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Institute of Astronomy

 

Comparing gravitational wave background predictions from cosmological simulations to pulsar timing observations

Recent IoA Publications - Mon, 14/09/2026 - 10:59
arXiv:2607.05208v2 Announce Type: replace Abstract: The recent detection of a gravitational wave background (GWB) by pulsar timing arrays (PTAs) may represent the first evidence of gravitational waves from merging supermassive black hole binaries, opening a new window on the low-frequency end of the gravitational wave spectrum. These inspiralling binaries are expected to dominate the signal, although most theoretical models seem to predict somewhat lower amplitudes than what is observed. We present the first comprehensive statistical framework to quantify the tension between PTA measurements and theoretical predictions, maximising the constraining power of current data and allowing straightforward application to future PTA datasets. We further investigate how different assumptions in the observational inference, particularly the use of a power-law model for the GWB spectrum, can bias tension estimates and potentially overstate discrepancies with theory. We apply our framework to compare predictions from the FABLE cosmological simulation with the NANOGrav 15-year dataset. For our fiducial black hole population, we find tension values of $1\sigma$-$2.5\sigma$, indicating no statistically significant disagreement with the observations. We further explore physically motivated modifications to the merging black hole population, guided by electromagnetic observations and theoretical uncertainties. In particular, scenarios with boosted black hole masses at high redshift and more equal-mass mergers substantially increase the predicted GWB amplitude, improving agreement with PTA data. Finally, we investigate the high-mass end of the black hole mass function and the impact of finite simulation volume. We find that the $(100 \, \mathrm{cMpc} \, h^{-1})^3$ FABLE box is sufficient to robustly predict the GWB signal at the most constraining frequency.

Comparing gravitational wave background predictions from cosmological simulations to pulsar timing observations

Cosmology and Fundamental physics - Mon, 14/09/2026 - 10:59
arXiv:2607.05208v2 Announce Type: replace Abstract: The recent detection of a gravitational wave background (GWB) by pulsar timing arrays (PTAs) may represent the first evidence of gravitational waves from merging supermassive black hole binaries, opening a new window on the low-frequency end of the gravitational wave spectrum. These inspiralling binaries are expected to dominate the signal, although most theoretical models seem to predict somewhat lower amplitudes than what is observed. We present the first comprehensive statistical framework to quantify the tension between PTA measurements and theoretical predictions, maximising the constraining power of current data and allowing straightforward application to future PTA datasets. We further investigate how different assumptions in the observational inference, particularly the use of a power-law model for the GWB spectrum, can bias tension estimates and potentially overstate discrepancies with theory. We apply our framework to compare predictions from the FABLE cosmological simulation with the NANOGrav 15-year dataset. For our fiducial black hole population, we find tension values of $1\sigma$-$2.5\sigma$, indicating no statistically significant disagreement with the observations. We further explore physically motivated modifications to the merging black hole population, guided by electromagnetic observations and theoretical uncertainties. In particular, scenarios with boosted black hole masses at high redshift and more equal-mass mergers substantially increase the predicted GWB amplitude, improving agreement with PTA data. Finally, we investigate the high-mass end of the black hole mass function and the impact of finite simulation volume. We find that the $(100 \, \mathrm{cMpc} \, h^{-1})^3$ FABLE box is sufficient to robustly predict the GWB signal at the most constraining frequency.

Mass-Orbital Period Distribution of Massive White Dwarfs Formed Through Stable Mass Transfer

Stars and stellar evolution - Mon, 14/09/2026 - 10:46
arXiv:2606.06141v3 Announce Type: replace Abstract: White dwarfs (WDs) in binaries can form through either the stable mass-transfer process or common envelope evolution (CEE). Compared to CEE, the stable mass-transfer process can lead to a distinct mass$-$orbital period ($M_{ \mathrm{WD}}$-$P_{ \mathrm{orb}}$) relation. Thus, this relation of WDs contains the information about the evolution channels. We can study the relation in WD binary systems to determine whether their progenitors undergo a CEE. We use the stellar evolution code MESA as our primary computational tool and adopt the quasi-adiabatic criterion to ensure that our models satisfy the conditions for stable mass transfer. Our study considers different mass-transfer schemes, varying metallicities, and the relation for both low-mass and intermediate-mass progenitors. Previous studies have focused on the relation for low-mass progenitors, which cannot explain some long-period, high-mass WD binaries. Our results show that the $M_{ \mathrm{WD}}$-$P_{ \mathrm{orb}}$ distribution for intermediate-mass progenitors whose cores remain nondegenerate prior to central helium burning can account for the formation channels of long-period and massive WD binaries.

Mass-Orbital Period Distribution of Massive White Dwarfs Formed Through Stable Mass Transfer

Recent IoA Publications - Mon, 14/09/2026 - 10:46
arXiv:2606.06141v3 Announce Type: replace Abstract: White dwarfs (WDs) in binaries can form through either the stable mass-transfer process or common envelope evolution (CEE). Compared to CEE, the stable mass-transfer process can lead to a distinct mass$-$orbital period ($M_{ \mathrm{WD}}$-$P_{ \mathrm{orb}}$) relation. Thus, this relation of WDs contains the information about the evolution channels. We can study the relation in WD binary systems to determine whether their progenitors undergo a CEE. We use the stellar evolution code MESA as our primary computational tool and adopt the quasi-adiabatic criterion to ensure that our models satisfy the conditions for stable mass transfer. Our study considers different mass-transfer schemes, varying metallicities, and the relation for both low-mass and intermediate-mass progenitors. Previous studies have focused on the relation for low-mass progenitors, which cannot explain some long-period, high-mass WD binaries. Our results show that the $M_{ \mathrm{WD}}$-$P_{ \mathrm{orb}}$ distribution for intermediate-mass progenitors whose cores remain nondegenerate prior to central helium burning can account for the formation channels of long-period and massive WD binaries.

The cosmic coincidences that made our universe – and us – possible

Astronomy News - Mon, 14/09/2026 - 10:26
The sun and moon are positioned just right for us to see total solar eclipses, and the make-up of the universe is just right for life. Columnist Leah Crane wonders if it’s really all one big coincidence

Five night sky events to look out for this autumn

Astronomy News - Sun, 13/09/2026 - 18:25

From meteor showers to a November supermoon, there are a number of impressive sights to behold in the autumn night sky.

NASA’s Chandra Spots Galactic Gem

Astronomy News - Sat, 12/09/2026 - 15:58
X-ray: NASA/CXC/SAO; Optical: NASA/ESA/STScI; Infrared: NASA/ESA/CSA/STScI; Image Processing: NASA/CXC/SAO/L. Frattare and J. Major

Two galaxies merge at a furious rate in this Aug. 25, 2026, image of the II Zw 096 system. This and several other images of both visually and scientifically interesting galaxies were released by NASA’s Chandra X-ray Observatory and other telescopes.

Chandra X-ray data (magenta) pinpoint powerful black hole activity and hot gas, while optical data (blue and white) from NASA’s Hubble Space Telescope and infrared data from NASA’s James Webb Space Telescope illuminate vast stellar nurseries hidden behind interstellar dust. Systems like II Zw 096 show us how powerful galaxy collisions shaped the early universe.

See more galaxy photos from Chandra.

Image credit: X-ray: NASA/CXC/SAO; Optical: NASA/ESA/STScI; Infrared: NASA/ESA/CSA/STScI; Image Processing: NASA/CXC/SAO/L. Frattare and J. Major

Planetary Accretion Is Less Frequent in Wide Binaries: Evidence from Metal-Enriched White Dwarfs in DESI DR1

Recent IoA Publications - Fri, 11/09/2026 - 10:47
arXiv:2609.11798v1 Announce Type: new Abstract: Binary stars are common in the Galaxy, and understanding how stellar binarity influences the formation and evolution of planetary systems is an active area of research. In this study, we use metal-enriched white dwarfs in wide binaries as tracers of long-lived planetary systems. With Data Release 1 from the Dark Energy Spectroscopic Instrument (DESI), we find that the fraction of cool metal-enriched white dwarfs in wide binaries is 9.8\,$\pm$\,2.1\%, significantly lower (4.7\,$\sigma$) than the 20.5\,$\pm$\,0.9\% in a control sample of single systems. Furthermore, we identify a tentative dependence of metal enrichment on projected separation and white dwarf effective temperature, where enrichment fraction decreases at smaller separations and lower temperatures. These findings indicate that, compared to single stars, binary systems either start with smaller initial planetary reservoirs due to suppressed planetesimal formation or undergo more rapid depletion of planetary material during the initial part of the white dwarf stage.

Planetary Accretion Is Less Frequent in Wide Binaries: Evidence from Metal-Enriched White Dwarfs in DESI DR1

Planetary systems - Fri, 11/09/2026 - 10:47
arXiv:2609.11798v1 Announce Type: new Abstract: Binary stars are common in the Galaxy, and understanding how stellar binarity influences the formation and evolution of planetary systems is an active area of research. In this study, we use metal-enriched white dwarfs in wide binaries as tracers of long-lived planetary systems. With Data Release 1 from the Dark Energy Spectroscopic Instrument (DESI), we find that the fraction of cool metal-enriched white dwarfs in wide binaries is 9.8\,$\pm$\,2.1\%, significantly lower (4.7\,$\sigma$) than the 20.5\,$\pm$\,0.9\% in a control sample of single systems. Furthermore, we identify a tentative dependence of metal enrichment on projected separation and white dwarf effective temperature, where enrichment fraction decreases at smaller separations and lower temperatures. These findings indicate that, compared to single stars, binary systems either start with smaller initial planetary reservoirs due to suppressed planetesimal formation or undergo more rapid depletion of planetary material during the initial part of the white dwarf stage.

A Novel Approach to 3D Dust Mapping of the Central Molecular Zone

Recent IoA Publications - Fri, 11/09/2026 - 09:37
arXiv:2609.10782v1 Announce Type: new Abstract: The 3D distribution of dust and gas in the Milky Way's Central Molecular Zone (CMZ) is key to understanding gas inflows toward the Galactic Centre (GC), the process of star formation in this extreme environment, and the propagation of energetic cosmic rays originating from Sgr A*. However, while recent efforts have combined datasets in a Bayesian framework to estimate the near/far positions of individual molecular clouds in the CMZ, conflicts between different methodologies still remain and we are still lacking a comprehensive, model-independent map of all of the gas and dust in the CMZ, which is critical to address key science questions. Here we develop a new methodology to infer the 3D dust distribution of the CMZ. The key idea of the method is to use \emph{stellar} proper motions to get probabilistic information about the unknown stellar distances through a model of the distribution of star positions and velocities of the nuclear stellar disc (NSD), co-spatial to the CMZ. Taking \emph{stellar} proper motions and extinctions as input, the latter adopted as a proxy of the dust column density, the method returns the 3D dust distribution. It is non parametric, makes no a-priori assumption on the dust distribution, and is fundamentally distinct and largely independent of all existing methods. We show that the method can robustly and effectively reconstruct the mock 3D CMZ structure by testing it on a range of mock dust distributions, both analytically generated and taken from hydrodynamical simulations. Finally, we discuss the prospects for applying the method to real data.

A Novel Approach to 3D Dust Mapping of the Central Molecular Zone

Near-field cosmology - Fri, 11/09/2026 - 09:36
arXiv:2609.10782v1 Announce Type: new Abstract: The 3D distribution of dust and gas in the Milky Way's Central Molecular Zone (CMZ) is key to understanding gas inflows toward the Galactic Centre (GC), the process of star formation in this extreme environment, and the propagation of energetic cosmic rays originating from Sgr A*. However, while recent efforts have combined datasets in a Bayesian framework to estimate the near/far positions of individual molecular clouds in the CMZ, conflicts between different methodologies still remain and we are still lacking a comprehensive, model-independent map of all of the gas and dust in the CMZ, which is critical to address key science questions. Here we develop a new methodology to infer the 3D dust distribution of the CMZ. The key idea of the method is to use \emph{stellar} proper motions to get probabilistic information about the unknown stellar distances through a model of the distribution of star positions and velocities of the nuclear stellar disc (NSD), co-spatial to the CMZ. Taking \emph{stellar} proper motions and extinctions as input, the latter adopted as a proxy of the dust column density, the method returns the 3D dust distribution. It is non parametric, makes no a-priori assumption on the dust distribution, and is fundamentally distinct and largely independent of all existing methods. We show that the method can robustly and effectively reconstruct the mock 3D CMZ structure by testing it on a range of mock dust distributions, both analytically generated and taken from hydrodynamical simulations. Finally, we discuss the prospects for applying the method to real data.

BINDing the lightcone: A suite of astrophysical ray-traced weak lensing and SZ maps

Recent IoA Publications - Fri, 11/09/2026 - 08:30
arXiv:2609.10710v1 Announce Type: new Abstract: Recent multiwavelength observations of galaxy group and cluster gas suggest stronger baryonic feedback than our best-calibrated hydrodynamical simulations produce, while modeling this feedback remains a primary source of uncertainty in Stage-IV weak-lensing (WL) analyses. We present a suite of ray-traced maps generated with BIND (Baryonic INpainting with Deep learning), a conditional flow-matching model that paints baryonic mass and gas thermodynamics onto the halos of dark-matter-only simulations, and which was developed in a companion paper. Applied to IllustrisTNG300-Dark and ray-traced, we generate convergence, optical depth, and Compton-$y$ maps at five source redshifts, each with $1000$ pseudo-independent realizations. We build lightcones across a 256-node Sobol sequence spanning the thirty-dimensional IllustrisTNG galaxy formation prior, with individual parameter variations and at the fiducial model. In validation, the maps match those built from the IllustrisTNG300 halos to within LSST-Y10-like precision for a range of WL statistics. Across the prior, the response to feedback exceeds Stage-IV statistical precision by more than an order of magnitude on small scales, and different statistics respond to different model sectors: galactic winds control the WL power spectrum and gas auto- and cross-spectra, while the stellar initial mass function slope and AGN parameters shape the morphological statistics (PDF, peaks, minima, and Minkowski functionals). Finally, we find that the response of statistics can be compressed into seven halo properties which linearly predict a range of WL and SZ statistics. We publicly release the maps, statistics, and model tables.

BINDing the lightcone: A suite of astrophysical ray-traced weak lensing and SZ maps

Galaxy Evolution and AGN - Fri, 11/09/2026 - 08:30
arXiv:2609.10710v1 Announce Type: new Abstract: Recent multiwavelength observations of galaxy group and cluster gas suggest stronger baryonic feedback than our best-calibrated hydrodynamical simulations produce, while modeling this feedback remains a primary source of uncertainty in Stage-IV weak-lensing (WL) analyses. We present a suite of ray-traced maps generated with BIND (Baryonic INpainting with Deep learning), a conditional flow-matching model that paints baryonic mass and gas thermodynamics onto the halos of dark-matter-only simulations, and which was developed in a companion paper. Applied to IllustrisTNG300-Dark and ray-traced, we generate convergence, optical depth, and Compton-$y$ maps at five source redshifts, each with $1000$ pseudo-independent realizations. We build lightcones across a 256-node Sobol sequence spanning the thirty-dimensional IllustrisTNG galaxy formation prior, with individual parameter variations and at the fiducial model. In validation, the maps match those built from the IllustrisTNG300 halos to within LSST-Y10-like precision for a range of WL statistics. Across the prior, the response to feedback exceeds Stage-IV statistical precision by more than an order of magnitude on small scales, and different statistics respond to different model sectors: galactic winds control the WL power spectrum and gas auto- and cross-spectra, while the stellar initial mass function slope and AGN parameters shape the morphological statistics (PDF, peaks, minima, and Minkowski functionals). Finally, we find that the response of statistics can be compressed into seven halo properties which linearly predict a range of WL and SZ statistics. We publicly release the maps, statistics, and model tables.

BIND (Baryonic INpainting with Deep learning): A Field-level Emulator for Galaxy Groups and Clusters

Recent IoA Publications - Fri, 11/09/2026 - 08:28
arXiv:2609.10709v1 Announce Type: new Abstract: Baryonic feedback is a dominant source of systematic uncertainty for upcoming weak-lensing surveys, but current tools for modeling its effect rely on spherical approximations and density profiles calibrated almost entirely on two-point statistics. We introduce BIND (Baryonic INpainting with Deep learning), a conditional flow-matching model that learns a field-level mapping from dark-matter-only halos to their hydrodynamical counterparts. BIND is trained on halos from the 1024 paired hydrodynamical and dark-matter-only simulations of the CAMELS $50\,h^{-1}\,\mathrm{Mpc}$ SB35 suite and samples dark matter, gas, and stellar mass fields over redshift across the full 35-dimensional $\Lambda$CDM and IllustrisTNG galaxy formation parameter space. BIND recovers dark matter, gas, and stellar masses at the percent level, reproduces azimuthally averaged profiles to $\lesssim10\%$ at all radii, and matches halo shape distributions with high fidelity. The learned parameter dependence captures the rank correlations between the generated fields and the subgrid parameters, and the field-level response to individual parameter variations is recovered in both sign and morphology. Halo mass is never supplied as conditioning, yet the baryon fraction, stellar-to-halo mass relation, inter-component scaling relations, and the joint covariance of their residuals are all reproduced. We finally show that, applied halo-by-halo to a $(50\,h^{-1}\,\mathrm{Mpc})^3$ $N$-body volume with $512^3$ particles, BIND reproduces the projected matter power spectrum suppression to the accuracy ceiling set by pasting in the hydrodynamical halos themselves, in minutes on one GPU. We release the trained BIND models and all generated halos as open-source tools. A companion paper extends BIND to thermodynamic fields and non-Gaussian weak-lensing statistics.

BIND (Baryonic INpainting with Deep learning): A Field-level Emulator for Galaxy Groups and Clusters

Galaxy Evolution and AGN - Fri, 11/09/2026 - 08:28
arXiv:2609.10709v1 Announce Type: new Abstract: Baryonic feedback is a dominant source of systematic uncertainty for upcoming weak-lensing surveys, but current tools for modeling its effect rely on spherical approximations and density profiles calibrated almost entirely on two-point statistics. We introduce BIND (Baryonic INpainting with Deep learning), a conditional flow-matching model that learns a field-level mapping from dark-matter-only halos to their hydrodynamical counterparts. BIND is trained on halos from the 1024 paired hydrodynamical and dark-matter-only simulations of the CAMELS $50\,h^{-1}\,\mathrm{Mpc}$ SB35 suite and samples dark matter, gas, and stellar mass fields over redshift across the full 35-dimensional $\Lambda$CDM and IllustrisTNG galaxy formation parameter space. BIND recovers dark matter, gas, and stellar masses at the percent level, reproduces azimuthally averaged profiles to $\lesssim10\%$ at all radii, and matches halo shape distributions with high fidelity. The learned parameter dependence captures the rank correlations between the generated fields and the subgrid parameters, and the field-level response to individual parameter variations is recovered in both sign and morphology. Halo mass is never supplied as conditioning, yet the baryon fraction, stellar-to-halo mass relation, inter-component scaling relations, and the joint covariance of their residuals are all reproduced. We finally show that, applied halo-by-halo to a $(50\,h^{-1}\,\mathrm{Mpc})^3$ $N$-body volume with $512^3$ particles, BIND reproduces the projected matter power spectrum suppression to the accuracy ceiling set by pasting in the hydrodynamical halos themselves, in minutes on one GPU. We release the trained BIND models and all generated halos as open-source tools. A companion paper extends BIND to thermodynamic fields and non-Gaussian weak-lensing statistics.

Gamma ray burst may have been two supernovae in one

Astronomy News - Fri, 11/09/2026 - 08:16
A group of astronomers proposes that a series of events in a distant galaxy formed both a black hole and a pulsar, but other experts say the conclusion is premature

Dust and Water in Sagittarius A*

Astronomy News - Fri, 11/09/2026 - 08:15
ESA/Webb, NASA & CSA, F. Peißker, J. Lu, F. Yusef-Zadeh, N. B. Sabha, C. Chan

A brilliant concentration of stars takes center stage in this Aug. 11, 2026, image taken by NASA’s James Webb Space Telescope. Webb observed IRS 3, a star near the end of its life cycle, located within this starfield. Webb’s mid-infrared data revealed the clear signature of oxygen-rich silicate dust, as well as, for the first time, water, in its surrounding dust envelope.

Read more about this discovery.

Image Credit: ESA/Webb, NASA & CSA, F. Peißker, J. Lu, F. Yusef-Zadeh, N. B. Sabha, C. Chan

Research Associate (Grade 7) or Assistant Research Professor (Grade 9) in AI for Fundamental Physics (Fixed Term)

Vacancies - Fri, 11/09/2026 - 01:00

Fixed-term: The funds for this post are available until 30 September 2030 in the first instance.

Applications are invited for a circa four-year research position in AI for fundamental physics and cosmology in the Handley Lab at the Kavli Institute for Cosmology, Institute of Astronomy, University of Cambridge. Appointment will be at Research Associate level (Grade 7) or Assistant Research Professor level (Grade 9), according to the successful candidate's skills, experience and research profile. Please see the Further Particulars associated with this vacancy for more information on what is required of both the Grade 7 and the Grade 9 role.

Please note that appointment at Grade 9 is subject to application and approval to the Faculty Board. If any Faculty Board application is unsuccessful then appointment will be made at Grade 7 Research Associate.

The conventional account of fundamental physics begins with a Lagrangian, derives its observable consequences and ends with a comparison against data. In modern cosmology, the middle of this process has become the difficult part. New theories require substantial calculations, specialised numerical methods and research software capable of carrying their predictions through to cosmological observables. Much of this machinery is concentrated in large collaborations and established frameworks, while tractability at cosmological scales often relies on effective descriptions which have integrated out the physics under investigation.

This creates a bias in which theories are tested. So long as it is substantially harder to investigate a new theory from scratch than to rerun an established model, our attention will be directed towards the theories which are easiest to implement rather than those which are most scientifically promising.

The project will use AI-assisted development and GPU-accelerated inference to change what can be attempted by a small research group. The postholder will derive physical predictions, direct the construction of the software needed to test them, and confront the resulting models with cosmological and astrophysical data. The scientific judgement remains with the researcher: deciding which problems are worth pursuing, understanding what the calculations mean, and recognising when the machinery is wrong.

The position offers a larger than usual amount of research freedom. Candidates will be encouraged to shape the programme around their own interests and may come from any relevant area of theoretical or computational physics, including gravitation, field theory, lattice and numerical field theory, cosmological perturbation theory, Bayesian computation, GPU and differentiable programming, or AI-assisted scientific software development.

The postholder will also develop GPU-accelerated Bayesian inference methods, including nested sampling, publish and present their research, and contribute to the fundamental physics, cosmology and astronomy communities in Cambridge.

Applicants should have, or be close to obtaining, a PhD in physics, astronomy, applied mathematics or a closely related field. Theoretical capability is the essential criterion. Fluency in directing AI agents matters more than prior strength as a programmer, provided the candidate has the judgement to assess their outputs and correct the implementation.

Click the 'Apply' button below to register an account with our recruitment system (if you have not already) and apply online.

Applications should include a cover letter, curriculum vitae, publication list, statement of research interests, a GitHub username (or equivalent evidence of computational skills and experience), and contact details for two academic referees. One referee should be your most recent line manager.

The covering letter should outline how you match the criteria for the post and why you are applying for the role.

Where applicants indicate that they give permission, referees will be contacted for shortlisted candidates before the interview process via the University recruitment system.

If you upload any additional documents which have not been requested, we will not be able to consider these as part of your application.

Informal enquiries are welcomed and should be directed to: Dr Will Handley Email: wh260@cam.ac.uk

If you have any queries regarding the application process please contact HR@ast.cam.ac.uk.

The closing date for applications is: 23:59 GMT on Friday 25th September 2026. The interview date is not yet confirmed but could be as early as week commencing 28th September 2026.

Please quote reference LG51052 on your application and in any correspondence about this vacancy.

The University actively supports equality, diversity and inclusion and encourages applications from all sections of society.

The University has a responsibility to ensure that all employees are eligible to live and work in the UK.

Relevant information on current research activities can be found at:

https://handley-lab.co.uk

https://willhandley.co.uk

https://www.ast.cam.ac.uk

https://www.kicc.cam.ac.uk

Optical Depths from the Thermal Sunyaev-Zel'dovich Effect with ACT DR6 and DESI DR1 Spectroscopic Galaxies and Optically-Selected Clusters

Galaxy Evolution and AGN - Thu, 10/09/2026 - 11:22
arXiv:2609.08939v2 Announce Type: replace Abstract: We present stacked thermal Sunyaev-Zel'dovich (tSZ) effect measurements for three samples of galaxy groups and clusters: those traced by the Dark Energy Spectroscopic Intstrument Data Release 1 (DESI DR1) luminous red galaxies (LRG) and the DESI DR1 Bright Galaxy Sample (BGS), and an eROMaPPer optically-selected sample from the DESI Legacy Imaging Survey. We use the latest Atacama Cosmology Telescope DR6 (ACT)+Planck component-separated internal linear combination (ILC) Compton-$y$ maps and ACT+Planck coadded 90, 150, and 220 GHz temperature maps to extract the tSZ signal within a $\sim2'$ disk aperture for sources binned by luminosity, richness, or mass. We measure the average tSZ signal with high statistical significance, with signal-to-noise ratios surpassing 38 for LRG, 27 for BGS, and 39 for the eROMaPPer sample using the 90 GHz ACT DR6+Planck map. We conduct a detailed study of systematics and foregrounds such as dust and cosmic infrared background (CIB) contamination, which remain a core challenge for tSZ analysis. For the LRG and BGS samples, we find that dust and radio source emission dominate the tSZ signal at scales near and below the disk aperture radius. Large-scale ($R>4'$) contamination from the CIB is less significant. We mitigate these contaminants to isolate the tSZ signal and use a combination of simulated and real measurements to develop Compton-$y-$optical depth ($\bar y-\bar \tau$) scaling relations to infer optical depths, which are found to be in agreement with values measured using the pairwise kinematic SZ effect for the same tracer samples. The $\bar y-\bar \tau$ scaling relation for the eROMaPPer sample is the first such relationship to be derived directly from SZ measurements.