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1.
Redshift-Space Distortions in Lagrangian Perturbation Theory / Chen, Shi-Fan (UC, Berkeley) ; Vlah, Zvonimir (Cambridge U., KICC ; Cambridge U., DAMTP ; CERN) ; Castorina, Emanuele (Milan U. ; CERN) ; White, Martin (UC, Berkeley)
We present the one-loop 2-point function of biased tracers in redshift space computed with Lagrangian perturbation theory, including a full resummation of both long-wavelength (infrared) displacements and associated velocities. The resulting model accurately predicts the power spectrum and correlation function of halos and mock galaxies from two different sets of N-body simulations at the percent level for quasi-linear scales, including the damping of the baryon acoustic oscillation signal due to the bulk motions of galaxies. [...]
arXiv:2012.04636.- 2021-03-29 - 36 p. - Published in : JCAP 2103 (2021) 100 Fulltext: PDF;
2.
Modeling features in the redshift-space halo power spectrum with perturbation theory / Chen, Shi-Fan (UC, Berkeley) ; Vlah, Zvonimir (CERN) ; White, Martin (UC, Berkeley)
We study the ability of perturbative models with effective field theory contributions and infra-red resummation to model the redshift space clustering of biased tracers in models where the linear power spectrum has "features" -- either imprinted during inflation or induced by non-standard expansion histories. We show that both Eulerian and Lagrangian perturbation theory are capable of reproducing the Fourier space two-point functions of halos up to the non-linear scale from a suite of $4096^3$ particle N-body simulations. [...]
arXiv:2007.00704.- 2020-11-18 - 21 p. - Published in : JCAP 2011 (2020) 035 Fulltext: PDF;
3.
Consistent Modeling of Velocity Statistics and Redshift-Space Distortions in One-Loop Perturbation Theory / Chen, Shi-Fan (UC, Berkeley) ; Vlah, Zvonimir (CERN) ; White, Martin (UC, Berkeley)
The peculiar velocities of biased tracers of the cosmic density field contain important information about the growth of large scale structure and generate anisotropy in the observed clustering of galaxies. Using N-body data, we show that velocity expansions for halo redshift-space power spectra are converged at the percent-level at perturbative scales for most line-of-sight angles $\mu$ when the first three pairwise velocity moments are included, and that the third moment is well-approximated by a counterterm-like contribution. [...]
arXiv:2005.00523; CERN-TH-2020-068.- 2020-07-29 - 59 p. - Published in : JCAP 2007 (2020) 062 Fulltext: PDF;
4.
The reconstructed power spectrum in the Zeldovich approximation / Chen, Shi-Fan (UC, Berkeley) ; Vlah, Zvonimir (CERN) ; White, Martin (UC, Berkeley)
Density-reconstruction sharpens the baryon acoustic oscillations signal by undoing some of the smoothing incurred by nonlinear structure formation. In this paper we present an analytical model for reconstruction based on the Zeldovich approximation, which for the first time includes a complete set of counterterms and bias terms up to quadratic order and can fit real and redshift-space data pre- and post-reconstruction data in both Fourier and configuration space over a wide range of scales. [...]
arXiv:1907.00043.- 2019-09-09 - 45 p. - Published in : JCAP 1909 (2019) 017 Fulltext: PDF; External links: 00001 Fits for the pre- and post-reconstruction redshift-space power spectrum monopole (left) and quadrupole (right) for halos in the mass range $12.5 < \log_{10}(M/M_\odot) < 13.0.$ The fractional residuals $\Delta P/P$ are defined in Figure~\ref{fig:real_space_pks}. All spectra were fit using a consistent set of bias parameters $(b_1, b_2) = (0.02, -0.8)$, whose independent contributions are shown in the top row, determined by fitting the pre-reconstruction data, such that only the counterterms were fitted in constructing the curves in the bottom two rows. Our model with the full set of three counterterms fit both the reconstructed monopole and quadrupole in both schemes out to $k = 0.2 \kMpc$ to a few percent and reproduce the phase and amplitude of the oscillatory BAO wiggles.; 00009 Like Figure~\ref{fig:pkrsd_fit}, but for halos in the mass bin $13.0 < \log(M/h^{-1} M_\odot) < 13.5.$ Here, our model prefers the bias parameters $(b_1, b_2) = (0.23, -1.0)$ and accurately fits the data over a similar range of scales.; 00000 Fits for the pre- and post-reconstruction redshift-space power spectrum monopole (left) and quadrupole (right) for halos in the mass range $12.5 < \log_{10}(M/h^{-1} M_\odot) < 13.0.$ The fractional residuals $\Delta P/P$ are defined in Figure~\ref{fig:real_space_pks}. All spectra were fit using a consistent set of bias parameters $(b_1, b_2) = (0.02, -0.8)$, whose independent contributions are shown in the top row, determined by fitting the pre-reconstruction data, such that only the counterterms were fitted in constructing the curves in the bottom two rows. Our model with the full set of six counterterms---three each for the monopole and quadrupole respectively---fits both the reconstructed monopole and quadrupole in both schemes out to $k = 0.2 \kMpc$ to a few percent and reproduce the phase and amplitude of the oscillatory BAO wiggles.; 00003 Shifts in the recovered isotropic BAO scale, $\alpha_{\rm BAO}$, in redshift space fit using a model with only $b_1$ nonzero and polynomial broadband contributions in both the monopole and quadrpole, when truth is given by the Zeldovich approximation with nonzero quadratic bias. Values of $b_1$ and $b_2$ were chosen according to the peak-background split, while values for $b_s$ were taken from ref.~\cite{Abidi18}. (Left) Shifts in the BAO scale at $z = 0$. Fitting with the empirical model results in only sub-percent shifts across a wide range of halo masses, which are further more than halved after reconstruction. The solid and dashed lines show the shift with and without the quadratic shear bias $b_s$, whose effect is subdominant to $b_2$. (Right) The same shifts calculated at $z = 1.2$. Even prior to reconstruction, fitting with the empirical model results in less than a tenth of a percent shift in the BAO scale over a wide range of biases; after reconstruction the shift due to nonlinear bias becomes essentially zero.; 00004 Nonlinear corrections to the reconstructed matter power spectrum due to the Lagrangian-to-Eulerian mapping at one loop order, for $z=0$ and $R = 15\ h^{-1}$ Mpc. The left and right panels show contributions to the $ds$ and $dd$ power spectra, respectively. Even for the worst case of $z=0$, the corrections are never more than a few percent of the total reconstructed power spectrum, though they can become larger than the constituent $dd, ds$ spectra at large or small scales.; 00006 Halos in {\tt DarkSky} exhibit significant excess power compared to theory at large scales in Fourier space which should be well-described by linear theory. (Left) Fits to the real-space power spectrum with and without our ad hoc correction $P_{\rm lw} = A\ (k/k_0)^n,$ shown in blue and orange respectively. At the largest scales shown, the excess power is significantly larger than the scatter. The fits prefer slighly different, though qualitatively similar, bias values. (Right) The same fits in configuration space. The uncorrected data systematically trends below the data at separataions above the BAO peak and in the BAO ``dip,'' while the fit with $P_{\rm lw}$ added goes through all the data points.; 00001 The linear wiggle power spectrum for three choices of $P_{\rm nw}$. The conventional choice (EH98 \cite{EH1998}) does not accurately capture the large scale power, and we have investigated two possible methods to mitigate this discrepancy: one based on B-splines, described in ref.~\cite{Vlah16} and another based on a Savitsky-Golay filter in $\ln(k)$. The wiggle power spectra isolated using these three methods exhibit visibly different oscillatory behavior.; 00014 Lagrangian space two point functions used to compute reconstructed power spectra. Dashed quantities have been multiplied by an overall negative sign, and reflect that the shifted field is defined to be negatively correlated with the underlying matter field. Roughly speaking, the shifted and displaced correlators reproduce the general trend for the total matter correlators, shown in black, on large and small scales, respectively. An exception is $X^{ds}$, whose non-vanishing value on small scales reflect that the point values of $\bPsi^d$ and $\bPsi^s$ differ exactly by the Zeldovich displacement. Note also the small but visible features around $q = 100 \Mpc$, i.e. the BAO scale.; 00005 A sub-percent level feature in the power spectrum near $k=0.1\kMpc$ can lead to visible distortions in the BAO feature in $\xi(r)$. (Left) Residuals for the fit as a fraction of total measured power in the simulations, as defined in the caption of Figure~\ref{fig:real_space_pks}. The orange curve shows the residuals when our theory is corrected using a Gaussian profile localized at $k = 0.1 \kMpc$ compared to the fiducial fit (blue), whose residuals exhibit a dip centered at $k = 0.1 \kMpc.$ (Right) The fiducial and corrected correlation functions. The bump in the left panel, whose Fourier transform is shown magnified in the green curve, induces distortions in the BAO feature across a range of separations $r \sim 60 - 120\,h^{-1}$Mpc.; 00002 (Top) Real-space power spectra contributions, displaced-displaced, displaced-shifted and shifted-shifted, for the lowest order bias terms $1$, $b_1$, $b_1^2$, and their sum, compared to linear theory at $z = 0$. The pure matter piece is the only term that receives contributions from all three combinations of $d$ and $s$, and the $b_1^2$ term consists only of the $dd$ contribution. All three bias terms tend to linear theory on large scales but exhibit somewhat different broadband behavior at high $k$. (Bottom) The ratio of the above bias terms with the linear theory power spectrum, compared with the pre-reconstruction Zeldovich power spectrum. While both the pre- and post-reconstruction Zeldovich spectra differ with the linear spectrum in the broadband at small scales, the Zeldovich approximation predicts that the the oscillatory features in the reconstructed spectrum are almost identical to those in the linear spectrum, such that the wiggles are almost completely normalized out for the reconstructed spectrum.; 00012 The $z = 0$ Zeldovich power spectrum at $\nu = 0.5$, before and after reconstruction using Rec-Sym, shown with and without contributions from the quadratic bias and shear biases when $(b_1, b_2, b_s) = (5,20,10)$. For comparison, the RWiggle prediction is shown in the diamond points, and the isolated $b_2$ contributions are shown as a black dot-dashed line multiplied by a factor of five. For the unreconstructed spectrum, the $b_2$ contributions (with shear bias set to zero) can be seen to be essentially out-of-phase with the linear theory wiggles and induce a phase shift in the power spectrum. These contributions are greatly reduced in the reconstructed spectrum. The shear contributions, on the other hand, are more-or-less in phase with linear theory and unchanged by reconstruction. For completeness, we have also plotted contributions from a possible derivative bias $b_{\nabla^2}$, which modulate the amplitude of the wiggles in a manner growing with wave number.; 00008 Comparison of Zeldovich with IR-resummed linear theory (RWiggle) for reconstructed and unreconstructed spectra at $z=0$ and $\nu = 0$ and $0.5$ with $b_1 = 0.5$ using Rec-Sym with higher biases set to zero. RWiggle slightly under-predicts damping at high $k$ (but see footnote~\ref{fn:damp_fac}), especially for the unreconstructed power spectra.; 00010 Contributions to the pre- and post-reconstruction (dashed and solid) power spectra and correlations functions (left and right columns) in real space from linear through quadratic bias terms at $z = 0$. Note that the matter (blue) and $b_1^2$ (green) curves in the top right panel are essentially degenerate, especially at the large scales shown.; 00007 Same as Figure~\ref{fig:precon_biasterms_z0_sym}, but for \textbf{Rec-Iso} at $z = 0$. Unlike in \textbf{Rec-Sym}, the linear bias contributions to the monopole and quadrupole do not tend to the Kaiser limit on large scales but to the real space linear power spectrum, as evidenced by reduced power in the monopole compared to the pre-reconstruction Zeldovich power spectrum, and contributions to the quadrupole vanishing on large scales. However, many of the higher bias contributions are identical to those in \textbf{Rec-Sym} (Fig.~\ref{fig:precon_biasterms_z0_sym}).; 00011 Bias contributions to the pre- and post-reconstruction (dashed and solid) $z = 0$ redshift space power spectra monopole and quadrupoles in the \textbf{Rec-Sym} scheme. The color scheme and line styles follow those in Figure~\ref{fig:precon_biasterms_z0}. The lowest-order contributions to the reconstructed monopole and quadrupole due to the linear bias $b_1$ tend to the Kaiser approximation at large scales. Note the different $y$-axis ranges on different panels.; 00013 Fits to the pre- and post-reconstruction real-space halo power spectra in {\tt DarkSky} for halos of mass between $12.5 < \log_{10}(M/ h^{-1} M_\odot) < 13.0$ at three smoothing scales ($R = 10$, $15$, $20\kMpc$), assuming Zeldovich power spectra with biases $(b_1, b_2)$ and one counterterm per spectrum (three total for the reconstructed case). The upper plot of each vertical pair of panels shows the product of the wavevector magnitude and power spectrum $k\ P(k)$ while the lower plot shows the fit residuals as a fraction of measure power $\Delta P/P = (P_{\rm fit} - P_{\rm nbody})/P_{\rm nbody}$. In the top-left pair of panels we show the incremental contributions from $b_2$ and the counterterm $\alpha$ (which contributes close to $10\%$ of the power at $k = 0.1 \kMpc$) to the fit, which agrees with the simulation at the percent level (dotted line in the lower plots) at all scales shown. In the remaining panels we use the same bias parameters to fit the reconstructed power spectrum, allowing only counterterms to vary. Our model with three counterterms can fit the data at the percent level out to $k = 0.2 \kMpc$, though a bump-like feature at $k = 0.1 \kMpc$ becomes more prominent at smaller smoothing scales, where nonlinear corrections beyond the Zeldovich approximation presumably become more important (see text). Also shown in orange are fits using one counterterm -- or equivanlently one derivative bias -- which fit less well past $k = 0.1 \kMpc$. We fined that setting the counterterm $\alpha_{ss}$ to zero does not materially affect our fits. Note that there is excess power in the data at the largest scales shown, as discussed in the text.; 00012 Shifts in the recovered isotropic BAO scale, $\alpha_{\rm BAO}$, in redshift space fit using a model with only $b_1$ nonzero and polynomial broadband contributions in both the monopole and quadrpole, when truth is given by the Zeldovich approximation with nonzero quadratic bias. Values of $b_1$ and $b_2$ were chosen according to the peak-background split, while values for $b_s$ were taken from ref.~\cite{Abidi18}. Fitting with the empirical model results in only sub-percent shifts across a wide range of halo masses, which are further more than halved after reconstruction. The solid and dashed lines show the shift with and without the quadratic shear bias $b_s$, whose effect is subdominant to $b_2$.

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