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The data result iu final rus noise levels of 125. 115. 75. aud 4:J2y | over 160. 618. 185. and ((18.75.. τοι 18.75. and MMIIZ). widths for IRASFF10211]1721. the Cloverleaf. JJOO911|0551. and 00751|2716. respectively. | The data result in final rms noise levels of 125, 115, 75, and $\mu$ $^{-1}$ over 160, 648, 185, and (18.75, 70, 18.75, and MHz) widths for F10214+4724, the Cloverleaf, J0911+0551, and 0751+2716, respectively. |
Maps of the velocitv-iutegrated CO ./-1 >0 line enuission vield svuthesized clean bem sizes of 2.7742.37. 3,7742,4", 3:3«2. |". and 3.17«2. 1", | Maps of the velocity-integrated CO $J$ $\to$ 0 line emission yield synthesized clean beam sizes of $''$$\times$ $''$, $''$$\times$ $''$, $''$$\times$ $''$, and $''$$\times$ $''$. |
We observed the eenisson line toward IRASFFILO211)0721. the Cloverleaf. SAMALIISOU35|10277. (:—2.816). and 00751]2716. using the facility Ika baud receiver on the GBT with the digital Spectrometer backend (GBT/S) aud the Zpectrometer analog lag cross-correlation spectrometer backend (CBT/Z: instantaneously covering— GGIIz: Waris= et citevearhar0?:: see Table 1)). | We observed the emission line toward F10214+4724, the Cloverleaf, J04135+10277 $z$ =2.846), and 0751+2716, using the facility Ka band receiver on the GBT with the digital Spectrometer backend (GBT/S) and the Zpectrometer analog lag cross-correlation spectrometer backend (GBT/Z; instantaneously covering GHz; Harris et \\citeyear{har07}; see Table \ref{t1}) ). |
This vields a typical beam size of 423. | This yields a typical beam size of $\sim$ $''$. |
GBT/S observations were carried out under acceptable to good weather conditions during Ll sessious between 2007 October 10 aud 2008 October 12. vielding typical system temperatures of T4512 STR (with hnieher Zi toward hieher observing frequencies due to the atinosphere). | GBT/S observations were carried out under acceptable to good weather conditions during 14 sessions between 2007 October 10 and 2008 October 12, yielding typical system temperatures of $T_{\rm sys}$ K (with higher $T_{\rm sys}$ toward higher observing frequencies due to the atmosphere). |
This resulted iu. 1.3.3.7. 2.5. and lilix on-source observing time for FFI021111721. the Cloverleaf. SMNEJJO1135|10277. and 00751|2716. respectively, | This resulted in 4.3, 3.7, 2.5, and hr on-source observing time for F10214+4724, the Cloverleaf, J04135+10277, and 0751+2716, respectively. |
Iu addition. the Cloverleaf was observed with the GBT/Z for another 6 sessions between 2008 March 02 and 2009 March 12. | In addition, the Cloverleaf was observed with the GBT/Z for another 6 sessions between 2008 March 02 and 2009 March 12. |
This resulted in hy of observing time. about half of which was speut on the Cloverleaf. | This resulted in hr of observing time, about half of which was spent on the Cloverleaf. |
The GBT/S was configured with AITz bandwidth. vielding a spectral resolution of kKkIIz. | The GBT/S was configured with MHz bandwidth, yielding a spectral resolution of kHz. |
The GBT/Z samples its GGIIz bandwidth with SAMIMIIZ spectral channels | The GBT/Z samples its GHz bandwidth with MHz spectral channels. |
Its instrmucutal spectral response is nearly a sine function with an EWIIM of AMATIz. 10. individual MMIIZ spectral channels are rot statistically independent. | Its instrumental spectral response is nearly a sinc function with an FWHM of MHz, i.e., individual MHz spectral channels are not statistically independent. |
However. the line width correction for the iustruinental response for spectral ines with intrinsic Caussian FWIIMO of 30 MMIIZ (~300 ) Is mune. | However, the line width correction for the instrumental response for spectral lines with intrinsic Gaussian FWHM of $>$ MHz $\sim$ ) is minor. |
Subreflector beam switching was used every LOss for all observations (GDT/S and CBT/Z) to observe μοι sources alternately with the receivers νο jns. With the offsource beam monitoring the skv ckeround in parallel. | Subreflector beam switching was used every s for all observations (GBT/S and GBT/Z) to observe the sources alternately with the receiver's two beams, with the off-source beam monitoring the sky background in parallel. |
To remove continuum fluxes aud atinosphieric/mstriunenutal effects. low-order polvunonials were fitted to the the spectral baseliues of the calibrated. iue-averaged GBT/S observations. | To remove continuum fluxes and atmospheric/instrumental effects, low-order polynomials were fitted to the the spectral baselines of the calibrated, time-averaged GBT/S observations. |
For the CDT/Z observations. à nearby second. faint source was observed with the same subreflector switching pattern. alternating )etwoeen targets with Simin cveles. | For the GBT/Z observations, a nearby second, faint source was observed with the same subreflector switching pattern, alternating between targets with min cycles. |
Residual structure roni optical beam imbalance in the “sourcesky" differeuce spectra of the two targets was then removed x ditfereuciug the resulting spectra of both sources (the second source was not detected). | Residual structure from optical beam imbalance in the “source–sky” difference spectra of the two targets was then removed by differencing the resulting spectra of both sources (the second source was not detected). |
This strategv vields a dat baseline (offset. from zero flux bv the difference. of he two sources continua) without standard polviuonmial | This strategy yields a flat baseline (offset from zero flux by the difference of the two source's continua) without standard polynomial |
NB816 imaged line flux. | NB816 imaged line flux. |
This difference is larger than is expected for a point source, unless the object fell on the edge of our 1/’55-wide slit. | This difference is larger than is expected for a point source, unless the object fell on the edge of our 5-wide slit. |
As noted above, in the narrow-band image coordinates, MSDM 80-3 is 0744 north of the slit-center. | As noted above, in the narrow-band image coordinates, MSDM 80+3 is 4 north of the slit-center. |
Using the point source slit loss models from Martin et al. ( | Using the point source slit loss models from Martin et al. ( |
2008), at this we only about a slit loss. | 2008), at this position we expect only about a slit loss. |
The effect of the positionnon-uniform expectresponse of the NB816 filter on SuprimeCam is negligible for MSDM 80-3, because our measured wavelength is near the central wavelength of the NB816 transmission. | The effect of the non-uniform response of the NB816 filter on SuprimeCam is negligible for MSDM 80+3, because our measured wavelength is near the central wavelength of the NB816 transmission. |
Furthermore, lines at wavelengths away from the center of the NB816 bandpass would have decreased observed fflux relative to our spectroscopic measurement- the opposite of what we observe. | Furthermore, lines at wavelengths away from the center of the NB816 bandpass would have decreased observed flux relative to our spectroscopic measurement– the opposite of what we observe. |
Generally, sources found through blind spectroscopy do not fall at the center of the slit; for larger samples the impact of slit-losses on the luminosity function is modeled statistically. | Generally, sources found through blind spectroscopy do not fall at the center of the slit; for larger samples the impact of slit-losses on the luminosity function is modeled statistically. |
widths, UV luminosities, and UV continuum derived star Equivalentformation rates are given in Table 1.. | Equivalent widths, UV luminosities, and UV continuum derived star formation rates are given in Table \ref{phot_table}. |
We assume a flat UV spectrum (fος A), consistent with observations of LAEs with lluminosities and redshifts similar to those of our objects (Pirzkaletal.2007),, and with z~6 LBGs in the NICMOS Ultra Deep Field (Stanwayetal.2005;Bouwens2009).. | We assume a flat UV spectrum $f_{\lambda} \propto \lambda^{-2}$ ), consistent with observations of LAEs with luminosities and redshifts similar to those of our objects \citep{Pirzkal}, and with $z\sim6$ LBGs in the NICMOS Ultra Deep Field \citep{Stanway05, Bouwens_uvslope}. |
Therefore, although the center of the ffilter corresponds to ~1700 iin the rest frame, our best estimate is that k-corrections are negligible. | Therefore, although the center of the filter corresponds to $\sim 1700$ in the rest frame, our best estimate is that k-corrections are negligible. |
We note that Mj——20.2 at z~~6 (Bouwensetal. 2007),, so the UV-luminosities that we measure are consistent with typical sources observed at this redshift- within a factor of two of L* for the two J1;9-—detected sources. | We note that $M^*_{UV} = -20.2$ at $z\sim6$ \citep{Bouwens07}, so the UV-luminosities that we measure are consistent with typical sources observed at this redshift– within a factor of two of $L^*$ for the two –detected sources. |
Star formation rates (SFRs) are derived using the 1500 cconversion from Madauetal.(1998). | Star formation rates (SFRs) are derived using the 1500 conversion from \cite{MPD98}. |
UV-continuum based estimates of star-formation rates are thought to be more reliable than those fromLya;; nevertheless, these continuum-based estimates come with several caveats. | UV-continuum based estimates of star-formation rates are thought to be more reliable than those from; nevertheless, these continuum-based estimates come with several caveats. |
First, the conversion is valid only when the characteristic stellar age is older than the main sequence lifetime of O- and B-stars. | First, the conversion is valid only when the characteristic stellar age is older than the main sequence lifetime of O- and B-stars. |
At young ages (<20 Myrs), the true SFR may be a few times larger. | At young ages $\la 20$ Myrs), the true SFR may be a few times larger. |
Second, we have not corrected the UV-luminosities for dust extinction, so again, the SFRs given in Table | may be underestimated. | Second, we have not corrected the UV-luminosities for dust extinction, so again, the SFRs given in Table \ref{phot_table} may be underestimated. |
However, in general, z~6 galaxies are not thought to be very dusty (Bouwens2009),, so dust corrections to our SFRs need not be very large. | However, in general, $z\sim6$ galaxies are not thought to be very dusty \citep{Bouwens_uvslope}, so dust corrections to our SFRs need not be very large. |
Third, uncertainties in the IMF slope and mass cutoffs may be just as important, as they can change the SFR by a factor of a few etal.2009).. | Third, uncertainties in the IMF slope and mass cutoffs may be just as important, as they can change the SFR by a factor of a few \citep{thesis}. |
On the other hand, the two-photon nebular(Henry continuum is not expected to make a significant contribution to the UV-luminosity, since it is generally dwarfed by the stellar contribution. | On the other hand, the two-photon nebular continuum is not expected to make a significant contribution to the UV-luminosity, since it is generally dwarfed by the stellar contribution. |
While some sources are purported to have spectra dominated by the photon continuum, such objects appear to be rare (Fosburyal.2003;Raiteret2010),, and are predicted to have eequivalent widths >1000 ((Schaerer2002,, with coefficients from Aller1984)). | While some sources are purported to have spectra dominated by the two-photon continuum, such objects appear to be rare \citep{Fosbury03, Raiter}, and are predicted to have rest-frame equivalent widths $\ga 1000$ \citealt{Schaerer02}, with coefficients from \citealt{Aller}) ). |
The equivalent widths that we measure are consistent with those of LAEs at high redshift, as shown in Figure 3.. | The equivalent widths that we measure are consistent with those of LAEs at high redshift, as shown in Figure \ref{ewplot}. |
We do not make any correction for IGM absorption on the eemission, as has been done for some objects at z~6 citealtShimasaku)). | We do not make any correction for IGM absorption on the emission, as has been done for some objects at $z\sim6$ \\citealt{Shimasaku}) ). |
While it is possible that the eemission emergent from the galaxy is larger than observed, the amount of attenuation is uncertain because the resonant scattering of pphotons shifts the emission towards redder wavelengths (Verhammeetal. | While it is possible that the emission emergent from the galaxy is larger than observed, the amount of attenuation is uncertain because the resonant scattering of photons shifts the emission towards redder wavelengths \citep{Verhamme}. |
2008).. It is not surprising that we do not observe any sources that are both UV luminous and have high-equivalent widths. | It is not surprising that we do not observe any sources that are both UV luminous and have high-equivalent widths. |
As Nilssonetal.(2009) point out, this may be a consequence of both classes of objects being rare, rather than a correlation of equivalent width with UV luminosity as has been suggested by Andoetal.(2006). | As \cite{Nilsson} point out, this may be a consequence of both classes of objects being rare, rather than a correlation of equivalent width with UV luminosity as has been suggested by \cite{Ando}. |
. The three LAEs that we present are consistent with the range of equivalent widths that are easily explained by “normal” stellar populations, with ages older than 10 Myrs and a Salpeter IMF. | The three LAEs that we present are consistent with the range of equivalent widths that are easily explained by “normal” stellar populations, with ages older than 10 Myrs and a Salpeter IMF. |
However, deeper continuum observations of MSDM 80+3 could prove that its equivalent width is much larger. | However, deeper continuum observations of MSDM 80+3 could prove that its equivalent width is much larger. |
There are several different models that can explain very equivalent widths. | There are several different models that can explain very large equivalent widths. |
First, extremely young ages and/or largetop-heavy initialmass functions (IMFs) can result in rest-frame equivalent width Wy>240 citealtMRO04)). | First, extremely young ages and/or top-heavy initialmass functions (IMFs) can result in rest-frame equivalent width $W_{0} > 240$ \\citealt{MR04}) ). |
Second, a multi-phase interstellar medium has sometimes been invoked to preferentially absorb UV continuum photons (Neufeld1991;Hansen&Oh2006;Scarlataetal.2009;Finkelstein 2009)); and third, gravitational cooling radiation in the absence of star formation is predicted to result in Wo>1000 (Dijkstra 2009)) | Second, a multi-phase interstellar medium has sometimes been invoked to preferentially absorb UV continuum photons \citealt{Neufeld, HO06, Scarlata, Finkelstein09}) ); and third, gravitational cooling radiation in the absence of star formation is predicted to result in $W_{0} > 1000$ \citealt{Dijkstra09}) ). |
However, such equivalent width objects are probably rare, as only a few highsources in Figure 3 lie at Wo>240A. | However, such high equivalent width objects are probably rare, as only a few sources in Figure \ref{ewplot} lie at $W_{0} > 240$. |
. It is important to note that the uncertainty on such high equivalent width sources typically exceeds bbecause of weak continuum detections, so these measurements should be viewed with caution. | It is important to note that the uncertainty on such high equivalent width sources typically exceeds because of weak continuum detections, so these measurements should be viewed with caution. |
It is interesting to consider whether the LAEs in our survey would be selected as i— dropout LBGs at z~ 6, because the connection between the two populations is currently unclear. | It is interesting to consider whether the LAEs in our survey would be selected as $i-$ dropout LBGs at $z\sim6$ , because the connection between the two populations is currently unclear. |
While it is generally understood that LAEs can be missed by LBG searches when their continuum is too faint, the selection of brighter sources can also be influenced by strong line | While it is generally understood that LAEs can be missed by LBG searches when their continuum is too faint, the selection of brighter sources can also be influenced by strong line |
the right. panel o£ Fig. 1.. | the right panel of Fig. \ref{gf}. |
Phe old approximation f—OL.στι is plotted in the bottom right panel in Fig. 1.. | The old approximation $f= \Omega^{0.6}_{\rm m}$, is plotted in the bottom right panel in Fig. \ref{gf}. |
Phe dotted lines represent the ratio f=OUσπα to the exact solution for each of the dark energy mocels. | The dotted lines represent the ratio $f = \Omega^{0.6}_{\rm m}$ to the exact solution for each of the dark energy models. |
Lt is clear that this approximation for the growth factor is not as accurate as the formula in Eq. | It is clear that this approximation for the growth factor is not as accurate as the formula in Eq. |
1 over the same range of redshifts. | \ref{linder} over the same range of redshifts. |
We use the N-body simulations carried out by ?.. | We use the N-body simulations carried out by \citet{2010MNRAS.401.2181J}. |
These simulations were performed at. the Institute. of Computational Cosmology using a memory. cllicient version of the TreePAL code Gabpcrr-2. called. (?).. | These simulations were performed at the Institute of Computational Cosmology using a memory efficient version of the TreePM code , called \citep{Springel:2005mi}. |
For the ACDAL mocel we usec the following cosmological xwameters: 04,=0.26. Opp=0.74. Οι,=0.044. h=0.715 and a spectral tilt of ny=0.96 (2)... | For the $\Lambda$ CDM model we used the following cosmological parameters: $\Omega_{\rm m} = 0.26$, $\Omega_{\rmn{DE}}=0.74$, $\Omega_{\rm b} = 0.044$, $h = 0.715$ and a spectral tilt of $n_{\mbox{s}} =0.96$ \citep{2009MNRAS.400.1643S}. |
Phe linear theory rms Lluctuation in spheres of radius N f Alpe ds set o be a,=OS. | The linear theory rms fluctuation in spheres of radius 8 $h^{-1}$ Mpc is set to be $\sigma_8 = 0.8$. |
For each of the quintessence models. a our variable parametrization of the dark energy. equation of state is used as described above. | For each of the quintessence models, a four variable parametrization of the dark energy equation of state is used as described above. |
In cach case. the cosmological parameters used are the best fitting parameters o observational constraints from. the cosmic microwave xckground. barvonic acoustic oscillations anc supernovae la taking into account the impact of the quintessence mocoel. (StageLlintheterminologyof 2).. | In each case, the cosmological parameters used are the best fitting parameters to observational constraints from the cosmic microwave background, baryonic acoustic oscillations and supernovae Ia taking into account the impact of the quintessence model. \citep[Stage III in the terminology of ][]{2010MNRAS.401.2181J}. . |
The simulations use No=646%~26910" particles o represent the matter distribution in a computational« box of comoving length 15007. Mpe. | The simulations use $N=646^3 \sim 269 \times 10^6$ particles to represent the matter distribution in a computational box of comoving length $1500 h^{-1}$ Mpc. |
The comoving softening eneth is 50h thkpe. | The comoving softening length is $50 h^{-1}$ kpc. |
"The particle mass in the ACDAIL simulation is 9.0210hAL. and is slightly different in he other runs due to changes in £3, (see Table 1). | The particle mass in the $\Lambda$ CDM simulation is $9.02 \times 10^{11} h^{-1}
M_{\sun}$ and is slightly different in the other runs due to changes in $\Omega_{\rm{m}}$ (see Table 1). |
Phe initial conditions were set up starting from a glass configuration of particles (?22).. | The initial conditions were set up starting from a glass configuration of particles \citep{1994RvMA....7..255W,Baugh:1995hv}. |
In order to limit the impact of the initial displacement scheme we chose a starting redshift of +=200. | In order to limit the impact of the initial displacement scheme we chose a starting redshift of $z=200$. |
The linear theory power spectrum used to generate the initial conditions was obtained using CAMD (2).. | The linear theory power spectrum used to generate the initial conditions was obtained using CAMB \citep{Lewis:2002ah}. |
We use a nmocified version of CAMD which incorporates the inlluence of dark energy on dark matter clustering at carly times (?).. | We use a modified version of CAMB which incorporates the influence of dark energy on dark matter clustering at early times \citep{Fang:2008sn}. |
In each model the power spectrum at redshift. zero is normalised to have ox=0.8. | In each model the power spectrum at redshift zero is normalised to have $\sigma_8 = 0.8$. |
Using the linear growth [actor for each dark energy model. the linear theory (4) was then evolved backwards to the starting redshift of z=200 in order to generate the initial conditions. | Using the linear growth factor for each dark energy model, the linear theory $P(k)$ was then evolved backwards to the starting redshift of $z=200$ in order to generate the initial conditions. |
The power spectrum. was computed by assigning the particles to a mesh using the cloud in cell (CIC) assignment scheme (2). ancl performing a [ast Fourier transform (FET) ofthe density field. | The power spectrum was computed by assigning the particles to a mesh using the cloud in cell (CIC) assignment scheme \citep{1981csup.book.....H} and performing a fast Fourier transform (FFT) ofthe density field. |
To compensate for the mass assignment scheme we perform an approximate ce-convolution following ?.. | To compensate for the mass assignment scheme we perform an approximate de-convolution following \citet{1991ApJ...375...25B}. |
In Sections 41 and 4.2. we present the redshift. space distortions measured. from the simulations in. CDM and quintessence cosmologics. and we compare with the predictions of the linear and non-linear models cliseussec in Section 2.3.. | In Sections \ref{4.1} and \ref{4.2} we present the redshift space distortions measured from the simulations in $\Lambda$ CDM and quintessence cosmologies, and we compare with the predictions of the linear and non-linear models discussed in Section \ref{2.2}. |
In the left panel of Fig. 2.. | In the left panel of Fig. \ref{lcdm}, |
we plot the ratio of the redshift space to real space power spectra. measured from the AC DAL simulation at z=O and z=1. | we plot the ratio of the redshift space to real space power spectra, measured from the $\Lambda$ CDM simulation at $z=0$ and $z=1$. |
Using the plane parallel approximation. we assume the observer is at infinitv ancl as à result the velocity distortions are iniposed. along one direction in A-space. | Using the plane parallel approximation, we assume the observer is at infinity and as a result the velocity distortions are imposed along one direction in $k$ -space. |
Lowe choose the line of sight. direction to be the c-axis. for example. then (i=hefh where &=nma | If we choose the line of sight direction to be the $z$ -axis, for example, then $\mu = k_z/k$ where $k =|\vec{k}|$ . |
In this paper the power spectrum in redshift space represents the average of P(k.=hifh). Pii=beyfh) and P(k.p=Aefh) where theji line of sight. components are parallel to the ον y and z directions respectively. | In this paper the power spectrum in redshift space represents the average of $P(k,\mu=k_x/k)$, $P(k,\mu=k_y/k)$ and $P(k,\mu=k_z/k)$ where the line of sight components are parallel to the $x$ , $y$ and $z$ directions respectively. |
We use this average as there is a significant scatter in the amplitudes of the three redshift space power spectra on large scales. even for a computational box as large as the one we jwe used. | We use this average as there is a significant scatter in the amplitudes of the three redshift space power spectra on large scales, even for a computational box as large as the one we have used. |
The three monopoles of the redshift space power spectra Pk.mhigh). Phimhyfh) and Pl.ji=heefh) measured in oneji of the realisations are plotted as the evan. surple ancl red. dashed. lines respectively. to illustrate the scalter. | The three monopoles of the redshift space power spectra $P(k,\mu=k_x/k)$, $P(k,\mu=k_y/k)$ and $P(k,\mu=k_z/k)$ measured in one of the realisations are plotted as the cyan, purple and red dashed lines respectively, to illustrate the scatter. |
In Fig. | In Fig. |
2. the Ixaiser formula. given by Eq. 6... | \ref{lcdm} the Kaiser formula, given by Eq. \ref{mr}, |
is Xotted as a blue dotted line. using a value of f=Ως) or CDM. | is plotted as a blue dotted line, using a value of $f = \Omega^{0.55}_m(z)$ for $\Lambda$ CDM. |
The error. bars. plotted. represent. the scatter over four realisations after averaging over Lh) obtained by reating the «oy and z directions as the line of sight. | The error bars plotted represent the scatter over four realisations after averaging over $P(k)$ obtained by treating the $x, y$ and $z$ directions as the line of sight. |
Ht is clear from this plot that the linear perturbation theory limit is only attained on extremely large scales (&«0.035 1) ab οΞθ and at >=1. | It is clear from this plot that the linear perturbation theory limit is only attained on extremely large scales $(k <0.03 h$ $^{-1}$$)$ at $z=0$ and at $z=1$. |
Non-linear effects are significant on scales 0.03«&(hMpe 1)<0.1 which are usually considered o be in the linear regime. | Non-linear effects are significant on scales $0.03<k (h$ $^{-1}$$)<0.1$ which are usually considered to be in the linear regime. |
The measured. variance in the matter power spectrun on these scales is 10.7«0?«107. | The measured variance in the matter power spectrum on these scales is $10^{-3}<\sigma^2 <10^{-2}$. |
In the right panel of Fig. | In the right panel of Fig. |
2 we plot the ratio £715 or ACDAL at >=0 and z=1. | 2 we plot the ratio $P^s_2/P^s_0$ for $\Lambda$ CDM at $z=0$ and $z=1$. |
The ratio agrees with he Ixaiser limit (given in Eq. | The ratio agrees with the Kaiser limit (given in Eq. |
7) down to smaller scales. ko«0.065 ". compared to the monopole ratio. plotted in the left. panel. | 7) down to smaller scales, $k<0.06 h$ $^{-1}$, compared to the monopole ratio plotted in the left panel. |
Our results agree with previous work on he quacrupole and monopole moments of the redshift space »»wer spectrum for CDM (777) | Our results agree with previous work on the quadrupole and monopole moments of the redshift space power spectrum for $\Lambda$ CDM \citep{Cole:1993kh,1999MNRAS.310.1137H,Scoccimarro:2004tg}. |
At.=1. the damping cllects are less prominent and the Ixaiser limit is attained over a slightly wider range of scales. &<O.hAlpe 1. as non-linear effects. are. smaller then at 2=0. | At $z=1$, the damping effects are less prominent and the Kaiser limit is attained over a slightly wider range of scales, $k < 0.1 h$ $^{-1}$, as non-linear effects are smaller then at $z=0$. |
In the nextsection. we consider these ratios for the quintessence dark energy models in more detail. | In the nextsection, we consider these ratios for the quintessence dark energy models in more detail. |
For cach nioclel we find that the analytic expression for the quadrupole to monopole ralio describes the simulation results over a wider range of wavenumber then the analogous result for the monopole moment. | For each model we find that the analytic expression for the quadrupole to monopole ratio describes the simulation results over a wider range of wavenumber then the analogous result for the monopole moment. |
The linear theory relationship between the real and redshift space power spectra given in Eq. | The linear theory relationship between the real and redshift space power spectra given in Eq. |
6. assumes various non- elfects are small and can be neglected on largescales. | \ref{mr} assumes various non-linear effects are small and can be neglected on largescales. |
‘These assumptions are listed in Section 2.2.. | These assumptions are listed in Section \ref{1.1}. . |
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