The Effect of Fiber Collisions on the Galaxy Power Spectrum Multipole

TL;DR

This work addresses systematic biases from fiber collisions in galaxy power spectrum multipoles, focusing on the monopole $P_0(k)$ and quadrupole $P_2(k)$. It develops two complementary strategies: (i) line-of-sight reconstruction (LRec) that statistically relocates collided galaxies along the line of sight using an empirically measured $p(d_{\rm LOS})$, thereby correcting the data-based power spectrum (notably the monopole) without over-relying on mocks, and (ii) an effective window (EW) method that forward-models the collision effect as a $k$-dependent convolution with a 2D top-hat window, enabling theory predictions for $P_0(k)$ and $P_2(k)$ including a controllable set of nuisance parameters. The NN method alone is shown to be insufficient, especially for $k\gtrsim0.1\,h/{\rm Mpc}$, while LRec substantially restores the monopole accuracy (within sample variance up to $k\sim0.53\,h/{\rm Mpc}$) though it struggles for the quadrupole, and EW provides robust, forward-modelable corrections up to the theoretical limits with a small set of nuisance terms. Together these approaches enable robust extraction of cosmological information from mildly non-linear scales in current and future fiber-fed surveys, with explicit pathways to marginalize small-scale fiber-collision power in parameter inference.

Abstract

Fiber-fed multi-object spectroscopic surveys, with their ability to collect an unprecedented number of redshifts, currently dominate large-scale structure studies. However, physical constraints limit these surveys from successfully collecting redshifts from galaxies too close to each other on the focal plane. This ultimately leads to significant systematic effects on galaxy clustering measurements. Using simulated mock catalogs, we demonstrate that fiber collisions have a significant impact on the power spectrum, $P(k)$, monopole and quadrupole that exceeds sample variance at scales smaller than $k\sim0.1~h/Mpc$. We present two methods to account for fiber collisions in the power spectrum. The first, statistically reconstructs the clustering of fiber collided galaxy pairs by modeling the distribution of the line-of-sight displacements between them. It also properly accounts for fiber collisions in the shot-noise correction term of the $P(k)$ estimator. Using this method, we recover the true $P(k)$ monopole of the mock catalogs with residuals of $<0.5\%$ at $k=0.3~h/Mpc$ and $<4\%$ at $k=0.83~h/Mpc$ -- a significant improvement over existing correction methods. The quadrupole, however, does not improve significantly. The second method models the effect of fiber collisions on the power spectrum as a convolution with a configuration space top-hat function that depends on the physical scale of fiber collisions. It directly computes theoretical predictions of the fiber-collided $P(k)$ multipoles and reduces the influence of smaller scales to a set of nuisance parameters. Using this method, we reliably model the effect of fiber collisions on the monopole and quadrupole down to the scale limits of theoretical predictions. The methods we present in this paper will allow us to robustly analyze galaxy power spectrum multipole measurements to much smaller scales than previously possible.

Figures (10)

• Figure 1: Normalized galaxy redshift distribution of the Nseries (orange), QPM (blue), and BigMultiDark (red) mock catalogs. The normalized redshift distribution of BOSS DR12 CMASS sample galaxies is also plotted (black). Each of the distributions were computed with a bin size of $\Delta z = 0.025$. All of the mock catalogs used in this work closely trace the BOSS CMASS redshift distribution.
• Figure 2: Power spectrum monopole $P_0(k)$ and quadrupole $|P_2(k)|$ measurements for the Nseries (orange), QPM (blue), and BigMultiDark (red) mock catalogs (Section \ref{['sec:catalog']}). The $P_l(k)$ measurements for the Nseries and QPM mock catalogs are averaged over the multiple mock realizations and the width of the power spectra represents the sample variance ($\sigma_l(k)$; Eq. \ref{['eq:pk_var']}) of the realizations. For the quadrupole, we plot the $|{P_2(k)}|$ instead of ${P_2(k)}$ because the measurement becomes negative for $k \gtrsim 0.35\;h/\mathrm{Mpc}$. For comparison, we also include the monopole and quadrupole power spectra of the BOSS DR12 CMASS sample, which are calculated using the same estimator but with statistical weights described in Eq. (\ref{['eq:weight']}). While fiber collisions are inevitably included in the BOSS CMASS power spectra, they are not yet applied to the mock catalogs power spectra measurements above.
• Figure 3: The fiber collision power spectrum residual, $(P_l^\mathrm{NN}-P_l^\mathrm{true})$ (Section \ref{['sec:fc_pk']}), for the monopole (top) and quadrupole (bottom) of the Nseries (left), QPM (middle), and BigMultiDark (right) mock catalogs. For the Nseries and QPM mocks, we plot the sample variances $\sigma_l(k)$ (grey shaded region) of $P_l^\mathrm{true}(k)$ for comparison. The power spectrum residual for the NN method is an improvement over the residual with no correction ($\Delta P_l^\mathrm{NoW}(k)$; x) at most scales probed. However, we highlight that at $k > 0.1 \;h/\mathrm{Mpc}$ and $k > 0.2\;h/\mathrm{Mpc}$, for the monopole and quadrupole respectively, the residuals from fiber collision surpass the sample variance. At smaller scales, NN method does not sufficiently account for the effects of fiber collisions in $P_l(k)$ measurements.
• Figure 4: Top Panel: The normalized residuals, $1 - \overline{P_0^\mathrm{NN}}/\overline{P_0^\mathrm{true}}(k)$, of the NN method for the Nseries (orange), QPM (blue), and BigMultiDark (red) power spectrum monopole. We also plot the normalized sample variance $\sigma_0(k) / P_0(k)$ (gray shaded region) of the Nseries mocks for comparison. The QPM $\sigma_0(k) / P_0(k)$ is effectively the same as the Nseries $\sigma_0(k)/P_0(k)$, so we do not included in the figure. The comparison reveals that the effect of fiber collisions not only biases the power spectrum beyond sample variance at $k \gtrsim 0.1 \;h/\mathrm{Mpc}$, but that the effect increases relative to sample variance at smaller scales. At $k = 0.2\;h/\mathrm{Mpc}$, the normalized residual is greater than $4$ times the normalized sample variance. Bottom Panel: We mark $k_{\chi^2}$ where $\Delta \chi^2(k_{\chi^2}) = 1$ (Eq. \ref{['eq:chisquared']}) for the NN method. $k^\mathrm{NN}_{\chi^2}$ is a conservative scale limit of the NN method. Arrows above the dashed line mark $k_{\chi^2}$ for the monopole while the arrows below the dashed line mark $k_{\chi^2}$ for the quadrupole. The color of the arrows indicate the mock catalog: Nseries (orange), QPM (blue), and BigMultiDark (red). Averaged over the three mock catalogs, we get $k^\mathrm{NN}_{\chi^2} = 0.068$ and $0.17 \;h/\mathrm{Mpc}$. for the monopole and quadrupole respectively.
• Figure 5: Normalized distribution of $d_{\mathrm{LOS}}$ for Nseries (orange), QPM (blue), and BigMultiDark (green) mock catalogs. The normalized $d_{\mathrm{LOS}}$ distribution of BOSS DR12 is also plotted (black). The mock catalog distributions have bin sizes of $\Delta d = 0.2\, \mathrm{Mpc}$, while the CMASS distribution has a bin size of $\Delta d = 0.5\, \mathrm{Mpc}$. The distribution extends beyond the range of the above plot to $\sim \pm 500 \; \mathrm{Mpc}$. In the discussion of Section \ref{['sec:dlospeak']}, we focus mainly on the peak of the distribution at roughly $-20 \; \mathrm{Mpc} < d_\mathrm{LOS} < 20 \;\mathrm{Mpc}$.