In this paper we derive and discuss several implications of the analytic form of a modified blackbody, also called greybody, which is widely used in Astrophysics, and in particular in the study of ...star formation in the far-infrared/submillimetre domain. The research in this area has been greatly improved thanks to recent observations taken with the Herschel satellite, so that it became important to clarify the sense of the greybody approximation, to suggest possible further uses, and to delimit its intervals of validity. First, we discuss the position of the greybody peak, making difference between the optically thin and thick regimes. Second, we analyse the behaviour of bolometric quantities as a function of the different greybody parameters. The ratio between the bolometric luminosity and the mass of a source, the ratio between the so-called ‘submillimetre luminosity’ and the bolometric one, and the bolometric temperature are observables used to characterize the evolutionary stage of a source, and it is of primary importance to have analytic equations describing the dependence of such quantities on the greybody parameters. Here we discuss all these aspects, providing analytic relations, illustrating particular cases, and providing graphical examples. Some equations reported here are well known in Astrophysics, but are often spread over different publications. Some of them, instead, are brand new and represent a novelty in Astrophysics literature. Finally, we indicate an alternative way to obtain, under some conditions, the greybody temperature and dust emissivity index directly from an observing spectral energy distribution, avoiding a best-fitting procedure.
Context. Herschel
observations of nearby clouds in the Gould Belt support a paradigm for low-mass star formation, starting with the generation of molecular filaments, followed by filament ...fragmentation, and the concentration of mass into self-gravitating prestellar cores. In the case of the Ophiuchus molecular complex, a rich star formation activity has been documented for many years inside the clumps of L1688, the main and densest cloud of the complex, and in the more quiescent twin cloud L1689 thanks to extensive surveys at infrared and other wavelengths.
Aims.
With the unique far-infrared and submillimeter continuum imaging capabilities of the
Herschel
Space observatory, the closeby (
d
= 139 pc) Ophiuchus cloud was extensively mapped at five wavelengths from 70 to 500
μ
m with the aim of providing a complete census of dense cores in this region, including unbound starless cores, bound prestellar cores, and protostellar cores.
Methods.
Taking full advantage of the high dynamic range and multi-wavelength nature of the
Herschel
data, we used the multi-scale decomposition algorithms
getsources
and
getfilaments
to identify an essentially complete sample of dense cores and filaments in the cloud and study their properties.
Results.
The densest clouds of the Ophiuchus complex, L1688 and L1689, which thus far are only indirectly described as filamentary regions owing to the spatial distribution of their young stellar objects, are now confirmed to be dominated by filamentary structures. The tight correlation observed between prestellar cores and filamentary structures in L1688 and L1689 supports the view that solar-type star formation occurs primarily in dense filaments. While the sub clouds of the complex show some disparities, L1689 being apparently less efficient than L1688 at forming stars when considering their total mass budgets, both sub clouds share almost the same prestellar core formation efficiency in dense molecular gas. We also find evidence in the
Herschel
data for a remarkable concentric geometrical configuration in L1688 which is dominated by up to three arc-like compression fronts and has presumably been created by shockwave events emanating from the Sco OB2 association, including the neighboring massive (O9V) star
σ
Sco.
Conclusions.
Our
Herschel
study of the well-documented Ophiuchus region has allowed us to further analyze the influence of several early-type (OB) stars surrounding the complex, thus providing positive feedback and enhancing star formation activity in the dense central part of the region, L1688.
We present a detailed study of the Orion B molecular cloud complex (
d
~ 400 pc), which was imaged with the PACS and SPIRE photometric cameras at wavelengths from 70 to 500
μ
m as part of the
...Herschel
Gould Belt survey (HGBS). We release new high-resolution maps of column density and dust temperature for the whole complex, derived in the same consistent manner as for other HGBS regions. In the filamentary subregions NGC 2023 and 2024, NGC 2068 and 2071, and L1622, a total of 1768 starless dense cores were identified based on
Herschel
data, 490–804 (~28−45%) of which are self-gravitating prestellar cores that will likely form stars in the future. A total of 76 protostellar dense cores were also found. The typical lifetime of the prestellar cores was estimated to be
t
pre
OrionB
= 1.7
−0.6
+0.8
Myr. The prestellar core mass function (CMF) derived for the whole sample of prestellar cores peaks at ~0.5
M
⊙
(in d
N
/dlog
M
format) and is consistent with a power-law with logarithmic slope −1.27 ± 0.24 at the high-mass end, compared to the Salpeter slope of − 1.35. In the Orion B region, we confirm the existence of a transition in prestellar core formation efficiency (CFE) around a fiducial value
A
V
bg
~ 7 mag in background visual extinction, which is similar to the trend observed with
Herschel
in other regions, such as the Aquila cloud. This is not a sharp threshold, however, but a smooth transition between a regime with very low prestellar CFE at
A
V
bg
< 5 and a regime with higher, roughly constant CFE at
A
V
bg
≳ 10. The total mass in the form of prestellar cores represents only a modest fraction (~20%) of the dense molecular cloud gas above
A
V
bg
≳ 7 mag. About 60–80% of the prestellar cores are closely associated with filaments, and this fraction increases up to >90% when a more complete sample of filamentary structures is considered. Interestingly, the median separation observed between nearest core neighbors corresponds to the typical inner filament width of ~0.1 pc, which is commonly observed in nearby molecular clouds, including Orion B. Analysis of the CMF observed as a function of background cloud column density shows that the most massive prestellar cores are spatially segregated in the highest column density areas, and suggests that both higher- and lower-mass prestellar cores may form in denser filaments.
Many biological tissues exhibit a non-standard continuum mechanics behavior: they are able to modify their placement in absence of external loads. The activity of the muscles is usually represented ...in solid mechanics in terms of an active stress, to be added to the standard one. A less popular approach is to introduce a multiplicative decomposition of the tensor gradient of deformation in two factors: the passive and the active one. Both approaches should satisfy due mathematical properties, namely frame indifference and ellipticity of the total stress. At the same time, the constitutive laws should reproduce the observed physiological behavior of the specific living tissue. In this paper we focus on cardiac contractility. We review some constitutive examples of active stress and active strain taken from the literature and we discuss them in terms of precise mathematical and physiological properties. These arguments naturally suggest new possible models.
Context. The mechanism of formation of massive stars is still a matter of debate. It is not yet clear if it can be considered to be a scaled-up analogue of the low-mass star regime, or if there are ...additional agents like merging of lower-mass forming objects or accretion from initially unbound material. Most of the uncertainties come from the lack of diagnostic tools to evolutionarily classify large samples of candidate massive protostellar objects that can then be studied in more detail. Aims. We want to verify whether diagnostic tools like the SED shape and the relationship between envelope mass and bolometric luminosity can be extended to the study of high-mass star formation. Methods. The 8-1200 μm SED of YSOs in 42 regions of massive star formation has been reconstructed using MSX, IRAS, and submm data partly available from previous works. Apart from IRAS catalogue fluxes, the fluxes in the Mid-IR and sub-mm/mm were derived directly from the images. The SEDs were fitted to an extensive grid of envelope models with embedded ZAMS stars, available from the literature. Sources that could not be fitted with a single model were then fitted with a two-component model composed of an embedded ZAMS for the mid-IR part and a single-temperature optically thin greybody for the longer wavelength emitting component. Sources were classified as “IR” if they were fitted with an embedded ZAMS envelope, and “MM” if they could only be fitted with a greybody with a peak at high λ; further subclassification was based on being the most massive object in the field (“P”, for primary) or not (“S”, for secondary). Results. The different classes of sources identified in our analysis have very different SEDs and occupy distinct areas in the $L_\mathrm{\rm bol}{-}M_\mathrm{env}$ diagram; by analogy with the low-mass regime, we see that MM-P, IR-P and IR-S objects could be interpreted as the high-mass analogue of Class 0-I-II. Evolutionary tracks obtained from a simple model based on the turbulent core prescriptions show that the three classes of sources possibly mark different periods in the formation of a massive YSO. The IR-P objects are consistent with being at the end of the main accretion phase, while MM-P sources are probably in an earlier evolutionary stage. The timescales for the formation decrease from ~ 4$\times$105 to ~ 1$\times$105 years with stellar mass increasing from ~6 to ~40 $M_{\odot}$; these timescales, and the association with young clusters with median stellar age of a few 106 years suggest that the most massive objects are among the last ones to form. Conclusions. Our results are consistent with the high-mass star formation being a scaled-up analogue of the traditional accretion-dominated paradigm valid for the low-mass regime.
Abstract
We present a new derivation of the Milky Way’s current star formation rate (SFR) based on the data of the Herschel InfraRed Galactic Plane Survey (Hi-GAL). We estimate the distribution of ...the SFR across the Galactic plane from the star-forming clumps identified in the Hi-GAL survey and calculate the total SFR from the sum of their contributions. The estimate of the global SFR amounts to 2.0 ± 0.7
M
⊙
yr
−1
, of which 1.7 ± 0.6
M
⊙
yr
−1
coming from clumps with reliable heliocentric distance assignment. This value is in general agreement with estimates found in the literature of last decades. The profile of SFR density averaged in Galactocentric rings is found to be qualitatively similar to others previously computed, with a peak corresponding to the Central Molecular Zone and another one around Galactocentric radius
R
gal
∼ 5 kpc, followed by an exponential decrease as
log
(
Σ
SFR
/
M
⊙
yr
−
1
kpc
−
2
)
=
a
R
gal
/
kpc
+
b
, with
a
= −0.28 ± 0.01. In this regard, the fraction of SFR produced within and outside the solar circle is 84% and 16%, respectively; the fraction corresponding to the far outer Galaxy (
R
gal
> 13.5 kpc) is only 1%. We also find that, for
R
gal
> 3 kpc, our data follow a power law as a function of density, similarly to the Kennicutt–Schmidt relation. Finally, we compare the distribution of the SFR density across the face-on Galactic plane and those of median parameters, such as temperature, luminosity/mass ratio, and bolometric temperature, describing the evolutionary stage of Hi-GAL clumps. We found no clear correlation between the SFR and the clump evolutionary stage.
Distance of Hi-GAL sources Mège, P.; Russeil, D.; Zavagno, A. ...
Astronomy & astrophysics,
02/2021, Volume:
646
Journal Article
Peer reviewed
Open access
Aims.
Distances are key to determining the physical properties of sources. In the Galaxy, large (> 10 000) homogeneous samples of sources for which distance are available, covering the whole Galactic ...distance range, are still missing. Here we present a catalog of velocity and distance for a large sample (> 100 000) of Hi-GAL compact sources.
Methods.
We developed a fully automatic Python package to extract the velocity and determine the distance. To assign a velocity to a Hi-GAL compact source, the code uses all the available spectroscopic data complemented by a morphological analysis. Once the velocity is determined, if no stellar or maser parallax distance is known, the kinematic distance is calculated and the distance ambiguity (for sources located inside the Solar circle) is solved with the H
I
self-absorption method or from distance–extinction data.
Results.
Among the 150 223 compact sources of the Hi-GAL catalog, we obtained a distance for 124 069 sources for the 5
σ
catalog (and 128 351 sources for the 3
σ
catalog), where
σ
represents the noise level of each molecular spectrum used for the line detections made at 5
σ
and 3
σ
to produce the respective catalogs.
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of ...high-fidelity models without compromising the accuracy of the estimates. This approach has recently gained widespread attention in uncertainty quantification 1. This is partly due to the availability of optimal strategies for the estimation of the expectation of scalar quantities-of-interest 2. In practice, the optimal strategy for the expectation is also used for the estimation of variance and sensitivity indices 3. However, a general strategy is still lacking for vector-valued problems, nonlinearly statistically-dependent models, and estimators for which a closed-form expression of the error is unavailable. The focus of the present work is to generalize the standard multifidelity estimators to the above cases. The proposed generalized estimators lead to an optimization problem that can be solved analytically and whose coefficients can be estimated numerically with few runs of the high- and low-fidelity models. We analyze the performance of the proposed approach on a selected number of experiments, with a particular focus on cardiac electrophysiology, where a hierarchy of physics-based low-fidelity models is readily available.
•Standard multifidelity estimators require a priori knowledge of mean squared error.•They also assume linear correlation between models and scalar outputs.•The proposed estimators estimate the error a posteriori from sampling the models.•Easy to extend to vector-valued and nonlinearly statistically-dependent outputs.•The cardiac activation map is estimated combining multiple electrophysiology models.
The complex of star-forming regions in Perseus is one of the most studied due to its proximity (about 300 pc). In addition, its regions show variation in star-formation activity and age, with ...formation of low-mass and intermediate-mass stars. In this paper, we present analyses of images taken with the
Herschel
ESA satellite from 70
μ
m to 500
μ
m. From these images, we first constructed column density and dust temperature maps. We then identified compact cores in the maps at each wavelength, and characterised the cores using modified blackbody fits to their spectral energy distributions (SEDs): we identified 684 starless cores, of which 199 are bound and potential prestellar cores, and 132 protostars. We also matched the
Herschel
-identified young stars with
Gaia
sources to model distance variations across the Perseus cloud. We measure a linear gradient function with right ascension and declination for the entire cloud. This function is the first quantitative attempt to derive the gradient in distance across Perseus, from east to west, in an analytical form. We derived mass and temperature of cores from the SED fits. The core mass function can be modelled with a log-normal distribution that peaks at 0.82
M
⊙
suggesting a star formation efficiency of 0.30 for a peak in the system initial mass function of stars at 0.25
M
⊙
. The high-mass tail can be modelled with a power law of slope ~−2.32, which is close to the Salpeter’s value. We also identify the filamentary structure of Perseus and discuss the relation between filaments and star formation, confirming that stars form preferentially in filaments. We find that the majority of filaments with ongoing star formation are transcritical against their own internal gravity because their linear masses are below the critical limit of 16
M
⊙
pc
−1
above which we expect filaments to collapse. We find a possible explanation for this result, showing that a filament with a linear mass as low as 8
M
⊙
pc
−1
can already be unstable. We confirm a linear relationship between star formation efficiency and the slope of dust probability density function, and we find a similar relationship with the core formation efficiency. We derive a lifetime for the prestellar core phase of 1.69 ± 0.52 Myr for the whole Perseus complex but different regions have a wide range in prestellar core fractions, suggesting that star formation began only recently in some clumps. We also derive a free-fall time for prestellar cores of 0.16 Myr.
Abstract
We describe new Hi-GAL based maps of the entire Galactic Plane, obtained using continuum data in the wavelength range 70–500 μm. 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 online. We briefly describe PPMAP and present some illustrative examples of the results. These include (a) multi-temperature maps of the Galactic H ii 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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