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While the unperturbed surface density decreases due to the shell expansion at constant mass. the perturbed surface ensitv grows at a rate which depends on the external pressure and. on the number of SNell. | While the unperturbed surface density decreases due to the shell expansion at constant mass, the perturbed surface density grows at a rate which depends on the external pressure and on the number of SNeII. |
Ehe comparison of e different: panelsin Fig. | The comparison of the different panelsin Fig. |
4. shows that the development | \ref{fig:disc_sig1init} shows that the development |
variation) from +1 pixels (for IIST images) aud £3 pixels (for eround-based images) around the pixel. where the peak of the companion candidate should be located according to its position. | variation) from $\pm 4$ pixels (for HST images) and $\pm 3$ pixels (for ground-based images) around the pixel, where the peak of the companion candidate should be located according to its position. |
The limits eiven correspond to au intensity of 20 above the mean background. | The limits given correspond to an intensity of $3 \sigma$ above the mean background. |
No additonal conanion candidates (within 7") were detected iu the erouud-based Huaces, | No additonal companion candidates (within $^{\prime \prime}$ ) were detected in the ground-based images. |
A first check. whether or not a companion candidate may )o trucly bound (hence at the same distance and age as xiuarv). ie. whether or uot it is as cool as expected from he magnitude difference. can be done with the optical and IR colors. | A first check, whether or not a companion candidate may be truely bound (hence at the same distance and age as primary), i.e. whether or not it is as cool as expected from the magnitude difference, can be done with the optical and IR colors. |
For several companion candidates. one can Bud a solution for the observed magnitudes aud colors for either a moderately reddened L- or T-type companion or. alternatively. for a highly reddened backerouud star. | For several companion candidates, one can find a solution for the observed magnitudes and colors for either a moderately reddened L- or T-type companion or, alternatively, for a highly reddened background star. |
Iu the next section. we eo through such an estimate for the conipauion candiate near Cia Tah. | In the next section, we go through such an estimate for the companion candidate near Cha $\alpha$ 5. |
colunu density ratios is smaller than some of the model differcuces. holding pronmüse for observations to eventually distinenish between models. | column density ratios is smaller than some of the model differences, holding promise for observations to eventually distinguish between models. |
Oue thine we cau already sav is that the observed abundances of rrequire active carbon chemistry. such as that described πι Aetindezotal.(2008).. as models without such uetworks produce nowhere near enough: Hu the iuner disk atmosphere: for exiuuple. Willacy&Woods(2009) find rratios of ~102" (not plotted). | One thing we can already say is that the observed abundances of require active carbon chemistry, such as that described in \citet{Agundez08}, as models without such networks produce nowhere near enough in the inner disk atmosphere; for example, \citet{Willacy09} find ratios of $\sim10^{-10}$ (not plotted). |
Alternatively, the ligh abundance of ccould be produced by the burning of polveyclie aromatic hydrocarbons (PAIIs: though the production of PATIs may require aas a precursor: see discussion in &6.1)). | Alternatively, the high abundance of could be produced by the burning of polycyclic aromatic hydrocarbons (PAHs; though the production of PAHs may require as a precursor; see discussion in \ref{sec:pah}) ). |
A more promising approach to comparing models aud observations may be to couple thermo-chemical models with linc-geucrating radiative transfer code. aud directly colpare output model spectra with observations. | A more promising approach to comparing models and observations may be to couple thermo-chemical models with line-generating radiative transfer code, and directly compare output model spectra with observations. |
This approach has been pursued. for example. bv Iaipetal.(2010) for atomic fne-structure lines and low-J rotational CO lines. as well as Moeijeriuketal.(2008) and Woitkeetal.(2009). for far-IR rotational lines ofITO. | This approach has been pursued, for example, by \citet{Kamp10} for atomic fine-structure lines and low-J rotational CO lines, as well as \citet{Meijerink08} and \citet{Woitke09} for far-IR rotational lines of. |
.. Au alternative approach is to map abundance structures using observations and raciative transfer. aud compare these to the abundances predicted. by various theriuo-chemical models. | An alternative approach is to map abundance structures using observations and radiative transfer, and compare these to the abundances predicted by various thermo-chemical models. |
This approach has already vielded interesting results about water abuudauces (ALeijeriuketal. 2009).. aud we expect that it will lead to siguificaut progress m the conrparison of chemical models and observations in the near future. | This approach has already yielded interesting results about water abundances \citep{Meijerink09}, and we expect that it will lead to significant progress in the comparison of chemical models and observations in the near future. |
Iu Figure8 15.. we show molecular ratios with respect to CO. | In Figure \ref{fig:co_ratio_plot}, we show molecular ratios with respect to CO. |
We find ThO//CO ratios slightly above 1 nearly the same as that found by Carr&Najita(2008) and wing between verticallyautcerated aud disk surface model ratios. | We find /CO ratios slightly above 1 — nearly the same as that found by \citet{Carr08} and lying between vertically-integrated and disk surface model ratios. |
Glasseoldetal.(2009) also find IID5O//CO ratios near 1 for several types of models. | \citet{Glassgold09} also find /CO ratios near 1 for several types of models. |
Again. other molecular ratios are differeut from those found in Carr&Najita(2008) because of our choice of modeling asstumptious. | Again, other molecular ratios are different from those found in \citet{Carr08} because of our choice of modeling assumptions. |
The scatter in 0ο ratio is only ~0.5-1 dex aud so these ratios may prove helpful iu distineuishing between chemical models. | The scatter in /CO ratio is only $\sim$ 0.5-1 dex and so these ratios may prove helpful in distinguishing between chemical models. |
Note. however. that we have found significantly different enüttiug areas for CO aud and so the NIRSPEC aud IRS cussion lines are alinost certainly probing different emüittiug recionus. | Note, however, that we have found significantly different emitting areas for CO and and so the NIRSPEC and IRS emission lines are almost certainly probing different emitting regions. |
We lave presented aud analyzed Spitzer-IRS spectra ofIT;O.. OIL. ICN. aand COs. and IKeck-NIRSPEC spectra of CO from a large sample of ¢TT aud WAcBe disks. | We have presented and analyzed Spitzer-IRS spectra of, OH, HCN, and $_2$ and Keck-NIRSPEC spectra of CO from a large sample of cTT and HAeBe disks. |
In addition to the detection dependence on spectral type aud SED class (transitional versus classical) noted iu Paper I. we also find that detection efficiency depends on the disk color. nia339. Wa equivalent width aud. tentatively. ou AL. | In addition to the detection dependence on spectral type and SED class (transitional versus classical) noted in Paper I, we also find that detection efficiency depends on the disk color, $n_{13-30}$, $\alpha$ equivalent width and, tentatively, on $\dot{M}$. |
Radiative transfer disk models sugeest a number of wavs fo chhance line emission. including increasing the molecular abuudance. lowerime the cust/eas ratio i the disk atinosphere. aud increasing eas heating (Moeierimketal. 2009). | Radiative transfer disk models suggest a number of ways to enhance line emission, including increasing the molecular abundance, lowering the dust/gas ratio in the disk atmosphere, and increasing gas heating \citep{Meijerink09}. |
. Since my339 18 a measure of the settling of sinall grains iu the disk atiuosphere. these data suggest that if may be necessary to lower the dust/eas ratio in the atimosphere in order to produce these lines. | Since $n_{13-30}$ is a measure of the settling of small grains in the disk atmosphere, these data suggest that it may be necessary to lower the dust/gas ratio in the atmosphere in order to produce these lines. |
Iu addition. the correlation with IIo suggests that accretion is also portant. perhaps because it provides additional heating for the excitation of lines. | In addition, the correlation with $\alpha$ suggests that accretion is also important, perhaps because it provides additional heating for the excitation of lines. |
We fud that detections. line fluxes and lne-to-continu ratios for nearly all molecules are correlated. sugeesting a conmuon orient or conunon oexcitatiou conditious for this forest of lines. | We find that detections, line fluxes and line-to-continuum ratios for nearly all molecules are correlated, suggesting a common origin or common excitation conditions for this forest of lines. |
Line fluxes (Gwhenu detected) are also correlated with contiuuua flux aud | Line fluxes (when detected) are also correlated with continuum flux and |
20011150 gas responds strongly to. nonaxisvmmetries in a eravitational field. it was recognized more than two decades ago as à sensitive tracer of galactic potentials. | Because gas responds strongly to nonaxisymmetries in a gravitational field, it was recognized more than two decades ago as a sensitive tracer of galactic potentials. |
Therefore. a model for such a potential can be tested by simulating the eas Dow within it. and comparing the resulting morphology and kinematies to observations. | Therefore, a model for such a potential can be tested by simulating the gas flow within it, and comparing the resulting morphology and kinematics to observations. |
Phe earliest efforts to apply such à method used general formis for the potential derived either from. N-bocly simulations (Hluntlev 1978). or. [rom analvtic considerations (Sanders anc Lubbs 1980). | The earliest efforts to apply such a method used general forms for the potential derived either from N-body simulations (Huntley 1978) or from analytic considerations (Sanders and Tubbs 1980). |
The parameters of these model potentials were then constrained bv comparing results. from. hydrodyvnamical simulations performed with the beam scheme (Sanders and Prendergast 1974) to the morphology and kinematics of NGC 5383. | The parameters of these model potentials were then constrained by comparing results from hydrodynamical simulations performed with the beam scheme (Sanders and Prendergast 1974) to the morphology and kinematics of NGC 5383. |
The aim was to understand. how the general features of the eas in a typical SBb(s) galaxy. arose. | The aim was to understand how the general features of the gas in a typical SBb(s) galaxy arose. |
Since NGC 5383 was being used as a representative of SBb(s) galaxies. Duval and Athanassoula (1983) recognized the importance of doing a careful observational study of it and hence obtained. more complete spectral ancl photometric data for it. | Since NGC 5383 was being used as a representative of SBb(s) galaxies, Duval and Athanassoula (1983) recognized the importance of doing a careful observational study of it and hence obtained more complete spectral and photometric data for it. |
However using better data did not resolve the discrepancies between modeled and observed kinematics. | However using better data did not resolve the discrepancies between modeled and observed kinematics. |
Phey blamed it both on an inhomogeneity of the observations anc an. inadecuacy of the models. | They blamed it both on an inhomogeneity of the observations and an inadequacy of the models. |
Subsequent. efforts to constrain disk galaxy potentials via hydrodynamical simulations have benefited from improvements in hvdrocodes ancl have focused: on deriving galactic potentials from specific galaxies rather than assuming a general form for them (eEnelancd 1950. CGarcia-Durillo. Combes Cerin 1993. Sempere. | Subsequent efforts to constrain disk galaxy potentials via hydrodynamical simulations have benefited from improvements in hydrocodes and have focused on deriving galactic potentials from specific galaxies rather than assuming a general form for them (England 1989, Garcia-Burillo, Combes Gerin 1993, Sempere, |
line. | line. |
No significant coutiuuun enission was detected iu the nina data. cousisteut with expectations (Table 2). | No significant continuum emission was detected in the mm data, consistent with expectations (Table 2). |
All derived line fixes aud coutimmun flux densities are sunuuarized in Table 2. | All derived line fluxes and continuum flux densities are summarized in Table 2. |
Iu the following we briefly discuss the individual sources. | In the following we briefly discuss the individual sources. |
This ποιree Is one of the fust SAICs (Sssojn 72620 nay. Ivison et 11998) ever detected in CO onisijou (7=3. Fraver et11998)9. | This source is one of the first SMGs $_{850\mu m}$ $\pm$ mJy, Ivison et 1998) ever detected in CO emission $J$ =3, Frayer et. |
. It has subsequently been studied in detail iu CO emission Cenzel et 22003. /—1: Ivison et 220102). | It has subsequently been studied in detail in CO emission $J$ =3: Genzel et 2003, $J$ =1: Ivison et 2010a). |
Twison et ((1998) noted that this source hosts a dusty ACN: its QSO lines are discussed in Villa-Martíu et ((1999) and Vernet Ciuatti (2001). | Ivison et (1998) noted that this source hosts a dusty AGN; its QSO lines are discussed in n et (1999) and Vernet Cimatti (2001). |
In the {μις Lxvy plane JJO23990136 has the same huninosities as the Cloverleaf (Alexander et 22005a). | In the $L_{\rm FIR}$ $L_{\rm X-ray}$ plane J02399–0136 has the same luminosities as the Cloverleaf (Alexander et 2005a). |
Tvison et ((2010b) conclude that this source comprises a inerecr between a FIRbhuuiuous starburst. a QSO vost and a faint third coumponceut. | Ivison et (2010b) conclude that this source comprises a merger between a FIR–luminous starburst, a QSO host and a faint third component. |
For our analysis we adopt à FWZI of ~1000kius ‘for SMMEJJO23990136. | For our analysis we adopt a FWZI of $\sim$ for J02399–0136. |
The line is clearly detected in both individual chancel maps (Figure 1) and the iutegrated line cussion (Fieure 2. oft). | The line is clearly detected in both individual channel maps (Figure 1) and the integrated line emission (Figure 2, left). |
The total lux of the line is 1.90.2aus. | The total flux of the line is $\pm$. |
The contin at πα is not cetected at a 230 Πιτ of Syooc, <O-Sluundy (Figure 2. uiddle). | The continuum at mm is not detected at a $\sigma$ limit of $_{\rm 129\,GHz}<$ mJy (Figure 2, middle). |
The source is clearly resolved im the liunuau coutimmunun at GGIIZz with a total fux density of Soyo cyy=6.2£0.2nunty (Figure 2. right). | The source is clearly resolved in the mm continuum at GHz with a total flux density of $_{\rm
212\,GHz}$ $\pm$ mJy (Figure 2, right). |
Given the arge huewidths in SAIALIS023990136 it is difficult to separate the contiuuumn frou possible eeniüssion in this source at Linn wavelengths. | Given the large linewidths in J02399–0136 it is difficult to separate the continuum from possible emission in this source at mm wavelengths. |
(σοι et ((2003) have derived a total continu flux of TOLL. nuu measured at CCH. | Genzel et (2003) have derived a total continuum flux of $\pm$ mJy measured at GHz. |
If we assume that this is the correct contiuuun flux. we would expect a 212GCGIIz fiux of ~ mud or about 1.3nunuJv less than what is observed. | If we assume that this is the correct continuum flux, we would expect a GHz flux of $\sim$ mJy, or about mJy less than what is observed. |
We conclude that some of the | We conclude that some of the |
-- 37 aat the bright filamentary edge. | = -27 at the bright filamentary edge. |
Similar behaviour is shown in Fig. | Similar behaviour is shown in Fig. |
5 for the previous pv array along slit 2. | 5 for the previous pv array along slit 2. |
Some sort of three dimensional expansion at > 68 mmust be occurring with the bright NE outer are filaments being viewed tangentially through the edge of an expanding shell. | Some sort of three dimensional expansion at $\geq$ 68 must be occurring with the bright NE outer arc filaments being viewed tangentially through the edge of an expanding shell. |
However. this partial (?) | However, this partial (?) |
shell cannot have a simple, radially expanding. quasi-spherical structure for no receding velocities are detected within its circumference. | shell cannot have a simple, radially expanding, quasi-spherical structure for no receding velocities are detected within its circumference. |
The pv arrays in Fig. | The pv arrays in Fig. |
3 for the southwestern end of cut 5 cover the filamentary feature that could be an inner extension of the ‘jet’ in Fig. | 3 for the southwestern end of cut 5 cover the filamentary feature that could be an inner extension of the `jet' in Fig. |
6. | 6. |
Within this complication, radial velocities are in receding directions as the SW outer arc is crossed which is consistent with the NE and SW outer arcs in Fig. | Within this complication, radial velocities are in receding directions as the SW outer arc is crossed which is consistent with the NE and SW outer arcs in Fig. |
6 being part of the same. albeit not simple. bipolar structure. | 6 being part of the same, albeit not simple, bipolar structure. |
Only very limited information is in the present kinematical data concerning the nature of the possiblejet and bow-shock whose morphology is discussed in Sect. | Only very limited information is in the present kinematical data concerning the nature of the possible jet and bow–shock whose morphology is discussed in Sect. |
3.1. | 3.1. |
The most telling behaviour is the Hubble-type increase in radial velocity along the possible inner part of the jet as shown along the southwestern end of the pv array in Fig. | The most telling behaviour is the Hubble–type increase in radial velocity along the possible inner part of the jet as shown along the southwestern end of the pv array in Fig. |
3. | 3. |
The radial velocities in the knots in the ‘jet’ change systematically from ==-10 aat about ffrom the central star out to ==10 aat the bottom end of the array. | The radial velocities in the knots in the `jet' change systematically from = -10 at about from the central star out to = 10 at the bottom end of the array. |
Unfortunately the jet-like feature nearest the outer envelope was not covered in the present observations. | Unfortunately the jet-like feature nearest the outer envelope was not covered in the present observations. |
No direct kinematical information has yet been obtained over the bow-shaped filament in the northwestern quadrant (Fig. | No direct kinematical information has yet been obtained over the bow–shaped filament in the northwestern quadrant (Fig. |
6). | 6). |
However, the UV GALEX image reveals this to be the edge of extensive complex filamentary structure up to the central bright helical filaments and the outer are may only be the edge of a three dimensional structure typical of bow-shocks. | However, the UV GALEX image reveals this to be the edge of extensive complex filamentary structure up to the central bright helical filaments and the outer arc may only be the edge of a three dimensional structure typical of bow-shocks. |
In this case it could be possible that the extreme velocity feature out to ==-110 | In this case it could be possible that the extreme velocity feature out to = -110 |
and its Mellin transforms: Comparing the last equation with (B16)) is possible to obtain an analytical expression in terms of the Fox H-function for the surface mass density of the Emasto profile: Writting the surface mass density as a Fox H-function has an inconvenient. | and its Mellin transforms: Combining equations \ref{eq:08}) ), \ref{eq:09}) ) and \ref{eq:central_feature_mellin}) ) with $u=2y$ and $m=1/\alpha$ yields: Comparing the last equation with \ref{eq:Fox-H-1}) ) is possible to obtain an analytical expression in terms of the Fox H-function for the surface mass density of the Einasto profile: Writting the surface mass density as a Fox H-function has an inconvenient. |
The Fox H-function despite having a great potential for analytical work in Mathematics. sciences and engineering no numerical routines has been implemented yet. | The Fox H-function despite having a great potential for analytical work in Mathematics, sciences and engineering no numerical routines has been implemented yet. |
We prefer to describe the lensing properties of the Einasto profile in terms of analytical functions that have numerical routines already implemented to facilitate its use m strong and weak lensing studies. | We prefer to describe the lensing properties of the Einasto profile in terms of analytical functions that have numerical routines already implemented to facilitate its use in strong and weak lensing studies. |
The Meijer G-function meets the requirement pointed out before. | The Meijer G-function meets the requirement pointed out before. |
A list of the relevant properties of the Meijer G-function can be found in Appendix AppendixB:.. | A list of the relevant properties of the Meijer G-function can be found in Appendix \ref{sec:B}. |
We can use this function to write expressions m analytical form for most of the lensing properties of the Einasto profile. | We can use this function to write expressions in analytical form for most of the lensing properties of the Einasto profile. |
The Meter G-function had been implemented in several commercial and free available CAS. | The Meijer G-function had been implemented in several commercial and free available CAS. |
This means that using the Meijer G-function in lensing studies is just as simple as use other special functions like Hypergeometric. Gamma and Bessel functions for example. | This means that using the Meijer G-function in lensing studies is just as simple as use other special functions like Hypergeometric, Gamma and Bessel functions for example. |
Using a similar procedure to the one used by ?. to obtain an analytical expression for the luminosity density in terms of the Meijer G-function for all rational values of the Sérrsic index we proceed to do the same to derive an expression for the surface mass density of the Einasto profile for all values of the Einasto index. | Using a similar procedure to the one used by \citet{2011A&A...525A.136B}
to obtain an analytical expression for the luminosity density in terms of the Meijer G-function for all rational values of the Sérrsic index we proceed to do the same to derive an expression for the surface mass density of the Einasto profile for all values of the Einasto index. |
null | , |
low nias halos discussed above. | low mass halos discussed above. |
This progenitor forms an isentropic core of radius r. at the cluster ceuter. | This progenitor forms an isentropic core of radius $r_{c}$ at the cluster center. |
Iw eutropv of gas outside of the core. however. will be affected. bv shocks. | The entropy of gas outside of the core, however, will be affected by shocks. |
Recent high resolution ποτΊσα] sinulatious sugeest that the eutropy profile for eas outside this core can be adequately represented by a simple analytic expression giveu by lnA(r)2luAy|alu(esr) (Lewis ct al. | Recent high resolution numerical simulations suggest that the entropy profile for gas outside this core can be adequately represented by a simple analytic expression given by $\ln{K(r)}
= \ln{K_0} + \alpha \ln{(r/r_c)}$ (Lewis et al. |
2000). where à~1.1 for themassive. hot clusters (Tyο3 keV) of interest here (Tozzi Nonuan 2001: DBLP02). | 2000), where $\alpha \sim 1.1$ for themassive, hot clusters $T_X \gtrsim 3$ keV) of interest here (Tozzi Norman 2001; BBLP02). |
It should be noted that in the case of hese inassive systems. the accretion of gas ds limited w eravitational infall. and lence they accrete their full compliment of barvous [Le Vyas=(Qn 9,,)M]. | It should be noted that in the case of these massive systems, the accretion of gas is limited by gravitational infall, and hence they accrete their full compliment of baryons [i.e., $M_{gas} = (\Omega_b / \Omega_m) M$ ]. |
It is asstuned that the mass of barvous locked. up iu stars is ieglieible(as suggested by. for example. Roussel et al. | It is assumed that the mass of baryons locked up in stars is negligible (as suggested by, for example, Roussel et al. |
2000: Balogh et al. | 2000; Balogh et al. |
2001). | 2001). |
Following this prescription aud specitvine the owanieters He. οκον and a (as discussed in BBLP02} colmpletely determines the models. | Following this prescription and specifying the parameters $r_c$, $\rho_{gas}(r_c)$, and $\alpha$ (as discussed in BBLP02) completely determines the models. |
Under all conditions. he gas is assunied to be in hydrostatic equilibria within he dark halo poteutial. | Under all conditions, the gas is assumed to be in hydrostatic equilibrium within the dark halo potential. |
The effects of radiative cooling are neglected by these models. | The effects of radiative cooling are neglected by these models. |
Preheating will affect the MiTy relation in two wavs: (1) by altering the| temperature profile aud increasing the ciission-weighted gas temperature of cluster and (2) by altering the eas density profile aud reducing the gas mass in the cluster core. | Preheating will affect the $M_{gas} - T_X$ relation in two ways: (1) by altering the temperature profile and increasing the emission-weighted gas temperature of a cluster and (2) by altering the gas density profile and reducing the gas mass in the cluster core. |
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