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Indeed. ? find a temporal offset of the secondary eclipse. which can be attributed to a slight orbit eccentricity or another interacting body. | Indeed, \citet{Gillon2010} find a temporal offset of the secondary eclipse, which can be attributed to a slight orbit eccentricity or another interacting body. |
Because transit timing variations larger then 10 s are excluded by the CoRoT light curve (2). ?. conclude that the planetary orbit has an eccentricity of ~0.014. | Because transit timing variations larger then 10 s are excluded by the CoRoT light curve \citep{Alonso2009}, \citeauthor{Gillon2010} conclude that the planetary orbit has an eccentricity of $\sim0.014$. |
Given the present eccentricity of the orbit. the anomalous radius of the planet can be explained by evolutionary scenarios if the models include a third planetarybody in the system. | Given the present eccentricity of the orbit, the anomalous radius of the planet can be explained by evolutionary scenarios if the models include a third planetarybody in the system. |
?. propose two possible scenarios. which would result in a relatively recent (~20 Ma) start of the circularization process of the orbit. | \citet{GuillotHavel2011} propose two possible scenarios, which would result in a relatively recent $\sim20$ Ma) start of the circularization process of the orbit. |
One requires a planetary encounter and the other is based on the Kozai interaction with a distant body. | One requires a planetary encounter and the other is based on the Kozai interaction with a distant body. |
Our findings clearly favor the latter scenario. | Our findings clearly favor the latter scenario. |
The ssystem may be à key to à more profound understanding of the early evolution of planetary systems. | The system may be a key to a more profound understanding of the early evolution of planetary systems. |
We studied new optical and X-ray data. | We studied new optical and X-ray data. |
Our analysis showed that magnetic activity can be traced through all layers of the stellar atmosphere from the photosphere to the corona and provided new evidence. helping to answer questions about the age. distance. and evolution of the system. | Our analysis showed that magnetic activity can be traced through all layers of the stellar atmosphere from the photosphere to the corona and provided new evidence, helping to answer questions about the age, distance, and evolution of the system. |
A detailed analysis of several age indicators showed that an age between 100 and 300 Ma ts most likely. | A detailed analysis of several age indicators showed that an age between $100$ and $300$ Ma is most likely. |
Furthermore. we were able to provide an estimate of 270 pe for the distance ofCoRoT-2A.. but with a large uncertainty. | Furthermore, we were able to provide an estimate of $270$ pc for the distance of, but with a large uncertainty. |
Beyond answering questions. our analysis also raised new problems. | Beyond answering questions, our analysis also raised new problems. |
Most notably. the true nature ofJ192706364-0122577.. the optical and potentially physical stellar companion ofCoRoT-2A.. remains doubtful. | Most notably, the true nature of, the optical and potentially physical stellar companion of, remains doubtful. |
The apparent presence of a gravitationally bound and. therefore. most likely coeval K-type stellar companion. which. nonetheless. shows no detectable activity. would challenge our picture of the ssystem. | The apparent presence of a gravitationally bound and, therefore, most likely coeval K-type stellar companion, which, nonetheless, shows no detectable activity, would challenge our picture of the system. |
Either the companion is old enough to have already become inactive. or aappears to be younger than it actually is. | Either the companion is old enough to have already become inactive, or appears to be younger than it actually is. |
A third body would have a substantial impact on the evolutionary dynamics of the whole system. | A third body would have a substantial impact on the evolutionary dynamics of the whole system. |
It may account for the eccentricity of the planetary orbit and may even be responsible for the observed anomalously large radius of CoRoT-2b.. | It may account for the eccentricity of the planetary orbit and may even be responsible for the observed anomalously large radius of . |
We shall first solve the iuduction equation (1)) with a prescribed flow that is a statistically steady solution of the randomly driveu Navier-Stokes ecquations Here p is the pressure (whose role is to maiutaiu incompressibility). 7 isthe viscosity aud f£ isa random force. the specific properties of which we detail below. | We shall first solve the induction equation \ref{eq:induction}) ) with a prescribed flow that is a statistically steady solution of the randomly driven Navier-Stokes equations Here $p$ is the pressure (whose role is to maintain incompressibility), $\nu$ isthe viscosity and $\mathbf{f}$ is a random force, the specific properties of which we detail below. |
We have neglected the Lorentz force since we are considering the kinematic case in which the maguetic field is weak ancl heuce doesu't dfect the flow. | We have neglected the Lorentz force since we are considering the kinematic case in which the magnetic field is weak and hence doesn't affect the flow. |
The equations (1..10 are solved on the πριν periodic domain x€[0.24]. | The equations \ref{eq:induction}, \ref{eq:momentum}) ) are solved on the triply periodic domain $\mathbf{x}\in [0,2\pi]$. |
We note iat although the Kazaustey model is defiued ou the infinite domain r€[0.x]. it is anticipated (αι. verified below) that the periodie boundary couditious do uot play a crucial role if it is ensured that the energy coutatuing scales of the flow aud tlie magnetic field are significantly sinaller than 27. | We note that although the Kazanstev model is defined on the infinite domain $r\in [0,\infty]$, it is anticipated (and verified below) that the periodic boundary conditions do not play a crucial role if it is ensured that the energy containing scales of the flow and the magnetic field are significantly smaller than $2\pi$. |
— is pointed out that this requirement. together with the restrictions placed by currently available computational power. does however severely limit the extent of the inertial rauge of the simulated flow. | It is pointed out that this requirement, together with the restrictions placed by currently available computational power, does however severely limit the extent of the inertial range of the simulated flow. |
Iu order to couduct a ineaningful comparison with the lxazantsev model the simulated velocity unt have the required spatial properties. Le. it inust be small-scale (significantly smaller than the box size 27) aud spatially homogeneous aud isotropic. | In order to conduct a meaningful comparison with the Kazantsev model the simulated velocity must have the required spatial properties, i.e. it must be small-scale (significantly smaller than the box size $2\pi$ ) and spatially homogeneous and isotropic. |
For this first study we also restrict our attention to the nou-helical case. | For this first study we also restrict our attention to the non-helical case. |
The idea is to impose ou the forcing function the properties that are required of the velocity. | The idea is to impose on the forcing function the properties that are required of the velocity. |
Then. at least iu the strouglv diffusive case where the solution of equation (10)) represents a balance between the diffusive terms aud the force. the flow will inherit those characteristics. | Then, at least in the strongly diffusive case where the solution of equation \ref{eq:momentum}) ) represents a balance between the diffusive terms and the force, the flow will inherit those characteristics. |
We therefore choose a rauco. divergeuce-Iree. non-helical. homogeneous and isotropic force with Fourier coelficieuts Here A is a (constant) amplituce that is chosen so that the resultingrims velocity [Iuctuations are ol order unity. (075zz1. | We therefore choose a random, divergence-free, non-helical, homogeneous and isotropic force with Fourier coefficients Here $A$ is a (constant) amplitude that is chosen so that the resulting velocity fluctuations are of order unity, $\langle u^2 \rangle \approx 1$. |
The k-dependent atmplitucle. eg. is chosen with the aim of concentrating[n] the enerey in the velocity [Iuctuations at scales that are neither too large (since we wish to limit the effects of the bouudary couclitious) uor too small (since the magnetic field will grow on smaller scales aud we must be able to resolve both aud couduct. the simulation over a number of eddy turnover times at the largest scale). | The $\mathbf{k}$ -dependent amplitude, $a_{\mathbf{k}}$, is chosen with the aim of concentrating the energy in the velocity fluctuations at scales that are neither too large (since we wish to limit the effects of the boundary conditions) nor too small (since the magnetic field will grow on smaller scales and we must be able to resolve both and conduct the simulation over a number of eddy turnover times at the largest scale). |
We choose the Gaussian profile where &=|k| aud we take yy=z/1. | We choose the Gaussian profile where $k=|\mathbf{k}|$ and we take $y_0=\pi/4$. |
At each timestep the unit vector ek(/) is rotated about oue of the three coordinate axes at random by an amount O,(/). with QOg(/) aud the raudoim phase Ok(/) being drawn independently [from uniform distributions on [—w.7] at each timestep. | At each timestep the unit vector $\mathbf{\hat e_k}(t)$ is rotated about one of the three coordinate axes at random by an amount $\theta_\mathbf{k}(t)$ , with $\theta_\mathbf{k}(t)$ and the random phase $\phi_\mathbf{k}(t)$ being drawn independently from uniform distributions on $[-\pi,\pi]$ at each timestep. |
This | This |
potential non-detected companions. | potential non-detected companions. |
Since LOCT can sieuificautlv reduce the flux. of auy detected poiut source. detection limits need to be based on the retrieval of fake companions and cannot be derived solely from the noise in the final imaee. | Since LOCI can significantly reduce the flux of any detected point source, detection limits need to be based on the retrieval of fake companions and cannot be derived solely from the noise in the final image. |
A complicating factor in our case is the inhomogeneous seusitivitv across the final nuages. | A complicating factor in our case is the inhomogeneous sensitivity across the final images. |
We decided to put fake planets in regions where ouly data from one hemisphere is combined aud not im the overapping regions. | We decided to put fake planets in regions where only data from one hemisphere is combined and not in the overlapping regions. |
This approach is represcutative for a “typical” APP observing run and the results are represcutative for typical APP detection limits. | This approach is representative for a "typical" APP observing run and the results are representative for typical APP detection limits. |
We used the data of hemisphere 1 for HID115592 aud of hemisphere 2 for IID172555. | We used the data of hemisphere 1 for HD115892 and of hemisphere 2 for HD172555. |
For ΠΟ19502, 10681 and 9615 frames were combined for scparatious <O.8” and DOGS. respectively, | For HD115892, 10681 and 9615 frames were combined for separations $\le$ $''$ and $>$ 0.8”, respectively. |
For IID172555 we could combine 1697 and 3016 frames in these regions. | For HD172555 we could combine 4697 and 3046 frames in these regions. |
As fake plaucts we used for cach target the median-combined PSF of au unsaturated data set and scaled it to different contrast ratios based on the average count rate of the unsaturated nuages and the difference iu exposure time between he unsaturated and the saturated images. | As fake planets we used for each target the median-combined PSF of an unsaturated data set and scaled it to different contrast ratios based on the average count rate of the unsaturated images and the difference in exposure time between the unsaturated and the saturated images. |
These fake auets with known brightuess were then inserted in he individual ska-subtracted raw frames atf cliffereut radii taking into account the field rotation that occurred jetween the exposures. | These fake planets with known brightness were then inserted in the individual sky-subtracted raw frames at different radii taking into account the field rotation that occurred between the exposures. |
Finally. we repeated the data reduction described above aud determined the S/N of ake plauets that we recovered in the final image. | Finally, we repeated the data reduction described above and determined the S/N of fake planets that we recovered in the final image. |
We did aperture photometry on the recovered planets and conrpared it to the standard deviation of background xxels iu an auuulus ceutered on the central star. | We did aperture photometry on the recovered planets and compared it to the standard deviation of background pixels in an annulus centered on the central star. |
This anuulus had the same radial distance as the planet and a width twice as wide as the aperture radius. | This annulus had the same radial distance as the planet and a width twice as wide as the aperture radius. |
We excluded those regions in the aunulus where fewer frames were combined than at the position of the planet. aud we excluded the region around the planet itself οι 3 FWHAL centered on the plauet) as LOCT can create artificial holes left aud rielt of a detected point source. | We excluded those regions in the annulus where fewer frames were combined than at the position of the planet, and we excluded the region around the planet itself (i.e., 3 FWHM centered on the planet) as LOCI can create artificial 'holes' left and right of a detected point source. |
The S/N of the fake planet can then beexpressed as with Fi being the flix of the planct. 0 the staudaxd deviation of the pixels in the aunulus (both measured iu ‘count rate] aud ray the aperture radius. | The S/N of the fake planet can then beexpressed as with $F_{\rm pl}$ being the flux of the planet, $\sigma$ the standard deviation of the pixels in the annulus (both measured in 'count rate') and $r_{\rm ap}$ the aperture radius. |
We inserted ake planets with a contrast between 9 and 11 mag in the IIDI15592 data aud between 5 aud 9 mae iu he IID172555 data aud computed the S/N for two aperture sizes (2 and 23 pixels radius). | We inserted fake planets with a contrast between 9 and 11 mag in the HD115892 data and between 8 and 9 mag in the HD172555 data and computed the S/N for two aperture sizes (2 and 3 pixels radius). |
The final contrast limit for a given separation was then derived o» averaging the S/N iu both apertures. taking those ake planets where the averaged S/N was the lowest mt 25 aud extrapolating the contrast of the planet to a value that would correspond to a Soa detection. | The final $\sigma$ contrast limit for a given separation was then derived by averaging the S/N in both apertures, taking those fake planets where the averaged S/N was the lowest but $\ge$ 5 and extrapolating the contrast of the planet to a value that would correspond to a $\sigma$ detection. |
We emphasize that we did not apply anv sort of filtering or ckeround smoothing to our data which males our final S/N estimates rather conservative. | We emphasize that we did not apply any sort of filtering or background smoothing to our data which makes our final S/N estimates rather conservative. |
Also the optimized extraction of a PSF template could lead to the robust detection of fainter companions. | Also the optimized extraction of a PSF template could lead to the robust detection of fainter companions. |
Tu Figure 3. we show the final detection limits for both objects between 1.07. | In Figure \ref{detection_limits} we show the final $\sigma$ detection limits for both objects between $''$. |
Overplotted are detectable mass Buts for a eiven contrast aud the age of the star (Table 1)). | Overplotted are detectable mass limits for a given contrast and the age of the star (Table \ref{targets}) ). |
These mass linuts are derived from the DUSTY and COND evolutionary models (Chahricretal.2000:Baraffe 2003). | These mass limits are derived from the DUSTY and COND evolutionary models \citep{chabrier2000,baraffe2003}. |
. We use the COND models for objects with effective. temperatures below ~1700 IS and the DUSTY ποσο] for hotter objects. | We use the COND models for objects with effective temperatures below $\sim$ 1700 K and the DUSTY models for hotter objects. |
For the 350 Myr old object IID115892 our data reach a contrast between ~10.5 11.3 mae at angular separations between 1.0% (718 AU). | For the 350 Myr old object HD115892 our data reach a contrast between $\sim$ 10.5–11.3 mag at angular separations between $''$ (7–18 AU). |
This coutrast corresponds to detectable mass limit between LO15 Mq. | This contrast corresponds to detectable mass limit between 10–15 $_{\rm Jup}$ . |
At 0.3” AU) the contrast is —9.1 mag and we are still scusitive to objects with masses 725 ALinp. | At $''$ $\sim$ 5.5 AU) the contrast is $\sim$ 9.4 mag and we are still sensitive to objects with masses $\gtrsim$ 25 $_{\rm Jup}$ . |
For the 12 Mwr IID172555 system the coutrast is ~9.2 9.8 inae af separations between 1.07 (1529 AU) which corresponds to mass linüts of 23 Mau, | For the 12 Myr HD172555 system the contrast is $\sim$ 9.2–9.8 mag at separations between $''$ (15–29 AU) which corresponds to mass limits of 2–3 $_{\rm Jup}$. |
At 0.1" (~11 AU) the achieved contrast is ~8.9 mae and we are stil seusitive to objects with zl AL. | At $''$ $\sim$ 11 AU) the achieved contrast is $\sim$ 8.9 mag and we are still sensitive to objects with $\gtrsim$ 4 $_{\rm Jup}$. |
Due to the sinaller1 held rotation for this object we can not probe INA 0.3. | Due to the smaller field rotation for this object we can not probe IWA $\le$ $''$. |
Both our datasets have comparable total iutegratiou nues and factoring in the apparent brightucss of the stars both curves are comparable in teris of detectable xiehtuess for potential coupanions. | Both our datasets have comparable total integration times and factoring in the apparent brightness of the stars both curves are comparable in terms of detectable brightness for potential companions. |
Iu addition. both contrast curves are relatively flat for separations Z0.5". | In addition, both contrast curves are relatively flat for separations $\gtrsim$ $''$. |
This sugecsts that the APP achieves close to background inited performance for these separations. | This suggests that the APP achieves close to background limited performance for these separations. |
We computed he expected backeround limit for the ITD115892 data set sed on the sky noise in mdividual frames far away from he star. | We computed the expected background limit for the HD115892 data set based on the sky noise in individual frames far away from the star. |
The dashed line in the left panel in Figure 3 shows the result and confirms that our data are indeed (mostlv) limited by the background and not bv the contrast. | The dashed line in the left panel in Figure \ref{detection_limits} shows the result and confirms that our data are indeed (mostly) limited by the background and not by the contrast. |
Due to the lack of appropriate dark frames we could not repeat this exercise for ΠΟΤΟ2ΡΟΣ, | Due to the lack of appropriate dark frames we could not repeat this exercise for HD172555. |
Given the node data coverage in azimuth he detection Linitshomogeneous derived above vary between differeut oositious around each object. | Given the non-homogeneous data coverage in azimuth the detection limits derived above vary between different positions around each object. |
To estimate the elobal detection linits we only cousider those regions where we have combined at least half as may frames as for he analvsis. | To estimate the global detection limits we only consider those regions where we have combined at least half as many frames as for the analysis. |
For IID115892 we then have to exclude au azimuthal wedee between ~22° 1317 (East of North). and for IIDI172555 it’s regions between —177 1077 (see also right colum Fieure 2)). | For HD115892 we then have to exclude an azimuthal wedge between $\sim$ $^\circ$ $^\circ$ (East of North), and for HD172555 it's regions between $\sim$ $^\circ$ $^\circ$ (see also right column Figure \ref{images}) ). |
In all the other parts of he images the detection limits shown im Figure 2. apply with a sienificance of 223.56 with the lowest significance applving only in very small wedees directly adjacent to he exchided parts. | In all the other parts of the images the detection limits shown in Figure \ref{detection_limits} apply with a significance of $\ge$ $\sigma$ with the lowest significance applying only in very small wedges directly adjacent to the excluded parts. |
Lagrangeetal.(2009b)/ used radial velocity to search for plauetarv niass conrpaudons to both of our targets. | \citet{lagrange2009c} used radial velocity to search for planetary mass companions to both of our targets. |
Although they did not find they could put some constraints on the occurrence of massive planets im short period orbits. | Although they did not find any they could put some constraints on the occurrence of massive planets in short period orbits. |
For IID115592 they could exclude objectsY more dnassive than 1.7. 3.8 and 100.0 in 10, and LOO dav orbits. respectively, with >99% Mj,couficlence. | For HD115892 they could exclude objects more massive than 1.7, 3.8 and 100.0 $_{\rm Jup}$ in 3, 10, and 100 day orbits, respectively, with $>$ confidence. |
These orbital periods correspond. to -... axes of 0.06. 0.123. and. 0.62 AU asstuunineg circular orbits. | These orbital periods correspond to semi-major axes of $\sim$ 0.06, 0.13, and 0.62 AU assuming circular orbits. |
For IID172555 the same coufidence level was achieved for objects more massive than 11.3 in a 3 or 10 day orbit (ie. ~0.05 AU and —0.11 AU). Marespectively. | For HD172555 the same confidence level was achieved for objects more massive than 11.3 $_{\rm Jup}$ in a 3 or 10 day orbit (i.e., $\sim$ 0.05 AU and $\sim$ 0.11 AU), respectively. |
For a 100 day orbit (ιο, at 0.53 AU) the detection limit was 33 | For a 100 day orbit (i.e., at 0.53 AU) the detection limit was 33 $_{\rm Jup}$ . |
In addition. Billerctal.(2007). used NACO in spectralMaas: differential maging (SDI) mode to search for low-mass companionaround IID172555. | In addition, \citet{biller2007} used NACO in spectral differential imaging (SDI) mode to search for low-mass companionaround HD172555. |
Whileour data are more sensitive iu the innermost 1" (io. for separations «230 AU). their data cover regious out to 2" and they could have detected objects with masses Z5 ALinp for separation between 30.60 AU. | Whileour data are more sensitive in the innermost $''$ (i.e., for separations $<$ 30 AU), their data cover regions out to $''$ and they could have detected objects with masses $\gtrsim$ 5 $_{\rm Jup}$ for separation between $\sim$ 30–60 AU. |
2+hl | (1+z_s)^2. |
Eqation (9)) can be put into the form of a Heu1 equaton and its solution lias been given in terms of Heun funetious in Ixantowski(1905). | Equation \ref{Area}) ) can be put into the form of a Heun equation and its solution has been given in terms of Heun functions in \cite{KR98}. |
.. Ever hougl the Heun eqtation is only slightly More couplicatecd than the hypergeometric equation. it] as | regular singular points rather than 3. Heuu fuuctious are not vet available in stauda«d libraries. | Even though the Heun equation is only slightly more complicated than the hypergeometric equation, it has 4 regular singular points rather than 3, Heun functions are not yet available in standard libraries. |
Consequeuly. such. expressions are nol yarticularly useful for comparison with data. at this (ine. | Consequently, such expressions are not particularly useful for comparison with data, at this time. |
Because tie exponeuts of tliree of the sugular poluts of the area equation (in standa‘| Heun form) are 0 and 1/2 [see ((13) in Ixautowski(199 8)]]. equation (9)) is actually equivalent to tie cloubly perodic Lame’ equation. | Because the exponents of three of the singular points of the area equation (in standard Heun form) are 0 and 1/2 [see (13) in \cite{KR98}] ], equation \ref{Area}) ) is actually equivalent to the doubly periodic $^{\prime}$ equation. |
We now show that it reduces to the associated Legendre equiion for the spatially flat universe. Qu—1. | We now show that it reduces to the associated Legendre equation for the spatially flat universe, $\OO=1$. |
The required chauge of dependent. aud iudependeut va‘lables are res»ectively | The required change of dependent and independent variables are respectively. |
The resulting associated Legendre equation is SESpeso(19) with initial conditio | The resulting associated Legendre equation is + P =, with initial conditions: |_s = . |
us: | The resulting luminosity distance is then given by |
is very evident below V—18. | is very evident below $V = 18$. |
If the result is that main sequence stars spread into the area in which field stars are counted, then the derived (observed) luminosity function will be too small. | If the result is that main sequence stars spread into the area in which field stars are counted, then the derived (observed) luminosity function will be too small. |
Because of the difficulty in quantifying this effect, we should consider whether there are dynamical processes, omitted from the models, which could also account for the mismatch at the faint end of the luminosity function. | Because of the difficulty in quantifying this effect, we should consider whether there are dynamical processes, omitted from the models, which could also account for the mismatch at the faint end of the luminosity function. |
The difference in the luminosity functions for V>16 mag suggests some mechanism by which the open cluster M67 very efficiently removed a substantial fraction of low mass stars (M« 0.7Mc) during its evolution. | The difference in the luminosity functions for $V > 16$ mag suggests some mechanism by which the open cluster M67 very efficiently removed a substantial fraction of low mass stars $M < 0.7 M_{\odot}$ ) during its evolution. |
There are two possibilities: | There are two possibilities: |
We present the abundances of Π.Ο. CO, 00», and CH, for the case of Teg = 1500KK, T. = 1700KK, and logg=4.5 for the models of the UCM-c ( applied to 2MASS J152322--3014 in Section ??)) and UCM-a (applied to SDSS J083008--4828) series in Figure 2 as the solid and dashed lines, respectively. | We present the abundances of $_2$ O, CO, $_2$ , and $_4$ for the case of $T_\mathrm{eff}$ = K, $T_{\rm cr}$ = K, and $\log g = 4.5$ for the models of the UCM-c ( applied to 2MASS $+$ 3014 in Section \ref{sec:spc}) ) and UCM-a (applied to SDSS $+$ 4828) series in Figure \ref{fig:fig2} as the solid and dashed lines, respectively. |
The increased C O abundances result in the increases of CO, CO», and H2O abundances as expected. | The increased C O abundances result in the increases of CO, $_2$, and $_2$ O abundances as expected. |
The increase of the CO» abundance in the UCM-a series is quite significant for the reason noted before. | The increase of the $_2$ abundance in the UCM-a series is quite significant for the reason noted before. |
On the contrary, the CH4 abundance shows a decrease in the UCM-a series and this unexpected result may be because the direct effect of the increased carbon abundance on the CH4 abundance is superseded by the dissociation of CH4 due to the elevated temperatures in the model of the UCM-a series (Figure 1)). | On the contrary, the $_4$ abundance shows a decrease in the UCM-a series and this unexpected result may be because the direct effect of the increased carbon abundance on the $_4$ abundance is superseded by the dissociation of $_4$ due to the elevated temperatures in the model of the UCM-a series (Figure \ref{fig:fig1}) ). |
As another example, we show the case of Tog = 1200KK, Ty, = 1900KK, and logg=4.5 in Figure 3.. | As another example, we show the case of $T_\mathrm{eff}$ = K, $T_{\rm cr}$ = K, and $\log g = 4.5$ in Figure \ref{fig:fig3}. |
The results are again shown for the UCM-c and UCM-a series with the solid and dashed lines, respectively. | The results are again shown for the UCM-c and UCM-a series with the solid and dashed lines, respectively. |
In this case, the effects of the abundance changes are more pronounced, especially for CO». | In this case, the effects of the abundance changes are more pronounced, especially for $_2$ . |
We will see in Section ?? that thecase of the UCM-a series is approximately realized in 2MASS J055919—1404 in which the CO» bandappears to be very strong. | We will see in Section \ref{sec:spc} that thecase of the UCM-a series is approximately realized in 2MASS $-$ 1404 in which the $_2$ bandappears to be very strong. |
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