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If this is taken as significant it represents, using equation 6, a decrease in [Fe/H] from ~—1.07 in the centre to ~—1.10 at Rec~4 kpc. | If this is taken as significant it represents, using equation 6, a decrease in [Fe/H] from $\sim-1.07$ in the centre to $\sim-1.10$ at $R_{GC} \sim 4$ kpc. |
It seems to us that the drop in C/M at greater values of Rec can be hardly be attributed to an increase in mean metallicity. | It seems to us that the drop in C/M at greater values of $R_{GC}$ can be hardly be attributed to an increase in mean metallicity. |
It seems much more likely that this is due to a change in age of the dominant population. | It seems much more likely that this is due to a change in age of the dominant population. |
It is natural to assume that this is due to older populations being more prominent on the outskirts of the LMC. | It is natural to assume that this is due to older populations being more prominent on the outskirts of the LMC. |
These, of course, might be metal poor. | These, of course, might be metal poor. |
These conclusions are surprisingly different from those in C09 and we are very grateful to Dr Cioni for send us details of her work. | These conclusions are surprisingly different from those in C09 and we are very grateful to Dr Cioni for send us details of her work. |
This consisted of deriving the C/M for each bin and these, converted to [Fe/H] using equation 6 are plotted in C09 fig. | This consisted of deriving the C/M for each bin and these, converted to [Fe/H] using equation 6 are plotted in C09 fig. |
2. | 2. |
A problem arises in this case since in the outer parts of the LMC the number of C or M stars per bin is very small and may be zero. | A problem arises in this case since in the outer parts of the LMC the number of C or M stars per bin is very small and may be zero. |
For instance in the annulus at Rec= 3.76kpc, there are 408 bins of which 4 have no M stars, 96 have no C stars and two have neither C nor M stars. | For instance in the annulus at $R_{GC}= 3.76$ kpc, there are 408 bins of which 4 have no M stars, 96 have no C stars and two have neither C nor M stars. |
The procedure in C09 was to omit bins when either the number of likely C stars or M stars was zero. | The procedure in C09 was to omit bins when either the number of likely C stars or M stars was zero. |
Since in general C/M<1, this will tend to bias the results towards higher C/M ratios. | Since in general $\rm C/M < 1$, this will tend to bias the results towards higher C/M ratios. |
That this is a significant effect can be seen from Fig. | That this is a significant effect can be seen from Fig. |
6 which shows results from counts in annuli as before, but now with all bins omitted which have no likely C stars or M stars. | 6 which shows results from counts in annuli as before, but now with all bins omitted which have no likely C stars or M stars. |
Within the uncertainties and the question of assigning proper weight to individual bins, Fig. | Within the uncertainties and the question of assigning proper weight to individual bins, Fig. |
6 converted to [Fe/H] by equation 6 would replicate the results of 009. | 6 converted to [Fe/H] by equation 6 would replicate the results of C09. |
Thus we believe these results are significantly affected by this selection procedure. | Thus we believe these results are significantly affected by this selection procedure. |
It is at first sight rather strange than in an initial discussion of these data Cioni | It is at first sight rather strange than in an initial discussion of these data Cioni |
s! and is associated with the emission peak from gas in the outer galaxy. | $^{-1}$ and is associated with the emission peak from gas in the outer galaxy. |
This absorption feature's reality is further supported by the continuum-subtracted HI channel map at the peak of the absorption at -67 km s! (Fig. | This absorption feature's reality is further supported by the continuum-subtracted HI channel map at the peak of the absorption at -67 km $^{-1}$ (Fig. |
3). | 3). |
This clearly shows the spatial association between the lower HI brightness temperature. caused by absorption. and the peak of the 1420 MHz continuum source. | This clearly shows the spatial association between the lower HI brightness temperature, caused by absorption, and the peak of the 1420 MHz continuum source. |
We estimate the uncertainties in our HI absorption spectrum using the standard derivation of T). taken from the velocity range 60 to 100 km/s. where the spectrum is dominated by noise. | We estimate the uncertainties in our HI absorption spectrum using the standard derivation of $\tau$ ), taken from the velocity range 60 to 100 km/s, where the spectrum is dominated by noise. |
The resulting standard derivation is 0.14. | The resulting standard derivation is 0.14. |
This yields that the absorption feature at ~ -67 km s! | This yields that the absorption feature at $\sim$ -67 km $^{-1}$ |
|bpdeO where the dimensionless cocllicicnt —=( | +, where the dimensionless coefficient =. |
2) The dependencePiwin! of luminosity on the halo barvon fraction introduces a. dependence. of the galaxy number density on the barvon [luctuations (i.c. on r(&)). | The dependence of luminosity on the halo baryon fraction introduces a dependence of the galaxy number density on the baryon fluctuations (i.e., on $r(k)$ ). |
Putting our results together. for a Dux-limited survey we find | C'huauubpa)8 | Cyuiubyr(k) — ross]?.(3) and rh= | Duia))bra]? | Dados rh) russe.(3) where =.(3) with (£3 evaluated for £=Luis. | Putting our results together, for a flux-limited survey we find = + ) + [r(k) - ], and = + ) ] + ) [r(k) - ], where =, with $\langle L \rangle$ evaluated for $L=\Lmin$. |
In the limit where Zi, is well below the peak of the luminosity function. C4 and Di both approach zero. and these expressions simplify to the previous ones (equations and 2.2)). | In the limit where $\Lmin$ is well below the peak of the luminosity function, $\Cmin$ and $\Dmin$ both approach zero, and these expressions simplify to the previous ones (equations \ref{dn} and \ref{dL2}) ). |
In the opposite limit. e.g.. in the exponential tail of aSehechter function. we can approximately set Ob)xeE, and then Chuμιος and DyinC'uinLiiuf(GLuin|Ls) ave both z1 when LuiXL. | In the opposite limit, e.g., in the exponential tail of aSchechter function, we can approximately set $\phi(L)
\propto e^{-L/L_*}$, and then $\Cmin = \Lmin / L_*$ and $\Dmin = \Cmin \Lmin/(\Lmin + L_*)$ are both $\gg 1$ when $\Lmin \gg L_*$. |
As we have shown. both the galaxy luminosity density and (for a ΕικΠατο. sample) number density depend on the halo gas fraction. | As we have shown, both the galaxy luminosity density and (for a flux-limited sample) number density depend on the halo gas fraction. |
Ehe scale-dependence of the relation between the barvon and. dark matter Huctuations implies that the BAOs can be observed. in. ratios that. previously would have been expected to be scale-independent. | The scale-dependence of the relation between the baryon and dark matter fluctuations implies that the BAOs can be observed in ratios that previously would have been expected to be scale-independent. |
One proposal is to compare the power spectrum. of luctuations in the galaxy number density (72) with that of the luminosity densitv (2,). with both measured for the same galaxy sample. | One proposal is to compare the power spectrum of fluctuations in the galaxy number density $P\rn$ ) with that of the luminosity density $P\rL$ ), with both measured for the same galaxy sample. |
Taking the ratio may help to clear away some svstematic effects that alfect both power spectra. | Taking the ratio may help to clear away some systematic effects that affect both power spectra. |
Their ratio (seuare-rooted) should have the form (assuming rk) <1): 03 “=f, 11 | D» -r(h) where the various bias factors enter into the coelIicients D, and D». | Their ratio (square-rooted) should have the form (assuming $r(k) \ll 1$ ): ( = B_1 1 + B_2 [r(k) - , where the various bias factors enter into the coefficients $B_1$ and $B_2$. |
M we denote the bias ratio 6,=6,4/b,. then b=E 2 NEZ Note that in the limit where most of the galaxy population is observed (i.e. the Hux limits are unimportant). these expressions simplify to D,=1|ὃν and D»=bi.xf(b,D). | If we denote the bias ratio $b\rr \equiv b_{\rm L;t} / b\rn$, then B_1 =, and B_2 = Note that in the limit where most of the galaxy population is observed (i.e., the flux limits are unimportant), these expressions simplify to $B_1 = 1 + b\rr$ and $B_2 = b_{\rm L;\Delta} /(b\rn B_1)$. |
In practice. using these expressions is not as daunting as it may appear. | In practice, using these expressions is not as daunting as it may appear. |
For a given galaxy sample. C, and Di, can be calculated. from the measured. luminosity function. | For a given galaxy sample, $\Cmin$ and $\Dmin$ can be calculated from the measured luminosity function. |
This leaves two unknowns. 5, and the ratio bp./6,. | This leaves two unknowns, $b\rr$ and the ratio $b_{\rm L;\Delta} /b\rn$. |
Within the ratio. we have a well-motivated expectation for bj.=bidfou. given that 9,zzLibby cLA 2.1). and ol,&3 [rom simulations (sce 3). | Within the ratio, we have a well-motivated expectation for $b_{\rm L;\Delta} =
b_{\rm L;f} A_r/\dc$ , given that $\dc \approx 1.7$, $b_{\rm
L;f} \approx 1.4$ 2.1), and $A_r \approx 3$ from simulations (see 3). |
Now. if r were independent. of scale. then we could only measure à degenerate combination of the unknown quantities. | Now, if $r$ were independent of scale, then we could only measure a degenerate combination of the unknown quantities. |
However. a precise measurement of the power spectrum ratio can separate out the constant and BAO terms. thus vielding D, and D» separately. which in turn vields 6, and the ratio bp./b,. | However, a precise measurement of the power spectrum ratio can separate out the constant and BAO terms, thus yielding $B_1$ and $B_2$ separately, which in turn yields $b\rr$ and the ratio $b_{\rm L;\Delta} /b\rn$. |
Although it is implicit in the equations. r(&) and russ are also declining functions of time. | Although it is implicit in the equations, $r(k)$ and $\rLSS$ are also declining functions of time. |
However. even ab low redshift r(&) contains a signature of the BAOs. since the BAOs are still imprinted more strongly in the barvon Uuctuations than in those of the dark matter or 1e total matter. | However, even at low redshift $r(k)$ contains a signature of the BAOs, since the BAOs are still imprinted more strongly in the baryon fluctuations than in those of the dark matter or the total matter. |
This clear signature ollers a chance to detect this οσοι. even if the various bias factors that we have assumed to be constant actually vary slowly with &. | This clear signature offers a chance to detect this effect, even if the various bias factors that we have assumed to be constant actually vary slowly with $k$. |
A detection of the ellect can be combined with an estimate of by from comparing £3, with the underlying matter power spectrum (c.g. as measured with weak lensing on large scales). | A detection of the effect can be combined with an estimate of $b\rn$ from comparing $P\rn$ with the underlying matter power spectrum (e.g., as measured with weak lensing on large scales). |
Extraction of the value of bp. would vield a new quantity in galaxy formation. a combination of the wav in which the luminosity of a galaxy depends on the barvonic 'oatent. of its host halo. and of how this baryonic content epends on the underlying dillerence between the barvon and total density [uctuations. | Extraction of the value of $b_{\rm
L;\Delta}$ would yield a new quantity in galaxy formation, a combination of the way in which the luminosity of a galaxy depends on the baryonic content of its host halo, and of how this baryonic content depends on the underlying difference between the baryon and total density fluctuations. |
Another possibility is to compare the power spectraof luminosity censity (or Dux-limited number density) between two cilferent samples. | Another possibility is to compare the power spectraof luminosity density (or flux-limited number density) between two different samples. |
Their ratio should again have a form similar to equation (2.4)). from which the constant and BAO term can he separately measured. | Their ratio should again have a form similar to equation \ref{Ps}) ), from which the constant and BAO term can be separately measured. |
LO is well known that galaxy bias depends on galaxy [uminosity (Lahay190601.. but here the bias would be scale dependent in a way that depends on Livin. | It is well known that galaxy bias depends on galaxy luminosity \citep{l96}, but here the bias would be scale dependent in a way that depends on $L_{\rm min}$. |
For our quantitative results. we use the CAMD lincar perturbation code (Lewisetal.2000).. with the WALAP 5-vear cosmological parameters (Ixomatsu2009).. matching thesimulation that we compare with below. | For our quantitative results, we use the CAMB linear perturbation code \citep{CAMB}, with the WMAP 5-year cosmological parameters \citep{WMAP5}, matching thesimulation that we compare with below. |
We show the dependence of + on both wavenumber and redshift in Figure 1.. | We show the dependence of $r$ on both wavenumber and redshift in Figure \ref{f:r}. . |
Ata given redshift. r(A) approachesa constantvalue (rp) at &20.5 h/Mpe. | At a given redshift, $r(k)$ approachesa constantvalue $\rLSS$ ) at $k \simgt 0.5$ h/Mpc. |
Using russ (itself a function only of redshift) we can separate out the two variables & and z in their effect on r. as shown in Figure 2.. | Using $\rLSS$ (itself a function only of redshift) we can separate out the two variables $k$ and $z$ in their effect on $r$ , as shown in Figure \ref{f:r2}. . |
The function. ως) Lis independent of redshift (i... | The function $[r(k)/\rLSS]-1$ is independent of redshift (i.e., |
that a Alpuσ of the form given by. equation (5)) must follow. | that a $M_{\rm BH} - \sigma$ of the form given by equation \ref{msig}) ) must follow. |
Llowever the total gas mass that the outllow can ultimately remove is given by considering the total energy La. as the outllow rapidlv becomes energydriven. | However the total gas mass that the outflow can ultimately remove is given by considering the total energy $E_{\rm out}$, as the outflow rapidly becomes energy–driven. |
By equating {μι and ££ we find that i.c. only a small increase in SMDII mass is needed. to sweep the bulge clear of any remaining gas. | By equating $E_{\rm out}$ and $E_{\rm
esc}$ we find that i.e. only a small increase in SMBH mass is needed to sweep the bulge clear of any remaining gas. |
We quantify this further below. | We quantify this further below. |
We have argued that momentumcriven outllows from star formation tend to produce a bulge stellar mass Llere we assume that Ao in equation (11)) is of order the virialised gas mass within the dark matter halo. Le. Ade. where M, is the total virial mass. and. a captures the uncertainty in the amount of momentum feedback the system can absorb before star formation is suppressed. | We have argued that momentum–driven outflows from star formation tend to produce a bulge stellar mass Here we assume that $M_0$ in equation \ref{mass_bulge_limit}) ) is of order the virialised gas mass within the dark matter halo, i.e. $M_{\rm
g,vir} = f_g\,M_v$ , where $M_v$ is the total virial mass, and $\eta$ captures the uncertainty in the amount of momentum feedback the system can absorb before star formation is suppressed. |
For the sake of simplicity. we also assume that both the gas and dark matter follow isothermal mass distributions. and that the velocity dispersion e of the bulge and its underlying dark matter halo are the same. | For the sake of simplicity, we also assume that both the gas and dark matter follow isothermal mass distributions, and that the velocity dispersion $\sigma$ of the bulge and its underlying dark matter halo are the same. |
Neither of these assumptions are likely hold in detail. but their effect. is quantitative rather than qualitative. | Neither of these assumptions are likely hold in detail, but their effect is quantitative rather than qualitative. |
Assuming isothermalitv. how does the virial gas mass Aa vary with velocity dispersion o? | Assuming isothermality, how does the virial gas mass $M_{\rm g,vir}$ vary with velocity dispersion $\sigma$? |
We make the standard.vir assumption that matter. is virialised. within a radius such that the mean density is 200 times the critical value: for the particular case of an isothermal sphere. this gives where ες)=100h(z)kms*\Ipe+ is the Lubble parameter αἲ the given. redshift 2. with Ας) the dimensionless Llubble parameter. | We make the standard assumption that matter is virialised within a radius such that the mean density is 200 times the critical value; for the particular case of an isothermal sphere, this gives where $H(z)=100\,h(z)\rm kms^{-1} Mpc^{-1}$ is the Hubble parameter at the given redshift $z$, with $h(z)$ the dimensionless Hubble parameter. |
Because M,=26?R0 we find that when combined with equation (5)). we find that in reasonable agreement with. for example. Hring& (2004).. | Because $M_v = 2\sigma^2R_v/G$ we find that when combined with equation \ref{msig}) ), we find that in reasonable agreement with, for example, \citet{2004ApJ...604L..89H}. |
We expect deviations from this relation and the simple Alay~ot law. as Alou may grow above AL, by an amount Zona in expelling any remaining gas. | We expect deviations from this relation and the simple $M_{\rm BH} \sim
\sigma^4$ law, as $M_{\rm BH}$ may grow above $M_{\sigma}$ by an amount $\la \Delta M_{\rm BH}$ in expelling any remaining gas. |
Combining (20)) with (16)) where we assume that Au is equal to Ade and (17)) gives the predicted maximum deviation from cithe theoretical relation This implies that AZpgg should tend. to increase above Al, with redshift and with o | Combining \ref{mm2}) ) with \ref{deltam}) ) – where we assume that $M_{\rm gas}$ is equal to $M_{\rm g,vir}$ – and \ref{mbulge}) ) gives the predicted maximum deviation from the theoretical relation This implies that $M_{\rm BH}$ should tend to increase above $M_{\sigma}$ with redshift and with $\sigma$. |
With Adpy=Al,|AALpH the black hole bulge mass relation finally becomes Assuming //—0.7 at z—0. this implies that fora galaxy with goog=1. close to the observed relation (2)). | With $M_{\rm BH} =
M_{\sigma} + \Delta M_{\rm BH}$ the black hole – bulge mass relation finally becomes Assuming $h=0.7$ at $z=0$, this implies that for a galaxy with $\sigma_{200} = 1$, close to the observed relation \ref{mm}) ). |
This relation should curve slightly upwards for larger σ. | This relation should curve slightly upwards for larger $\sigma$. |
We have assumed that star formation in galaxy bulges is selfregulating through momentum feedback acting on σας in the galaxw’s dark. matter halo. | We have assumed that star formation in galaxy bulges is self–regulating through momentum feedback acting on gas in the galaxy's dark matter halo. |
This puts a limit on the total mass of the stars that can form within the halo (equation 17)). | This puts a limit on the total mass of the stars that can form within the halo (equation \ref{mbulge}) ). |
Crucially. this maximum bulee mass scales as m5 with the galaxy velocity dispersion. | Crucially, this maximum bulge mass scales as $\sigma^4$ with the galaxy velocity dispersion. |
Given that the SALDIL mass also scales as σ (cf.Kine2003.2005:Mur-pavetal. 2005)... this results in a linear AgaAd, relation. close to the observed one (Llaring&Rix2004).. | Given that the SMBH mass also scales as $\sigma^4$ \citep[cf.][]{2003ApJ...596L..27K,2005ApJ...635L.121K,2005ApJ...618..569M}, this results in a linear $M_{\rm BH} - M_b$ relation, close to the observed one \citep{2004ApJ...604L..89H}. |
This relation arises because both the SAIBLL ancl the bulge are limited by essentially the same (quantity the maximum momentum thrust that the svstem can take before the gas is blown away. | This relation arises because both the SMBH and the bulge are limited by essentially the same quantity – the maximum momentum thrust that the system can take before the gas is blown away. |
The best match to the observed relation (LHàring&Itix2004) is obtained for the dimensionless parameter ap0.7 | The best match to the observed relation \citep{2004ApJ...604L..89H} is obtained for the dimensionless parameter $\eta \sim 0.7$ . |
In the context of our order of magnitude derivation in §2.. a value of 5g less than one implies that the bulge is not entirely self-sullicient in limiting its own growth. and that à SMDII or à NC are required to terminate bulge growth completely. | In the context of our order of magnitude derivation in \ref{sec:star_formation}, a value of $\eta$ less than one implies that the bulge is not entirely self-sufficient in limiting its own growth, and that a SMBH or a NC are required to terminate bulge growth completely. |
Finally. we argued in $4 that if the SMDILD growth timescale (lew « Salpeter) is shorter than the star formation (dvnamical) timescale. the growth of the central black hole is able to shut olf star formation in the bulge early. | Finally, we argued in \ref{sec:mbhmb} that if the SMBH growth timescale (few $\times$ Salpeter) is shorter than the star formation (dynamical) timescale, the growth of the central black hole is able to shut off star formation in the bulge early. |
In this case the extra SMDLIL growth introduces a mild upward trend in the Mpggxol relation. | In this case the extra SMBH growth introduces a mild upward trend in the $M_{\rm BH} \propto
\sigma^4$ relation. |
Vhe authors thank the anonymous referee. for. their comments that helped. to improve the clarity of the manuscript. | The authors thank the anonymous referee for their comments that helped to improve the clarity of the manuscript. |
CP and IZ acknowledge support via an STECtheoretical astrophysics rolling grant ancl an STEC stucentship respectively. | CP and KZ acknowledge support via an STFCtheoretical astrophysics rolling grant and an STFC studentship respectively. |
The results of the multi-epoch mmeasurements over 1.5 yr are illustrated in Fig. ].. | The results of the multi-epoch measurements over $\sim$ 1.5 yr are illustrated in Fig. \ref{fwpm}. |
The top panel shows the positions of the two persistent maser features. one detected at all 6 epochs. the other only at 5 epochs. | The top panel shows the positions of the two persistent maser features, one detected at all 6 epochs, the other only at 5 epochs. |
These have been fitted with a model taking into account the apparent motion due to the annual parallax plus a constant velocity vector: 210.3 mas yr! in R.A. and -2.7 mas yi! in Dee. for the feature at 23.2 s!.. and -10.2 mas yr! in R.A. and -].9 mas yr! in Dec. for the feature at 26.4s!. | These have been fitted with a model taking into account the apparent motion due to the annual parallax plus a constant velocity vector: –10.3 mas $^{-1}$ in R.A. and –2.7 mas $^{-1}$ in Dec. for the feature at –3.2 , and –10.2 mas $^{-1}$ in R.A. and –1.9 mas $^{-1}$ in Dec. for the feature at –6.4. |
. This vector accounts for both the motion of the local system (the star) relative to the Sun and the motion of the spots relative to the star. | This vector accounts for both the motion of the local system (the star) relative to the Sun and the motion of the spots relative to the star. |
The assumption of constant velocity has proved successful in similar experiments (see Reid et al. | The assumption of constant velocity has proved successful in similar experiments (see Reid et al. |
2009b and references therein) and in the case of iis supported by the conical jet model of Moscadelli et al. (2000.. 2005)). | \cite{reid09b} and references therein) and in the case of is supported by the conical jet model of Moscadelli et al. \cite{mosca00}, \cite{mosca05}) ). |
The curves in Fig. | The curves in Fig. |
| are the best fit to the data. corresponding to a parallax of 061+0702. re. a distance of 1.64+0.05 kpe. | \ref{fwpm} are the best fit to the data, corresponding to a parallax of $0\farcs61\pm0\farcs02$, i.e. a distance of $1.64\pm0.05$ kpc. |
In the bottom panel of the figure. we show the residual position offsets at the six epochs. after subtracting the contribution of the constant velocity vector. | In the bottom panel of the figure, we show the residual position offsets at the six epochs, after subtracting the contribution of the constant velocity vector. |
The fundamental conclusion that can be drawn from this result is that the distance adopted so far in the literature (1.7 kpe) for wwas correct. | The fundamental conclusion that can be drawn from this result is that the distance adopted so far in the literature (1.7 kpc) for was correct. |
This confirms all the estimates of important physical parameters. in particular the stellar mass (~7 Ms) and bolometric luminosity (~10 L4). | This confirms all the estimates of important physical parameters, in particular the stellar mass $\sim7~M_\odot$ ) and bolometric luminosity $\sim10^4~L_\odot$ ). |
We can thus conclude that iis indeed a 80.5 protostar surrounded by a Keplerian accretion disk (Cesaront et al. 20055). | We can thus conclude that is indeed a B0.5 protostar surrounded by a Keplerian accretion disk (Cesaroni et al. \cite{cesa05}) ). |
Methanol masers have been claimed by several authors to be associated with circumstellar disks (see e.g. Norris et al. 1998.. | Methanol masers have been claimed by several authors to be associated with circumstellar disks (see e.g. Norris et al. \cite{norris}, |
Minier et al. 2000.. | Minier et al. \cite{mini00}, |
Pestalozzi et al. 20095). | Pestalozzi et al. \cite{pesta}) ). |
In tthey appear to lie in the north-eastern part of the disk (Minier et al. 2001: | In they appear to lie in the north-eastern part of the disk (Minier et al. \cite{mini01}; |
Edris et al. 2005)) | Edris et al. \cite{edris}) ) |
and their velocities are blue- consistent with the Keplerian rotation pattern observed in thermal lines. | and their velocities are blue-shifted, consistent with the Keplerian rotation pattern observed in thermal lines. |
Our EVN images are consistent with this finding. as illustrated in Fig. 2.. | Our EVN images are consistent with this finding, as illustrated in Fig. \ref{fmpm}, |
where the mmaser features are overlayed on the disk silouhette. | where the maser features are overlayed on the disk silouhette. |
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