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Paul C. Clark

Publications and source records attributed to Paul C. Clark.

At least 19 recordsLinked to original sources

SEEDZ: Rapid Galaxy Assembly as a Pathway to Supermassive Stars, Dense Stellar Environments and Massive Black Hole Seeds

We investigate the assembly history of early galaxies in the SEEDZ hydrodynamic simulations, to investigate the high inflow rates believed to be required for the formation of supermassive stars (SMSs), dense stellar clusters and subsequently heavy seed black holes. Using a heavy seed formation criteria of $>$1 M$_\odot$ yr$^{-1}$ flowing into 10 pc regions, we find that heavy seeds form in halos that grow rapidly compared to those halos that never meet the criteria. Halos with growth rates of $\gtrsim$1 M$_\odot$ yr$^{-1}$ at their virial radius (scales of a few hundred pc) are able to sustain a flow rate of 0.1 M$_\odot$ yr$^{-1}$ into the inner 1 pc of the halo, maintaining higher density environments within the central 10 - 100~pc. These halos continue to grow rapidly after their initial collapse, typically forming heavy seeds $\sim$100 Myr after forming their first stars and stellar mass black holes. By $z=10$, most heavy seeds form in regions of near-solar metallicity, although a minority of heavy seeds do continue to form in low metallicity (10$^{-2}$ Z$_\odot$) regions. Under the assumption that a SMS forms as the progenitor to a heavy seed if it forms in a region of low (10$^{-2}$ Z$_\odot$) metallicity, and can sustain high accretion rates above 0.02 M$_\odot$ yr$^{-1}$ throughout the SMS lifetime of 2 Myr, we find a number density of SMSs of 0.1 cMpc$^{-3}$, meaning that only a fraction of 10$^{-4}$ of these SMSs would need to be visible to JWST to account for the observed population of Little Red Dot galaxies.

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Black Hole Feedback, Galaxy Quenching and Outflows at Cosmic Dawn: Analysis of the SEEDZ Simulations

Here we analyse the growth and feedback effects of massive black holes (MBHs) in the SEEDZ simulations. The most massive black holes grow to masses of $\sim10^{6}$ M$_\odot$ by $z=12.5$ during short bursts of super-Eddington accretion, sustained over a period of 5-30 Myr. We find that the determining factor that cuts off this initial growth is feedback from the MBH itself, rather than nearby supernovae or exhausting the available gas reservoir. Our simulations show that for the most actively accreting MBHs, feedback completely evacuates the gas from the host halo and ejects it into the inter-galactic medium. Despite implementing a relatively weak feedback model, the energy injected into the gas surrounding the MBH exceeds the binding energy of the halo. These results either indicate that MBH feedback in the early ($Λ$CDM) Universe is much weaker than previously assumed, or that at least some of the high redshift galaxies we currently observe with JWST formed via a two-step process, whereby a MBH initially quenches its host galaxy and later reconstitutes its baryonic reservoir, either through mergers with gas rich galaxies or from accretion from the cosmic web. Moreover, the maximum black hole masses that emerge in SEEDZ are effectively set by a combination of MBH feedback modelling and the binding potential of the host halo. Unless feedback is extremely ineffective at early times (for example if growth is merger dominated rather than accretion dominated or feedback is contained close to the MBH) then the maximum mass of black holes at redshift before 12.5 should not significantly exceed $10^6$ M$_\odot$.

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The Impact of Radiation Environment on the Evolution and Fragmentation of Protostellar Discs

We present high-resolution zoom-in simulations of molecular clouds exposed to an interstellar radiation field and cosmic ray ionisation rate up to 1000 times stronger than that of the solar neighbourhood. We detail the evolution of the accretion discs that form around the first protostar in each simulation, for a total of 7 discs, for up to 100 kyr. The use of a zoom-in procedure allows for the au-scale discs to be well resolved (with resolution < 0.25 au) whilst retaining the structure of the wider parsec-scale molecular cloud. We find that discs exposed to a stronger radiation field tend to be more massive, hotter and denser. Similarly, their host stars grow to become more massive as a result of accreting more rapidly from their surroundings. All the discs show evidence of recurrent instability during the simulations, but only some of them fragment. We investigate whether stability metrics, such as the Toomre $Q$, $α$ viscosity, and $β$ cooling parameter, can predict fragmentation by calculating them just before the discs fragment. We find that the metrics are generally unable to do so, as the discs appear stable even up to a few hundred years before fragmenting. In solar-like environments fragments are typically of planetary mass and often migrate to the centre of the disc, whereas fragments in a high-radiation environment are massive ($\rm > 0.1 \, M_\odot$) and fully disrupt/accrete from the progenitor disc. We conclude that the evolution and properties of circumstellar discs depend on both their radiation and physical environment.

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The Impact of Fuzzy Dark Matter Dynamics on the Accumulation and Fragmentation of Primordial Gas

Fuzzy Dark Matter (FDM), particularly in the $10^{-22}$ eV mass regime is frequently used to characterize wave-like interference effects. It exhibits macroscopic wave properties, which drive distinct baryonic dynamics within collapsed haloes. Using the hydrodynamical code AREPO with the AxiREPO module and primordial chemistry, we simulate the assembly of haloes with masses $3 \times 10^{8} \le M_{\mathrm{h}} \le 8 \times 10^{9} \: M_\odot$ across a range of axion masses $1 \times 10^{-22} \le m_{\mathrm{a}} \le 7 \times 10^{-22}$ eV. We investigate how small-scale dynamics of the FDM density field affect the accumulation of cold, dense gas essential for primordial star formation. We demonstrate that gas collapse is suppressed by a two-fold mechanism: a delay driven by the geometry of the FDM solitonic core and a secondary dynamical barrier caused by stochastic wave fluctuations. While the flattened solitonic potential profile itself inhibits central gas accumulation, these wave-driven dynamics provide a further layer of disruption and angular momentum support, which in certain regimes prevents gas from reaching the central, compact, high-density configurations characteristic of CDM. Consequently, sites of star formation are shifted away from a single central peak toward a population of lower-mass clusters. Our work provides a physical framework for calibrating halo mass-dependent star formation efficiencies in FDM cosmologies, where internal processes may delay Cosmic Dawn beyond the effects of the initial power spectrum cut-off. These results are essential for interpreting realistic observational constraints from future 21-cm signal observations and the faint-end luminosity functions observed by the JWST, as well as providing an upper bound on the baryonic effects in the context of Mixed Dark Matter scenarios.

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The SEEDZ Simulations: Methodology and First Results on Massive Black Hole Seeding and Early Galaxy Growth

Here we introduce the SEEDZ simulations, a suite of cosmological hydrodynamic simulations exploring the formation and growth of the first massive black holes in the Universe. SEEDZ includes models for Population III star formation, supernovae explosions and the resulting formation of light seed black holes, metal enrichment and subsequent Population II star formation, heavy seed black hole formation, Eddington and super-Eddington accretion schemes as well as black hole feedback. In this paper, we cover the overall methodologies employed and present our current results at $z=15$. Our main result so far is that black holes initially grow faster than their host galaxy, and hence over-massive black holes are a feature of the high-redshift Universe. The fundamental black hole-galaxy relationships we observe at $z = 0$ (especially the M$_{\rm BH}$ - M$_*$ relationship) likely only emerge in more mature galaxies. At high-redshift, that relationship has not yet been established. We find that even at these high redshifts, MBHs can grow from their initial heavy seed mass of $\sim$10$^4$ M$_\odot$ up to 10$^6$ M$_\odot$. At the high end of our MBH masses, our simulated galaxy M$_{\rm BH}$ - M$_*$ relations match the observed high redshift trends i.e. over-massive BHs with M$_{\rm BH}$/M$_{\rm star} \sim 10^{-2}$. This initial set of simulations will continue to run down to $z=10$, where we will perform a comprehensive comparison of simulated MBH number densities and M$_{\rm BH}$ - M$_*$ relations with JWST observations. Further simulations with higher resolution will then follow.

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The fragmentation of molecular clouds in starburst environments

A significant amount of star formation occurs and has occurred in environments unlike the solar neighbourhood. The majority of stars formed closer to the peak of the cosmic star formation rate (z > 1.3) and a great deal of star formation presently occurs in the central molecular zone (CMZ) of the Galaxy. These environments are unified by the presence of a high interstellar radiation field (ISRF) and a high cosmic ray ionisation rate (CRIR). Numerical studies of stellar birth typically neglect this fact, and those that do not have thus far been limited in scope. In this work we present the first comprehensive analysis of hydrodynamical simulations of star formation in extreme environments where we have increased the ISRF and CRIR to values typical of the CMZ and starburst galaxies. We note changes in the fragmentation behaviour on both the core and stellar system scale, leading to top-heavy core and stellar system mass functions in high ISRF/CRIR clouds. Clouds fragment less on the core scale, producing fewer but more massive cores. Conversely, the cores fragment more intensely and produce richer clusters of stellar systems. We present a picture where high ISRF/CRIR clouds fragment less on the scale of cores and clumps, but more on the scale of stellar systems. The change in fragmentation behaviour subsequently changes the mass function of the stellar systems that form through enhanced accretion rates.

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Do stars still form in molecular gas within CO-dark dwarf galaxies?

In the Milky Way and other main-sequence galaxies, stars form exclusively in molecular gas, which is traced by CO emission. However, low metallicity dwarf galaxies are often `CO-dark' in the sense that CO emission is not observable even at the high resolution and sensitivities of modern observing facilities. In this work we use ultra high-resolution simulations of four low-metalicity dwarf galaxies (which resolve star formation down to the scale of star-forming cores, 0.01 pc) combined with a time-dependent treatment of the chemistry of the interstellar medium, to investigate the star formation environment in this previously hidden regime. By generating synthetic observations of our models we show that the galaxies have high to extremely high dark gas fractions (0.13 to 1.00 dependent on beam size and conditions), yet despite this form stars. However, when examined on smaller scales, we find that the stars still form in regions dominated by molecular gas, it is simply that these are far smaller than the scale of the beam (1.5"). Thus, while stars in CO-dark dwarf galaxies form in small molecular cores like larger galaxies, their cloud-scale environment is very different.

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Assessing the accuracy of the star formation rate measurements by direct star count in molecular clouds

Star formation estimates based on the counting of YSOs is commonly applied to nearby star-forming regions in the Galaxy. With this method, the SFRs are measured using the counts of YSOs in a particular protostellar Class, a typical protostellar mass, and the lifetime associated with this Class. However, the assumptions underlying the validity of the method such as that of a constant star formation history (SFH) and whether the method is valid for all protostellar Classes has never been fully tested. In this work, we use Monte Carlo models to test the validity of the method. We build synthetic clusters in which stars form at times that are randomly drawn from a specified SFH. The latter is either constant or time-dependent with a burst like behavior. The masses of the protostars are randomly drawn from an IMF which can be either similar to that of the Milky Way field or be variable . For each star in every cluster, the lifetimes associated with the different protostellar classes are also randomly drawn from Gaussian distribution functions centered around their most likely value as suggested by the observations. We find that only the SFR derived using the Class 0 population can reproduce the true SFR at all epochs, and this is true irrespective of the shape of the SFH. For a constant SFH, the SFR derived using the more evolved populations of protostars (Classes I, F, II, and III) reproduce the real SFR only at later epochs which correspond to epochs at which their numbers have reached a steady state. For a time-dependent burst-like SFH, all SFR estimates based on the number counts of the evolved populations fail to reproduce the true SFR. We also show how the offsets between Class I and Class II based SFRs and the true SFR plotted as a function of the number ratios of Class I and Class II versus Class III YSOs can be used in order to constrain the SFH of observed molecular clouds.

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Self-consistent modelling of the Milky Way structure using live potentials

To advance our understanding of the evolution of the interstellar medium (ISM) of our Galaxy, numerical models of Milky Way (MW) type galaxies are widely used. However, most models only vaguely resemble the MW (e.g. in total mass), and often use imposed analytic potentials (which cannot evolve dynamically). This poses a problem in asserting their applicability for the interpretation of observations of our own Galaxy. The goal of this work is to identify a numerical model that is not only a MW-type galaxy, but one that can mimic some of the main observed structures of our Galaxy, using dynamically evolving potentials, so that it can be used as a base model to study the ISM cycle in a galaxy like our own. This paper introduces a suite of 15 MW-type galaxy models developed using the {\sc arepo} numerical code, that are compared to Galactic observations of $^{12}$CO and \ion{H}{I} emission via longitude-velocity plots, from where we extract and compare the skeletons of major galactic features and the terminal gas velocities. We found that our best-fitting model to the overall structure, also reproduces some of the more specific observed features of the MW, including a bar with a pattern speed of $30.0 \pm 0.2$ km\,s$^{-1}$\,kpc$^{-1}$, a bar half-length of $3.2 \pm 0.8$\,kpc. Our model shows large streaming motions around spiral arms, and strong radial motions well beyond the inner bar. This model highlights the complex motions of a dynamic MW-type galaxy and has the potential to offer valuable insight into how our Galaxy regulates the ISM and star formation.

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Population III star formation: multiple gas phases prevent the use of an equation of state at high densities

Advanced primordial chemistry networks have been developed to model the collapse of metal-free baryonic gas within the gravitational well of dark matter (DM) halos and its subsequent collapse into Population III stars. At the low densities of 10^-26-10^-21 g cm-3 (10-3-10^2 cm-3) the collapse is dependent on H2 production, which is a function of the compressional heating provided by the DM potential. Once the gas decouples from the DM, the temperature-density relationship follows a well established path dictated by various chemical reactions until the formation of the protostar at 10^-4 g cm-3 (10^19 cm-3). Here we explore the feasibility of replacing the chemical network (CN) with a barotropic equation of state (EoS) just before the formation of the first protostar, to reduce the computational load of simulating the further fragmentation, evolution and characteristics of the very high density gas. We find a significant reduction in fragmentation when using the EoS. The EoS method produces a protostellar mass distribution that peaks at higher masses when compared to CN runs. The change in fragmentation behaviour is due to a lack of cold gas falling in through the disc around the first protostar when using an EoS. Despite this, the total mass accreted across all sinks was invariant to the switch to an EoS, hence the star formation rate (Msun yr^-1) is accurately predicted using an EoS. The EoS routine is approximately 4000 times faster than the CN, however this numerical gain is offset by the lack of accuracy in modelling secondary protostar formation and hence its use must be considered carefully.

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Heavy Black Hole Seed Formation in High-z Atomic Cooling Halos

Halos with masses in excess of the atomic limit are believed to be ideal environments in which to form heavy black hole seeds with masses above 10^3 Msun. In cases where the H_2 fraction is suppressed this is expected to lead to reduced fragmentation of the gas and the generation of a top heavy initial mass function. In extreme cases this can result in the formation of massive black hole seeds. Resolving the initial fragmentation scale and the resulting protostellar masses has, until now, not been robustly tested. Cosmological simulations were performed with the moving mesh code Arepo using a primordial chemistry network until z = 11. Three haloes with masses in excess of the atomic cooling mass were then selected for detailed examination via zoom-ins. The highest resolution simulations resolve densities up to 10^-6 g cm^-3 (10^18 cm^-3) and capture a further 100 yr of fragmentation behaviour at the center of the halo. Our simulations show intense fragmentation in the central region of the halos, leading to a large number of near-solar mass protostars. Despite the increased fragmentation the halos produce a protostellar mass spectrum that peaks at higher masses relative to standard Population III star forming halos. The most massive protostars have accretion rates of 10^-3-10^-1 Msun yr^-1 after the first 100 years of evolution, while the total mass of the central region grows at 1 Msun yr^-1. Lower resolution zoom-ins show that the total mass of the system continues to accrete at 1 Msun yr^-1 for at least 10^4 yr, although how this mass is distributed amongst the rapidly growing number of protostars is unclear. However, assuming that a fraction of stars can continue to accrete rapidly the formation of a sub-population of stars with masses in excess of 10^3 Msun is likely in these halos.

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From dark matter halos to pre-stellar cores: High resolution follow-up of cosmological Lyman-Werner simulations

Molecular hydrogen allows cooling in primordial gas, facilitating its collapse into Population III stars within primordial halos. Lyman-Werner (LW) radiation from these stars can escape the halo and delay further star formation by destroying H$_2$ in other halos. As cosmological simulations show that increasing the background LW field strength increases the average halo mass required for star formation, we perform follow-up simulations of selected halos to investigate the knock-on effects this has on the Population III IMF. We follow 5 halos for each of the $J_{21}$ = 0, 0.01 and 0.1 LW field strengths, resolving the pre-stellar core density of $10^{-6}$ g cm$^{-3}$ (10$^{18}$ cm$^{-3}$) before inserting sink particles and following the fragmentation behaviour for hundreds of years further. We find that the mass accreted onto sinks by the end of the simulations is proportional to the mass within the $\sim 10^{-2}$ pc molecular core, which is not correlated to the initial mass of the halo. As such, the IMFs for masses above the brown dwarf limit show little dependence on the LW strength, although they do show variance in the number of low-mass clumps formed. As the range of background LW field strengths tested here covers the most likely values from literature, we conclude that the IMF for so-called Pop III.2 stars is not significantly different from the initial population of Pop III.1 stars. The primordial IMF therefore likely remains unchanged until the formation of the next generation of Population II stars.

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On the density regime probed by HCN emission

HCN J$\, =\,$1$\, -\,$0 emission is commonly used as a dense gas tracer, thought to mainly arise from gas with densities $\mathrm{\sim 10^4\ -\ 10^5\ cm^{-3}}$. This has made it a popular tracer in star formation studies. However, there is increasing evidence from observational surveys of `resolved' molecular clouds that HCN can trace more diffuse gas. We investigate the relationship between gas density and HCN emission through post-processing of high resolution magnetohydrodynamical simulations of cloud-cloud collisions. We find that HCN emission traces gas with a mean volumetric density of $\mathrm{\sim 3 \times 10^3\ cm^{-3}}$ and a median visual extinction of $\mathrm{\sim 5\ mag}$. We therefore predict a characteristic density that is an order of magnitude less than the "standard" characteristic density of $\mathrm{n \sim 3 \times 10^4\ cm^{-3}}$. Indeed, we find in some cases that there is clear HCN emission from the cloud even though there is no gas denser than this standard critical density. We derive luminosity-to-mass conversion factors for the amount of gas at $A_{\rm V} > 8$ or at densities $n > 2.85 \times 10^{3} \: {\rm cm^{-3}}$ or $n > 3 \times 10^{4} \: {\rm cm^{-3}}$, finding values of $α_{\rm HCN} = 6.79, 8.62$ and $27.98 \: {\rm M_{\odot}} ({\rm K \, km \, s^{-1} \, pc^{2}})$, respectively. In some cases, the luminosity to mass conversion factor predicted mass in regions where in actuality there contains no mass.

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Towards the impact of GMC collisions on the star formation rate

Collisions between giant molecular clouds (GMCs) are one of the pathways for massive star formation, due to the high densities created. However the enhancement of the star formation rate (SFR) is not well constrained. In this study we perform a parameter study of cloud-cloud collisions, and investigate how the resulting SFR depends on the details of set-up. Our parameter study explores variations in: collision speed; magnetic field inclination (with respect to the collisional axis); and resolution, as defined by the number of cells per Jeans length. In all our collision simulations we find a factor of 2-3 increase in the SFR compared to our no collision simulation, with star formation beginning sooner with a) high collisional velocities, b) parallel orientation between the magnetic field and collision axis, c) and lower resolution. The mean virial parameter of high density (and thus possible star-forming) gas increases with collisional velocity, but has little variation with magnetic field inclination. The alignment of the velocity and magnetic field remains uniform in low density environments but becomes more perpendicular with increasing density, indicating the compression of the magnetic field by collapsing gas. Comparing the trends in the SFR with other GMC collision studies, we find good agreement with studies that account for the gravitational boundedness of the gas in their star formation algorithm, but not with those that simply form stars above a prescribed density threshold. This suggests that the latter approach should be used with caution when modelling star formation on resolved cloud scales.

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Fragmentation induced starvation in Population III star formation: a resolution study

The Population III initial mass function (IMF) is currently unknown, but recent studies agree that fragmentation of primordial gas gives a broader IMF than the initially suggested singular star per halo. In this study we introduce sink particle mergers into Arepo, to perform the first resolution study for primordial star formation simulations and present the first Population III simulations to run up to densities of 10-6g cm-3 for hundreds of years after the formation of sink particles. The total number of sinks formed increases with increasing sink particle creation density, without achieving numerical convergence. The total mass in sinks remains invariant to the maximum resolution and is safe to estimate using low resolution studies. This results in an IMF that shifts towards lower masses with increasing resolution. Greater numbers of sinks cause increased fragmentation-induced starvation of the most massive sink, yielding lower accretion rates, masses and ionising photons emitted per second. The lack of convergence up to densities 2 orders of magnitudes higher than all relevant chemical reactions suggests that the number of sinks will continue to grow with increasing resolution until H2 is fully dissociated and the collapse becomes almost adiabatic at 10-4g cm-3. These results imply that many Population III studies utilising sink particles have produced IMFs which have overestimated the masses of primordial stars, and underestimated the number of stars formed. In the highest resolution runs, sinks with masses capable of surviving until the present day had an ejection fraction of 0.21.

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High contrast and resolution near infrared photometry of the core of R136

We present the sharpest and deepest near infrared photometric analysis of the core of R136, a newly formed massive star cluster at the centre of the 30 Doradus star forming region in the Large Magellanic Cloud. We used the extreme adaptive optics of the SPHERE focal instrument implemented on the ESO Very Large Telescope and operated in its IRDIS imaging mode, for the second time with longer exposure time in the H- and K filters. Our aim was to (i) increase the number of resolved sources in the core of R136, and (ii) to compare with the first epoch to classify the properties of the detected common sources between the two epochs. Within the field of view (FOV) of 10.8"x12.1" (2.7pc x3.0pc), we detected 1499 sources in both H and K filters, for which 76% of these sources have visual companions closer than 0.2". The larger number of detected sources, enabled us to better sample the mass function (MF). The MF slopes are estimated at ages of 1, 1.5 and 2 Myr, at different radii, and for different mass ranges. The MF slopes for the mass range of 10-300 solar-mass are about 0.3 dex steeper than the mass range of 3-300 solar-mass, for the whole FOV and different radii. Comparing the JHK colours of 790 sources common in between the two epochs, 67% of detected sources in the outer region (r >3") are not consistent with evolutionary models at 1-2 Myr and with extinctions similar to the average cluster value, suggesting an origin from ongoing star formation within 30 Doradus, unrelated to R136.

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The Cloud Factory II: Gravoturbulent Kinematics of Resolved Molecular Clouds in a Galactic Potential

We present a statistical analysis of the gravoturbulent velocity fluctuations in molecular cloud complexes extracted from our "Cloud Factory" galactic-scale ISM simulation suite. For this purpose, we produce non-LTE $^{12}$CO J=1-0 synthetic observations and apply the Principal Component Analysis (PCA) reduction technique on a representative sample of cloud complexes. The velocity fluctuations are self-consistently generated by different physical mechanisms at play in our simulations, which include galactic-scale forces, gas self-gravity, and supernova feedback. The statistical analysis suggests that, even though purely gravitational effects are necessary to reproduce standard observational laws, they are not sufficient in most cases. We show that the extra injection of energy from supernova explosions plays a key role in establishing the global turbulent field and the local dynamics and morphology of molecular clouds. Additionally, we characterise structure function scaling parameters as a result of cloud environmental conditions: some of the complexes are immersed in diffuse (inter-arm) or dense (spiral-arm) environments, and others are influenced by embedded or external supernovae. In quiescent regions, we obtain time-evolving trajectories of scaling parameters driven by gravitational collapse and supersonic turbulent flows. Our findings suggests that a PCA-based statistical study is a robust method to diagnose the physical mechanisms that drive the gravoturbulent properties of molecular clouds. Also, we present a new open source module, the PCAFACTORY, which smartly performs PCA to extract velocity structure functions from simulated or real data of the ISM in a user-friendly way. Software DOI: 10.5281/zenodo.3822718

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Simulations of the Milky Way's central molecular zone -- II. Star formation

The Milky Way's central molecular zone (CMZ) has emerged in recent years as a unique laboratory for the study of star formation. Here we use the simulations presented in Tress et al. 2020 to investigate star formation in the CMZ. These simulations resolve the structure of the interstellar medium at sub-parsec resolution while also including the large-scale flow in which the CMZ is embedded. Our main findings are as follows. (1) While most of the star formation happens in the CMZ ring at $R\gtrsim100 {\, \rm pc}$, a significant amount also occurs closer to SgrA* at $R \lesssim 10{\, \rm pc}$. (2) Most of the star formation in the CMZ happens downstream of the apocentres, consistent with the "pearls-on-a-string" scenario, and in contrast to the notion that an absolute evolutionary timeline of star formation is triggered by pericentre passage. (3) Within the timescale of our simulations ($\sim100$ Myr), the depletion time of the CMZ is constant within a factor of $\sim2$. This suggests that variations in the star formation rate are primarily driven by variations in the mass of the CMZ, caused for example by AGN feedback or externally-induced changes in the bar-driven inflow rate, and not by variations in the depletion time. (4) We study the trajectories of newly born stars in our simulations. We find several examples that have age and 3D velocity compatible with those of the Arches and Quintuplet clusters. Our simulations suggest that these prominent clusters originated near the collision sites where the bar-driven inflow accretes onto the CMZ, at symmetrical locations with respect to the Galactic centre, and that they have already decoupled from the gas in which they were born.

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