We describe the design and performance of the near-infrared (1.51-1.70μm), fiber-fed, multi-object (300 fibers), high resolution (R = λ/∆λ ̃22,500) spectrograph built for the Apache Point Observatory GalacticEvolution Experiment (APOGEE). APOGEE is a survey of ̃10⁵ redgiant stars that systematically sampled all Milky Way populations(bulge, disk, and halo) to study the Galaxy’s chemical and kinematicalhistory. It was part of the Sloan Digital Sky Survey III (SDSS-III) from2011 to 2014 using the 2.5 m Sloan Foundation Telescope at Apache PointObservatory, New Mexico. The APOGEE-2 survey is now using thespectrograph as part of SDSS-IV, as well as a second spectrograph, aclose copy of the first, operating at the 2.5 m du Pont Telescope at LasCampanas Observatory in Chile. Although several fiber-fed, multi-object,high resolution spectrographs have been built for visual wavelengthspectroscopy, the APOGEE spectrograph is one of the first suchinstruments built for observations in the near-infrared. Theinstrument’s successful development was enabled by several keyinnovations, including a “gang connector” to allow simultaneousconnections of 300 fibers; hermetically sealed feedthroughs to allowfibers to pass through the cryostat wall continuously; the firstcryogenically deployed mosaic volume phase holographic grating; and alarge refractive camera that includes mono-crystalline silicon and fusedsilica elements with diameters as large as ̃400 mm. This paper containsa comprehensive description of all aspects of the instrument includingthe fiber system, optics and opto-mechanics, detector arrays, mechanicsand cryogenics, instrument control, calibration system, opticalperformance and stability, lessons learned, and design changes for thesecond instrument.

We apply an iterative reconstruction method to galaxy mocks in redshiftspace obtained from N-body simulations. Comparing the two-pointcorrelation functions for the reconstructed density field, we find thatalthough the performance is limited by shot noise and galaxy biascompared to the matter field, the iterative method can still reconstructthe initial linear density field from the galaxy field better than thestandard method both in real and in redshift space. Furthermore, theiterative method is able to reconstruct both the monopole and quadrupolemore precisely, unlike the standard method. We see that as the numberdensity of galaxies gets smaller, the performance of reconstruction getsworse due to the sparseness. However, the precision in the determinationof bias ({̃ }20{{ per cent}}) hardly impacts on the reconstructionprocesses.

We probe the higher-order galaxy clustering in the final data release ofthe Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey(BOSS) using germ-grain Minkowski functionals (MFs). Our data selectioncontains 979 430 BOSS galaxies from both the Northern and SouthernGalactic Caps over the redshift range z = 0.2-0.6. We extract thehigher-order part of the MFs, detecting the deviation from the purelyGaussian case with χ ^2 ̃ O(10^3) on 24 degrees of freedom across theentire data selection. We measure significant redshift evolution in thehigher-order functionals for the first time. We find 15-35{{ per cent}}growth, depending on functional and scale, between our redshift binscentred at z = 0.325 and z = 0.525. We show that the structure inhigher-order correlations grows faster than that in the two-pointcorrelations, especially on small scales where the excess approaches afactor of 2. We demonstrate how this trend is generalizable by findinggood agreement of the data with a hierarchical model in which the higherorders grow faster than the lower-order correlations. We find that thenon-Gaussianity of the underlying dark matter field grows even fasterthan the one of the galaxies. Our method can be adapted to study theredshift evolution of the three-point and higher functions individually.

Covariance matrix estimation is a persistent challenge for cosmology,often requiring a large number of synthetic mock catalogues. The off-diagonal components of the covariance matrix also make it difficult toshow representative error bars on the 2-point correlation function(2PCF) since errors computed from the diagonal values of the covariancematrix greatly underestimate the uncertainties. We develop a routine fordecorrelating the projected and anisotropic 2PCF with simple and scale-compact transformations on the 2PCF. These transformation matrices aremodelled after the Cholesky decomposition and the symmetric square rootof the Fisher matrix. Using mock catalogues, we show that thetransformed projected and anisotropic 2PCF recover the same structure asthe original 2PCF while producing largely decorrelated error bars.Specifically, we propose simple Cholesky-based transformation matricesthat suppress the off-diagonal covariances on the projected 2PCF by {̃ }95{{ per cent}} and that on the anisotropic 2PCF by {̃ } 87{{ percent}}. These transformations also serve as highly regularized models ofthe Fisher matrix, compressing the degrees of freedom so that one canfit for the Fisher matrix with a much smaller number of mocks.