arXiv subjects

Nathan Deg

Publications and source records attributed to Nathan Deg.

At least 19 recordsLinked to original sources

arXiv2026

Testing dark matter models and modified gravity theories with spatially resolved HI observations

Understanding the nature of dark matter (DM) is one of the most pressing questions of modern physics. The flat rotation curves of galaxies, especially the extended HI rotation curves from radio observations at 21 cm, played a key historical role to establish the DM problem and continue to be a major tool to test different galaxy formation models, particle DM models, and modified gravity theories. The SKA observatory will revolutionize the study of HI rotation curves thanks to its unprecedented angular resolution, sensitivity, and survey speed. In combination with optical and near-infrared ancillary data, HI surveys with SKA-Mid AA4 will allow us to (1) obtain HI data at spatial resolutions of 1"-2", probing the inner galaxy dynamics with unprecedented details (e.g., the cusp-core problem); (2) move from representative samples of a few hundreds of objects to statistical samples of tens of thousands of objects, allowing us to study the dynamical scaling laws of galaxies and their DM properties with unprecedented statistical power across different cosmic environments; (3) move from galaxies at z~0 to galaxies at z~1, probing DM halos at earlier cosmic epochs and exploring the redshift evolution of the dynamical laws across about 8 Gyrs. The massive SKA data, however, will pose important technical challenges for the derivation of HI rotation curves with automated kinematic software. Developing such kinematic software in the SKA era will be crucial to reach major scientific goals, such as discriminating between different solutions to the DM problem.

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arXiv2026

The Low-$\alpha$ Splash Population in the Milky Way

The Milky Way in-situ halo, also known as the Splash, consists of old (age $>$ 10 Gyr), metal-rich ([Fe/H] $> -0.7$), high-$\alpha$ stars, i.e., thick disk-like chemistry, on halo-like orbits (eccentricity $>$ 0.6). Its origin is linked to stars formed in the disk and dynamically heated by either internal or external agents. In this work, we investigate its low-$\alpha$ counterpart, the low-$\alpha$ Splash, motivated by recent findings of an old thin disk population. We conjecture that any mechanism capable of heating disk stars should affect both of present-day high- and low-$\alpha$ old populations. Using data from the APOGEE DR17 spectroscopic catalog, we identify metal-rich low-$\alpha$ stars with halo-like kinematics similar to those of the classical high-$\alpha$ Splash. We investigate their possible heating mechanisms using the GASTRO suite of simulations, which allows us to explore the effects of star-forming clumps as well as a major merger in the proto-disk of a Milky Way analog galaxy. Our main results show that only clumpy Milky Way models are able to produce Splash populations through scattering by clumps in the early Galaxy, including the low-$\alpha$ counterpart, whereas the model including only the merger and without an early clumpy phase fails to produce these populations. In the models, the low-$\alpha$ Splash corresponds to a subset of the old thin disk that was dynamically heated by the same mechanism responsible for the formation of the high-$\alpha$ Splash.

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arXiv2026

WALLABY pilot survey: HI depletion times within the stellar discs of nearby galaxies

Neutral atomic hydrogen (HI) reservoirs typically extend far beyond the inner star-forming regions of galaxies, and global HI measurements, which mix these distinct environments, limit our understanding of the gas-star formation cycle. In particular, global HI depletion times combine gas and star formation from different physical scales, contributing to long measured timescales (5-9 Gyr) and large scatter compared to molecular gas. Using 841 gas-rich galaxies from the Widefield ASKAP L-band Legacy All-sky Blind Survey (WALLABY) pilot observations, we investigate how HI depletion time and its scaling relations change when HI and star formation are both confined to the stellar disc (R25, the isophotal radius at 25 mag arcsec-2 in i-band). We find that depletion times within this region are on average 1.4 Gyr shorter than global values, though some remain very long, indicating that a substantial fraction of HI remains inactive for star formation. HI depletion times anti-correlate strongly with stellar surface density, and this trend becomes even tighter within the stellar disc. The Kennicutt-Schmidt relation further reveals an almost constant HI depletion time at fixed stellar surface density, similar to the behaviour seen for molecular gas, suggesting that HI and star formation are regulated by conditions that enable HI-to-H2 conversion, traced by stellar surface density. Beyond the stellar disc, HI depletion times are on average almost 10 Gyr longer than within R25, confirming extremely inefficient star formation in low-density outer regions. These results highlight the critical role of spatial location and local conditions for HI to serve as a fuel for star formation.

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arXiv2026

Kinematic diagnostics for non-axisymmetry in the Milky Way's nuclear stellar disc

There is now strong evidence that the Milky Way (MW) hosts a nuclear stellar disc (NSD). However, whether the NSD is purely axisymmetric or contains a nuclear bar remains unresolved. Since approximately $50\%$ of barred galaxies with MW-like mass in the local Universe host a nuclear bar, investigating whether the MW hosts one is of interest. We conduct a systematic analysis to identify robust kinematic diagnostics capable of determining whether the MW hosts a nuclear bar. Using N-body simulations, we explore the kinematic signatures indicative of a nuclear bar. Using the phase-space coordinates longitude $(\ell)$, latitude $(b)$, proper motions ($\mu_\ell$ and $\mu_{\rm b})$ and line-of-sight velocity $(v_{\rm los})$, we test various diagnostics assuming different nuclear bar orientations. We also evaluate how sample size, dust extinction and bar amplitude influence the efficacy of the diagnostics. We identify two independent kinematic diagnostics capable of revealing a nuclear bar in the MW: (1) the vertex deviation, $l_{\rm v}$, of the ($v_{\ell}-v_{\rm los}$) velocity ellipse; and (2) The asymmetry in the $\mu_{\ell}$ vs $\ell$ distribution. While both are impacted by the sample size and extinction, the vertex deviation proves more robust, especially when combining stars from multiple observational fields. We also assess the correlation between the line-of-sight velocity and the $h_3$ Gauss-Hermite moment ("skewness") of the line-of-sight velocity but find no clear distinction between an NSD and a nuclear bar based on this metric. Our results suggest that data from the current KMOS survey may allow a marginal detection of a nuclear bar using the vertex deviation method. A companion paper provides further validation and detailed analysis of this approach. Nonetheless, future surveys will provide the high quality data necessary to fully exploit the diagnostics outlined in this study.

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arXiv2026

WALLABY pilot survey: Blinded by the light -- discovery of a fourth member in the ESO 179-013 system

We present new ASKAP/WALLABY HI observations of the nearby dwarf galaxy system ESO 179-013 (Kathryn's Wheel), the nearest known collisional ring galaxy, located 10 Mpc away in the Local Void. The system is composed of three previously known dwarf galaxies embedded in a large HI envelope, with a newly discovered fourth member identified through HI and radio continuum emission behind a bright foreground binary. Galaxy D exhibits the highest star formation rate in the group and deviates from the HI mass-diameter relation, suggesting it is a compact, gas-rich dwarf missed due to stellar foreground contamination. The HI data reveal for the first time an extended HI envelope around the whole system, the neutral gas counterpart of the star-forming ring and gas bridges among members, suggesting a more complex interaction history than the previously proposed collisional ring scenario. ESO 179-013 thus provides a rare opportunity to study hierarchical assembly and gas dynamics in underdense environments and demonstrates the power of blind HI surveys in identifying faint members of low-mass compact groups.

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arXiv2026

Modeling the recent interactions between the Magellanic Clouds and Milky Way

The Large and Small Magellanic Clouds (LMC and SMC, respectively) are the largest satellite galaxies of the Milky Way (MW) and their interactions with each other have given rise to multiple stellar substructures in their periphery as well as the gaseous Magellanic Stream. To better understand the origin of the stellar substructures and constrain their past orbit, we model the past 2.5 Gyr of the interactions between the MW and the LMC and SMC using N-body simulations. Due to the strong interactions, analytical orbit integrations are insufficient to analyze the past galaxy orbits accurately. Therefore, we use a genetic algorithm in combination with N-body simulations to determine the LMC and SMC initial positions and velocities 2.5 Gyr ago that result in the Magellanic Clouds (MCs) arriving near their observed locations and velocities at the current time. After running ~8,000 simulations, our best matching model includes two close interactions between the MCs (940 Myr and 140 Myr ago) and reproduces some observed features of the MCs, including the LMC disc warp, a ring-shaped overdensity in the LMC, the tidal expansion of the SMC, and a greater distance dispersion on the eastern side of the SMC. The LMC disc warp is caused by the most recent interaction with the SMC, which occurred ~140 Myr before the present. The interaction causes global ripples in the LMC disc with a mean amplitude of 1.3 kpc.

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arXiv2026

Insights into the Physical Nature of Polar Ring Galaxies from H I Observations

Polar ring galaxies (PRGs) host an outer ring of gas and stars oriented nearly perpendicular to the main stellar body. They represent extreme examples of misaligned systems and provide valuable insight into galaxy interactions, gas accretion, and peculiar gas dynamics. We compile a complete sample of kinematically confirmed PRGs and collect their H I measurements. Combining literature data with new observations from FAST, we detect H I emission in 22 sources, identify one potential H I absorption feature, and find four non-detections among 40 confirmed PRGs. Compared to galaxies in the ALFALFA and xGASS surveys, PRGs predominantly occupy the green valley or quenched regimes but exhibit higher gas fractions than typical early-type galaxies, suggesting gas accretion. The H I profile asymmetry and shape for PRGs are not consistent with that of the ALFALFA sample with p<0.05. We examine their Tully-Fisher relation (TFR) and baryonic TFR (bTFR), linking the systems' rotation velocities to their masses. The extreme outliers in TFRs for the control sample tend to display single-peaked H I profiles. PRGs do not follow a tight TFR or bTFR if the H I resides primarily in the host galaxy. But the scatter decreases significantly if we assume the gas is mainly distributed in the polar ring. Spatially resolved H I observations are essential to disentangle the gas distribution and kinematics in PRGs, which are key to understanding their formation mechanisms.

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arXiv2025

GASTRO library II: Exploring Chemical Bimodalities in Disk Galaxies with GSE-like Mergers and Massive Star-forming Clumps

We use several smoothed particle hydrodynamics+N-body models as part of the GASTRO library to study the role of high-density star-forming clumpy regions and a single merger on the formation of the $\alpha$-rich and $\alpha$-poor populations in the disk galaxies. These experiments are tailored to mimic what is expected to be the Gaia-Sausage/Enceladus (GSE) accretion event, which occurred circa 10 Gyr ago in the Milky Way (MW). We find that either an early clumpy phase or a retrograde merger significantly reduces the star formation rate (SFR) of the disk, giving rise to a chemical bimodality qualitatively similar to the MW's. The decrease of the SFR as the cause of the chemical bimodality is consistent with previous idealized and cosmological simulations. On the other hand, a prograde radial merger does not significantly modify the SFR of the disk, resulting in no clear chemical bimodality. We further show that stars originating from the inner regions ($R_{form}<4$ kpc) do not create the disk's chemical bimodality, although they can enhance it. Finally, only the models with an early clumpy phase can produce a significant fraction of old, age $>11$ Gyr, $\alpha-$poor stars with disk-like orbits, similar to what has been recently observed in the MW. Our results strengthen the case of clumpy disky galaxies observed at redshift $z\approx 1-2$ as likely progenitors of our Galaxy.

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arXiv2025

Baryonic Masses and Properties of Gaseous Satellite Galaxies

We present a sample of 127 gas-bearing dwarf galaxies around 56 late-type host galaxies within 30 Mpc using 21-cm HI data from the WALLABY, MHONGOOSE, and ALFALFA surveys. We characterize the environment of each dwarf galaxy based on its host galaxy halo and derive optical properties using the DESI Legacy Surveys for 110. The gaseous satellites span $\log (M_{\rm HI}/M_{\odot}) = 5.8-9.7$ and $\log (M_{\star}/M_{\odot}) = 5.6-10.0$, with a median velocity line-width of $W_{50}=40$ km/s, comparable to the Local Group gaseous dwarf galaxies. We assess the HI mass sensitivity of the data by injecting model dwarf galaxies and find $M_{\rm HI,lim} \approx 10^{6.7} M_{\odot}$ for WALLABY and $M_{\rm HI,lim} \approx 10^{5.4} M_{\odot}$ for MHONGOOSE at 10 Mpc. Our sample has lower average atomic gas fractions ($M_{\rm HI}/M_{\star}$) than previous gaseous dwarf samples in field and satellite environments, although this offset partly reflects differences in HI sensitivity. The abundance of gaseous satellites per host is low and increases with host mass: $0-2$ for dwarf centrals and $0-5$ for Milky Way-mass spiral hosts. These numbers are consistent with the Milky Way, M31, and star-forming satellite abundances from recent deep optical surveys. The inferred quenched fractions and gas-depleted satellites indicate that environmental quenching is effective in Milky Way-mass hosts, likely driven by gas stripping processes.

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arXiv2025

The Distribution of Atomic Hydrogen in the Host Galaxies of FRBs

We probe the atomic hydrogen (HI) emission from the host galaxies of fast radio bursts (FRBs) to investigate the emerging trend of disturbance and asymmetry in the population. Quadrupling the sample size, we detect 16 out of 17 new hosts in HI, with the single non-detection arising in a galaxy known to be transitioning towards quiescence. With respect to typical local Universe galaxies, FRB hosts are generally massive in HI ($M_{HI}>10^9 M_\odot$), which aligns with previous studies reporting that FRB hosts also tend to have high stellar masses and are star-forming. However, they span a broad range of other HI derived properties. Using visual inspection alongside various asymmetry metrics, we identify six unambiguously settled host galaxies, demonstrating for the first time that a disturbed HI morphology is not a universal feature of FRB host galaxies. However, we find another six that show clear signs of disturbance, one borderline case, and three which require deeper or more targeted observations to reach a conclusion; this brings the confirmed ratio of disturbed-to-settled FRB hosts to 11:6. Given that roughly a 1:1 ratio is expected for random background galaxies of similar type, our observed ratio yields a p-value of 0.222. Therefore, we conclude that contrary to earlier indications, there is no statistically significant excess of HI disturbance in this sample of FRB host galaxies with respect to the general galaxy population, and hence we find no evidence for a fundamental connection between FRB progenitor formation and merger-induced star formation activity.

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arXiv2025

HI asymmetries in spatially resolved SIMBA galaxies

We present a study of the neutral atomic hydrogen (HI) content of spatially resolved, low-redshift galaxies in the SIMBA cosmological simulations. We create synthetic HI data cubes designed to match observations from the Apertif Medium-Deep HI imaging survey, and follow an observational approach to derive the HI size-mass relation. The HI size-mass relation for SIMBA is in broad agreement with the observed relation to within 0.1 dex, but SIMBA galaxies are slightly smaller than expected at fixed HI mass. We quantify the HI spectral ($A_{\mathrm{flux}}$) and morphological ($A_{\mathrm{mod}}$) asymmetries of the galaxies and motivate standardizing the relative spatial resolution when comparing values in a sample that spans several orders of magnitude in HI mass. Galaxies are classified into three categories (isolated, interacted, or merged) based on their dynamical histories over the preceding ~2 Gyr to contextualize disturbances in their HI reservoirs. We determine that the interacted and merged categories have higher mean asymmetries than the isolated category, with a larger separation between the categories' $A_{\mathrm{mod}}$ distributions than between their $A_{\mathrm{flux}}$ distributions. For the interacted and merged categories, we find an inverse correlation between baryonic mass and $A_{\mathrm{mod}}$ that is not observed between baryonic mass and $A_{\mathrm{flux}}$. These results, coupled with the weak correlation found between $A_{\mathrm{flux}}$ and $A_{\mathrm{mod}}$, highlight the limitations of only using $A_{\mathrm{flux}}$ to infer the HI distributions of spatially unresolved HI detections.

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arXiv2025

Investigating the HI distribution and kinematics of ESO444-G084 and [KKS2000]23: New insights from the MHONGOOSE survey

We present the HI distribution, kinematics, mass modeling, and disk stability of the dwarf irregular galaxies ESO444-G084 and [KKS2000]23 using high-resolution, high-sensitivity MHONGOOSE survey data from MeerKAT. ESO444-G084 shows centrally concentrated HI emission, while [KKS2000]23 exhibits irregular high-density clumps. Total HI fluxes measured down to 10^19 and 10^18 cm^-2 are nearly identical, indicating that the increased HI diameter at lower column densities results mainly from the larger beam, with no significant extra emission detected. We derive total HI masses of (1.1 +/- 0.1) x 10^8 and (6.1 +/- 0.3) x 10^8 solar masses for ESO444-G084 and [KKS2000]23, respectively. Using PyFAT and TiRiFiC, we extract 3D rotation curves that reveal disk-like kinematics in both galaxies. ESO444-G084 shows a warp beyond ~1.8 kpc and a fast-rising curve consistent with a centrally concentrated dark matter distribution, while [KKS2000]23's more gradual rise suggests a more extended halo. Mass modeling with an isothermal halo and stellar mass-to-light ratios of 0.20 for ESO444-G084 and 0.18 for [KKS2000]23 yields consistent results. We analyze disk stability using spatially resolved Toomre Q and gas-to-critical surface density ratios, linking these with H-alpha and FUV-based star formation. ESO444-G084 supports localized star formation despite global stability, while [KKS2000]23 appears gravitationally unstable yet lacks H-alpha, suggesting that turbulence, gas depletion, or past feedback suppresses star formation. No inflows or outflows are detected, indicating internal processes regulate star formation. This study highlights the interplay between HI morphology, kinematics, dark matter distribution, and disk stability, showing how internal processes shape dwarf galaxy evolution.

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arXiv2025

WALLABY pilot survey: Spatially resolved gas scaling relations within the stellar discs of nearby galaxies

The scatter in global atomic hydrogen (HI) scaling relations is partly attributed to differences in how HI and stellar properties are measured, with HI reservoirs typically extending beyond the inner regions of galaxies where star formation occurs. Using pilot observations from the WALLABY survey, we present the first measurements of HI mass enclosed within the stellar-dominated regions of galaxies for a statistical sample of 995 local gas-rich systems, investigating the factors driving its variation. We examine how global HI scaling relations change when measurements are restricted to R25 and R24 -- the isophotal radii at 25 and 24 mag arcsec$^{-2}$ in the i-band -- and explore how the fraction of HI mass and HI surface density within these radii correlate with other galaxy properties. On average, 68% of the total HI mass is enclosed within R25 and 54% within R24, though significant variation exists between galaxies. The fraction of HI mass within R25 shows a mild correlation with stellar properties, with galaxies of higher stellar mass, greater stellar surface density, or redder colours enclosing a larger fraction of their HI reservoirs. These correlations do not significantly strengthen when considering R24. Conversely, global HI surface densities show no significant correlation with stellar mass or stellar surface density, but trends start emerging when these are measured within the inner regions of galaxies. The strongest correlation is observed with optical colour, with bluer galaxies having higher average HI surface densities within R25. This trend strengthens when we restrict from R25 to R24, suggesting a closer connection between inner HI reservoirs and star formation. This study underscores the value of (at least marginally) resolved HI surveys of statistical samples for advancing our understanding of the gas-star formation cycle in galaxies. [Abriged]

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arXiv2025

WALLABY Pilot Survey & ASymba: Comparing HI Detection Asymmetries to the SIMBA Simulation

An avenue for understanding cosmological galaxy formation is to compare morphometric parameters in observations and simulations of galaxy assembly. In this second paper of the ASymba: Asymmetries of HI in SIMBA Galaxies series, we measure atomic gas HI asymmetries in spatially-resolved detections from the untargetted WALLABY survey, and compare them to realizations of WALLABY-like mock samples from the SIMBA cosmological simulations. We develop a Scanline Tracing method to create mock galaxy HI datacubes which minimizes shot noise along the spectral dimension compared to particle-based methods, and therefore spurious asymmetry contributions. We compute 1D and 3D asymmetries for spatially-resolved WALLABY Pilot Survey detections, and find that the highest 3D asymmetries A3D>0.5 stem from interacting systems or detections with strong bridges or tails. We then construct a series of WALLABY-like mock realizations drawn from the SIMBA 50 Mpc simulation volume, and compare their asymmetry distributions. We find that the incidence of high A3D detections is higher in WALLABY than in the SIMBA mocks, but that difference is not statistically significant (p-value = 0.05). The statistical power of quantitative comparisons of asymmetries such as the one presented here will improve as the WALLABY survey progresses, and as simulation volumes and resolutions increase.

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arXiv2024

WALLABY Pilot Survey: Star Formation Enhancement and Suppression in Gas-rich Galaxy Pairs

Galaxy interactions can significantly affect the star formation in galaxies, but it remains a challenge to achieve a consensus on the star formation rate (SFR) enhancement in galaxy pairs. Here, we investigate the SFR enhancement of gas-rich galaxy pairs detected by the Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY). We construct a sample of 278 paired galaxies spanning a stellar mass ($M_\ast$) range from $10^{7.6}$ to $10^{11.2}M_\odot$. We obtain individual masses of atomic hydrogen (HI) for these paired galaxies, using a novel deblending algorithm for HI data cubes. Quantifying the interaction stages and strengths with parameters motivated by first principles, we find that at fixed stellar and HI mass, the alteration in SFR of galaxy pairs starts when their dark matter halos encounter. For galaxies with stellar mass lower than $10^9M_\odot$, their SFRs show tentative suppression of 1.4 sigma after the halo encounter, and then become enhanced when their HI disks overlap, regardless of mass ratios. In contrast, the SFRs of galaxies with $M_\ast > 10^9M_\odot$ increase monotonically toward smaller projected distances and radial velocity offsets. When a close companion is present, a pronounced SFR enhancement is found for the most HI-poor high-mass galaxies in our sample. Collecting the observational evidence, we provide a coherent picture of the evolution of galaxy pairs, and discuss how the tidal effects and hydrodynamic processes shape the SFR enhancement. Our results provide a coherent picture of gas-rich galaxy interactions and impose constraints on the underlying physical processes.

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arXiv2024

WALLABY Pilot Survey: HI source-finding with a machine learning framework

The data volumes generated by the WALLABY atomic Hydrogen (HI) survey using the Australiian Square Kilometre Array Pathfinder (ASKAP) necessitate greater automation and reliable automation in the task of source-finding and cataloguing. To this end, we introduce and explore a novel deep learning framework for detecting low Signal-to-Noise Ratio (SNR) HI sources in an automated fashion. Specfically, our proposed method provides an automated process for separating true HI detections from false positives when used in combination with the Source Finding Application (SoFiA) output candidate catalogues. Leveraging the spatial and depth capabilities of 3D Convolutional Neural Networks (CNNs), our method is specifically designed to recognise patterns and features in three-dimensional space, making it uniquely suited for rejecting false positive sources in low SNR scenarios generated by conventional linear methods. As a result, our approach is significantly more accurate in source detection and results in considerably fewer false detections compared to previous linear statistics-based source finding algorithms. Performance tests using mock galaxies injected into real ASKAP data cubes reveal our method's capability to achieve near-100% completeness and reliability at a relatively low integrated SNR~3-5. An at-scale version of this tool will greatly maximise the science output from the upcoming widefield HI surveys.

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arXiv2024

WALLABY Pilot Survey: the Tully-Fisher relation in the NGC 4808, Vela and NGC 5044 fields

The Tully-Fisher Relation (TFR) is a well-known empirical relationship between the luminosity of a spiral galaxy and its circular velocity, allowing us to estimate redshift independent distances. Here we use high signal-to-noise HI 21-cm integrated spectra from the second pilot data release (PDR2, 180 deg2) of the Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY). In order to prepare for the full WALLABY survey, we have investigated the TFR in phase 2 of the pilot survey with a further three fields. The data were obtained with wide-field Phased Array Feeds on the Australian Square Kilometre Array Pathfinder (ASKAP) and have an angular resolution of 30 arcsec and a velocity resolution of ~4 km/s. Galaxy luminosities have been measured from the Wide-field Infrared Survey Explorer (WISE), and optical galaxy inclinations from the Dark Energy Camera Legacy Survey. We present TFRs for wavelengths from 0.8-3.4{\mu}m. We examine sources of galaxy inclination data and investigate magnitudes from the DECam Local Volume Exploration Survey (DELVE) and DENIS catalogues and the 4HS target catalogue based on the VISTA Hemisphere Survey (VHS). We consider the baryonic TFR. These are all of interest for TFR using the full WALLABY survey of 200,000 galaxies. We demonstrate that WALLABY TFR distances can take their place among state of the art studies of the local velocity field.

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arXiv2023

Orbital support and evolution of flat profiles of bars (shoulders)

Many barred galaxies exhibit upturns (shoulders) in their bar major-axis density profile. Simulation studies have suggested that shoulders are supported by looped $x_1$ orbits, occur in growing bars, and can appear after bar-buckling. We investigate the orbital support and evolution of shoulders via frequency analyses of orbits in simulations. We confirm that looped orbits are shoulder-supporting, and can remain so, to a lesser extent, after being vertically thickened. We show that looped orbits appear at the resonance $(\Omega_\varphi - \Omega_\mathrm{P})/\Omega_R=1/2$ (analogous to the classical Inner Lindblad Resonance, and here called ILR) with vertical-to-radial frequency ratios $1 \lesssim\Omega_z/\Omega_R \lesssim 3/2$ (vertically warm orbits). Cool orbits at the ILR (those with $\Omega_z/\Omega_R > 3/2$) are vertically thin and have no loops, contributing negligibly to shoulders. As bars slow and thicken, either secularly or by buckling, they populate warm orbits at the ILR. Further thickening carries these orbits towards crossing the vertical ILR [vILR, $(\Omega_\varphi - \Omega_\mathrm{P})/\Omega_z=1/2$], where they convert in-plane to vertical motion, become chaotic, kinematically hotter and less shoulder-supporting. Hence, persistent shoulders require bars to trap new stars, consistent with the need for a growing bar. Since buckling speeds up trapping on warm orbits at the ILR, it can be followed by shoulder formation, as seen in simulations. This sequence supports the recent observational finding that shoulders likely precede the emergence of BP-bulges. The python module for the frequency analysis, naif, is made available.

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