We use smoothed particle hydrodynamic simulations of cold, uniform density, self-gravitating filaments, to investigate their longitudinal collapse time-scales; these time-scales are important because ...they determine the time available for a filament to fragment into cores. A filament is initially characterized by its line-mass, μO, its radius, R
O (or equivalently its density
$\rho _{{\rm O}}= \mu _{{\rm O}}/\pi R_{{\rm O}}^2$
), and its aspect ratio, A
O (≡Z
O/R
O, where Z
O is its half-length). The gas is only allowed to contract longitudinally, i.e. parallel to the symmetry axis of the filament (the z-axis). Pon et al. (2012) have considered the global dynamics of such filaments analytically. They conclude that short filaments (A
O ≲ 5) collapse along the z-axis more-or-less homologously, on a time-scale t
HOM ∼ 0.44 A
O (GρO)−1/2; in contrast, longer filaments (A
O ≳ 5) undergo end-dominated collapse, i.e. two dense clumps form at the ends of the filament and converge on the centre sweeping up mass as they go, on a time-scale
$t_{{\rm END}} \sim 0.98\,A_{{\rm O}}^{1/2}\,(G\rho _{{\rm O}})^{-1/2}$
. Our simulations do not corroborate these predictions. First, for all A
O ≳ 2, the collapse time satisfies a single equation
\begin{equation*}
t_{{\rm COL}}\sim (0.49+0.26A_{{\rm O}})(G\rho _{{\rm O}})^{-1/2}\,,
\end{equation*}
which for large A
O is much longer than the Pon et al. prediction. Secondly, for all A
O ≳ 2, the collapse is end-dominated. Thirdly, before being swept up, the gas immediately ahead of an end-clump is actually accelerated outwards by the gravitational attraction of the approaching clump, resulting in a significant ram pressure. For high aspect ratio filaments, the end-clumps approach an asymptotic inward speed, due to the fact that they are doing work both accelerating and compressing the gas they sweep up. Pon et al. appear to have neglected the outward acceleration and its consequences.
We present point process mapping (PPMAP), a Bayesian procedure that uses images of dust continuum emission at multiple wavelengths to produce resolution-enhanced image cubes of differential column ...density as a function of dust temperature and position. PPMAP is based on the generic ‘point process formalism, whereby the system of interest (in this case, a dusty astrophysical structure such as a filament or pre-stellar core) is represented by a collection of points in a suitably defined state space. It can be applied to a variety of observational data, such as Herschel images, provided only that the image intensity is delivered by optically thin dust in thermal equilibrium. PPMAP takes full account of the instrumental point-spread functions and does not require all images to be degraded to the same resolution. We present the results of testing using simulated data for a pre-stellar core and a fractal turbulent cloud, and demonstrate its performance with real data from the Herschel infrared Galactic Plane Survey (Hi-GAL). Specifically, we analyse observations of a large filamentary structure in the CMa OB1 giant molecular cloud. Histograms of differential column density indicate that the warm material (T ≳ 13 K) is distributed lognormally, consistent with turbulence, but the column densities of the cooler material are distributed as a high-density tail, consistent with the effects of self-gravity. The results illustrate the potential of PPMAP to aid in distinguishing between different physical components along the line of sight in star-forming clouds, and aid the interpretation of the associated Probability distribution functions (PDFs) of column density.
Dispersal of molecular clouds by ionizing radiation Walch, S. K.; Whitworth, A. P.; Bisbas, T. ...
Monthly notices of the Royal Astronomical Society,
21 November 2012, Letnik:
427, Številka:
1
Journal Article
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ABSTRACT
Feedback from massive stars is believed to be a key element in the evolution of molecular clouds. We use high‐resolution 3D smoothed particle hydrodynamics simulations to explore the ...dynamical effects of a single O7 star‐emitting ionizing photons at 1049 s−1 and located at the centre of a molecular cloud with mass 104 M⊙ and radius 6.4 pc; we also perform comparison simulations in which the ionizing star is removed. The initial internal structure of the cloud is characterized by its fractal dimension, which we vary between D=2.0 and 2.8, and the standard deviation of the approximately log‐normal initial density
PDF, which is σ10 = 0.38 for all clouds. (i) As regards star formation, in the short term ionizing feedback is positive, in the sense that star formation occurs much more quickly (than in the comparison simulations), in gas that is compressed by the high pressure of the ionized gas. However, in the long term ionizing feedback is negative, in the sense that most of the cloud is dispersed with an outflow rate of up to ∼10−2 M⊙yr−1, on a time‐scale comparable with the sound‐crossing time for the ionized gas (∼1−2 Myr ), and triggered star formation is therefore limited to a few per cent of the cloud's mass. We will describe in greater detail the statistics of the triggered star formation in a companion paper. (ii) As regards the morphology of the ionization fronts (IFs) bounding the H ii region and the systematics of outflowing gas, we distinguish two regimes. For low D≲2.2, the initial cloud is dominated by large‐scale structures, so the neutral gas tends to be swept up into a few extended coherent shells, and the ionized gas blows out through a few large holes between these shells; we term these H ii regions shell dominated. Conversely, for high D≳2.6, the initial cloud is dominated by small‐scale structures, and these are quickly overrun by the advancing IF, thereby producing neutral pillars protruding into the H ii region, whilst the ionized gas blows out through a large number of small holes between the pillars; we term these H ii regions pillar dominated. (iii) As regards the injection of bulk kinetic energy, by ∼1 Myr, the expansion of the H ii region has delivered a mass‐weighted rms velocity of ∼6 km s−1; this represents less than 0.1 per cent of the total energy radiated by the O7 star.
ABSTRACT
Collisions between interstellar gas clouds are potentially an important mechanism for triggering star formation. This is because they are able to rapidly generate large masses of dense gas. ...Observationally, cloud collisions are often identified in position–velocity (PV) space through bridging features between intensity peaks, usually of CO emission. Using a combination of hydrodynamical simulations, time-dependent chemistry, and radiative transfer, we produce synthetic molecular line observations of overlapping clouds that are genuinely colliding, and overlapping clouds that are just chance superpositions. Molecules tracing denser material than CO, such as NH3 and HCN, reach peak intensity ratios of 0.5 and 0.2 with respect to CO in the ‘bridging feature’ region of PV space for genuinely colliding clouds. For overlapping clouds that are just chance superpositions, the peak NH3 and HCN intensities are co-located with the CO intensity peaks. This represents a way of confirming cloud collisions observationally and distinguishing them from chance alignments of unrelated material.
Perturbation growth in accreting filaments Clarke, S. D; Whitworth, A. P; Hubber, D. A
Monthly notices of the Royal Astronomical Society,
05/2016, Letnik:
458, Številka:
1
Journal Article
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We use smoothed particle hydrodynamic simulations to investigate the growth of perturbations in infinitely long filaments as they form and grow by accretion. The growth of these perturbations leads ...to filament fragmentation and the formation of cores. Most previous work on this subject has been confined to the growth and fragmentation of equilibrium filaments and has found that there exists a preferential fragmentation length-scale which is roughly four times the filament's diameter. Our results show a more complicated dispersion relation with a series of peaks linking perturbation wavelength and growth rate. These are due to gravo-acoustic oscillations along the longitudinal axis during the sub-critical phase of growth. The positions of the peaks in growth rate have a strong dependence on both the mass accretion rate onto the filament and the temperature of the gas. When seeded with a multiwavelength density power spectrum, there exists a clear preferred core separation equal to the largest peak in the dispersion relation. Our results allow one to estimate a minimum age for a filament which is breaking up into regularly spaced fragments, as well as an average accretion rate. We apply the model to observations of filaments in Taurus by Tafalla & Hacar and find accretion rates consistent with those estimated by Palmeirim et al.
ABSTRACT
Filaments are an ubiquitous feature of molecular clouds, and appear to play a critical role in assembling the material to form stars. The dominant filaments are observed to have a rather ...narrow range of widths around $\sim 0.1 \, {\rm pc}$, and to be preferentially aligned perpendicularly to the direction of the local magnetic field. We have previously argued that the observed filament widths can be explained if filaments are formed by converging, mildly supersonic flows, resulting from large-scale turbulent motions in the parent molecular cloud. Here we demonstrate that the introduction of a magnetic field perpendicular to the filament long axis does not greatly alter this conclusion, as long as the mass-to-flux ratio is supercritical. The distribution of widths for supercritical magnetized filaments formed via this mechanism is peaked at slightly higher values, and is slightly broader, than for non-magnetized filaments, but still reproduces the basic properties of the width distributions derived from far-infrared observations of molecular clouds. In contrast, subcritical filaments have width distributions with a fundamentally different shape, and typically have much larger widths than those observed. Both subcritical and supercritical filaments are consistent with the observed lack of correlation between filament widths and filament surface densities.
Massive clumps within the swept-up shells of bubbles, like that surrounding the galactic H ii region RCW 120, have been interpreted in terms of the collect and collapse (C&C) mechanism for triggered ...star formation. The cold, dusty clumps surrounding RCW 120 are arranged in an almost spherical shell and harbour many young stellar objects. By performing high-resolution, three-dimensional smoothed particle hydrodynamics simulations of H ii regions expanding into fractal molecular clouds, we investigate whether the formation of massive clumps in dense, swept-up shells necessarily requires the C&C mechanism. In a second step, we use radmc-3d to compute the synthetic dust continuum emission from our simulations, in order to compare them with observations of RCW 120 made with APEX-LABOCA (The Large APEX BOlometer CAmera) at 870 μm. We show that a distribution of clumps similar to the one seen in RCW 120 can readily be explained by a non-uniform initial molecular cloud structure. Hence, a shell-like configuration of massive clumps does not imply that the C&C mechanism is at work. Rather, we find a hybrid form of triggering, which combines elements of C&C and radiation driven implosion (RDI). In addition, we investigate the reliability of deriving clump masses from their 870 μm emission. We find that for clumps with more than 100 M⊙ the observational estimates are accurate to within a factor of 2, while the agreement between simulated and observed masses is much worse for smaller clumps. We also find that even at 870 μm it is important to account for the radiative heating from triggered, embedded protostars.
ABSTRACT
We explore a simple semi-analytic model for what happens when an O star (or cluster of O stars) forms in an isolated filamentary cloud. The model is characterized by three configuration ...parameters: the radius of the filament, $R_{_{\rm FIL}}$, the mean density of H2 in the filament, $n_{_{\rm FIL}}$, and the rate at which the O star emits ionizing photons, $\dot{\cal N}_{_{\rm LyC}}$. We show that for a wide range of these configuration parameters, ionizing radiation from the O star rapidly erodes the filament, and the ionized gas from the filament disperses into the surroundings. Under these circumstances the distance, L, from the O star to the ionization front (IF) is given approximately by $L(t) \sim 5.2 {\rm pc} R_{_{\rm FIL}}/0.2 {\rm pc}^{-1/6} n_{_{\rm FIL}}/10^4 {\rm cm^{-3}}^{-1/3} \dot{\cal N}_{_{\rm LyC}}/10^{49} {\rm s}^{-1}^{1/6} t/{\rm Myr}^{2/3}$, and we derive similar simple power-law expressions for other quantities, for example the rate at which ionized gas boils off the filament, $\dot{M}_{_{\rm IF}}(t)$, and the mass, $M_{_{\rm SCL}}(t)$, of the shock-compressed layer that is swept up behind the IF. We show that a very small fraction of the ionizing radiation is expended locally, and a rather small amount of molecular gas is ionized and dispersed. We discuss some features of more realistic models, and the extent to which they might modify or invalidate the predictions of this idealized model. In particular we show that, for very large $R_{_{\rm FIL}}$ and/or large $n_{_{\rm FIL}}$ and/or low $\dot{\cal N}_{_{\rm LyC}}$, continuing accretion on to the filament might trap the ionizing radiation from the O star, slowing erosion of the filament even further.
Star formation triggered by cloud–cloud collisions Balfour, S. K; Whitworth, A. P; Hubber, D. A ...
Monthly notices of the Royal Astronomical Society,
11/2015, Letnik:
453, Številka:
3
Journal Article
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We present the results of smoothed particle hydrodynamics simulations in which two clouds, each having mass M
O = 500 M⊙ and radius R
O = 2 pc, collide head-on at relative velocities of Δv
O = 2.4, ...2.8, 3.2, 3.6 and 4.0 km s−1. There is a clear trend with increasing Δv
O. At low Δv
O, star formation starts later, and the shock-compressed layer breaks up into an array of predominantly radial filaments; stars condense out of these filaments and fall, together with residual gas, towards the centre of the layer, to form a single large-N cluster, which then evolves by competitive accretion, producing one or two very massive protostars and a diaspora of ejected (mainly low-mass) protostars; the pattern of filaments is reminiscent of the hub and spokes systems identified recently by observers. At high Δv
O, star formation occurs sooner and the shock-compressed layer breaks up into a network of filaments; the pattern of filaments here is more like a spider's web, with several small-N clusters forming independently of one another, in cores at the intersections of filaments, and since each core only spawns a small number of protostars, there are fewer ejections of protostars. As the relative velocity is increased, the mean protostellar mass increases, but the maximum protostellar mass and the width of the mass function both decrease. We use a Minimal Spanning Tree to analyse the spatial distributions of protostars formed at different relative velocities.
ABSTRACT
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 $10\, {\rm K}$, $\mu _{{\rm CRIT}}\simeq 16\, {\rm M_{\odot }\, pc^{-1}}$, the filament is on average trans-critical, with ${\bar{\mu }}\sim \mu _{{\rm CRIT}};\,\,$ local sections where μ > μCRIT tend to lie close to prestellar cores. (iv) The ability of ppmap to distinguish different types of dust, i.e. dust characterized by different values of the emissivity index, β, reveals that the dust in the filament has a lower emissivity index, β ≲ 1.5, than the dust outside the filament, β ≳ 1.7, implying that the physical conditions in the filament have effected a change in the properties of the dust.
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