- The dynamics of collapsing cores and star formation
Low-mass stars are generally understood to form by the gravitational collapse of
the dense molecular clouds known as starless cores. Continuum observations
have not been able to distinguish among the several different hypotheses that describe
the collapse because their
predicted density distributions are the almost the same, as they are
for all spherical self-gravitating clouds. However, the predicted radial profiles of the
contraction velocity are different enough that the models can be discriminated
by comparing the inward velocities at large and small radii. This can be
done by observing at least two different molecular line transitions that are
excited at different densities. For example, the spectral lines of
the H2O (110 - 101) and C18O (1-0) have
critical densities for collisional de-excitation that differ by 5 orders of
magnitude. We compare observations of these lines from the contracting
starless core L1544 against the spectra predicted for several different hypothetical models
of contraction including the Larson-Penston flow, the inside-out collapse of the
singular isothermal sphere,
the quasi-equilibrium contraction of an unstable Bonnor-Ebert sphere, and the
non-equilibrium collapse of an over-dense Bonnor-Ebert sphere. Only the model of the
unstable quasi-equilibrium Bonnor-Ebert sphere is able to produce the observed shapes of both
spectral lines. This model allows us to interpret other observations of molecular lines in
L1544 to find that the inward velocities seen in observations
of CS(2-1) and N2H+ are located within the starless core itself, in particular
in the region where the density profiles follows an inverse square law. If these
conclusions were to hold in the analysis of other starless cores, this would
imply that the formation of hydrostatic clouds within the turbulence
of the interstellar medium is not only possible but not exceptional
and may be an evolutionary phase in low-mass star formation.
Eric Keto, Jonathan Rawlings, and Paola Caselli, 2014, MNRAS in press
- Chemistry and Radiative Transfer of Water in Cold, Dense Clouds
The Herschel Space Observatory's recent detections
of water vapor in the cold, dense cloud L1544
allow a direct comparison between observations and
chemical models for oxygen species in
just before star formation.
We explain a chemical model for gas
phase water, simplified for the limited number of
reactions or processes that are active in extreme cold (< 15 K).
In this model, water
is removed from the gas phase by freezing onto grains
and by photodissociation.
Water is formed as ice
on the surface of dust grains from O and OH
and released into the gas phase by photodesorption.
The reactions are fast enough with respect to the slow dynamical evolution
of L1544 that the gas phase water is in equilibrium for the local
conditions thoughout the cloud.
We explain the paradoxical radiative transfer
of the H2O (110-101) line.
Despite discouragingly high optical depth
caused by the large Einstein A coefficient, the
subcritical excitation in the cold,
rarefied H2 causes
the line brightness to scale linearly with column
density. Thus the water line can
provide information on
the chemical and dynamical processes in the darkest region
in the center of a cold, dense cloud.
The inverse P-Cygni profile of the observed
water line generally indicates a contracting cloud.
This profile is reproduced with a dynamical model
of slow contraction
from unstable quasi-static
hydrodynamic equilibrium (an unstable Bonnor-Ebert sphere).
Eric Keto, Jonathan Rawlings, and Paola Caselli, 2014, MNRAS, 440, 2616
- From Filaments to Oscillating Starless Cores
Long wavelength sonic oscillations are observed or inferred in many of the small, dark molecular clouds, the starless cores, that are the precursors to protostars. The oscillations provide significant internal energy and the time scale for their dissipation may control the rate of star formation in starless cores.
Despite their importance, their origin is unknown. We explore one hypothesis
that the oscillations develop as a starless core forms from a filament. We model this
process with a numerical hydrodynamic simulation and generate synthetic
molecular line observations with a radiative transfer simulation. Comparison with
actual observations shows general agreement suggesting the proposed
mechanism is viable.
Eric Keto and Andreas Burkert, 2014, MNRAS 441, 1468
- First Detection of Water Vapor in a Pre-stellar Core
Water is a crucial molecule in molecular astrophysics as it controls much of the gas/grain chemistry, including the formation and evolution of more complex organic molecules in ices. Pre-stellar cores provide the original reservoir of material from which future planetary systems are built, but few observational constraints exist on the formation of water and its partitioning between gas and ice in the densest cores. Thanks to the high sensitivity of the Herschel Space Observatory, we report on the first detection of water vapor at high spectral resolution toward a dense cloud on the verge of star formation, the pre-stellar core L1544. The line shows an inverse P-Cygni profile, characteristic of gravitational contraction. To reproduce the observations, water vapor has to be present in the cold and dense central few thousand AU of L1544, where species heavier than helium are expected to freeze out onto dust grains, and the ortho:para H2 ratio has to be around 1:1 or larger. The observed amount of water vapor within the core (about 1.5E-6 solar masses) can be maintained by far-UV photons locally produced by the impact of galactic cosmic rays with H2 molecules. Such FUV photons irradiate the icy mantles, liberating water vapor in the core center. Our Herschel data, combined with radiative transfer and chemical/dynamical models, shed light on the interplay between gas and solids in dense interstellar clouds and provide the first measurement of the water vapor abundance profile across the parent cloud of a future solar-type star and its potential planetary system.
Paola Caselli, Eric Keto et al., 2012, ApJL 759, L37
- Water vapor toward starless cores: The Herschel view
Previous studies by the satellites SWAS and Odin provided stringent upper limits on the gas phase water abundance of dark clouds (x(H2O) < 7 E-9). We investigate the chemistry of water vapor in starless cores beyond the previous upper limits using the highly improved angular resolution and sensitivity of Herschel and measure the abundance of water vapor during evolutionary stages just preceding star formation.
Methods. High spectral resolution observations of the fundamental ortho water (o-H2O) transition (557 GHz) were carried out with the Heterodyne Instrument for the Far Infrared onboard Herschel toward two starless cores: Barnard 68 (hereafter B68), a Bok globule, and LDN 1544 (L1544), a prestellar core embedded in the Taurus molecular cloud complex. Detailed radiative transfer and chemical codes were used to analyze the data.
Results. The RMS in the brightness temperature measured for the B68 and L1544 spectra is 2.0 and 2.2 mK, respectively, in a velocity bin of 0.59 km s-1. The continuum level is 3.5 +- 0.2 mK in B68 and 11.4 +- 0.4 mK in L1544. No significant feature is detected in B68 and the 3 sigma upper limit is consistent with a column density of o-H2O N(o-H2O) < 2.5 E13 cm-2, or a fractional abundance x(o-H2O) < 1.3E-9, more than an order of magnitude lower than the SWAS upper limit on this source. The L1544 spectrum shows an absorption feature at a 5$\sigma$ level from which we obtain the first value of the o-H2O column density ever measured in dark clouds: N(o-H2O) = (8 +- 4) E12 cm-2. The corresponding fractional abundance is x(o-H2O) ~ 5E-9 at radii >7000 AU and toward the center. The radiative transfer analysis shows that this is consistent with a x(o-H2O) profile peaking at $\simeq$10-8, 0.1 pc away from the core center, where both freeze-out and photodissociation are negligible.
Conclusions. Herschel has provided the first measurement of water vapor in dark regions. Column densities of o-H2O are low, but prestellar cores such as L1544 (with their high central densities, strong continuum, and large envelopes) appear to be very promising tools to finally shed light on the solid/vapor balance of water in molecular clouds and oxygen chemistry in the earliest stages of star formation.
Paola Caselli, Eric Keto et al., 2010, A&A 521, L29
- Dynamics and Depletion in Thermally Super-critical Starless Cores
In previous studies we identified two classes of starless cores, thermally subcritical and supercritical, distinguished by different dynamical behavior and internal structure. Here we study the evolution of the dynamically-unstable, thermally-supercritical cores by means of a numerical hydrodynamic simulation that includes radiative equilibrium and simple molecular chemistry. From an initial state as an unstable Bonnor-Ebert (BE) sphere, a contracting core evolves toward the configuration of a singular isothermal sphere (SIS) by inside-out collapse.We follow the gas temperature and abundance of CO during the contraction. The temperature is predominantly determined by radiative equilibrium, but in the rapidly contracting center of the core, compressive heating raises the gas temperature by a few degrees over its value in static equilibrium. The time scale for the equilibration of CO depends on the gas density and is everywhere shorter than the dynamical timescale. The result is that the dynamics do not much affect the abundance of CO which is always close to that of a static sphere of the same density profile, and CO cannot be used as a chemical clock in starless cores. We use our non-LTE radiative transfer code MOLLIE to predict observable CO and N2H+ line spectra, including the non-LTE hyperfine ratios of N2H+, during the contraction. These are compared against observations of the starless core L1544. The comparison indicates that the dust in L1544 has an opacity consistent with ice-covered rather than bare grains, the cosmic ray ionization rate is about 1E-17 s-1, and the density structure of L1544 is approximately that of a Bonnor-Ebert sphere with a maximum central density of 2E7 cm-3, equivalent to an average density of 3E6 cm-3 within a radius of 500 AU. The observed CO line widths and intensities are reproduced if the CO desorption rate is about 30 times higher than the rate expected from cosmic-ray strikes alone, indicating that other desorption processes are also active.
Eric Keto & Paola Caselli, 2010, MNRAS 402, 1625
- The Different Structures of the Two Classes of Starless Cores
Previous observations and theoretical models of starless
cores suggest that the different temperature and density
structures observed in individual cores and their different
dynamical behaviors can be described by a consistent
set of physics.
Here we develop a model for the thermal
and dynamical equilibrium of starless cores that
includes the radiative transfer of the gas and
dust, and simple CO chemistry.
The model shows that
the behavior of the cores is significantly different
depending on whether the central density is either above
or below about 1E5 cm-3. This is
close to the critical density for both gas cooling by gas-dust collisions
and also for dynamical stability, given the typical properties of the
Thus the model divides the starless cores into two classes that
we refer to as thermally super-critical and thermally sub-critical.
This simple model allows an improved interpretation of observational data
to better understand the evolution of starless cores,
their dust opacity, and the rate of cosmic-ray ionization that heats them.
Eric Keto & Paola Caselli, 2008, ApJ 683, 238
- Oscillating Starless Cores: The Nonlinear Regime
In a previous paper, we modeled the oscillations of a
thermally-supported (Bonnor-Ebert) sphere as non-radial, linear
perturbations following a standard analysis developed for stellar
pulsations. The predicted column density variations and molecular
spectral line profiles are similar to those observed in the Bok
globule B68 suggesting that the motions in some starless cores may
be oscillating perturbations on a thermally supported equilibrium structure.
However, the linear analysis is unable to address several questions, among
them the stability, and lifetime of the perturbations.
In this paper we simulate the oscillations using a three-dimensional numerical
hydrodynamic code. We find that the oscillations are damped
predominantly by non-linear mode-coupling, and the damping time scale is
typically many oscillation periods, corresponding to millions of
years, and persisting over the inferred lifetime of gobules.
Avery E. Broderick, Eric Keto, Charles J. Lada & Ramesh Narayan, 2007, ApJ, 671, 1832
- Oscillations of Starless Cores
If the split, asymmetric
molecular spectral line profiles that are seen in many starless cores are interpreted
as indicative of global collapse or expansion of the core then one possible implication
is that most starless cores have short lifetimes
on the order of the collapse or sound crossing time scale. An alternative interpretation
of the line profiles as indicative of perturbations on an underlying equilibrium structure
leads to the opposite implication, that many cores have long lifetimes. While
evidence suggests that some cores are collapsing on a free-fall time scale,
we show that observations of some other starless cores can be reproduced by a
model of non-radial oscillations about the equilibrium configuration of a
pressure-bounded, thermally-supported sphere (Bonnor-Ebert sphere). We model
the oscillations as linear perturbations following a standard analysis developed
for stellar pulsations and compare the column densities and molecular spectral
line profiles predicted from a particular model to observations of the Bok
Eric Keto, Avery E. Broderick, Charles J. Lada & Ramesh Narayan, 2007, ApJ, 652, 1366
- Dark Cloud Cores and Gravitational Decoupling from Turbulent Flow
We test the hypothesis that the starless cores may be
gravitationally bound clouds supported largely by thermal pressure by comparing
observed molecular line spectra to theoretical spectra produced by a
simulation that includes hydrodynamics, radiative cooling, variable
molecular abundance, and radiative transfer in a simple one-dimensional
The results suggest that the starless cores can be divided into two categories:
stable starless cores that are in approximate equilibrium and
will not evolve to form protostars, and unstable
pre-stellar cores that are proceeding toward gravitational collapse and the
formation of protostars.
The starless cores might be formed from the interstellar
medium as objects at the lower end of the inertial cascade of interstellar
Additionally, we identify a thermal instability in the starless cores. Under particular
conditions of density and mass, a core may be unstable to expansion if
the density is just above the critical density for the collisional coupling
of the gas and dust so that as the core expands the gas-dust coupling that cools
the gas is reduced and the gas warms, further driving the expansion.
Eric Keto & George B. Field, 2005, ApJ, 635, 1151