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Collisions of captured particles with the local xuwvous trausfer and redistribute thermal οσον. aud lower the central eniperature bv a few perceut. | Collisions of captured particles with the local baryons transfer and redistribute thermal energy, and lower the central temperature by a few percent. |
In thermal equilibiuu. he kinetic energy of dark matter particles is balanced by he local exavitational potential (Sperec&Press1985 7 | In thermal equilibrium, the kinetic energy of dark matter particles is balanced by the local gravitational potential \citep{art-SpergelPress1985}. . |
An estimation of the radius of the dark matter core is even bv ry,~(91, where nPH and a, are. respectively. TOP)the massv ofimpfin, the proton aud the mass of the dark uatter particle. T, aud p, are the central temperature aud the central density of the Suus core. aud & aud G are. respectively. the Boltzimaun and Newton eravitational constants. | An estimation of the radius of the dark matter core is given by $r_x\sim \left(9 k T_c/4\pi G\rho_c m_p\right)\;\sqrt{m_p/m_x}$ where $m_p$ and $m_x$ are, respectively, the mass of the proton and the mass of the dark matter particle, $T_c$ and $\rho_c$ are the central temperature and the central density of the Sun's core, and $k$ and $G$ are, respectively, the Boltzmann and Newton gravitational constants. |
This expression approxinatelv gives the radius of the dark matter core in the Suu's interior. | This expression approximately gives the radius of the dark matter core in the Sun's interior. |
It folkανν that the more massive a dark matter particle. the simaller is the radius of the dark matter core. aud the less ia»ortant is the impact of dark latter in the evolution oftje Sun. | It follows that the more massive a dark matter particle, the smaller is the radius of the dark matter core, and the less important is the impact of dark matter in the evolution of the Sun. |
The Suu shows acuplex pattern of surface oscillations whose restoring orcees are produced either by compressibility or buovancy. | The Sun shows a complex pattern of surface oscillations whose restoring forces are produced either by compressibility or buoyancy. |
The pressure perturbations eive rise to acoustic sound waves in the high-frequency part of the spectrum. auk buovanev variations drive eravity waves in the low-frecuencv range of the spectra. | The pressure perturbations give rise to acoustic sound waves in the high-frequency part of the spectrum, and buoyancy variations drive gravity waves in the low-frequency range of the spectrum. |
The small amplitude surtac ‘perturbations observed. iu the Sun can be clescribec as a sun of cigenstates. | The small amplitude surface perturbations observed in the Sun can be described as a sum of eigenstates. |
Each cigenstate has a sρα] counterpart that is defined by a spatial cigeifunetion that depends on the thermodvuamical strucure of the backeround state (the Suus internal structiro) aud a tine-depeudenut clecnfiuction that is characerized by the frequency μι | Each eigenstate has a spatial counterpart that is defined by a spatial eigenfunction that depends on the thermodynamical structure of the background state (the Sun's internal structure), and a time-dependent eigenfunction that is characterized by the frequency $\nu_{n,l}$. |
The numbers / and (0are positive integers. known as the degree aud radial order of t16 modoe(e.e..Cough 1993).. | The numbers $l$ and $n$are positive integers, known as the degree and radial order of the \citep[e.g.,][]{art-Gough1993}. . |
During the last 50 wears. accurate measurements of | During the last 50 years, accurate measurements of |
sight has a value of ~ 607. declining to 10 bby JD +274. when y has a value of ~ 70°. | sight has a value of $\sim$ $^{\circ}$, declining to 10 by JD +274, when $\chi$ has a value of $\sim$ $^{\circ}$. |
These widths correspond to speeds of 900 and 450 km s7!. respectively. and the data are represented fairly well by the relation where s, 1s the width cx translated into speed in km !. | These widths correspond to speeds of 900 and 450 km $^{-1}$, respectively, and the data are represented fairly well by the relation where $s_w$ is the width $\sigma$ translated into speed in km $^{-1}$ . |
The speeds in the wings of the wind Πα line are even greater. | The speeds in the wings of the wind $\alpha$ line are even greater. |
Thus typical wind speeds are very roughly an order of magnitude greater than the orbital speec of the compact object. anda parcel of wind covers a distance of roughly 1.5 105 km in a single day. | Thus typical wind speeds are very roughly an order of magnitude greater than the orbital speed of the compact object, anda parcel of wind covers a distance of roughly 1.5 $10^{8}$ km in a single day. |
This distance is several times larger than the semi-major axis of the binary system and because the fast wind is predominantly perpendicular to the accretion disk (see also Perez Blundell 2010) it tends to be out of the plane of the orbit. | This distance is several times larger than the semi-major axis of the binary system and because the fast wind is predominantly perpendicular to the accretion disk (see also Perez Blundell 2010) it tends to be out of the plane of the orbit. |
It remains to make a quantitative estimate of the effect of any given region of the wind emitting over a period of perhaps several days. | It remains to make a quantitative estimate of the effect of any given region of the wind emitting over a period of perhaps several days. |
| approximate the line of sight to the orbital plane (it actually makes an angle of ~12°) and suppose a circular orbit. so that the recessional velocity of a source co-moving with the compact object would be given by where w is given by 2z/P. | I approximate the line of sight to the orbital plane (it actually makes an angle of $\sim$ $^{\circ}$ ) and suppose a circular orbit, so that the recessional velocity of a source co-moving with the compact object would be given by where $\omega$ is given by $2\pi /P$. |
Thus when f is one quarter of the period. P after primary eclipse. the compact object is approaching with speed v, and is receding with speed v, a quarter of a period before primary eclipse. | Thus when $t$ is one quarter of the period $P$ after primary eclipse, the compact object is approaching with speed $v_x$ and is receding with speed $v_x$ a quarter of a period before primary eclipse. |
I now assume that a shell of wind lights up suddenly (say in He) at time ¢ but became detached a time s earlier. the centroid moving with speed v, tangential to the orbit. | I now assume that a shell of wind lights up suddenly (say in $\alpha$ ) at time $t$ but became detached a time $s$ earlier, the centroid moving with speed $v_x$ tangential to the orbit. |
For a delay s of 0.25P. the most redshifted centroid is observed when ;=P rather than 0.75P. | For a delay $s$ of $0.25P$ , the most redshifted centroid is observed when $t=P$ rather than $0.75P$. |
The phasing of the wind centroid relative to the photometric ephemeris only requires a delay of ~2 days. | The phasing of the wind centroid relative to the photometric ephemeris only requires a delay of $\sim$ 2 days. |
The final step is to suppose that the H« emission dies away over a timescale of several days. | The final step is to suppose that the $\alpha$ emission dies away over a timescale of several days. |
This will atfect the phase and also makes an average of the line-of-sight velocity of the Hw centroid. thereby reducing the amplitude of v, below v. | This will affect the phase and also makes an average of the line-of-sight velocity of the $\alpha$ centroid, thereby reducing the amplitude of $v_r$ below $v_x$. |
This may be calculated by specifying some emission function of s with a delay parameter r and a duration parameter 7: f(s:r.T). | This may be calculated by specifying some emission function of $s$ with a delay parameter $\tau$ and a duration parameter $T$; $f(s; \tau ,T)$. |
At time f. the centroid of the shell detached a time s earlier has recessional velocity given by The value perceived at time fis obtained by averaging over all s. using f(s:r.7) as the weight. | At time $t$, the centroid of the shell detached a time $s$ earlier has recessional velocity given by The value perceived at time $t$ is obtained by averaging over all $s$, using $f(s;\tau ,T)$ as the weight. |
The important point is that for durations of a few days the average over s. «v(t)>. represents very well the data in both amplitude and phase. | The important point is that for durations of a few days the average over $s$, $<v_r(t)>$ , represents very well the data in both amplitude and phase. |
For the purpose of illustration I have used two different functions for the emission factor f(s). | For the purpose of illustration I have used two different functions for the emission factor $f(s)$. |
In the first case I supposed a rectangular profile as a function of s. with a duration of T. | In the first case I supposed a rectangular profile as a function of $s$, with a duration of $T$. |
This switches on at s=tT—7/2 and switches off at s=7+77/2. it being supposed that 7 exceeds 7/2. | This switches on at $s= \tau - T/2$ and switches off at $s= \tau + T/2$, it being supposed that $\tau$ exceeds $T/2$. |
The weighted average is then This is not a realistic form. but it makes the point and the structure is easy to visualise. | The weighted average is then This is not a realistic form, but it makes the point and the structure is easy to visualise. |
For the particular case of the parameter r=7/2 (ignition immediately on launch) and duration time 7=P/2. the centroid of the wind 1s most redshifted at orbital phase 0. one quarter of a period late. and the amplitude is v,sincGe/2). which for v, 175 km s! is 111 km sl. | For the particular case of the parameter $\tau = T/2$ (ignition immediately on launch) and duration time $T=P/2$, the centroid of the wind is most redshifted at orbital phase 0, one quarter of a period late, and the amplitude is $v_x$ $(\pi /2)$, which for $v_x$ 175 km $^{-1}$ is 111 km $^{-1}$. |
These results are very close to the behaviour of the data. | These results are very close to the behaviour of the data. |
The parameters 7 and r might exhibit some fluctuation with time - winds can be gusty. | The parameters $T$ and $\tau$ might exhibit some fluctuation with time - winds can be gusty. |
A probably more realistic form is to suppose exponential decay of the emission factor after the initial light. up. | A probably more realistic form is to suppose exponential decay of the emission factor after the initial light up. |
In this case the duration parameter 7 is the decay time of the exponential. and there is a delay 7 between launch and ignition. | In this case the duration parameter $T$ is the decay time of the exponential, and there is a delay $\tau$ between launch and ignition. |
The weighted average recession is now For the simple case of «T=1. the decay time Τ is about two days. the amplitude of the oscillation is v./v2 (124 km sl) and the recession velocity is greatest at orbital phase 0.875 for the case of instant ignition. 7.=0. | The weighted average recession is now For the simple case of $\omega T=1$, the decay time $T$ is about two days, the amplitude of the oscillation is $v_x/\sqrt 2$ (124 km $^{-1}$ ) and the recession velocity is greatest at orbital phase 0.875 for the case of instant ignition, $\tau =0$. |
Thus these simple models have demonstrated that both the amplitude and the phase of the centroid of the broad component of Ha. relative to the photometric ephemeris. are easily understood in terms of a wind that becomes detached fromthe orbiting source and decays away in Πα over a few days. | Thus these simple models have demonstrated that both the amplitude and the phase of the centroid of the broad component of $\alpha$, relative to the photometric ephemeris, are easily understood in terms of a wind that becomes detached fromthe orbiting source and decays away in $\alpha$ over a few days. |
The amplitude and phase of thewind centroid is reconciled with the way in which the line-of-sight wind speed varies with the nodding of the disk (Blundell. Bowler Schmidtobreick 2008). | The amplitude and phase of thewind centroid is reconciled with the way in which the line-of-sight wind speed varies with the nodding of the disk (Blundell, Bowler Schmidtobreick 2008). |
1n the magnitude-mean surface brightness diagram and the Fundamental Plane (PP.2)... dwarf ancl giant early-tvpe galaxies seem to form two distinct sequences joining at around Alp=IS mag (see?.andreferencesthercein).. | In the magnitude-mean surface brightness diagram and the Fundamental Plane \citep[FP,][]{DD87}, dwarf and giant early-type galaxies seem to form two distinct sequences joining at around $M_B = -18$ mag \citep[see][and
references therein]{KFCB09}. |
Llowever. this bi-modal distribution can be explained as a projection of the two known monotonous relations of other structural properties of early-type galaxies. as. functions of a galaxy luminosity on-to this parameter space: (a) light) profile concentration index and (b) central surface brightness (?7?7?77).. | However, this bi-modal distribution can be explained as a projection of the two known monotonous relations of other structural properties of early-type galaxies as functions of a galaxy luminosity on-to this parameter space: (a) light profile concentration index and (b) central surface brightness \citep{GG03,HMI03,KDG03,Ferrarese+06}. |
Only objects classified as compact elliptical (cI2) or ultra-compact dwarf (UCD. ?2)) galaxies strongly depart from these relations. | Only objects classified as compact elliptical (cE) or ultra-compact dwarf (UCD, \citealp{MHI02,Drinkwater+03}) ) galaxies strongly depart from these relations. |
They represent the two classes of galaxies supposecdly forming by tidal threshing of more massive progenitors (??7).. i.e. they must have sharply decreased. their stellar masses during the evolution. | They represent the two classes of galaxies supposedly forming by tidal threshing of more massive progenitors \citep{BCDG01,BCDS03}, i.e. they must have sharply decreased their stellar masses during the evolution. |
Both cl and UCD classes are represented by only a [ον dozens of known members including several transitional cI/UC objects. discovered recently (27)... | Both cE and UCD classes are represented by only a few dozens of known members including several transitional cE/UCD objects discovered recently \citep{CM08,Price+09}. |
Since all these objectsD. are very dense ancl small. much. higher. stellar velocity clispersions are required to keep them in equilibrium. compared. to. dwarf elliptical (dL) or dwarf spheroidal (dSph) galaxies of similar luminosities. thus putting them above the locus of dis on the 0 vs Alp (2?) relation. | Since all these objects are very dense and small, much higher stellar velocity dispersions are required to keep them in equilibrium compared to dwarf elliptical (dE) or dwarf spheroidal (dSph) galaxies of similar luminosities, thus putting them above the locus of dEs on the $\sigma$ vs $M_B$ \citep{FJ76} relation. |
Stellar population properties of cls and UCDs are very different [rom typical cle/dsph usually being very old. (with rare. exceptions such as Messier 32) and notably more metal-rich. | Stellar population properties of cEs and UCDs are very different from typical dE/dSph usually being very old (with rare exceptions such as Messier 32) and notably more metal-rich. |
Among known compact elliptical galaxies only AL 32 (Local group) NGC 4486B (Virgo cluster). NGC 5846À (NGC 5846 group). and. possibly. ACO 3526 J124853.0]411905.8 (Centaurus cluster) reside sullicientlv nearby. to allow. spatiallv-resolved: studies of their kinematies ancl stellar populations using ground-based telescopes. | Among known compact elliptical galaxies only M 32 (Local group), NGC 4486B (Virgo cluster), NGC 5846A (NGC 5846 group), and possibly ACO 3526 $J124853.91-411905.8$ (Centaurus cluster) reside sufficiently nearby to allow spatially-resolved studies of their kinematics and stellar populations using ground-based telescopes. |
They were considered. unique objects until the recent. discovery (??77T) of cEs located at a distance of the Coma cluster or further. which are. however. spatially unresolved for ground- optical observations. | They were considered unique objects until the recent discovery \citep{Mieske+05,Chilingarian+07,Price+09,Chilingarian+09} of cEs located at a distance of the Coma cluster or further, which are, however, spatially unresolved for ground-based optical observations. |
In this we report the detection. of the | In this we report the detection of the |
1.Many [fundamental properties ofmatter al thequantum level can beannounced without ment | covariance requirements imposed on the discrete relations between the generators of the quark algebra. |
ion | 2. |
ing parücles andanti-particles. electriccharge ancl barvonicnumber conservation belongto (his category. Quantum mechanics itself can be formulated | At present, the most successful theoretical descriptions of fundamental interactions are based on the quark model, despite the fact that isolated quarks cannot be observed. |
without any mention ofspace. as wasshown byDorn. JordanandIHeisenberg [1].intheir version ofmatrix mechanics. orinJ. | The only experimentally accessible states are either three-quark or three-anti-quark combinations (fermions) or the quark-anti-quark states (bosons). |
von Neumann's [0]. formulation ofquantum theory interms ofthe C algebras. The non-conmiutati | Whenever one has to do with a tri-linear combination of fields (or operators), one must investigate the behavior of such states under permutations. |
ve geometry [0].gives anotherexample ofinterpreting the space-time relationships inpure algebraicterms. Einstein'sdream wastobe abletoderive (heproperties ofmatter. and perhaps ilsvery existence. fromt | Let us introduce $N$ generators spanning a linear space over complex numbers, satisfying the following relations which are a cubic generalization of anti-commutation in the ususal (binary) case (see e.g. \cite{Kerner3}, \cite{VARKBLR}) ): with $j = e^{i \pi/3}$, the primitive cubic root of $1$. |
he singularities of fields definedon | We have ${\bar{j}} = j^2$ and $1+j+j^2 = 0$. |
the space-time. andifpossible. from ihe geometry and topology of the ο).Bul defend alternative point ofview supposing that(he existence ofma | We shall also introducea similar set of generators, ${\bar{\theta}}^{\dot{A}}$, $\dot{A}, \dot{B},... = 1,2,...,N$, satisfying similar condition with $j^2$ replacing $j$: Let us denote this algebra by ${\bf{\cal{A}}}$. |
tter one withcanan tothat of Inthislisht. the ideatoderivethe iseeonmeltric primary properliesrespectof space-time. | We shall endow this algebra with a natural $Z_3$ grading, considering the generators $\theta^A$ as grade $1$ elements, and their conjugates ${\bar{\theta}}^{\dot{A}}$ being of grade $2$ . |
theandspace-time. perhaps If the the space-time istobe derived [romthe interactions offandamental constituents ol matter. | The grades add up modulo $3$, so that the products $\theta^{A} \theta^{B}$ span a linear subspace of grade $2$, and the cubic products $ \theta^A \theta^B \theta^C$ are of grade $0$. |
thenit seems reasonable to choosethe strongest ineractions available. which are (he interactions between quarks. The difficulty. resides inthe factthat we should deline these “quarks” (or (heir states) withoutanv mention of space-time. The minimal requirementsfor the definition of quarksat(heiniti | Similarly, all quadratic expressions in conjugate generators, ${\bar{\theta}}^{\dot{A}} {\bar{\theta}}^{\dot{B}}$ are of grade $2 + 2 = 4_{mod \, 3} = 1$, whereas their cubic products are again of grade $0$, like the cubic products od $\theta^A$ 's. Combined with the associativity, these cubic relations impose finite dimension on the algebra generated by the $Z_3$ graded generators. |
alstage ofmodel buildingare the lollowing: 0.5cm2)The mathematical entities | As a matter of fact, cubic expressions are the highest order that does not vanish identically. |
representing quarks should form alinear space over complex numbers. so that we couldproduce their linear combinations coellicients. 0.5em 2) Thev shouldalso form an associative algebra. and AP) anti-quarks.and (he conjugation isomorphic algebras (iransformation (hat (wpemapsoneof corresponding these quarksontoanother.A A. algebras 0.5cm The Chree quark three anti-euark)and the quark-anti-quark combinations | The proof isimmediate: 0.2cm 0.2cm 0.2cm and because $j^4 = j \neq 1$ , the only solution is Therefore the total dimension of the algebra defined via the cubic relations \ref{ternary1}) ) is equal to $N + N^2 + (N^3 - N)/3$: the $N$ generators of grade $1$, the $N^2$ independent products of two generators, and $(N^3-N)/3$ independent cubic expressions, because the cube of any generator must be zero, and the remaining $N^3-N$ ternary products are divided by $3$ , by virtue of the constitutive relations \ref{ternary1}) ). |
shouldbe ze) distinguishedinà certain(orwav. for algebra spannedbythe generators. With thisin m | The conjugate generators${\bar{\theta}}^{\dot{B}}$ span an algebra ${\bf{\bar{\cal{A}}}}$ isomorphic with ${\bf{\cal{A}}}$ . |
indwe ean start to explorethe algebraic propertiesofquarks | Both algebras splitquite naturally into sums of linear subspaces with definite grades: |
Additionally we have to follow the dynamical evolution of halos and embedded: MDBlIs all the way to z=0 in order o determine the occupation fraction of. MDBlIIs ancl their ooperties. | Additionally we have to follow the dynamical evolution of halos and embedded MBHs all the way to $z=0$ in order to determine the occupation fraction of MBHs and their properties. |
We focus here on the ellect that MBLL ejections. namely due to gravitational waves recoils. have on the operties of the MBII population at z=0. | We focus here on the effect that MBH ejections, namely due to gravitational waves recoils, have on the properties of the MBH population at $z=0$. |
The magnitude of the recoil depends on the mass ratio of the merging MDlIIS. he spins of the MBlIs. the orbital parameters of the binary | The magnitude of the recoil depends on the mass ratio of the merging MBHs, the spins of the MBHs, the orbital parameters of the binary. |
First. to evaluate mass ratios. we have to model he mass-erowth5 of MBlIs. | First, to evaluate mass ratios, we have to model the mass-growth of MBHs. |
We base our modeling5 on jausible assumptions. supported by both simulations of AGN triggering and feedback. (Springelctal.2005).. and analvsis of the relationship between MDBII masses (Mg) and the properties of their hosts (Mebure&Dunlop2004:Writhe&Loeb 2005). | We base our modeling on plausible assumptions, supported by both simulations of AGN triggering and feedback \citep{Springel2005b}, and analysis of the relationship between MBH masses $M_{BH}$ ) and the properties of their hosts \citep{Mclure2004,Wyithe2005}. |
. Wyithe&Loeb(2005). show that if the relationship between the mass ofà MBLIL and the velocity dispersion. of the host. found. for local galaxies. (Tremaine does not evolve with redshift. then the correlation between the masses of AIBLIs and their hosts evolves with redshift in a wav compatible with observational results by Mebure&Dunlop (2004). | \cite{Wyithe2005} show that if the relationship between the mass of a MBH and the velocity dispersion of the host found for local galaxies \citep{Tremaine2002,Ferrarese2000,Gebhardt2000} does not evolve with redshift, then the correlation between the masses of MBHs and their hosts evolves with redshift in a way compatible with observational results by \cite{Mclure2004}. |
. Xdditionallv. Springeletal.(2005). suggest that the ditto Adleyσι relation is established during galaxy mergers that also fuel AIBIL aceretion and form bulges. | Additionally, \cite{Springel2005b} suggest that the ditto $M_{BH}-\sigma_*$ relation is established during galaxy mergers that also fuel MBH accretion and form bulges. |
We therefore assume that after every merger between two ealaxies with a mass ratio larger than 10. their \IBLIs attain the mass predicted by the Aleaσ. tor each of the merging galaxies. | We therefore assume that after every merger between two galaxies with a mass ratio larger than $1:10$, their MBHs attain the mass predicted by the $M_{BH}-\sigma_*$ for each of the merging galaxies. |
Lenec. although in our models the presence of a ML is not uniquely coupled with bulge formation. the mass of à black hole is set during the same event that forms the host bulge. | Hence, although in our models the presence of a MBH is not uniquely coupled with bulge formation, the mass of a black hole is set during the same event that forms the host bulge. |
Accordinglv. when a binary of MDlIs merge. their mass ratio scales with the Aldeaσι relation appropriate for the velocity cüspersions of the progenitor halos of the MILI. | Accordingly, when a binary of MBHs merge, their mass ratio scales with the $M_{BH}-\sigma_*$ relation appropriate for the velocity dispersions of the progenitor halos of the MBHs. |
Note that ifthe few—e. relation scales with redshift as suggested by. c.g. Wooetal.(2006):Treu(2004). the mass ratio of merging binaries would be unchanged. so the occupation fraction of black holes would not be allectect. | Note that if the $M_{BH}-\sigma_*$ relation scales with redshift as suggested by, e.g. \cite{Woo2006, Treu2004} the mass ratio of merging binaries would be unchanged, so the occupation fraction of black holes would not be affected. |
We further assume that AIBIIs merge within the merger timescale of their host halos. which is a likely assumption for MIB binaries formed after gas rich galaxy mergers (Escalaetal.2004:Dotti2006.2007 ). | We further assume that MBHs merge within the merger timescale of their host halos, which is a likely assumption for MBH binaries formed after gas rich galaxy mergers \citep{Escalaetal2004,Dottietal2006,Dotti2006c}. |
. To determine the efficiency of MILI. cjeetions due to gravitational recoils. we need also information on the magnitude and. orientation of AIBIL spins at the time of the merger. | To determine the efficiency of MBH ejections due to gravitational recoils, we need also information on the magnitude and orientation of MBH spins at the time of the merger. |
We will express AIBLL spins as a function of the dimensionless parameter @—JifSine=cJ,(COALay. where J, is the angular momentum of the black hole. | We will express MBH spins as a function of the dimensionless parameter $\hat a \equiv J_h/J_{max}=c \, J_h/G \, M_{\rm MBH}^2$, where $J_h$ is the angular momentum of the black hole. |
Non-spinning MDlIs. or binaries where ALIBI spins are aligned with the orbital angular momentum are expected o recoil with velocities below 200 kms4+. | Non-spinning MBHs, or binaries where MBH spins are aligned with the orbital angular momentum are expected to recoil with velocities below 200 $\rm{km\,s^{-1}}$. |
The recoil velocity is largest for MBlIIS with large spins. when the spin vectors have opposite directions and are in the orbital plane (Campanellietal.2007a:Conzález2007:Canipan-οetal. 2007b). | The recoil velocity is largest for MBHs with large spins, when the spin vectors have opposite directions and are in the orbital plane \citep{Campanelli2007b,Gonzalez2007,Campanelli2007}. |
. Assumine that Bills at the time of the merger always have antialignecl spins in the orbital plane (asinVolonteri2007) would. provide a strict upper limit to he elfect of the recoil. | Assuming that BHs at the time of the merger always have antialigned spins in the orbital plane \citep[as in][]{Volonteri2007} would provide a strict upper limit to the effect of the recoil. |
However. the configuration vielding he highest recoil velocities is probably rather uncommon. as »xointed out by BogdanoviéoOetal. | However, the configuration yielding the highest recoil velocities is probably rather uncommon, as pointed out by \cite{Bogdanovic2007}. |
(2007).. Bogdanoviéὃνοἱal.(2007) suggest that when the MBII merger happens in a gas rich environment. and is accompanied by accretion. the most ikely configuration has spins aligned (or anti-aligned) with he orbital angular momentum. thus avoiding the highest recoil velocity. | \cite{Bogdanovic2007} suggest that when the MBH merger happens in a gas rich environment, and is accompanied by accretion, the most likely configuration has spins aligned (or anti-aligned) with the orbital angular momentum, thus avoiding the highest recoil velocity. |
Conversely. in gas poor mergers there is no oeferential spin alignment. so all spin/orbital parameters configurations are equally probable. | Conversely, in gas poor mergers there is no preferential spin alignment, so all spin/orbital parameters configurations are equally probable. |
We will assume in the ollowing that orbital parameters and spin configuration are isotropically clistributed. likely providing a softmil o the strength of the recoil. | We will assume in the following that orbital parameters and spin configuration are isotropically distributed, likely providing a soft to the strength of the recoil. |
The distribution and. most. probable value. of ALBLI spins is observationallv [largely unconstrained. | The distribution and most probable value of MBH spins is observationally largely unconstrained. |
“Phere is evidence that MBlISs in some local AGN ealaxies do spin (Streblyanskactal.2005:Conmastriet2006:Drenne- based on iron line profiles (Miller2007:Fabianetal.1989:Laor 1991). | There is evidence that MBHs in some local AGN galaxies do spin \citep{Streblyanska2005,Comastri2006,Brenneman2006}, based on iron line profiles \citep{Miller2007,Fabian1989,Laor1991}. |
. High spins in bright quasars are also indicated by the high radiative elliciency of quasars. as. deduced: from observations. by applying Soltan's argument (Soltan1982:Wangetal.2006.andreferences.therein ).. | High spins in bright quasars are also indicated by the high radiative efficiency of quasars, as deduced from observations, by applying Soltan's argument \citep [and references therein ]{Soltan1982,Wang2006}. |
However. neither observation firmly establishes that most MDlIIs have large spins. although there are theoretical. arguments to expect so. (Alocerskietal.1998:Volonteri2005) as spin-up is a natural consequence of prolonged. disc-mocdoe accretion for any hole that has (for instance) doubled. its mass by capturing material with constant angular momentun. axis (Barcleon1970:Phorne 1974). | However, neither observation firmly establishes that most MBHs have large spins, although there are theoretical arguments to expect so \citep{Moderski1998,Volonterietal2005} as spin-up is a natural consequence of prolonged disc-mode accretion for any hole that has (for instance) doubled its mass by capturing material with constant angular momentum axis \citep{Bardeen1970,Thorne1974}. |
. lxingetal.(2005). argue instead that most MDIIs have very low or no spin. due to preferential accretion of counter-rotating material. or to short-lived accretion episodes (Ixingetal.2005). | \cite{King2005} argue instead that most MBHs have very low or no spin, due to preferential accretion of counter-rotating material, or to short-lived accretion episodes \citep{King2005}. |
. Waiting for additionalobservations". we Consider here two extreme cases. that likely allow us to bracket the typical configurations: cither that all AIBLIs have exactly null spin. or that all AIBLIs have @=0.9. | Waiting for additional, we consider here two extreme cases, that likely allow us to bracket the typical configurations: either that all MBHs have exactly null spin, or that all MBHs have $\hat a=0.9$. |
The latter value is slightly. lower than the canonical @=0.998 (Vhorne1974).. but it is consistent with magnetohyvcrodyvnamical simulations of dise acerction (Gammicetal.2004). | The latter value is slightly lower than the canonical $\hat a=0.998$ \citep{Thorne1974}, but it is consistent with magnetohydrodynamical simulations of disc accretion \citep{Gammieetal2004}. |
.. We also run a control simulation where we set the recoil velocity to zero for all ALBLL mergers. | We also run a control simulation where we set the recoil velocity to zero for all MBH mergers. |
For every galaxy merger we track jointly the dynamical evolution of the ALBIIs ancl of the host halo. | For every galaxy merger we track jointly the dynamical evolution of the MBHs and of the host halo. |
In addition to the dynamics of AIBL binaries. as described above. we trace the mass evolution of their hosts. including the due to galaxy mergers and the due to mass stripping of the halo within the gravitational potential of the halo. | In addition to the dynamics of MBH binaries, as described above, we trace the mass evolution of their hosts, including the due to galaxy mergers and the due to mass stripping of the halo within the gravitational potential of the halo. |
Our treatment is very simple: we integrate the equation of motion of the satellite in the gravitational potential of the cluster (assuming a non singular isothermal sphere). including the cvnamiucal friction term. | Our treatment is very simple: we integrate the equation of motion of the satellite in the gravitational potential of the cluster (assuming a non singular isothermal sphere), including the dynamical friction term. |
At every step of the integration we compare the density of the satellite to the density of the cluster halo at the location of the satellite. | At every step of the integration we compare the density of the satellite to the density of the cluster halo at the location of the satellite. |
‘Tidal stripping occurs at the radius within which the mean density of the satellite exceeds the density of the galaxy interior to its orbital racius. (Lavlor&Babul 2001).. | Tidal stripping occurs at the radius within which the mean density of the satellite exceeds the density of the galaxy interior to its orbital radius \citep{Taylor2001}. . |
We trace tidal stripping of all satellites from the time of the merger to.— 0. | We trace tidal stripping of all satellites from the time of the merger to $z=0$ . |
14479.9 line and selected stars with rather low rotational velocities aand. therefore. with the 44481.2 line well resolved from the 44479.9 line. | 4479.9 line and selected stars with rather low rotational velocities and, therefore, with the 4481.2 line well resolved from the 4479.9 line. |
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