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While the ellects of the sweeping i44 resonance are analogous to the 14. only affecting inclinations instead of eccentricities. a [ull analvsis of the asteroid belt inclinations is bevond the scope of the present work. but will be explored in a future study.
While the effects of the sweeping $\nu_{16}$ resonance are analogous to the $\nu_6$, only affecting inclinations instead of eccentricities, a full analysis of the asteroid belt inclinations is beyond the scope of the present work, but will be explored in a future study.
A number of other studies have derived limits on the speed of planetesimal-driven giant planet migration.
A number of other studies have derived limits on the speed of planetesimal-driven giant planet migration.
Murrav-Clay&Chiang(2005) exclude an e—[olding migration timescale TXl]Mv to 99.65% confidence based on the lack of a large observed. asvimetry in the population of Nuiper belt objects in the two libration centers of the 2:1 Neptune mean motion resonance.
\cite{MurrayClay:2005p209} exclude an $e-$ folding migration timescale $\tau\leq 1\My$ to $99.65\%$ confidence based on the lack of a large observed asymmetry in the population of Kuiper belt objects in the two libration centers of the 2:1 Neptune mean motion resonance.
Ποιόοἱal.(2009). exclude 7<My based on the observed obliquity of saturn.
\cite{Boue:2009p1626} exclude $\tau\leq 7\My$ based on the observed obliquity of Saturn.
The latter lower limit on (he migration timescale is slightly incompatible with the lower limit on the rate of Saturn's migration of ds>0.15AUMy+ we derive based on the existence of the inner asteroid belt.
The latter lower limit on the migration timescale is slightly incompatible with the lower limit on the rate of Saturn's migration of $\dot{a}_6>0.15\AU\My^{-1}$ we derive based on the existence of the inner asteroid belt.
One way these can be reconciled is if Saturns orbital eccentricity were a factor 2 smaller than its present value as it migrated from 8.5 AU to 9.2 AU: then. some mechanism would need to have increased Saturn's eccentricity up to its present value bv the time Saturn reached its present semimajor axis of ~9.6AU.
One way these can be reconciled is if Saturn's orbital eccentricity were a factor $\sim2$ smaller than its present value as it migrated from 8.5 AU to 9.2 AU; then, some mechanism would need to have increased Saturn's eccentricity up to its present value by the time Saturn reached its present semimajor axis of $\sim9.6\AU$.
The authors would like to thank the anonymous reviewer and (he editor Eric Feigelson for useful comments.
The authors would like to thank the anonymous reviewer and the editor Eric Feigelson for useful comments.
This research was supported in part bv NSF grant no.
This research was supported in part by NSF grant no.
AST-0806828 and NASA:NESSF grant no.
AST-0806828 and NASA:NESSF grant no.
NNNOSAW?25II. The work of David Minton was additionally partially supported by NASA NLSI/CLOE research grant no.
NNX08AW25H. The work of David Minton was additionally partially supported by NASA NLSI/CLOE research grant no.
NNAO9DD32AÀ The binned eccentricity distribution max be modeled as a Gaussian probability distribution function. given bv: where σ is the standard deviation. fois (he mean. and is the random variable: in our case vis the eccentricity.
NNA09DB32A The binned eccentricity distribution may be modeled as a Gaussian probability distribution function, given by: where $\sigma$ is the standard deviation, $\mu$ is the mean, and $x$ is the random variable; in our case $x$ is the eccentricity.
With an appropriate scaling factor. equation (AL)) can be used to model the number of asteroids per eccentricity bin.
With an appropriate scaling factor, equation \ref{e:gaussian}) ) can be used to model the number of asteroids per eccentricity bin.
However. rather than fit the binned distribution. we instead. perform a least squares fit of the unbinned sample to the Gaussian cumulative distribution function given bv:
However, rather than fit the binned distribution, we instead perform a least squares fit of the unbinned sample to the Gaussian cumulative distribution function given by:
1998b).
.
Moreover. the frequency separation in the Atoll source 11636-536 seems not to (e consistent with the half of the frequency of the QPO in type L bursts (Méndez&vanParadijs.1998)..
Moreover, the frequency separation in the Atoll source 1636-536 seems not to be consistent with the half of the frequency of the QPO in type I bursts \cite{Mendez98c}.
-- Though he beat-frequeney. models are the most hopeful in explaining the QDPO-phenomenology it has to be awaited row the variation of the frequency separation and deviation rom the QPO frequency in bursts can be incorporated. to hese mocdels.
Though the beat-frequency models are the most hopeful candidates in explaining the QPO-phenomenology it has to be awaited how the variation of the frequency separation and deviation from the QPO frequency in bursts can be incorporated to these models.
One of us (Ch.
One of us (Ch.
5$.) gratefully acknowledges the Bavarian State for financial support.
S.) gratefully acknowledges the Bavarian State for financial support.
We would like to thank Norman CGlendenning and Jürrgen Schalfner-Bielich for providing us tables of their EOSs.
We would like to thank Norman Glendenning and Jürrgen Schaffner-Bielich for providing us tables of their EOSs.
Mukherjee luminosity function.
Mukherjee luminosity function.
The integrated fluxes of each blazar for Fo>1 GeV and E-10 GeV were used to eenerale observed fluxes using Poisson distributions equivalent to (wo full vears of exposure.
The integrated fluxes of each blazar for $E>1$ GeV and $E>10$ GeV were used to generate observed fluxes using Poisson distributions equivalent to two full years of exposure.
For each blazar. we caleulated the ratio between these fluxes.
For each blazar, we calculated the ratio between these fluxes.
The error in each flux ratio Was"us sesel dO Dpatiomu=FUETI1GeV]OppLOσον]2|(ολο.FUEπαTDITrees.ο). where oy is the statistical error of the flix measurement in each energv range.
The error in each flux ratio was set to $\sigma_{ratio}=\frac{1}{F(E\,>\,1\,\rm~GeV)}\sqrt{{\sigma_{F(E\,>\,10\,\rm~GeV)}}^{2}+(\frac{F(E\,>\,10\,\rm~GeV)}{F(E\,>\,1\,\rm~GeV)}\sigma_{F(E\,>\,1\,\rm~GeV)})^{2}}$, where $\sigma_{F}$ is the statistical error of the flux measurement in each energy range.
The crosses in Figure 2 show the weighted mean ratio in each recdshilt bin.
The crosses in Figure \ref{fig2} show the weighted mean ratio in each redshift bin.
To avoid the bias of small number Poisson statistics toward lower values. the flix ratio of each source was weighted by Cie Poisson error of the E>1 GeV flux. rather than the formal. propagated error of the fIux ratio.
To avoid the bias of small number Poisson statistics toward lower values, the flux ratio of each source was weighted by the Poisson error of the $E>1$ GeV flux, rather than the formal, propagated error of the flux ratio.
The diamonds show the same ratio when the intergalactic absorption is removed [rom the observed blazar [Iuxes.
The diamonds show the same ratio when the intergalactic absorption is removed from the observed blazar fluxes.
In all cases the error bars are statistical. obtained by computing the rms scatter within each redshift bin and dividing by VN.
In all cases the error bars are statistical, obtained by computing the rms scatter within each redshift bin and dividing by $\sqrt{N}$.
The analvticallvy derived flux ratio using (he opacity model of Salamon Stecker is plotted as a solid curve.
The analytically derived flux ratio using the opacity model of Salamon Stecker is plotted as a solid curve.
For comparison. the dashed lines in Figure 2. show the same results with no intergalactic absorption.
For comparison, the dashed lines in Figure \ref{fig2} show the same results with no intergalactic absorption.
We repeated (he entire analvsis with the blazar spectra changed from single power laws with mean index -2.15 to broken power laws with mean index -2.15 below 50 GeV (at the source) and -3.15 above.
We repeated the entire analysis with the blazar spectra changed from single power laws with mean index -2.15 to broken power laws with mean index -2.15 below 50 GeV (at the source) and -3.15 above.
The results are plotted as crosses in Figure 4.
The results are plotted as crosses in Figure \ref{fig3}.
Although fewer blazars have detected [ας above 10 GeV. the effects of absorption are still apparent.
Although fewer blazars have detected flux above 10 GeV, the effects of absorption are still apparent.
Note that sources wilh no detectable flux above 10 GeV (zero photons) still provide important information: indeed. neglecting them introduces a bias.
Note that sources with no detectable flux above 10 GeV (zero photons) still provide important information; indeed, neglecting them introduces a bias.
The modified 47 statistic used here (Mighell 1999) accounts for these sources.
The modified $\chi^{2}$ statistic used here (Mighell 1999) accounts for these sources.
The ratio obtained without EBL absorption is presented as diamonds. along with the analytically derived. {lux ratio (dashed line).
The ratio obtained without EBL absorption is presented as diamonds, along with the analytically derived flux ratio (dashed line).
As can be easily seen. this flux ratio is nol constant as a [unction of redshift.
As can be easily seen, this flux ratio is not constant as a function of redshift.
This is a consequence of defining the break in the index for a given energv at the source.
This is a consequence of defining the break in the index for a given energy at the source.
Primack and collaborators combined. theoretical modeling with observational data to develop semi-analvtic models of galaxy. formation aud evolution (Primack et al.
Primack and collaborators combined theoretical modeling with observational data to develop semi-analytic models of galaxy formation and evolution (Primack et al.
1999).
1999).
Their
Their
We have performed a survey of the most massive galaxies present at z>3, over an area of 0.6 deg? of the UKIDSS UDS field.
We have performed a survey of the most massive galaxies present at $z \geq 3$, over an area of 0.6 $^2$ of the UKIDSS UDS field.
To have the best possible proxy for a stellar mass complete sample, we made our selection in the Spitzer/IRAC band, which maps rest-frame near-IR wavelengths at these high redshifts.
To have the best possible proxy for a stellar mass complete sample, we made our selection in the /IRAC band, which maps rest-frame near-IR wavelengths at these high redshifts.
We followed up our master 4.5mcatalogue of 50,321 sources in 10 broad bands, from the U-band through the IRAC 3.6 um channel.
We followed up our master catalogue of 50,321 sources in 10 broad bands, from the $U$ -band through the IRAC 3.6 $\rm \mu m$ channel.
The multi-wavelength follow up has allowed us to model the SEDs of all our galaxies and, with this, obtain redshift estimates and derive stellar masses.
The multi-wavelength follow up has allowed us to model the SEDs of all our galaxies and, with this, obtain redshift estimates and derive stellar masses.
Our final sample consists of 1292 galaxies at redshifts 3.0<z«5.23.
Our final sample consists of 1292 galaxies at redshifts $3.0\leq z < 5.23$.
'The main goal of our work was the study of the galaxy stellar mass function at 3.0€z«5.0, particularly the evolution of its high-mass end within this redshift range.
The main goal of our work was the study of the galaxy stellar mass function at $3.0 \leq z<5.0$, particularly the evolution of its high-mass end within this redshift range.
Our deep and homogeneous datasets over a large field are particularly suitable for this purpose.
Our deep and homogeneous datasets over a large field are particularly suitable for this purpose.
We have found the following: Another key result of our work is the absence of massive galaxies at redshifts z> 5.
We have found the following: Another key result of our work is the absence of massive galaxies at redshifts $z>5$ .
Within our surveyed area of 0.6 deg?, we find only two quite secure candidates at such high redshifts, and only one with stellar mass M>10!
Within our surveyed area of 0.6 $^2$, we find only two quite secure candidates at such high redshifts, and only one with stellar mass $M>10^{11} \, \rm M_\odot$.
Instead, optical surveys have discovered a substantial Mo.number of intermediate stellar-mass sources at these redshifts.
Instead, optical surveys have discovered a substantial number of intermediate stellar-mass sources at these redshifts.
These findings strongly suggest that massive galaxies as a significant population only appear at later times, and that the epoch around redshifts z~3—6 is critical to understand the formation of the first massive Systems.
These findings strongly suggest that massive galaxies as a significant population only appear at later times, and that the epoch around redshifts $z\sim3-6$ is critical to understand the formation of the first massive systems.
In addition, we have found that a significant fraction of the most massive galaxies present at 3€z«4 would be missed by optical surveys, even asdeep as R«27 or
In addition, we have found that a significant fraction of the most massive galaxies present at $3\leq z<4$ would be missed by optical surveys, even asdeep as $R<27$ or
Postage stamps images in the four bands are shown for one of the 142 fLSB candidates with photo-z<0.2 in Fig.
Postage stamps images in the four bands are shown for one of the 142 fLSB candidates with $-z<0.2$ in Fig.
ΑΙ (galaxy #1128 in Table A3)).
\ref{fig:post} (galaxy 128 in Table \ref{tab:liste3}) ).
The corresponding surface brightness profile is given in Fig. A2..
The corresponding surface brightness profile is given in Fig. \ref{fig:prof}.
Based on the large spectroscopic and photometric catalogues aequired for Abell 496 (Boué et al.
Based on the large spectroscopic and photometric catalogues acquired for Abell 496 (Boué et al.
2008). we have estimated the spectral type of each galaxy with the Le Phare photometric redshift software.
2008), we have estimated the spectral type of each galaxy with the Le Phare photometric redshift software.
Galaxies are then assigned a spectral type: type | for ellipticals. type 2 for early type spirals. type 3 for intermediate type spirals and type 4 for late type spirals.
Galaxies are then assigned a spectral type: type 1 for ellipticals, type 2 for early type spirals, type 3 for intermediate type spirals and type 4 for late type spirals.
In order to search for substructures. we applied the Serna Gerbal (1996) software to galaxies with measured spectroscopic redshifts and magnitudes.
In order to search for substructures, we applied the Serna Gerbal (1996) software to galaxies with measured spectroscopic redshifts and magnitudes.
This hierarchical method allows to extract galaxy substructures or groups from a catalogue containing positions. magnitudes and redshifts. based on the calculation of their relative (negative) binding energies.
This hierarchical method allows to extract galaxy substructures or groups from a catalogue containing positions, magnitudes and redshifts, based on the calculation of their relative (negative) binding energies.
The method gives as output a list of galaxies belonging to each group. as well as the information on the binding energy of the group itself. and on the mass of each substructure. assuming a mass to luminosity ratio (M/L).
The method gives as output a list of galaxies belonging to each group, as well as the information on the binding energy of the group itself, and on the mass of each substructure, assuming a mass to luminosity ratio (M/L).
We used herea M/L ratio in the 7 band of 200. as previously assumed for the Coma cluster by Adami et al. (
We used herea M/L ratio in the $r'$ band of 200, as previously assumed for the Coma cluster by Adami et al. (
2005). based on the Coma cluster M/L ratio given by Lokas Mamon (2003).
2005), based on the Coma cluster M/L ratio given by okas Mamon (2003).
The Serna Gerbal analysis shows the existence of three substructures (also see Section 4).
The Serna Gerbal analysis shows the existence of three substructures (also see Section 4).
These all have low masses (smaller than a few 10 M..) and therefore their existence does not contradict the overall relaxed structure of the cluster.
These all have low masses (smaller than a few $10^{12}$ $_\odot$ ) and therefore their existence does not contradict the overall relaxed structure of the cluster.
If we analyze the morphological type distribution of the galaxies belonging to these three substructures (also see Fig. 5)).
If we analyze the morphological type distribution of the galaxies belonging to these three substructures (also see Fig. \ref{fig:type}) ),
we find that only one galaxy is of type 4 (late type spiral). corresponding to ~1% of all the galaxies in substructures.
we find that only one galaxy is of type 4 (late type spiral), corresponding to $\sim$ of all the galaxies in substructures.
If we estimate the percentage of type + galaxies in the cluster (1.5. 1n the [0.0229.0.0429] redshift range) that are not included in substructures. we find a value of 23%..
If we estimate the percentage of type 4 galaxies in the cluster (i.e. in the [0.0229,0.0429] redshift range) that are not included in substructures, we find a value of .
The difference between these two values could be
The difference between these two values could be
equilibrium points are also made linearly stable by continuous corrections of their halo rq}).
equilibrium points are also made linearly stable by continuous corrections of their halo ).
In other words the collinear equilibrium points are metastable points in (he sense (hat. like a ball sitting on top of a hill.
In other words the collinear equilibrium points are metastable points in the sense that, like a ball sitting on top of a hill.
However. in practice these Lagrange points have proven to be very useful indeed since à spacecralt can be made {ο execute a small orbit about one of these Lagrange points with a very small expenditure of energy[please see 1969)]].
However, in practice these Lagrange points have proven to be very useful indeed since a spacecraft can be made to execute a small orbit about one of these Lagrange points with a very small expenditure of energy[please see \citet{Farquhar1967JSpRo,Farquhar1969AsAer}] ].
We considered ihe Chermuvkh’s problem which is a new kind of restricted (hree body problem. il was first Gime studied by Chermauvkh(1987).
We considered the Chermnykh's problem which is a new kind of restricted three body problem, it was first time studied by \citet{Chermnykh1987}.
. This problem generalizes two Classical problems of Celestial mvechanics: (he two fixed center problem and the restricted three body problem.
This problem generalizes two classical problems of Celestial mechanics: the two fixed center problem and the restricted three body problem.
This gives wide perspectives for applications of the problem in celestial mechanics and astronomy.
This gives wide perspectives for applications of the problem in celestial mechanics and astronomy.
The importance of (he problem in astronomy has been addressed bv JiangandYeh(2004a)..
The importance of the problem in astronomy has been addressed by \citet{Jiang2004IJBC}.
Some planetary systems are claimed (ο have discs of dust and thev are regarded (to be young analogues of the Ixuiper Bell in our Solar System.
Some planetary systems are claimed to have discs of dust and they are regarded to be young analogues of the Kuiper Belt in our Solar System.
If these disces are massive enough. thev should play important roles in the origin of orbital elements.
If these discs are massive enough, they should play important roles in the origin of orbital elements.
Since (he belt of planetesimal often exists within a planetary svstem and provides (he possible mechanism of orbital circularization. it is important to understand the solutions of dynamical svstems with the planet-belt interaction.
Since the belt of planetesimal often exists within a planetary system and provides the possible mechanism of orbital circularization, it is important to understand the solutions of dynamical systems with the planet-belt interaction.
The Chermnykhs problem has been studied bv many scientists such as JiangandYeh(2004b).. Papaclakis(2004)..Papacdakis (2005) and JiangaudYeh(2006):and(2006)..
The Chermnykh's problem has been studied by many scientists such as \citet{JiangYeh2004AJ}, \citet{Papadakis2004A&A}, \citet{Papadakis2005Ap&SS299} and \citet{JiangYeh2006Ap&SSI,YehJiang2006Ap&SSII}.
The present paper investigates the nature of collinear equilibrium point Lo because of the interested point to locate an artificial satellite.
The present paper investigates the nature of collinear equilibrium point $L_2$ because of the interested point to locate an artificial satellite.
Although there are (vo new equilibrium points due to mass of the belt(larger than 0.15) as obtained by. (200G).. but they are left to be examined.
Although there are two new equilibrium points due to mass of the belt(larger than 0.15) as obtained by \citet{JiangYeh2006Ap&SSI,YehJiang2006Ap&SSII}, but they are left to be examined.
All the results are computed numerically using same technique as in GrebennikovandIxozak-Skoworodkin(2007).. because pure analvtical nuethods are not suitable.
All the results are computed numerically using same technique as in \cite{Grebennikov2007CMMPh}, because pure analytical methods are not suitable.
For specific time intervals. and initial values. (ese results provide jew information on the behavior of trajectories around (he Lagrangian point Le.
For specific time intervals, and initial values, these results provide new information on the behavior of trajectories around the Lagrangian point $L_2$.
It is supposed that the motion of an infinitesimal mass particle is influenced. by the eravitational force from primaries aud a belt of mass M.
It is supposed that the motion of an infinitesimal mass particle is influenced by the gravitational force from primaries and a belt of mass $M_b$.
The units of the mass and the distance are taken such that sum of (he masses ancl (he distance between primaries are unities.
The units of the mass and the distance are taken such that sum of the masses and the distance between primaries are unities.
The unit of the time ie. the time period of mn about m2 consists of 2x units such that the
The unit of the time i.e. the time period of $m_1$ about $m_2$ consists of $2\pi$ units such that the
hereafter discard filaments whose lengths are shorter than the smoothing length as non-physical.
hereafter discard filaments whose lengths are shorter than the smoothing length as non-physical.
The traditional picture of large-scale structure as a ‘cosmic web’ (7) suggests that filaments are connected, one-dimensional strands that end abruptly at their points of intersection.
The traditional picture of large-scale structure as a `cosmic web' \citep{CosmicWeb} suggests that filaments are connected, one-dimensional strands that end abruptly at their points of intersection.
As one filament begins and another ends, the local axis of structure should change direction rapidly.
As one filament begins and another ends, the local axis of structure should change direction rapidly.
The C parameter denotes the maximum angular rate of change in the axis of structure along a filament.
The $C$ parameter denotes the maximum angular rate of change in the axis of structure along a filament.
If this threshold is exceeded, filament tracing is stopped.
If this threshold is exceeded, filament tracing is stopped.
In order to test the sensitivity of the output filaments to the value of the C parameter, we set K=1 and generated filament networks in the N-body simulation with a range of C.
In order to test the sensitivity of the output filaments to the value of the $C$ parameter, we set $K=1$ and generated filament networks in the N-body simulation with a range of $C$.
In all of these tests, increasing the value of C led to an increase in the average length of the filaments and a decrease in the total number of filaments found.
In all of these tests, increasing the value of $C$ led to an increase in the average length of the filaments and a decrease in the total number of filaments found.
If the curvature criterion is not strict enough, a filament will be traced past its vertex and into another filament.
If the curvature criterion is not strict enough, a filament will be traced past its vertex and into another filament.
Since our algorithm only prevents filaments from starting within previously-identified filaments (they are allowed to cross one this can lead to double detections of filaments.
Since our algorithm only prevents filaments from starting within previously-identified filaments (they are allowed to cross one another), this can lead to double detections of filaments.
We can another),obtain a rough count of these double detections by comparing filament elements to one another, where a filament element is definedas a single step (of interval, A) on the grid.
We can obtain a rough count of these double detections by comparing filament elements to one another, where a filament element is definedas a single step (of interval, $\Delta$ ) on the grid.
In other words, for each step along a given filament, we find the closest filament element that is not a member of that same filament.
In other words, for each step along a given filament, we find the closest filament element that is not a member of that same filament.
If the closest filament element is within a smoothing length and has an axis of structure within C, then the original element is labelled a ‘repeat detection.’
If the closest filament element is within a smoothing length and has an axis of structure within $C$, then the original element is labelled a `repeat detection.'
The total number of repeat detections in an output filament network is denoted by R.
The total number of repeat detections in an output filament network is denoted by $R$.