arXiv subjects

A. P. Whitworth

Publications and source records attributed to A. P. Whitworth.

At least 37 records · Page 2Linked to original sources

arXiv2019

L1495 Revisited: A PPMAP View of a Star-Forming Filament

We have analysed the Herschel and SCUBA-2 dust continuum observations of the main filament in the Taurus L1495 star forming region, using the Bayesian fitting procedure PPMAP. (i) If we construct an average profile along the whole length of the filament, it has fwhm $\simeq 0.087\pm 0.003\,{\rm pc};\;$, but the closeness to previous estimates is coincidental. (ii) If we analyse small local sections of the filament, the column-density profile approximates well to the form predicted for hydrostatic equilibrium of an isothermal cylinder. (iii) The ability of PPMAP to distinguish dust emitting at different temperatures, and thereby to discriminate between the warm outer layers of the filament and the cold inner layers near the spine, leads to a significant reduction in the surface-density, $\varSigma$, and hence in the line-density, $μ$. If we adopt the canonical value for the critical line-density at a gas-kinetic temperature of $10\,{\rm K}$, $μ_{_{\rm CRIT}}\simeq 16\,{\rm M_{_\odot}\,pc^{-1}}$, the filament is on average trans-critical, with ${\barμ}\sim μ_{_{\rm CRIT}};\;$ local sections where $μ>μ_{_{\rm CRIT}}$ tend to lie close to pre-stellar cores. (iv) The ability of PPMAP to distinguish different types of dust, i.e. dust characterised by different values of the emissivity index, $β$, reveals that the dust in the filament has a lower emissivity index, $β\leq1.5$, than the dust outside the filament, $β\geq 1.7$, implying that the physical conditions in the filament have effected a change in the properties of the dust.

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arXiv2019

Modelling the structure of star clusters with fractional Brownian motion

The degree of fractal substructure in molecular clouds can be quantified by comparing them with Fractional Brownian Motion (FBM) surfaces or volumes. These fields are self-similar over all length scales and characterised by a drift exponent $H$, which describes the structural roughness. Given that the structure of molecular clouds and the initial structure of star clusters are almost certainly linked, it would be advantageous to also apply this analysis to clusters. Currently, the structure of star clusters is often quantified by applying $\mathcal{Q}$ analysis. $\mathcal{Q}$ values from observed targets are interpreted by comparing them with those from artificial clusters. These are typically generated using a Box-Fractal (BF) or Radial Density Profile (RDP) model. We present a single cluster model, based on FBM, as an alternative to these models. Here, the structure is parameterised by $H$, and the standard deviation of the log-surface/volume density $σ$. The FBM model is able to reproduce both centrally concentrated and substructured clusters, and is able to provide a much better match to observations than the BF model. We show that $\mathcal{Q}$ analysis is unable to estimate FBM parameters. Therefore, we develop and train a machine learning algorithm which can estimate values of $H$ and $σ$, with uncertainties. This provides us with a powerful method for quantifying the structure of star clusters in terms which relate to the structure of molecular clouds. We use the algorithm to estimate the $H$ and $σ$ for several young star clusters, some of which have no measurable BF or RDP analogue.

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arXiv2018

Evolution of Hubble wedges in episodic protostellar outflows

Young low-mass protostars undergo short phases of high accretion and outburst activity leading to lumpy outflows. Recent observations have shown that the position-velocity and mass-velocity diagrams of such outflows exhibit individual bullet-like features; some of these bullets subscribe to a `Hubble Law' velocity relation, and others are manifest as `Hubble wedges'. In order to explore the origin of these features, we have developed a new episodic outflow model for the SPH code {\sc gandalf}, which mimics the accretion and ejection behaviour of FU Ori type stars. We apply this model to simulations of star formation, invoking two types of initial conditions: spherically symmetric cores in solid-body rotation with $ρ\propto r^{-2}$, and spherically symmetric turbulent cores with density proportional to the density of a Bonnor-Ebert sphere. For a wide range of model parameters, we find that episodic outflows lead to self-regulation of the ejected mass and momentum, and we achieve acceptable results, even with relatively low resolution. Using this model, we find that recently ejected outflow bullets produce a `Hubble wedge' in the position-velocity relation. However, once such a bullet hits the leading shock front, it decelerates and aligns with older bullets to form a `Hubble-law'. Bullets can be identified as bumps in the mass-velocity relation, which can be fit with a power-law, $dM/d\upsilon_{_{\rm RAD}}\propto\upsilon_{_{\rm RAD}}^{-1.5}$.

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arXiv2018

RCW 120: A possible case of hit and run, elucidated by multi temperature dust mapping

We present resolution-enhanced images of warm dust at multiple temperatures and opacity index values in the star-forming bubble/HII region, RCW 120. The image set, representing a 4D hypercube of differential column density, was obtained using our Bayesian procedure, ppmap. The cool peripheral material ($\sim16$-22 K) exhibits ragged clumpy structure as noted previously by others. However, at higher temperatures ($\stackrel{>}{_\sim}26$ K) the geometry changes dramatically, showing a bubble boundary which is accurately circular in projection, except for the previously-reported opening in the north. Comparison with Spitzer 8 $μ$m data suggests that the $\sim26$-30 K dust seen by Herschel resides in the photodissociation region (PDR) surrounding the HII region. Its projected radial profile is consistent with that of a spherical shell, thus arguing against previous suggestions of cylindrical or planar geometry. The inferred geometry is, in fact, consistent with previous interpretations of the HII region as a classical Strömgren sphere, except for the fact that the ionising star (CD -38.11636; O8V) is displaced by more than half a radius from its geometric centre. None of the previously published models has satisfactorily accounted for that displacement. It could, however, be explained by proper motion of the O star at $\sim2$-4 km s$^{-1}$ since its formation, possibly due to a cloud-cloud collision. We suggest that the current spherical bubble constitutes the fossilised remnant of the initial expansion of the HII region following the formation of the star, which now continues to flee its formation site.

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arXiv2018

A simple approach to CO cooling in molecular clouds

CO plays an important role in interstellar molecular clouds, both as a coolant, and as a diagnostic molecule. However, a proper evaluation of the cooling rate due to CO requires a determination of the populations of many levels, the spontaneous and stimulated radiative de-excitation rates between these levels, and the transfer of the emitted multi-line radiation; additionally, this must be done for three isotopologues. It would be useful to have a simple analytic formulation that avoided these complications; this could then be used in situations where CO plays an important role as a coolant, but the details of this role are not the main concern. We derive such a formulation here, by first considering the two asymptotic forms that obtain in the limits of (a) low volume-density and optical depth, and (b) high volume-density and optical depth. These forms are then combined in such a way as to fit the detailed numerical results from Goldsmith \& Langer (1978), which cover low temperatures, and a range of physical conditions where the interplay of thermal and sub-thermal excitation, optical-depth effects, and the contributions from rare isotopologues, are all important. The fit is obtained using the Metropolis-Hastings method, and reproduces the results of GL78 well. It is a purely local and analytic function of state --- specifically a function of the density, $ρ$, isothermal sound speed, $a$, CO abundance, $X_{_{\rm CO}}$, and velocity divergence, $\nabla\cdot{\boldsymbol\upsilon}$. As an application, we consider the cooling layer following a slow steady non-magnetic planar J-shock. We show that, if the post-shock cooling is dominated by CO and its isotopologues, the thickness of the post-shock cooling layer is very small and approximately independent of the pre-shock velocity, $\upsilon_o$, or pre-shock isothermal sound speed, $a_o$.

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arXiv2018

Dust in the Eye of Andromeda

We present new Herschel-derived images of warm dust in the Andromeda Galaxy, M31, with unprecedented spatial resolution (~ 30 pc), column density accuracy, and constraints on the three-dimensional distributions of dust temperature and dust opacity index (hence grain size and composition), based on the new PPMAP Bayesian analysis procedure. We confirm the overall radial variation of dust opacity index reported by other recent studies, including the central decrease within ~ 3 kpc of the nucleus. We also investigate the detailed distribution of dust in the nuclear region, a prominent feature of which is a ~ 500 pc bar-like structure seen previously in Hα. The nature of this feature has been the subject of some debate. Our maps show it to be the site of the warmest dust, with a mean line-of-sight temperature ~ 30 K. A comparison with the stellar distribution, based on 2MASS data, provides strong evidence that it is a gravitationally induced bar. A comparison with radial velocity maps suggests the presence of an inflow towards the nucleus from opposite directions along this bar, fed presumably by the nuclear spiral with which it appears to connect. Such behaviour is common in large-scale bars in spiral galaxies, as is the phenomenon of nested bars whereby a subkiloparsec nuclear bar exists within a large-scale primary bar. We suggest that M31 represents an example of such nesting.

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arXiv2018

Synthetic C$^{18}$O observations of fibrous filaments: the problems of mapping from PPV to PPP

Molecular-line observations of filaments in star-forming regions have revealed the existence of elongated coherent features within the filaments; these features are termed fibres. Here we caution that, since fibres are traced in PPV space, there is no guarantee that they represent coherent features in PPP space. We illustrate this contention using simulations of the growth of a filament from a turbulent medium. Synthetic C$^{18}$O observations of the simulated filaments reveal the existence of fibres very similar to the observed ones, i.e. elongated coherent features in the resulting PPV data-cubes. Analysis of the PPP data-cubes (i.e. 3D density fields) also reveals elongated coherent features, which we term sub-filaments. Unfortunately there is very poor correspondence between the fibres and the sub-filaments in the simulations. Both fibres and sub-filaments derive from inhomogeneities in the turbulent accretion flow onto the main filament. As a consequence, fibres are often affected by line-of-sight confusion. Similarly, sub-filaments are often affected by large velocity gradients, and even velocity discontinuities. These results suggest that extreme care should be taken when using velocity coherent features to constrain the underlying substructure within a filament.

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arXiv2018

The unexpectedly large proportion of high-mass star-forming cores in a Galactic mini-starburst

Understanding the processes that determine the stellar Initial Mass Function (IMF) is a critical unsolved problem, with profound implications for many areas of astrophysics. In molecular clouds, stars are formed in cores, gas condensations which are sufficiently dense that gravitational collapse converts a large fraction of their mass into a star or small clutch of stars. In nearby star-formation regions, the core mass function (CMF) is strikingly similar to the IMF, suggesting that the shape of the IMF may simply be inherited from the CMF. Here we present 1.3 mm observations, obtained with ALMA, the world's largest interferometer, of the active star-formation region W43-MM1, which may be more representative of the Galactic-disk regions where most stars form. The unprecedented resolution of these observations reveals, for the first time, a statistically robust CMF at high masses, with a slope that is markedly shallower than the IMF. This seriously challenges our understanding of the origin of the IMF.

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arXiv2018

J plots: a new method for characterizing structures in the interstellar medium

Large scale surveys have brought about a revolution in astronomy. To analyse the resulting wealth of data, we need automated tools to identify, classify, and quantify the important underlying structures. We present here a method for classifying and quantifying a pixelated structure, based on its principal moments of inertia. The method enables us to automatically detect, and objectively compare, centrally condensed cores, elongated filaments and hollow rings. We illustrate the method by applying it to (i) observations of surface-density from Hi-GAL, and (ii) simulations of filament growth in a turbulent medium. We limit the discussion here to 2D data; in a future paper we will extend the method to 3D data.

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arXiv2017

Synthetic observations of protostellar multiple systems

Observations of protostars are often compared with synthetic observations of models in order to infer the underlying physical properties of the protostars. The majority of these models have a single protostar, attended by a disc and an envelope. However, observational and numerical evidence suggests that a large fraction of protostars form as multiple systems. This means that fitting models of single protostars to observations may be inappropriate. We produce synthetic observations of protostellar multiple systems undergoing realistic, non-continuous accretion. These systems consist of multiple protostars with episodic luminosities, embedded self-consistently in discs and envelopes. We model the gas dynamics of these systems using smoothed particle hydrodynamics and we generate synthetic observations by post-processing the snapshots using the \textsc{spamcart} Monte Carlo radiative transfer code. We present simulation results of three model protostellar multiple systems. For each of these, we generate $4\times10^4$ synthetic spectra at different points in time and from different viewing angles. We propose a Bayesian method, using similar calculations to those presented here, but in greater numbers, to infer the physical properties of protostellar multiple systems from observations.

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arXiv2017

Multi-temperature mapping of dust structures throughout the Galactic Plane using the PPMAP tool with Herschel Hi-GAL data

We describe new Hi-GAL based maps of the entire Galactic Plane, obtained using continuum data in the wavelength range 70-500 $μ$m. These maps are derived with the PPMAP procedure, and therefore represent a significant improvement over those obtained with standard analysis techniques. Specifically they have greatly improved resolution (12 arcsec) and, in addition to more accurate integrated column densities and mean dust temperatures, they give temperature-differential column densities, i.e., separate column density maps in twelve distinct dust temperature intervals, along with the corresponding uncertainty maps. The complete set of maps is available on-line. We briefly describe PPMAP and present some illustrative examples of the results. These include (a) multi-temperature maps of the Galactic HII region W5-E, (b) the temperature decomposition of molecular cloud column-density probability distribution functions, and (c) the global variation of mean dust temperature as a function of Galactocentric distance. Amongst our findings are: (i) a strong localised temperature gradient in W5-E in a direction orthogonal to that towards the ionising star, suggesting an alternative heating source and providing possible guidance for models of the formation of the bubble complex, and (ii) the overall radial profile of dust temperature in the Galaxy shows a monotonic decrease, broadly consistent both with models of the interstellar radiation field and with previous estimates at lower resolution. However, we also find a central temperature plateau within ~ 6 kpc of the Galactic centre, outside of which is a pronounced steepening of the radial profile. This behaviour may reflect the greater proportion of molecular (as opposed to atomic) gas in the central region of the Galaxy.

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arXiv2017

Properties of Hi-GAL clumps in the inner Galaxy]{The Hi-GAL compact source catalogue. I. The physical properties of the clumps in the inner Galaxy ($-71.0^{\circ}< \ell < 67.0^{\circ}$)

Hi-GAL is a large-scale survey of the Galactic plane, performed with Herschel in five infrared continuum bands between 70 and 500 $μ$m. We present a band-merged catalogue of spatially matched sources and their properties derived from fits to the spectral energy distributions (SEDs) and heliocentric distances, based on the photometric catalogs presented in Molinari et al. (2016a), covering the portion of Galactic plane $-71.0^{\circ}< \ell < 67.0^{\circ}$. The band-merged catalogue contains 100922 sources with a regular SED, 24584 of which show a 70 $μ$m counterpart and are thus considered proto-stellar, while the remainder are considered starless. Thanks to this huge number of sources, we are able to carry out a preliminary analysis of early stages of star formation, identifying the conditions that characterise different evolutionary phases on a statistically significant basis. We calculate surface densities to investigate the gravitational stability of clumps and their potential to form massive stars. We also explore evolutionary status metrics such as the dust temperature, luminosity and bolometric temperature, finding that these are higher in proto-stellar sources compared to pre-stellar ones. The surface density of sources follows an increasing trend as they evolve from pre-stellar to proto-stellar, but then it is found to decrease again in the majority of the most evolved clumps. Finally, we study the physical parameters of sources with respect to Galactic longitude and the association with spiral arms, finding only minor or no differences between the average evolutionary status of sources in the fourth and first Galactic quadrants, or between "on-arm" and "inter-arm" positions.

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arXiv2017

Filamentary fragmentation in a turbulent medium

We present the results of smoothed particle hydrodynamic simulations investigating the evolution and fragmentation of filaments that are accreting from a turbulent medium. We show that the presence of turbulence, and the resulting inhomogeneities in the accretion flow, play a significant role in the fragmentation process. Filaments which experience a weakly turbulent accretion flow fragment in a two-tier hierarchical fashion, similar to the fragmentation pattern seen in the Orion Integral Shaped Filament. Increasing the energy in the turbulent velocity field results in more sub-structure within the filaments, and one sees a shift from gravity-dominated fragmentation to turbulence-dominated fragmentation. The sub-structure formed in the filaments is elongated and roughly parallel to the longitudinal axis of the filament, similar to the fibres seen in observations of Taurus, and suggests that the fray and fragment scenario is a possible mechanism for the production of fibres. We show that the formation of these fibre-like structures is linked to the vorticity of the velocity field inside the filament and the filament's accretion from an inhomogeneous medium. Moreover, we find that accretion is able to drive and sustain roughly sonic levels of turbulence inside the filaments, but is not able to prevent radial collapse once the filaments become supercritical. However, the supercritical filaments which contain fibre-like structures do not collapse radially, suggesting that fibrous filaments may not necessarily become radially unstable once they reach the critical line-density.

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arXiv2016

$\mathcal{Q}^{+}$: Characterising the structure of young star clusters

Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of sub-structure. We suggest that, even at the simplest level, the internal structure of a fractal cluster requires the specification of three parameters. (i) The 3D fractal dimension, $\mathcal{D}$, measures the extent to which the clusters on one level of the nested hierarchy fill the volume of their parent cluster. (ii) The number of levels, $\mathcal{L}$, reflects the finite ratio between the linear size of the large root-cluster at the top of the hierarchy, and the smallest leaf-clusters at the bottom of the hierarchy. (iii) The volume-density scaling exponent, $\mathcal{C}=-\textrm{d}\ln[δn]/\textrm{d}\ln[L]$ measures the factor by which the excess density, $δn$, in a structure of scale $L$, exceeds that of the background formed by larger structures; it is similar, but not exactly equivalent, to the exponent in Larson's scaling relation between density and size for molecular clouds. We describe an algorithm which can be used to constrain the values of $({\cal D},{\cal L},{\cal C})$ and apply this method to artificial and observed clusters. We show that this algorithm is able to reliably describe the three dimensional structure of an artificial star cluster from the two dimensional projection, and quantify the varied structures observed in real and simulated clusters.

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arXiv2016

SPAMCART: a code for smoothed particle Monte Carlo radiative transfer

We present a code for generating synthetic SEDs and intensity maps from Smoothed Particle Hydrodynamics simulation snapshots. The code is based on the Lucy (1999) Monte Carlo Radiative Transfer method, i.e. it follows discrete luminosity packets, emitted from external and/or embedded sources, as they propagate through a density field, and then uses their trajectories to compute the radiative equilibrium temperature of the ambient dust. The density is not mapped onto a grid, and therefore the calculation is performed at exactly the same resolution as the hydrodynamics. We present two example calculations using this method. First, we demonstrate that the code strictly adheres to Kirchhoff's law of radiation. Second, we present synthetic intensity maps and spectra of an embedded protostellar multiple system. The algorithm uses data structures that are already constructed for other purposes in modern particle codes. It is therefore relatively simple to implement.

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arXiv2016

A theoretical perspective on the formation and fragmentation of protostellar discs

We discuss the factors influencing the formation and gravitational fragmentation of protostellar discs. We start with a review of how observations of prestellar cores can be analysed statistically to yield plausible initial conditions for simulations of their subsequent collapse. Simulations based on these initial conditions show that, despite the low levels of turbulence in prestellar cores, they deliver primary protostars and associated discs which are routinely subject to stochastic impulsive perturbations; consequently misalignment of the spins and orbits of protostars are common. Also, the simulations produce protostars that collectively have a mass function and binary statistics matching those observed in nearby star formation regions, but only if a significant fraction of the turbulent energy in the core is solenoidal, and accretion onto the primary protostar is episodic with a duty cycle > 3000 yr. Under this circumstance a core typically spawns between 4 and 5 protostars, with high efficiency, and the lower-mass protostars are mainly formed by disc fragmentation. The requirement that a proto-fragment in a disc lose thermal energy on a dynamical timescale dictates that {\bf there is a sweet spot for} disc fragmentation at radii 70 AU < R < 100 AU and temperatures 10 K < T < 20 K, and this might explain the Brown Dwarf Desert.

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arXiv2016

A ram-pressure threshold for star formation

In turbulent fragmentation, star formation occurs in condensations created by converging flows. The condensations must be sufficiently massive, dense and cool to be gravitationally unstable, so that they start to contract; {\it and} they must then radiate away thermal energy fast enough for self-gravity to remain dominant, so that they continue to contract. For the metallicities and temperatures in local star forming clouds, this second requirement is only met robustly when the gas couples thermally to the dust, because this delivers the capacity to radiate across the full bandwidth of the continuum, rather than just in a few discrete spectral lines. This translates into a threshold for vigorous star formation, which can be written as a minimum ram-pressure Pcrit ~ 4 10^-11 dyne. Pcrit is independent of temperature, and corresponds to flows with molecular hydrogen number-density nH2 and velocity v satisfying nH2 v^2 > 800 cm^-3 (km/s)^2. This in turn corresponds to a minimum molecular hydrogen column-density for vigorous star formation, NH2crit ~ 4 10^21 cm^-2 (SIGMAcrit ~ 100 MSun pc^-2), and a minimum visual extinction AVcrit ~ 9. The characteristic diameter and line-density for a star-forming filament when this threshold is just exceeded -- a sweet spot for local star formation regions -- are 2Rfil ~ 0.1 pc and mufil ~ 13 MSun pc^-2. The characteristic diameter and mass for a prestellar core condensing out of such a filament are 2Rcore ~ 0.1 pc, and Mcore ~ MSun. We also show that fragmentation of a shock-compressed layer is likely to commence while the convergent flows creating the layer are still ongoing, and we stress that, under this circumstance, the phenomenology and characteristic scales for fragmentation of the layer are fundamentally different from those derived traditionally for pre-existing layers.

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arXiv2016

Evidence that widespread star formation may be underway in G0.253+016, "The Brick"

Image cubes of differential column density as a function of dust temperature are constructed for Galactic Centre molecular cloud G0.253+0.016 ("The Brick") using the recently described PPMAP procedure. The input data consist of continuum images from the Herschel Space Telescope in the wavelength range 70-500 $μ$m, supplemented by previously published interferometric data at 1.3 mm wavelength. While the bulk of the dust in the molecular cloud is consistent with being heated externally by the local interstellar radiation field, our image cube shows the presence, near one edge of the cloud, of a filamentary structure whose temperature profile suggests internal heating. The structure appears as a cool ($\sim 14$ K) tadpole-like feature, $\sim 6$ pc in length, in which is embedded a thin spine of much hotter ($\sim$ 40-50 K) material. We interpret these findings in terms of a cool filament whose hot central region is undergoing gravitational collapse and fragmentation to form a line of protostars. If confirmed, this would represent the first evidence of widespread star formation having started within this cloud.

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