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They found that richer and more massive superclusters tend to be more filamentary and have à more complicated inner structure (high values of the genus in their study).
They found that richer and more massive superclusters tend to be more filamentary and have a more complicated inner structure (high values of the genus in their study).
Future evolution of the structure in the Universe has been addressed in simulations by several authors. we refer to fora review and references.
Future evolution of the structure in the Universe has been addressed in simulations by several authors, we refer to for a review and references.
studied the evolution of the shape and inner structure of superclusters in simulations from the present time to a distant future (from a=| tod =100. a is the expansion factor).
studied the evolution of the shape and inner structure of superclusters in simulations from the present time to a distant future (from $a = 1$ to $a = 100$, $a$ is the expansion factor).
In their study superclusters were defined as high-mass bound objects. and the supercluster shape was approximated by triaxial ellipses.
In their study superclusters were defined as high-mass bound objects, and the supercluster shape was approximated by triaxial ellipses.
To analyse the substructure of superclusters they used the multiplicity function of clusters in superclusters.
To analyse the substructure of superclusters they used the multiplicity function of clusters in superclusters.
showed that superclusters are elongated. prolate structures. there are no thin pancakes among them.
showed that superclusters are elongated, prolate structures, there are no thin pancakes among them.
Future superclusters are typically much more spherical than present-day superclusters.
Future superclusters are typically much more spherical than present-day superclusters.
Presently. the superclusters contain a large number of clusters. which may merge into a single cluster in the far future. 1.e.. multispiders and multibranching filaments may evolve into simple spiders and filaments.
Presently, the superclusters contain a large number of clusters, which may merge into a single cluster in the far future, i.e., multispiders and multibranching filaments may evolve into simple spiders and filaments.
Comparisons of the properties of rich and poor superclusters have revealed several differences between them.
Comparisons of the properties of rich and poor superclusters have revealed several differences between them.
The mean and maximum number densities of galaxies in rich superclusters are higher than in poor superclusters.
The mean and maximum number densities of galaxies in rich superclusters are higher than in poor superclusters.
Rich superclusters are more asymmetrical than poor superclusters(?).
Rich superclusters are more asymmetrical than poor superclusters.
. Rich superclusters contain high-density cores(2).
Rich superclusters contain high-density cores.
. The fraction of rich clusters and X-ray clusters in rich superclusters is larger than in poor superclusters(??).. and the core regions of the richest superclusters may contain merging X-ray clusters(??).
The fraction of rich clusters and X-ray clusters in rich superclusters is larger than in poor superclusters, and the core regions of the richest superclusters may contain merging X-ray clusters.
. However. we still lack a detailed analysis of whether the differences between the properties of the galaxy and group content of rich and poor superclusters are related also to the differences in morphology of superclusters.
However, we still lack a detailed analysis of whether the differences between the properties of the galaxy and group content of rich and poor superclusters are related also to the differences in morphology of superclusters.
In we compared the properties of the two richest superclusters from the 2dF Galaxy Redshift Survey. the superclusters SCI 126 (SCI 061 in the present study). and the Sculptor supercluster (SCI 9 in EOI).
In we compared the properties of the two richest superclusters from the 2dF Galaxy Redshift Survey, the superclusters SCl 126 (SCl 061 in the present study), and the Sculptor supercluster (SCl 9 in E01).
We used Minkowski functionals to quantify the fine structure of these superclusters as traced by different galaxy populations.
We used Minkowski functionals to quantify the fine structure of these superclusters as traced by different galaxy populations.
Our calculations showed that in the supercluster SCI 126 the population of red. early type galaxies is more clumpy than the population of blue. late type galaxies. especially in the outskirts of the supercluster.
Our calculations showed that in the supercluster SCl 126 the population of red, early type galaxies is more clumpy than the population of blue, late type galaxies, especially in the outskirts of the supercluster.
In contrast. in the supercluster SCI 9 the clumpiness of galaxies of different type is quite similar in its outskirts.
In contrast, in the supercluster SCl 9 the clumpiness of galaxies of different type is quite similar in its outskirts.
In the core of the supercluster SCI 9 the clumpiness of blue. late type galaxies is larger than the clumpiness of red. early type galaxies.
In the core of the supercluster SCl 9 the clumpiness of blue, late type galaxies is larger than the clumpiness of red, early type galaxies.
In the supercluster SCI] 111 in the SGW the clumpiness of red galaxies is larger than that of blue galaxies(?).
In the supercluster SCl 111 in the SGW the clumpiness of red galaxies is larger than that of blue galaxies.
. Morphologically the supercluster SCI 126 resembles a multibranching filament. while the Sculptor supercluster and SCI 111 resemble a multispider.
Morphologically the supercluster SCl 126 resembles a multibranching filament, while the Sculptor supercluster and SCl 111 resemble a multispider.
We need to study the morphology and galaxy populations of a larger sample of superclusters to find out whether the differences between galaxy populations in superclusters are also related to their different morphology.
We need to study the morphology and galaxy populations of a larger sample of superclusters to find out whether the differences between galaxy populations in superclusters are also related to their different morphology.
recently studied the structure and morphologies of elements that define the cosmic web with the Multiscale Morphology Filter and data from ACDM simulations.
recently studied the structure and morphologies of elements that define the cosmic web with the Multiscale Morphology Filter and data from $\Lambda$ CDM simulations.
The authors found several typical morphologies for filaments. which they deseribe as line. grid. star. and complex filaments.
The authors found several typical morphologies for filaments, which they describe as line, grid, star, and complex filaments.
chosing the structures to be associated with the thiourea group. consideration of cosimic abundances slows that simple hydrocarbons may be considered as useful radicals for our purpose.
chosing the structures to be associated with the thiourea group, consideration of cosmic abundances shows that simple hydrocarbons may be considered as useful radicals for our purpose.
The astronomical 21-44. feature extends redward to merge with another prominent band peaking between 25 and 30 juu. also known as the 30-;24 baud.
The astronomical $\mu$ m feature extends redward to merge with another prominent band peaking between 25 and 30 $\mu$ m, also known as the $\mu$ m band.
Following the same line of thought. it is found that this ubiquitous baud cau be modelled by the combined spectra of a large uuuber of aliphatic chains. made of CIT» eroups. oxveen bridges and ΟΠ eroups.
Following the same line of thought, it is found that this ubiquitous band can be modelled by the combined spectra of a large number of aliphatic chains, made of $_{2}$ groups, oxygen bridges and OH groups.
The experimental literature on thiourea anc its derivatives iu the gas phase is scant. despite arecent surge of interest spured by possible chemical applications (see Lesarri (200 1))).
The experimental literature on thiourea and its derivatives in the gas phase is scant, despite a recent surge of interest spured by possible chemical applications (see Lesarri \cite{les}) ).
It is therefore necessary to resort to theory and computational chemustry (see Alia et al.(1999).. Masunov. et al. (2000)...
It is therefore necessary to resort to theory and computational chemistry (see Alia et \cite{ali}, Masunov et al. \cite{mas},
Brvautsey et al. (2006)..
Bryantsev et al. \cite{bry},
etc.).
etc.).
Fortunately. the latter has progressed cousicderably in the last decade. especially due to the ereatlIy increased speed of computers.
Fortunately, the latter has progressed considerably in the last decade, especially due to the greatly increased speed of computers.
The procedure followed in the preseut work is the same as that which was described iu detail in Papoular ((2001)3). except that the adopted elieniical software was updated to version 7 of Ibvpercheumi (Hypercuboe. Tne.).
The procedure followed in the present work is the same as that which was described in detail in Papoular \cite{pap01}) ), except that the adopted chemical software was updated to version 7 of Hyperchem (Hypercube, Inc.).
This software delivers. for cach mode. the IR intensity aud eraphic illustration of the movement of cach atom im the structure. together with the frequency of vibration.
This software delivers, for each mode, the IR intensity and graphic illustration of the movement of each atom in the structure, together with the frequency of vibration.
This is of ereat help in selecting chemical elemeuts auc molecular structures of interest. and later estimating their relative abundances in the moctel.
This is of great help in selecting chemical elements and molecular structures of interest, and later estimating their relative abundances in the model.
The semi-empirical. PMS/RIIE computation method was preferred for the aliphatic structures because it was specifically optimized for hwdrocarbon structures and gives sufficicutly accurate IR. freqencies (better than about 5%) within reasonable computation times.
The semi-empirical, PM3/RHF computation method was preferred for the aliphatic structures because it was specifically optimized for hydrocarbon structures and gives sufficiently accurate IR freqencies (better than about 5 $\%$ ) within reasonable computation times.
For the thiourea family. the enipirieal AMI method was chosen for its more accurate treatiuent of N aud S atous.
For the thiourea family, the semi-empirical AM1 method was chosen for its more accurate treatment of N and S atoms.
Sections 2 and 3 respectively deal with the 2 ecneric classes of molecules defined above.
Sections 2 and 3 respectively deal with the 2 generic classes of molecules defined above.
In cach case. several examples of structures are illustrated. together with the correspoudiug IR spectra. aud. whenever possible. the tvpe of molecular vibration is described.
In each case, several examples of structures are illustrated, together with the corresponding IR spectra, and, whenever possible, the type of molecular vibration is described.
Iu Section {. we svuthesize all the above line spectra and exhibit typical Cluission spectra. differing in the temperatures and abuudanuces of the enütters. to be compared with typical observations.
In Section 4, we synthesize all the above line spectra and exhibit typical emission spectra, differing in the temperatures and abundances of the emitters, to be compared with typical observations.
The required relative abundauces of the various atomic species are indicated im Sec.
The required relative abundances of the various atomic species are indicated in Sec.
5.
5.
a rapid gas capture from a protoplanetary disk to form a massive gas envelope, when its mass exceeds a critical mass (Mizuno1980;Bodenheimer&Pollack1986).
a rapid gas capture from a protoplanetary disk to form a massive gas envelope, when its mass exceeds a critical mass \citep{hm80,bp86}.
. That critical core mass must be reached within the lifetime of the disk gas of several million years 2001),, which places a limit on the core mass of a formed gas giant.
That critical core mass must be reached within the lifetime of the disk gas of several million years \citep[e.g.][]{h01}, which places a limit on the core mass of a formed gas giant.
Because of the slow increase in the critical core mass with core accretion rate (Stevenson2000),, faster formation in general results in larger core mass.
Because of the slow increase in the critical core mass with core accretion rate \citep{ds82,mi00}, faster formation in general results in larger core mass.
Indeed, in many core-accretion models that are successful in forming Jupiter within several Myr (PollacketInabaetal.2003;Alibert2005, etc.),, the resultant core mass is as large as ~10Ma or more.
Indeed, in many core-accretion models that are successful in forming Jupiter within several Myr \citep[][etc.]{jbp96,iiw03,alibert05}, the resultant core mass is as large as $\sim 10M_\oplus$ or more.
In contrast, the mass of Jupiter’s present core is inferred to be small.
In contrast, the mass of Jupiter's present core is inferred to be small.
Saumon made an extensive investigation of the interior structure of Jupiter, finding successful models that are consistent with the observed values of its gravitational moments and equatorial radius by using a variety of equations of state (EOSs) for hydrogen and helium.
\citet{sg04} made an extensive investigation of the interior structure of Jupiter, finding successful models that are consistent with the observed values of its gravitational moments and equatorial radius by using a variety of equations of state (EOSs) for hydrogen and helium.
They demonstrated that the possible core mass of Jupiter is smaller than ~10Ma.
They demonstrated that the possible core mass of Jupiter is smaller than $\sim 10~M_\oplus$.
This is also supported by recent calculations with aninitio EOS derived in the first-principle approach (Nettelmannetal.2008).
This is also supported by recent calculations with an EOS derived in the first-principle approach \citep{nn08}.
. While a more massive core of >10M is reported by Militzeretal.(2008) who used their own EOS of hydrogen-helium mixtures based on density functional molecular dynamics, Fortney&Nettelmann(2009) pointed out the difference in the mass fraction of helium used by the two groups is responsible for this discrepancy in the derived value of Jupiter's core mass.
While a more massive core of $>10 M_\oplus$ is reported by \citet{bm08} who used their own EOS of hydrogen-helium mixtures based on density functional molecular dynamics, \citet{fn09} pointed out the difference in the mass fraction of helium used by the two groups is responsible for this discrepancy in the derived value of Jupiter's core mass.
Although this pending problem about Jupiter's core may arise from the uncertainty of EOS, the core mass suggested by interior modeling is, on an average, smaller than that derived by formation theories.
Although this pending problem about Jupiter's core may arise from the uncertainty of EOS, the core mass suggested by interior modeling is, on an average, smaller than that derived by formation theories.
This fact motivates us to know how small a core can start the rapid gas accretion to form a massive envelope within several Myr.
This fact motivates us to know how small a core can start the rapid gas accretion to form a massive envelope within several Myr.
Reduction of opacity in the protoplanet's envelope has the potential to make a
Reduction of opacity in the protoplanet's envelope has the potential to make a
modeling.
modeling.
Methane ancl anunonia photolvsis are expected to aller (he atmospheric chemistry by allowing additional carbon- and nitrogen-bearing molecules to form. some of which do not appear in significant abundances under (he assumption of chemical equilibrium.
Methane and ammonia photolysis are expected to alter the atmospheric chemistry by allowing additional carbon- and nitrogen-bearing molecules to form, some of which do not appear in significant abundances under the assumption of chemical equilibrium.
However. the effects of non-equilibrium chemistvy do not extend (o pressures greater (han 1 mbar at a sullicient level to have anv major effects on our modeled transmission spectra.
However, the effects of non-equilibrium chemistry do not extend to pressures greater than 1 mbar at a sufficient level to have any major effects on our modeled transmission spectra.
When fitting the available transmission spectroscopy data for GJ 1214b. however. an intriguing possibility is raised that methane photolvsis may be much more efficient than what we predict [rom our photochemical modeling.
When fitting the available transmission spectroscopy data for GJ 1214b however, an intriguing possibility is raised that methane photolysis may be much more efficient than what we predict from our photochemical modeling.
The (transmission data are best [it bv a model with no methane and clouds or hazes that affect the optical and near-IR spectrum.
The transmission data are best fit by a model with no methane and clouds or hazes that affect the optical and near-IR spectrum.
This is consistent with GJ 1214b having a hvdrogen-riceh atmosphere where methane is efficiently photolvzed. aud carbon-rich hazes form readily.
This is consistent with GJ 1214b having a hydrogen-rich atmosphere where methane is efficiently photolyzed, and carbon-rich hazes form readily.
Uc(ill. much degeneracy remains in the modeling efforts. which is due partly to the small amount of spectral data available for GJ 1214b's atmosphere.
Still, much degeneracy remains in the modeling efforts, which is due partly to the small amount of spectral data available for GJ 1214b's atmosphere.
Additional data will provide much-needed constraints (o our modeling efforts.
Additional data will provide much-needed constraints to our modeling efforts.
It still remains to be confirmed that GJ 1214b does indeed possess a low mean molecular weight atmosphere.
It still remains to be confirmed that GJ 1214b does indeed possess a low mean molecular weight atmosphere.
This interpretation is so [ar based upon a single Ixs-band data point from ?.. which should be corroborated with additional data.
This interpretation is so far based upon a single Ks-band data point from \citet{cro11}, which should be corroborated with additional data.
If methane is absent from GJ. 1214b's atmosphere. then confirmation of GJ 1214b's low mean molecular weight through the observation of deep spectral features in (ransmission should be done by observing water features in the planets spectrum. al wavelengths longward of 1-2 jm where the effects of clouds should not be significant.
If methane is absent from GJ 1214b's atmosphere, then confirmation of GJ 1214b's low mean molecular weight through the observation of deep spectral features in transmission should be done by observing water features in the planet's spectrum at wavelengths longward of 1-2 $\mu$ m where the effects of clouds should not be significant.
Additional observations at the wavelengths of methane features are also needed to confirm that this molecule is truly absent [vom (he (transmission spectrum.
Additional observations at the wavelengths of methane features are also needed to confirm that this molecule is truly absent from the transmission spectrum.
The interpretation of a low methane abundance so far depends strongly on (he flat transmission spectrum observed by ?. with warm Spitzer. who should have seen strong methane absorption in the 3.6 jm IRAC band if this molecule was present in modest abundances.
The interpretation of a low methane abundance so far depends strongly on the flat transmission spectrum observed by \citet{des11} with warm Spitzer, who should have seen strong methane absorption in the 3.6 $\mu$ m IRAC band if this molecule was present in modest abundances.
If GJ I214bs atmosphere does in fact have a high mean molecular weight. then the abmosphere must be water-rich to be consistent wilh models of theinterior of the planet (e.g.?)..
If GJ 1214b's atmosphere does in fact have a high mean molecular weight, then the atmosphere must be water-rich to be consistent with models of theinterior of the planet \citep[e.g.][]{rog10}.
In this case the photochemistry should be driven by photolvsis of water into OI and 11. Such an atmosphere would surely be affected by escape of atomic hydrogen. resulting in (he atmosphere slowly becoming more oxidized with time.
In this case the photochemistry should be driven by photolysis of water into OH and H. Such an atmosphere would surely be affected by escape of atomic hydrogen, resulting in the atmosphere slowly becoming more oxidized with time.
The level of oxidation of the abmosphere should then be highlv dependent on the rate of atmospheric escape. which is currentlv unconstrained.
The level of oxidation of the atmosphere should then be highly dependent on the rate of atmospheric escape, which is currently unconstrained.
Additional study of the photochemistry of a water-rich atmosphere for GJ 1214b is bevond the scope of this work but merits additional investigation.
Additional study of the photochemistry of a water-rich atmosphere for GJ 1214b is beyond the scope of this work but merits additional investigation.
GJ 1214b is now one of a growing group of transiting super-IEarth exoplanets.
GJ 1214b is now one of a growing group of transiting super-Earth exoplanets.
To date. 8 (ransiting super-Earths have been confirmed. and another 288 "super-Izuth candidates [rom Kepler with radii between 1.25 and 2 Π still await confirmation (?)..
To date, 8 transiting super-Earths have been confirmed, and another 288 “super-Earth” candidates from Kepler with radii between 1.25 and 2 $R_{\earth}$ still await confirmation \citep{bor11}. .
Additionally.
Additionally,
where. making the substitution⋅⋅ 4,=$7M4P;By(Ai). can be written as: The minimization of Eq. (9))
where, making the substitution $t_k^j = \sum_{i=1}^{M} \Phi_{ij} B_k(\lambda_i)$, can be written as: The minimization of Eq. \ref{eq:l2norm}) )
can be easily done calculating the derivatives with respect to each e; and equating them to zero.
can be easily done calculating the derivatives with respect to each $a_k$ and equating them to zero.
In other words. eiven the vector ο of length N with the observations (photometry). we define (he metric function: where o5.> is. the variance- associated- to ο, and discussed- in- relsecnfluence.rrors..
In other words, given the vector $\mathbf{o}$ of length $N$ with the observations (photometry), we define the metric function: where $\sigma^2_{o_j}$ is the variance associated to $o_j$ and discussed in \\ref{sec:influence_errors}.
Then. weendupiwiththefollowingsetoflinearequalionsfora.: In matrix form. we have: where The /s are defined [rom (he principal components of the spectra ancl (he photometric svstem they are common for all objects.
Then, we end up with the following set of linear equations for $a_k$: In matrix form, we have: where The $t$ 's are defined from the principal components of the spectra and the photometric system –they are common for all objects.
The only additional information needed for each object is the photometry ancl its expected uncertainties.
The only additional information needed for each object is the photometry and its expected uncertainties.
Each spectrum is reconstructed by computing the b vector. calculating Gtb. and using these numbers in the linear combination of Eq. (10)).
Each spectrum is reconstructed by computing the $\mathbf{b}$ vector, calculating $\mathbf{G}^{-1} \mathbf{b}$, and using these numbers in the linear combination of Eq. \ref{eq:develop}) ).
It is also of interest to note that the solution to Eq. (9))
It is also of interest to note that the solution to Eq. \ref{eq:l2norm}) )
can alternatively. be easily carried out using the SVD of the matrix 9sW'.
can alternatively be easily carried out using the SVD of the matrix $\mathbf{\Phi} \mathbf{W}^\dag$.
We have verified empirically that this matrix of size .NxM fulfills that rank(W!)=Αι
We have verified empirically that this matrix of size $N \times M$ fulfills that $\mathrm{rank}(\mathbf{\Phi} \mathbf{W}^\dag) = N$.
Thus. in order to reconstruct the spectrum using AN principal components. we need to have. al least. Vo measurements.
Thus, in order to reconstruct the spectrum using $N$ principal components, we need to have, at least, $N$ measurements.
Since we have only
Since we have only
We will refer (ο extended components. rather than. disks as we lack resolved kinematic data for most objects.
We will refer to 'extended components' rather than 'disks' as we lack resolved kinematic data for most objects.
Morphologies are often disk-like for larger LCDGs (see 1)). bui ambiguous for small objects which could be either spheroids or disks.
Morphologies are often disk-like for larger LCBGs (see \ref{fig3}) ), but ambiguous for small objects which could be either spheroids or disks.
Fieure 3. compares (he extended components of the LCBGs to samples of wilh exponential 5DPs.
Figure \ref{fig4} compares the extended components of the LCBGs to samples of with exponential SBPs.
The disk sample bv Lu(1998) was chosen because of ils completeness of local field disk scalelengthis. aud theUAMa-cluster sample by Tullyetal.(1996). was added to include disks [rom higher density environments.
The disk sample by \citet{lu98} was chosen because of its completeness of local field disk scalelengths, and theUMa-cluster sample by \citet{tully96} was added to include disks from higher density environments.
It is evident that the extended components of almost all LCBGs have small scale lengths (RoS 2kkpc): at any given luminosity. (hey are comparable to the local disk galaxies with the smallest. R..
It is evident that the extended components of almost all LCBGs have small scale lengths $R_s\la2$ kpc): at any given luminosity, they are comparable to the local disk galaxies with the smallest $R_s$.
This result is robust against uncertainties of Z2,.
This result is robust against uncertainties of $R_s$.
The less Iuminous exponential components are also compatible with those of relatively compact. luminous local cwarl ealaxies (compact dEs. or stellar hosts of DCDs).
The less luminous exponential components are also compatible with those of relatively compact, luminous local dwarf galaxies (compact dEs, or stellar hosts of BCDs).
The only two exceptions are UDFO900 (the LCDG with the largest A. in Fig. 3..
The only two exceptions are UDF0900 (the LCBG with the largest $R_s$ in Fig. \ref{fig4},
see also Fig. 1)).
see also Fig. \ref{fig3}) ),
which shows a large LSB component (Hop£222.9mag/LI". HR,=4.4 kkpe) with an exponential SBP but no spiral features. (Fig. »D)
which shows a large LSB component $\mu _{0,B}\approx 22.9{\rm mag}/\square\arcsec$, $R_s=4.4$ kpc) with an exponential SBP but no spiral features, (Fig. \ref{fig4})
? Both galaxies have bright central regions that led to their classification as LCBCs.
Both galaxies have bright central regions that led to their classification as LCBGs.
This structural study of their extended components reveals that ~90% of LCDGs αἱ 2~0.2-1.3 are (ruly small galaxies.
This structural study of their extended components reveals that $\sim 90\%$ of LCBGs at $z\sim 0.2-1.3$ are truly small galaxies.
For (hese. suspected large disks wilh J, similar to the MAW. or the extended low-surlace brightness component found in a local LCDG 77673). can be ruled out down to surface brightnesses >26Dmag/L (cf.
For these, suspected large disks with $R_s$ similar to the MW, or the extended low-surface brightness component found in a local LCBG 7673), can be ruled out down to surface brightnesses $\ga 26 \,B\,{\rm mag}/\square\arcsec$ (cf.
Fig. 1)).
Fig. \ref{fig3}) ).
m (14) we wish we could also write this in terms of the external density by making the substitution Klo=Mppostf2Poxt-
= If we wish we could also write this in terms of the external density by making the substitution $kT_{\rm ext} = m_p p_{\rm ext} /2\rho_{\rm ext}$.