arXiv subjects

Paul Martini

Publications and source records attributed to Paul Martini.

At least 37 records · Page 2Linked to original sources

arXiv2025

Iron-corrected Single-epoch Black Hole Masses of DESI Quasars at low redshift

We present a study on the possible overestimation of single-epoch supermassive black hole (SMBH) masses in previous works, based on more than 55,000 type 1 quasars at $0.25 < z < 0.8$ from the Dark Energy Spectroscopic Instrument (DESI). We confirm that iron emission strength serves as a good tracer of the Eddington ratio, and estimate SMBH masses using an iron-corrected $R$-$L$ relation for H$β$, where $R$ is the broad line region size and $L$ is the continuum luminosity. Compared to our measurements, previous canonical measurements without the iron correction are overestimated by a factor of 1.5 on average. The overestimation can be up to a factor of 5 for super-Eddington quasars. The fraction of super-Eddington quasars in our sample is about 5%, significantly higher than 0.4% derived from the canonical measurements. Using a sample featuring both H$β$ and MgII emission lines, we calibrate MgII-based SMBH masses using iron-corrected, H$β$-based SMBH masses and establish an iron-corrected $R$-$L$ relation for MgII. The new relation adds an extra term of $-0.34R_{\mathrm{Fe}}$ to the $R$-$L$ relation, where $R_{\mathrm{Fe}}$ denotes the relative iron strength. We use this formula to build a catalog of about 0.5 million DESI quasars at $0.6<z<1.6$. If these iron-corrected $R$-$L$ relations for H$β$ and MgII are valid at high redshift, current mass measurements of luminous quasars at $z\ge6$ would have been overestimated by a factor of 2.3 on average, alleviating the tension between SMBH mass and growth history in the early universe.

astro-ph.GA↗

arXiv2025

GD-1 Stellar Stream and Cocoon in the DESI Early Data Release

We present 115 new spectroscopically identified members of the GD-1 tidal stream observed with the 5000-fiber Dark Energy Spectroscopic Instrument (DESI). We confirm the existence of a ``cocoon'' which is a broad (FWHM~2.932 deg ~ 460 pc) and kinematically hot (velocity dispersion, sigma ~ 5-8 km/s) component that surrounds a narrower (FWHM~ 0.353 deg ~ 55) and colder (sigma = 3.09+/-0.76 km/s) thin stream component (based on a median per star velocity precision of 2.7 km/s). The cocoon extends over at least a 30 degree segment of the stream observed by DESI. The thin and cocoon components have similar mean values of [Fe/H]: -2.54+/- 0.04 dex and -2.47+/- 0.06 dex suggestive of a common origin. The data are consistent with the following scenarios for the origin of the cocoon. The progenitor of the GD-1 stream was an accreted globular cluster (GC) and: (a) the cocoon was produced by pre-accretion tidal stripping of the GC while it was still inside its parent dwarf galaxy; (b) the cocoon is debris from the parent dwarf galaxy; (c) an initially thin GC tidal stream was heated by impacts from dark subhalos in the Milky Way; (d) an initially thin GC stream was heated by a massive Sagittarius dwarf galaxy; or a combination of some these. Future DESI spectroscopy and detailed modeling may enable us to distinguish between these possible origins.

astro-ph.GA↗

arXiv2024

ELG Spectroscopic Systematics Analysis of the DESI Data Release 1

Dark Energy Spectroscopic Instrument (DESI) uses more than 2.4 million Emission Line Galaxies (ELGs) for 3D large-scale structure (LSS) analyses in its Data Release 1 (DR1). Such large statistics enable thorough research on systematic uncertainties. In this study, we focus on spectroscopic systematics of ELGs. The redshift success rate ($f_{\rm goodz}$) is the relative fraction of secure redshifts among all measurements. It depends on observing conditions, thus introduces non-cosmological variations to the LSS. We, therefore, develop the redshift failure weight ($w_{\rm zfail}$) and a per-fibre correction ($η_{\rm zfail}$) to mitigate these dependences. They have minor influences on the galaxy clustering. For ELGs with a secure redshift, there are two subtypes of systematics: 1) catastrophics (large) that only occur in a few samples; 2) redshift uncertainty (small) that exists for all samples. The catastrophics represent 0.26\% of the total DR1 ELGs, composed of the confusion between O\,\textsc{ii} and sky residuals, double objects, total catastrophics and others. We simulate the realistic 0.26\% catastrophics of DR1 ELGs, the hypothetical 1\% catastrophics, and the truncation of the contaminated $1.31<z<1.33$ in the \textsc{AbacusSummit} ELG mocks. Their $P_\ell$ show non-negligible bias from the uncontaminated mocks. But their influences on the redshift space distortions (RSD) parameters are smaller than $0.2σ$. The redshift uncertainty of \Yone ELGs is 8.5 km/s with a Lorentzian profile. The code for implementing the catastrophics and redshift uncertainty on mocks can be found in https://github.com/Jiaxi-Yu/modelling_spectro_sys.

astro-ph.CO↗

arXiv2024

Forward modeling fluctuations in the DESI LRGs target sample using image simulations

We use the forward modeling pipeline, Obiwan, to study the imaging systematics of the Luminous Red Galaxies (LRGs) targeted by the Dark Energy Spectroscopic Instrument (DESI). We update the Obiwan pipeline, which had previously been developed to simulate the optical images used to target DESI data, to further simulate WISE images in the infrared. This addition makes it possible to simulate the DESI LRGs sample, which utilizes WISE data in the target selection. Deep DESI imaging data combined with a method to account for biases in their shapes is used to define a truth sample of potential LRG targets. We simulate a total of 15 million galaxies to obtain a simulated LRG sample (Obiwan LRGs) that predicts the variations in target density due to imaging properties. We find that the simulations predict the trends with depth observed in the data, including how they depend on the intrinsic brightness of the galaxies. We observe that faint LRGs are the main contributing power of the imaging systematics trend induced by depth. We also find significant trends in the data against Galactic extinction that are not predicted by Obiwan. These trends depend strongly on the particular map of Galactic extinction chosen to test against, implying Large-Scale Structure systematic contamination (e.g. Cosmic-Infrared Background) in the Galactic extinction maps is a likely root cause. We additionally observe that the DESI LRGs sample exhibits a complex dependency on a combination of seeing, depth, and intrinsic galaxy brightness, which is not replicated by Obiwan, suggesting discrepancies between the current simulation settings and the actual observations. The detailed findings we present should be used to guide any observational systematics mitigation treatment for the clustering of the DESI LRG sample.

astro-ph.CO↗

arXiv2024

New measurements of the Lyman-$α$ forest continuum and effective optical depth with LyCAN and DESI Y1 data

We present the Lyman-$α$ Continuum Analysis Network (LyCAN), a Convolutional Neural Network that predicts the unabsorbed quasar continuum within the rest-frame wavelength range of $1040-1600$ Angstroms based on the red side of the Lyman-$α$ emission line ($1216-1600$ Angstroms). We developed synthetic spectra based on a Gaussian Mixture Model representation of Nonnegative Matrix Factorization (NMF) coefficients. These coefficients were derived from high-resolution, low-redshift ($z<0.2$) Hubble Space Telescope/Cosmic Origins Spectrograph quasar spectra. We supplemented this COS-based synthetic sample with an equal number of DESI Year 5 mock spectra. LyCAN performs extremely well on testing sets, achieving a median error in the forest region of 1.5% on the DESI mock sample, 2.0% on the COS-based synthetic sample, and 4.1% on the original COS spectra. LyCAN outperforms Principal Component Analysis (PCA)- and NMF-based prediction methods using the same training set by 40% or more. We predict the intrinsic continua of 83,635 DESI Year 1 spectra in the redshift range of $2.1 \leq z \leq 4.2$ and perform an absolute measurement of the evolution of the effective optical depth. This is the largest sample employed to measure the optical depth evolution to date. We fit a power-law of the form $τ(z) = τ_0 (1+z)^γ$ to our measurements and find $τ_0 = (2.46 \pm 0.14)\times10^{-3}$ and $γ= 3.62 \pm 0.04$. Our results show particular agreement with high-resolution, ground-based observations around $z = 2$, indicating that LyCAN is able to predict the quasar continuum in the forest region with only spectral information outside the forest.

astro-ph.CO↗

arXiv2024

High redshift LBGs from deep broadband imaging for future spectroscopic surveys

Lyman break galaxies (LBGs) are promising probes for clustering measurements at high redshift, $z>2$, a region only covered so far by Lyman-$α$ forest measurements. In this paper, we investigate the feasibility of selecting LBGs by exploiting the existence of a strong deficit of flux shortward of the Lyman limit, due to various absorption processes along the line of sight. The target selection relies on deep imaging data from the HSC and CLAUDS surveys in the $g,r,z$ and $u$ bands, respectively, with median depths reaching 27 AB in all bands. The selections were validated by several dedicated spectroscopic observation campaigns with DESI. Visual inspection of spectra has enabled us to develop an automated spectroscopic typing and redshift estimation algorithm specific to LBGs. Based on these data and tools, we assess the efficiency and purity of target selections optimised for different purposes. Selections providing a wide redshift coverage retain $57\%$ of the observed targets after spectroscopic confirmation with DESI, and provide an efficiency for LBGs of $83\pm3\%$, for a purity of the selected LBG sample of $90\pm2\%$. This would deliver a confirmed LBG density of $\sim 620$ deg$^{-2}$ in the range $2.3<z<3.5$ for a $r$-band limiting magnitude $r<24.2$. Selections optimised for high redshift efficiency retain $73\%$ of the observed targets after spectroscopic confirmation, with $89\pm4\%$ efficiency for $97\pm2\%$ purity. This would provide a confirmed LBG density of $\sim 470$ deg$^{-2}$ in the range $2.8<z<3.5$ for a $r$-band limiting magnitude $r<24.5$. A preliminary study of the LBG sample 3d-clustering properties is also presented and used to estimate the LBG linear bias. A value of $b_{LBG} = 3.3 \pm 0.2 (stat.)$ is obtained for a mean redshift of 2.9 and a limiting magnitude in $r$ of 24.2, in agreement with results reported in the literature.

astro-ph.CO↗

arXiv2024

Validation of the DESI 2024 Lyman Alpha Forest BAL Masking Strategy

Broad absorption line quasars (BALs) exhibit blueshifted absorption relative to a number of their prominent broad emission features. These absorption features can contribute to quasar redshift errors and add absorption to the Lyman-alpha (LyA) forest that is unrelated to large-scale structure. We present a detailed analysis of the impact of BALs on the Baryon Acoustic Oscillation (BAO) results with the LyA forest from the first year of data from the Dark Energy Spectroscopic Instrument (DESI). The baseline strategy for the first year analysis is to mask all pixels associated with all BAL absorption features that fall within the wavelength region used to measure the forest. We explore a range of alternate masking strategies and demonstrate that these changes have minimal impact on the BAO measurements with both DESI data and synthetic data. This includes when we mask the BAL features associated with emission lines outside of the forest region to minimize their contribution to redshift errors. We identify differences in the properties of BALs in the synthetic datasets relative to the observational data, as well as use the synthetic observations to characterize the completeness of the BAL identification algorithm, and demonstrate that incompleteness and differences in the BALs between real and synthetic data also do not impact the BAO results for the LyA forest.

astro-ph.CO↗

arXiv2024

Performance of the Dark Energy Spectroscopic Instrument(DESI) Fiber System

The recently commissioned Dark Energy Spectroscopic Instrument (DESI) will measure the expansion historyof the universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasarsover 14000 sq deg will be measured during the life of the experiment. A new prime focus corrector for theKPNO Mayall telescope delivers light to 5000 fiber optic positioners. The fibers in turn feed ten broad-bandspectrographs. We describe key aspects and lessons learned from the development, delivery and installation ofthe fiber system at the Mayall telescope.

astro-ph.IM↗

arXiv2024

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Ly$α$ forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and eBOSS, offer independent measurements of baryon acoustic oscillation (BAO) measurements of angular-diameter distances and Hubble distances relative to the sound horizon, $r_d$, from eight different samples and six measurements of the growth rate parameter, $fσ_8$, from redshift-space distortions (RSD). This composite sample is the most constraining of its kind and allows us to perform a comprehensive assessment of the cosmological model after two decades of dedicated spectroscopic observation. We show that the BAO data alone are able to rule out dark-energy-free models at more than eight standard deviations in an extension to the flat, $Λ$CDM model that allows for curvature. When combined with Planck Cosmic Microwave Background (CMB) measurements of temperature and polarization the BAO data provide nearly an order of magnitude improvement on curvature constraints. The RSD measurements indicate a growth rate that is consistent with predictions from Planck primary data and with General Relativity. When combining the results of SDSS BAO and RSD with external data, all multiple-parameter extensions remain consistent with a $Λ$CDM model. Regardless of cosmological model, the precision on $Ω_Λ$, $H_0$, and $σ_8$, remains at roughly 1\%, showing changes of less than 0.6\% in the central values between models. The inverse distance ladder measurement under a o$w_0w_a$CDM yields $H_0= 68.20 \pm 0.81 \, \rm km\, s^{-1} Mpc^{-1}$, remaining in tension with several direct determination methods. (abridged)

astro-ph.CO↗

arXiv2024

Validation of the DESI 2024 Ly$α$ forest BAO analysis using synthetic datasets

The first year of data from the Dark Energy Spectroscopic Instrument (DESI) contains the largest set of Lyman-$α$ (Ly$α$) forest spectra ever observed. This data, collected in the DESI Data Release 1 (DR1) sample, has been used to measure the Baryon Acoustic Oscillation (BAO) feature at redshift $z=2.33$. In this work, we use a set of 150 synthetic realizations of DESI DR1 to validate the DESI 2024 Ly$α$ forest BAO measurement. The synthetic data sets are based on Gaussian random fields using the log-normal approximation. We produce realistic synthetic DESI spectra that include all major contaminants affecting the Ly$α$ forest. The synthetic data sets span a redshift range $1.8<z<3.8$, and are analysed using the same framework and pipeline used for the DESI 2024 Ly$α$ forest BAO measurement. To measure BAO, we use both the Ly$α$ auto-correlation and its cross-correlation with quasar positions. We use the mean of correlation functions from the set of DESI DR1 realizations to show that our model is able to recover unbiased measurements of the BAO position. We also fit each mock individually and study the population of BAO fits in order to validate BAO uncertainties and test our method for estimating the covariance matrix of the Ly$α$ forest correlation functions. Finally, we discuss the implications of our results and identify the needs for the next generation of Ly$α$ forest synthetic data sets, with the top priority being to simulate the effect of BAO broadening due to non-linear evolution.

astro-ph.CO↗

arXiv2024

JWST Observations of Starbursts: Polycyclic Aromatic Hydrocarbon Emission at the Base of the M 82 Galactic Wind

We present new observations of the central 1 kpc of the M 82 starburst obtained with the James Webb Space Telescope (JWST) near-infrared camera (NIRCam) instrument at a resolution ~0.05"-0.1" (~1-2 pc). The data comprises images in three mostly continuum filters (F140M, F250M, and F360M), and filters that contain [FeII] (F164N), H2 v=1-0 (F212N), and the 3.3 um PAH feature (F335M). We find prominent plumes of PAH emission extending outward from the central starburst region, together with a network of complex filamentary substructure and edge-brightened bubble-like features. The structure of the PAH emission closely resembles that of the ionized gas, as revealed in Paschen alpha and free-free radio emission. We discuss the origin of the structure, and suggest the PAHs are embedded in a combination of neutral, molecular, and photoionized gas.

astro-ph.GA↗

arXiv2024

eDIG-CHANGES II: Project Design and Initial Results on NGC 3556

The extraplanar diffuse ionized gas (eDIG) represents ionized gases traced by optical/UV lines beyond the stellar extent of galaxies. We herein introduce a novel multi-slit narrow-band spectroscopy method to conduct spatially resolved spectroscopy of the eDIG around a sample of nearby edge-on disk galaxies (eDIG-CHANGES). In this paper, we introduce the project design and major scientific goals, as well as a pilot study of NGC 3556 (M108). The eDIG is detected to a vertical extent of a few kpc above the disk, comparable to the X-ray and radio images. We do not see significant vertical variation of the [N II]/H$α$ line ratio. A rough examination of the pressure balance between different circum-galactic medium (CGM) phases indicates the magnetic field is in a rough pressure balance with the X-ray emitting hot gas, and may play an important role in the global motion of both the eDIG and the hot gas in the lower halo. At the location of an HST/COS observed UV bright background AGN $\sim29\rm~kpc$ from the center of NGC 3556, the magnetic pressure is much lower than that of the hot gas and the ionized gas traced by UV absorption lines, although the extrapolation of the pressure profiles may cause some biases in this comparison. By comparing the position-velocity diagrams of the optical and CO lines, we also find the dynamics of the two gas phases are consistent with each other, with no evidence of a global inflow/outflow and a maximum rotation velocity of $\sim150\rm~km~s^{-1}$.

astro-ph.GA↗

arXiv2024

Stability of C$_{59}$ Knockout Fragments from Femtoseconds to Infinity

We have studied the stability of C$_{59}$ anions as a function of time, from their formation on femtosecond timescales to their stabilization on second timescales and beyond, using a combination of theory and experiments. The C$_{59}^-$ fragments were produced in collisions between C$_{60}$ fullerene anions and neutral helium gas at a velocity of 90 km/s (corresponding to a collision energy of 166 eV in the center-of-mass frame). The fragments were then stored in a cryogenic ion-beam storage ring at the DESIREE facility where they were followed for up to one minute. Classical molecular dynamics simulations were used to determine the reaction cross section and the excitation energy distributions of the products formed in these collisions. We found that about 15 percent of the C$_{59}^-$ ions initially stored in the ring are intact after about 100 ms, and that this population then remains intact indefinitely. This means that C$_{60}$ fullerenes exposed to energetic atoms and ions, such as stellar winds and shock waves, will produce stable, highly reactive products, like C$_{59}$, that are fed into interstellar chemical reaction networks.

physics.chem-ph↗

arXiv2024

Constraining primordial non-Gaussianity from DESI quasar targets and Planck CMB lensing

We detect the cross-correlation between 2.7 million DESI quasar targets across 14,700 deg$^2$ (180 quasars deg$^{-2}$) and Planck 2018 CMB lensing at $\sim$30$σ$. We use the cross-correlation on very large scales to constrain local primordial non-Gaussianity via the scale dependence of quasar bias. The DESI quasar targets lie at an effective redshift of 1.51 and are separated into four imaging regions of varying depth and image quality. We select quasar targets from Legacy Survey DR9 imaging, apply additional flux and photometric redshift cuts to improve the purity and reduce the fraction of unclassified redshifts, and use early DESI spectroscopy of 194,000 quasar targets to determine their redshift distribution and stellar contamination fraction (2.6%). Due to significant excess large-scale power in the quasar autocorrelation, we apply weights to mitigate contamination from imaging systematics such as depth, extinction, and stellar density. We use realistic contaminated mocks to determine the greatest number of systematic modes that we can fit, before we are biased by overfitting and spuriously remove real power. We find that linear regression with one to seven imaging templates removed per region accurately recovers the input cross-power, $f_{\textrm{NL}}$ and linear bias. As in previous analyses, our $f_{\textrm{NL}}$ constraint depends on the linear primordial non-Gaussianity bias parameter, $b_ϕ = 2(b - p)δ_c$ assuming universality of the halo mass function. We measure $f_{\textrm{NL}} = -26^{+45}_{-40}$ with $p=1.6$ $(f_{\textrm{NL}} = -18^{+29}_{-27}$ with $p=1.0$), and find that this result is robust under several systematics tests. Future spectroscopic quasar cross-correlations with Planck lensing lensing can tighten the $f_{\textrm{NL}}$ constraints by a factor of 2 if they can remove the excess power on large scales in the quasar auto power spectrum.

astro-ph.CO↗

arXiv2024

DESI z >~ 5 Quasar Survey. I. A First Sample of 400 New Quasars at z ~ 4.7-6.6

We report the first results of a high-redshift ($z$ >~ 5) quasar survey using the Dark Energy Spectroscopic Instrument (DESI). As a DESI secondary target program, this survey is designed to carry out a systematic search and investigation of quasars at $z$ >~ 5, up to redshift 6.8. The target selection is based on the DESI Legacy Imaging Surveys (the Legacy Surveys) DR9 photometry, combined with the Pan-STARRS1 data and $J$-band photometry from public surveys. A first quasar sample has been constructed from the DESI Survey Validation 3 (SV3) and first-year observations until May 2022. This sample includes more than 400 new quasars at redshift 4.7 <= $z$ < 6.6, down to 21.5 magnitude in the $z$ band, discovered from 35% of the entire target sample. Remarkably, there are 220 new quasars identified at $z$ >= 5, more than one third of existing quasars previously published at this redshift. The observations so far result in an average success rate of 23% at $z$ > 4.7. The current spectral dataset has already allowed analysis of interesting individual objects (e.g., quasars with damped Ly$α$ absorbers and broad absorption line features), and statistical analysis will follow the survey's completion. A set of science projects will be carried out leveraging this program, including quasar luminosity function, quasar clustering, intergalactic medium, quasar spectral properties, intervening absorbers, and properties of early supermassive black holes. Additionally, a sample of 38 new quasars at $z$ ~ 3.8-5.7 discovered from a pilot survey in the DESI SV1 is also published in this paper.

astro-ph.GA↗

arXiv2024

High-quality Extragalactic Legacy-field Monitoring (HELM) with DECam

High-quality Extragalactic Legacy-field Monitoring (HELM) is a long-term observing program that photometrically monitors several well-studied extragalactic legacy fields with the Dark Energy Camera (DECam) imager on the CTIO 4m Blanco telescope. Since Feb 2019, HELM has been monitoring regions within COSMOS, XMM-LSS, CDF-S, S-CVZ, ELAIS-S1, and SDSS Stripe 82 with few-day cadences in the $(u)gri(z)$ bands, over a collective sky area of $\sim 38$ deg${\rm ^2}$. The main science goal of HELM is to provide high-quality optical light curves for a large sample of active galactic nuclei (AGNs), and to build decades-long time baselines when combining past and future optical light curves in these legacy fields. These optical images and light curves will facilitate the measurements of AGN reverberation mapping lags, as well as studies of AGN variability and its dependences on accretion properties. In addition, the time-resolved and coadded DECam photometry will enable a broad range of science applications from galaxy evolution to time-domain science. We describe the design and implementation of the program and present the first data release that includes source catalogs and the first $\sim 3.5$ years of light curves during 2019A--2022A.

astro-ph.GA↗

arXiv2024

Optimal 1D Ly$α$ Forest Power Spectrum Estimation -- III. DESI early data

The one-dimensional power spectrum $P_{\mathrm{1D}}$ of the Ly$α$ forest provides important information about cosmological and astrophysical parameters, including constraints on warm dark matter models, the sum of the masses of the three neutrino species, and the thermal state of the intergalactic medium. We present the first measurement of $P_{\mathrm{1D}}$ with the quadratic maximum likelihood estimator (QMLE) from the Dark Energy Spectroscopic Instrument (DESI) survey early data sample. This early sample of $54~600$ quasars is already comparable in size to the largest previous studies, and we conduct a thorough investigation of numerous instrumental and analysis systematic errors to evaluate their impact on DESI data with QMLE. We demonstrate the excellent performance of the spectroscopic pipeline noise estimation and the impressive accuracy of the spectrograph resolution matrix with two-dimensional image simulations of raw DESI images that we processed with the DESI spectroscopic pipeline. We also study metal line contamination and noise calibration systematics with quasar spectra on the red side of the Ly$α$ emission line. In a companion paper, we present a similar analysis based on the Fast Fourier Transform estimate of the power spectrum. We conclude with a comparison of these two approaches and implications for the upcoming DESI Year 1 analysis.

astro-ph.CO↗

arXiv2023

The DESI One-Percent Survey: Exploring A Generalized SHAM for Multiple Tracers with the UNIT Simulation

We perform SubHalo Abundance Matching (SHAM) studies on UNIT simulations with \{$σ, V_{\rm ceil}, v_{\rm smear}$\}-SHAM and \{$σ, V_{\rm ceil},f_{\rm sat}$\}-SHAM. They are designed to reproduce the clustering on 5--30$\,\hmpc$ of Luminous Red Galaxies (LRGs), Emission Line Galaxies (ELGs) and Quasi-Stellar Objects (QSOs) at $0.4<z<3.5$ from DESI One Percent Survey. $V_{\rm ceil}$ is the incompleteness of the massive host (sub)haloes and is the key to the generalized SHAM. $v_{\rm smear}$ models the clustering effect of redshift uncertainties, providing measurments consistent with those from repeat observations. A free satellite fraction $f_{\rm sat}$ is necessary to reproduce the clustering of ELGs. We find ELGs present a more complex galaxy--halo mass relation than LRGs reflected in their weak constraints on $σ$. LRGs, QSOs and ELGs show increasing $V_{\rm ceil}$ values, corresponding to the massive galaxy incompleteness of LRGs, the quenched star formation of ELGs and the quenched black hole accretion of QSOs. For LRGs, a Gaussian $v_{\rm smear}$ presents a better profile for sub-samples at redshift bins than a Lorentzian profile used for other tracers. The impact of the statistical redshift uncertainty on ELG clustering is negligible. The best-fitting satellite fraction for DESI ELGs is around 4 per cent, lower than previous estimations for ELGs. The mean halo mass log$_{10}(\langle M_{\rm vir}\rangle)$ in $\Msun{}$ for LRGs, ELGs and QSOs are ${13.16\pm0.01}$, ${11.90\pm0.06}$ and ${12.66\pm0.45}$ respectively. Our generalized SHAM algorithms facilitate the production of mult-tracer galaxy mocks for cosmological tests.

astro-ph.CO↗