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Ou the other hand. when averaging over all encounter geometries and plausible asteroid spin states. the mean r* can become lower than 5 Zt. | On the other hand, when averaging over all encounter geometries and plausible asteroid spin states, the mean $r^*$ can become lower than 5 $R_{\rm pl}$. |
Thus. for the lack of additional constraints on 7. we will tentatively assume below. as a guideline lor discussion. that ro~5 Ay. | Thus, for the lack of additional constraints on $r^*$, we will tentatively assume below, as a guideline for discussion, that $r^* \sim 5$ $R_{\rm pl}$. |
If we set r*=5 fiy our results described in 823 and 84H imply that /a,7L My. | If we set $r^*=5$ $R_{\rm pl}$ our results described in 3 and 4 imply that $t_{\rm sw}\sim1$ My. |
At first sight. this SW timescale seems (o be comparable to that obtained [rom comparative studies ol asteroid families in the main belt and OC meteorites in the RELAD database (NJWIO5 Vernazza et al. | At first sight, this SW timescale seems to be comparable to that obtained from comparative studies of asteroid families in the main belt and OC meteorites in the RELAB database (NJWI05, Vernazza et al. |
2009). | 2009). |
For example. Vernazza οἱ al. ( | For example, Vernazza et al. ( |
2009) proposed that the SW timescale is <1 My. | 2009) proposed that the SW timescale is $\lesssim1$ My. |
Their result hinges on observations ol (wo largest members of (he Datura family bv à catastrophic Dusv0.5 Mvud ago (Nesvorny et al. | Their result hinges on observations of two largest members of the Datura family that formed by a catastrophic breakup $\approx$ 0.5 My ago (Nesvorný et al. |
2006. Vokrouhlicky et al. | 2006, Vokrouhlický et al. |
(hatnm2009). | 2009). |
M nedThese two objects.12 Dherd 90265 2003CL5. appear to be significantly completely) space weal (MothéDiniz and Nesvorny 2008). which implies that the SW timescale should be to or shorter than the Datura family's age. | These two objects, 1270 Datura and 90265 2003CL5, appear to be significantly (but not completely) space weathered (Mothé–Diniz and Nesvorný 2008), which implies that the SW timescale should be comparable to or shorter than the Datura family's age. |
This poses a problem because {κdiasS0.5 My comparabledoes not fit the NEA constraint (unless (à>5 fiy). | This poses a problem because $t_{\rm sw} \lesssim 0.5$ My does not fit the NEA constraint (unless $r^* > 5$ $R_{\rm pl}$ ). |
Below we discuss possible to this problem. | Below we discuss possible solutions to this problem. |
Observations of 2001 WY35. one of the smallest known members of the Datura family (absolute magnitude JF= 17). indicate that (his object is not space weathered at all (MothéDiniz and Nesvorny 2003). | Observations of 2001 WY35, one of the smallest known members of the Datura family (absolute magnitude $H=17$ ), indicate that this object is not space weathered at all (Mothé–Diniz and Nesvorný 2008). |
IE these observations were correct. (hey. would indicate that (at least some) km-sized asteroids may weather on timescales significantly longer Chan ασ) My. | If these observations were correct, they would indicate that (at least some) km-sized asteroids may weather on timescales significantly longer than $\approx$ 0.5 My. |
For example. small kin-sizecl fragments ejected from asteroid breakup events may nol retain/accumulate sufficient regolith laver on (heir surface in (he immediate aftermath of the collision. | For example, small km-sized fragments ejected from asteroid breakup events may not retain/accumulate sufficient regolith layer on their surface in the immediate aftermath of the collision. |
The SW ellects may be delayed for such objects unül a particulate surface laver develops on (heir surface. for example. by subsequent impact shattering of the exposed rock. | The SW effects may be delayed for such objects until a particulate (SW-sensitive) surface layer develops on their surface, for example, by subsequent impact shattering of the exposed rock. |
Thus. the regolith formation and ‘earcdening” can be an important part of the problem (Jedicke et al. | Thus, the regolith formation and `gardening' can be an important part of the problem (Jedicke et al. |
2004. Willman οἱ al. | 2004, Willman et al. |
2008). | 2008). |
We should not forget distinc!that the (wo constraints on the SW Uimescale discussed here come from studies of two population of objects that are affected. by different. plvsical processes. | We should not forget that the two constraints on the SW timescale discussed here come from studies of two distinct population of objects that are affected by different physical processes. |
The asteroids in (he main-belt families are born by violent collisions. and spend most of their lifetime bevond 2 AU. | The asteroids in the main-belt families are born by violent collisions and spend most of their lifetime beyond 2 AU. |
The NEAs. on the other hand. are exposed (o more extreme solar-wind and temperature environment. | The NEAs, on the other hand, are exposed to more extreme solar-wind and temperature environment. |
They are olivine-vich and may therefore be more susceptible to SW effects than an average AIBA (Sasaki et al. | They are olivine-rich and may therefore be more susceptible to SW effects than an average MBA (Sasaki et al. |
2001. Marchi et al. | 2001, Marchi et al. |
2005). | 2005). |
While large impacts on NEAs should be rare. bombardment of their surface by | While large impacts on NEAs should be rare, bombardment of their surface by |
reeions characterized by a constant Q-profile (Pickett et al. 1997)). | regions characterized by a constant $Q$ -profile (Pickett et al. \cite{pickett}) ). |
Au accretion disk mav be subject to efficient cooling by a variety of mechanisuis. depending on the plysical conditions that characterize the specific. astrophysical system under consideration. | An accretion disk may be subject to efficient cooling by a variety of mechanisms, depending on the physical conditions that characterize the specific astrophysical system under consideration. |
From this poiut of view. the cooling necessary for the establishment of selfreeulation may occur effiiieutlv already via the radiative processes iuchided in “standard” models (see the general discussion of the outer disk bv Dardouoet al. 1998.. | From this point of view, the cooling necessary for the establishment of self-regulation may occur efficiently already via the radiative processes included in “standard" models (see the general discussion of the outer disk by Bardouet al. \cite{bardou}, |
which we wil sununuizeiu Sect. | which we will summarize in Sect. |
5.1). | 5.1). |
Iu reality. the cwuamics of uatter slowly accreting ina disk can be significantly more conrplex. | In reality, the dynamics of matter slowly accreting in a disk can be significantly more complex. |
Cold svstenis. such as a protogalactic disk. a xotostellar disk. or the outer parts of the disk in an ACN, nay have a composite and complex structure. | Cold systems, such as a protogalactic disk, a protostellar disk, or the outer parts of the disk in an AGN, may have a composite and complex structure. |
They max include dust. eas clouds. aud other particulate objects with a whole varicty of sizes and “temperatures”. | They may include dust, gas clouds, and other particulate objects with a whole variety of sizes and “temperatures". |
Much ike for the III component of the iterstellar medina. the nain contribution to the effective teniperature of the disk uieht be from the turbulent speed of an otherwise cold neditmm. | Much like for the HI component of the interstellar medium, the main contribution to the effective temperature of the disk might be from the turbulent speed of an otherwise cold medium. |
Ou the oue hand. for these systems it may be iud or even impossible to wiite out a simple "ideal οποίον transport equation. | On the one hand, for these systems it may be hard or even impossible to write out a simple “ideal" energy transport equation. |
Ou the other hand. such a complex environment is likely to possess all the desired cooling aud heatiug mechanisnis that cooperate iu selfreeulatiou. | On the other hand, such a complex environment is likely to possess all the desired cooling and heating mechanisms that cooperate in self-regulation. |
Iu this respect. oue is thus encouraged to bypass the predem of definingo a representative set of equations for cherey transport. and to use imstead the senmüenipirieal prescription of Eq. (8)). | In this respect, one is thus encouraged to bypass the problem of defining a representative set of equations for energy transport, and to use instead the semiempirical prescription of Eq. \ref{jeans}) ). |
Somewhat in a simular way. our inability to derive from first principles a satisfactory set of equations for moment trausport is often taken to justify the adoption of the o-prescription of Eq. (5)). | Somewhat in a similar way, our inability to derive from first principles a satisfactory set of equations for momentum transport is often taken to justify the adoption of the $\alpha$ -prescription of Eq. \ref{nu}) ). |
These phenomenologicaloO prescriptions lave several lBaitatious. but may stil work as a useful enice to our efforts and provide interesting models to be compared with the observations. | These phenomenological prescriptions have several limitations, but may still work as a useful guide to our efforts and provide interesting models to be compared with the observations. |
To be sure. some types of accretion disk. or soie reeions inside accretion disks (for example. very close to the center: see Sect. | To be sure, some types of accretion disk, or some regions inside accretion disks (for example, very close to the center; see Sect. |
5.1). nav lack the physical ineredicuts invoked above. | 5.1), may lack the physical ingredients invoked above. |
In act. there is no reason to claim that selteravitv mustalwys be important. | In fact, there is no reason to claim that self-gravity must be important. |
Therefore. we will study the structure of sclfreeulated accretion disks. as a viable class of astrophysical systems. while we do recognize that warier. nou-reeulated disks may exist and are likely to be basically free from the effects associated with the selt-exavitv. of the disk. | Therefore, we will study the structure of self-regulated accretion disks, as a viable class of astrophysical systems, while we do recognize that warmer, non-regulated disks may exist and are likely to be basically free from the effects associated with the self-gravity of the disk. |
The sclfreeulation mechanisia las been demonstrated by considering a simplified set of equations (Bertin 19913) where efBeieunt cooling is inchided and the role of selt-eravitv is unmodeled by means of a heating term with an analytic expression (nverselv proportional to a high power of Q) i11caut to incorporate the results of αναίσα] studies that show that heating is indeed very sensitive to he value of Q. The main features of this formula. with its hreshold at Qz1. aimed at represcuting the “thermal evolution of the disk. are somewhat analogous to the jeuristie characterization of the viscosity dependence ou Q adopted by Lin Prinele (19903) in the parallel problem of coustructing he ποιοπα transport equatious when selferavitv is nuportaut. | The self-regulation mechanism has been demonstrated by considering a simplified set of equations (Bertin \cite{bertiniau}) ) where efficient cooling is included and the role of self-gravity is modeled by means of a heating term with an analytic expression (inversely proportional to a high power of $Q$ ) meant to incorporate the results of dynamical studies that show that heating is indeed very sensitive to the value of Q. The main features of this formula, with its threshold at $Q \approx 1$, aimed at representing the “thermal evolution" of the disk, are somewhat analogous to the heuristic characterization of the viscosity dependence on $Q$ adopted by Lin Pringle \cite{lin2}) ) in the parallel problem of constructing the momentum transport equations when self-gravity is important. |
Iu our discussion of sel£regulated accretion disks. we actually have no doubt that sclf-eravity is likely to have anu important iapact on viscosity. aud this is still tacitly incorporated iu the a prescription. | In our discussion of self-regulated accretion disks, we actually have no doubt that self-gravity is likely to have an important impact on viscosity, and this is still tacitly incorporated in the $\alpha$ prescription. |
This impact is even more obvious if one recalls that a self-gravitatiug disk can be subject to non-axisvnunetrie instabilitics. which are bound to contribute significantly to angular imonientuu transport. | This impact is even more obvious if one recalls that a self-gravitating disk can be subject to non-axisymmetric instabilities, which are bound to contribute significantly to angular momentum transport. |
Our class of axisviinetric. steady-state accretion models represeuts oulv one approximate idealization of the actual svstem that we are addressiug. | Our class of axisymmetric, steady-state accretion models represents only one approximate idealization of the actual system that we are addressing. |
Civen the indications of several ανασα studies (iu addition to those of Lin Pringle. see. for example. Laughlin Bocdenheiuner 1991.. Laughlin Rózvvezka 1996)). a nore complete analysis should thus iuclude one further relation between à aud Q. | Given the indications of several dynamical studies (in addition to those of Lin Pringle, see, for example, Laughlin Bodenheimer \cite{laugh}, Laughlin R\'{o}\\.{z}yyczka \cite{laugh2}) ), a more complete analysis should thus include one further relation between $\alpha$ and $Q$. |
In ecneral.o this imuüeht practically require that the phenomenological prescription (5)) be used with a parameter a varving with radius. | In general, this might practically require that the phenomenological prescription \ref{nu}) ) be used with a parameter $\alpha$ varying with radius. |
Iu reality. we believe that the proper way to iuclude the relevant plysical effects; expecially those associatcca with non-axisviunietrie instabilities. wouldbe through some coustraint. | In reality, we believe that the proper way to include the relevant physical effects, especially those associated with non-axisymmetric instabilities, wouldbe through some constraint. |
Until such elobal descriptio- rendus not available. the assuniptiou of a free. constant à may provide a first approximation. best applicable when Q is self-reeulated. | Until such global description remains not available, the assumption of a free, constant $\alpha$ may provide a first approximation, best applicable when $Q$ is self-regulated. |
This choice can be plysically consisteutposteriori, at least for the sclfsimilar solution of Sect. | This choice can be physically consistent, at least for the self-similar solution of Sect. |
25 | 2.2. |
After this digression. we can now proceed with the analysis of the problem as formulated in Sect. | After this digression, we can now proceed with the analysis of the problem as formulated in Sect. |
2. | 2. |
In the presence of a central poiut mass (AL,z 0) we expect the lenethscale re toamark the transition from a Ixepleriau disk to a fully selt-eravitatiug disk with flat rotation curve. | In the presence of a central point mass $M_{\star}\neq 0$ ) we expect the lengthscale $r_s$ to mark the transition from a Keplerian disk to a fully self-gravitating disk with flat rotation curve. |
Surprisingly. in our class of sclfreeulated accretion disks the role of the disk sclberavity turus out to be significant all the wav down to the center. | Surprisingly, in our class of self-regulated accretion disks the role of the disk self-gravity turns out to be significant all the way down to the center. |
Tu Fig. | In Fig. |
1 we illustrate the behavior of the rotation curves in our class of models for several values of the aneular imonientuni flux paramcter £. | \ref{fig:rotazione} we illustrate the behavior of the rotation curves in our class of models for several values of the angular momentum flux parameter $\xi$. |
For comparison. we also VArow the Ikepleriau curve Vy that is obtained by setting —|p 0. | For comparison, we also show the Keplerian curve $V_K$ that is obtained by setting $1+\rho=0$ . |
We note that the difference from the Keplerian decline is significant even at r= Ori). | We note that the difference from the Keplerian decline is significant even at $r=O(r_s)$ . |
For example. for the €20 case we find (V.ViViz100€ at r= 2r. | For example, for the $\xi=0$ case we find $(V-V_K)/V_K\approx 100\%$ at $r=2r_s$ . |
is correlated with recent star formation in hosts in AGN pairs, and how such a correlation, if present, compares to that in ordinary AGNs. | is correlated with recent star formation in hosts in AGN pairs, and how such a correlation, if present, compares to that in ordinary AGNs. |
Figure 11 displays aand Lgoi/Lraa as a functionLiom of aand ffor the pair and tidal samples. | Figure \ref{fig:sfagncorr} displays and $L_{{\rm
Bol}}/L_{{\rm Edd}}$ as a function of and for the pair and tidal samples. |
Also shown for comparison are contours from control AGN samples matched in redshift and stellar mass distributions. | Also shown for comparison are contours from control AGN samples matched in redshift and stellar mass distributions. |
There is a correlation between Lionaand ((D,,(4000)) when Hd,=2 < 1.6) for the pair sample and when =—2 (D,(4000)< 1.9) for the tidal sample, respectively. | There is a correlation between and ) when $\gtrsim 2$ $\lesssim 1.6$ ) for the pair sample and when $\gtrsim
-2$ $\lesssim 1.9$ ) for the tidal sample, respectively. |
Lgo/Lgaa is also correlated with aand ffor both samples, at least part of the correlation is driven by the mass althoughdependence of both c.. (and by extension Lgaa) and ((D,(4000)). | $L_{{\rm Bol}}/L_{{\rm Edd}}$ is also correlated with and for both samples, although at least part of the correlation is driven by the mass dependence of both $\sigma_{\ast}$ (and by extension $L_{{\rm Edd}}$ ) and ). |
The relation between AGN luminosity and ((D,(4000)) of the sample is almost identical to that of the control AGN sample. | The relation between AGN luminosity and ) of the pair sample is almost identical to that of the control AGN sample. |
pair While the tidal sample occupies a similar scaling relation between AGN luminosity and ((D,,(4000)) to that of the control sample, it is skewed towards higher AGN luminosities and larger starburst fractions (younger mean stellar ages). | While the tidal sample occupies a similar scaling relation between AGN luminosity and ) to that of the control sample, it is skewed towards higher AGN luminosities and larger starburst fractions (younger mean stellar ages). |
We discuss implications of our results on tidally enhanced star formation and BH accretion. | We discuss implications of our results on tidally enhanced star formation and BH accretion. |
We compare our results with previous observations of inactive galaxy pairs and of single AGNs in galaxy pairs in §??,, and to predictions from galaxy merger simulations in 29 | We compare our results with previous observations of inactive galaxy pairs and of single AGNs in galaxy pairs in \ref{subsec:compare}, and to predictions from galaxy merger simulations in \ref{subsec:comparesim}. . |
We have detected a correlation between ((and D,(4000)) and projected separation τρ in AGN pairs; systems with smaller separations have larger aand smaller iindicative of SSFRs, with the enhancement becoming significant for higherr,< 10-30 kkpc (Figure 3)). | We have detected a correlation between (and ) and projected separation $r_p$ in AGN pairs; systems with smaller separations have larger and smaller indicative of higher SSFRs, with the enhancement becoming significant for $r_p \lesssim 10$ $30$ kpc (Figure \ref{fig:sf}) ). |
We also hz)find a weak correlation between ((and D,(4000)) and Av in both our tidal and samples, after excluding small values of Av which are pairdominated by redshift measurement errors. | We also find a weak correlation between (and ) and $\Delta v$ in both our tidal and pair samples, after excluding small values of $\Delta v$ which are dominated by redshift measurement errors. |
These results are in broad agreement with previous findings based on statistical samples limi | These results are in broad agreement with previous findings based on statistical samples of inactive galaxy pairs \citep{barton00,lambas03,alonso04,nikolic04,ellison08,li08a,darg10b}. |
ted sample of 12,492 main galaxies from the SDSS DRI (?) selected to have photometric companions within 300 kpc, ? used SFRs inferred from lluminosities to find that the mean SSFR is significantly enhanced for ry<30 kkpc. | For example, in a volume-limited sample of 12,492 main galaxies from the SDSS DR1 \citep{SDSSDR1} selected to have photometric companions within 300 kpc, \citet{nikolic04} used SFRs inferred from luminosities to find that the mean SSFR is significantly enhanced for $r_p < 30$ kpc. |
These authors alsohj find a weak anti-correlation between SSFR and recessional difference Av (seealso?).. | These authors also find a weak anti-correlation between SSFR and recessional velocity difference $\Delta v$ \citep[see
also][]{lambas03}. |
Similarly, ? found an enhancementvelocity in the star formation rates of galaxy pairs at < 30-40 kkpc in a study of ry1716 emission-linehz} galaxies selected from the SDSS DR4 (?) with companions within Av<500 km s, ry«80 kkpc, and stellar mass ratios smaller than 10. | Similarly, \citet{ellison08} found an enhancement in the star formation rates of galaxy pairs at $r_p
<$ 30–40 kpc in a study of 1716 emission-line galaxies selected from the SDSS DR4 \citep{SDSSDR4} with companions within $\Delta v < 500$ km $^{-1}$, $r_p< 80$ kpc, and stellar mass ratios smaller than 10. |
The average SSFR enhancement level we observe inAGN pairs is 0.7-0.9 £0.2 dex from r,=100 to ~5 kkpc. | The average SSFR enhancement level we observe inAGN pairs is $0.7$ $0.9\pm0.2$ dex from $r_p \gtrsim 100$ to $\sim 5$ kpc. |
This is comparable to some previous estimatesh5} based on inactive galaxy pairs factorsof1.5-4from>100toτρ=20kpc; ?),(e.g. but seems to be larger γρthan others taken at face value (e.g.; ? and ?. found an enhancement of a factor of 2). | This is comparable to some previous estimates based on inactive galaxy pairs \citep[e.g., factors of 1.5--4
from $r_p> 100$ to $r_p = 20$ kpc;][]{li08a}, but seems to be larger than others taken at face value (e.g., \citealt{alonso04} and \citealt{darg10b} found an enhancement of a factor of 2). |
The variation in the observed enhancement levels may be due to differences in the galaxy samples studied. | The variation in the observed enhancement levels may be due to differences in the galaxy samples studied. |
For example, the ? results are based on galaxy pairs selected in galaxy groups or clusters with virial masses in the rage of 10P—10' M and therefore may be biased towards early-type galaxies. | For example, the \citet{alonso04} results are based on galaxy pairs selected in galaxy groups or clusters with virial masses in the rage of $10^{13}$ $10^{15} M_{\odot}$ and therefore may be biased towards early-type galaxies. |
Indeed, we find tentative evidence that the star formation enhancement is more prominent and occurs at larger separations in late-type than in early-type galaxies (Figure 7)). | Indeed, we find tentative evidence that the star formation enhancement is more prominent and occurs at larger separations in late-type than in early-type galaxies (Figure \ref{fig:sf:bulge}) ). |
The variation in the observed enhancement levels may also be due to differences in the interaction stages examined. | The variation in the observed enhancement levels may also be due to differences in the interaction stages examined. |
For example, the factor of 2 difference inferred by ? refers to the average difference between their sample (including various separations hence interaction mergerstages) and the control sample, which may be much smaller than the difference observed for small separation pairs. | For example, the factor of 2 difference inferred by \citet{darg10b} refers to the average difference between their merger sample (including various separations hence interaction stages) and the control sample, which may be much smaller than the difference observed for small separation pairs. |
Other factors that may affect the observed level of enhancement include how control are defined and the contamination from closely separated samplesgalaxy pairs that are not tidally interacting. | Other factors that may affect the observed level of enhancement include how control samples are defined and the contamination from closely separated galaxy pairs that are not tidally interacting. |
We find that the enhancement level of recent star formation in AGN pairs with host stellar mass ratios M..1/M.»>3 (minor mergers or interactions) is comparable to (if not slightly smaller than) that in those with stellar mass ratios M.4/M.o«3 (major mergers or interactions), at least when the two galaxiesare separated by more than r,~5 | We find that the enhancement level of recent star formation in AGN pairs with host stellar mass ratios $M_{\ast,1}/M_{\ast,2}>3$ (minor mergers or interactions) is comparable to (if not slightly smaller than) that in those with stellar mass ratios $M_{\ast,1}/M_{\ast,2}<3$ (major mergers or interactions), at least when the two galaxiesare separated by more than $r_p \sim 5$ kpc. |
In addition, the relative enhancement level is hz}similar in kkpc.both the primaries and the secondaries in AGN pairs with stellar mass ratios M.1/M.»> 3. | In addition, the relative enhancement level is similar in both the primaries and the secondaries in AGN pairs with stellar mass ratios $M_{\ast,1}/M_{\ast,2}>3$ . |
Similarly, ? detected SFR enhancement in their sample of inactive galaxy— pairs | Similarly, \citet{ellison08}
detected SFR enhancement in their sample of inactive galaxy pairs |
angles is somehow smaller in the complete caleulation. as it is expected when the finite (albeit small) size of the caps is accounted for. | angles is somehow smaller in the complete calculation, as it is expected when the finite (albeit small) size of the caps is accounted for. |
This also max explain the somehow different conclusions reached by Sclavope et al. ( | This also may explain the somehow different conclusions reached by Schwope et al. ( |
2009). who used a treatment valid only for poiut-like Caps. | 2009), who used a treatment valid only for point-like caps. |
The small opening of the N-rav enüttiusg regions does not constrain the geometry too much. aud several combinations of the angles £ and X are possible. | The small opening of the X-ray emitting regions does not constrain the geometry too much, and several combinations of the angles $\xi$ and $\chi$ are possible. |
We performed deep optical observatious of 1771 in the R baud with aat the to obtain the first characterisation of its optical spectrin. | We performed deep optical observations of 1774 in the R band with at the to obtain the first characterisation of its optical spectrum. |
We did not detect 1771 candidate counterpart at its expected position down to a 36 inuiting magnitude of R~27. | We did not detect 1774 candidate counterpart at its expected position down to a $3 \sigma$ limiting magnitude of $R\sim 27$. |
The constraint on the colour of the caucliclate counterpart. (DRx50.6. rules ou a foreground Weobject. positionally coincident with the XN-rav source. | The constraint on the colour of the candidate counterpart, $(B-R)\la0.6$, rules out a foreground object, positionally coincident with the X-ray source. |
analysed the ddata of musing new calibrations a1 response files(see Sect. | We re-analysed the data of using new calibrations and response files (see Sect. |
3.2). | 3.2). |
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