source
stringlengths 1
2.05k
⌀ | target
stringlengths 1
11.7k
|
|---|---|
In this section we consider the non-linear terms in the gradient of theline of sight velocity field ancl explore the scales at which it is correct to ignore such elfects in the redshift space power spectrum. | In this section we consider the non-linear terms in the gradient of theline of sight velocity field and explore the scales at which it is correct to ignore such effects in the redshift space power spectrum. |
As a first. step. we compare the model in. Iq. 10.. | As a first step, we compare the model in Eq. \ref{SM}, , |
to measurements from Ντον simulations for different quintessence dark energy models. without the damping term | to measurements from N-body simulations for different quintessence dark energy models, without the damping term |
of diffusion near “unhealthy” zones. | of diffusion near “unhealthy” zones. |
This feature is implemented as a Lax-Friedrichs flux, where the failed state Uj,;,~—U;;, according to where for brevity, we have written the fluxes in the x-direction only, and d=3 is the number of dimensions, and 9;41/2,;,4=1 if zones (i,j,k) or (i+1,1,ἆ) have been flagged as unhealthy, and 0 otherwise. | This feature is implemented as a Lax-Friedrichs flux, where the failed state $\vct{U}_{i,j,k} \mapsto
\vct{U'}_{i,j,k}$ according to where for brevity, we have written the fluxes in the $x$ -direction only, and $d=3$ is the number of dimensions, and $\theta_{i+1/2,j,k}=1$ if zones $(i,j,k)$ or $(i+1,j,k)$ have been flagged as unhealthy, and $0$ otherwise. |
The effect of this prescription is to replace U;,;; with a weighted average of itself and the average of its neighboring cells, adding the most diffusion when r—1 and none when r—0. | The effect of this prescription is to replace $\vct{U}_{i,j,k}$ with a weighted average of itself and the average of its neighboring cells, adding the most diffusion when $r \rightarrow
1$ and none when $r \rightarrow 0$. |
Throughout this study we have used r=0.2. | Throughout this study we have used $r=0.2$. |
This formulation for the addition of diffusive terms has several important features. | This formulation for the addition of diffusive terms has several important features. |
Firstly, it naturally obeys the global conservation of U, but secondly it obeys the solenoidal magnetic field constraint, because the constrained transport method may be applied to the Lax-Friedrichs magnetic field fluxes before adding them in Equation 7.. | Firstly, it naturally obeys the global conservation of $\vct{U}$, but secondly it obeys the solenoidal magnetic field constraint, because the constrained transport method may be applied to the Lax-Friedrichs magnetic field fluxes before adding them in Equation \ref{eqn:lax-diffusion}. |
Our simulations take place in the periodic cube of length L centered at the origin. | Our simulations take place in the periodic cube of length $L$ centered at the origin. |
We initialize the domain as a uniform and stationary fluid having rest mass density po=1.0 and gas pressure pg=po/3. | We initialize the domain as a uniform and stationary fluid having rest mass density $\rho_0 = 1.0$ and gas pressure $p_g =
\rho_0/3$. |
We apply a uniform magnetic field along the x-direction with magnitude 10-?. | We apply a uniform magnetic field along the $x$ -direction with magnitude $10^{-3}$. |
The flow is driven stochastically on large scales according to a prescription we have adapted from ?.. | The flow is driven stochastically on large scales according to a prescription we have adapted from \cite{Schmidt:2009p2393}. |
The driving mechanism is intended to mimic the effect of larger flow structures in which our domain is embedded, and should thus be time-correlated with the turnover time of the largest eddies, which is of order one light-crossing time of the domain, Tj,=L/c. | The driving mechanism is intended to mimic the effect of larger flow structures in which our domain is embedded, and should thus be time-correlated with the turnover time of the largest eddies, which is of order one light-crossing time of the domain, $T_{lc}=L/c$. |
We achieve smooth time correlation by advancing the Fourier modes a(k,t) of the driving field according to an Ornstein-Uhlenbeck process (7?) dà(k,t), which consists of a restoring force together with| a complex-valued random-walking term, dW(k,t): The projection operator, is applied to the vector deviate dW(k,t) in order to select compressive and vortical driving modes separately, according to the parameter C. | We achieve smooth time correlation by advancing the Fourier modes $\tilde{\vct{a}}(\vct{k},t)$ of the driving field according to an Ornstein-Uhlenbeck process \citep{Uhlenbeck:1930p4602}
$d\tilde{\vct{a}}(\vct{k},t)$, which consists of a restoring force together with a complex-valued Gaussian-distributed random-walking term, $d\tilde{\vct{W}} (\vct k, t)$: The projection operator, is applied to the vector deviate $d\tilde{\vct{W}} (\vct k, t)$ in order to select compressive and vortical driving modes separately, according to the parameter $\zeta$. |
In this study, we use ¢=1 which corresponds to a purely vortical driving field. | In this study, we use $\zeta=1$ which corresponds to a purely vortical driving field. |
For a detailed study how ¢ effects the turbulence statistics, see ?.. | For a detailed study how $\zeta$ effects the turbulence statistics, see \cite{Federrath:2010p4876}. |
The acceleration field is applied to the 4-velocity of the flow, u at every time step, u(x,t)-+a(x, where the spatial realization isobtainedu(x,t) by taking the t)dt/u°,real part of the Fourier mode superposition The spectral profile, o?(k)οςk9e-9*/: (2?) 18 normalized to unity over the driven wavenumbers. | The acceleration field is applied to the 4-velocity of the flow, $u^\mu$ at every time step, $\vct{u}(\vct{x},t) \mapsto \vct{u}(\vct{x},t) +
\vct{a}(\vct{x},t) dt/u^0$ , where the spatial realization isobtained by taking the real part of the Fourier mode superposition The spectral profile, $\sigma^2(\vct{k}) \propto k^6 e^{-8k/k_1}$ \citep{Vestuto:2003p3456, Lemaster:2009p2711} is normalized to unity over the driven wavenumbers. |
The length scale of maximum driving, ¢;= 27/k, and the cutoff (p=2-/Kp are chosen to be L/4, and L/2 | The length scale of maximum driving, $\ell_1=2\pi/k_1$ , and the cutoff $\ell_F=2\pi/K_F$ are chosen to be $L/4$ , and $L/2$ |
The result above is also related to the detection of at least nine AGN in the sample. | The result above is also related to the detection of at least nine AGN in the sample. |
Again. this is not a surprising result since redshift το2 corresponds to the peak of the AGN number density distribution (see e.g. Wolf et al. | Again, this is not a surprising result since redshift $z \sim 2$ corresponds to the peak of the AGN number density distribution (see e.g. Wolf et al. |
2003 and references therein). | 2003 and references therein). |
The number density of AGN in this sample is in principle consistent with surveys at higher redshift. but is likely to be higher by à factor of two. | The number density of AGN in this sample is in principle consistent with surveys at higher redshift, but is likely to be higher by a factor of two. |
The ratio of UV to Lyo derived SFRs has a higher median value in this survey than results at redshift ;.~3. | The ratio of UV to $\alpha$ derived SFRs has a higher median value in this survey than results at redshift $z \sim 3$. |
The spread is large. but the trend is clear. | The spread is large, but the trend is clear. |
This result. and the smaller EWs discovered in general for this sample (see also the next point) at high redshift may indicate that LAEs in this survey are expected to be more affected by dust than LAEs at .~3. | This result, and the smaller EWs discovered in general for this sample (see also the next point) at high redshift may indicate that LAEs in this survey are expected to be more affected by dust than LAEs at $z \sim 3$. |
Another intriguing and related result is that of the narrower equivalent width distribution. | Another intriguing and related result is that of the narrower equivalent width distribution. |
Firstly. as detailed in section ??.. the distribution is. difficult to. explain. without invoking complicated arguments about the properties of the galaxies. | Firstly, as detailed in section \ref{ewsec}, the distribution is difficult to explain without invoking complicated arguments about the properties of the galaxies. |
A possible explanation would be that the star formation histories of Ίνα emitters are complex. | A possible explanation would be that the star formation histories of $\alpha$ emitters are complex. |
Secondly. the difference in the distributions between redshifts three and two is further evidence ofa higher dust quantity in the lower redshift galaxies. | Secondly, the difference in the distributions between redshifts three and two is further evidence of a higher dust quantity in the lower redshift galaxies. |
In conclusion. by comparing observations of Ένα emitters at redshift +=2.25 with galaxies selected in the same manner at higher redshifts. several evolutionary. signatures become evident in the properties of these galaxies. | In conclusion, by comparing observations of $\alpha$ emitters at redshift $z = 2.25$ with galaxies selected in the same manner at higher redshifts, several evolutionary signatures become evident in the properties of these galaxies. |
At lower redshifts. there appear to be fewer objects. with redder colours and higher dust contents. smaller equivalent widths. and a higher fraction of objects containing AGN. | At lower redshifts, there appear to be fewer objects, with redder colours and higher dust contents, smaller equivalent widths, and a higher fraction of objects containing AGN. |
Future SED fitting of these galaxies will reveal more information into the properties such as dust. mass and age (Nilsson et al.. | Future SED fitting of these galaxies will reveal more information into the properties such as dust, mass and age (Nilsson et al., |
in prep.). | in prep.). |
created by subtracting the STY fit (rom the SWALL points at the faint end. | created by subtracting the STY fit from the SWML points at the faint end. |
The LE at the faint end can then be described by the combination where (@.b)=(4.7.0.50). | The LF at the faint end can then be described by the combination where $(a,b)=(4.7,0.50)$. |
The uncertainties in these parameters are quite large (40.9.£0.06). an obvious consequence of the large errors in the SWALL points at these magnitudes, | The uncertainties in these parameters are quite large $(\pm0.9,\pm0.06)$, an obvious consequence of the large errors in the SWML points at these magnitudes. |
We. estimate. the scatter. in. our derived. Schechter. parameters by performing a large. number. of random realisations drawn from the estimated. Les. | We estimate the scatter in our derived Schechter parameters by performing a large number of random realisations drawn from the estimated LFs. |
In. addition to this sampling variance we also take into account the uncertainties in our Av-corrections (20%) and in the number | In addition to this sampling variance we also take into account the uncertainties in our $K$ -corrections $20\%$ ) and in the number |
During such a sinall time the scale factor of the universe e(f) changes very little. | During such a small time the scale factor of the universe $a(t)$ changes very little. |
It is typically assumed that muder such coucitions. this scenario is consistent with the Einstein equatious for a linearized perturbation off a FRW> spacetime. | It is typically assumed that under such conditions, this scenario is consistent with the Einstein equations for a linearized perturbation off a FRW spacetime. |
The consistency of a general cosmological lensing scenario with the Eimstein equations is studied iu Futamase& | The consistency of a general cosmological lensing scenario with the Einstein equations is studied in \citet{futamase}. |
Sasaki(1950), By Eq. 5.. | By Eq. \ref{poisson}, , |
the poteutial y is an explicit fiction of the proper distance r, but not the time f. | the potential $\varphi$ is an explicit function of the proper distance $r_p$ but not the time $t$. |
Necessarily, thus. the potential is a function of both the comoving distance r aud the coordinate tie f Via: Consequently. the metric. Eq. L. | Necessarily, thus, the potential is a function of both the comoving distance $r$ and the coordinate time $t$ via: Consequently, the metric, Eq. \ref{m1}, |
is not strictly static in the comoving coordinate svsteni. | is not strictly static in the comoving coordinate system. |
This Issue is somewhat obscure in the staudard references. including the excellent books bw Schneideretal.(1992). and Pettersetal.(2001)... where the potential is said to be "time independent.” | This issue is somewhat obscure in the standard references, including the excellent books by \citet{ehlers} and \citet{petters}, where the potential is said to be “time independent.” |
The time-variation of the potential is suall. however. in the conditions of lensing. where the scale factor changes very little during the passage of a lightray (one has dyf/df(dafdt)«(ría)s Oqür). | The time-variation of the potential is small, however, in the conditions of lensing, where the scale factor changes very little during the passage of a lightray (one has $d\varphi/dt = (da/dt)\times(r/a)\times \partial\varphi/\partial
r$ ). |
So diving the passage through the leus one may approxinate the scale factor by its value at some time f; representative of the time at which the lhehtrav passes the lens. | So during the passage through the lens one may approximate the scale factor by its value at some time $t_l$ representative of the time at which the lightray passes the lens. |
This would make the metric around the lens approximately static for the purposes of calculating. for instance. the time delay due to the Tens. | This would make the metric around the lens approximately static for the purposes of calculating, for instance, the time delay due to the lens. |
For our purposes the metric is needed for the eutire trajectory from the source to the lens. along which one expects the scale factor to chanec perhaps significantly, | For our purposes the metric is needed for the entire trajectory from the source to the lens, along which one expects the scale factor to change perhaps significantly. |
The metric is uot. thus. independent of time. but it is conformal to an approximately time-independent metric. | The metric is not, thus, independent of time, but it is conformal to an approximately time-independent metric. |
Since the uull ecodesics of conformally related spacetimes are identical. we may choose to approximate the scale factor with its value at the lens or uot. | Since the null geodesics of conformally related spacetimes are identical, we may choose to approximate the scale factor with its value at the lens or not. |
Although the approximation is very valuable for the purpose of obtaining a closed forma expression for the lens equation iu the conventional approach. it brings no real advantage to the nuucerical integration of the τα. eeoclesics. so woe prefer to maintain the time dependence as prescribed bv Poissous equation. | Although the approximation is very valuable for the purpose of obtaining a closed form expression for the lens equation in the conventional approach, it brings no real advantage to the numerical integration of the null geodesics, so we prefer to maintain the time dependence as prescribed by Poisson's equation. |
The equations of motion are more complicated (ii particular. they. do not decouple) but the added complications do not represent a real obstacle. | The equations of motion are more complicated (in particular, they do not decouple) but the added complications do not represent a real obstacle. |
Since the lens model Eq. | Since the lens model Eq. |
Lis spherically svinmnetric. the particle trajectories are planar. and there is no loss of generality iun choosing the plane as 0=7/2. | \ref{m1} is spherically symmetric, the particle trajectories are planar, and there is no loss of generality in choosing the plane as $\theta = \pi/2$. |
The geodesic equations can be found explicitly as the Euler-Lagrange equations of the Lagrangian to first order iu yz. | The geodesic equations can be found explicitly as the Euler-Lagrange equations of the Lagrangian to first order in $\varphi$. |
The Lagrangian is equal to zero because the eeodesics are null. | The Lagrangian is equal to zero because the geodesics are null. |
Since the coordinate o is evclic. the Euler-Lagrange equations are equivalent to five order ODEs. which we can write as These equations are obtained by workiug to first order in y aud making use of £=0 in the form The paramcter > arises from ο=0 and is related to the "observation angle” at the observer or the anele between the lehtray aud the optical (radial) axis connecting the observer to the lens. | Since the coordinate $\phi$ is cyclic, the Euler-Lagrange equations are equivalent to five first-order ODEs, which we can write as These equations are obtained by working to first order in $\varphi$ and making use of ${\mathcal{L}} = 0$ in the form The parameter $b$ arises from $\ddot \phi = 0$ and is related to the “observation angle” at the observer or the angle between the lightray and the optical (radial) axis connecting the observer to the lens. |
The relationship is determined by taking the dot product of the spatial part of thenull vector at the observer with a unit vector pointing towards the origin. | The relationship is determined by taking the dot product of the spatial part of thenull vector at the observer with a unit vector pointing towards the origin. |
Using the spatial part of the metric. Eq. £L. | Using the spatial part of the metric, Eq. \ref{m1}, , |
one obtains | one obtains |
TDGs. (Duc et al | TDGs, (Duc et al. |
2000) are characterized by a hnuuinositv colparable to that of typical dwarf galaxies. an exteuded morphology. high metallicity. aud blue colors (BV2:0.5 and VRoc to as a result of an active starburst. | 2000) are characterized by a luminosity comparable to that of typical dwarf galaxies, an extended morphology, high metallicity, and blue colors $B-V\approx 0.5$ and $V-R\approx 0.4$ ) as a result of an active starburst. |
These properties. however. have been outlined for objects found at the tip of the optical tails. some of them kinematically decoupled frou the surrounding material but stilleisually embedded in the collision debris. | These properties, however, have been outlined for objects found at the tip of the optical tails, some of them kinematically decoupled from the surrounding material but still embedded in the collision debris. |
Ou the other houd. more nuuerous ( cL TDC per collision) TDG caudidates have been found. both in broad baud optical anages (Woilbacher et al. | On the other hand, more numerous ( $\approx 4$ TDG per collision) TDG candidates have been found, both in broad band optical images (Weilbacher et al. |
2000) aud in Ho emissiou (elesias-Parraino Vilchez 2001). distributed all along the tidal features. | 2000) and in $\alpha$ emission (Iglesias-Párramo lchez 2001), distributed all along the tidal features. |
However. it remains uuclear whether these ↴↴∙structures HENnüsht become trulyEM detached dwufs⊽∙ iu | However, it remains unclear whether these structures might become truly detached dwarfs in the future. |
Tow. TDG doesqr. an average mncrger forma | How many TDG does an average merger form? |
’Shown for future.μα HUNοςof encounters between equalaiass the galaxics (Barnes. private commuuication) show the formation of zz LOObound the tidal tails. with a distribution of distances from the mereer that is very broad aud evolves with time as the tail expands. | Computer simulations of encounters between equal-mass disk galaxies (Barnes, private communication) show the formation of $\approx 100$ along the tidal tails, with a distribution of distances from the merger that is very broad and evolves with time as the tail expands. |
Oulv a few bound systems have masses above 5«10? AM. and they are located randomly throughout the tail. at an approximate mean distance of 100 kpc. | Only a few bound systems have masses above $5\times10^{8}$ $M_{\odot}$ and they are located randomly throughout the tail, at an approximate mean distance of 100 kpc. |
Among these most 1iassive seltf-eravitating structures. those with larger radii are the best candidates for becoming mdepeudeut dwarf galaxies in the loug term (Barnes EHeruquist 1992. Elmeercen et al. | Among these most massive self-gravitating structures, those with larger radii are the best candidates for becoming independent dwarf galaxies in the long term (Barnes Hernquist 1992, Elmegreen et al. |
1993). | 1993). |
Most of the other bound structures would fall back to the central galaxy within a Cyr. | Most of the other bound structures would fall back to the central galaxy within a Gyr. |
One should however consider that iu the case of tuteractious between unequal mass galaxies. the length of the tidal tail should be much smaller than in the case reported above. | One should however consider that in the case of interactions between unequal mass galaxies, the length of the tidal tail should be much smaller than in the case reported above. |
Correspoudiugly. darf eaudidates would be located iuuimch closer to the nuclei of the interacting pair. | Correspondingly, dwarf candidates would be located much closer to the nuclei of the interacting pair. |
One iueht imagine a dynamic scenario in which. depending on the nature (umorphologv. mass) of the galaxies involved iu the collision aud the stage at which the interaction is being observed. TDG do not uecessarilv have the properties observed in their vouug counterparts. | One might imagine a dynamic scenario in which, depending on the nature (morphology, mass) of the galaxies involved in the collision and the stage at which the interaction is being observed, TDG do not necessarily have the properties observed in their young counterparts. |
Τους could have formed. developed a massive starburst. and faded away. as well as decoupled frou the main stream | TDGs could have formed, developed a massive starburst, and faded away, as well as decoupled from the main stream |
‘There is now strong observational evidence that all massive galaxies (AM,m1017 107? M.) in the nearby Universe host a central supermassive black hole (SMDII: Mpgzm10 ΙΟNL+ 23). | There is now strong observational evidence that all massive galaxies $M_* \approx 10^{10}$ $10^{12} \Msun$ ) in the nearby Universe host a central supermassive black hole (SMBH; $\Mbh \approx 10^6$ $10^9
\Msun$; \citealt{kormendy95}) ). |
These SMDIIS have grown through mass accretion events (e.g. 2: 2)). during so-called active galactic nucleus (AGN) phases. | These SMBHs have grown through mass accretion events (e.g., \citealt{soltan82}; \citealt{rees84}) ), during so-called active galactic nucleus (AGN) phases. |
The seminal discovery that the masses of SMBlIS are proportional to those of their stellar spheroids implies a strong physical. association between AGN activity and galaxy. evolution (c.g. Tu Tu 7). | The seminal discovery that the masses of SMBHs are proportional to those of their stellar spheroids implies a strong physical association between AGN activity and galaxy evolution (e.g., \citealt{magorrian98}; \citealt{ferrarese00}; \citealt{gebhardt00}; \citealt{tremaine02}) ). |
Yo fully interpret the role plaved. by ΑΝ. in this svmbiosis requires a complete census of obscured ancl unobscured AGNs across cosmic time. | To fully interpret the role played by AGN in this symbiosis requires a complete census of obscured and unobscured AGNs across cosmic time. |
Unbiased. deep ancl wide-field. X-ray surveys have been instrumental in the identification of a large proportion of the AGN population to high redshifts (2~5: e.g.. ???2??)). | Unbiased deep and wide-field X-ray surveys have been instrumental in the identification of a large proportion of the AGN population to high redshifts $z \sim 5$; e.g., \citealt{dma01,barger03,fiore03,tozzi06,brusa10}) ). |
Using the exceptional sensitivities of and theObservatory. 7SO per cent. of the X-ray background (ΝΑ) has been resolved into discrete sources ab soft. energies (0.55 keV: eg. ?777)). | Using the exceptional sensitivities of and the, $> 80$ per cent of the X-ray background (XRB) has been resolved into discrete sources at soft energies (0.5–5 keV; e.g., \citealt{worsley05, hickox06, hickox07a}) ). |
However. AGN synthesis models for the NRB predict that ~50 per cent of the AGN population may be heavily obseured ancl remains uncleteetod at Lo26 keV in deep X-ray surveys (e.g.. 2?)) | However, AGN synthesis models for the XRB predict that $\sim 50$ per cent of the AGN population may be heavily obscured and remains undetected at $E >
6$ keV in deep X-ray surveys (e.g., \citealt{gilli07, treister09}) ). |
matrix is Uat-bottomecl due to the eutolf at 2=0.12. | matrix is flat-bottomed due to the cutoff at $z=0.12$. |
Fie. | Fig. |
S shows a strong dependency upon magnitude: (ie. Classical Malmeuist bias as expected) ancl also upon surface brightness. | 8 shows a strong dependency upon magnitude (i.e. classical Malmquist bias as expected) and also upon surface brightness. |
This surface brightness depencdeney is particularly strong near the LO’ Alpe? volume limit. as the data becomes sparse. | This surface brightness dependency is particularly strong near the $10^{4}$ $^{3}$ volume limit, as the data becomes sparse. |
Inside. this volume limit the contour lines generally mimic the curve of the visibility-derived. volume boundary. | Inside this volume limit the contour lines generally mimic the curve of the visibility-derived volume boundary. |
This suggests that visibility theory provides a good description. of the. combined volume dependency. | This suggests that visibility theory provides a good description of the combined volume dependency. |
“Phe sharp cutoll along the high surface brightness edge may be real but. could also be a manifestation. of the complex star-egalaxy separation algorithm (see. Maddox. 1990a). | The sharp cutoff along the high surface brightness edge may be real but could also be a manifestation of the complex star-galaxy separation algorithm (see Maddox 1990a). |
Given that a galaxy seen over a larger distance appears more compact and that local dwarls have smaller scale lengths than giants (ef | Given that a galaxy seen over a larger distance appears more compact and that local dwarfs have smaller scale lengths than giants (cf. |
Mateo 1998). this seems reasonable. | Mateo 1998), this seems reasonable. |
We will investigate this further through high-resolution imaging. | We will investigate this further through high-resolution imaging. |
The main point to take away from Fig. | The main point to take away from Fig. |
& is that the visibility surface of the αν input catalogue is complex and dependent on both AM and yr (although predominantly Al) | 8 is that the visibility surface of the 2dFGRS input catalogue is complex and dependent on both $M$ and $\mu_e$ (although predominantly $M$ ). |
Any methodologv which ignores surface brightness information and implements a volume-bias correction in luminosity onlv. is implicitly assuming uniform. visibility in surface brightness. | Any methodology which ignores surface brightness information and implements a volume-bias correction in luminosity only, is implicitly assuming uniform visibility in surface brightness. |
The 2dEGIU data clearly show that this is not the case. | The 2dFGRS data clearly show that this is not the case. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.