D. Stamatellos - A. P. Whitworth - D. F. A. Boyd - S. P. Goodwin
School of Physics & Astronomy, Cardiff University, 5 The Parade, Cardiff CF24 3YB, Wales, UK
Received 28 February 2005 / Accepted 25 April 2005
Abstract
We study the transition from a prestellar core to a Class 0 protostar,
using SPH to simulate the dynamical evolution, and a Monte Carlo radiative
transfer code to generate the SED and isophotal maps. For a prestellar core
illuminated by the standard interstellar radiation field, the luminosity
is low and the SED peaks at
.
Once a protostar has
formed, the luminosity rises (due to a growing contribution from accretion
onto the protostar) and the peak of the SED shifts to shorter wavelengths
(
). However, by the end of the Class 0 phase,
the accretion rate is falling, the luminosity has decreased, and the peak of
the SED shifts back towards longer wavelengths (
).
In our simulations, the density of material around the protostar remains
sufficiently high well into the Class 0 phase that the protostar only
becomes visible in the NIR if it is displaced from the centre dynamically.
Raw submm/mm maps of Class 0 protostars tend to be much more centrally
condensed than those of prestellar cores. However, when convolved with a
typical telescope beam, the difference in central concentration is less
marked, although the Class 0 protostars appear more circular. Our results
suggest that, if a core is deemed to be prestellar on the basis of having
no associated IRAS source, no cm radio emission, and no
outflow, but it has a circular appearance and an SED which peaks at
wavelengths below
,
it may well contain a very
young Class 0 protostar.
Key words: stars: formation - ISM: clouds - dust, extinction - methods: numerical - radiative transfer - hydrodynamics
The details of how molecular clouds form, why they collapse, and how
the collapse proceeds to form stars are not very well understood. Over
the last two decades, observations of the different stages of this
process have lead to an evolutionary scenario of star formation:
starless core
prestellar core
Class 0
object
Class I object
Class II object
Class III object (see André et al. 2000).
Starless cores (e.g. Myers et al. 1983; Myers & Benson 1983) are
dense cores in molecular clouds in which there is no evidence that
star formation has occurred (i.e. no IRAS detection, Beichman et al.
1986). Some of these starless cores are thought to be close to
collapse or already collapsing, and they are labelled prestellar
cores (Ward-Thompson et al. 1994, 1999); for the rest, it is not
always clear whether they are in hydrostatic equilibrium (e.g.
Alves et al. 2001) or transient structures
within a turbulent cloud (e.g. Ballesteros-Paredes et al. 2003).
Prestellar cores have been observed both in
relative isolation (e.g. L1544, L63; Ward-Thompson et al. 1999) and
in protoclusters (e.g. Oph, Motte et al. 1998; NGC 2068/2071,
Motte et al. 2001). They have typical sizes
AU
and masses from 0.05 to
.
From statistical arguments
(e.g. André et al. 2000) it is inferred that prestellar cores live
only a few million years.
Class 0 objects represent the stage when a protostar has just been
formed in the centre of the core, but the protostar is still less
massive than its surrounding envelope (André et al. 1993). The
protostar is deeply embedded in the core and cannot be observed
directly, but its presence can often be inferred from bipolar
molecular outflows or compact centimetre radio emission. The Class 0 phase last
for a few
and is characterised by a
large accretion rate (
yr-1). Most of
the mass of the protostar is delivered during this phase (e.g.
Whitworth & Ward-Thompson 2001).
Once the protostar becomes more massive than its surrounding envelope,
the core enters the Class I phase. Accretion onto the central protostar,
or onto the disc around the protostar, continues, but at a lower rate
(
yr-1). This phase lasts for a few
,
and delivers most of the rest of the mass of the protostar.
Finally, Class II and Class III objects correspond to even later stages
of star formation, when most of the envelope has disappeared, and the
star is visible in the optical. Class I objects are Classical T Tauri
stars (CTTSs), with ongoing accretion (but at much lower levels than
before,
yr-1) and well defined discs. Class III objects are weak-line T Tauri stars (WTTs) with little sign of
accretion and no inner disc.
In their quest to identify the youngest protostars, André et al.
(1993, 2000) set 3 criteria for Classifying an object as Class 0: (i) the presence of a central luminosity source, as indicated by the
detection of a compact centimetre radio source, or a bipolar molecular
outflow, or internal heating; (ii) centrally peaked but extended
submillimetre continuum emission, indicating the presence of an
envelope around the central source; and (iii) a high ratio (>0.005)
of submillimetre to bolometric luminosity, where the submillimetre is
defined as
.
Criteria (ii) and (iii) are
used to distinguish between Class 0 and Class I objects, whereas
criterion (i) is used to distinguish between Class 0 objects and
prestellar cores. However, criterion (i) may be inadequate to
distinguish between the youngest Class 0 objects and the oldest
prestellar cores: (a) the cm emission may be be too weak to be
observed, especially in the earliest stages of protostar formation;
(b) the region may be too complex for the molecular outflows to be
detectable; and (c) internal heating may be difficult to establish,
if the protostar is deeply embedded in the core.
The origin of radio emission from Class 0 objects is uncertain (cf. Gibb
1999). Theoretical models show that once a protostar forms at the centre
of a collapsing core, the infalling gas accelerates to supersonic velocities
and an accretion shock develops on the surface of the protostar and/or on
the surface of the disc that surrounds the protostar (Winkler & Newman
1980; Cassen & Moosman 1981). The heating provided by the shock ionises
the surrounding gas, which then emits free-free radio radiation (e.g.
Bertout 1983; Neufeld & Hollenbach 1994, 1996). The radio luminosity
depends on the mass of the protostar, the accretion rate and the observer's
viewing angle. For a low-mass protostar, ,
the
predicted flux is below detection limits (Neufeld & Hollenbach 1996),
unless the accretion rate is high,
yr-1. Another
possibility is that the radio emission is produced by an ionised disc wind
(e.g. Martin 1996), or from a partially ionised jet that emanates from the
protostar and propagates into the collapsing envelope producing shocks
(Curiel et al. 1987). The detection of radio emission from many Class 0
protostars, using the VLA (e.g. Bontemps et al. 1995), points toward the
latter two explanations.
Recently Young et al. (2004), using the Spitzer space telescope, detected NIR radiation from L1014, a dense core that was previously classified as prestellar. The detection of NIR radiation strongly suggests that this is a young Class 0 object, and supports the view that even younger Class 0 objects may not be detectable in the NIR, with IRAS, or even with Spitzer.
The goal of this paper is to study the transition from prestellar cores to Class 0 objects, and to seek new criteria for distinguishing between these two stages, in particular criteria which can be used before the standard signatures of protostar birth, such as compact radio emission and/or bipolar molecular outflows, become detectable. We use SPH to simulate to the dynamics of a collapsing molecular core, and a Monte Carlo code to treat the transfer of radiation within the core. The radiative transfer is treated fully in 3D, which is important for the correct interpretation of the observations (cf. Boss & Yorke 1990; Whitney et al. 2003a,b; Steinacker et al. 2004). We use a newly developed method for performing Monte Carlo radiative transfer simulations on SPH density fields, which constructs radiative transfer cells using the SPH tree structure (Stamatellos 2003; Stamatellos & Whitworth 2005, hereafter Paper I).
In Sect. 2 we describe the SPH simulation of the collapse of a turbulent molecular core. In Sect. 3 we describe the radiative transfer method, focusing on how we construct radiative transfer cells. We also discuss the radiation sources and the properties of the dust used in our model. In Sect. 4 we present our results for the dust temperature fields, SEDs and isophotal maps of prestellar cores and young Class 0 protostars. In Sect. 5 we discuss how SEDs and isophotal maps at submm and mm wavelengths might be used to distinguish between late-phase prestellar cores and early-phase Class 0 objects. In Sect. 6 we summarise our results.
We use the Smoothed Particle Hydrodynamics code DRAGON (Goodwin et al. 2004a) to simulate the collapse of a turbulent molecular core and the resulting star formation. Here, we briefly describe the main elements of the model. For a more detailed discussion we refer to Goodwin et al. (2004b).
The initial conditions in the core, before the start of collapse, are
dictated by observations of prestellar cores (e.g. Ward-Thompson et al.
1999; Alves et al. 2001). Prestellar cores appear to have approximately
uniform density in their central regions, and the density then falls off
in the envelope. If the density in the envelope is fitted with a power
law,
,
then
.
Here
is characteristic of more extended prestellar cores in
dispersed star formation regions (e.g. L1544, L63 and L43), whereas
is characteristic of more compact cores in protoclusters (e.g.
Oph and NGC 2068/2071). These features can be represented by a
Plummer-like density profile (Plummer 1915),
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(1) |
Collapse of the turbulent core leads to the formation of a single star
surrounded by a disc, and the material in the disc then slowly accretes
onto the star. A sink particle, representing the star and the inner
part of the disc, is created where the density first exceeds
,
and incorporating all
the matter within
of this point (Bate et al. 1995). (The values of
and
are
dictated by computational constraints. If
is
increased,
must be reduced, and more computational
time is needed.)
We use a newly developed type of sink called a smartie, which is a
rotating oblate spheroid with radius
and half-thickness
(Fig. 1). The star is a point mass
at the centre of the smartie, and the spheroid represents
the inner part of the accretion disc surrounding the star.
and
are calculated by assuming that the inner part of the
accretion disc (the part inside the spheroid) has uniform density,
temperature and angular speed, and that its internal energy and spin
angular momentum balance its self-gravity and the gravity of the central
star.
The SPH particles which enter the smartie during a timestep,
,
are assimilated by it at the end of the timestep,
,
and their
mass is initially added to the mass of the smartie,
,
i.e. to
the mass of the inner disc,
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Figure 1: We use an oblate spheroidal sink particle, called a smartie, which contains a central star and a disc, and launches a bipolar outflow. |
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The smartie mass evolves according to
The second term on the right of Eq. (6)
represents accretion onto the central star, and is given by
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= | ![]() |
(7) |
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= | ![]() |
(8) |
The third term on the right of Eq. (6) represents mass loss from
the smartie, which can occur in two ways. (i) SPH particles are created at
rate
and launched along the rotation
axis with speed
to form a bipolar outflow. These jets
push the surrounding material aside and create hourglass cavities about the
rotation axis. (ii) In the present model the outflow does not remove any angular
momentum. Therefore the redistribution of angular momentum which drives accretion
onto the central star causes the residual inner disc (which has to carry all
the angular momentum assimilated by the smartie) to expand. When this happens,
the smartie is allowed to expand until
.
Thereafter,
is held constant by excreting SPH particles - and
with them angular momentum - just outside the equator of the smartie.
The luminosity of the star is given by
The mean smartie temperature, and hence also the mean smartie sound speed, are determined by the balance between radiative cooling, heating by radiation from the star and from the background radiation field, and viscous dissipation in the inspiralling gas of the smartie. A full description of the implementation of smarties is given in Boyd (2003), and the consequences of feedback from bipolar outflows are explored in detail in Boyd et al. (in preparation).
For the radiative transfer simulations, we use a version of PHAETHON, a Monte Carlo radiative transfer code which we have developed (Stamatellos & Whitworth 2003) and optimised for radiative transfer simulations on SPH density fields (Paper I). The main developments of the optimised version are (i) that it uses the tree structure inherent within the SPH code to construct a grid of cubic radiative transfer (RT) cells, spanning the entire computational domain, the global grid; and (ii) that in addition it constructs a local grid of concentric spherical RT cells around each star, a star grid, to capture the steep temperature gradients that are expected in the vicinity of a star. The code reemits luminosity packets as soon as they are absorbed (Lucy 1999) and uses the frequency distribution adjustment technique developed by Bjorkman & Wood (2000).
To construct RT cells for a given time-frame from an SPH simulation, we
take advantage of the fact that SPH uses an octal tree structure (to group
particles together when calculating gravity forces and also to find
neighbours; for details see Paper I). The SPH tree is a recursive
hierarchical division of the computational domain into cubic cells within
cubic cells (Barnes & Hut 1986). When the SPH tree is being built, we
record information about the size of each cell and the number of SPH particles it contains. The RT cells of the global grid are then the largest
SPH cells which contain
particles. This means that
the RT cells automatically have comparable mass. We choose
,
i.e. somewhat larger than the mean number of SPH neighbours,
.
Consequently the size of the RT cells is on the order of the smoothing length, h, and so the temperature
resolution is similar to the density resolution of the SPH simulation.
In order to increase the resolution of the radiative transfer simulation, we use particle splitting (Kitsionas & Whitworth 2002). This method replaces each SPH particle (parent particle) with a small group of 13 particles (children particles), each one having 1/13 of the mass of the parent particle. The children are placed on an hexagonal close-packed array, with one of them in the centre of the array and the other 12 equidistant from the first one. By doing this the smoothing length is decreased by a factor of 13-1/3=0.425, and the average size of the radiative transfer cells is reduced by the same factor.
In Paper I we discussed the need for a high-resolution grid of radiative transfer cells - a star grid - in order to capture the steep temperature gradients that are expected in the vicinity of a star. The star grid discussed there was developed for treating the unresolved region inside a spherically symmetric sink, and so a one-dimensional star grid consisting of concentric spherical cells centred on the star was sufficient.
In the case we examine here the sinks are smarties, i.e. oblate spheroids, and the unresolved region inside a smartie represents both the protostar and the inner protostellar disc. Thus a spherically symmetric one-dimensional star grid is inappropriate. Instead we adopt a similar approach to Kurosawa et al. (2004) and represent the unresolved region near the star with a flared disc (Fig. 2).
However, the properties of the inner disc are not imposed externally, as in
Kurosawa et al. (2004), but are determined by the properties of the smartie,
and therefore attempt to capture the physics of a protostellar disc accreting
onto a newly-formed protostar (as outlined in Sect. 2).
Specifically, we adopt an inner disc with inner radius
,
outer
radius
,
and constant ratio of thickness, H, to radius, r,
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(10) |
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(11) |
We put
,
since this is the maximum size of a
smartie, and it is comparable with the size of the local global RT cells
(the cubic cells constructed from the SPH tree).
For
and
,
the density
of the inner disc is given by
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(12) |
The inner disc is then divided into RT cells by spherical and conical surfaces (see Fig. 2). The spherical surfaces are evenly spaced in logarithmic radius and there are typically 20 of them. The conical surfaces are evenly spaced in polar angle and there are typically 30 of them.
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Figure 2:
The star grid consists of concentric spherical surfaces centred
on the star, with equal spacing in ![]() ![]() |
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Figure 3: Dotted line: the external illumination field (BISRF + emission from PAHs). Solid line: the radiation scattered by the molecular cloud. This is similar for all the time-frames and viewing angles, for the models we examine here. |
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Table 1: Model parameters.
The core is illuminated externally by the interstellar radiation field and internally by the newly formed protostar (once it has formed).
For the external radiation field we adopt a revised version of the Black (1994) interstellar radiation field (BISRF). The BISRF consists of radiation from giant stars and dwarfs, thermal emission from dust grains, cosmic background radiation, and mid-infrared emission from transiently heated small PAH grains (André et al. 2003), as illustrated in Fig. 3. Typically the BISRF is represented by 109-1010 L-packets.
The protostar luminosity,
,
and effective temperature,
are given by Eq. (9); a blackbody spectrum at
is assumed.
For the systems examined here, the accretion contribution to the luminosity
dominates, because the mass of the protostar is small (<
)
and the accretion rate is high (>
yr-1). Typically the
protostar is represented by
L-packets.
Like other studies of prestellar cores (e.g. Evans et al. 2001; Young et al. 2004) we use the Ossenkopf & Henning (1994) opacity for a standard
MRN interstellar grain mixture (53% silicate and 47% graphite) which has
coagulated and accreted thin ice mantles over a period of 105 yr at a
density of
.
However, we emphasize that the opacity
of the dust in cores is very uncertain (e.g. Bianchi et al. 2003).
We perform radiative transfer simulations on 6 time-frames during the collapse of a star-forming core. We focus our attention just before and just after the formation of the first protostar in the core. The characteristics of each time-frame are listed in Table 1. The simulations are 3-dimensional and provide dust temperature fields, SEDs and isophotal maps.
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Figure 4: Cross sections of density and dust temperature on a plane parallel to the x=0 plane ( left two columns) and parallel to the z=0 plane ( right two columns). Each row corresponds to a different time frame from Table 1, top to bottom t0 to t5. The planes are chosen so as to include the maximum density region (t0 and t1) or the protostar (t2 to t5). |
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In Fig. 4 we present the density fields and dust-temperature
fields for the 6 time-frames in Table 1. We plot the density
and the temperature on 2 cuts through the computational domain, one parallel to
the x=0 plane and one parallel to the z=0 plane. Each of these planes passes
through the protostar, or, if there is no protostar (as in the first 2 time-frames),
through the densest part of the core. The plots show only the central region of the
core (
). Additionally, in
Fig. 5, we plot the density and the temperature of each RT cell versus distance r from the centre of coordinates, on a logarithmic scale,
in order to depict better the regions very close to the protostar.
Our results for the temperature are broadly similar to those of previous 1D and
2D studies of prestellar cores and Class 0 objects. Before the collapse, the
precollapse prestellar core is quite cold (
)
and it becomes even
colder (
)
as the collapse proceeds and the central regions
become very dense and opaque. As soon as a protostar forms, the region around it
becomes very hot (up to the dust destruction temperature), but the temperature still
drops below
beyond a few
from the protostar,
because of the high optical depth in the dense accretion flow onto the protostar.
The luminosity of the protostar is dominated by the contribution from accretion.
Initially the accretion luminosity increases due to the increasing mass of the
protostar, but then it falls as the accretion rate declines.
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Figure 5: Log-log plot of density ( left column) and dust temperature ( right column) versus distance from the centre of coordinates, in a collapsing core which forms a protostar; from top to bottom, time-frames t0 to t5 (see Table 1). |
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The SEDs of the 6 time-frames in Table 1 are presented in
Fig. 6. These SEDs have been calculated assuming that the core is
at
.
SEDs are plotted for 6 different viewing angles, i.e. 3 polar
angles (
,
,
)
and 2 azimuthal angles
(
,
). Hence on each graph there are 6 curves. However, in
several cases the SED is so weakly dependent on viewing angle that the curves
overlap. We plot only the thermal emission from the core, i.e. we neglect both
the long-wavelength background radiation that just passes through the cloud, and
the short-wavelength radiation that is scattered by the outer layers of the cloud.
The effective temperature of the core, as inferred from the peak of the SED, rises
and falls with the accretion luminosity of the protostar. For a prestellar core,
the SED peaks at
,
implying
.
Once the protostar has formed and inputs energy into the system, the peak moves
steadily to shorter wavelengths, reaching
(
)
as the accretion luminosity reaches its maximum, and then moving back
to longer wavelengths again as the accretion luminosity declines. By the final frame
it has reached
(
).
The peak of the SED of a prestellar core is independent of viewing angle, since
the core is optically thin to the radiation it emits. In contrast, the peak of the
SED of a Class 0 object does depend on viewing angle, albeit weakly, because of the
presence of an optically thick disc around the protostar. However, even allowing for
variations in the viewing angle, the SED of a Class 0 object does not peak at the
wavelengths characteristic of prestellar cores (
).
Our model predicts that a young protostar embedded in a core
is not observable in the NIR, unless the protostar is displaced from
the central high-density region. This contradicts the recent results of
Whitney et al. (2003b) and Young et al. (2004). We attribute the difference
between our model and that of Young et al. to the density they use for the
region around the protostar (
), which may be too
low for a Class 0 objects and more appropriate for a prestellar core.
Whitney et al. use a higher density in the central region (
), but it is still more than one order of magnitude lower
than the density produced by our SPH simulation (
). Additionally, they use different dust properties for the
different regions in their configuration (cloud, disc mid-plane, disc atmosphere,
outflow); in particular, the opacity of their dust in the disc midplane is smaller
than the opacity in our model, at wavelengths shorter than
.
There
are also some differences in the properties of the discs used in the different
models, but these are less relevant to the escape of NIR radiation.
The models reported by Shirley et al. (2002) use central densities and dust opacities similar to our models, but they confine their study to the FIR/mm region of the spectrum, so a comparison is not possible.
Ultimately, the density distribution within
of the centre of
a core or protostar is not well constrained by observations, and therefore
radiative transfer calculations have to rely on theoretical models of core
collapse. Dust opacities are also poorly constrained (e.g. Bianchi et al.
2003). Comparison of our model with those of Whitney et al. (2003b) and Young
et al. (2004) suggests that the presence or absence of NIR emission from a
confirmed Class 0 object might be used to constrain the density profile within
a few
of the protostar and/or the opacity of the dust in the
same region.
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Figure 6:
SEDs of the 6 time-frames in Table 1, from 3 polar
angles (
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Figure 7:
850
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Figure 8:
As Fig. 7, but after convolving with
a Gaussian beam having
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The shapes of prestellar cores and Class 0 objects depend on viewing angle.
In Fig. 7 we present isophotal maps at
,
for 3 different time-frames (t1, t3, t5), and from
3 different viewing angles. At
the core is optically thin,
and the temperature does not vary much (
,
apart from the region very close to the protostar in time-frames
t3 and t5), so the maps are effectively column density maps.
Class 0 objects are more centrally condensed than prestellar cores. They
also show more structure, due to bipolar outflows, which clear low-density
cavities (see images at
and
in
Fig. 7).
In Fig. 8 we present a selection of isophotal maps after
convolving them with a Gaussian beam having
.
Assuming the cloud is 150 pc away, this corresponds to an angular resolution
of
,
which is similar to the beam size of current submm and mm
telescopes (e.g. SCUBA, IRAM). On these maps, Class 0 objects look very
similar to prestellar cores, apart from the fact that they tend to appear
more circular and featureless (cf. Fig. 7).
The reason for this is that the emission from a core that contains a protostar is
concentrated in the central few hundred AU, and so, when it is convolved with
a
beam, it produces an image rather like the beam, i.e.
round and smooth. In contrast, the emission from a prestellar cores has structure
on scales of several thousand AU, much of which survives convolution with a
beam. Thus we should expect cores that contain protostars to
appear rounder than prestellar cores, and indeed this is what is observed
(Goodwin et al. 2002).
Time-frame t0, precollapse prestellar core. The core is
heated exclusively by the ambient radiation field, and so the outer
parts of the cloud are warmer (
)
than the interior. The
temperature falls to
in the central
of the cloud, where the density is high,
106 cm-3 (cf. Evans
et al. 2001; Zucconi et al. 2001; Stamatellos & Whitworth 2003;
Gonçalves et al. 2004; Stamatellos et al. 2004). The cloud emission
peaks at
which implies
.
The SED is fairly typical for a prestellar core (e.g. Ward-Thompson et al.
2002), except that
is a little higher than for the majority
of prestellar cores (where it is
). This is because the SED
plotted here includes the outer, warmer layers of the core, and this shifts
the peak of the SED to shorter wavelengths.
Time-frame t1, collapsing prestellar core. The collapse
of the core results in a flattened, disc-like region in the centre of the cloud.
Heating is still provided only by the ambient radiation field. The
temperature at the centre of cloud is even lower ()
than
in time-frame t0, because the density - and hence the optical depth -
is even higher (>
). The SED looks very similar to time-frame
t0, even though the collapse has started and the cloud is denser
and colder at its centre. Thus the SED does not distinguish between a precollapse
prestellar core and a collapsing prestellar core.
Time-frame t2, Class 0 object. A protostar has formed at
the centre of the core, and started heating the core. The protostar has low mass
(
), but the accretion rate onto it is high
(
yr-1), and hence the
accretion luminosity is also quite high,
.
The dust temperature increases very close to the protostar, but drops down below
within a few
from the protostar, and then rises
towards the edge where the core is heated by the ambient radiation field (cf.
Shirley et al. 2002). Thus, at this early stage, it is necessary to probe the
inner
to infer the presence of the protostar. The peak of the
SED has moved to
(depending on viewing angle),
which implies an effective temperature
.
The dependence of the SED on viewing angle is due to the disc around
the protostar.
Time-frame t3, Class 0 object. The bipolar jets from the
protostar have created hourglass cavities, as can be seen on the density plots of
Fig. 4. As a consequence, the accretion rate onto the
protostar decreases to
yr-1, but
its mass has increased (to
), and so the luminosity
injected into the cloud increases (to
).
As a result, the temperature is >
within
,
and it does not fall below
in the inner
.
The SED peaks at
(depending on viewing angle),
which implies
.
Time-frame t4, Class 0 object. The total luminosity injected
into the cloud is lower (
)
due to the reduced
accretion rate onto the protostar (
yr-1). The temperature distribution is similar to the previous
time-frame (time-frame t2), but slightly cooler due to the reduced
luminosity. The SED is also similar, but there is a slightly stronger dependence on
viewing angle. The SED now peaks at
,
implying
.
Time-frame t5, Class 0 object. Asymmetries in the pattern
of accretion onto the protostar have given it a small peculiar velocity,
,
and by t5 it is displaced from the dense
central region by
100 AU. Consequently the accretion rate onto the
protostar is reduced (to
yr-1)
and with it the accretion luminosity (to
).
As illustrated in the temperature cross section parallel to the x=0 plane in
Fig. 4, the upper half of the core is warmed to >
by the displaced protostar. In contrast, the lower half of the core is not affected
by the protostar, and the temperature here does not rise above
,
apart from in the outer layers of the core, which are still heated by the ambient
radiation field. As a consequence of the reduced accretion luminosity, the peak of
the SED moves back to longer wavelengths (
)
and cooler effective
temperature (
). The displacement of the protostar also means that
it is now visible at shorter wavelengths (
), from viewing
angles close to the rotation axis.
We have simulated the collapse of a turbulent molecular core using SPH, and performed 3-dimensional Monte Carlo radiative transfer simulations at different stages of this collapse, to predict dust temperature fields, SEDs and isophotal maps. We focus on the initial stages of protostar formation, i.e. just before and just after the formation of a protostar, and derive criteria for distinguishing between genuine prestellar cores and cores that contain very young protostars. As pointed out by Masunaga et al. (1998), very young protostars are difficult to observe directly, because they are deeply embedded, and may be wrongly classified as prestellar cores. Hence it is important to consider ways in which their presence might be inferred indirectly. The main results of this study are as follows.
Acknowledgements
We thank P. André for providing the revised version of the Black (1994) ISRF, that accounts for the PAH emission. We also thank D. Ward-Thompson for useful discussions and suggestions. This work was partly supported from the EC Research Training Network "The Formation and Evolution of Young Stellar Clusters'' (HPRN-CT-2000-00155), and partly by PPARC grant PPA/G/O/2002/00497.