background intensity from which they use to constrain a model for the formation of heavy metals as a function of cosmic time. |
Their models show that the comoving density of heavy metals created by some redshift z. given that star formation commenced at some epoch ssp follows the form We assume that a fixed. fraction of heavy metals condense into dust. grains so that the comoving density in dust. Qu(2). follows a similar dependence as equation (3)). | Their models show that the comoving density of heavy metals created by some redshift $z$, given that star formation commenced at some epoch $z_{SF}$ follows the form We assume that a fixed fraction of heavy metals condense into dust grains so that the comoving density in dust, $\Omega_{d}(z)$, follows a similar dependence as equation \ref{omegaZ}) ). |
The density in dust relative to the present.closure density in my exponential disks per unit comoving volume is given by where p,=BUG/SxC and M, is the dust mass in a single exponential disk. | The density in dust relative to the presentclosure density in $n_{0}$ exponential disks per unit comoving volume is given by where $\rho_{c}=3H_{0}^{2}/8\pi G$ and $M_{d}$ is the dust mass in a single exponential disk. |
This mass can be estimated. using 150.17-24 from Spitzer (1978) where the total density in dust. fa ds related to the extinction ely along a path length £ in kpe by | This mass can be estimated using Eq.7-24 from Spitzer (1978) where the total density in dust, $\rho_{d}$ , is related to the extinction $A_{V}$ along a path length $L$ in kpc by |
above. this requires the IIT disk to be inhereutly elougate with an axis ratio of at least 2:1. | above, this requires the HI disk to be inherently elongated with an axis ratio of at least 2:1. |
Such a highly nou circular disk would be very uuusual. | Such a highly non circular disk would be very unusual. |
Further. the imucr regions of the ealaxy (νο, the distance at which the rotation curve of Carignanctal.(1990) ooeaks) will complete one rotation in ~ NO Ann. while the rotation period at the edge of the disk is ~ 1 Cor. | Further, the inner regions of the galaxy (i.e. the distance at which the rotation curve of \cite{carignan90} peaks) will complete one rotation in $\sim$ 80 Myr, while the rotation period at the edge of the disk is $\sim$ 1 Gyr. |
Houce. his differeutial rotation will wine up any clongation in the| disk on a timescale that is short compared to the age of he galaxy. | Hence, this differential rotation will wind up any elongation in the disk on a timescale that is short compared to the age of the galaxy. |
Alternatively. as first proposed by. Loetal.(1993).. the observed velocity field of GRS could also be the result of radial mo 1 the eas Le expansion or contraction. | Alternatively, as first proposed by \cite{lo93}, the observed velocity field of GR8 could also be the result of radial motions in the gas i.e expansion or contraction. |
Since t the inclination of tje galaxy ΕΕ it is ot possible to distinguish between nsvard and outware motions. | Since the sign of the inclination of the galaxy is unknown, it is not possible to distinguish between inward and outward radial motions. |
Large scale bulk radial gas flows. al ifficult to understaxl in the context of normal spiral galaxies. could nonetheless be plausible iu siuall ea ike (115. | Large scale bulk radial gas flows, although difficult to understand in the context of normal spiral galaxies, could nonetheless be plausible in small galaxies like GR8. |
Iu models of dwart ealaxy formation a lon. enerev iyectce into the ISAL from stellar wiids and supernova explosions could daive significant expansive motions m the gasο | In models of dwarf galaxy formation and evolution, energy injected into the ISM from stellar winds and supernova explosions could drive significant expansive motions in the gas. |
Iu fact. in such inodels. « axies below a critical halo circular velocity of ~ LOO lare expected to lose a sjeuificaut fraction of their ISM. from the first burst of star formation (e.g. Dekel&Silk(1986).. 2)). | In fact, in such models, dwarf galaxies below a critical halo circular velocity of $\sim$ 100 are expected to lose a significant fraction of their ISM from the first burst of star formation (e.g. \cite{dekel86}, \cite{efstathiau00}) ). |
Expulsion of the ISM because of the energy input frou superiovae is also postulated as a possible mechlauisui for produci dwarf elliptical galaxies from eas rich progenitors (6.8B. Aliralda-Exscude Rees 1997). | Expulsion of the ISM because of the energy input from supernovae is also postulated as a possible mechanism for producing dwarf elliptical galaxies from gas rich progenitors (e.g. Miralda-Escude Rees 1997). |
Observatiounallv. outflows of ionized material have been seen iu star bursting (wart ealaxies (e.gB. Alay al. | Observationally, outflows of ionized material have been seen in star bursting dwarf galaxies (e.g. Marlowe et al. |
1995). | 1995). |
Of course. these models deal with the expulsion of hot superuovae heated eas, where as. in tUs instance we are dealing with cold neutral gas. | Of course, these models deal with the expulsion of hot supernovae heated gas, where as, in this instance we are dealing with cold neutral gas. |
For sufficiently small galaxies however. inodoel calculations (Ferrara Tolstoy 2000) suggest that the ISM could be “blown away" ie. that he züuubieut medi could be swept oit bv the hot expanding superuovae superbubbles. | For sufficiently small galaxies however, model calculations (Ferrara Tolstoy 2000) suggest that the ISM could be “blown away” i.e. that the ambient medium could be swept out by the hot expanding supernovae superbubbles. |
This coutrast to the situation iu slightly larger galaxies where there is mstead a "blow ot ie. the supernovae heated hot eas nerces the πι disk material aud escapes iuto the iutergalactic nediuu. | This is in contrast to the situation in slightly larger galaxies where there is instead a “blow out” i.e. the supernovae heated hot gas pierces the ambient disk material and escapes into the intergalactic medium. |
Althougho a situation where the entire ISM is expaudiug outwards has not vet been observed. expansio1i of the neutral ISAL on simaller scales has beci observed in a muuber of starbursting cwarf galaxies. | Although a situation where the entire ISM is expanding outwards has not yet been observed, expansion of the neutral ISM on smaller scales has been observed in a number of starbursting dwarf galaxies. |
81ch expawine III supershells have been secu in. for exame. Holubere II (Puche et al. | Such expanding HI supershells have been seen in, for example, Holmberg II (Puche et al. |
1992). IC 2571 (Walter Brinks 1999) aud Hohluberg I (Ott et al. | 1992), IC 2574 (Walter Brinks 1999) and Holmberg I (Ott et al. |
2001). | 2001). |
One should note lOWOCVOT. that while the observational evidence for expanding shells in the ISAL of these galaxies is reasoably eood. the mechanism by which these shells have heen created is less well established. | One should note however, that while the observational evidence for expanding shells in the ISM of these galaxies is reasonably good, the mechanism by which these shells have been created is less well established. |
Stewart&Walter(2000) find that the eiut supershell iu IC 2!f lis probably driven by energv input from supernovac. while Rhodeetal.(1999).. despite deep optical imaging. do uot find the star clusters that would be expected to be present iu this scenario. at the centers of the IIT holes iu Wolubere IT Tn light of the above discussion. aud the ougoing star formation in CRS. if mav be reasonable to assume that there are large scale racial flows in the galaxy. | \cite{stewart00} find that the giant supershell in IC 2574 is probably driven by energy input from supernovae, while \cite{rhode99}, despite deep optical imaging, do not find the star clusters that would be expected to be present in this scenario, at the centers of the HI holes in Holmberg II In light of the above discussion, and the ongoing star formation in GR8, it may be reasonable to assume that there are large scale radial flows in the galaxy. |
If we make this assumption. then the line of sight velocity Vj. is related to the circular velocity Vi; aud the racial velocity Vi by the relation where Vau is the svsteiie velocity. / is the iuclinatiou anele. and o is the azinnthal angle in the plane of the ealaxy (ο=0 along he receding half of the kiueimatical niajor axis) | If we make this assumption, then the line of sight velocity $V_{\rm los}$ is related to the circular velocity $V_{\rm rot}$ and the radial velocity $V_{\rm exp}$ by the relation where $V_{\rm sys}$ is the systemic velocity, $i$ is the inclination angle, and $\phi$ is the azimuthal angle in the plane of the galaxy $\phi = 0$ along the receding half of the kinematical major axis). |
The sin such aodel is oue iu which there is no rotation. | The simplest such model is one in which there is no rotation. |
[ | Fig. \ref{fig:model}[ [ |
C] shows such a model for CGRea. | C] shows such a model for GR8. |
Iu this model ‘huation angle of the disk is taken to be 20" aud the posiion angle 350". | In this model the inclination angle of the disk is taken to be $20^o$ and the position angle $350^o$. |
These values were chosen to mate served velocity field. aud are in good agreemen he values expected from the cllipse fitting to the outer III contours (see Sect. 3.1: | These values were chosen to match the observed velocity field, and are in good agreement with the values expected from the ellipse fitting to the outer HI contours (see Sect. \ref{ssec:HI_dis}; |
note hat in the case of radial motion. the velocity eracdieut is mmasxinuun along the morpiological minor axis aud nof he morphological major axis). | note that in the case of radial motion, the velocity gradient is maximum along the morphological minor axis and not the morphological major axis). |
The expansion is taken o be centered ou the kinematical center obtained from he velocity field. and not the morphological ceuter. | The expansion is taken to be centered on the kinematical center obtained from the velocity field, and not the morphological center. |
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