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Iu the solar ucighbourhood. we are not able to observe the first category of orbits as the Sun is outside corotation. | In the solar neighbourhood, we are not able to observe the first category of orbits as the Sun is outside corotation. |
But at the present time we observe nearthe Sim some uunber of hot orbit stars which are able to visit our uciehibbourhood after spending more or less time in the inner region of the bar. | But at the present time we observe nearthe Sun some number of hot orbit stars which are able to visit our neighbourhood after spending more or less time in the inner region of the bar. |
Iu particular metabrich old disc | In particular metal-rich old disc |
form at the same redshift; (iv) finally the composition of the matter ejected by stars into the ISM is given by stellar yields. | form at the same redshift; (iv) finally the composition of the matter ejected by stars into the ISM is given by stellar yields. |
These yields are detailed in the next subsection. | These yields are detailed in the next subsection. |
Once the chemical evolution is known, it can be inverted to estimate the redshift of formation of a star from its observed abundance, as explained in5. | Once the chemical evolution is known, it can be inverted to estimate the redshift of formation of a star from its observed abundance, as explained in. |
1.2.. The models considered here are bimodal. | The models considered here are bimodal. |
Each model contains a normal mode with stellar masses between 0.1 Mo and 100 Mo, with an IMF with a near Salpeter slope. | Each model contains a normal mode with stellar masses between 0.1 $_{\odot}$ and 100 $_{\odot}$, with an IMF with a near Salpeter slope. |
The SFR of the normal mode peaks at z73. | The SFR of the normal mode peaks at $z \approx 3$. |
In addition, we allow for a massive component, which dominates star formation at high redshift. | In addition, we allow for a massive component, which dominates star formation at high redshift. |
We primarily focus on stars with 40-100 Mo, which terminate as type II supernovae. | We primarily focus on stars with 40-100 $M_\odot$, which terminate as type II supernovae. |
The nucleosynthetic pattern of pair-instability SN (PISN) is briefly commented on in the conclusions. | The nucleosynthetic pattern of pair-instability SN (PISN) is briefly commented on in the conclusions. |
In addition to the SFR, the IMF and stellar data, this simple model introduces only two other parameters: the minimum mass of the dark matter halo in collapsed structures, Mmin, and the efficiency of supernovae to power outflows from collapsed structures, ε. | In addition to the SFR, the IMF and stellar data, this simple model introduces only two other parameters: the minimum mass of the dark matter halo in collapsed structures, $M_\mathrm{min}$, and the efficiency of supernovae to power outflows from collapsed structures, $\epsilon$. |
The impact of these two parameters has been discussed in detail in Daigne et al. | The impact of these two parameters has been discussed in detail in Daigne et al. |
2006. | 2006. |
In the present paper, we adopt a typical scenario with Mmin=107Mo ande=3x1073. | In the present paper, we adopt a typical scenario with $M_\mathrm{min}=10^{7}\ \mathrm{M_\odot}$ and $\epsilon=3\times 10^{-3}$. |
This minimum mass, Mmin, is also deduced from hydrodynamical simulations at z~15. | This minimum mass, $M_\mathrm{min}$, is also deduced from hydrodynamical simulations at $z\sim 15$. |
Note that ? consider Mmin=105M at z= 12.5 (seealso???).. | Note that \cite{2009arXiv0902.3263J} consider $M_{\rm min}=10^{8} M_\odot$ at $z=$ 12.5 \citep[see
also][]{2006ApJ...647..773D,2009arXiv0902.0853B,2009ApJ...694..879T}. |
e primarly impacts on the enrichment of IGM, which is not considered in this paper. | $\epsilon$ primarly impacts on the enrichment of IGM, which is not considered in this paper. |
The lifetimes of intermediate mass stars (0.9«M/Mo< 8) are taken from ? and from ? for more massive stars. | The lifetimes of intermediate mass stars $0.9<M/\msun <8$ ) are taken from \citet{1989A&A...210..155M} and from \citet{2002A&A...382...28S} for more massive stars. |
Old halo stars with masses below ~0.9M have lifetime long enough to be observed today. | Old halo stars with masses below $\sim 0.9\, \msun$ have a lifetime long enough to be observed today. |
They inherit the abundancesa of the ISM at the time of their formation. | They inherit the abundances of the ISM at the time of their formation. |
Thus, their observed abundances reflect, in a complex way (due to exchanges with the IGM), the yields of all massive stars that have exploded earlier. | Thus, their observed abundances reflect, in a complex way (due to exchanges with the IGM), the yields of all massive stars that have exploded earlier. |
The yields of stars depend on their mass and their metallicity, but not on their status (i.e. PopII/I or PopIII). | The yields of stars depend on their mass and their metallicity, but not on their status (i.e. PopII/I or PopIII). |
Some PoplI/I stars are massive, although in only a very small proportion since we use a steep Salpeter IMF. | Some PopII/I stars are massive, although in only a very small proportion since we use a steep Salpeter IMF. |
PoplII stars areall very massive stars. | PopIII stars areall very massive stars. |
Weuse the tables of yields (and remnant types) given in ? for intermediatemass stars (< 8Mo), and the tables in ? for massive stars (8«M/Mo40 ). | Weuse the tables of yields (and remnant types) given in \citet{1997A&AS..123..305V} for intermediatemass stars $<8 \msun$ ), and the tables in \citet{1995ApJS..101..181W} for massive stars $8<M/\msun <40$ ). |
An interpolation is made between different metallicities (7-0 and Z=10~*7? E97.) and we extrapolate the tabulated values beyond 40 | An interpolation is made between different metallicities (Z=0 and $10^{-4,\, -3,\, -2,\, -1,\, 0}$ $_\odot$ ) and we extrapolate the tabulated values beyond 40. |
Mo.. ? have provided new stellar yields in the mass range 10—100Mo,, but only at zero-metallicity. | \citet{2008arXiv0803.3161H} have provided new stellar yields in the mass range $10-100$, but only at zero-metallicity. |
At zero-metallicity, and in the 40—100 range, we have checked that our extrapolated values are consistentmass with those yields. | At zero-metallicity, and in the $40-100$ mass range, we have checked that our extrapolated values are consistent with those yields. |
Indeed, their favored model corresponds to very little mixing and a high oxygen to iron ratio, in agreement with the ? model we chose. | Indeed, their favored model corresponds to very little mixing and a high oxygen to iron ratio, in agreement with the \citet{1995ApJS..101..181W} model we chose. |
We explicitly checked that our results were not modified using either ? or? at metallicity. | We explicitly checked that our results were not modified using either \citet{1995ApJS..101..181W} or \citet{2008arXiv0803.3161H}
at zero-metallicity. |
Taking into account the results of recent observations on the PopII/I SFR (?), we reanalyse the reionization capability of thesestars. | Taking into account the results of recent observations on the PopII/I SFR \citep{2007ApJ...670..928B}, we reanalyse the reionization capability of thesestars. |
The WMAPS upper limit on the Thomson optical depth is then used to set constraints on the PopIII SFR. | The WMAP5 upper limit on the Thomson optical depth is then used to set constraints on the PopIII SFR. |
We fit the SFR history of ΡορΡΗ/ stars to the data compiled in (from z=0 to 5), and to the recent measurement at z~7 by ? (see Fig. 1)). | We fit the SFR history of PopII/I stars to the data compiled in \citet{2006ApJ...651..142H} (from $z=0$ to 5), and to the recent measurement at $z\sim 7$ by \citet{2007ApJ...670..928B} (see Fig. \ref{f:SFRenv}) ). |
The behaviour of the SFR at high redshift is still disputed. | The behaviour of the SFR at high redshift is still disputed. |
Some indirect measurements hint against a decline of the SFR beyond z~ (?),, but direct observations of zg50-dropout galaxies seem to confirm3 a sharp decrease of the SFR at z~6—7 (?).. | Some indirect measurements hint against a decline of the SFR beyond $z\sim3$ \citep{2008ApJ...682L...9F}, but direct observations of $z_{850}$ -dropout galaxies seem to confirm a sharp decrease of the SFR at $z\sim 6-7$ \citep{2009ApJ...690.1350O}. . |
The low level of the ? data thus places strong constraints on the PopII/I SFR. | The low level of the \citet{2007ApJ...670..928B} data thus places strong constraints on the PopII/I SFR. |
The fit for the SFR, Φ(2). is based on the mathematical form proposed in ?:: The amplitude (astration rate) and the redshift of the SFR maximum are given by v and zm respectively, while b and b—a are related to its slope at low and high redshifts respectively. | The fit for the SFR, $\psi(z)$, is based on the mathematical form proposed in \citet{2003MNRAS.339..312S}: The amplitude (astration rate) and the redshift of the SFR maximum are given by $\nu$ and $z_m$ respectively, while $b$ and $b-a$ are related to its slope at low and high redshifts respectively. |
In the following, we use the subscripts II/I and III for parameters related to PopII/I and PopIII SFRs respectively. | In the following, we use the subscripts II/I and III for parameters related to PopII/I and PopIII SFRs respectively. |
The thick black curve in is computed with 11/7=0.3 Mo yr! Mpcὃ, Zmr/1= 2.6, απ/=1.9 and br;= 1.2. | The thick black curve in is computed with $\nu_{\rm II/I}=0.3$ $_\odot$ $^{-1}$ $^{-3}$ , $z_{\rm m\, II/I}=2.6$ , $a_{\rm II/I}=1.9$ and $b_{\rm II/I}=1.2$ . |
The parameter values chosen here differ fromthat in ? so as to better account for the high redshift data point (?).. | The parameter values chosen here differ fromthat in \citet{2006MNRAS.373..128G} so as to better account for the high redshift data point \citep{2007ApJ...670..928B}. . |
To be conservative with respect to the reionization constraint (see below), we choose a SFR consistent | To be conservative with respect to the reionization constraint (see below), we choose a SFR consistent |
the gravitational potential [rom that of a point mass aud. cousequenly. of the orbits of P2 and P1 from Ivedlerian orbits are noutrivial. even if P2 aud Pl can be treated as test. particles. | the gravitational potential from that of a point mass and, consequently, of the orbits of P2 and P1 from Keplerian orbits are nontrivial, even if P2 and P1 can be treated as test particles. |
Τιe SeCOILLC result Grom the orbit-fitting that suggests nou-Ixepleriau orbits for P2 aud PL is the σοιfirinatio1 of the restult of Weaveretal.(2006). 1iat the o‘bital periods of Charon. P2. aud P1 €are nearly in the ratio 1::6. | The second result from the orbit-fitting that suggests non-Keplerian orbits for P2 and P1 is the confirmation of the result of \citet{wea06} that the orbital periods of Charon, P2, and P1 are nearly in the ratio 1:4:6. |
This means that the orbits of P2 aud Pl could be stroigly allectec "NV resolali Or near-resohant interactions. | This means that the orbits of P2 and P1 could be strongly affected by resonant or near-resonant interactions. |
As we shall see. tje strongest effects come rom the proxlity of P2 aud PI to the 3:2 mean-motion comujenisurabiity. whicl is the lowest order Connieisurabiliy amoug the satellites. even though P2 aud PL are nuch smaller than Charo | As we shall see, the strongest effects come from the proximity of P2 and P1 to the 3:2 mean-motion commensurability, which is the lowest order commensurability among the satellites, even though P2 and P1 are much smaller than Charon. |
lu Section 2 we present au aualvtie theory [or the ο‘bits of P2 and P1 that is vali the limit tlat the satellites have negligible masses aud cau ye treated as tes paricles. | In Section 2 we present an analytic theory for the orbits of P2 and P1 that is valid in the limit that the satellites have negligible masses and can be treated as test particles. |
It. sl hat the moion cau be represeuted by the superposition of Ije Circular moion of a guiding ler. the forced oscillatious due to tle non-axisymauietrie coiipouents of the j»otential rotating at the lueali noion of Pluto-Charon. he epicyelie motion. and Ithe vertical motion. | It shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto-Charon, the epicyclic motion, and the vertical motion. |
It also gives analytic results for the deviation [rom ]xepler's third law auc Ιthe periapse aud nodal precession rates. | It also gives analytic results for the deviation from Kepler's third law and the periapse and nodal precession rates. |
Iu Sectio1 3+) we present direοἱ nunerical orbit integratiousdL with different assumed masses for P2 aud PI within the ranges allowed by the uncertainties in the albedos. | In Section 3 we present direct numerical orbit integrations with different assumed masses for P2 and P1 within the ranges allowed by the uncertainties in the albedos. |
The numerical results are Cuparec to the analytic theoΝ in Section 2. amd the increasing iuportance of the proximity {κ» the DD.2 commenstrability with lucreasing lasses is exanined. | The numerical results are compared to the analytic theory in Section 2, and the increasing importance of the proximity to the 3:2 commensurability with increasing masses is examined. |
In fact. for the παΧΙΙ lasses ΟΥΤΟΣΞΡΟΙcling to the lowest expected albedos. P2 axl Pl may be in the 3:2 meau-motiou resouauce. wih the resonance variable involving the periapse longitude of PI librating. | In fact, for the maximum masses corresponding to the lowest expected albedos, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. |
In Section | we unmarize our results aud discuss tle prospects fo' detecting uou-Ixepleriau behaviors and putting straits on the masses of P2 and Pl with existing aud future observations. | In Section 4 we summarize our results and discuss the prospects for detecting non-Keplerian behaviors and putting constraints on the masses of P2 and P1 with existing and future observations. |
Iu this sectjon we develyp an analytic theory for the orbits of the satellites P2 and PI that is valid in tle limit that the saellites have negligible masses and cau be treated as test particles. | In this section we develop an analytic theory for the orbits of the satellites P2 and P1 that is valid in the limit that the satellites have negligible masses and can be treated as test particles. |
The latest orbital fit show that tlie orbit of Charon relative to Pluto is cousisteut with zero eccentricity (see Table 1) | The latest orbital fit show that the orbit of Charon relative to Pluto is consistent with zero eccentricity (see Table \ref{table1}) ). |
Thus we assuue that the orbit of Charon relative to Pluto is Ixepleriau aud circular. with seni1naJOr axis ape ald mean motion(or circular frequency) np.=[CCinptite);HelEL> where ny aud i, are the 1asses of Pluto aud. Charon. respectively. | Thus we assume that the orbit of Charon relative to Pluto is Keplerian and circular, with semimajor axis $a_{pc}$ and mean motion(or circular frequency) $n_{pc} = [G (m_p + m_c)/a_{pc}^3]^{1/2}$, where $m_p$ and $m_c$ are the masses of Pluto and Charon, respectively. |
la a cylindrical coordinate sSysleln with the origin at tve center of mass of the Pluto-Charon system aud the Q plane being the orbital plane of Pluto-Charon.the positiousof Charon andPluto are r.=(ας. 64.0). and m,(ttp.Oc+ 5.0). respectively. where ajpee(ng+ ne). 0epeHIpfCin(gy+ ane). OL)=tpel+ pe. aM Spe lsa coustant. | In a cylindrical coordinate system with the origin at the center of mass of the Pluto-Charon system and the $z = 0$ plane being the orbital plane of Pluto-Charon,the positionsof Charon andPluto are $\mbox{\boldmath $ $}_c = (a_c, \phi_c, 0)$ , and $\mbox{\boldmath $ $}_p = (a_p, \phi_c+\pi, 0)$ , respectively, where $a_p = a_{pc} m_c/(m_p+m_c)$ $a_c = a_{pc} m_p/(m_p+m_c)$ , $\phi_c(t)
= n_{pc} t + \varphi_{pc}$ , and $\varphi_{pc}$ isa constant. |
refimodel. | . |
. À summary of our model. a discussion of the significance KIT 15D carries in our overall understanding of the evolution of circumstellar. presumably. protoplanetary disks. and a listing of directions for future research. are contained in reldiscussion.. | A summary of our model, a discussion of the significance KH 15D carries in our overall understanding of the evolution of circumstellar, presumably protoplanetary disks, and a listing of directions for future research, are contained in \\ref{discussion}. |
Motivated by (1) significant radial velocity variations of INI 15D as measured by Johnson el al. ( | Motivated by (1) significant radial velocity variations of KH 15D as measured by Johnson et al. ( |
2004. submitted). (2) the observation of a central reversal in 1995 [or which the peak brightness exceeded (he out-ol-eclipse brishtness. and (3) the systematically. greater brightness of the system in 19671982 as compared to recent vears. we consider the IX star [XII 15D (o possess an orbital companion. | 2004, submitted), (2) the observation of a central reversal in 1995 for which the peak brightness exceeded the out-of-eclipse brightness, and (3) the systematically greater brightness of the system in 1967–1982 as compared to recent years, we consider the pre-main-sequence K star KH 15D to possess an orbital companion. |
The cata described. by Johnson Winn (2003) are consistent with a companion (hereafter. IN) whose luminosity is ~20'% greater than that of WI 15D (hereafter. IX). | The data described by Johnson Winn (2003) are consistent with a companion (hereafter, $'$ ) whose luminosity is $\sim$ greater than that of KH 15D (hereafter, K). |
All quantities superscripted with a prime reler to the orbital companion of WI 15D. The mass of IX’ should be nearly the same as that of IX. and we assign each a mass of my=mjO.5.AL. consistent with (he ο... T Taurilike spectrum. | All quantities superscripted with a prime refer to the orbital companion of KH 15D. The mass of $'$ should be nearly the same as that of K, and we assign each a mass of $m_b = m_b' = 0.5 M_{\odot}$ consistent with the system's T Tauri-like spectrum. |
We identify the eclipse period of 48.4 davs with the orbital period of the binary: for our chosen parameters. (he semi-major axis of each orbit referred to the centler-ol-nassis a,=d;0.13 AU. | We identify the eclipse period of 48.4 days with the orbital period of the binary; for our chosen parameters, the semi-major axis of each orbit referred to the center-of-massis $a_b = a_b' = 0.13$ AU. |
We assign an orbital eccentricity of ej=0.5 based on a preliminary analysis of data taken by Johnson et al. ( | We assign an orbital eccentricity of $e_b = 0.5$ based on a preliminary analysis of data taken by Johnson et al. ( |
2004). | 2004). |
The precise value is nol important; the only requirement is Chat the orbital eccentricity be of order unity. | The precise value is not important; the only requirement is that the orbital eccentricity be of order unity. |
The eclipses are caused bv an annulus of dust-laden gas that encircles both stars. beginning at a distance d;>a), as measured [rom (he binary center-ol-imass. and ending at an outer radius a,—a;+Aa. | The eclipses are caused by an annulus of dust-laden gas that encircles both stars, beginning at a distance $a_i > a_b$ as measured from the binary center-of-mass, and ending at an outer radius $a_f = a_i + \Delta a$. |
The symmetry plane of the ring is inclined with respect to the binary plane by J>0. | The symmetry plane of the ring is inclined with respect to the binary plane by $\bar{I} > 0$. |
We defer to refrigid| (he issue of how such a ring maintains a non-zero J against differential nodal precession. | We defer to \\ref{rigid}
the issue of how such a ring maintains a non-zero $\bar{I}$ against differential nodal precession. |
The ring will nodally regress at an angular speed of where @ is the mean radius of the ring and » is the mean motion evaluated at that radius. | The ring will nodally regress at an angular speed of where $\bar{a}$ is the mean radius of the ring and $\bar{n}$ is the mean motion evaluated at that radius. |
Equation (1)). derived [rom standard celestial mechanics perturbation theory. is only accurate Lo order-of-magnitude. since it relies on an expansion that is only valid to first order in mj/ my. | Equation \ref{regress}) ), derived from standard celestial mechanics perturbation theory, is only accurate to order-of-magnitude, since it relies on an expansion that is only valid to first order in $m_b'/m_b$ . |
Nonetheless. it is sufficiently. accurate to establish (he reasonableness of our picture in the | Nonetheless, it is sufficiently accurate to establish the reasonableness of our picture in the |
angular momentum as that in the disk. and is continuously accreted to the central black hole due to the viscous angular momentum transfer similar to that in accretion disks. | angular momentum as that in the disk, and is continuously accreted to the central black hole due to the viscous angular momentum transfer similar to that in accretion disks. |
The cifüng-in gas is steadily re-supplied by the gas evaporating from the transition laver between je corona and (he thin disk. and an equilibrium state of the svstem can be reached. | The drifting-in gas is steadily re-supplied by the gas evaporating from the transition layer between the corona and the thin disk, and an equilibrium state of the system can be reached. |
There are three factors crucial to (he evaporation rate. ie. (he heating of the corona. 1e thermal concuetion. and the radiative cooling in the transition laver. | There are three factors crucial to the evaporation rate, i.e. the heating of the corona, the thermal conduction, and the radiative cooling in the transition layer. |
Anv new physical —xocess related to these three factors can influence the evaporation rate and eventually make 1e. final configuration of the accretion flow different (e.g. Liu. Mever Mever-IHofmeister 2005). | Any new physical process related to these three factors can influence the evaporation rate and eventually make the final configuration of the accretion flow different (e.g. Liu, Meyer Meyer-Hofmeister 2005). |
One important relevant [actor is (he magnetic field because it has overall influence on accretion disks. | One important relevant factor is the magnetic field because it has overall influence on accretion disks. |
Firstly. it enhances the viscosity (Balbus Hawley 1991). | Firstly, it enhances the viscosity (Balbus Hawley 1991). |
Secondly. magnetic field contxibutes to the total pressure. | Secondly, magnetic field contributes to the total pressure. |
The viscous heating changes bx both the viscous coelficient ancl (he pressure. | The viscous heating changes by both the viscous coefficient and the pressure. |
Thirdly. strong entangled magnetic field largely moclilies the heat conduction of the plasma (Tao 1995: Chandran Cowley 1998: Naravan Medvedey 2001). | Thirdly, strong entangled magnetic field largely modifies the heat conduction of the plasma (Tao 1995; Chandran Cowley 1998; Narayan Medvedev 2001). |
Fourthly. in (he presence of magnetic field. (here should be exclotron-synchrotron radiation. | Fourthly, in the presence of magnetic field, there should be cyclotron-synchrotron radiation. |
In addition. magnetic dissipation/reconnection can be an additional heating mechanism to (he corona. | In addition, magnetic dissipation/reconnection can be an additional heating mechanism to the corona. |
llowever. how magnetic field influences the viscosity. parameter a is still unclear. | However, how magnetic field influences the viscosity parameter $\alpha$ is still unclear. |
The contribution could already be included if à is as large as 0.3. | The contribution could already be included if $\alpha$ is as large as 0.3. |
The dependence of evaporation rale on the viscosity. parameter has been discussed in Mever-Iofhnelster Meyer. (2001). | The dependence of evaporation rate on the viscosity parameter has been discussed in Meyer-Hofmeister Meyer (2001). |
lere we concentrate our investigations on (he influences of magnetic pressure and heal conduction on (he disk evaporation process. | Here we concentrate our investigations on the influences of magnetic pressure and heat conduction on the disk evaporation process. |
The evelotron-synchirotron radiation is optically thick in our corona aud could only be important when the electron temperature is higher than I0?I. which is the case in the upper boundary lavers. | The cyclotron-synchrotron radiation is optically thick in our corona and could only be important when the electron temperature is higher than $10^9$ K, which is the case in the upper boundary layers. |
Compared with the cooling from heat conduction. the cooling from optically-thick svnchrotron radiation in (he upper lavers can be neglected as long as the electron temperature is not (oo much higher than 10? K. which is indeed (he case in our computations (see also Mever Meyer-IHofmneister 2002). | Compared with the cooling from heat conduction, the cooling from optically-thick synchrotron radiation in the upper layers can be neglected as long as the electron temperature is not too much higher than $10^9$ K, which is indeed the case in our computations (see also Meyer Meyer-Hofmeister 2002). |
Thus. the evelotron-svnelirotron radiation will not be included in our caleulations. | Thus, the cyclotron-synchrotron radiation will not be included in our calculations. |
For simplicity. we assume a chaotic magnetic field. which provides an isotropic magnetic pressure in (he COLPOLnDa. | For simplicity, we assume a chaotic magnetic field, which provides an isotropic magnetic pressure in the corona. |
The basic equations aud boundary. conditions we adopted in (his work are the same as (hose in Liu et al. ( | The basic equations and boundary conditions we adopted in this work are the same as those in Liu et al. ( |
2002a). only with some minor changes. | 2002a), only with some minor changes. |
The viscosity parameter (5513) is sel to à=0.3. | The viscosity parameter (SS73) is set to $\alpha=0.3$. |
As having been shown in many previous works. the characteristics of disk evaporation are independent on the mass of central black hole. (he results are the same for svslenms with stelar-mass aud supermassive black holes. | As having been shown in many previous works, the characteristics of disk evaporation are independent on the mass of central black hole, the results are the same for systems with stellar-mass and supermassive black holes. |
For clarity. we reproduce the basic equations here. | For clarity, we reproduce the basic equations here. |
(e.g.Kesteven1968:Whiteoak&Green1996).. ~2.8 (Roger 1)). 2)). (Rogeretal. | \citep[e.g.][]{kes,whiteoak96}, $\sim 2-8$ \citep{roger85,whiteoak96} \ref{galaxy}) \ref{field}) \citep{roger85}. |
1985). ;/Àm (Whiteoak | $\mu$ \citep{whiteoak96}. |
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