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Accounting for this substructure is important on scales smaller than the virial radii of typical halos. | Accounting for this substructure is important on scales smaller than the virial radii of typical halos. |
The effects are more pronounced for statistics which treat the subclumps preferentially. such as. the power spectrum measured in studies of weak galaxy eravitational lensing. | The effects are more pronounced for statistics which treat the subclumps preferentially, such as the power spectrum measured in studies of weak galaxy–galaxy gravitational lensing. |
Substructure will also change the clynamics within halos. | Substructure will also change the dynamics within halos. |
Although we have not done so here. it is straightforward to insert our model for substructure into the halo model of the cosmic virial theorem. and the mean pairwise velocity and velocity dispersion developed in Sheth οἱ al. ( | Although we have not done so here, it is straightforward to insert our model for substructure into the halo model of the cosmic virial theorem, and the mean pairwise velocity and velocity dispersion developed in Sheth et al. ( |
2001). | 2001). |
The stable clustering limit is a physically appealing deseription of ¢lustering on small scales (Peebles 1980). | The stable clustering limit is a physically appealing description of clustering on small scales (Peebles 1980). |
lt has been argued that a model with smooth halos is inconsistent with this limit (Ala Fry 2000: Scoccimarro et al. | It has been argued that a model with smooth halos is inconsistent with this limit (Ma Fry 2000; Scoccimarro et al. |
2001). | 2001). |
Substructure changes the shape of the smal scale power spectrum (ef. | Substructure changes the shape of the small scale power spectrum (c.f., |
Fig. 1)): | Fig. \ref{pksubclumps}) ); |
at least in. principle. it can bring the halo model predictions into agreement with the stable clustering solution. | at least in principle, it can bring the halo model predictions into agreement with the stable clustering solution. |
However. it is not obvious tha stable clustering is. indeed. the correct. physical limit. | However, it is not obvious that stable clustering is, indeed, the correct physical limit. |
Smith et al. ( | Smith et al. ( |
2002) argue that the stable clustering assumption is inconsistent with the results of high resolution numerica simulations. | 2002) argue that the stable clustering assumption is inconsistent with the results of high resolution numerical simulations. |
Thev also find that the simulations do no follow the small scale scaling predicted by models in which halos are smooth. | They also find that the simulations do not follow the small scale scaling predicted by models in which halos are smooth. |
Once an accurate model of the subclump mass function is available. it will be interesting to compare the predictions of our description of substructure with their results. | Once an accurate model of the subclump mass function is available, it will be interesting to compare the predictions of our description of substructure with their results. |
Although wei have focussed primarily on. the implications of substructure for the halo model of nonlinear clustering. our results have a wide range of other applications. | Although we have focussed primarily on the implications of substructure for the halo model of nonlinear clustering, our results have a wide range of other applications. |
For example. excess power in the Fourier transforms of images of galaxies or distant clusters can be used. to infer the existence of spiral arms or substructure. | For example, excess power in the Fourier transforms of images of galaxies or distant clusters can be used to infer the existence of spiral arms or substructure. |
This is the subject. of work in progress. | This is the subject of work in progress. |
Closely related. is the question of what images of high redshift galaxies may look like. | Closely related is the question of what images of high redshift galaxies may look like. |
Observations through a filter which has a fixed wavelength: range probe the emission. from high recshilt ealaxies at shorter restframe wavelengths than for galaxies at low recshift. | Observations through a filter which has a fixed wavelength range probe the emission from high redshift galaxies at shorter restframe wavelengths than for galaxies at low redshift. |
If obscuration by cust is not a problem. and the UV. luminosity is dominated. by patchy star forming regions. then the images of high. redshift galaxies should garow considerable substructure. | If obscuration by dust is not a problem, and the UV luminosity is dominated by patchy star forming regions, then the images of high redshift galaxies should show considerable substructure. |
Our results suggest. that. in this case. the power spectrum. obtained. by Fourier ransforming the image of a high redshift patch of sky ga1o0uld show an increase in small scale power. | Our results suggest that, in this case, the power spectrum obtained by Fourier transforming the image of a high redshift patch of sky should show an increase in small scale power. |
In addition. although we have phrased the entire iscussion of substrucutre in terms of spatial statistics. this is not really necessary. | In addition, although we have phrased the entire discussion of substrucutre in terms of spatial statistics, this is not really necessary. |
Large databases describing various observed. characteristics of galaxies are now becoming available (6.8... the 2dFGRS and SDSS surveys) | Large databases describing various observed characteristics of galaxies are now becoming available (e.g., the 2dFGRS and SDSS surveys). |
lf some of n | If some of $n$ |
Knowledge of the initial Mass function is. crucial for understanding the formation processes of stars. brown dwarfs and free-floating planetary-mass objects. | Knowledge of the initial mass function is crucial for understanding the formation processes of stars, brown dwarfs and free-floating planetary-mass objects. |
Whether and where there is a limit for the creation of objects by direct collapse and fragmentation of molecular clouds has become one of the major goals in the study of very young populations. | Whether and where there is a limit for the creation of objects by direct collapse and fragmentation of molecular clouds has become one of the major goals in the study of very young populations. |
Planetary-mass candidates with masses in the interval 3-13 Jovian masses μμ) have been found in various star-forming regions (e.g.. Lucas Roche 2000:; Zapatero Osorio et al. 2000:; | Planetary-mass candidates with masses in the interval 3–13 Jovian masses ) have been found in various star-forming regions (e.g., Lucas Roche \cite{lucas00}; Zapatero Osorio et al. \cite{osorio00}; ; |
Chauvin et al. 2004:; | Chauvin et al. \cite{chauvin04}; |
Lucas et al. 2005:: | Lucas et al. \cite{lucas05}; |
Luhman et al. 2005:; | Luhman et al. \cite{luhman05}; ; |
Jayawardhana Ivanov 2006:; Allers et al. 2006:; | Jayawardhana Ivanov \cite{ray06}; ; Allers et al. \cite{allers06}; |
1aet al. 2006:: | a et al. \cite{gonzalez06}; |
Caballero et al. 2007)). | Caballero et al. \cite{caballero07}) ). |
These objects are mostly free-floating but in in a few cases appear as wide companions to young brown dwarfs or low-mass stars. | These objects are mostly free-floating but in in a few cases appear as wide companions to young brown dwarfs or low-mass stars. |
OOri J053810.1—023626) is the coolest free- planetary-mass candidate so far reported in. the literature. | Ori $-$ 023626) is the coolest free-floating, planetary-mass candidate so far reported in the literature. |
It was discovered by Zapatero Osorio et al. (2002a)) and lies in the direction of the cluster (352 pe and 1-8 Myr. with a best estimate at 3 Myr: Perryman et al. 1997:: | It was discovered by Zapatero Osorio et $.$ \cite{osorio02a}) ) and lies in the direction of the cluster (352 pc and 1–8 Myr, with a best estimate at 3 Myr; Perryman et al. \cite{perryman97}; |
Oliveira et al. 2002: | Oliveira et al. \cite{oliveira02}; |
Zapatero Osorio et al. 2002b:; | Zapatero Osorio et al. \cite{osorio02b}; |
Sherry et al. 2004)). | Sherry et al. \cite{sherry04}) ). |
The spectral type of was determined at T5.5x 11.0 from molecular indices measured over infrared H- and K-band low-resolution spectra. | The spectral type of was determined at $\pm$ 1.0 from molecular indices measured over near-infrared $H$ - and $K$ -band low-resolution spectra. |
in Zapatero Osorio (2003)) obtained an intermediate-resolution spectrum from 1.17 to 1.37 jm (J-band). in which the doublet at 1.254/m was detected. | n Zapatero Osorio \cite{martin03}) ) obtained an intermediate-resolution spectrum from 1.17 to 1.37 $\mu$ m $J$ -band), in which the doublet at $\mu$ m was detected. |
After comparison with theoretical spectra from Allard et al. (2001)). | After comparison with theoretical spectra from Allard et al. \cite{allard01}) ), |
the authors inferred an effective temperature and surface gravity of Taj K and logg 33.54£00.5 em s. in agreement22 with 111005the expectations for a few megayears-old T dwarf. | the authors inferred an effective temperature and surface gravity of $T_{\rm
eff}$ $^{+200}_{-100}$ K and $g$ $\pm$ 0.5 cm $^{-2}$, in agreement with the expectations for a few megayears-old T dwarf. |
State-of-the-art evolutionary models (Chabrier Baratte 2000:; Burrows et al. 1997:: | State-of-the-art evolutionary models (Chabrier Baraffe \cite{chabrier00}; Burrows et al. \cite{burrows97}; |
Baraffe et al. 1998)) | Baraffe et al. \cite{baraffe98}) ) |
yield a mass of 33 if 70°ss very young age is finally confirmed. | yield a mass of $^{+5}_{-1}$ if s very young age is finally confirmed. |
Burgasser et al. (2004)). | Burgasser et al. \cite{burgasser04}) ), |
in contrast. have raised doubts about the low-gravity atmosphere and true cluster membership of70. | in contrast, have raised doubts about the low-gravity atmosphere and true cluster membership of. |
. Based on the supposed similarity of the observed spectra to field T6—T7 dwarfs. these authors argued that the OOri object is "an old. massive field brown dwarf lying in the foreground of the cluster". | Based on the supposed similarity of the observed spectra to field T6–T7 dwarfs, these authors argued that the Ori object is “an old, massive field brown dwarf lying in the foreground of the cluster”. |
However. this work relied on low signal-to-noise ratio data. | However, this work relied on low signal-to-noise ratio data. |
Better quality photometry and spectra are needed to assess the true nature of this candidate. | Better quality photometry and spectra are needed to assess the true nature of this candidate. |
Here we present astrometric measurements. IRAC/Spitzer data and JHK, photometry for70. | Here we present astrometric measurements, IRAC/Spitzer data and $JHK_s$ photometry for. |
. We find that this object has colors unexpected for its spectral classification. which is measured in the range T4.5-T7 with a best estimate at T6. | We find that this object has colors unexpected for its spectral classification, which is measured in the range T4.5–T7 with a best estimate at T6. |
We ascribe this to a low gravity atmosphere. with a different metallicity being an alternative. but less likely. explanation. | We ascribe this to a low gravity atmosphere, with a different metallicity being an alternative, but less likely, explanation. |
was observed in J. H. and Κι broad-band filters with prime focus wide field camera Omega-2000 (2048x2042c pixels: Bailer-Jones et al. 20000) | was observed in $J$, $H$, and $K_s$ broad-band filters with prime focus wide field camera Omega-2000 $\times$ 2048 pixels; Bailer-Jones et al. \cite{bailer00}) ) |
on the 3.5 m telescope at the Calar Alto (CAHA) Observatory. | on the 3.5 m telescope at the Calar Alto (CAHA) Observatory. |
We also imaged with the NIRSPEC-3 (similar to 7. see Fig. AI) | We also imaged with the NIRSPEC-3 (similar to $J$, see Fig. \ref{filters}) ) |
and K' filters and the slit-viewing camera (256x256 pixels) ofthe near-infrared spectrometer NIRSPEC (McLean et al. 2000)) | and $K'$ filters and the slit-viewing camera $\times$ 256 pixels) ofthe near-infrared spectrometer NIRSPEC (McLean et al. \cite{mclean00}) ) |
on the Keck II telescope (Hawari). | on the Keck II telescope (Hawai'i). |
The observing log containingσι instrumental information. dates of observations. and exposure times perfilter is provided inTable 1.. | The observing log containing instrumental information, dates of observations, and exposure times perfilter is provided inTable\ref{obslog}. . |
Images (J-band) of the T4.5 spectral standard dwarf 4— JJ0559]91404488 (J0559-]4 from now on) were collected with NIRSPEC | Images $J$ -band) of the T4.5 spectral standard dwarf $-$ 1404488 $-$ 14 from now on) were collected with NIRSPEC |
only the SMC metallicity mass ranges differ visibly from the solar and LMC estimates. | only the SMC metallicity mass ranges differ visibly from the solar and LMC estimates. |
Somewhat surprisingly. the early-type SMC dwarfs seem to have/ower masses than their MW and LMC cousins. according to the models and definitions used here. | Somewhat surprisingly, the early-type SMC dwarfs seem to have masses than their MW and LMC cousins, according to the models and definitions used here. |
This is almost certainly because of the earlier mentioned perhaps unexpected fact that the SMC O stars result in a lower scale for O stars than for LMC objects. | This is almost certainly because of the earlier mentioned perhaps unexpected fact that the SMC O stars result in a lower scale for O stars than for LMC objects. |
Interestingly. all but two of the (dwarf) stars located in the LMC in Fig. 6)) | Interestingly, all but two of the (dwarf) stars located in the LMC in Fig. \ref{fig:comp_V}) ) |
lie below the here derived solar and LMC metallicity evolutionary mass ranges. | lie below the here derived solar and LMC metallicity evolutionary mass ranges, |
diffusion rate is high (low) when the ionization degree is low (high). | diffusion rate is high (low) when the ionization degree is low (high). |
The MBI cau survive at temperature T. LOOOTS due to the thermal ionization. | The MRI can survive at temperature $T>1000$ K due to the thermal ionization. |
This temperature can be reached in the inner region of the nebula inside Mercury. | This temperature can be reached in the inner region of the nebula inside Mercury. |
Cosmic ravs can partially ionize the part of 1ο nebula where they can penctrate (ITavasli 1981). | Cosmic rays can partially ionize the part of the nebula where they can penetrate (Hayashi 1981). |
So le cosmic rav lonizafion is more siguificant where X is ow. which is the outer region of the icbula. | So the cosmic ray ionization is more significant where $\Sigma$ is low, which is the outer region of the nebula. |
Thus the MRI can survive there. | Thus the MRI can survive there. |
An estimate of the location of ie transition zone between the outer region and the oetermediate region (where the MBRI cau uot survive) cau ος found by equating the cosmic rav penetration depth Ver = lOO ο 7 with X. | An estimate of the location of the transition zone between the outer region and the intermediate region (where the MRI can not survive) can be found by equating the cosmic ray penetration depth $\Sigma_{CR}$ = 100 g $^{-2}$ with $\Sigma$. |
For an casy estimate. T use Tavashi (1981) surface density aud fud that the transition zone is around 7 ~7TAU. which is Jupiter-Saturn region. | For an easy estimate, I use Hayashi (1981) surface density and find that the transition zone is around $r \sim$ 7AU, which is Jupiter-Saturn region. |
Notice tha this racius is larger when the nebula has were mass thaw he ninimaiuin mass. | Notice that this radius is larger when the nebula has more mass than the minimum mass. |
MITD simulations (Fleming Stone 2003) finds that the viscosity can drop below o10. twhere € is Euge. | MHD simulations (Fleming Stone 2003) finds that the viscosity can drop below $\alpha \sim
10^{-4}$ where $\Sigma$ is large. |
To stammarize.ALRT (Fig. | To summarize, (Fig. |
1). | 1). |
Lets look at the mass euhancenieut in Jupiter-Saturu region due to the above nonuniform à (AMT). | Lets look at the mass enhancement in Jupiter-Saturn region due to the above nonuniform $\alpha$ (AMT). |
The radial inflow velocity is (Pringle 1981) where ÉBois the kinematic viscositv. ος is the sound speed. LF is the nebula thickness. and © is the angular velocity. | The radial inflow velocity is (Pringle 1981) where $\nu$ is the kinematic viscosity, $c_s$ is the sound speed, $H$ is the nebula thickness, and $\Omega$ is the angular velocity. |
The negative sign micans that the material flows inwards to the Sun. | The negative sign means that the material flows inwards to the Sun. |
Notice that the more efficient. AMT drives faster radial iuflow.cone ( | Notice that the more efficient AMT drives faster radial inflow. ( |
Fig 1). | Fig 1). |
This meaus that Jupiter and Saturn have access to more material. | This means that Jupiter and Saturn have access to more material. |
Mathematically. the mass cuhaneement iu Jupiter-Saturn region can be shown as the following. | Mathematically, the mass enhancement in Jupiter-Saturn region can be shown as the following. |
The mass inflow rate at any radius r is (Pringle 1951) Let δρ) be the solution of the surface density with constant a=a, (the à value in the outer region). | The mass inflow rate at any radius $r$ is (Pringle 1981) Let $\Sigma_0(r)$ be the solution of the surface density with constant $\alpha =\alpha_o$ (the $\alpha$ value in the outer region). |
Asstuning that Xy is not chaneed for the first order. the mass enhaucenment rate iu the transition zoue compared with coustaut © solution is where BR;H aud &, are the immer aud outer radii of the transition zone. aud o, is the nomunuiform a. | Assuming that $\Sigma_0$ is not changed for the first order, the mass enhancement rate in the transition zone compared with constant $\alpha$ solution is where $R_i$ and $R_o$ are the inner and outer radii of the transition zone, and $\alpha_n$ is the nonuniform $\alpha$ . |
The term iu first parcuthesis is the mass chauge rate in the zone with nonuuiforui à and the secoud is the rate with coustaut 0—0, | The term in first parenthesis is the mass change rate in the zone with nonuniform $\alpha$ and the second is the rate with constant $\alpha=\alpha_o$. |
Since a,=a, atr =BR, two terms at FR, are cancelled. | Since $\alpha_n = \alpha_o$ at $r=R_o$, two terms at $R_o$ are cancelled. |
We have by using equation (1) where o; is the à. value in the interiiediate region. | We have by using equation (1) where $\alpha_i$ is the $\alpha$ value in the intermediate region. |
It is straightforward to sce that there is à mass enliancemenut oeithe transition zone which is Jupiter-Saturn region since a; is significauth lower than νι | It is straightforward to see that there is a mass enhancement in the transition zone which is Jupiter-Saturn region since $\alpha_i$ is significantly lower than $\alpha_o$. |
The cuhancement is ue to the ciffereuce in the racial velocity. caused by the ifercuce of à. value. | The enhancement is due to the difference in the radial velocity caused by the difference of $\alpha$ value. |
If the nebula ever reaches a quasi-PAteady state (AZ does not change with r). equation (2) ooOives that X is higher in the lower o region which is the oeiterinediate region. | If the nebula ever reaches a quasi-steady state $\dot M$ does not change with $r$ ), equation (2) gives that $\Sigma$ is higher in the lower $\alpha$ region which is the intermediate region. |
Tn the process of the planet formation. graius are ccoupled from the gas when they erow into larger solid bodies. | In the process of the planet formation, grains are decoupled from the gas when they grow into larger solid bodies. |
The inflow keeps the same initial solar composition before the decoupling. | The inflow keeps the same initial solar composition before the decoupling. |
4). After the decoupling. the eas will coutinue its inflow. | After the decoupling, the gas will continue its inflow. |
The inflow time is (Pringle 1981) where the value of J7/r from HHavashi (1981) is usec. | The inflow time is (Pringle 1981) where the value of $H/r$ from Hayashi (1981) is used. |
I list à and caleulated inflow times at the heliocentric radius of the planets in Table 2. | I list $\alpha$ and calculated inflow times at the heliocentric radius of the planets in Table 2. |
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