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A fat ACDAL cosmology is assumed with μι=0.25. 0,=0.045. h—4073. Q4—0.75. n=1. and ox=0.9. | A flat $\Lambda$ CDM cosmology is assumed with $\Omega_{\rm m}=0.25$, $\Omega_{\rm b}=0.045$, $h=0.73$, $\Omega_\Lambda=0.75$, $n=1$, and $\sigma_8=0.9$. |
Full particle data are stored. at G4 output times. | Full particle data are stored at 64 output times. |
For each output. haloes are identified: using a friencis-of-Eriencds (FOR) egroup-linder. | For each output, haloes are identified using a friends-of-friends (FOF) group-finder. |
Substructures (or subhaloes). within a FOR halo are located. using the SUDEIND algorithm of 7.. | Substructures (or subhaloes) within a FOF halo are located using the SUBFIND algorithm of \citet{springel2001}. |
"Phe. ποσο part of the FOR group. itself also appear in the substructure list. | The self-bound part of the FOF group itself also appear in the substructure list. |
This main subhalo typically contains 90 percent of the mass of the FOL group. | This main subhalo typically contains 90 percent of the mass of the FOF group. |
After finding all substructures in all the output snapshots. subhalo merging trees are built that describe in detail how these systems merge and grow as the universe evolves. | After finding all substructures in all the output snapshots, subhalo merging trees are built that describe in detail how these systems merge and grow as the universe evolves. |
Since structures merge hicrarchically in CDM. universes. for any given subhalo. there can be several progenitors. but. in eencral cach subhalo only has one descendant. | Since structures merge hierarchically in CDM universes, for any given subhalo, there can be several progenitors, but in general each subhalo only has one descendant. |
Merger trees are thus constructed. by defining a unique descendant. for each subhalo. | Merger trees are thus constructed by defining a unique descendant for each subhalo. |
We refer belowhalo to the main substructure that can represent the POL halo. whilesubhialo refers to substructure other than the main one. | We refer below to the main substructure that can represent the FOF halo, while refers to substructure other than the main one. |
Halo merger happens when two FOE group merge into one group and one of the haloes becomes a subhalo of the larger structure. | Halo merger happens when two FOF group merge into one group and one of the haloes becomes a subhalo of the larger structure. |
The substructure merger trees form the basic. input to the semi-analvtic mocel used to associate galaxies with haloes/subhaloes (2).. | The substructure merger trees form the basic input to the semi-analytic model used to associate galaxies with haloes/subhaloes \citep{delucia2007}. |
The semi-analvtic galaxy. catalogue we are using in this study is publicly available. | The semi-analytic galaxy catalogue we are using in this study is publicly available. |
A description of the publicly available catalogues. anc a link to the database can be found at the webpage: http://wwwΠπρα-garching.mpe.de/millennituay. | A description of the publicly available catalogues, and a link to the database can be found at the webpage: http://www.mpa-garching.mpg.de/millennium/. |
Once a halo appears in the simulation. a (central) galaxy begins to form within it. | Once a halo appears in the simulation, a (central) galaxy begins to form within it. |
The central galaxy is located at the position of the most bound particle of the halo. | The central galaxy is located at the position of the most bound particle of the halo. |
As the simulation evolves. the halo may merge with a larger structure and become a subhalo. | As the simulation evolves, the halo may merge with a larger structure and become a subhalo. |
The central galaxy then becomes a satellite galaxy in the larger structure. | The central galaxy then becomes a satellite galaxy in the larger structure. |
The galaxv's position and velocity are. specified by the position ancl velocity of the most. bound. particle of its host halo/subhalo. | The galaxy's position and velocity are specified by the position and velocity of the most bound particle of its host halo/subhalo. |
Even if the subhalo hosting the galaxy is tidally disrupted. the position ancl velocity of the galaxy is still traced. through this most bound. particle. | Even if the subhalo hosting the galaxy is tidally disrupted, the position and velocity of the galaxy is still traced through this most bound particle. |
Galaxies hus only clisappear from the simulation if they merge with another galaxy. | Galaxies thus only disappear from the simulation if they merge with another galaxy. |
Phe time taken for a galaxy without subhalo o merge with the central object is given by the time taken or dynamical friction to erode its orbit. causing it to spiral into the centre ancl merge. | The time taken for a galaxy without subhalo to merge with the central object is given by the time taken for dynamical friction to erode its orbit, causing it to spiral into the centre and merge. |
This is calculated using the μαandard Chancdrasckhar formula. | This is calculated using the standard Chandrasekhar formula. |
All the information about 1e formation and merging history of galaxies is stored. | All the information about the formation and merging history of galaxies is stored. |
By analyzing these halo and galaxy merger trees. we are ible to track when two haloes merge together and whether 1e galaxies within them also merge into a single object by 1e present day. | By analyzing these halo and galaxy merger trees, we are able to track when two haloes merge together and whether the galaxies within them also merge into a single object by the present day. |
In this study. we focus on mergers between satellite and central galaxies. ancl exclude mergers between wo satellites. | In this study, we focus on mergers between satellite and central galaxies, and exclude mergers between two satellites. |
Phese events are rare (2). and neglecting then gaj0uld not. allect our conclusions about the incidence and ueling of black holes in galaxies. | These events are rare \citep{springel2001} and neglecting them should not affect our conclusions about the incidence and fueling of black holes in galaxies. |
In this study. we assume that black holes form when a galaxy undergoes a major merging event. | In this study, we assume that black holes form when a galaxy undergoes a major merging event. |
Galaxies that have never experienced a major merger do not have a black hole. | Galaxies that have never experienced a major merger do not have a black hole. |
We define major mergers as events in which the mass ratio of he two progenitors is greater than 0.3. | We define major mergers as events in which the mass ratio of the two progenitors is greater than $0.3$. |
For halo merger. he mass ratio is the virial mass ratio of two progenitor idoes. | For halo merger, the mass ratio is the virial mass ratio of two progenitor haloes. |
For galaxy merger. it is the stellar mass ratio of wo progenitor galaxies. | For galaxy merger, it is the stellar mass ratio of two progenitor galaxies. |
When we track mergers in the simulation. we include major mergers that occur in all xanches of the tree. not just the “main branch”. | When we track mergers in the simulation, we include major mergers that occur in all branches of the tree, not just the “main branch”. |
Since galaxies reside in dark matter haloes and are able o merge only once their host haloes have coalesced. we begin » analyzing the merging histories of the dark matter haloes hemselves. | Since galaxies reside in dark matter haloes and are able to merge only once their host haloes have coalesced, we begin by analyzing the merging histories of the dark matter haloes themselves. |
In the left panel of Fig. L.. | In the left panel of Fig. \ref{fig:halofrac}, |
we plot the average number of major mergers a present day clark matter halo has experienced over its lifetime as a function of halo mass. | we plot the average number of major mergers a present day dark matter halo has experienced over its lifetime as a function of halo mass. |
Note hat in this analysis we track mergers down to an elfective resolution limit of 20 particles. which corresponds to a halo of mass L7101h.FAL. | Note that in this analysis we track mergers down to an effective resolution limit of $20$ particles, which corresponds to a halo of mass $1.7 \times
10^{10}h^{-1}M_{\odot}$. |
We see that the number of major mergers (above the resolution limit) experienced by a halo is a strongly increasing function of mass: haloes with present-day masses of 1017A4. have typically experienced only one one major merger. whereas the progenitors of. present-cdavy haloes with masses of LOMAL. have merged with each other close to LOO times. | We see that the number of major mergers (above the resolution limit) experienced by a halo is a strongly increasing function of mass; haloes with present-day masses of $10^{12} M_{\odot}$ have typically experienced only one one major merger, whereas the progenitors of present-day haloes with masses of $10^{15} M_{\odot}$ have merged with each other close to 100 times. |
In the right panel. we show the fraction of haloes that have had at least one major merger during their lifetime. as à function of halo mass. | In the right panel, we show the fraction of haloes that have had at least one major merger during their lifetime, as a function of halo mass. |
Thefraction of haloes that have had major mergers also increases rapidly with halo mass. | Thefraction of haloes that have had major mergers also increases rapidly with halo mass. |
Almost all haloes more massive than LOA1. have had | Almost all haloes more massive than $10^{13}h^{-1}M_{\odot}$ have had |
Ly-« Ly-« (see?.forarecentreview).. | $\alpha$ $\alpha$ \citep[see][for a recent review]{igm:m09}. |
(?) z=0 1000A 2x10°photons/enr/s/ster/eV. (22).. | \citep{jnu:hm01} $z=0$ $1000\AA$ $2\times10^3\dim{photons}/\dim{cm}^2/\dim{s}/\dim{ster}/\dim{eV}$ \citep{h2:d78,h2:mmp83}. |
z~3 z=0 (??).. (?).. (e.g.22222??.ete).. | $z\sim3$ $z=0$ \citep{jnu:hm01,jnu:flzh09}. \citep{hizgal:cppp09}, \citep[e.g.][etc]{sims:co92,sims:kwh96,sims:ns97,sims:k03,sims:ck09,sims:svbw09,sims:honj09}. |
=0. the simulations used in this paper have been recently described in great detail elsewhere (??).. | $z=0$ the simulations used in this paper have been recently described in great detail elsewhere \citep{ng:gk10a,ng:gk10b}. |
As a brief reminder. the simulations have been performed with the Adaptive Refinement Tree (ART) code (2???) that uses adaptive mesh refinement in both the gas dynamics and gravity calculations to achieve high dynamic range in spatial scale. | As a brief reminder, the simulations have been performed with the Adaptive Refinement Tree (ART) code \citep{misc:k99,misc:kkh02,sims:rzk08} that uses adaptive mesh refinement in both the gas dynamics and gravity calculations to achieve high dynamic range in spatial scale. |
The simulations include star formation and supernova enrichment and thermal energy feedback. as well as a highly detailed ISM model. | The simulations include star formation and supernova enrichment and thermal energy feedback, as well as a highly detailed ISM model. |
The 3D radiative transfer of UV radiation from individual stellar particles 1s followed self-consistently with the OTVET approximation (?).. | The 3D radiative transfer of UV radiation from individual stellar particles is followed self-consistently with the OTVET approximation \citep{ng:ga01}. |
The simulations incorporate non-equilibrium chemical network of hydrogen and helium and non-equilibrium. metallicity-dependent cooling and heating rates. and a phenomenological model of molecular hydrogen formation on and shielding by cosmic dust. as well as H» self-shielding (??).. | The simulations incorporate non-equilibrium chemical network of hydrogen and helium and non-equilibrium, metallicity-dependent cooling and heating rates, and a phenomenological model of molecular hydrogen formation on and shielding by cosmic dust, as well as $\H2$ self-shielding \citep{ng:gk10a,ng:gk10b}. |
Particular simulations used in this paper model a small region including a Milky-Way progenitor galaxy and a number of smaller galaxies with the mass resolution of 1.3x10°M. in dark matter. 2.2x10?M. in baryons. and with the spatial resolution of 65pex[4/€1+:)] (n physical units) within the fully refined region. | Particular simulations used in this paper model a small region including a Milky-Way progenitor galaxy and a number of smaller galaxies with the mass resolution of $1.3\times10^6\Msun$ in dark matter, $2.2\times 10^5\Msun$ in baryons, and with the spatial resolution of $65\dim{pc}\times[4/(1+z)]$ (in physical units) within the fully refined region. |
Star formation in. the simulation is occurring. in. the molecular gas only. using the prescriptions of ?.— and ?.. | Star formation in the simulation is occurring in the molecular gas only, using the prescriptions of \citet{sfr:km05} and \citet{sfr:kt07}. |
The exact formulation of the star formation recipe is shown in Equation (2) of ?.. | The exact formulation of the star formation recipe is shown in Equation (2) of \citet{ng:gk10b}. |
For the purpose of this paper. two simulations. are considered that differ only by the inclusion of the cosmic UV background from ?.. | For the purpose of this paper, two simulations are considered that differ only by the inclusion of the cosmic UV background from \citet{jnu:hm01}. |
In the simulation without the cosmic UV background. the local radiation field produced by nearby massive stars is still included in exactly the same manner as in the simulation with the UV background. | In the simulation without the cosmic UV background, the local radiation field produced by nearby massive stars is still included in exactly the same manner as in the simulation with the UV background. |
Thus. these two simulations can be used to evaluate the particular effect of the cosmic UV background on the properties of model galaxies. | Thus, these two simulations can be used to evaluate the particular effect of the cosmic UV background on the properties of model galaxies. |
Because of computational expense. the simulations are not continued beyond z=2. | Because of computational expense, the simulations are not continued beyond $z=2$. |
The simulation with the cosmic. UV background ts the same one as described in ?.. | The simulation with the cosmic UV background is the same one as described in \citet{ng:gk10a}. |
That reference also shows good agreement of that simulation with several observationalconstraints on theproperties of high redshift galaxies. | That reference also shows good agreement of that simulation with several observationalconstraints on theproperties of high redshift galaxies. |
A direct comparisonofstellar massesand star formation rates between the galaxies in the two simulations 1s shown in | A direct comparisonofstellar massesand star formation rates between the galaxies in the two simulations is shown in |
and The WB invariants for neutrino mass matrices of type Bs can be obtained by interchanging the ji and 7 indices in the above relations. | and The WB invariants for neutrino mass matrices of type $B_2$ can be obtained by interchanging the $\mu$ and $\tau$ indices in the above relations. |
For neutrino mass matrices of tvpe By. we have and The WB invariants for class By can be obtained from the interchange of the yt and 7 indices in the above relations. | For neutrino mass matrices of type $B_3$, we have and The WB invariants for class $B_4$ can be obtained from the interchange of the $\mu$ and $\tau$ indices in the above relations. |
The conditions for the CP invariance of neutrino mass matrices of class B have been summarized in Table 2. | The conditions for the CP invariance of neutrino mass matrices of class B have been summarized in Table 2. |
These conditions on the phases of the neutrino mass matrix can be viewed as the fine (unines required to have CP invariance. | These conditions on the phases of the neutrino mass matrix can be viewed as the fine tunings required to have CP invariance. |
For neutrino mass matrices of tvpe C. we have I, The neutrino mass matrix of class C will be CP invariant if (he phases of (he mass matrix are [ime tuned to satislv the condition | For neutrino mass matrices of type $C$, we have and The neutrino mass matrix of class C will be CP invariant if the phases of the mass matrix are fine tuned to satisfy the condition |
We have shown that the relative strengths of the mid-IR. aromatic features for Seyfert galaxies differ significantly from those for star-forming galaxies, with the 6.2, 7.7, and 8.6 um features being suppressed relative to the 11.3 um feature in Seyferts. | We have shown that the relative strengths of the mid-IR aromatic features for Seyfert galaxies differ significantly from those for star-forming galaxies, with the 6.2, 7.7, and 8.6 $\mu$ m features being suppressed relative to the 11.3 $\mu$ m feature in Seyferts. |
The sources with the smallest L(7.7 wm)/L(11.3 um) aromatic feature ratios also exhibit the strongest Ἡ» S(3) rotational lines, which likely trace shocked gas (see Figure 6)). | The sources with the smallest L(7.7 $\mu$ m)/L(11.3 $\mu$ m) aromatic feature ratios also exhibit the strongest $_2$ S(3) rotational lines, which likely trace shocked gas (see Figure \ref{fig:h2}) ). |
We explore the relevant physical and chemical effects that could produce the observed aromatic spectra. | We explore the relevant physical and chemical effects that could produce the observed aromatic spectra. |
An enhanced fraction of neutral aromatic molecules could produce qualitatively similar behavior, but the observed ratios lie beyond model predictions for completely neutral molecules and the presence of an AGN would be expected to increase the level of ionization rather than reduce it. | An enhanced fraction of neutral aromatic molecules could produce qualitatively similar behavior, but the observed ratios lie beyond model predictions for completely neutral molecules and the presence of an AGN would be expected to increase the level of ionization rather than reduce it. |
Destruction of the smallest aromatic molecules could explain the suppression of shorter wavelength features, but the expected variations in the relative strengths of the 6.2, 7.7, and 8.6 jm features are not seen. | Destruction of the smallest aromatic molecules could explain the suppression of shorter wavelength features, but the expected variations in the relative strengths of the 6.2, 7.7, and 8.6 $\mu$ m features are not seen. |
A modification of the molecular structure that enhances the C-H/C-C ratio could reproduce the observed behavior, and an open C skeleton with fewer adjacent C-H groups would furthermore explain the reduced strength of the 12.7 um feature. | A modification of the molecular structure that enhances the C–H/C–C ratio could reproduce the observed behavior, and an open C skeleton with fewer adjacent C–H groups would furthermore explain the reduced strength of the 12.7 $\mu$ m feature. |
Given the connection between strong Hz emission and modified aromatic ratios, we speculate that shock processing could produce such structures. | Given the connection between strong $_2$ emission and modified aromatic ratios, we speculate that shock processing could produce such structures. |
Finally, we show that the aromatic features correlate well with ((i.e., star formation) but not with ((i.e., AGN luminosity), indicating that AGN excitation of aromatic emission is not significant and that aromatic-based estimates of the SFR are generally reasonable. | Finally, we show that the aromatic features correlate well with (i.e., star formation) but not with (i.e., AGN luminosity), indicating that AGN excitation of aromatic emission is not significant and that aromatic-based estimates of the SFR are generally reasonable. |
There are a few outliers with strong Hz emission, small L(7.7 wm)/L(11.3 xm) ratios, and small rratios, but for these sources the 11.3 jum aromatic/[Ne feature is stillτῇ a reasonably robust tracer of the SFR. | There are a few outliers with strong $_2$ emission, small L(7.7 $\mu$ m)/L(11.3 $\mu$ m) ratios, and small ratios, but for these sources the 11.3 $\mu$ m feature is still a reasonably robust tracer of the SFR. |
We acknowledge useful discussions with and assistance from Anthony Jones, Yong Shi, Amelia Stutz, Alexander Tielens, Jonathan Trump, and Gregory Walth. | We acknowledge useful discussions with and assistance from Anthony Jones, Yong Shi, Amelia Stutz, Alexander Tielens, Jonathan Trump, and Gregory Walth. |
We thank the anonymous referee for helpful suggestions that have improved the manuscript. | We thank the anonymous referee for helpful suggestions that have improved the manuscript. |
This work was supported by contract 1255094 from Caltech/JPL to the University of Arizona. | This work was supported by contract 1255094 from Caltech/JPL to the University of Arizona. |
.. | A_z |
Forsubtiractions 4.3 Generalization to coupled channels Both met | _i This has been used, e.g., in \cite{Baacke:1995bw}, for computing the fluctuation determinant for bubble nucleation in the $SU(2)$ Higgs model at large temperature. |
hodscan begeneralized to co | We have again stated the theorem in its naive form, without cutoff. |
upled channel | If the potential $\bfV^n$ is well-behaved, we again have $\bfJ_n(0,\Lambda^2)=\bfJ_n(0)-\bfJ(\Lambda^2)$. |
svstems with aspherical svininelty, The operatorM ancl ilspart | The situation changes if we consider the fluctuation determinant for a topological soliton, indeed some matrix elements of the potential $\bfV_n$ in the gauge-Higgs sector are singular as $r\to 0$. |
ial wavereductionΝΤnowbe | This will be discussed in subsection \ref{swave}. . |
come Nx Ninatrices. The solutions [=(.rv7) arereplaced bya | If one analyzes the operator $\bfM_n$ for the case of the Abelian instanton one finds that the centrifugal barriers are modified in relation to the nontrivial winding number. |
fundamental svstem of solutionsfME SGH.7(r. $72) | Indeed the potential $\bfV^n$ contains terms proportional to $1/r^2$ in the $33$, $44$ and $34$ and $43$ components. |
whereindex7 labels thecomponent and theindexà labels the solution. Both indices run | While in the topologically trivial vacuum sector the pattern of centrifugal barriers near $r=0$ for the gauge-Higgs system is $\{n_i\}=\{n-1,n+1,n,n\}$ within the subspace of angular momentum $n$, in the instanton sector this becomes $\{\tilde n_i\}=\{n-1,n+1,n+1,n-1\}$. |
from 1(oJN. so thatthe | For $n=0$ we have $\{n_i\} =\{1,1,0,0\}$ which is distorted to $\{\tilde n_i\}=\{1,1,1,1\}$. |
fundamental system QUE Bradd then (he Green's function is givenbv (4.34) labelgreenf G(r yaw | As a consequence the partial waves near $r=0$ no longer behave as the Bessel functions $I_{n_i}(\kappa r)$ , and the functions $h^{\alpha\pm}_{n,i}(r,\nu^2)$ no longer become constant near $r=0$. |
Par (nM nnOo From thisGreen’function again to computethe | For $n\neq 0$ two mixtures of the components with $i=3,4$ behave as $1/r$ and $r$ , respectively; for $n=0$ both Higgs components behave as $r$. |
de | In Refs. |
terminantee using methods I.We wehave are able fInctuation G (sf rdrG, Gran. (4.36)... and(he subsequentsteps are performed as described | \cite{Baacke:1994bk} and \cite{Baacke:1993aj,Baacke:1994ix} the method I was used in order to compute the fluctuation determinant for the Abelian instanton in $1+1$ and the of sphaleron in $3$dimensions (the high-temperature limit of the $3+1$ dimensional theory), respectively. |
above. In terms of the functions77.see Eq.?? wehave | The summation over partial waves was done before the integration over $\nu^2$and thecutoff was sent to infinity after suitable |
angle. | angle. |
However. the points obtained with model A lie significantly below this line. showing that the relationship is not universal. | However, the points obtained with model A lie significantly below this line, showing that the relationship is not universal. |
A point of particular interest relates to the interpretation of Arnett's Rule (2) which is commonly used to estimate Ni masses in studies of SNe Ta light curves (e.g. 2: 2: 2::2: 2). | A point of particular interest relates to the interpretation of Arnett's Rule \citep{arnett82} which is commonly used to estimate Ni masses in studies of SNe Ia light curves (e.g. \citealt{arnett85}; ; \citealt{branch92}; ; \citealt{stritzinger05}; \citealt{howell06}) ). |
Arnett's Rule states that at maximum light. the luminosity roughly balances the instantaneous rate of energy generation in the SN. | Arnett's Rule states that at maximum light, the luminosity roughly balances the instantaneous rate of energy generation in the SN. |
Adopting the convenient notation of ?. this relation is stated as where L? is the peak luminosity. £(/)) is the rate of energy generation at the time of maximum light (/)) and AM; is the total mass of "Ni. | Adopting the convenient notation of \citet{branch92} this relation is stated as where $L^{\mbox{\scriptsize p}}$ is the peak luminosity, $R(t_{\mbox{\scriptsize p}})$ is the rate of energy generation at the time of maximum light $t_{\mbox{\scriptsize p}}$ ) and $M_{ \mbox{\scriptsize Ni}}$ is the total mass of $^{56}$ Ni. |
The proportionality factor. a. is expected to be of order unity. | The proportionality factor, $\alpha$ , is expected to be of order unity. |
2(/) is given by where / is measured in davs. | $R(t)$ is given by where $t$ is measured in days. |
The numerical coefficients have been computed using the lifetimes and decay energies from ?.. | The numerical coefficients have been computed using the lifetimes and decay energies from \citet{ambwani88}. |
It is well-known from several previous studies that Arnett's Rule can usually be used to derive a reasonable estimate for Als; Tom the light curve. | It is well-known from several previous studies that Arnett's Rule can usually be used to derive a reasonable estimate for $M_{\mbox{\scriptsize Ni}}$ from the light curve. |
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