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We finally conclude and. cliscuss our results in section 6.. | We finally conclude and discuss our results in section \ref{sect:concl}. |
Given a fulbsky map of the temperature fluctuations (n) of some signal. it can be decomposed. in the spherical harmonic basis with the usual orthonormal spherical harmonics Y, Observational data is pixelised. so that the integral is replaced by a sum over pixels. | Given a full-sky map of the temperature fluctuations $\Delta
T(\mathbf{n})$ of some signal, it can be decomposed in the spherical harmonic basis with the usual orthonormal spherical harmonics $Y_{\ell m}$ Observational data is pixelised, so that the integral is replaced by a sum over pixels. |
We will assume that the solid angle of a pixel. Quis. is à constant. which is for example the case for the pixelisation scheme that we will adopt for the numerical caleulations. | We will assume that the solid angle of a pixel, $\Omega_{\mathrm{pix}}$, is a constant, which is for example the case for the pixelisation scheme that we will adopt for the numerical calculations. |
In this case we have that This cisereteness ellect will be important e.g. in section Lrm | In this case we have that This discreteness effect will be important e.g. in section \ref{sect:shot}. |
In order to compute the angular bispectrum. which is the harmonic transform of the 3-point correlation function. we will resort to scale-maps as defined by 2? and also used by ? and ?.. where 75 is the Legendre polynomial of order f. | In order to compute the angular bispectrum, which is the harmonic transform of the 3-point correlation function, we will resort to scale-maps as defined by \cite{Spergel1999} and also used by \cite{Aghanim:2003fs} and \cite{DeTroia:2003tq}, , where $P_{\ell}$ is the Legendre polynomial of order $\ell$. |
ο optimal bispectrum estimator is then (?):: or it can be written in the form: where the expression in brackets represents the Wigner 3j svmbols. | The optimal bispectrum estimator is then \citep{Spergel1999}: or it can be written in the form: where the expression in brackets represents the Wigner $3j$ symbols. |
Equation (5)) is computationally expensive when implemented at. high { due to the aree number of Wiener svimbols to calculate. | Equation \ref{eq:biseq}) ) is computationally expensive when implemented at high $\ell$ due to the large number of Wigner symbols to calculate. |
Equation (4)) still requires a few cpu-davs for a full computation at a Planck-like resolution. Nside-1024 - 2048. | Equation \ref{eq:estimbisp}) ) still requires a few cpu-days for a full computation at a Planck-like resolution, Nside=1024 - 2048. |
Binning the multipoles in f. às ?..has the advantage of speeding up the computations and smoothing out the variations clue to cosmic variance. | Binning the multipoles in $\ell$, as \cite{Bucher2010},has the advantage of speeding up the computations and smoothing out the variations due to cosmic variance. |
For a given triangle in harmonic space (£4.{οι(ο). the number of independent configurations on the sphere Is: When multipoles are binned in bins of width Af the expression for the scale-maps (eq. 3)) | For a given triangle in harmonic space $(\ell_1,\ell_2,\ell_3)$ the number of independent configurations on the sphere is: When multipoles are binned in bins of width $\Delta\ell$ the expression for the scale-maps (Eq. \ref{scalemapfullsky}) ) |
becomes: and oa binned bispectrum estimator identically weighting triangles is given by: where One can easily check that the obtained binned bispectrum estimator is unbiased for a constant bispectrum and that the bias can be neglected as long as the bispectrum does not vary significantly within a bin Af. | becomes: and a binned bispectrum estimator identically weighting triangles is given by: where One can easily check that the obtained binned bispectrum estimator is unbiased for a constant bispectrum and that the bias can be neglected as long as the bispectrum does not vary significantly within a bin $\Delta\ell$. |
In the following. we have chosen fais.=2048 and a bin width Af=64 for simplicity and computational speed while retaining enough information on the scale dependence (?).. | In the following, we have chosen $\ell_\mathrm{max}=2048$ and a bin width $\Delta\ell=64$ for simplicity and computational speed while retaining enough information on the scale dependence \citep{Bucher2010}. |
The most studied: and constrained form of primordial non-Gaussianity is the local ansatz. whose amplituce is parametrised by a non-linear coupling constant fine: where Gr) is the Dardeen. potential and. @e;(r) is a Gaussian field. | The most studied and constrained form of primordial non-Gaussianity is the local ansatz, whose amplitude is parametrised by a non-linear coupling constant $f_\mathrm{NL}$ : where $\Phi(x)$ is the Bardeen potential and $\Phi_G(x)$ is a Gaussian field. |
Vhis form of NG vields the following CAIBangular bispectrum (?):: with | This form of NG yields the following CMBangular bispectrum \citep{Komatsu:2001rj}: : with |
detected below =3 CeV. ouly au upper lait on the source fux cau be derived in this euergv baud. | detected below $\simeq 3$ GeV, only an upper limit on the source flux can be derived in this energy band. |
As is discussed above. the source spectrum in the :5H300 CeV energy band cau have two contiübutions: the direct suenal from the primary source and emission from the electromagnetic cascade developing in the ICAL | As is discussed above, the source spectrum in the 3-300 GeV energy band can have two contributions: the direct signal from the primary source and emission from the electromagnetic cascade developing in the IGM. |
Tt is not clear a-priori if the measured spectral slope. consistent with P=1.5. characterizes the intrinsic source spectiuni. the spectrum of the cascade conrponeut. or Comprises a sununued spectrum of the two (similar in strength) contributions. | It is not clear a-priori if the measured spectral slope, consistent with $\Gamma\simeq 1.5$, characterizes the intrinsic source spectrum, the spectrum of the cascade component, or comprises a summed spectrum of the two (similar in strength) contributions. |
For instance. a spectral index harder then 1.5. as found iu the analysis of Stecker&Sully(2008) in the TeV baud. would be iudicative of a GeV spectu which results from the sum of both the iutriusic spectruui and that of the cascade. | For instance, a spectral index harder then 1.5, as found in the analysis of \cite{stecker_1ES0229} in the TeV band, would be indicative of a GeV spectrum which results from the sum of both the intrinsic spectrum and that of the cascade. |
Different possibilities for the dominance of oue of the two conponeuts in the spectrum are illustrated in the two panels of Fig. 1.. | Different possibilities for the dominance of one of the two components in the spectrum are illustrated in the two panels of Fig. \ref{soft}. |
In both models the normalization of the iutrimsic spectrum is cliosen to fit the IIESS measurements in the TeV baud. | In both models the normalization of the intrinsic spectrum is chosen to fit the HESS measurements in the TeV band. |
We also asstuue that the intrinsic source spectrum has a lieh-οποίον cut-off at Z4,=5 TeV. As it was shown by Tavloretal.(2011).. this choice minimizes the strength of the cascade contribution iu the Fermi/LAT energy. baud. | We also assume that the intrinsic source spectrum has a high-energy cut-off at $E_{cut}=5$ TeV. As it was shown by \cite{TaylorEGMF}, this choice minimizes the strength of the cascade contribution in the Fermi/LAT energy band. |
Iu the upper panel the main contribution to the X Ce source flux is elven by the direct flux of the primary source. shown by the thin solid line. | In the upper panel the main contribution to the 3-300 GeV source flux is given by the direct flux of the primary source, shown by the thin solid line. |
This is possible oulv if the cascade component is suppressed by the influence of a strong enough. ECATF. | This is possible only if the cascade component is suppressed by the influence of a strong enough EGMF. |
If the EGAIF is neelieible. the fux of the direct aud cascade emission (thick solid line) will largely dominate over the direct enüssioun. | If the EGMF is negligible, the flux of the direct and cascade emission (thick solid line) will largely dominate over the direct emission. |
οποιος ECGME (210IT (D) is needed to sufficieutlv suppress the cascade ciissiou down to the level of the error bars of the LAT measurements in the 3-300 GeV range. | Strong EGMF $\ge 10^{-17}$ G) is needed to sufficiently suppress the cascade emission down to the level of the error bars of the LAT measurements in the 3-300 GeV range. |
If the EGALF is weaker than ~3«10| G. the cascade cluission provides the dominant contribution o the source spectrum. as is illustrated in the lower xucel of Fie. l.. | If the EGMF is weaker than $\sim 3\times 10^{-17}$ G, the cascade emission provides the dominant contribution to the source spectrum, as is illustrated in the lower panel of Fig. \ref{soft}. |
The only possibility to make the LAT measurement cousisteut with observatious is fo assmuc hat the iutriusic spectrum of the primary source las a slope harder than P—1.5. | The only possibility to make the LAT measurement consistent with observations is to assume that the intrinsic spectrum of the primary source has a slope harder than $\Gamma=1.5$. |
The hardness of the intrinsic source spectrum depends on the ECALIF streusth. | The hardness of the intrinsic source spectrum depends on the EGMF strength. |
For the uwtieular exanuple shown iu the lower pauel of Fie. 1.. | For the particular example shown in the lower panel of Fig. \ref{soft}, |
ho assuuption that the EGME streneth B«3«10.1 G iuposes a constraint on the iutrinsic source spoectruui Dx12. | the assumption that the EGMF strength $B\le 3\times 10^{-17}$ G imposes a constraint on the intrinsic source spectrum $\Gamma\le 1.2$. |
In fact. if the iutrimsic source spectrin is even rarder. the intrinsic source flux οσοποια to the 3-300 GeV baud flux becomes neeheibleη aud the fux is colpletely dominated by the cascade emission. | In fact, if the intrinsic source spectrum is even harder, the intrinsic source flux contribution to the 3-300 GeV band flux becomes negligible and the flux is completely dominated by the cascade emission. |
The overall normalization of the cascade cuissio is determined bv the deusitv of the EBL. | The overall normalization of the cascade emission is determined by the density of the EBL. |
An increase of the EBL deusity leads to the stronger absorption of αμαΤον 5. rays and. consequently. το stronger cascade eniüsson. | An increase of the EBL density leads to the stronger absorption of multi-TeV $\gamma$ rays and, consequently, to stronger cascade emission. |
To the contrary. reducing the EBL normalization down to the level of the lower bouud frou the direct source counts opens up the possibility of a weaker EGME. down to ~6«1048 G. The effect of changing the EBL normalization is illustrated in Fig. 2.. | To the contrary, reducing the EBL normalization down to the level of the lower bound from the direct source counts opens up the possibility of a weaker EGMF, down to $\sim 6 \times 10^{-18}$ G. The effect of changing the EBL normalization is illustrated in Fig. \ref{EBL_scaling}. |
Tn this figure a spectral slope of P—1.5 and ECAIF of LO19 C have been adopted. aud three different and in terms of the EBL level reported by Franceschinietal. (200833) levels of EBL have been usec. | In this figure a spectral slope of $\Gamma=1.5$ and EGMF of $10^{-16}$ G have been adopted, and three different, and in terms of the EBL level reported by \cite{Franceschini_EBL}) ) levels of EBL have been used. |
The masimal normalization of the EBL which can stil be consistent with the data depends on the streugth of the EGAIF. | The maximal normalization of the EBL which can still be consistent with the data depends on the strength of the EGMF. |
Too strong au EBL can result iu à large over-prediction of the streugth of the cascade emission. even after taking iuto account the suppression ofthis cussion by the EGAIF effects. | Too strong an EBL can result in a large over-prediction of the strength of the cascade emission, even after taking into account the suppression of this emission by the EGMF effects. |
Thus. the upper bound ou the EBL derivable from the oobservatious of LES 0229|200 is ECGME-depeudoenut. | Thus, the upper bound on the EBL derivable from the observations of 1ES 0229+200 is EGMF-dependent. |
Tn order to fud this bound. we compute the allowed ranges of the EBL normalization for a set of ECGME streugths and intrinsic spectrum spectral indices. | In order to find this bound, we compute the allowed ranges of the EBL normalization for a set of EGMF strengths and intrinsic spectrum spectral indices. |
The range of the ECAIF strengths scanned over lav in the range 341019 G tolO1! G. while the spectral indices were varied within the range from 1.5 to 0. | The range of the EGMF strengths scanned over lay in the range $3 \times 10^{-19}$ G to $10^{-14}$ G, while the spectral indices were varied within the range from 1.5 to 0. |
We then fud the best-fit set of values in this D parameter space. aud chose an appropriate confidence reeion. | We then find the best-fit set of values in this $\Gamma$ parameter space, and chose an appropriate confidence region. |
The projection of this region outo the plaue is shown iu Fie. | The projection of this region onto the plane is shown in Fig. |
3 and comprises the not hatched part of the plot. | \ref{EBL_exclusion} and comprises the not hatched part of the plot. |
The hatched part thus represcuts the EBL-dependent bouud on the EGAIF (or. | The hatched part thus represents the EBL-dependent bound on the EGMF (or, |
simultaneous tasks: it classifies objects into stars. galaxies. QSOs. and white dwarfs based on their colours. and for galaxies and QSOs it also estimates redshifts. | simultaneous tasks: it classifies objects into stars, galaxies, QSOs, and white dwarfs based on their colours, and for galaxies and QSOs it also estimates redshifts. |
Here. we used a setup forcing the galaxy interpretation in order to better compare the results to the other codes which assume a priori that all objects are galaxies. | Here, we used a setup forcing the galaxy interpretation in order to better compare the results to the other codes which assume a priori that all objects are galaxies. |
The code is currently not publicly available. | The code is currently not publicly available. |
For all template details we refer the reader to 2).. | For all template details we refer the reader to \cite{2004A&A...421..913W}. |
No explicit redshift-dependent prior is used. however. for the shallow purely optical datasets of COMBO-17 and GaBoDS. only galaxy redshifts up to 1.4 are considered. while for the ΕΡΕ dataset the whole range from z=0 to =7 is allowed. | No explicit redshift-dependent prior is used, however, for the shallow purely optical datasets of COMBO-17 and GaBoDS, only galaxy redshifts up to 1.4 are considered, while for the FDF dataset the whole range from $z=0$ to $z=7$ is allowed. |
The code determines the redshift probability. distribution p(s) and reports the mean of this distribution as a Minimum-Error-Variance (MEV) redshift and its RMS as an error estimate. | The code determines the redshift probability distribution $p(z)$ and reports the mean of this distribution as a Minimum-Error-Variance (MEV) redshift and its RMS as an error estimate. |
The code also tests the shape of p(z) for bimodality. and determines redshift and error from the mode with the higher integral probability (foralldetailssee?).. | The code also tests the shape of $p(z)$ for bimodality, and determines redshift and error from the mode with the higher integral probability \citep[for all details
see][]{2001A&A...365..660W}. |
BPZ (Bayesian photo-z’s) is a publiccode*.. which implements the method deseribed in ?).. | BPZ (Bayesian $z$ 's) is a public, which implements the method described in \cite{2000ApJ...536..571B}. |
It is an SED fitting method combined with a redshift/type prior. pCz.T|ji. which depends on the observed magnitude of the galaxies. | It is an SED fitting method combined with a redshift/type prior, $p(z,T|m)$, which depends on the observed magnitude of the galaxies. |
It originally used a set of 6 templates formed by the 4 CWW set and two starburst templates from ?) which were shown to significantly improve the photo-z estimation. | It originally used a set of 6 templates formed by the 4 CWW set and two starburst templates from \cite{1996ApJ...467...38K} which were shown to significantly improve the $z$ estimation. |
It should be stressed that the extrapolation to the UV and IR of the optical CWW templates used by is quite different from the one used byHyperz. | It should be stressed that the extrapolation to the UV and IR of the optical CWW templates used by is quite different from the one used by. |
. The template library has been calibrated using a set of HST and other ground based observations as deseribed in ?).. | The template library has been calibrated using a set of HST and other ground based observations as described in \cite{2004ApJS..150....1B}. |
This template set has been shown to remarkably well represent the colours of galaxies in HST observations. to the point of being able to photometrically calibrate the NIC3 Hubble UDF observations with a 0.03 magnitude error as shown in ?).. | This template set has been shown to remarkably well represent the colours of galaxies in HST observations, to the point of being able to photometrically calibrate the NIC3 Hubble UDF observations with a 0.03 magnitude error as shown in \cite{2006AJ....132..926C}. |
In the latter paper two additional. very blue templates from the Bruzual Charlot library were introduced. so the current library contains 8 templates. | In the latter paper two additional, very blue templates from the Bruzual Charlot library were introduced, so the current library contains 8 templates. |
The redshift likelihood is calculated by i1 a similar way as by minimising the y of observed and predicted colours. | The redshift likelihood is calculated by in a similar way as by minimising the $\chi^2$ of observed and predicted colours. |
However. in contrast to no reddening is applied to the templates relying on the completeness of the given set. | However, in contrast to no reddening is applied to the templates relying on the completeness of the given set. |
After the calculation of the likelihood. Bayes theorem ts applied incorporating the prior probability. | After the calculation of the likelihood, Bayes theorem is applied incorporating the prior probability. |
The actual shape of this prior is dependent on template type and /-band magnitude and was derived from the observed redshift distributions of different galaxy types in the Hubble Deep Field. | The actual shape of this prior is dependent on template type and $I$ -band magnitude and was derived from the observed redshift distributions of different galaxy types in the Hubble Deep Field. |
By applying this prior the rate of outliers with catastrophically wrong zassignments can be reduced. | By applying this prior the rate of outliers with catastrophically wrong $z$ assignments can be reduced. |
For details on the procedure see 2). | For details on the procedure see \cite{2000ApJ...536..571B}. |
BPZ has been extensively used in the ACS GTO program. the GOODS and COSMOS surveys and others. | BPZ has been extensively used in the ACS GTO program, the GOODS and COSMOS surveys and others. |
The performance of one particular setup is characterised by some basic quantities which are described in the following. | The performance of one particular setup is characterised by some basic quantities which are described in the following. |
the dynamic range in refewn.plot or (also) increase the scatter. | the dynamic range in \\ref{ewn.plot} or (also) increase the scatter. |
Such studies will be possible with the full 3D-HST dataset. which will provide WFC3 and ACS spectroscopy and imaging of large samples of galaxies at ς>1. | Such studies will be possible with the full 3D-HST dataset, which will provide WFC3 and ACS spectroscopy and imaging of large samples of galaxies at $z>1$. |
Combined with deep imaging from the CANDELS project and the wide array of ancillary data in the survey fields. 3D-HST will provide a qualitatively new way of surveying the heyday of galaxy formation at |<2<3 | Combined with deep imaging from the CANDELS project and the wide array of ancillary data in the survey fields, 3D-HST will provide a qualitatively new way of surveying the heyday of galaxy formation at $1<z<3$ . |
resolution. the nucleus of 11239 at 1.6 Giz is resolved in two components separated by ~ 50 mas ( ~ 30 pe). with position angle of 40° (Fig. | resolution, the nucleus of 1239 at 1.6 GHz is resolved in two components separated by $\sim$ 50 mas ( $\sim$ 30 pc), with position angle of $^{\circ}$ (Fig. |
4cc). | \ref{m1239}c c). |
The lack of multi-frequency observations with similar resolution does not allow us to study the spectral index of these The lux density measured on the VLBA image at 1.6 Cll is 10.2 mJx. Le. only of the VLA flux density at. 1.6 CGllz. obtained. re-scaling the 1.4 Gllz VLA lux density with the spectral index computed between 1.4 and 4.8 ος (a = 0.6). | The lack of multi-frequency observations with similar resolution does not allow us to study the spectral index of these The flux density measured on the VLBA image at 1.6 GHz is 10.2 mJy, i.e. only of the VLA flux density at 1.6 GHz, obtained re-scaling the 1.4 GHz VLA flux density with the spectral index computed between 1.4 and 4.8 GHz $\alpha$ = 0.6). |
This indicates that almost of the [Lux density measured. with the VLA is missing in the VLBA Image, | This indicates that almost of the flux density measured with the VLA is missing in the VLBA image. |
The VLBA image at 1.6 111. with a resolution of ο 07.008 (Fig. S)). | The VLBA image at 1.6 GHz, with a resolution of $^{\prime\prime}$ $\times$ $^{\prime\prime}$ .008 (Fig. \ref{n3783}) ), |
is presented. for the first time. | is presented for the first time. |
In this 005.image. the nucleus is unresolved with a linear size < + pe. | In this image, the nucleus is unresolved with a linear size $<$ 4 pc. |
Phe total Hux density measured on the VLBA image is 4.6 my. that represents only a of the Dux density of the unresolved. component in VLA observations (Ungeretal. 1986). | The total flux density measured on the VLBA image is 4.6 mJy, that represents only a of the flux density of the unresolved component in VLA observations \citep{unger86}. |
. This indicates that the majority (7804) of the ας measured with the VLA is missing in the VLBA New VLA images at 4.8 and SA Cllz with resolution of 07.48. 0 37 and οστ 0" 20 respectively. are shown in Fie. | This indicates that the majority $\sim$ ) of the flux measured with the VLA is missing in the VLBA New VLA images at 4.8 and 8.4 GHz with resolution of $^{\prime\prime}$ $\times$ $^{\prime\prime}$ .37 and $^{\prime\prime}$ $\times$ $^{\prime\prime}$ .20 respectively, are shown in Fig. |
Saab. Phe source displavs an unresolved. central component with a diffuse wine-like emission. cxtencing mainlv to the north-west and cast part of the nucleus. | \ref{n5506}a a,b. The source displays an unresolved central component with a diffuse wing-like emission extending mainly to the north-west and east part of the nucleus. |
The high. dynamic range. namely the ratio between the »eak flux density and le noise level. of our images allows us to detect. also at δε Cillz the extended: low-surlace xightness halo (Figs. | The high dynamic range, namely the ratio between the peak flux density and $\sigma$ noise level, of our images allows us to detect also at 8.4 GHz the extended low-surface brightness halo (Figs. |
baa.b). | \ref{n5506}a a,b). |
This has a diameter of ~ ο τὸ (~ 350 pc) enshrouding the central features. | This has a diameter of $\sim$ $^{\prime\prime}$ .75 $\sim$ 350 pc) enshrouding the central features. |
The nucleus is unresolved in our VLA images. giving an upper imit of «07.08 («10 pe). | The nucleus is unresolved in our VLA images, giving an upper limit of $<$ $^{\prime\prime}$ .08 $<$ 10 pc). |
Phe nucleus. accounts for the majority. (το) of the radio emission. | The nucleus accounts for the majority ) of the radio emission. |
Its spectral. index isoOS+0.1. | Its spectral index is $\alpha \sim 0.8
\pm 0.1$. |
The low-surface brightness halo and he extended: wing-like structures have a slightly steeper spectral index a=0.9c0.1. A comparison between simultaneous SUERLIN and EVN observations at 18 anc 6 cm clearly indicates. that almost of the Dux density detected by ALERLIN cannot be recovered in EWN images (Micdelbergctal.2004). | The low-surface brightness halo and the extended wing-like structures have a slightly steeper spectral index $\alpha = 0.9 \pm 0.1$ A comparison between simultaneous MERLIN and EVN observations at 18 and 6 cm clearly indicates that almost of the flux density detected by MERLIN cannot be recovered in EVN images \citep{middelberg04}. |
. 1n fact. a dilluse emission. detected by ALERLIN observations. is not. seen by the EVN. as the EWN is. insensitive to structures larger than 35 and 11 mas at 18 and 6 cm. We produced new VLA image at 8.4 CGllz with a resolution of 07.2. 0".18 (Fig. | In fact, a diffuse emission, detected by MERLIN observations, is not seen by the EVN, as the EVN is insensitive to structures larger than 35 and 11 mas at 18 and 6 cm, We produced new VLA image at 8.4 GHz with a resolution of $^{\prime\prime}$ $\times$ $^{\prime\prime}$ .18 (Fig. |
6bb) obtained without the shortest («35 kA) baselines in order to pinpoint the compact central structure and to reduce the contamination from the surrounding ring. | \ref{n7469}b b) obtained without the shortest $<35$ $\lambda$ ) baselines in order to pinpoint the compact central structure and to reduce the contamination from the surrounding ring. |
The radio emission is dominated. hy an unresolved. central component. surrounded. by a ring of star-Forming regions with a diameter of about 3.7 (— | The radio emission is dominated by an unresolved central component surrounded by a ring of star-forming regions with a diameter of about $^{''}$ .7 $\sim$ |
metal line radiative cooling in the optically thin limit. | metal line radiative cooling in the optically thin limit. |
To simulate metals in our simulations, we define a generic mass scalar in FLASH, which is advected with any flows. | To simulate metals in our simulations, we define a generic mass scalar in FLASH, which is advected with any flows. |
For the cooling rates we use the tabulated results from Weirsma (2008), which assume local thermodynamic equilibrium, and in all cases we use standard solar abundance ratios. | For the cooling rates we use the tabulated results from Weirsma (2008), which assume local thermodynamic equilibrium, and in all cases we use standard solar abundance ratios. |
The radiative rates are defined over a large temperature range, from 10? K through 10? K. The specific cooling rate for a given temperature is found using a table lookup from a data file and scaling by the local metallicity. | The radiative rates are defined over a large temperature range, from $10^2$ K through $10^9$ K. The specific cooling rate for a given temperature is found using a table lookup from a data file and scaling by the local metallicity. |
Having described the new physical processes, we return our attention to the model developed in Paper I. Again we assume a ACDM cosmology with h = 0.7, Qo = 0.3, Ωλ = 0.7, and Ων = 0.045 (e.g., Spergel 2007), where h is the Hubble constant in units of 100 km s-! Mpc!, and Qo, Qa, and My are the total matter, vacuum, and baryonic densities in units of the critical density. | Having described the new physical processes, we return our attention to the model developed in Paper I. Again we assume a $\Lambda$ CDM cosmology with $h$ = 0.7, $\Omega_0$ = 0.3, $\Omega_{\Lambda}$ = 0.7, and $\Omega_{b}$ = 0.045 (e.g., Spergel 2007), where $h$ is the Hubble constant in units of 100 km $^{-1}$ $^{-1}$, and $\Omega_0$, $\Omega_{\Lambda}$, and $\Omega_b$ are the total matter, vacuum, and baryonic densities in units of the critical density. |
The critical density for our choice of h is pci; = 9.2 x 107? gcm-?. | The critical density for our choice of $h$ is $\rho_{\rm crit}$ = 9.2 $\times$ $^{-30}$ g $^{-3}$. |
We begin with a neutral primordial minihalo, which is composed of helium and hydrogen with a total mass of both dark and baryonic matter of M, = 3.0 x 106 Mo. | We begin with a neutral primordial minihalo, which is composed of helium and hydrogen with a total mass of both dark and baryonic matter of $_c$ = 3.0 $\times$ $^{6}$ $_{\sun}$. |
The initial minihalo has a total radial density profile given by Navarro (1997): p((R) —, where c is the halo concentration factor, x=R/R., R,(=0.393)kpc is the virial radius, F(t) =In(1+t) - qi, and pe=6.54x1077? g cm? is the mean cluster density. | The initial minihalo has a total radial density profile given by Navarro (1997): (R) =, where $c$ is the halo concentration factor, $x \equiv R/R_{\rm c}$, $R_{\rm c} (= 0.393) \ {\rm kpc}$ is the virial radius, $F(t)$ $\equiv {\rm ln}(1+t)$ - $\frac{t}{1+t}$, and $\rho_{\rm c} = 6.54 \times 10^{-25}$ g $^{-3}$ is the mean cluster density. |
The baryonic matter is taken to be in hydrostatic equilibrium and follows an isothermal radial profile with a virial temperature of T — 1650 K: =P oe?,,(22)where the escape velocity is vi.(rRy)=2v(cr)+ex(1ex)l]|F(c)-i and po = 2.16 x 10773[F g cm?. | The baryonic matter is taken to be in hydrostatic equilibrium and follows an isothermal radial profile with a virial temperature of T = 1650 K: = _0, where the escape velocity is $v^2_{\rm esc}(xR_{\rm vir}) = 2 v_c^2 [F(cx)+cx(1+cx)^{-1}][xF(c)]^{-1}$ and $\rho_0$ = 2.16 $\times$ $^{-23}$ g $^{-3}$. |
Gravity is treated using the multigrid Poisson solver for self gravity of the gas (Ricker 2008) as well an additional component of gravitational acceleration due to dark matter. | Gravity is treated using the multigrid Poisson solver for self gravity of the gas (Ricker 2008) as well an additional component of gravitational acceleration due to dark matter. |
T'he initial metallicity of the halo and surrounding gas is set to zero, and the initial values of X and L are set to of the total internal energy and one parsec respectively. | The initial metallicity of the halo and surrounding gas is set to zero, and the initial values of $K$ and $L$ are set to of the total internal energy and one parsec respectively. |
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