Narrow Redshift Bins Research Articles

From VIPERS to SDSS: Unveiling galaxy spectra evolution over 9 Gyr through unsupervised machine learning

Aims. This study aims to trace the chronological evolution of galaxy spectra over cosmic time. Focusing on the VIPERS dataset, we seek to understand the diverse population of galaxies within narrow redshift bins, comparing our findings with the previously mapped diversity of SDSS galaxies. Methods. We used Fisher-EM, an unsupervised sub-space model-based classification algorithm to classify a dataset of 79 224 galaxy spectra from the VIMOS Public Extragalactic Redshift Survey (VIPERS). The dataset was divided into 26 samples by bins of redshift ranging from z ∼ 0.4 to z ∼ 1.2, which were classified independently. Classes of subsequent bins were linked through the k-nearest neighbours method to create a chronological tree of classes at different epochs. Results. Based on the optical spectra, three main chronological galaxy branches emerged: (i) red passive, (ii) blue star forming, and (iii) very blue, possibly associated with AGN activity. Each of the branches differentiates into sub-branches, discriminating finer properties such as D4000 break, colour, star-formation rate, and stellar masses, and/or disappear with cosmic time. Notably, these classes align remarkably well with the branches identified in a previous SDSS analyses, indicating a robust and consistent classification across datasets. The chronological ‘tree’ constructed from VIPERS data provides valuable insights into the temporal evolution of these spectral classes. Conclusions. The synergy between VIPERS and SDSS datasets enhances our understanding of the evolutionary pathways of galaxy spectra. The remarkable correspondence between independently derived branches in both datasets underscores the reliability of our unsupervised machine-learning approach. The three sub-trees show complex branching structures that highlight different physical and evolutionary behaviours. This study contributes to the broader comprehension of galaxy evolution by providing a chronologically organised framework for interpreting optical spectra within specific redshift ranges.

Tomographic cross correlations between galaxy surveys and the CMB gravitational lensing potential. Effect of the redshift bin mismatch

Upcoming surveys of the large-scale structure of our Universe will employ a large coverage area of about half of the sky and will significantly increase the observational depth. With these surveys, we will be able to cross-correlate cosmic microwave background (CMB) gravitational lensing and galaxy surveys divided into narrow redshift bins to map the evolution of the cosmological parameters with redshift. We study the effect of the redshift bin mismatch of objects that is due to photometric redshift errors in tomographic cross-correlation measurements. We used the code FLASK to create Monte Carlo simulations of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and Planck CMB lensing convergence. We simulated log-normal fields and divided galaxies into nine redshift bins with the Gaussian and modified Lorentzian photometric redshift errors. To estimate the parameters, we used angular power spectra of CMB lensing and galaxy density contrast fields and the maximum likelihood estimation method. We show that even with simple Gaussian errors with a standard deviation of $ the galaxy auto-power spectra in tomographic bins are offset by $2-15<!PCT!>$. The estimated cross-power spectra between galaxy clustering and CMB lensing are also biased, with smaller deviations $<5<!PCT!>$. As a result, the $ $ parameter deviates between $0.2-1.2\ due to the redshift bin mismatch of the objects. We propose a computationally fast and robust method based on the scattering matrix approach to correct for the redshift bin mismatch of the objects. The estimates of the parameters in tomographic studies such as the linear galaxy bias, the cross-correlation amplitude, and $ $ are biased due to the redshift bin mismatch of the objects. The biases in these parameters are alleviated with our scattering matrix approach.

Can the Distance‒Redshift Relation be Determined from Correlations between Luminosities?

We explore whether an independent determination of the distance‒redshift relation, and hence cosmological model parameters, can be obtained from the apparent correlations between two different wave-band luminosities or fluxes, as has been claimed in recent works using the X-ray and ultraviolet luminosities and fluxes of quasars. We show that such an independent determination is possible only if the correlation between luminosities is obtained independently of the cosmological model and measured fluxes and redshifts, for example, based on sound theoretical models or unrelated observations. In particular, we show that if the correlation is determined empirically for two luminosities obtained from fluxes and redshifts, then the method suffers from circularity. In the case where the observed correlation between fluxes in very narrow redshift bins is used as a proxy for the luminosity correlation, we show that one is dealing with a pure tautology with no information on distances and cosmological model. We argue that the problem arises because of the incomplete treatment of the correlation, and we use numerical methods with a joint X-ray and ultraviolet quasar data set to demonstrate this shortcoming.

Speeding up the detectability of the harmonic-space galaxy bispectrum

We present a method that allows us for the first time to estimate the signal-to-noise ratio (SNR) of the harmonic-space galaxy bispectrum induced by gravity, a complementary probe to already well established Fourier-space clustering analyses. We show how to do it considering only ∼1000 triangle configurations in multipole space, corresponding to a computational speedup of a factor \U0001d4aa(102)−\U0001d4aa(103), depending on the redshift bin, when including mildly non-linear scales. Assuming observational specifications consistent with forthcoming spectroscopic and photometric galaxy surveys like the \\euc\\ satellite and the Square Kilometre Array (phase 1), we show: that given a single redshift bin, spectroscopic surveys outperform photometric surveys; and that—due to shot-noise and redshift bin width balance—bins at redshifts z∼1 bring higher cumulative SNR than bins at lower redshifts z ∼ 0.5. Our results for the largest cumulative SNR ∼ 15 suggest that the harmonic-space bispectrum is detectable within narrow (Δ z ∼ 0.01) spectroscopic redshift bins even when including only mildly non-linear scales. Tomographic reconstructions and inclusion of highly non-linear scales will further boost detectability with upcoming galaxy surveys. In addition, we discuss how, using the Karhunen-Loève transform, a detection analysis only requires a 1 × 1 covariance matrix for a single redshift bin.

Nonlinear contributions to angular power spectra

Future galaxy clustering surveys will probe small scales where non-linearities become important. Since the number of modes accessible on intermediate to small scales is very high, having a precise model at these scales is important especially in the context of discriminating alternative cosmological models from the standard one. In the mildly non-linear regime, such models typically differ from each other, and galaxy clustering data will become very precise on these scales in the near future. As the observable quantity is the angular power spectrum in redshift space, it is important to study the effects of non-linear density and redshift space distortion (RSD) in the angular power spectrum. We compute non-linear contributions to the angular power spectrum using a flat-sky approximation that we introduce in this work, and compare the results of different perturbative approaches with $N$-body simulations. We find that the TNS perturbative approach is significantly closer to the $N$-body result than Eulerian or Lagrangian 1-loop approximations, effective field theory of large scale structure or a halofit-inspired model. However, none of these prescriptions is accurate enough to model the angular power spectrum well into the non-linear regime. In addition, for narrow redshift bins, $\Delta z \lesssim 0.01$, the angular power spectrum acquires non-linear contributions on all scales, right down to $\ell=2$, and is hence not a reliable tool at this time. To overcome this problem, we need to model non-linear RSD terms, for example as TNS does, but for a matter power spectrum that remains reasonably accurate well into the deeply non-linear regime, such as halofit.

The Angular Fractal Dimension in Galaxy’s Distributions

The study of large scale structure (LSS) of the Universe has entered a precision era due to all-sky surveys and numerical simulations. The new data has provided a way to bring new methods to bear to analyze the cosmology as probed by large scale structure. We use wavelet packets to investigate fractal point-processes on galactic scales. In particular, we develop a method to calculate the angular fractal dimension of galaxy distributions as a function of cosmological comoving distance. Taking advantage of the self-similarity and localization properties of discrete wavelets, we compute the angular fractal dimension of galaxies in narrow redshift bins. The narrow bins assure that dynamical evolution in the range being studied has not occurred to a significant extent. We use both real and simulated data from the Baryon Oscillation Spectroscopic Survey (BOSS) and the Mock Galaxy Catalogs produced by the Sloan Digital Sky Survey (SDSS). Using the wavelet packet power spectrum, we find areas in the galaxy distribution which have power law like behavior indicating fractal processes are present. The exponent of the power law is the Hurst exponent H, which is directly related to the fractal dimension of spatial point processes. We find the fractal dimension ranges from D = 1.1 to D = 1.4 for BOSS Galaxies while it ranges from D = 1.4 to D = 1.8 for Mock Galaxy Catalogs. The results are mildly dependent on the number of galaxies present in each redshift bin and less so on the resolution at which the data is binned. We conclude that this method can be used to characterize large scale structure and its evolution as a function of redshift. There are hints that the galaxy distribution may be fractal at higher redshifts than previously reported, however more data is necessary before a firmer conclusion is reached.

The full-sky angular bispectrum in redshift space

We compute the redshift-dependent angular bispectrum of galaxy number counts at tree-level, including nonlinear clustering bias and estimating numerically for the first time the effect of redshift space distortions (RSD). We show that for narrow redshift bins the amplitude of nonlinear RSD is comparable with the matter density perturbations. While our numerical results only include terms relevant on sub-horizon scales, the formalism can readily be extended to the full tree-level bispectrum. Our approach does not rely on the flat-sky approximation and it can be easily generalized to different sources by including the appropriate bias expansion. We test the accuracy of Limber approximation for different z-bins. We highlight the subtle but relevant differences in the angular bispectrum of galaxy number counts with respect to CMB, due to the different scale dependence of perturbations. Our formalism can also be directly applied to the angular HI intensity mapping bispectrum.

Combining spectroscopic and photometric surveys using angular cross-correlations – III. Galaxy bias and stochasticity

In the first paper of this series, we studied the effect of baryon acoustic oscillations (BAO), redshift space distortions (RSD) and weak lensing (WL) on measurements of angular cross-correlations in narrow redshift bins. Paper-II presented a multitracer forecast as Figures of Merit (FoM), combining a photometric and spectroscopic stage-IV survey. The uncertainties from galaxy bias, the way light traces mass, is an important ingredient in the forecast. Fixing the bias would increase our FoM equivalent to 3.3 times larger area for the combined constraints. This paper focus on how the modelling of bias affect these results. In the combined forecast, lensing both help and benefit from the improved bias measurements in overlapping surveys after marginalizing over the cosmological parameters. Adding a second lens population in counts-shear does not have a large impact on bias error, but removing all counts-shear information increases the bias error in a significant way. We also discuss the relative impact of WL, magnification, RSD and BAO, and how results change as a function of bias amplitude, photo-z error and sample density. By default we use one bias parameter per bin (with 72 narrow bins), but we show that the results do not change much when we use other parameterizations, with at least 3 parameters in total. Bias stochasticity, even when added as one new free parameter per bin, only produce moderate decrease in the FoM. In general, we find that the degradation in the figure of merit caused by the uncertainties in the knowledge of bias is significantly smaller for overlapping surveys.

Cosmological constraints from multiple tracers in spectroscopic surveys

We use the Fisher matrix formalism to study the expansion and growth history of the Universe using galaxy clustering with 2D angular cross-correlation tomography in spectroscopic or high resolution photometric redshift surveys. The radial information is contained in the cross correlations between narrow redshift bins. We show how multiple tracers with redshift space distortions cancel sample variance and arbitrarily improve the constraints on the dark energy equation of state $\omega(z)$ and the growth parameter $\gamma$ in the noiseless limit. The improvement for multiple tracers quickly increases with the bias difference between the tracers, up to a factor $\sim4$ in $\text{FoM}_{\gamma\omega}$. We model a magnitude limited survey with realistic density and bias using a conditional luminosity function, finding a factor 1.3-9.0 improvement in $\text{FoM}_{\gamma\omega}$ -- depending on global density -- with a split in a halo mass proxy. Partly overlapping redshift bins improve the constraints in multiple tracer surveys a factor $\sim1.3$ in $\text{FoM}_{\gamma\omega}$. This findings also apply to photometric surveys, where the effect of using multiple tracers is magnified. We also show large improvement on the FoM with increasing density, which could be used as a trade-off to compensate some possible loss with radial resolution.

Blending bias impacts the host halo masses derived from a cross-correlation analysis of bright submillimetre galaxies

Placing bright sub-millimetre galaxies (SMGs) within the broader context of galaxy formation and evolution requires accurate measurements of their clustering, which can constrain the masses of their host dark matter halos. Recent work has shown that the clustering measurements of these galaxies may be affected by a `blending bias,' which results in the angular correlation function of the sources extracted from single-dish imaging surveys being boosted relative to that of the underlying galaxies. This is due to confusion introduced by the coarse angular resolution of the single-dish telescope and could lead to the inferred halo masses being significantly overestimated. We investigate the extent to which this bias affects the measurement of the correlation function of SMGs when it is derived via a cross-correlation with a more abundant galaxy population. We find that the blending bias is essentially the same as in the auto-correlation case and conclude that the best way to reduce its effects is to calculate the angular correlation function using SMGs in narrow redshift bins. Blending bias causes the inferred host halo masses of the SMGs to be overestimated by a factor of $\sim6$ when a redshift interval of $\delta z=3$ is used. However, this reduces to a factor of $\sim2$ for $\delta z=0.5$. The broadening of photometric redshift probability distributions with increasing redshift can therefore impart a mild halo `downsizing' effect onto the inferred host halo masses, though this trend is not as strong as seen in recent observational studies.

Galaxy clustering with photometric surveys using PDF redshift information

Photometric surveys produce large-area maps of the galaxy distribution, but with less accurate redshift information than is obtained from spectroscopic methods. Modern photometric redshift (photo-z) algorithms use galaxy magnitudes, or colors, that are obtained through multi-band imaging to produce a probability density function (PDF) for each galaxy in the map. We used simulated data to study the effect of using different photo-z estimators to assign galaxies to redshift bins in order to compare their effects on angular clustering and galaxy bias measurements. We found that if we use the entire PDF, rather than a single-point (mean or mode) estimate, the deviations are less biased, especially when using narrow redshift bins. When the redshift bin widths are $\Delta z=0.1$, the use of the entire PDF reduces the typical measurement bias from 5%, when using single point estimates, to 3%.

Combining spectroscopic and photometric surveys using angular cross-correlations – I. Algorithm and modelling

Weak lensing (WL) clustering is studied using 2D (angular) coordinates, while redshift space distortions (RSD) and baryon acoustic oscillations (BAO) use 3D coordinates, which requires a model dependent conversion of angles and redshifts into comoving distances. This is the first paper of a series, which explore modelling multi-tracer galaxy clustering (of WL, BAO and RSD), using only angular (2D) cross-correlations in thin redshift bins. This involves evaluating many thousands cross-correlations, each a multidimensional integral, which is computationally demanding. We present a new algorithm that performs these calculations as matrix operations. Nearby narrow redshift bins are intrinsically correlated, which can be used to recover the full (radial) 3D information. We show that the Limber approximation does not work well for this task. In the exact calculation, both the clustering amplitude and the RSD effect increase when decreasing the redshift bin width. For narrow bins, the cross-correlations has a larger BAO peak than the auto-correlation because smaller scales are filtered out by the radial redshift separation. Moreover, the BAO peak shows a second (ghost) peak, shifted to smaller angles. We explore how WL, RSD and BAO contribute to the cross-correlations as a function of the redshift bin width and present a first exploration of non-linear effects and signal-to-noise ratio on these quantities. This illustrates that the new approach to clustering analysis provides new insights and is potentially viable in practice.

Combining spectroscopic and photometric surveys using angular cross-correlations – II. Parameter constraints from different physical effects

Future spectroscopic and photometric surveys will measure accurate positions and shapes of an increasing number of galaxies. In the previous paper of this series we studied the effects of Redshift Space Distortions (RSD), baryon acoustic oscillations (BAO) and Weak gravitational Lensing (WL) using angular cross-correlation. Here, we provide a new forecast that explores the contribution of including different observables, physical effects (galaxy bias, WL, RSD, BAO) and approximations (non-linearities, Limber approximation, covariance between probes). The radial information is included by using the cross-correlation of separate narrow redshift bins. For the auto correlation the separation of galaxy pairs is mostly transverse, while the cross-correlations also includes a radial component. We study how this information adds to our figure of merit (FoM), which includes the dark energy equation of state $w(z)$ and the growth history, parameterized by $\gamma$. We show that the Limber approximation and galaxy bias are the most critical ingredients to the modelling of correlations. Adding WL increases our FoM by 4.8, RSD by 2.1 and BAO by 1.3. We also explore how overlapping surveys perform under the different assumption and for different figures of merit. Our qualitative conclusions depend on the survey choices and scales included, but we find some clear tendencies that highlight the importance of combining different probes and can be used to guide and optimise survey strategies.

THE NUMBER DENSITY OF QUIESCENT COMPACT GALAXIES AT INTERMEDIATE REDSHIFT

Massive compact systems at 0.2<z<0.6 are the missing link between the predominantly compact population of massive quiescent galaxies at high redshift and their analogs and relics in the local volume. The evolution in number density of these extreme objects over cosmic time is the crucial constraining factor for the models of massive galaxy assembly. We select a large sample of ~200 intermediate-redshift massive compacts from the BOSS spectroscopic dataset by identifying point-like SDSS photometric sources with spectroscopic signatures of evolved redshifted galaxies. A subset of our targets have publicly available high-resolution ground-based images that we use to augment the dynamical and stellar population properties of these systems by their structural parameters. We confirm that all BOSS compact candidates are as compact as their high-redshift massive counterparts and less than half the size of similarly massive systems at z~0. We use the completeness-corrected numbers of BOSS compacts to compute lower limits on their number densities in narrow redshift bins spanning the range of our sample. The abundance of extremely dense quiescent galaxies at 0.2<z<0.6 is in excellent agreement with the number densities of these systems at high redshift. Our lower limits support the models of massive galaxy assembly through a series of minor mergers over the redshift range 0<z<2.

Cross-correlating spectroscopic and photometric galaxy surveys

AbstractDoes photometric and spectroscopic survey benefit from overlapping areas? The photometric survey measures 2D Weak Lensing (WL) information from galaxy shape distortions. On the other hand, the higher redshift precision of an spectroscopic survey allows measurements of redshift space distortions (RSD) and baryonic accustic oscillations (BAO) from 3D galaxy counts.The two surveys are combined using 2D-correlations, using sufficiently narrow bins to capture the radial information. This poster present effects of RSD and intrinsic correlations between narrow redshift bins. In understanding how the effects affects cosmological constrains, we first define two stage-IV and then present forecast for various configurations. When surveys overlap, they benefit from additional cross-correlations and sample variance cancellations from overlapping volumes. For a combined dark energy and growth history figure of merit, the result increase 50% for overlapping surveys, corresponding to 30% larger area.

THE REDSHIFT EVOLUTION OF THE RELATION BETWEEN STELLAR MASS, STAR FORMATION RATE, AND GAS METALLICITY OF GALAXIES

We investigate the relation between stellar mass ($M_\star$), star formation rate (SFR), and metallicity ($Z$) of galaxies, so called the fundamental metallicity relation, in the galaxy sample of the Sloan Digital Sky Survey Data Release 7. We separate the galaxies into narrow redshift bins and compare the relation at different redshifts, and find statistically significant ($> 99$%) evolution. We test various observational effects that might cause seeming $Z$ evolution, and find it difficult to explain the evolution of the relation only by the observational effects. In the current sample of low redshift galaxies, galaxies with different $M_\star$ and SFR are sampled from different redshifts, and there is degeneracy between $M_\star$/SFR and redshift. Hence it is not straightforward to distinguish a relation between $Z$ and SFR from a relation between $Z$ and redshift. The separation of the intrinsic relation from the redshift evolution effect is a crucial issue to understand evolution of galaxies.

Cross-correlation of spectroscopic and photometric galaxy surveys: cosmology from lensing and redshift distortions

Cosmological galaxy surveys aim at mapping the largest volumes to test models with techniques such as cluster abundance, cosmic shear correlations or baryon acoustic oscillations (BAO), which are designed to be independent of galaxy bias. Here we explore an alternative route to constrain cosmology: sampling more moderate volumes with the cross-correlation of photometric and spectroscopic surveys. We consider the angular galaxy-galaxy autocorrelation in narrow redshift bins and its combination with different probes of weak gravitational lensing (WL) and redshift space distortions (RSD). Including the cross-correlation of these surveys improves by factors of a few the constraints on both the dark energy equation of state w(z) and the cosmic growth history, parametrized by \gamma. The additional information comes from using many narrow redshift bins and from galaxy bias, which is measured both with WL probes and RSD, breaking degeneracies that are present when using each method separately. We show forecasts for a joint w(z) and \gamma figure of merit using linear scales over a deep (i<24) photometric survey and a brighter (i<22.5) spectroscopic or very accurate (0.3%) photometric redshift survey. Magnification or shear in the photometric sample produce FoM that are of the same order of magnitude of those of RSD or BAO over the spectroscopic sample. However, the cross-correlation of these probes over the same area yields a FoM that is up to a factor 100 times larger. Magnification alone, without shape measurements, can also be used for these cross-correlations and can produce better results than using shear alone. For a spectroscopic follow-up survey strategy, measuring the spectra of the foreground lenses to perform this cross-correlation provides 5 times better FoM than targeting the higher redshift tail of the galaxy distribution to study BAO over a 2.5 times larger volume.

Extended Limber approximation

We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in $(\ensuremath{\ell}+1/2{)}^{\ensuremath{-}1}$. This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large $\ensuremath{\ell}$'s. We show that the error in ordinary Limber approximation is $\mathcal{O}({\ensuremath{\ell}}^{\ensuremath{-}2})$. We also provide a simple expression for the 2nd order correction to the Limber formula, which improves the accuracy to $\mathcal{O}({\ensuremath{\ell}}^{\ensuremath{-}4})$. This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the 0th order Limber formula has a large error. We also point out that using $\ensuremath{\ell}$ instead of $\ensuremath{\ell}+1/2$, as is often done in the literature, spoils the accuracy of the approximation to $\mathcal{O}({\ensuremath{\ell}}^{\ensuremath{-}1})$.

The correlation of line strength with luminosity and redshift from composite quasi-stellar object spectra

We have generated a series of composite quasi-stellar object (QSO) spectra using over 22 000 individual low-resolution (∼8-Å) QSO spectra obtained from the 2dF (18.25 bJ 20.85) and 6dF (16bJ≤18.25) QSO Redshift Surveys. The large size of the catalogue has enabled us to construct composite spectra in relatively narrow redshift (Δz = 0.25) and absolute magnitude (ΔMB = 0.5) bins. The median number of QSOs in each composite spectrum is ∼200, yielding typical signal-to-noise ratios of ∼100. For a given redshift interval, the composite spectra cover a factor of over 25 in luminosity. For a given luminosity, many of the major QSO emission lines (e.g. Mg iiλ2798, [Oii]λ3727) can be observed over a redshift range of 1 or greater. Using the composite spectra we have measured the line strengths (equivalent widths) of the major broad and narrow emission lines. We have also measured the equivalent width of the Ca iiλ3933 K absorption feature caused by the host galaxy of the active galactic nuclei (AGN). Under the assumption of a fixed host galaxy spectral energy distribution (SED), the correlation seen between Ca ii K equivalent width and source luminosity implies Lgal∝L0.42±0.05QSO. We find strong anticorrelations with luminosity for the equivalent widths of [O ii]λ3727 and [Ne v]λ3426. These provide hints to the general fading of the NLR in high-luminosity sources, which we attribute to the NLR dimensions becoming larger than the host galaxy. This could have important implications for the search for type 2 AGN at high redshifts. If average AGN host galaxies have SEDs similar to average galaxies, then the observed narrow [O ii] emission could be solely a result of the host galaxy at low luminosities (MB∼−20). This suggests that the [O ii] line observed in high-luminosity AGN may be emitted, to a large part, by intense star-forming regions. The AGN contribution to this line could be weaker than previously assumed. We measure highly significant Baldwin effects for most broad emission lines (C ivλ1549, C iii]λ1909, Mg iiλ2798, Hγ, Hβ) and show that they are predominantly caused by correlations with luminosity, not redshift. We find that the Hβ and Hγ Balmer lines show an inverse Baldwin effect and are positively correlated with luminosity, unlike the broad ultraviolet lines. We postulate that this previously unknown effect is caused by a luminosity-dependent change in the ratio of disc to non-disc continuum components.