arXiv subjects

E. Zari

Publications and source records attributed to E. Zari.

17 recordsLinked to original sources

arXiv2026

SDSS-V LVM: Verifying what, and where, the 'Galactic Center' Lobe is

The so-called 'Galactic Center' Lobe (GCL) is an extended (~1 deg) radio continuum feature situated above the Galactic Plane, for which the literature contains varying claims about both its nature and location. Using new optical integral field spectroscopic observations from the SDSS-V Local Volume Mapper, we confirm the characterization of the GCL as a foreground photoionized HII region, not associated with the Galactic center. We present a new analysis of the ionized gas morphology, line ratio diagnostics, and kinematics. From our [SIII]9532 emission line map, which suffers the least extinction, we identify ionized gas emission throughout a closed outer loop, which does not fill the GCL interior. All optical line ratio diagnostics are consistent with photoionization. By comparing the ionized gas reddening from the Balmer decrement with 3D dust maps, we directly constrain the distance to the GCL to ~2 kpc. [NII]6583 line kinematics show a uniform velocity structure across the GCL, further confirming that the entire bubble is one structure. The size and emission line morphology is strongly reminiscent of that seen in the nearby Barnard's Loop, providing a possible analog to explain how this outer shell may be photoionized by a more distant and off-center embedded young cluster. We suggest the acronym GCL be repurposed to instead abbreviate the name 'Greatly Confused Loop'.

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arXiv2025

The IACOB project XIV. New clues on the location of the TAMS in the massive star domain

Massive stars play a very important role in many astrophysical fields. Yet, some fundamental aspects of their evolution remain poorly constrained. In this regard, there is an open debate on the width of the main-sequence (MS) phase. We aim to create an updated Hertzsprung-Russell (HR) diagram that includes a volume-limited and statistically significant sample of massive stars. Our goal is to use this sample to investigate the extension of the MS, including information about projected rotational velocities ($v\sin i$) and the spectroscopic binary status. We combine spectroscopic parameters derived with FASTWIND stellar atmosphere code and Gaia distances to obtain stellar parameters for 876 Galactic luminous O- and B-type stars gathered within the IACOB project. We use the ${\tt iacob-broad}$ tool to derive $v\sin i$ estimates and multi-epoch spectra to identify single/double-line spectroscopic binaries (SB1/SB2). We present an HR diagram for 670 stars located within 2500pc balancing completeness and number. We evaluate the extension of the MS in terms of the drop in the relative number of stars as a function of effective temperature ($T_{\rm eff}$). We find a consistent boundary at $\approx$22.5kK within the full range of luminosities that we use to delineate the terminal-age main sequence (TAMS). We obtain a smooth decrease of the highest $v\sin i$ with $T_{\rm eff}$ along the MS, likely limited by the critical velocity. We consider this effect combined with a lower expected fraction of stars beyond the MS as the best explanation for the lack of fast-rotating objects in the post-MS region. Our results favor low to mild initial rotation for the full sample and a binary past for the tail of fast-rotating stars. The prominence of SB1/SB2 systems in the MS, and the 25% decrease in the relative fraction of SB1 systems when crossing the TAMS can further delineate its location.

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arXiv2024

Kinetic tomography of the Galactic plane within 1.25 kiloparsecs from the Sun. The interstellar flows revealed by HI and CO line emission and 3D dust

We present a reconstruction of the line-of-sight motions of the local interstellar medium (ISM) based on the combination of a model of the three-dimensional dust density distribution within 1.25 kpc from the Sun and the HI and CO line emission within Galactic latitudes $|b| < 5^{\circ}$. We used the histogram of oriented gradient (HOG) method, a computer vision technique for evaluating the morphological correlation between images, to match the plane-of-the-sky dust distribution across distances with the atomic and molecular line emission. We identified a significant correlation between the 3D dust model and the line emission. We employed this correlation to assign line-of-sight velocities to the dust across density channels and produce a face-on map of the local ISM radial motions with respect to the local standard of rest (LSR). We find that most of the material in the 3D dust model follows the large-scale pattern of Galactic rotation; however, we also report local departures from the rotation pattern with standard deviations of 10.8 and 6.6 km/s for the HI and CO line emission, respectively. The mean kinetic energy densities corresponding to these streaming motions are around 0.11 and 0.04 eV/cm$^{3}$ from either gas tracer. Assuming homogeneity and isotropy in the velocity field, these values are within a factor of a few of the total kinetic energy density. These kinetic energy values are roughly comparable to other energy densities, thus confirming the near-equipartition in the local ISM. Yet, we identify energy and momentum overdensities of around a factor of ten concentrated in local density structures. Although we do not find evidence of the local spiral arm's impact on these energy overdensities, their distribution suggests the influence of large-scale effects that, in addition to supernova feedback, shape the energy distribution and dynamics in the solar neighborhood.

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arXiv2024

The Great Wave: Evidence of a large-scale vertical corrugation propagating outwards in the Galactic disc

We analyse the three-dimensional structure and kinematics of two samples of young stars in the Galactic disc, containing respectively young giants ($\sim$17$\, $000 stars out to heliocentric distances of $\sim$7 kpc) and classical Cepheids ($\sim$3400 stars out to heliocentric distances of $\sim$15 kpc). The vertical structure of the two samples exhibit a consistent shape of the Milky Way's warp, whose amplitude reaches $\sim$700 pc at a Galactocentric radius R $\sim$ 14 kpc. Moreover, both samples show evidence of a large-scale vertical corrugation on top of the warp with a vertical height of $\sim$150-200 pc, extending over a large portion of the Galactic disc between Galactocentric radii $R \sim$ 10-12 kpc in the third Galactic quadrant (galactic longitudes $180^\circ < l < 270^\circ$) and $\sim$12-14 kpc in the second Galactic quadrant ($90^\circ < l < 180^\circ$). Its total length is at least 10 kpc and can possibly reach $\sim$ 20 kpc with the Cepheid sample. The stars in the corrugation exhibit both radial and vertical systematic motions, with Galactocentric radial velocities towards the outer disc of about 10-15 km/s. In the vertical motions, once the warp signature is subtracted, the residuals show a large-scale feature of systematically positive vertical velocities, which is shifted to slightly larger Galactocentric radii with respect to the spatial vertical corrugation (with a phase difference of roughly $\pi/2$), indicating an oscillatory behaviour. A comparison of the observed shift with a simple toy model suggests that the corrugation can be interpreted as a wave propagating towards the outer disc. The wave mapped in this work is located at larger heliocentric distances compared to the Radcliffe wave, a $\sim$2.7 kpc filament of dense gas clouds close to the Sun, and exhibits a larger coverage of the Galactic disc.

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arXiv2024

SDSS-V Local Volume Mapper (LVM): A Glimpse into Orion

The Orion Molecular Cloud complex, one of the nearest (D = 406 pc) and most extensively studied massive star-forming regions, is ideal for constraining the physics of stellar feedback, but its ~12 deg diameter on the sky requires a dedicated approach to mapping ionized gas structures within and around the nebula. The Sloan Digital Sky Survey (SDSS-V) Local Volume Mapper (LVM) is a new optical integral field unit (IFU) that will map the ionized gas within the Milky Way and Local Group galaxies, covering 4300 deg^2 of the sky with the new LVM Instrument. We showcase optical emission line maps from LVM covering 12 deg^2 inside of the Orion belt region, with 195,000 individual spectra combined to produce images at 0.07 pc (35.3") resolution. This is the largest IFU map made (to date) of the Milky Way, and contains well-known nebulae (the Horsehead Nebula, Flame Nebula, IC 434, and IC 432), as well as ionized interfaces with the neighboring dense Orion B molecular cloud. We resolve the ionization structure of each nebula, and map the increase in both the [SII]/Ha and [NII]/Ha line ratios at the outskirts of nebulae and along the ionization front with Orion B. [OIII] line emission is only spatially resolved within the center of the Flame Nebula and IC 434, and our ~0.1 pc scale line ratio diagrams show how variations in these diagnostics are lost as we move from the resolved to the integrated view of each nebula. We detect ionized gas emission associated with the dusty bow wave driven ahead of the star sigma Orionis, where the stellar wind interacts with the ambient interstellar medium. The Horsehead Nebula is seen as a dark occlusion of the bright surrounding photo-disassociation region. This small glimpse into Orion only hints at the rich science that will be enabled by the LVM.

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arXiv2023

A comparison of the Milky Way's recent star formation revealed by dust thermal emission and high-mass stars

We present a comparison of the Milky Way's star formation rate (SFR) surface density ($\Sigma_{\rm SFR}$) obtained with two independent state-of-the-art observational methods. The first method infers $\Sigma_{\rm SFR}$ from observations of the dust thermal emission from interstellar dust grains in far-infrared wavelengths registered in the Herschel infrared Galactic Plane Survey (Hi-GAL). The second method determines $\Sigma_{\rm SFR}$ by modeling the current population of O-, B-, and A-type stars in a 6 kpc $\times$ 6 kpc area around the Sun. We find an agreement between the two methods within a factor of two for the mean SFRs and the SFR surface density profiles. Given the broad differences between the observational techniques and the independent assumptions in the methods for computing the SFRs, this agreement constitutes a significant advance in our understanding of the star formation of our Galaxy and implies that the local SFR has been roughly constant over the past 10\,Myr.

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arXiv2022

Did the Milky Way just light up? The recent star formation history of the Galactic disc

[Abridged] We map the stellar age distribution ($\lesssim 1$ Gyr) across a 6kpc$\,\times\,$6kpc area of the Galactic disc to constrain our Galaxy's recent star-formation history. Our modelling draws on the sample of Zari et al. (2021) that encompasses all presumed disc OBA stars ($\sim 500,000$ sources) with $G<16$. To be less sensitive to reddening, we do not forward model the detailed CMD distribution of these stars, but instead the K-band absolute magnitude distribution, $n(M_K)$, among stars with $M_K<0$ and $T_{\mathrm{eff}} > 7000$K at a certain positions $\vec{x}$ in the disc as a step function with five age bins, $b(\tau~|~\vec{x}, \vec{\alpha})$, logarithmically-spaced in age from $\tau = 5$ Myr to $\tau = 1$ Gyr. Given a set of isochrones and a Kroupa (2001) initial mass function, we sample $b(\tau\,|\,\vec{x}, \vec{\alpha})$ to maximize the likelihood of the data, accounting for the selection function. This results in a set of mono-age stellar density maps across a sizeable portion of the Galactic disc. These maps show that some, but not all, spiral arms are reflected in overdensities of stars younger than 500 Myr. The maps of the youngest stars ($<10$ Myr) trace major star forming regions. The maps at all ages exhibit an outward density gradient and distinct spiral-like spatial structure, which is qualitatively similar on large scales among all age intervals. When summing over the maps' area and extrapolating to the whole disc, we find an effective star-formation rate over the last 10 Myr of $\approx 3.3 \mathrm{M_{\odot}/yr}$, higher than previously published estimates. Remarkably, our stellar age distribution implies that the star-formation rate has been three times lower throughout most of the last Gyr, having risen distinctly only in the very recent past.

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arXiv2021

Galactic spiral structure revealed by Gaia EDR3

Using the astrometry and integrated photometry from the Gaia Early Data Release 3 (EDR3), we map the density variations in the distribution of young Upper Main Sequence (UMS) stars, open clusters and classical Cepheids in the Galactic disk within several kiloparsecs of the Sun. Maps of relative over/under-dense regions for UMS stars in the Galactic disk are derived, using both bivariate kernel density estimators and wavelet transformations. The resulting overdensity maps exhibit large-scale arches, that extend in a clumpy but coherent way over the entire sampled volume, indicating the location of the spiral arms segments in the vicinity of the Sun. Peaks in the UMS overdensity are well-matched by the distribution of young and intrinsically bright open clusters. By applying a wavelet transformation to a sample of classical Cepheids, we find that their overdensities possibly extend the spiral arm segments on a larger scale (~10 kpc from the Sun). While the resulting map based on the UMS sample is generally consistent with previous models of the Sagittarius-Carina spiral arm, the geometry of the arms in the III quadrant (galactic longitudes $180^\circ < l < 270^\circ$) differs significantly from many previous models. In particular we find that our maps favour a larger pitch angle for the Perseus arm, and that the Local Arm extends into the III quadrant at least 4 kpc past the Sun's position, giving it a total length of at least 8 kpc.

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arXiv2021

Mapping Luminous Hot Stars in the Galaxy

[Abridged] Luminous hot stars dominate the stellar energy input to the interstellar medium throughout cosmological time, they are laboratories to test theories of stellar evolution and multiplicity, and they serve as luminous tracers of star formation in the Milky Way and other galaxies. Massive stars occupy well-defined loci in colour-colour and colour-magnitude spaces, enabling selection based on the combination of Gaia EDR3 astrometry and photometry and 2MASS photometry, even in the presence of substantive dust extinction. In this paper we devise an all-sky sample of such luminous OBA-type stars, designed to be quite complete rather than very pure, to serve as targets for spectroscopic follow-up with the SDSS-V survey. We estimate "astro-kinematic" distances by combining parallaxes and proper motions with a model for the expected velocity and density distribution of young stars; we show that this adds useful constraints on the stars' distances, and hence luminosities. With these distances we map the spatial distribution of a more stringently selected sub-sample across the Galactic disc, and find it to be highly structured, with distinct over- and under-densities. The most evident over-densities can be associated with the presumed spiral arms of the Milky Way, in particular the Sagittarius-Carina and Scutum-Centaurus arms. Yet, the spatial picture of the Milky Way's young disc structure emerging in this study is complex, and suggests that most young stars in our Galaxy ($t_{age}<t_{dyn}$) are not neatly organised into distinct spiral arms. The combination of the comprehensive spectroscopy to come from SDSS-V (yielding velocities, ages, etc..) with future Gaia data releases will be crucial to reveal the dynamical nature of the spiral arm themselves.

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arXiv2020

X-Shooter survey of disk accretion in Upper Scorpius I. Very high accretion rates at age>5 Myr

Determining the mechanisms that drive the evolution of protoplanetary disks is a necessary step to understand how planets form. Here we measured the mass accretion rate for young stellar objects at age >5 Myr, a critical test for the current models of disk evolution. We present the analysis of the spectra of 36 targets in the ~5-10 Myr old Upper Scorpius region for which disk masses were measured with ALMA. We find that the mass accretion rates in this sample of old but still survived disks are similarly high as those of the younger (<3 Myr old) star-forming regions of Lupus and Cha I, when considering the dependence on stellar and disk mass. In particular, several disks show high mass accretion rates >10^-9 Msun/yr while having low disk masses. Furthermore, the median values of the measured mass accretion rates in the disk mass ranges where our sample is complete at a level ~60-80% are compatible in these three regions. At the same time, the spread of mass accretion rates at any given disk mass is still >0.9 dex even at age>5 Myr. These results are in contrast with simple models of viscous evolution, which would predict that the values of the mass accretion rate diminish with time, and a tighter correlation with disk mass at age>5 Myr. Similarly, simple models of internal photoevaporation cannot reproduce the observed mass accretion rates, while external photoevaporation might explain the low disk masses and high accretion rates. A partial possible solution to the discrepancy with the viscous models is that the gas-to-dust ratio of the disks at >5 Myr is significantly different and higher than the canonical 100, as suggested by some dust and gas disk evolution models. The results shown here require the presence of several inter-playing processes, such as detailed dust evolution, external photoevaporation and possibly MHD winds, to explain the secular evolution of protoplanetary disks.

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arXiv2019

Structure, kinematics, and ages of the young stellar populations in the Orion region

We present a study of the three dimensional structure, kinematics, and age distribution of the Orion OB association, based on the second data release of the Gaia satellite (Gaia DR2). Our goal is to obtain a complete picture of the star formation history of the Orion complex and to relate our findings to theories of sequential and triggered star formation. We select the Orion population with simple photometric criteria, and we construct a three dimensional map in galactic Cartesian coordinates to study the physical arrangement of the stellar clusters in the Orion region. The map shows structures that extend for roughly $150 \, \mathrm{pc}$ along the line of sight, divided in multiple sub-clusters. We separate different groups by using the density based clustering algorithm DBSCAN. We study the kinematic properties of all the groups found by DBSCAN first by inspecting their proper motion distribution, and then by applying a kinematic modelling code based on an iterative maximum likelihood approach, which we use to derive their mean velocity, velocity dispersion and isotropic expansion. By using an isochrone fitting procedure we provide ages and extinction values for all the groups. We confirm the presence of an old population ($\sim 15$ Myr) towards the 25 Ori region, and we find that groups with ages of $12-15 \, \mathrm{Myr}$ are present also towards the Belt region. We notice the presence of a population of $\sim 10$ Myr also in front of the Orion A molecular cloud. Our findings suggest that star formation in Orion does not follow a simple sequential scenario, but instead consists of multiple events, which caused kinematic and physical sub-structure. To fully explain the detailed sequence of events, specific simulations and further radial velocity data are needed.

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arXiv2018

3D mapping of young stars in the solar neighbourhood with Gaia DR2

We study the three dimensional arrangement of young stars in the solar neighbourhood using the second release of the Gaia mission (Gaia DR2) and we provide a new, original view of the spatial configuration of the star forming regions within 500 pc from the Sun. By smoothing the star distribution through a gaussian filter, we construct three dimensional density maps for early-type stars (upper-main sequence, UMS) and pre-main sequence (PMS) sources. The PMS and the UMS samples are selected through a combination of photometric and astrometric criteria. A side product of the analysis is a three dimensional, G-band extinction map, which we use to correct our colour-magnitude diagram for extinction and reddening. Both density maps show three prominent structures, Scorpius-Centaurus, Orion, and Vela. The PMS map shows a plethora of lower mass star forming regions, such as Taurus, Perseus, Cepheus, Cassiopeia, and Lacerta, which are less visible in the UMS map, due to the lack of large numbers of bright, early-type stars. We report the finding of a candidate new open cluster towards $l, b \sim 218.5^{\circ}, -2^{\circ}$, which could be related to the Orion star forming complex. We estimate ages for the PMS sample and we study the distribution of PMS stars as a function of their age. We find that younger stars cluster in dense, compact clumps, and are surrounded by older sources, whose distribution is instead more diffuse. The youngest groups that we find are mainly located in Scorpius-Centaurus, Orion, Vela, and Taurus. Cepheus, Cassiopeia, and Lacerta are instead more evolved and less numerous. Finally, we find that the three dimensional density maps show no evidence for the existence of the ring-like structure which is usually referred to as the Gould Belt.

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arXiv2018

The Gaia-ESO Survey: kinematical and dynamical study of four young open clusters

Context. The origin and dynamical evolution of star clusters is an important topic in stellar astrophysics. Several models have been proposed to understand the formation of bound and unbound clusters and their evolution, and these can be tested by examining the kinematical and dynamical properties of clusters over a wide range of ages and masses. Aims. We use the Gaia-ESO Survey products to study four open clusters (IC 2602, IC 2391, IC 4665, and NGC 2547) that lie in the age range between 20 and 50 Myr. Methods. We employ the gravity index $γ$ and the equivalent width of the lithium line at 6708 $Å$, together with effective temperature $\rm{T_{eff}}$, and the metallicity of the stars in order to discard observed contaminant stars. Then, we derive the cluster radial velocity dispersions $σ_c$, the total cluster mass $\rm{M}_{tot}$, and the half mass radius $r_{hm}$. Using the $Gaia$-DR1 TGAS catalogue, we independently derive the intrinsic velocity dispersion of the clusters from the astrometric parameters of cluster members. Results. The intrinsic radial velocity dispersions derived by the spectroscopic data are larger than those derived from the TGAS data, possibly due to the different masses of the considered stars. Using $\rm{M}_{tot}$ and $r_{hm}$ we derive the virial velocity dispersion $σ_{vir}$ and we find that three out of four clusters are supervirial. This result is in agreement with the hypothesis that these clusters are dispersing, as predicted by the "residual gas expulsion" scenario. However, recent simulations show that the virial ratio of young star clusters may be overestimated if it is determined using the global velocity dispersion, since the clusters are not fully relaxed.

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arXiv2017

The Gaia-ESO Survey: open clusters in Gaia-DR1 - a way forward to stellar age calibration

We describe the methodologies that, taking advantage of Gaia-DR1 and the Gaia-ESO Survey data, enable the comparison of observed open star cluster sequences with stellar evolutionary models. The final, long-term goal is the exploitation of open clusters as age calibrators. We perform a homogeneous analysis of eight open clusters using the Gaia-DR1 TGAS catalogue for bright members, and information from the Gaia-ESO Survey for fainter stars. Cluster membership probabilities for the Gaia-ESO Survey targets are derived based on several spectroscopic tracers. The Gaia-ESO Survey also provides the cluster chemical composition. We obtain cluster parallaxes using two methods. The first one relies on the astrometric selection of a sample of bona fide members, while the other one fits the parallax distribution of a larger sample of TGAS sources. Ages and reddening values are recovered through a Bayesian analysis using the 2MASS magnitudes and three sets of standard models. Lithium depletion boundary (LDB) ages are also determined using literature observations and the same models employed for the Bayesian analysis. For all but one cluster, parallaxes derived by us agree with those presented in Gaia Collaboration et al. (2017), while a discrepancy is found for NGC 2516; we provide evidence supporting our own determination. Inferred cluster ages are robust against models and are generally consistent with literature values. The systematic parallax errors inherent in the Gaia DR1 data presently limit the precision of our results. Nevertheless, we have been able to place these eight clusters onto the same age scale for the first time, with good agreement between isochronal and LDB ages where there is overlap. Our approach appears promising and demonstrates the potential of combining Gaia and ground-based spectroscopic datasets.

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arXiv2017

Mapping young stellar populations towards Orion with Gaia DR1

We use the first data release of the Gaia mission to explore the three dimensional arrangement and the age ordering of the many stellar groups towards the Orion OB association, aiming at a new classification and characterization of the stellar population. We make use of the parallaxes and proper motions provided in the Tycho Gaia Astrometric Solution (TGAS) sub-set of the Gaia catalogue, and of the combination of Gaia and 2MASS photometry. In TGAS we find evidence for the presence of a young population, at a parallax $\varpi \sim 2.65 \, \mathrm{mas}$, loosely distributed around some known clusters: 25 Ori, $ε$ Ori and $σ$ Ori, and NGC 1980 ($ι$ Ori). The low mass counterpart of this population is visible in the color-magnitude diagrams constructed by combining Gaia and 2MASS photometry. We study the density distribution of the young sources in the sky. We find the same groups as in TGAS, and also some other density enhancements that might be related to the recently discovered Orion X group, the Orion dust ring, and to the $λ$ Ori complex. We estimate the ages of this population and we infer the presence of an age gradient going from 25 Ori (13-15 Myr) to the ONC (1-2 Myr). We confirm this age ordering by repeating the Bayesian fit using the Pan-STARRS1 data. The estimated ages towards the NGC 1980 cluster span a broad range of values. This can either be due to the presence of two populations coming from two different episodes of star formation or to a large spread along the line of sight of the same population. Our results form the first step towards using the Gaia data to unravel the complex star formation history of the Orion region in terms of the different star formation episodes, their duration, and their effects on the surrounding interstellar medium.

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arXiv2017

Gaia view of low-mass star formation

Understanding how young stars and their circumstellar disks form and evolve is key to explain how planets form. The evolution of the star and the disk is regulated by different processes, both internal to the system or related to their environment. The former include accretion of material onto the central star, wind emission, and photoevaporation of the disk due to high-energy radiation from the central star. These are best studied spectroscopically, and the distance to the star is a key parameter in all these studies. Here we present new estimates of the distance to a complex of nearby star-forming clouds obtained combining TGAS distances with measurement of extinction on the line of sight. Furthermore, we show how we plan to study the effects of the environment on the evolution of disks with Gaia, using a kinematic modelling code we have developed to model young star-forming regions.

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arXiv2015

Herschel-Planck dust optical depth and column density maps - II. Perseus

We present optical depth and temperature maps of the Perseus molecular cloud, obtained combining dust emission data from the Herschel and Planck satellites and 2MASS/NIR dust extinction maps. The maps have a resolution of 36 arcsec in the Herschel regions, and of 5 arcmin elsewhere. The dynamic range of the optical depth map ranges from $1\times10^{-2}\, \mathrm{mag}$ up to $20 \,\mathrm{mag}$ in the equivalent K band extinction. We also evaluate the ratio between the $2.2 \,\mathrm{μm}$ extinction coefficient and the $850 \,\mathrm{μm}$ opacity. The value we obtain is close to the one found in the Orion B molecular cloud. We show that the cumulative and the differential area function of the data (which is proportional to the probability distribution function of the cloud column density) follow power laws with index respectively $\simeq -2$, and $\simeq -3$. We use WISE data to improve current YSO catalogues based mostly on \emph{Spitzer} data and we build an up-to-date selection of Class~I/0 objects. Using this selection, we evaluate the local Schmidt law, $Σ_{\mathrm{YSO}} \propto Σ_{\mathrm{gas}}^β$, showing that $β=2.4 \pm 0.6$. Finally, we show that the area-extinction relation is important for determining the star formation rate in the cloud, which is in agreement with other recent works.

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