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This might interfere with the measurement of the total [ux from the NL. e. but should not seriously interfere with measurements of the ratios between NL and BL or between the continuumand the NL.
This might interfere with the measurement of the total flux from the NL, $a$, but should not seriously interfere with measurements of the ratios between NL and BL or between the continuumand the NL.
We also ignored the fitting of theratios between NLs which we do not think would alfect our estimates by much.
We also ignored the fitting of theratios between NLs which we do not think would affect our estimates by much.
The line
The line
We have compared the CDAL|A ecosmological model with a BSI initial spectrum of acliabatic perturbations given bv Eq. (
We have compared the $+\Lambda$ cosmological model with a BSI initial spectrum of adiabatic perturbations given by Eq. (
3) with recent observational data.
3) with recent observational data.
“Phe model is determined by four fundamental parameters Qy. 24 22hpA aand Eo. (in addition to the Hubble constant //5) out of which one (cL) is fixed. by the normalization to the CODE data.
The model is determined by four fundamental parameters $\Omega_\Lambda$ , $A_+$, $A_-\equiv p A_+$ and $k_0$, (in addition to the Hubble constant $H_0$ ) out of which one $A_-$ ) is fixed by the normalization to the COBE data.
Phe number of observational tests we use is sullicient to rule out many primordial spectra well-motivated by inllationary theories.
The number of observational tests we use is sufficient to rule out many primordial spectra well-motivated by inflationary theories.
For instance. to enlarge the allowed (h.O4) window. one could think of introducing a tiltecl or double inflationary spectrum. to reconcile observations on large scales (CODE) and small scales (as).
For instance, to enlarge the allowed $h, \Omega_\Lambda$ ) window, one could think of introducing a tilted or double inflationary spectrum to reconcile observations on large scales (COBE) and small scales $\sigma_8$ ).
However. there will be a generic lack of power on intermediate scales (bulk velocity. first CMD peak).
However, there will be a generic lack of power on intermediate scales (bulk velocity, first CMB peak).
Moreover. exactly at these scales. there may. be an unexpected excess of power.
Moreover, exactly at these scales, there may be an unexpected excess of power.
The initial spectrum that we study here allows a significant enlargement of the allowed (5. 34) region. especially smaller Os; without supressing power at intermediate scales.
The initial spectrum that we study here allows a significant enlargement of the allowed $h, \Omega_\Lambda$ ) region, especially smaller $\Omega_\Lambda$ 's, without supressing power at intermediate scales.
We have found allowed regions in the (P. O4) parameter plane for p ling in the region (0.51.7).
We have found allowed regions in the $h$, $\Omega_\Lambda$ ) parameter plane for $p$ lying in the region $(0.8-1.7)$.
These allowed regions are larger than in the case of a fat initial spectrum (p— 1).
These allowed regions are larger than in the case of a flat initial spectrum $p=1$ ).
The most interesting. and alltogether unexpected. successfull model appears to be that with an inverted step pl. where the power at intermediate scales is even more enhanced.
The most interesting, and alltogether unexpected, successfull model appears to be that with an inverted step $p<1$, where the power at intermediate scales is even more enhanced.
Lt appears that this latter case is suitable for the description of the feature in the cluster spectrum found in LEinasto (19972. 1997b. 19970).
It appears that this latter case is suitable for the description of the feature in the cluster spectrum found in Einasto (1997a, 1997b, 1997c).
The most distinctive feature of the class of models in question is the suppression of the second and higher acoustic (Doppler) peaks in the case p l.and their enhancement in the opposite case.
The most distinctive feature of the class of models in question is the suppression of the second and higher acoustic (Doppler) peaks in the case $p>1$, and their enhancement in the opposite case.
Phat is why the CAT CAIB experiment appears the most restrictive for the model.
That is why the CAT CMB experiment appears the most restrictive for the model.
So. the exact measurement of C1 [for /—500. i.c. around the second acoustic (Doppler) peak. will be the crucial test. for this model.
So, the exact measurement of $C_l$ for $l\sim500$, i.e. around the second acoustic (Doppler) peak, will be the crucial test for this model.
The forthcoming improvements of €CMD anisotropics measurements. especially baloon ancl satellite experiments. should be able either to rule out this model or to detect its signature in the next ten veers.
The forthcoming improvements of CMB anisotropies measurements, especially baloon and satellite experiments, should be able either to rule out this model or to detect its signature in the next ten years.
On the other hand. the inerease of the allowed region in the Ch. 4) plane and the allowed range for p itself are not large.
On the other hand, the increase of the allowed region in the $h$, $\Omega_\Lambda$ ) plane and the allowed range for $p$ itself are not large.
This shows the remarkable robustness of the |A ccosmological model with the simplest. inflationary initial conditions (O,,=Ὁ|QO,1: ηc1).
This shows the remarkable robustness of the $+\Lambda$ cosmological model with the simplest inflationary initial conditions $\Omega_{\mathrm tot}=\Omega+\Omega_\Lambda=1$; $n\simeq 1$ ).
Also. the fact that the allowed: values of p aare close to unity indicates that the form of the inflaton potential V(5) iis close to the case of a discontinuitv in its second. not first. derivative. which is more natural since. e.g.. it can occur as a result of an equilibrium second-order phase transition (some kind of non-analvtic behaviour of V(4) iis required in any case to obtain significant deviations from the flat. perturbation spectrum).
Also, the fact that the allowed values of $p$ are close to unity indicates that the form of the inflaton potential $V(\varphi)$ is close to the case of a discontinuity in its second, not first derivative, which is more natural since, e.g., it can occur as a result of an equilibrium second-order phase transition (some kind of non-analytic behaviour of $V(\varphi)$ is required in any case to obtain significant deviations from the flat perturbation spectrum).
Consideration of the latter case is under progress.
Consideration of the latter case is under progress.
AS. thanks the Ecole Normale Supérricure. Paris. for financial support. under the agreement between the Landau Institute for FPheoretical Physics. anc ENS. during his visit to France when this paper was completed.
A.S. thanks the Ecole Normale Supérrieure, Paris, for financial support, under the agreement between the Landau Institute for Theoretical Physics and ENS, during his visit to France when this paper was completed.
AS. also acknowledges financial support bv the Russian Foundation for Basic Research. grant 96-02-17591. and by the Russian research project“Cosmomicrophivsics”.
A.S. also acknowledges financial support by the Russian Foundation for Basic Research, grant 96-02-17591, and by the Russian research project“Cosmomicrophysics”.
Using automatic parallelization on 4 processors. the speed up factor is about 3.
Using automatic parallelization on 4 processors, the speed up factor is about 3.
Numerical stability. requires à. non-uniform grid with the same number of grid points per scale height and a very small input tux fi, of 0.25/64.
Numerical stability requires a non-uniform grid with the same number of grid points per scale height and a very small input flux $f_{\rm b}$ of 0.25/64.
These significantly increase the total (implicit plus explicit) computation time.
These significantly increase the total (implicit plus explicit) computation time.
Consequently. the minimum time for à full simulation is about a month.
Consequently, the minimum time for a full simulation is about a month.
After a series of numerical experiments (Robinson 1999) in a shell spanning 415° in latitude ancl longitude. a set. of parameters were found that generated a ‘sun-like’ rotation pattern.
After a series of numerical experiments (Robinson 1999) in a shell spanning $\pm 15^{ \circ}$ in latitude and longitude, a set of parameters were found that generated a `sun-like' rotation pattern.
These were ο=2.91.fi,035/64.Pr1 and ο=19 (about 5 pressure scale heights).
These were $\Omega_{\rm o} =2.91, f_{\rm b}= 0.25/64, {\rm Pr}=1$ and $ g_{\rm t} = 19$ (about 5 pressure scale heights).
Fixing these parameters. the latitudinal span was increased to 60 (30 above and below the equator).
Fixing these parameters, the latitudinal span was increased to $60^\circ$ $30^\circ$ above and below the equator).
Surprisingly. the rotation profile appeared. to be in some kind of 'quasi-steady state’.
Surprisingly, the rotation profile appeared to be in some kind of `quasi-steady state'.
Initially a "sun-like" profile was seen. but as the computation progressed. the radial angular velocity gradient ab the equator. switched. from. positive to negative.
Initially a `sun-like' profile was seen, but as the computation progressed, the radial angular velocity gradient at the equator, switched from positive to negative.
This simulation was run to completion and the averaged. results are classified as mocel A. Increasing ©, did not improve matters. and only when the longitudinal span was increased to 607. was a positive angular velocity. gradient sustained.
This simulation was run to completion and the averaged results are classified as model A. Increasing $\Omega_{\rm o}$ did not improve matters, and only when the longitudinal span was increased to $60^{ \circ}$, was a positive angular velocity gradient sustained.
The shel now covered the same longitudinal as latitudinal extent.
The shell now covered the same longitudinal as latitudinal extent.
This simulation was run independently of model (X. ane the averaged: results are. classified as model D. We founc out later that the flow reversal in A. was caused by a spurious meridional circulation.
This simulation was run independently of model A and the averaged results are classified as model B. We found out later that the flow reversal in A, was caused by a spurious meridional circulation.
Strong downllows at the impenetrable latitudinal boundaries generate a powerfu How. pointed from the equator towards the poles.
Strong downflows at the impenetrable latitudinal boundaries generate a powerful flow, pointed from the equator towards the poles.
This feature is cescribect in section 3
This feature is described in section \ref{lat}.
In a turbulent uid a quantity g can be split into a mean and a Lluctuating part. πι| @..0..1).
In a turbulent fluid a quantity $q$ can be split into a mean and a fluctuating part, q = )+ ,t).
The overbar represents a combined longitudinal and temporal average. Lo. ( ΙΟ) )di. fy.
The overbar represents a combined longitudinal and temporal average, i.e. ) = ( q d )dt. $t_1$,
is a time after the svstem has reached a selt- thermal equilibrium i.e. /,fedrfi.
is a time after the system has reached a self-consistent thermal equilibrium i.e. $t_1 > \int e dr /f_{\rm b}$.
ο is the internal energy at cach horizontal level.
$e$ is the internal energy at each horizontal level.
The time required [or statistical convergence (/2 £4) depends on the particular quantity being averaged.
The time required for statistical convergence $t_2-t_1$ ) depends on the particular quantity being averaged.
While the mean velocities required about LOO turnover times. turbulent quantities such as the velocity correlation ο took about 5 times as long.
While the mean velocities required about 100 turnover times, turbulent quantities such as the velocity correlation $\overline{ v_r' v_\phi'}$, took about 5 times as long.
The angular velocity averaged over time ancl longitude. relative to the rotating [rame of reference. is computed ancl shown in Fies 2 and 3 for model X. and in Figs 4 and 5. for model 3. In mocdel A. he isorotation contours are parallel o the rotation axis.
The angular velocity averaged over time and longitude, relative to the rotating frame of reference, is computed and shown in Figs \ref{contphi30} and \ref{avyphi30} for model A, and in Figs \ref{contphi60} and \ref{avyphi60} for model B. In model A, the isorotation contours are parallel to the rotation axis.
This means the angular velocity of a uid element at any point in the shell is determined by its »erpendicular distance from the rotation axis.
This means the angular velocity of a fluid element at any point in the shell is determined by its perpendicular distance from the rotation axis.
Fig.
Fig.
3. shows 1e angular velocity plotted. against nondimensional depth (given as a fraction of he total solar radius. Lo. r= r/R) --n the Northern hemisphere.
\ref{avyphi30} shows the angular velocity plotted against nondimensional depth (given as a fraction of the total solar radius, i.e. $r = $ r/R) in the Northern hemisphere.
Co-latitudes (90-Iatitude) of 907.85".TO and 67.5" are labelled: by solid. lone-cdashect. riple-dot dashed. ancl dot-dashed: curves. respectively.
Co-latitudes $90^\circ$ -latitude) of $90^\circ, 85^\circ, 79^\circ$ and $67.5^\circ$ are labelled by solid, long-dashed, triple-dot dashed and dot-dashed curves, respectively.
The slots show that the angular velocity decreases: racdiallv outwards anc away from the equator. in direct contrast to he rotational profile found in the SCZ.
The plots show that the angular velocity decreases radially outwards and away from the equator, in direct contrast to the rotational profile found in the SCZ.
Ifthe simulation is repeated with twice the longitudinal span. the cdiflerential rotation has a much more ‘stun-like’ appearance.
If the simulation is repeated with twice the longitudinal span, the differential rotation has a much more `sun-like' appearance.
In model DB. the shape of the isorotation contours resemble helioscismology observations in. two distinctive ways.
In model B, the shape of the isorotation contours resemble helioseismology observations in two distinctive ways.
Firstly. an initial increase then decrease in angular velocity. from the top inwards near the equator is found. as shown by the (wo closed. circular rotation contours (or equivalently. the radial angular velocity profile in Fig. 5)).
Firstly, an initial increase then decrease in angular velocity from the top inwards near the equator is found, as shown by the two closed circular rotation contours (or equivalently, the radial angular velocity profile in Fig. \ref{avyphi60}) ).
Lelioseismic results. Ixosovichev et al (1997). show that the increase inwards of angular velocity occurs at the equator and up to 60 degrees co-atitude. but the jury is still out on the behavior at higher co-Iatitudes. Schou ct al (1999).
Helioseismic results, Kosovichev et al (1997), show that the increase inwards of angular velocity occurs at the equator and up to 60 degrees co-latitude, but the jury is still out on the behavior at higher co-latitudes, Schou et al (1999).
As the computational shell only extends to about 60. degrees co-latitude. we will only consider behavior away from the boundaries as being representative of the actual convective How.
As the computational shell only extends to about 60 degrees co-latitude, we will only consider behavior away from the boundaries as being representative of the actual convective flow.
In that sense. within δι about the equator. the computed angular velocity “hump is at least qualitatively similar to the observed result.
In that sense, within $\pm 8^\circ$ about the equator, the computed angular velocity `bump' is at least qualitatively similar to the observed result.
Secondly. away from the equator towards micd-latitudes. the contours are about half way between the evlindrical contours (Clavlor Columns) seen in most earlier. global simulations (e.g. Glatzmaicr LOST). and the cone-like shape observed in the SCZ.
Secondly, away from the equator towards mid-latitudes, the contours are about half way between the cylindrical contours (Taylor Columns) seen in most earlier global simulations (e.g. Glatzmaier 1987), and the cone-like shape observed in the SCZ.
There is also good agreement with recent anclastic global LIES by Elliott. Miesch. Toone (2000).
There is also good agreement with recent anelastic global LES by Elliott, Miesch Toomre (2000).
Over the range of depth ancl latitude in common with their simulation and the present simulation. the isocontours éàyecsinilar.
Over the range of depth and latitude in common with their simulation and the present simulation, the isocontours are similar.
The amount of variation of angular velocity with latitude is also in agreement with the SCZ.
The amount of variation of angular velocity with latitude is also in agreement with the SCZ.
At the same colatitudes as in A. the mean angular velocity is plotted against depth. Fie. 5...
At the same colatitudes as in A, the mean angular velocity is plotted against depth, Fig. \ref{avyphi60}.
At the top of the shell the angular velocity. drops by about 0.2 between the equator (solid line) and co-latitucle of 67.5% (dot-dashed line).
At the top of the shell the angular velocity, drops by about 0.2 between the equator (solid line) and co-latitude of $67.5^\circ$ (dot-dashed line).
As ο, is about 3. the crop implies a 7% variation in rotation rate over 22.57. or extrapolating. a pole that spins 284wf faster than the equator.
As $\Omega_{\rm o}$, is about 3, the drop implies a $7\%$ variation in rotation rate over $22.5^\circ$, or extrapolating, a pole that spins $28\%$ faster than the equator.
This is in rough agreement. with the rotation rate at the surface of the Sun. which varies from 25 days at the equator to 35 days at the poles.
This is in rough agreement with the rotation rate at the surface of the Sun, which varies from 25 days at the equator to 35 days at the poles.
it will act dynamically as a single object.
it will act dynamically as a single object.
Adapting equation (7-26) of Binney Tremaine (1987) and equation (2) of Ebisuzaki et al. (
Adapting equation (7-26) of Binney Tremaine (1987) and equation (2) of Ebisuzaki et al. (
2001). the dvnamical friction time for such a cluster (ο sink [rom a distance r to the center of a galaxy with three-cimensional velocity dispersion σωμ 1s where InA is the Coulomb logarithm.
2001), the dynamical friction time for such a cluster to sink from a distance $r$ to the center of a galaxy with three-dimensional velocity dispersion $\sigma_{\rm gal}$ is where $\ln\Lambda$ is the Coulomb logarithm.
Therefore. a cluster will be able to sink to the center within much less than a Hubble time if it starts anywhere within the inner lew hundred parsecs of ils host galaxy.
Therefore, a cluster will be able to sink to the center within much less than a Hubble time if it starts anywhere within the inner few hundred parsecs of its host galaxy.
From this point. we expect the following sequence: (1) the cluster sinks until it is stripped ov lidally disrupted. thus releasing its IMDII. (2) the IMDII sinks rapidly until the stellar mass interior (o it is less than the mass of the IMDII. (3) the orbital radius of the IMDII around the SMDII shrinks via interactions with stars. as long as the relaxation time for the surrounding stars is less (han a Hubble time. and (4) the IMBII either merges with the SMDII due to interactions wilh stars followed by inspiral caused by gravitational radiation. or one or more acclitional INIBIIs settle to the center and interact dvnamically. causing mergers.
From this point, we expect the following sequence: (1) the cluster sinks until it is stripped or tidally disrupted, thus releasing its IMBH, (2) the IMBH sinks rapidly until the stellar mass interior to it is less than the mass of the IMBH, (3) the orbital radius of the IMBH around the SMBH shrinks via interactions with stars, as long as the relaxation time for the surrounding stars is less than a Hubble time, and (4) the IMBH either merges with the SMBH due to interactions with stars followed by inspiral caused by gravitational radiation, or one or more additional IMBHs settle to the center and interact dynamically, causing mergers.
We now discuss each of these steps.
We now discuss each of these steps. —
As the cluster sinks. it can lose stars in several wavs (a similar discussion in the context of stars al the Galactic center is in Hansen Milosavljevie 2003).
As the cluster sinks, it can lose stars in several ways (a similar discussion in the context of stars at the Galactic center is in Hansen Milosavljevic 2003).
The first is tidal stripping.
The first is tidal stripping.
That is. if (he cluster mass ancl radius are M4 ancl {τοι respectively. then the outer portions of the cluster will be stripped away when the cluster is a distance roc"πο [rom the center of the galaxy. where the tidal radius ric is given by Observations of the central regions of many galaxies suggest that the velocity dispersion is relatively. constant. (IX... Gebhardt. personal communication).
That is, if the cluster mass and radius are $M_{\rm cl}$ and $R_{\rm cl}$, respectively, then the outer portions of the cluster will be stripped away when the cluster is a distance $r<r_{\rm tide}$ from the center of the galaxy, where the tidal radius $r_{\rm tide}$ is given by Observations of the central regions of many galaxies suggest that the velocity dispersion is relatively constant (K. Gebhardt, personal communication).
This is therefore consistent wilh an isothermal density profile. in which A/(<r)=2e?r/G. where o is the velocity dispersion (see equation 4-123 of Binney Tremaine 1937).
This is therefore consistent with an isothermal density profile, in which $M(<r)=2\sigma^2 r/G$, where $\sigma$ is the three-dimensional velocity dispersion (see equation 4-123 of Binney Tremaine 1987).
Rewriting. we find (hat the tidal radius is or about 10—202,4 [for M4cfewxLO?AL. and a hall-mass radius 2.)~[ew pe.
Rewriting, we find that the tidal radius is or about $10-20R_{\rm cl}$ for $M_{\rm cl}\sim{\rm few} \times 10^5\,M_\odot$ and a half-mass radius $R_{\rm cl}\sim {\rm few}$ pc.
This will ivpically allow the cluster to sink in to ~30—50 pe. which it does within e10 vr if it started al e100 pe.
This will typically allow the cluster to sink in to $\sim 30-50$ pc, which it does within $\sim 10^8$ yr if it started at $\sim 100$ pc.
If wwe assume that the cluster itself has mass distributed roughly as an isothermal
If we assume that the cluster itself has mass distributed roughly as an isothermal
This paper presents new optical and infrared spectroscopic data and is structured as follows.
This paper presents new optical and infrared spectroscopic data and is structured as follows.
Observations and data reduction are described in Sect.
Observations and data reduction are described in Sect.
2 and the results are analyzed in Sect.
2 and the results are analyzed in Sect.
3.
3.
In Sect.
In Sect.
4 we constrain the excitation conditions of the gas and model the observed spectra in terms of photoionization from the AGN.
4 we constrain the excitation conditions of the gas and model the observed spectra in terms of photoionization from the AGN.
The derived chemical abundances are discussed in Sect.
The derived chemical abundances are discussed in Sect.
5 and in Seet.
5 and in Sect.
6 we draw our conclusions.
6 we draw our conclusions.
Long slit optical spectra were collected at the ESO NTT telescope in March 1995 using a dichroic beam splitter feeding both blue (1024° Tek-CCD with 0.37"//pix) and red (2048? Tek-CCD with 0.27"//pix) arms of EMMI.
Long slit optical spectra were collected at the ESO NTT telescope in March 1995 using a dichroic beam splitter feeding both blue $^2$ Tek-CCD with /pix) and red $^2$ Tek-CCD with /pix) arms of EMMI.
Simultaneous blue (3700-5000 with ~ 1.7 Á//pix) and red (8000—10000 with ~ 1.2 A//pix) spectra were obtained through a 2”slit centered on the optical nucleus at two position angles (cf.
Simultaneous blue (3700–5000 with $\simeq$ 1.7 /pix) and red (5000–10000 with $\simeq$ 1.2 /pix) spectra were obtained through a slit centered on the optical nucleus at two position angles (cf.
Fig. 1)).
Fig. \ref{showslit}) ).
The first was at PA=318". roughly aligned with the [OIII] cone axis and including the brightest [OIL] emitting knots. while the second was at and along the low excitation rim visible in the [SII] and "true colour” images shown in Fig.
The first was at $^\circ$, roughly aligned with the [OIII] cone axis and including the brightest [OIII] emitting knots, while the second was at $^\circ$ and along the low excitation rim visible in the [SII] and “true colour” images shown in Fig.
5 and Fig.
5 and Fig.
10 of M94..!.
10 of \cite{M94},.
. Several exposures were averaged and the total integration times of the spectra at PA=318" were 100. 75. 25 minutes over the 3700-5000. 5000-7300 and 7700-10080 wwavelength ranges. respectively.
Several exposures were averaged and the total integration times of the spectra at $^\circ$ were 100, 75, 25 minutes over the 3700–5000, 5000–7300 and 7700–10080 wavelength ranges, respectively.
The spectra at PAZ2437 covered 3700-5000 and 5000-7300 wwith a total integration time of 50 minutes per wavelength interval.
The spectra at $^\circ$ covered 3700-5000 and 5000–7300 with a total integration time of 50 minutes per wavelength interval.
Data were flux calibrated using observations of LTT3218 and reduced with MIDAS using standard procedures.
Data were flux calibrated using observations of LTT3218 and reduced with MIDAS using standard procedures.
Infrared spectra were collected in March 1995. also at the ESO NTT using the spectrometer IRSPEC equipped with a 62x58 SBRC InSb array whose pixel size was 2.2"along the slit and 7-5 along the dispersion direction.
Infrared spectra were collected in March 1995, also at the ESO NTT using the spectrometer IRSPEC equipped with a 62x58 SBRC InSb array whose pixel size was along the slit and $\simeq$ 5 along the dispersion direction.
Spectra of |Fell]1.644 jjm.. H» 2.121μπι. aand [SiV1]1.962 were obtained using a 4.4"slit at PA=318°.
Spectra of [FeII]1.644 , $_2$ 2.121, and [SiVI]1.962 were obtained using a slit at $^\circ$.
Each long-slit spectrum consisted of 4ABBA cycles (A=source. Bz'sky'. t.e. à region 300"E) with 2x60 sec integrations per position.
Each long-slit spectrum consisted of 4 ABBA cycles (A=source, B='sky', i.e. a region E) with 2x60 sec integrations per position.
The data were reduced using the IRSPEC context of MIDAS which was developed by one of us (EO) and which also allows the accurate subtraction of time variable OH sky lines.
The data were reduced using the IRSPEC context of MIDAS which was developed by one of us (EO) and which also allows the accurate subtraction of time variable OH sky lines.