[ascl:1211.003]
WVT Binning: Spatially adaptive 2-D binning

WVT Binning is a spatially adaptive 2-dimensional binning algorithm designed to bin sparse X-ray data. It can handle background subtracted, exposure corrected data to produce intensity images, hardness ratio maps, or temperature maps. The algorithm is an extension of Cappellari & Copin's (2003) Voronoi binning code and uses Weighted Voronoi Tesselations (WVT) to produce a very compact binning structure with a constant S/N per bin. The bin size adjusts to the required resolution in single-pixel steps, which minimizes the scatter around the target S/N. The code is very versatile and can in principle be applied to any type of data. The user manual contains instructions on how to apply the WVT binning code to X-ray data and how to extend the algorithm to other problems.

[ascl:1601.019]
WzBinned: Binned and uncorrelated estimates of dark energy EOS extractor

WzBinned extracts binned and uncorrelated estimates of dark energy equation of state w(z) using Type Ia supernovae Hubble diagram and other cosmological probes and priors. It can handle an arbitrary number of input distance modulus data (entered as an input file SNdata.dat) and various existing cosmological information.

[ascl:1312.005]
XAssist: Automatic analysis of X-ray astrophysics data

XAssist provides automation of X-ray astrophysics, specifically data reprocessing, source detection, and preliminary spatial, temporal and spectral analysis for each source with sufficient counts, with an emphasis on galaxies. It has been used for data from Chandra, ROSAT, XMM-Newton, and other various projects.

[ascl:1810.016]
XCLASS: eXtended CASA Line Analysis Software Suite

XCLASS (eXtended CASA Line Analysis Software Suite) extends CASA (ascl:1107.013) with new functions for modeling interferometric and single dish data. It provides a tool for calculating synthetic spectra by solving the radiative transfer equation for an isothermal object in one dimension, taking into account the finite source size and dust attenuation. It also includes an interface for MAGIX (ascl:1303.009) to find the parameter set that most closely reproduces the data.

[ascl:1708.026]
XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling

XDGMM uses Gaussian mixtures to do density estimation of noisy, heterogenous, and incomplete data using extreme deconvolution (XD) algorithms which is compatible with the scikit-learn machine learning methods. It implements both the astroML and Bovy et al. (2011) algorithms, and extends the BaseEstimator class from scikit-learn so that cross-validation methods work. It allows the user to produce a conditioned model if values of some parameters are known.

[ascl:1302.016]
XDQSO: Photometic quasar probabilities and redshifts

Bovy, Jo; Hennawi, Joseph F.; Hogg, David W.; Myers, Adam D.; Kirkpatrick, Jessica A.; Schlegel, David J.; Ross, Nicholas P.; Sheldon, Erin S.; McGreer, Ian D.; Schneider, Donald P.; Weaver, Benjamin A.

XDQSO, written in IDL, calculates photometric quasar probabilities to mimick SDSS-III’s BOSS quasar target selection or photometric redshifts for quasars, whether in three redshift ranges (z < 2.2; 2.2 leq z leq 3.5; z > 3.5) or arbitrary redshift ranges.

[ascl:1107.010]
XDSPRES: CL-based package for Reducing OSIRIS Cross-dispersed Spectra

We present a description of the CL-based package XDSPRES, which aims at being a complete reducing facility for cross-dispersed spectra taken with the Ohio State Infrared Imager/Spectrometer, as installed at the SOAR telescope. This instrument provides spectra in the range between 1.2um and 2.35um in a single exposure, with resolving power of R ~ 1200. XDSPRES consists of two tasks, namely xdflat and doosiris. The former is a completely automated code for preparing normalized flat field images from raw flat field exposures. Doosiris was designed to be a complete reduction pipeline, requiring a minimum of user interaction. General steps towards a fully reduced spectrum are explained, as well as the approach adopted by our code.

[ascl:1112.013]
XEphem: Interactive Astronomical Ephemeris

XEphem is a scientific-grade interactive astronomical ephemeris package for UNIX-like systems. Written in C, X11 and Motif, it is easily ported to systems. XEphem computes heliocentric, geocentric and topocentric information for all objects and has built-in support for all planets, the moons of Mars, Jupiter, Saturn, Uranus and Earth, central meridian longitude of Mars and Jupiter, Saturn's rings, and Jupiter's Great Red Spot. It allows user-defined objects including stars, deepsky objects, asteroids, comets and Earth satellites, provides special efficient handling of large catalogs including Tycho, Hipparcos, GSC, displays data in configurable tabular formats in conjunction with several interactive graphical views, and displays a night-at-a-glance 24 hour graphic showing when any selected objects are up. It also displays 3-D stereo Solar System views that are particularly well suited for visualizing comet trajectories, quickly finds all close pairs of objects in the sky, and sorts and prints all catalogs with very flexible criteria for creating custom observing lists. Its capabilities are listed more fully in the user manual introduction.

[ascl:1502.018]
XFGLENSES: Gravitational lens visualizer

XFGL visualizes gravitational lenses. It has an XFORM GUI and is completely interactive with the mouse. It uses OpenGL for the simulations.

[ascl:1807.031]
xGDS: Exploration Ground Data Systems

xGDS (Exploration Ground Data Systems) synthesizes real world data (from sensors, robots, ROVs, mobile devices, etc) and human observations into rich, digital maps and displays for analysis, decision making, and collaboration. xGDS processes and maps data (including video) in real-time during operations and uses it to support live role-based geolocated note taking. Notes can be used to search for and display important data. The software enables real-time analysis of data, permitting one to make inferences and plan new data collection operations while still in the field.

[ascl:1511.004]
Xgremlin: Interferograms and spectra from Fourier transform spectrometers analysis

Xgremlin is a hardware and operating system independent version of the data analysis program Gremlin used for Fourier transform spectrometry. Xgremlin runs on PCs and workstations that use the X11 window system, including cygwin in Windows. It is used to Fourier transform interferograms, plot spectra, perform phase corrections, perform intensity and wavenumber calibration, and find and fit spectral lines. It can also be used to construct synthetic spectra, subtract continua, compare several different spectra, and eliminate ringing around lines.

[ascl:1704.012]
XID+: Next generation XID development

XID+ is a prior-based source extraction tool which carries out photometry in the Herschel SPIRE (Spectral and Photometric Imaging Receiver) maps at the positions of known sources. It uses a probabilistic Bayesian framework that provides a natural framework in which to include prior information, and uses the Bayesian inference tool Stan to obtain the full posterior probability distribution on flux estimates.

[ascl:1303.021]
Xmatch: GPU Enhanced Astronomic Catalog Cross-Matching

Xmatch is a cross-platform, multi-GPU tool which allows for extremely fast cross-matching between two Astronomic catalogs. It is capable of asyncronously managing multiple GPUs, ideal for workstation and cluster environments.

[ascl:1402.020]
XNS: Axisymmetric equilibrium configuration of neutron stars

XNS solves for the axisymmetric equilibrium configuration of neutron stars in general relativity. It can model differentially rotating and magnetic fields that are either purely toroidal, purely poloidal or in the mixed twisted torus configuration. Einsten's equations are solved using the XCFC approximation for the metric in spherical coordinates.

[ascl:1502.019]
XPCell: Convective plasma cells simulator

XPCell simulates convective plasma cells. The program is implemented in two versions, one using GNUPLOT and the second OpenGL. XPCell offers a GUI to introduce the parameter required by the program.

[ascl:1212.002]
XPHOT: Estimation of properties of weak X-ray sources

XPHOT is an IDL implementation of a non-parametric method for estimating the apparent and intrinsic broad-band fluxes and absorbing X-ray column densities of weak X-ray sources. XPHOT is intended for faint sources with greater than ∼5-7 counts but fewer than 100-300 counts where parametric spectral fitting methods will be superior. This method is similar to the long-standing use of color-magnitude diagrams in optical and infrared astronomy, with X-ray median energy replacing color index and X-ray source counts replacing magnitude. Though XPHOT was calibrated for thermal spectra characteristic of stars in young stellar clusters, recalibration should be possible for some other classes of faint X-ray sources such as extragalactic active galactic nuclei.

[ascl:1509.001]
XSHPipelineManager: Wrapper for the VLT/X-shooter Data Reduction Pipeline

XSHPipelineManager provides a framework for reducing spectroscopic observations taken by the X-shooter spectrograph at the Very Large Telescope. This Python code wraps recipes developed by the European Southern Observatory and runs the full X-shooter data reduction pipeline. The code offers full flexibility in terms of what data reduction recipes to include and which calibration files to use. During the data reduction chain restart-files are saved, making it possible to restart at any step in the chain.

[submitted]
Xsmurf - Measuring multifractal properties with the continuous wavelet transform modulus maxima (WTMM) method

Xsmurf is a software package written in C/Tcl/Tk that implements the continuous wavelet transform modulus maxima method, an image processing tool for measuring fractal and multifractal properties in experimental and simulation data.

Multifractal analysis is described in the following page: http://www.scholarpedia.org/article/Wavelet-based_multifractal_analysis

Xsmurf has been used in multiple applications in astrophysics, e.g. :

- analysis of solar magnetograms for characterizing complexity of evolving regions

- fractal/multifractal nature and anisotropic structure of Galactic atomic hydrogen (H I)

- analysis of simulation data (velocity field, ...) of turbulent flow

[ascl:1207.008]
xSonify: Sonification software

xSonify maps scientific data to acoustic sequences. Listening to data can help discover patterns in huge amounts of data. Written in Java, xSonify allows visually impaired people to examine numerical data for patterns. The data can be imported from local files or from remote databases via the Internet. Single results of measurements from spacecraft instruments can be selected by their corresponding variables in a specific time frame. The results are transformed into MIDI sequences which can be played with a selection of different instruments from a soundbank. Another software module enables xSonify to convert the sonified data into other sound formats to make it easier to archive and exchange the Sonification results with other scientists.

[ascl:1805.016]
xspec_emcee: XSPEC-friendly interface for the emcee package

XSPEC_EMCEE is an XSPEC-friendly interface for emcee (ascl:1303.002). It carries out MCMC analyses of X-ray spectra in the X-ray spectral fitting program XSPEC (ascl:9910.005). It can run multiple xspec processes simultaneously, speeding up the analysis, and can switch to parameterizing norm

parameters in log space.

[ascl:9910.005]
XSPEC: An X-ray spectral fitting package

It has been over a decade since the first paper was published containing results determined using the general X-ray spectral-fitting program XSPEC. Since then XSPEC has become the most widely used program for this purpose, being the de facto standard for the ROSAT and the de jure standard for the ASCA and XTE satellites. Probably the most important features of XSPEC are the large number of theoretical models available and the facilities for adding new models.

[ascl:9910.008]
XSTAR: A program for calculating conditions and spectra of photoionized gases

XSTAR is a command-driven, interactive, computer program for calculating the physical conditions and emission spectra of photoionized gases. It may be applied in a wide variety of astrophysical contexts. Stripped to essentials, its job may be described simply: A spherical gas shell surrounding a central source of ionizing radiation absorbs some of this radiation and reradiates it in other portions of the spectrum; XSTAR computes the effects on the gas of absorbing this energy, and the spectrum of reradiated light. The user supplies the shape and strength of the incident continuum, the elemental abundances in the gas, its density or pressure, and its thickness; the code can be directed to return any of a large number of derived quantities, including (but not limited to) the ionization balance and temperature, opacity tables, and emitted line and continuum fluxes.

[ascl:1306.016]
Yaxx: Yet another X-ray extractor

Yaxx is a Perl script that facilitates batch data processing using Perl open source software and commonly available software such as CIAO/Sherpa, S-lang, SAS, and FTOOLS. For Chandra and XMM analysis it includes automated spectral extraction, fitting, and report generation. Yaxx can be run without climbing an extensive learning curve; even so, yaxx is highly configurable and can be customized to support complex analysis. yaxx uses template files and takes full advantage of the unique Sherpa / S-lang environment to make much of the processing user configurable. Although originally developed with an emphasis on X-ray data analysis, yaxx evolved to be a general-purpose pipeline scripting package.

[ascl:1305.008]
YNOGK: Calculating null geodesics in the Kerr spacetime

YNOGK, written in Fortran, calculates the null geodesics in the Kerr spacetime. It uses Weierstrass' and Jacobi's elliptic functions to express all coordinates and affine parameters as analytical and numerical functions of a parameter $p$, which is an integral value along the geodesic. The information about the turning points do not need to be specified in advance by the user, allowing applications such as imaging, the calculation of line profiles or the observer-emitter problem to become root finding problems. Elliptic integrations are computed by Carlson's elliptic integral method, which allows fast computation.

[ascl:1403.012]
YNOGKM: Time-like geodesics in the Kerr-Newmann Spacetime calculations

YNOGKM (Yun-Nan observatories geodesic in a Kerr-Newman spacetime for massive particles) performs fast calculation of time-like geodesics in the Kerr-Newman (K-N) spacetime; it is a direct extension of YNOGK (Yun-Nan observatories geodesic Kerr) calculating null geodesics in a Kerr spacetime. The four Boyer-Lindquis coordinates and proper time are expressed as functions of a parameter p semi-analytically by using the Weierstrass' and Jacobi's elliptic functions and integrals. The elliptic integrals are computed by Carlson's elliptic integral method, which guarantees the fast speed of the code. The source Fortran file ynogkm.f90 contains three modules: constants, rootfind, ellfunction, and blcoordinates.

[ascl:1312.009]
YODA: Yet another Object Detection Application

YODA, implemented in C++, performs object detection, photometry and star-galaxy classification on astronomical images. Developed specifically to cope with the multi-band imaging data common in modern extragalactic imaging surveys, it is modular and therefore easily adaptable to specific needs. YODA works under conditions of inhomogeneous background noise across the detection frame, and performs accurate aperture photometry in image sets not sharing a common coordinate system or pixel scale as is often the case in present-day extragalactic survey work.

[ascl:1203.010]
Youpi: YOUr processing PIpeline

Youpi is a portable, easy to use web application providing high level functionalities to perform data reduction on scientific FITS images. Built on top of various open source reduction tools released to the community by TERAPIX (http://terapix.iap.fr), Youpi can help organize data, manage processing jobs on a computer cluster in real time (using Condor) and facilitate teamwork by allowing fine-grain sharing of results and data. Youpi is modular and comes with plugins which perform, from within a browser, various processing tasks such as evaluating the quality of incoming images (using the QualityFITS software package), computing astrometric and photometric solutions (using SCAMP), resampling and co-adding FITS images (using SWarp) and extracting sources and building source catalogues from astronomical images (using SExtractor). Youpi is useful for small to medium-sized data reduction projects; it is free and is published under the GNU General Public License.

[ascl:1011.022]
yt: A Multi-Code Analysis Toolkit for Astrophysical Simulation Data

yt is an open source, community-developed volumetric analysis and visualization toolkit. Originally designed for handling Enzo's (ascl:1010.072) structure adaptive mesh refinement (AMR) data, yt has been extended to work with numerous simulation methods and simulation codes including Orion, RAMSES (ascl:1011.007), and FLASH (ascl:1010.082). Analysis and visualization with yt are oriented around physically relevant quantities rather than quantities native to data representation on-disk or in-memory. yt can be used for projections, multivariate volume rendering, multi-dimensional histograms, halo finding, light cone generation and topologically-connected isocontour identification.

yt benefits from the contributions of a broad range of community members, and a full list of credits for the code can be found on the yt website or in the source repository.

[ascl:1602.003]
ZAP: Zurich Atmosphere Purge

ZAP (Zurich Atmosphere Purge) provides sky subtraction for integral field spectroscopy; its approach is based on principal component analysis (PCA) developed for the Multi Unit Spectrographic Explorer (MUSE) integral field spectrograph. ZAP employs filtering and data segmentation to enhance the inherent capabilities of PCA for sky subtraction. ZAP reduces sky emission residuals while robustly preserving the flux and line shapes of astronomical sources; this method works in a variety of observational situations from sparse fields with a low density of sources to filled fields in which the target source fills the field of view. With the inclusion of both of these situations the method is generally applicable to many different science cases and should also be useful for other instrumentation.

[ascl:1607.012]
ZASPE: Zonal Atmospheric Stellar Parameters Estimator

ZASPE (Zonal Atmospheric Stellar Parameters Estimator) computes the atmospheric stellar parameters (Teff, log(g), [Fe/H] and vsin(i)) from echelle spectra via least squares minimization with a pre-computed library of synthetic spectra. The minimization is performed only in the most sensitive spectral zones to changes in the atmospheric parameters. The uncertainities and covariances computed by ZASPE assume that the principal source of error is the systematic missmatch between the observed spectrum and the sythetic one that produces the best fit. ZASPE requires a grid of synthetic spectra and can use any pre-computed library minor modifications.

[ascl:1807.017]
ZBARYCORR: Barycentric redshift calculator

ZBARYCORR determines the barycentric redshift (*z _{B}*) for a given star. It calculates the positions and velocities of solar system objects, applies the rotation, precession, nutation, and polar motion of the Earth, applies the stellar motion using the Markwardt library (ascl:1807.016), Shapiro delay, and light-travel term, and finally calculates the quantity

[ascl:1404.002]
ZDCF: Z-Transformed Discrete Correlation Function

The cross-correlation function (CCF) is commonly employed in the study of AGN, where it is used to probe the structure of the broad line region by line reverberation, to study the continuum emission mechanism by correlating multi-waveband light curves and to seek correlations between the variability and other AGN properties. The z -transformed discrete correlation function (ZDCF) is a method for estimating the CCF of sparse, unevenly sampled light curves. Unlike the commonly used interpolation method, it does not assume that the light curves are smooth and it does provide errors on its estimates.

[ascl:1110.005]
ZEBRA: Zurich Extragalactic Bayesian Redshift Analyzer

The current version of the Zurich Extragalactic Bayesian Redshift Analyzer (ZEBRA) combines and extends several of the classical approaches to produce accurate photometric redshifts down to faint magnitudes. In particular, ZEBRA uses the template-fitting approach to produce Maximum Likelihood and Bayesian redshift estimates based on: (1.) An automatic iterative technique to correct the original set of galaxy templates to best represent the SEDs of real galaxies at different redshifts; (2.) A training set of spectroscopic redshifts for a small fraction of the photometric sample; and (3.) An iterative technique for Bayesian redshift estimates, which extracts the full two-dimensional redshift and template probability function for each galaxy.

[ascl:1605.016]
zeldovich-PLT: Zel'dovich approximation initial conditions generator

zeldovich-PLT generates Zel'dovich approximation (ZA) initial conditions (i.e. first-order Lagrangian perturbation theory) for cosmological N-body simulations, optionally applying particle linear theory (PLT) corrections.

[ascl:1512.016]
ZeldovichRecon: Halo correlation function using the Zeldovich approximation

ZeldovichRecon computes the halo correlation function using the Zeldovich approximation. It includes 3 variants:

- zelrecon.cpp, which computes the various contributions to the correlation function;

- zelrecon_ctypes.cpp, which is designed to be called from Python using the ctypes library; and

- a version which implements the "ZEFT" formalism of "A Lagrangian effective field theory" [arxiv:1506.05264] including the alpha term described in that paper.

[ascl:1102.027]
ZENO: N-body and SPH Simulation Codes

The ZENO software package integrates N-body and SPH simulation codes with a large array of programs to generate initial conditions and analyze numerical simulations. Written in C, the ZENO system is portable between Mac, Linux, and Unix platforms. It is in active use at the Institute for Astronomy (IfA), at NRAO, and possibly elsewhere.

Zeno programs can perform a wide range of simulation and analysis tasks. While many of these programs were first created for specific projects, they embody algorithms of general applicability and embrace a modular design strategy, so existing code is easily applied to new tasks. Major elements of the system include structured data file utilities facilitate basic operations on binary data, including import/export of ZENO data to other systems; snapshot generation routines to create particle distributions with various properties; systems with user-specified density profiles can be realized in collisionless or gaseous form; multiple spherical and disk components may be set up in mutual equilibrium; and snapshot manipulation routines permit the user to sift, sort, and combine particle arrays, translate and rotate particle configurations, and assign new values to data fields associated with each particle.

Simulation codes include both pure N-body and combined N-body/SPH programs. Pure N-body codes are available in both uniprocessor and parallel versions. SPH codes offer a wide range of options for gas physics, including isothermal, adiabatic, and radiating models. Snapshot analysis programs calculate temporal averages, evaluate particle statistics, measure shapes and density profiles, compute kinematic properties, and identify and track objects in particle distributions. Visualization programs generate interactive displays and produce still images and videos of particle distributions; the user may specify arbitrary color schemes and viewing transformations.

[ascl:1306.014]
ZEUS-2D: Simulation of fluid dynamical flows

ZEUS-2D is a hydrodynamics code based on ZEUS which adds a covariant differencing formalism and algorithms for compressible hydrodynamics, MHD, and radiation hydrodynamics (using flux-limited diffusion) in Cartesian, cylindrical, or spherical polar coordinates.

[ascl:1102.028]
ZEUS-MP/2: Computational Fluid Dynamics Code

Hayes, John C.; Norman, Michael L.; Fiedler, Robert A.; Bordner, James O.; Li, Pak Shing; Clark, Stephen E.; Ud-Doula, Asif; Mac Low, Mordecai-Mark

ZEUS-MP is a multiphysics, massively parallel, message-passing implementation of the ZEUS code. ZEUS-MP offers an MHD algorithm that is better suited for multidimensional flows than the ZEUS-2D module by virtue of modifications to the method of characteristics scheme first suggested by Hawley & Stone. This MHD module is shown to compare quite favorably to the TVD scheme described by Ryu et al. ZEUS-MP is the first publicly available ZEUS code to allow the advection of multiple chemical (or nuclear) species. Radiation hydrodynamic simulations are enabled via an implicit flux-limited radiation diffusion (FLD) module. The hydrodynamic, MHD, and FLD modules can be used, singly or in concert, in one, two, or three space dimensions. In addition, so-called 1.5D and 2.5D grids, in which the "half-D'' denotes a symmetry axis along which a constant but nonzero value of velocity or magnetic field is evolved, are supported. Self-gravity can be included either through the assumption of a GM/r potential or through a solution of Poisson's equation using one of three linear solver packages (conjugate gradient, multigrid, and FFT) provided for that purpose. Point-mass potentials are also supported.

Because ZEUS-MP is designed for large simulations on parallel computing platforms, considerable attention is paid to the parallel performance characteristics of each module in the code. Strong-scaling tests involving pure hydrodynamics (with and without self-gravity), MHD, and RHD are performed in which large problems (2563 zones) are distributed among as many as 1024 processors of an IBM SP3. Parallel efficiency is a strong function of the amount of communication required between processors in a given algorithm, but all modules are shown to scale well on up to 1024 processors for the chosen fixed problem size.

[ascl:1511.022]
ZInCo: Zoomed Initial Conditions

ZInCo manipulates existing initial conditions (ICs) compatible with GADGET-2/3 (ascl:0003.001) ICs, allowing different flavors of zoom-in simulations rather then producing new ICs from scratch. The code can manipulate initial conditions with multiple types of particles, unlike the vast majority of zoom-in ICs codes available, preserving their properties and random field. This allows ZInCo to take advantage of other codes that produce ICs featuring a broad range of different cosmologies; it can be used also on existing ICs even in the unlikely case nothing is known about their properties. The code is written in C++ and parallelized using MPI.

[ascl:1202.002]
ZODIPIC: Zodiacal Cloud Image Synthesis

ZODIPIC synthesizes images of exozodiacal clouds. As a default, ZODIPIC creates an image of the solar zodiacal cloud as seen from 10 pc, but it contains many parameters that are tweakable from the command line, making it a handy general-purpose model for optically-thin debris disks that yields both accurate images and photometric information simultaneously. Written in IDL, ZODIPIC includes dust with real optical constants, user-specified dust maps and can compute images as seen through a linear polarizer.

[ascl:1011.003]
ZPEG: An Extension of the Galaxy Evolution Model PEGASE.2

Photometric redshifts are estimated on the basis of template scenarios with the help of the code ZPEG, an extension of the galaxy evolution model PEGASE.2 and available on the PEGASE web site. The spectral energy distribution (SED) templates are computed for nine spectral types including starburst, irregular, spiral and elliptical. Dust, extinction and metal effects are coherently taken into account, depending on evolution scenarios. The sensitivity of results to adding near-infrared colors and IGM absorption is analyzed. A comparison with results of other models without evolution measures the evolution factor which systematically increases the estimated photometric redshift values by $Delta z$ > 0.2 for z > 1.5. Moreover we systematically check that the evolution scenarios match observational standard templates of nearby galaxies, implying an age constraint of the stellar population at z=0 for each type. The respect of this constraint makes it possible to significantly improve the accuracy of photometric redshifts by decreasing the well-known degeneracy problem. The method is applied to the HDF-N sample. From fits on SED templates by a $chi^2$-minimization procedure, not only is the photometric redshift derived but also the corresponding spectral type and the formation redshift $z_for$ when stars first formed. Early epochs of galaxy formation z > 5 are found from this new method and results are compared to faint galaxy count interpretations.

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