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In 844.3 we noted that according to our model there should be ~2 times more red clusters than blue being formed. | In 4.3 we noted that according to our model there should be $\sim2$ times more red clusters than blue being formed. |
However. given the fact that the SFR of the disk and red component overlap (Figure 4). the later infalline clumps are more likely (to collide with existing disk eas rather (han other clamps or be tidally disrupted. | However, given the fact that the SFR of the disk and red component overlap (Figure 4), the later infalling clumps are more likely to collide with existing disk gas rather than other clumps or be tidally disrupted. |
It is assumed that not only will many fewer red clusters be formed. but that the compression of (his gas Irom infalling clumps will form stars whose kinematies can be expected to resemble the red clusters which survive in numbers comparable to blue clusters. ( | It is assumed that not only will many fewer red clusters be formed, but that the compression of this gas from infalling clumps will form stars whose kinematics can be expected to resemble the red clusters which survive in numbers comparable to blue clusters. ( |
In equation (10) 5 is effectively. reduced bv ~ 1/2). | In equation (10) $\eta$ is effectively reduced by $\sim1/2$ ). |
A thick disk component is thus created. | A thick disk component is thus created. |
The peak in the disk SFR at LO Gvr | The peak in the disk SFR at 10 Gyr |
By [ar the most abundant element in the universe is hvdrogen. | By far the most abundant element in the universe is hydrogen. |
Consequently Is is ihe most abundant molecule and is the dominant collision partner in dark interstellar clouds. | Consequently $_2$ is the most abundant molecule and is the dominant collision partner in dark interstellar clouds. |
Dust grain surfaces act as heterogeneous catalvsts in the formation of II» molecules from atomic hydrogen (Gould&Salpeter1963:Hollenbach1979). | Dust grain surfaces act as heterogeneous catalysts in the formation of $_2$ molecules from atomic hydrogen \citep{GS63,HS70}. |
. Devond this general consensus. the actual formation mechanism remains elusive and the internal energy distribution of the nascent hvdrogen molecule is unknown. | Beyond this general consensus, the actual formation mechanism remains elusive and the internal energy distribution of the nascent hydrogen molecule is unknown. |
During formation. the II5 binding energv AR,=4.476 eV must be partitioned between the vibrational excitation and translational energy of the nascent molecule and heating of the dust grain (Duley 1993). | During formation, the $_2$ binding energy $\Delta E_b = 4.476$ eV must be partitioned between the vibrational excitation and translational energy of the nascent molecule and heating of the dust grain \citep{DW93}. |
. Dv studying the formation pumping of molecular hydrogen. namely the vibrational distribution of nascent Il» molecules. we can constrain interstellar chemistry both in the phase anc on grain surfaces. | By studying the formation pumping of molecular hydrogen, namely the vibrational distribution of nascent $_2$ molecules, we can constrain interstellar chemistry both in the phase and on grain surfaces. |
If the internal ancl translational energies of nascent molecules are relatively small. then sgnificamt grain heating must take place. which mav lead (o the desorption of volatile molecules from the dust grain surface (Dulev&Williams1993:Robertsetal.2007). | If the internal and translational energies of nascent molecules are relatively small, then significant grain heating must take place, which may lead to the desorption of volatile molecules from the dust grain surface \citep{DW93,R07}. |
. The IH» internal energy distribution could have a significant impact on the chemistry occurring in the interstellar medium (ISM) because vibrationally excited Ils will increase the overall energy budget of phase processes. | The $_2$ internal energy distribution could have a significant impact on the chemistry occurring in the interstellar medium (ISM) because vibrationally excited $_2$ will increase the overall energy budget of phase processes. |
There have been many theoretical and. laboratory studies that predict HI» to be formed in highly excited vibrational states (e.g.. Sizunοἱal.2010:Tantardini2006 and references (herein). | There have been many theoretical and laboratory studies that predict $_2$ to be formed in highly excited vibrational states (e.g., \citealt{S10,MT06} and references therein). |
It is possible that. this formation punping mav be observable in the infrared (IIR) spectra of Hs molecules. | It is possible that this formation pumping may be observable in the infrared (IR) spectra of $_2$ molecules. |
The effects induced in the LR spectrum of H» by vibrational excitation of nascent molecules was first considered by Black&Dalearno(1976).. who emploved a formation punping model in which ecquipartition of the IL binding energy released was arbitrarily assumed. | The effects induced in the IR spectrum of $_2$ by vibrational excitation of nascent molecules was first considered by \citet{BD76}, who employed a formation pumping model in which equipartition of the H binding energy released was arbitrarily assumed. |
In this model. (he binding energy is split equally between (he internal energy of the nolecule. its translational energy on desorption [rom the erain surface and the heat imparted to the grain lattice. | In this model, the binding energy is split equally between the internal energy of the molecule, its translational energy on desorption from the grain surface and the heat imparted to the grain lattice. |
The molecule is formed at an elfective temperature T,~9000 Ix. The internal energy is spread wilh a Boltzmann distribution tiroughout the vibrational levels. with the para ratio (OPI) being approximately 3. | The molecule is formed at an effective temperature $T_f \sim 9000$ K. The internal energy is spread with a Boltzmann distribution throughout the vibrational levels, with the para ratio (OPR) being approximately 3. |
Subsequently. several classical nolecular dvnamics and quantum mechanical caleulations have been carried out [or I omnation on surlaces whose chemical compositions are analogous to interstellar dust grains. | Subsequently, several classical molecular dynamics and quantum mechanical calculations have been carried out for $_2$ formation on surfaces whose chemical compositions are analogous to interstellar dust grains, |
Ilot Jupiter exoplanets represent a fundamentally new class of planets that were not anticipated and are not present within our solar svstem. | Hot Jupiter exoplanets represent a fundamentally new class of planets that were not anticipated and are not present within our solar system. |
These planets exist in extreme environments. residing very close to their host stars at semi-major axes of several hundredths ol an A.U. The mechanism that allows hot Jupiters to migrate in (o the near vicinity of their host stars from a formation location Chat was prestunably much further out bevond the snow line is still very much an open (anc much debated) question. | These planets exist in extreme environments, residing very close to their host stars at semi-major axes of several hundredths of an A.U. The mechanism that allows hot Jupiters to migrate in to the near vicinity of their host stars from a formation location that was presumably much further out beyond the snow line is still very much an open (and much debated) question. |
In general. hot Jupiters fandamentally extend our understanding of planet atmosphere. structure. evolution. and migration into a new regine. ancl (therefore further study of these planets aimed αἱ characterizing and understanding their current states is warranted. | In general, hot Jupiters fundamentally extend our understanding of planet atmosphere, structure, evolution, and migration into a new regime, and therefore further study of these planets aimed at characterizing and understanding their current states is warranted. |
In particular. hot Jupiters lie in a very interesting regine in terms of their atmospheric ονπασα, in that they are expected to be Gdally locked fom simple (mescale arguments (e.g.?).. | In particular, hot Jupiters lie in a very interesting regime in terms of their atmospheric dynamics, in that they are expected to be tidally locked from simple timescale arguments \citep[e.g.][]{ras96}. |
This leads to the planets having permanent hot day sides aud colder night sides. | This leads to the planets having permanent hot day sides and colder night sides. |
An important outstanding question is the extent to which heat is recireulated from the day side to the night side of these planets. which has important implications for (heir global energv budgets. | An important outstanding question is the extent to which heat is recirculated from the day side to the night side of these planets, which has important implications for their global energy budgets. |
Some constraints have been made on dav-to-night heat redistribution on llow | Some constraints have been made on day-to-night heat redistribution on hot Jupiters by observing the planets' IR emission as a function of orbital phase \citep{har06, knu07, cow07, knu09, cro10}. |
ever. the patterns seem {ο vary. strongly [rom planet (ο planet. | However, the patterns seem to vary strongly from planet to planet. |
More insight remains to be gained from additional observations of this (wpe along with direct constraints on the winds in hot Jupiter atmosphleres. which ultimately govern the day-to-night heat Low. | More insight remains to be gained from additional observations of this type along with direct constraints on the winds in hot Jupiter atmospheres, which ultimately govern the day-to-night heat flow. |
Three-climensional models of the atmospheric ονπαΙός of hot Jupiters have been presented by a number of authors (e.g.2???7).. with the goal of understanding this new regime of abmospheric circulation. | Three-dimensional models of the atmospheric dynamics of hot Jupiters have been presented by a number of authors \citep[e.g.][]{sho09, dob10, rau10, hen11,
thr11}, with the goal of understanding this new regime of atmospheric circulation. |
While (hese models can vary considerably in (he treatinent. and level of complexitw of the underlving physics. à number of the qualitative results on hot Jupiter atmospheric dvnanmies have proved to be robust across most of the models. | While these models can vary considerably in the treatment and level of complexity of the underlying physics, a number of the qualitative results on hot Jupiter atmospheric dynamics have proved to be robust across most of the models. |
These are (1) winds al pressures of 1 bar set up an equatorial jet that moves in the direction of the planet's rotation (see?.forananalyticdescriptionthisbehavior)... (2) as a result of the equatorial wind pattern. the hottest point on the planet is shilted away from the substellar point in the direction of the planets rotation. and (3) winds hisher in the atmosphere al enbar pressures tend to [low directlv from (he hot day side to the cooler night side of the | These are (1) winds at pressures of $\sim 1$ bar set up an equatorial jet that moves in the direction of the planet's rotation \citep[see][for an analytic description this behavior]{sho11}, (2) as a result of the equatorial wind pattern, the hottest point on the planet is shifted away from the substellar point in the direction of the planet's rotation, and (3) winds higher in the atmosphere at $\sim$ mbar pressures tend to flow directly from the hot day side to the cooler night side of the |
Tf the circiwustellar wind of the SN progenitor is dense aud opically thick. the shock breakout signal is altered by the wind. | If the circumstellar wind of the SN progenitor is dense and optically thick, the shock breakout signal is altered by the wind. |
Photons enütted from the shock diffuse iu the wind ane the light curve (LC) of the shock breakout becomes broader 2011). | Photons emitted from the shock diffuse in the wind and the light curve (LC) of the shock breakout becomes broader . |
. Tf the wine is much denser. the shock breakout itself can take place in the wind. | If the wind is much denser, the shock breakout itself can take place in the wind. |
The shock breakout in the deuse wind is relatec to astrophysical pleromcua. 6.8.. PTF 090j 2010).. NRO 080109 2011).. and production of high cnerey ]outicles 2011). | The shock breakout in the dense wind is related to astrophysical phenomena, e.g., PTF 09uj , XRO 080109 , and production of high energy particles . |
. In particlar. associate lDuninous superrvovae (LSNe) to the shock breakout im the deuse wiud. | In particular, associate luminous supernovae (LSNe) to the shock breakout in the dense wind. |
Many LSNe ive believed to be brightened by the shock interaction between SN ejeca (or materials released from stellar surface) aud the deise ciretuustellar wind 2005). | Many LSNe are believed to be brightened by the shock interaction between SN ejecta (or materials released from stellar surface) and the dense circumstellar wind . |
.. This is because many LSNe are "spectroscopically classified as Type Hu SNe which show narrow spectral lines from the wind surrounding SN | This is because many LSNe are spectroscopically classified as Type IIn SNe which show narrow spectral lines from the wind surrounding SN |
In the PS74 scenario. at a fixed cosmological epoch. an ionized bubble grows around a galaxy of mass fig2)mhau(z). where Nhuin(2) represents the virial mass corresponding to 7/=107 K. the temperature at which hydrogen cooling becomes efficient. | In the PS74 scenario, at a fixed cosmological epoch, an ionized bubble grows around a galaxy of mass $m_{\rm gal} \ge m_{\rm min}(z)$, where $m_{\rm min}(z)$ represents the virial mass corresponding to $T=10^{4}$ K, the temperature at which hydrogen cooling becomes efficient. |
The mass associated to the ionized region is ng;=Qnia. where ¢ represents the ionization efficiency of the galaxy (here assumed to be constant). that depends on the star formation rate. on the escape fraction of photons and on the number of HII recombinations. | The mass associated to the ionized region is $m_{HII}=\zeta m_{\rm gal}$, where $\zeta$ represents the ionization efficiency of the galaxy (here assumed to be constant), that depends on the star formation rate, on the escape fraction of photons and on the number of HII recombinations. |
Since each region is thought to be isolated. it must contain enough collapsed mass to fully ionize the inner gas. | Since each region is thought to be isolated, it must contain enough collapsed mass to fully ionize the inner gas. |
Thus fi;n(9.C +. where foou is the collapsed volume fraction of a region of mass m Zyin With an inner overdensity 2. | Thus $f_{\rm coll}(\delta,m) \ge \zeta^{-1}$ , where $f_{\rm
coll}$ is the collapsed volume fraction of a region of mass m $\ge
m_{\rm min}$ with an inner overdensity $\delta$. |
In the FO4 formalism. this leads to the following condition for the overdensity inside a bubble of a given mass nm Gin Lagrangian space): where A(c)ertτιC 5 στ(m) is the variance of density fluctuations smoothed on the scale m and ez,=067 (maia). | In the F04 formalism, this leads to the following condition for the overdensity inside a bubble of a given mass $m$ (in Lagrangian space): where $K(\zeta) \equiv {\rm erf}^{-1}(1-\zeta^{-1})$ , $\sigma^{2}(m)$ is the variance of density fluctuations smoothed on the scale $m$ and $\sigma^{2}_{\rm min} \equiv \sigma^{2}(m_{\rm min})$ . |
As shown in F04. 8, represents the ionization threshold for the density fluctuations in the Lagrangian space and it is assumed to be a linear barrier with respect to σ(7): 0,(mi.2)~=Bolz)|Bi(z)o? (m). | As shown in F04, $\delta_{x}$ represents the ionization threshold for the density fluctuations in the Lagrangian space and it is assumed to be a linear barrier with respect to $\sigma^{2}(m)$: $\delta_{x}(m,z) \sim B(m,z)=B_{0}(z)+B_{1}(z)\sigma^{2}(m)$ . |
Hence it is possible to obtain an analytic expression for the distribution of the bubbles with mass in the range mcclin/2: where p is the mean comoving matter density of the universe. | Hence it is possible to obtain an analytic expression for the distribution of the bubbles with mass in the range $m\pm {\rm d}m/2$: where $\bar{\rho}$ is the mean comoving matter density of the universe. |
In a similar way. adopting the Lacey&Cole(1993) formalism. we can write the merger rate of the HII regions as: where dοD)f£dimsdt is the probability per unit time that a given halo of mass m2, merges with a halo of mass mj. | In a similar way, adopting the \citet{lacey1993} formalism, we can write the merger rate of the HII regions as: where ${\rm d}^{2} p(m_{1},m_{T},t)/{\rm d} m_{2}{\rm d} t$ is the probability per unit time that a given halo of mass $m_{1}$ merges with a halo of mass $m_{2}=m_{T}-m_{1}$ . |
From equation (8}). it is possible to define the merger kernel that represents the rate at which each region of mass ni, merges with a region of mass m». | From equation \ref{eq:3c}) ), it is possible to define the merger kernel that represents the rate at which each region of mass $m_{1}$ merges with a region of mass $m_{2}$. |
Since this quantity suffers from some limitations because the asymmetry in its arguments becomes important for large masses. then the useof (umims)—12Um).mo)|Qn».my)] is preferred for estimating the merger rate of the bubbles. | Since this quantity suffers from some limitations because the asymmetry in its arguments becomes important for large masses, then the useof $Q_{sym}(m_{1},m_{2})\equiv
1/2[Q(m_{1},m_{2})+Q(m_{2},m_{1})]$ is preferred for estimating the merger rate of the bubbles. |
This allows us to detine the fractional volume accretion for a bubble of mass 2, that merges with a mass maj: Finally. we recall that the global ionized fraction can be calculated as c;ςμαCz). where foc. is the global collapsed volume fraction. | This allows us to define the fractional volume accretion for a bubble of mass $m_{1}$ that merges with a mass $m_{1}$: Finally, we recall that the global ionized fraction can be calculated as $\bar{x}_{i}=\zeta f_{\rm coll,g}(z)$, where $f_{\rm coll,g}$ is the global collapsed volume fraction. |
Up to now. the recombination limit has been neglected. | Up to now, the recombination limit has been neglected. |
As a bubble grows. the photons propagate more deeply into the neutral IGM. and both the clumpiness and the recombination rate of the ionized gas increase. | As a bubble grows, the photons propagate more deeply into the neutral IGM, and both the clumpiness and the recombination rate of the ionized gas increase. |
The IGM distribution and its ionization state can be described using the analytic model of Miralda-Escudéetal.(2000) (MHROO). | The IGM distribution and its ionization state can be described using the analytic model of \citet{miralda2000}
(MHR00). |
Analysing numerical simulations at 2<4. they found an analytic expression for the volume-weighted distribution of the gus density: where A—p/p. oy is the rms. | Analysing numerical simulations at $z < 4$, they found an analytic expression for the volume-weighted distribution of the gas density: where $\Delta\equiv \rho/\bar{\rho}$, $\delta_{0}$ is the r.m.s. |
of density fluctuations smoothed on the Jeans mass at fixed z. so dyx(1|2)Iiis and Cy represent normalization constants and ;? can be set equal to 2.5 as predicted for isothermal spheres. | of density fluctuations smoothed on the Jeans mass at fixed $z$, so $\delta_{0}\propto (1+z)^{-1}$; $A_{0}$ and $C_{0}$ represent normalization constants and $\beta$ can be set equal to 2.5 as predicted for isothermal spheres. |
The ionization state of the IGM is determined by a density threshold A; such that the gas with A«A; is totally ionized and the gas with A7A; is neutral. | The ionization state of the IGM is determined by a density threshold $\Delta_{i}$ such that the gas with $\Delta < \Delta_{i}$ is totally ionized and the gas with $\Delta >
\Delta_{i}$ is neutral. |
Under this assumption. the recombination rate can be written as where (' represents the clumping factor and 21, is the recombination rate per hydrogen atom in gas at the mean density. | Under this assumption, the recombination rate can be written as where $C$ represents the clumping factor and $A_{u}$ is the recombination rate per hydrogen atom in gas at the mean density. |
In the FOS model. 4, is assumed consistently with the A-case of the MHROO model (seealsoMiralda-Escudé2003): 21,xαι]. where a4(101AN)=410 em?s. +. | In the F05 model, $A_{u}$ is assumed consistently with the A-case of the MHR00 model \citep[see also][]{miralda2003}: $A_{u}\propto
\alpha_{A}(T)$ , where $\alpha_{A}(10^{4} K)=4\times 10^{-13}$ $^{3}$ $^{-1}$. |
The MHROO model also provides a relationship between the mean free path A; of the photons and the ionized fraction of gas £(Ντ) namely: where Ay is a normalization constant such that λος)=60 kms ασ | The MHR00 model also provides a relationship between the mean free path $\lambda_{i}$ of the photons and the ionized fraction of gas $F_{V}(\Delta_{i})$, namely: where $\lambda_{0}$ is a normalization constant such that $\lambda_{0}H(z)=60$ km $^{-1}$ at $z < 4$. |
In the following. we assume that the mean free path derived in the MHROO model could be used also in the quintessence models. since the properties of this function should reflect the gas properties at the Jeans scale. which is much smaller than the scales we are interested in. | In the following, we assume that the mean free path derived in the MHR00 model could be used also in the quintessence models, since the properties of this function should reflect the gas properties at the Jeans scale, which is much smaller than the scales we are interested in. |
However. this approximation deserves further investigation with suitable hydrodynamical simulations. | However, this approximation deserves further investigation with suitable hydrodynamical simulations. |
To consider the recombination process it is necessary to relate he recombination rate to the smoothed matter overdensity. | To consider the recombination process it is necessary to relate the recombination rate to the smoothed matter overdensity. |
In doing his. it must be remarked that the main effect of an inhomogeneous gas distribution is an increasing gas clumpiness and subsequently an increasing HII recombination rate. | In doing this, it must be remarked that the main effect of an inhomogeneous gas distribution is an increasing gas clumpiness and subsequently an increasing HII recombination rate. |
As a consequence. 21,x(1| 0) | As a consequence, $A_{u}\propto(1+\delta)$ . |
When a bubble grows the ionizing photons are able o reach its edge. then the threshold must satisfy the condition A;GN;)=B that sets A;. | When a bubble grows the ionizing photons are able to reach its edge, then the threshold must satisfy the condition $\lambda_{i}(\Delta_{i}) \ge R$ that sets $\Delta_{i}$. |
However. at the same time. the inner ligh gas clumpiness causes an increase of the recombination rate and the photons can be absorbed inside the bubble before reaching he edge. | However, at the same time, the inner high gas clumpiness causes an increase of the recombination rate and the photons can be absorbed inside the bubble before reaching the edge. |
Then. for a growing region. the ionization rate has to be arger than the recombination rate at every time: where C'(/?) is computed as in equation (12)) for /?= A;. | Then, for a growing region, the ionization rate has to be larger than the recombination rate at every time: where $C(R)$ is computed as in equation \ref{eq:5c}) ) for $R=\lambda_{i}$ . |
The recombination barrier is obtained by searching for the minimun ὁ in the Lagrangian space that satisfies equation C149) at each given mass, | The recombination barrier is obtained by searching for the minimun $\delta$ in the Lagrangian space that satisfies equation \ref{eq:17c}) ) at each given mass. |
The recombination process affects the bubbles geometry. | The recombination process affects the bubbles geometry. |
When the ionizing photons are totally absorbed bythe inner recombination. the HIT region stops growing and reaches a | When the ionizing photons are totally absorbed bythe inner recombination, the HII region stops growing and reaches a |
2)) 111. (????).. citealpmarks09) | \citealp{schneider06}) \citealp{albrechtetal06, albrechtetal09,peacocketal06}, \citep{heymansetal06step,masseyetal07step,bridleetal10,kitchingetal10}. \\citealp{marks09}) |
). νο", u u (6,44 {0 P<1/(20,,4:). 1/(20,,44) rate Is sampled)). | $\propto { e}^{2\pi {\rm i}{\bf u}\cdot{\bf r}}$ ${\bf u}$ ${\bf u}$ $u_{\rm max}$ $P$ $P<1/(2u_{\rm max})$ $1/(2u_{\rm max})$ rate is ). |
Since it is possible to reconstruct the entire original image from oversampled data. operations such as interpolation/regridding. rotation. and translation can be carried out with no pixelization artifacts. | Since it is possible to reconstruct the entire original image from oversampled data, operations such as interpolation/regridding, rotation, and translation can be carried out with no pixelization artifacts. |
This makes oversampled data the preferred input for most precision image analysis applications. including weak lensing. | This makes oversampled data the preferred input for most precision image analysis applications, including weak lensing. |
The ideal location for weak lensing observations 1s a space-based telescope. where one is free from the blurring effects of the Earth's atmosphere and can achieve a level of stability of the opties and hence the PSF that is impossible from the ground. | The ideal location for weak lensing observations is a space-based telescope, where one is free from the blurring effects of the Earth's atmosphere and can achieve a level of stability of the optics and hence the PSF that is impossible from the ground. |
Weak lensing is thus a key project for proposed imaging missions such as the(WFIRST:: ?:; the reference design is based on the concept: ?)) and (?).. | Weak lensing is thus a key project for proposed space-based imaging missions such as the: \citealp{blandfordetal10}; the reference design is based on the concept: \citealt{gehrels10}) ) and \citep{refregieretal10}. |
However. in both cases. practical design considerations prohibit oversampling at the native pixel scale of the system. | However, in both cases, practical design considerations prohibit oversampling at the native pixel scale of the system. |
The optics of a space telescope deliver a PSF that preserves Fourier modes out to. (duasD/A where D is the outer diameter of the primary mirror and À is the wavelength of observation: the high spatial frequencies may be suppressed by e.g. charge diffusion. but in most cases (ax is still large. | The optics of a space telescope deliver a PSF that preserves Fourier modes out to $u_{\rm max}=D/\lambda$ where $D$ is the outer diameter of the primary mirror and $\lambda$ is the wavelength of observation; the high spatial frequencies may be suppressed by e.g. charge diffusion, but in most cases $u_{\rm max}$ is still large. |
Indeed. preserving the high spatial frequency components of the image is a major reason to choose a platform. | Indeed, preserving the high spatial frequency components of the image is a major reason to choose a space-based platform. |
If one is to oversample the image at the native pixel scale. then. one is forced to choose very small pixels. | If one is to oversample the image at the native pixel scale, then, one is forced to choose very small pixels. |
However. there are competing considerations that drive one to larger pixels. including (1) the desire for large field of view within engineering or cost constraints on the number of detectors: and (1) the high readnoise of near-infrareddetectors. whichresults in increased photometric errors as light froman object is spread over more pixels. | However, there are competing considerations that drive one to larger pixels, including (i) the desire for large field of view within engineering or cost constraints on the number of detectors; and (ii) the high readnoise of near-infrareddetectors, whichresults in increased photometric errors as light froman object is spread over more pixels. |
For these reasons. both | For these reasons, both |
For thesake of comparison we also present the expression for the photon emission rate of anequilibrated. hotQCD plasma. at zero chemical potential. with the LPAI effect. fully included. | FormainBodyEnd7325 mainBodyStart7326the themainBodyEnd7326 mainBodyStart7327sake sakemainBodyEnd7327 mainBodyStart7328of ofmainBodyEnd7328 mainBodyStart7329comparison comparisonmainBodyEnd7329 mainBodyStart7330we wemainBodyEnd7330 mainBodyStart7331also alsomainBodyEnd7331 mainBodyStart7332present presentmainBodyEnd7332 mainBodyStart7333the themainBodyEnd7333 mainBodyStart7334expression expressionmainBodyEnd7334 mainBodyStart7335for formainBodyEnd7335 mainBodyStart7336the themainBodyEnd7336 mainBodyStart7337photon photonmainBodyEnd7337
mainBodyStart7338emission emissionmainBodyEnd7338 mainBodyStart7339rate rate\tikzmark{mainBodyEnd7339} \tikzmark{mainBodyStart7340}of ofmainBodyEnd7340 mainBodyStart7341an anmainBodyEnd7341 mainBodyStart7342equilibrated, equilibrated,mainBodyEnd7342 mainBodyStart7343hot hotmainBodyEnd7343 mainBodyStart7344QCD QCDmainBodyEnd7344 mainBodyStart7345plasma, plasma,mainBodyEnd7345 mainBodyStart7346at atmainBodyEnd7346 mainBodyStart7347zero zeromainBodyEnd7347 mainBodyStart7348chemical chemicalmainBodyEnd7348
mainBodyStart7349potential, potential,mainBodyEnd7349 mainBodyStart7350with withmainBodyEnd7350 mainBodyStart7351the themainBodyEnd7351 mainBodyStart7352LPM LPMmainBodyEnd7352 mainBodyStart7353effect effectmainBodyEnd7353 mainBodyStart7354fully fully\tikzmark{mainBodyEnd7354} \tikzmark{mainBodyStart7355}included. |
Thespontaneous emissionrate of (2xydl,/d’k photons with a given momentum hk can berepresented. fortwo flavor QCD. as (Arnold et al. | included.mainBodyEnd7355 mainBodyStart7356The ThemainBodyEnd7356 mainBodyStart7357spontaneous spontaneousmainBodyEnd7357 mainBodyStart7358emission emissionmainBodyEnd7358 mainBodyStart7359rate ratemainBodyEnd7359
mainInlineStart7360( 2π) ^3dI_γ/d^3kmainInlineEnd7360 mainBodyStart7361of $\left( 2\pi \right) ^{3}dI_{\gamma }/d^{3}k$ ofmainBodyEnd7361 mainBodyStart7362photons photonsmainBodyEnd7362 mainBodyStart7363with withmainBodyEnd7363 mainBodyStart7364a amainBodyEnd7364 mainBodyStart7365given givenmainBodyEnd7365
mainBodyStart7366momentum momentum\tikzmark{mainBodyEnd7366} \tikzmark{mainInlineStart7367}$\vec{k}$\tikzmark{mainInlineEnd7367} \tikzmark{mainBodyStart7368}can $\vec{k}$ canmainBodyEnd7368 mainBodyStart7369be bemainBodyEnd7369 mainBodyStart7370represented, represented,mainBodyEnd7370 mainBodyStart7371for formainBodyEnd7371 mainBodyStart7372two twomainBodyEnd7372 mainBodyStart7373flavor flavormainBodyEnd7373 mainBodyStart7374QCD, QCD,mainBodyEnd7374 mainBodyStart7375as asmainBodyEnd7375 mainBodyStart7376(Arnold (ArnoldmainBodyEnd7376 mainBodyStart7377et etmainBodyEnd7377 mainBodyStart7378al. |
2001. Arnold et al. | al.mainBodyEnd7378
mainBodyStart73792001, 2001,mainBodyEnd7379 mainBodyStart7380Arnold ArnoldmainBodyEnd7380 mainBodyStart7381et etmainBodyEnd7381 mainBodyStart7382al. |
2002) whererp (w) is theFermi-Dirac distributionfunction. n;(ee)—lexp(w/T)41 bon is the thermal quark mass. givenby m2,=40.17 /3.and wilh C5.»Cr)z0.04Lr.|—0.3615+1.01exp(—1.35) andSltNp/616.2HezinarkimainBodyStartΤΙΟΟ CusCr)+ConninGr)= [0.548In(12.284L/ec)/c?40.1830/1oefΙΟ. | al.mainBodyEnd7382 mainBodyStart73832002) 2002)\tikzmark{mainBodyEnd7383}
\begin{equation}
\left( 2\pi \right) ^{3}\frac{dI_{\gamma }}{d^{3}k}=\frac{40\pi \alpha
\alpha _{s}}{9}T^{2}\frac{n_{f}\left( \omega \right) }{\omega }\left[ \ln
\frac{T}{m_{\infty }}+C_{tot}\left( \frac{\omega }{T}\right) \right] ,
\label{ar1}
\end{equation}
\tikzmark{mainBodyStart7384}where wheremainBodyEnd7384 mainInlineStart7385n_f( ω)mainInlineEnd7385 mainBodyStart7386is $n_{f}\left( \omega \right) $ ismainBodyEnd7386 mainBodyStart7387the themainBodyEnd7387 mainBodyStart7388Fermi-Dirac Fermi-DiracmainBodyEnd7388 mainBodyStart7389distribution distributionmainBodyEnd7389
mainBodyStart7390function, function,mainBodyEnd7390 mainInlineStart7391n_f( ω) =[ exp( ω /T) +1
] ^-1mainInlineEnd7391mainBodyStart7392, }$,\tikzmark{mainBodyEnd7392} \tikzmark{mainInlineStart7393}$m_{\infty }$\tikzmark{mainInlineEnd7393} \tikzmark{mainBodyStart7394}is $m_{\infty }$ ismainBodyEnd7394 mainBodyStart7395the themainBodyEnd7395 mainBodyStart7396thermal thermalmainBodyEnd7396 mainBodyStart7397quark quarkmainBodyEnd7397 mainBodyStart7398mass, mass,mainBodyEnd7398 mainBodyStart7399given givenmainBodyEnd7399 mainBodyStart7400by bymainBodyEnd7400 mainInlineStart7401m_∞^2=4πα _sT^2/3mainInlineEnd7401mainBodyStart7402, $m_{\infty
}^{2}=4\pi \alpha _{s}T^{2}/3$ ,mainBodyEnd7402 mainBodyStart7403and and\tikzmark{mainBodyEnd7403}
\begin{equation}
C_{tot}\left( \frac{\omega }{T}\right) \equiv \frac{1}{2}\ln \frac{2\omega }{%
T}+C_{2\leftrightarrow 2}\left( \frac{\omega }{T}\right) +C_{brem}\left(
\frac{\omega }{T}\right) +C_{annih}\left( \frac{\omega }{T}\right) ,
\label{ar2}
\end{equation}
\tikzmark{mainBodyStart7404}with withmainBodyEnd7404 mainInlineStart7405C_2↔ 2( x) ≈
0.041x^-1-0.3615+1.01exp (-1.35x)mainInlineEnd7405 mainBodyStart7406and $C_{2\leftrightarrow 2}\left( x\right) \approx
0.041x^{-1}-0.3615+1.01\exp (-1.35x)$ and\tikzmark{mainBodyEnd7406} \tikzmark{mainInlineStart7407}$C_{brem}\left( x\right)
+C_{annih}\left( x\right) =\sqrt{1+N_{f}/6}$\tikzmark{mainInlineEnd7407} \tikzmark{mainInlineStart7408}$\left[ 0.548\ln %anisia
(12.28+1/x)/x^{3/2}+0.133x/\sqrt{1+x/16.27}\tikzmark{mainInlineEnd7408}\\tikzmark{mainBodyStart7409}right] $C_{brem}\left( x\right)
+C_{annih}\left( x\right) =\sqrt{1+N_{f}/6}$ $\left[ 0.548\ln %anisia
(12.28+1/x)/x^{3/2}+0.133x/\sqrt{1+x/16.27}. |
For w/T<2.5. bremsstrahlung becomes the most important process. while [or 10. pair annihilation dominates. | For $\omega /T<2.5$, bremsstrahlung becomes the most important process, while for $\omega /T>10$ , pair annihilation dominates. |
The LPAI effect suppresses both. bremsstralilung and pair annihilation processes. butthe suppression is not severe (35% or less). except for photons with w<27 or very hard pair annihilation. | The LPM effect suppresses both bremsstrahlung and pair annihilation processes, butthe suppression is not severe $35\%$ or less), except for photons with $\omega <2T$ or very hard pair annihilation. |
In the limit of small temperatures. 7—0 and.— ox. | In the limit of small temperatures, $T\rightarrow 0$ and $%
x\rightarrow \infty . |
Hence οιο(0)——0.3615 and CremGr)+CuniCr)—0.133(e/T) | Hence $C_{2\leftrightarrow 2}\left( x\right)
\rightarrow -0.3615$ and $C_{brem}\left( x\right) +C_{annih}\left( x\right)
\rightarrow 0.133\left( \omega /T\right) ^{1/2}$. |
Dv neglecting the logarithmically divergent terms. the integration over all possible ranges of Irequencies in Eq. (52) | By neglecting the logarithmically divergent terms, the integration over all possible ranges of frequencies in Eq. ) |
) gives where UAD!eBraou[3/1INy/6(4—V2)zxπε(5/2)/4—0.3615/3) /9. with €(s) is the Riemann zeta function £(s)=$7554&. | gives where $\chi _{Br}^{(QCD)}\approx 5\pi \alpha \alpha _{s}\left[ 3\sqrt{%
1+N_{f}/6}\left( 4-\sqrt{2}\right) \pi ^{-3/2}\xi \left( 5/2\right)
/4-0.3615/3\right] / 9, with $\xi \left( s\right) $ is the Riemann zeta function $\xi \left( s\right) =\sum_{k=1}^{\infty }k^{-s}$. |
Therefore the perturbative QCD approach eives. in the low temperature limit. (he same temperature dependence of the bremsstrahlune spectrum as in Eq. (29). | Therefore the perturbative QCD approach gives, in the low temperature limit, the same temperature dependence of the bremsstrahlung spectrum as in Eq. ). |
However. we must point out that Eqs.(52)) and 3)) have been derived for a temperature of (he quark-eluon plasma higher (han 250 MeV. since the temperature ol the fireball formed in heavy ion collisions is of the order of 450 MeV. (IRenk 2003). | However, we must point out that ) and ) have been derived for a temperature of the quark-gluon plasma higher than $250$ MeV, since the temperature of the fireball formed in heavy ion collisions is of the order of $450$ MeV (Renk 2003). |
Recently. it has been argued that (he strange quark matter in the color-EHavor locked(CEL) phase of QCD. which occurs for large gaps (~100AeV). is rigorously electrically neutral. despite the unequal quark masses. and even in the presence ofelectron chemical potential ). | Recently, it has been argued that the strange quark matter in the color-flavor locked(CFL) phase of QCD, which occurs for large gaps $(\Delta
\sim 100MeV)$, is rigorously electrically neutral, despite the unequal quark masses, and even in the presence ofelectron chemical potential . |
. llowever. pointed outthat for sulliciently laree m, the low density reeime is rather expected to be in the 2-color-[lavor Superconductor” phase in which only à | However, pointed outthat for sufficiently large $m_{s}$ the low density regime is rather expected to be in the ”2-color-flavor Superconductor” phase in which only $u$ |
in plate scale of50%. | in plate scale of. |
. To accomplish this we developed an algorithm that finds the largest possible number of pairs between the active and inactive galaxies given the above criteria. | To accomplish this we developed an algorithm that finds the largest possible number of pairs between the active and inactive galaxies given the above criteria. |
This vielded 26 earlv-tvpe and 31 1ate-tvpe pairs. | This yielded 26 early-type and 31 late-type pairs. |
These 57 pairs comprises our main sample and we shall herealter refer to it as the "matched sample’. | These 57 pairs comprises our main sample and we shall hereafter refer to it as the “matched sample”. |
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