论文标题
平坦的天空近似与星系数计数
The Flat Sky Approximation to Galaxy Number Counts
论文作者
论文摘要
我们得出并测试了平面天空限制中星系数计数的角功率谱的近似值。结果近似中的标准密度和红移空间扭曲（RSD）项与Libber近似不同，为低至$ \ ell \ el \ simeq10 $的多尔斯提供了准确的结果，其中相应的纵横差近似完全不准确。在$ z <3 $的$ z = 5 $时，密度和RSD（标准）条款的准确性约为0.2％，即使到$ \ ell <50 $，密度和RSD（标准）条款的准确性约为0.2％。在不平等的红移下，如果我们考虑总功率谱，则仅在很小的红移差异的情况下，精度优于5％，$Δ<Δ_0（\ simeq 3.6 \ times10^{ - 4}（1+z）^{1+z）^{2.14}） 0.33（r（z）h（z））/（z+1））$，其中镜头术语占主导地位。纯镜头和镜头密度互相关项的平坦天空表达式等同于Limber近似。对于任意的红移差异，Limber近似的准确度为0.5％（纯镜头的$ \ ell \ el \ simeq 40 $高于$ \ ell \ simeq 40 $，而密度透镜的$ \ ell \ el \ simeq 80 $）。除了非常准确之外，平坦的天空近似在计算上要简单得多，因此对于使用MCMC方法的数据分析和预测非常有用。这对于将衡量星系数计数的功率谱的即将进行的星系调查特别重要。
We derive and test an approximation for the angular power spectrum of galaxy number counts in the flat sky limit. The standard density and redshift space distortion (RSD) terms in the resulting approximation are distinct to the Limber approximation, providing an accurate result for multipoles as low as $\ell\simeq10$, where the corresponding Limber approximation is completely inaccurate. At equal redshift the accuracy of the density and RSD (standard) terms is around 0.2% for $z<3$ and 0.5% at $z=5$, even to $\ell<50$. At unequal redshifts, if we consider the total power spectrum, the precision is better than 5% only for very small redshift differences, $δ<δ_0 (\simeq 3.6\times10^{-4}(1+z)^{2.14})$ where the standard terms are well-approximated, or for large enough redshift differences $δ>δ_1 (\simeq 0.33(r(z)H(z))/(z+1))$ where the lensing terms dominate. The flat sky expressions for the pure lensing and the lensing-density cross-correlation terms are equivalent to the Limber approximation. For arbitrary redshift differences, the Limber approximation achieves an accuracy of 0.5% (above $\ell\simeq 40$ for pure lensing and $\ell\simeq 80$ for density-lensing). Besides being very accurate, the flat sky approximation is computationally much simpler and can therefore be very useful for data analysis and forecasts with MCMC methods. This will be particularly crucial for upcoming galaxy surveys that will measure the power spectrum of galaxy number counts.
