星形成ゼミ
2018/10/05
SFN 308 #21-#30（論文番号付pdfに準拠、#22は欠番）

長谷川哲夫（国立天文台）

1

308 Does slow and steady win the race? Inves4ga4ng feedback processes in#21 giant molecular clouds
Lilian Garra8-Smithson,1,2‹ Graham A. Wynn,1 Chris Power2 and Chris J. Nixon1
MNRAS 480, 2985 (2018)

変光周期 5.25日

えっ、そう
なの（汗）

2

308 The orbital architecture and debris disks of the HR 8799 planetary system
Gozdziewski1 and Cezary Migaszewski1#23 Krzysztof
Accepted by ApJS h8p://arxiv.org/pdf/1807.05898

5

Hans Moritz Günther , T. Birnstiel , D. P. Huenemoerder , D. A. Principe , P. C. Schneider , S. J. Wolk
Franky Dubois5,6, Ludwig Logie5,6, Steve Rau5,6, and Sigfried Vanaverbeke5,6,7
1,

MIT, Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue, Cambridge, MA 02139, USA; hgunther@mit.edu
2
University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität München, Scheinerstr. 1, D-81679 Munich, Germany
3
Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029, Hamburg, Germany
4
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
5
Astrolab IRIS, Ieper, Belgium
6
Vereniging, D.
voor
Sterrenkunde, Werkgroep
Veranderlijke
Belgium
Hans Moritz Günther1 , T. Birnscel2
P.
Huenemoerder1, D. A. Principe1,
P. C.Sterren,
Schneider3,S. J. Wolk4 ,7Centerfor
PlasmaAstrophysics,
UniversityofLeuven,Belgium
Franky Dubois5,6, Ludwig Logie5,6, Steve Rau5,6, and Sigfried Vanaverbeke5,6,7Received 2017 December 22; revised 2018 May 22; accepted 2018 May 30; published 2018 July 18

308 Op4cal Dimming of RW Aur Associated with an Iron-rich Corona and Excep4onally#24 High Absorbing Column Density
AJ 156, 56 (2018)

Abstract
RWAur is a binary system composed of two young, low-mass stars. The primary, RWAurA, has undergone
visual dimming events (ΔV=2–3 mag) in 2011, 2014–16, and 2017–2018. Visual and IR observations indicate agray absorber that moved into the line of sight. This dimming is also associated with changes in the outﬂow. In
2017, when the optical brightness was almost 2mag below the long-term average, we triggered a Chandra
observation to measure the absorbing column density NH and to constrain dust properties and the gas-to-dust ratioof the absorber. In 2017, the X-ray spectrum is more absorbed than it was in the optically bright state(NH = (4 1) ´ 10 23 cm-2 ) and shows signiﬁcantly more hot plasma than in X-ray observations taken before.
Furthermore, a new emission feature at 6.63±0.02 keV (statistic) ±0.02 keV (systematic) appeared, indicating an
Fe abundance an order of magnitude above solar, in contrast with previous sub-solar Fe abundance measurements.
Comparing X-ray absorbing column density NH and optical extinction AV, we ﬁnd that either the gas-to-dust ratio
in the absorber is orders of magnitude higher than in the ISM, or the absorber has undergone signiﬁcant dust
evolution. Given the high column density coupled with changes in the X-ray spectral shape, this absorber isprobably located in the inner disk. We speculate that a breakup of planetesimals or a terrestrial planet could supply
large grains, causing gray absorption; some of these grains would be accreted and enrich the stellar corona withiron, which could explain the inferred high abundance.
Key words: circumstellar matter – protoplanetary disks – stars: individual (RW Aur) – stars: pre-main sequence –stars: variables: T Tauri, Herbig Ae/Be
1. Introduction
The formation of stars and planetary systems from largescale molecular clouds is a complicated process with many
interacting components. After the initial collapse of the cloud,an accretion disk forms around the central protostar. Low-massstars (<3 Me) at this stage are called classical T Tauri stars(CTTS), and their circumstellar disks are the sites of planet
formation. Disks regulate the angular momentum of the starand may launch a disk wind. Typical disks contain a mass of

distribution of grain sizes in the stellar environment differs
signiﬁcantly for different sight lines.
Stellar UV and X-ray emission ionize the upper layers of thedisk, particularly the inner disk edge. These ions couple
effectively to the star-disk magnetic ﬁeld. On the disk surface,ions can be accelerated magneto-centrifugally into a disk wind,possibly dredging along dust particles from the disk. 8Outﬂows
can be clumpy, presumably changing in response to themagnetic ﬁeld or the stellar irradiation (Bans & Königl 2012;

1

Department for Astrophysics, University of Vienna, Türkenschanzstraße 17, 1180 Vienna, Austria
University of Milan, Department of Physics, via Celoria 16, 20133, Milan, Italy
3
Centre for Astrophysics Research, University of Hertfordshire, Hatfield AL10 9AB, UK
4
Harvard-Smithsonian
Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
308
The HP2 Survey
5
Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands:1807.04286v1 [astro-ph.GA] 11 Jul 20182

#25 IV. The Pipe nebula: Eﬀec4ve dust temperatures in dense cores

Birgit Hasenberger1, Marco Lombardi2, João Alves1, Jan Forbrich3, 4, Alvaro Hacar5, and Charles J. Lada4
July 13, 2018
Accepted by Astronomy & Astrophysics h8ps://arxiv.org/pdf/1807.04286.pdf

ABSTRACTMulti-wavelength observations in the sub-mm regime provide information on the distribution of both the dust column density and thee↵ective dust temperature in molecular clouds. In this study, we created high-resolution and high-dynamic-range maps of the Pipenebula region and explored the value of dust-temperature measurements in particular towards the dense cores embedded in the cloud.
The maps are based on data from the Herschel and Planck satellites, and calibrated with a near-infrared extinction map based on
2MASS observations. We have considered a sample of previously defined cores and found that the majority of core regions contain atleast one local temperature minimum. Moreover, we observed an anti-correlation between column density and temperature. The slopeof this anti-correlation is dependent on the region boundaries and can be used as a metric to distinguish dense from di↵use areas in
the cloud if systematic e↵ects are addressed appropriately. Employing dust-temperature data thus allows us to draw conclusions on
the thermodynamically dominant processes in this sample of cores: external heating by the interstellar radiation field and shielding
by the surrounding medium. In addition, we have taken a first step towards a physically motivated core definition by recognising thatthe column-density-temperature anti-correlation is sensitive to the core boundaries. Dust-temperature maps therefore clearly containvaluable information about the physical state of the observed medium.
Key words. ISM: dust, extinction - ISM: structure - Submillimeter: ISM - Infrared: ISM - ISM: individual objects: Pipe nebula -Methods: data analysis

1. IntroductionDense cores are the direct predecessors of young stellar objects(YSOs), the cloud unit that will collapse to form a stellar system. Cores are likely to represent the end of a fragmentation hierarchy that characterises molecular clouds (e.g. Larson 1981;
Myers & Benson 1983; Goodman et al. 1998), and they embody
the connection between molecular cloud structure and star formation. This connection poses questions which are among themost fundamental in the field, from the initial physical conditions of collapse to the origin of the Initial Mass Function (e.g.
Motte et al. 1998; Alves et al. 2007; Lada et al. 2008; André et al.
2010; Könyves et al. 2015). For that reason, it is critical to study

perature distribution of a region, which is not used frequently inobservational core extraction studies (see, however, Marsh et al.
2015). Due to the intricate systematic uncertainties associatedwith deriving dust temperatures, for example, noise and line-ofsight confusion (Shetty et al. 2009a,b), it is not obvious a priori
how closely dust temperatures are related to the physical state of
the observed medium. In this work, we explore whether a statement on the thermodynamics of cores is possible based on dustemission measurements of temperature.
10

The advent of the ESA Planck and Herschel missions has
made it possible to use thermal dust emission at sub-mm wavelengths to map entire molecular cloud complexes at a relatively

B. Hasenberger et al.: The HP2 Survey: IV. The Pipe nebula8

Galactic Latitude

6

4

2
4

2

358

356

Galactic LongitudeFig. 1. Three-colour composite image of the intensity at the SPIRE bands, where blue, green, and red correspond to the bands centred at 250 µm,
350 µm, and 500 µm, respectively. In regions not covered by Herschel, the Planck dust model parameters were used to predict the intensity at the
SPIRE bands.

parameters, while the spectral index was set to the values foundin the Planck maps. We thus obtained maps of ⌧850 and T , alongwith maps of their corresponding errors. For simplicity, we denote the e↵ective dust temperature as T in this work, in contrast
to the thermodynamic gas temperature T g .
The map used here has a significantly lower resolution
0

The given errors include formal fit errors only and do not takesystematic uncertainties into account, for example those associated with the flux calibration or the choice of the fitting function.
An intercept significantly di↵erent from zero indicates thatthe flux calibration of Herschel data is inaccurate, or that there
is a shift in the extinction map, possibly caused by a suboptimal

11

Variability and Jet Activity in the YSO MHO 3252 Y3 in Serpens South
1

Klaus W. Hodapp1

and Rolf Chini2,3

University of Hawaii, Institute for Astronomy, 640 N. Aohoku Place, Hilo, HI 96720, USA; hodapp@ifa.hawaii.edu

308 Variability 2and
Jet Ac4vityin the YSO
MHO
3252 Y3
Serpens
Astronomisches
Institut, Ruhr-Universität
BochumUniversitätsstraße
150,inD-44801
Bochum,South
Germany3
InstitutodeAstronomia,
Universidad
CatolicadelNorte
AvenidaAngamos
0610,
Antofagasta,
Chile
W. Hodapp1 and Rolf Chini2,3#26 Klaus
Received 2018 May 18; revised 2018 July 10; accepted 2018 July 24; published 2018 September 13
ApJ 264, 172 (2018)

Abstract
The infrared young stellar outﬂow source MHO3252Y3 in the Serpens South star-forming region was found to bevariable. The available photometric data can be ﬁtted with a double-peaked light curve with a period of 904 days.
Color variations are consistent with variable extinction with a ﬂatter wavelength dependence than interstellar
extinction, i.e., larger grains. MHO3252Y3 is the source of a large-scale bipolar outﬂow, but the most recent
outﬂow activity has produced a microjet detectable in the shock-excited H2 1–0 S(1) line, while [Fe II] emission
appears conﬁned to the immediate vicinity of the central star. The proper motion of individual shock fronts in theH2 microjet has been measured and traces these knots back to ejection events in the past two centuries. Integral
ﬁeld spectroscopy with the Keck1 adaptive optics system and the OSIRIS instrument shows velocity components
near the launch region that are distinct from the microjet in both radial velocity and apparent proper motion. They
match the prediction of dual wind models with a distinct low-velocity disk wind component. We ﬁnd evidence forthe entrainment of this low-velocity component into the high-velocity microjet, leading to shock-excited emission
at intermediate velocities in an envelope around the microjet.
Key words: infrared: stars – ISM: jets and outﬂows – stars: formation – stars: protostars – stars: variables: general
1. Introduction
The accretion process forming stars out of much larger
molecular clouds can only proceed if the excess angularmomentum of the original—usually rotating—molecular cloud
material can be disposed of. This is achieved by the ejection ofa fraction of the infalling material in the form of bipolar
molecular outﬂows. The ﬁrst such outﬂow was discovered bySnell et al. (1980) in millimeter CO emission. Faster, more
collimated jets of molecular and atomic material werediscovered at optical wavelengths by proper-motion studies
of HH objects (Herbig & Jones 1981) and by the ﬁrst imaging
studies of the jets themselves by Dopita et al. (1982), Graham& Elias (1983), Mundt et al. (1983), and Mundt & Fried(1983). The region where jets are launched and then collimatedis so close to the central star that observations with the highest
achievable spatial resolution are required. Velocity-resolved
observations of the ﬁrst few hundred astronomical units of a jet
have been done with the Hubble Space Telescope (HST) atarcseconds in length can be observed that kinematically are only
decades to a few centuries old, therefore offering the best
opportunity for studying the conditions of their launch. Some
objects actually show both a jet and bubbles in different
excitation tracers. The very young outﬂow phase TTauri star
XZTau was imaged repeatedly by Krist et al. (2008) using HST
and shows a series of bubbles rather than a typical jet, while theimmediately adjacent HLTau shows classical jet features,studied in detail by Movsessian et al. (2007). A similar patternof bubbles traced in the H21–0S(1) line has been observed inNGC1333SVS13 studied by Hodapp & Chini (2014). In thisoutﬂow object a jet is observed in the high-excitation [Fe II] line,
while the lower-excitation H21–0S(1) line shows the morphology of a string of bubbles. Another example of spherically
expanding shock fronts, rather than jets, is the high-mass
12
protostar in CepheusAHW2, where Torrelles et al. (2001)
observed an expanding ring of H2O masers.
On the other hand, objects showing a well-collimatedmber 10

Hodapp & Chini

hat year was
es are shownand changes
anges in theon nebula are

The Astrophysical Journal, 864:172 (13pp), 2018 September 10

Figure 1, an
UKIRT S(1)ombined withtaken in 2017
ular hydrogenin this color
O3252Y3 isck fronts thatt close to theotions of S(1)image and the2012) that we
After initially
GEOMAP andimages was
fronts using
were done onning stars. We
round stars tod therefore we
f stars locallys. As a result,
re in reference
f the outﬂow.
rements of thent on the S(1)nt. One set ofy background
does not workors of thesethe microjet
IS datacubes
instrument ind of spurious
noise spikes.
y integrating
emission andarly integratoper motions
ss-correlation
ne-integrated
gration boxes
shift of thebtracted fromThe Astrophysical Journal, 864:172 (13pp), 2018 September 10

Figure 5. Keck I OSIRIS 100 mas pixel–1 data integrated over the H2 1–0 S(1)emission in MHO3252Y3. The image was rotated by 71°. 5 to show the jetaxis approximately vertical. MHO3252Y3 shows a well-collimated microjetwith pronounced knot structure, indicating a variable jet ejection speed. The
proper-motion vectors from 2012 to 2017, measured in the integration boxes
outlined in yellow, are indicated by the white arrows. The proper motions are
relative to the central star of MHO3252Y3, whose proper motion wasmeasured in the box outlined in black. The emission knots are labeled in thesame way as in Figures 6 and 7, and the approximate ejection date of each
emission knot calculated from its distance and the average proper motion isindicated.

Figure 6. Velocity (coded by color) times ﬂux (coded in color density) of
MHO3252Y3 in H2 1–0 S(1) based on the OSIRIS low-resolution data thatare displayed here on 50mas pixels. The image was rotated by 71°. 5 to show
the jet axis approximately vertical. The velocity range displayed in the full
RGB range is always 20km−1 VLSR, but the velocity window has beenshifted in the three different regions of the ﬁgure, separated by gray lines, sothat the display parameters could be individually adjusted to the different
intensities and velocity ranges of the emission features, so that the velocity
structure of the jet is shown optimally. A continuum image of the star has been
added in gray scale as a position reference. The highest velocities in the jet arenear its center axis, while its envelope shows lower velocity owing to theentrainment of the wider low-velocity disk wind, the BLVC.

measured a proper motion of 14.784mas yr−1 or 30.56kms−1
tangential motion at the adopted distance of 436pc.

3.3. OSIRIS Radial Velocity Measurements

Hodapp & Chini

Hodapp& ChiniFigure 7. Velocity (coded by color) times ﬂux (codedin colordensity) of
MHO3252 Y3 in H2 1–0 S(1) based on the high-resolution data (OSIRIS
20 mas scale) that are displayed here on 10 mas pixels. The image was rotatedby 71°. 5 counterclockwise to show the jet axis approximately vertical. The
velocity range is 35–95 km−1 as indicated by the color bar. A continuum imageof the star has been added in gray scale as a position reference. The velocity
range of this ﬁgure is 3 times that of Figure 6, reﬂecting the large difference ofthe velocities of the jet (HVC) and the BLVC.

From the 13CO measurements of Nakamura et al. (2017), thevelocity of the SerpensS molecular cloud and of the nearby
W40 complex is 7km s−1 relative to VLSR, and they argue
that both the angular proximity and essentially identicalvelocity strongly suggest a physical connection of the two
clouds. If we assume that the driving source of MHO3252Y3
has the same velocity as the surrounding molecular cloud, thejet velocities are 7km s−1 more blueshifted relative to the star.
We distinguish two velocity features: (1) the well-collimated, highly blueshifted velocity component that we will
Figure
7. Velocity
color)times
ﬂux (codedin colordensity) ofnested
simplyrefer(coded
to asbythe“jet,”
which
has an“onion-like”
based
the high-resolution
MHO3252
Y3 in
H2 1–0 S(1)velocity
structurewitha onfast-moving
core data
and(OSIRIS
a relatively
20 mas scale) that are displayed here on 10 mas pixels. The image was rotatedslowerenvelope;and(2)aspatiallymuch
wider,
distinctly
by 71°. 5 counterclockwise to show the jet axis approximately vertical. The−1
lower
in redin Figureas indicated indicatedby the color bar.
A continuum
image7, andvelocity
range velocity
is 35–95 kmcomponentof thevisible
star has mostly
been addedgrayscale as a positionreference.
velocity
in inthelower-velocity
panelsof TheFigure8, which
rangeweof thisﬁgure
isas
3 timesthat of Figure
6, reﬂecting
the large difference of
refer
to
the
BLVC
in
the
following.
the velocities of the jet (HVC) and the BLVC.
Individual wavelength planes of the continuum-subtracted
datacube of the 2015 data in the 20 mas spaxel scale are shownin Figure 8. The spatial scale has been magniﬁed
13 by a factor of
13COmeasurements
Nakamura
et al.
(2017),
Fromtwo,the sothe axis
tick marksofindicate
10 maspixels.
Thethevelocity
velocity
the SerpensS
cloud
and
the relative
nearby to therangeofcoveredby eachmolecular
wavelength
plane
is of
given
relative to VLSR,
and they argue
W40LSR.
complex7km s−1relative
Theis motion
the molecular
cloud, andthat presumably
both the angular
identical
blueshifted.
relative proximity
to the star,andis 7 essentiallykms−1 more

The Astrophysical Journal, 864:172 (13pp), 2018 September 10

Hodapp & Chini

Figure 9. Spectrum of [Fe II] emission in a 300 mas diameter aperture at theposition of the MHO3252Y3 central star. For comparison, the scaled proﬁleof the nearby OH 5–3 R1 (2.5) OH airglow line is shown, demonstrating thatthe [Fe II] line is not signiﬁcantly broadened.

Figure 8. Four wavelength channels of the 2015 OSIRIS data in the 20 mas
scale, displayed here on 10 mas pixels. These channel images were continuum
subtracted, but 10% of the ﬂux of the continuum image has been reinserted at
the position of the driving star to identify its position. Even ignoring the BLVC,
several areas in the jet show asymmetric features with wavelength that create arotational component to the velocity ﬁeld. However, the velocity ﬁeld is far
more complicated than simply a rigid rotation of the microjet.

We have indicated the position of the central star by insertingthe continuum image of the star at the correct position and with
10% of the original intensity. At the closest distance from thestar that we could measure the FWHM, the jet already appears
collimated and expands from that position monotonically witha small opening angle, until the jet passes through the BLVC.

form the [Fe II] line emission in an otherwise very low
excitation jet. Due to the low signal-to-noise ratio of thisdetection, we did not do any further analysis of this ﬁnding.
Using the nearby 5–3 R1 (2.5) OH airglow line as a wavelength
calibrator, we present the extracted spectrum in terms ofvelocity shift against the [Fe II] VLSR wavelength in Figure 9.
The [Fe II] emission is blueshifted relative to VLSR and theSerpens South systemic velocity of 7 km s−1 by about the sameamount as the S(1) velocity components in Figure 7. The line
width of the [Fe II] emission is not signiﬁcantly different fromthat of the spectrally unresolved OH airglow line, indicatingthat this [Fe II] emission originates in only one velocity
component.
4. Discussion
4.1. Photometric Variability
YSOs are almost all measurably variable, and the diversityof variability types has recently been reviewed by Hillenbrand& Findeisen (2015). The most common type of variability ofyoung stars is the rotational modulation 14
due to star-spots on thesurface, leading to short-period, small-amplitude variations.
MHO3252Y3 is clearly not of this nearly ubiquitous type ofvariability. Based on the Spitzer Space Telescope and the1:1804.02070v4 [astro-ph.SR] 1 Aug 2018

Universidad de Chile, Departamento de Astronomía, Casilla 36-D, Santiago, Chilee-mail: sebastian.jorquera.c@ing.uchile.cl2308
in BokKönigstuhl
globules:Mul4-wavelength
Max Magne4c
Planck Instituteﬁelds
for Astronomy,
17, 69117
Heidelberg, Germanypolarimetry as tracer across large
bertrang@mpia.de#27e-mail:spa4alscalesand G. H.-M. Bertrang1, 2August S.
2,Jorquera1
2018
Accepted by A&A h8p://adsabs.harvard.edu/pdf/2018arXiv180402070J
ABSTRACT
Context. The role of magnetic fields in the process of star formation is a matter of continuous debate. Clear observational proof of

the general influence of magnetic fields on the early phase of cloud collapse is still pending. First results on Bok globules with simple
structures indicate dominant magnetic fields across large spatial scales (Bertrang et al. 2014).
Aims. The aim of this study is to test the magnetic field influence across Bok globules with more complex density structures.
Methods. We apply near-infrared polarimetry to trace the magnetic field structure on scales of 104 105 au (⇠ 0.05 0.5pc) in selected
Bok globules. The combination of these measurements with archival data in the optical and sub-mm wavelength range allows us tocharacterize the magnetic field on scales of 103 106 au (⇠ 0.005 5pc).
Results. We present polarimetric data in the near-infrared wavelength range for the three Bok globules CB34, CB56, and[OMK2002]18, combined with archival polarimetric data in the optical wavelength range for CB34 and CB56, and in the submillimeter wavelength range for CB34 and [OMK2002]18. We find a strong polarization signal (P 2%) in the near-infrared for all
three globules. For CB34, we detect a connection between the structure on scales of 104 105 au (⇠ 0.05 0.5pc) to 105 106 au(⇠ 0.5 5pc). For CB56, we trace aligned polarization segments in both the near-infrared and optical data, suggesting a connection of
the magnetic field structure across the whole globule. In the case of [OMK2002]18, we find ordered polarization structures on scalesof 104 105 au (⇠ 0.05 0.5pc).
Conclusions. We find strongly aligned polarization segments on large scales which indicate dominant magnetic fields across Bok
globules with complex density structures. To reconcile our findings in globules, the lowest mass clouds known, and the results on
intermediate (e.g., Taurus) and more massive (e.g., Orion) clouds, we postulate a mass dependent role of magnetic fields, whereby
magnetic fields appear to be dominant on low and high mass but rather sub-dominant on intermediate mass clouds.
Key words. Magnetic fields – Polarization – Stars: formation – Stars: low-mass – ISM: clouds – Instrumentation: polarimeters

1. Introduction
The significance of magnetic fields on the star formation process
is subject of ongoing investigations (e.g., Kandori et al. 2007;
Galli 2009; Franco et al. 2010; Federrath 2015; Lizano & Galli2015; Sadavoy et al. 2018). Recent studies show comparatively
long lifetimes of massive (e.g., Orion) clouds (⇠ 10 Myr; e.g.,
Murray 2011; Meidt et al. 2015) and suggest "dynamically relevant" magnetic fields (e.g., Alves et al. 2008; Sugitani et al.

ing the magnetic field influence on globules with more complex
density structures.
The structure of magnetic fields in the dusty envelopesaround young stellar objects can be derived from the polarization of background starlight due to dichroic extinction and ther15
mal emission by dust grains (e.g., Weintraub et al. 2000;
Girartet al. 2008). In the case of polarization due to thermal emission,
the polarization direction is perpendicular to the magnetic fieldHD64299
WD0310-688

07:52:25.51
03:10:31.02-23:17:46.78-68:36:03.39

unpolarized
unpolarized

0.151 ± 0.032
0.051 ± 0.09

B
V

2
3

tional 3D radiative transfer modeling is essential
scope of this study.
In general, a high polarization signal is conne
netic field strong enough to align the dust grains
In Section 5, we find well-ordered polarization
scales of 103 au to 105 au (⇠ 0.005 0.5pc) in
Bok globules, CB34, CB56, and OMK[2002]18
the presence of dominant large-scale magnetic
globule.
In addition to this analysis, we can further est
netic field strength in the POS by using a method
by Chandrasekhar & Fermi (1953) (CF method):

References. (1) Whittet et al. (1992); (2) Turnshek et al. (1990); (3) Fossati et al. (2007).

5.3. OMK[2002]18

S. Jorquera and G. H.-M. Bertrang: Magnetic fields in Bok globules across large spatial scales

The polarization maps of OMK[2002]18 is shown in Fig. 3.
OMK[2002]18 shows a strong polarization signal, 2 P 10%,in all the regions observed in the near-IR (Fig. 4).
Two clearly divided regions of the globule can be observed in
the near-IR wavelength range. The western region of the globule
shows well-ordered polarization segments in North/North-West
距離of
1.5 kpc
orientation with strong polarization degrees
P ⇡ 8%. The
eastern region of the globule shows an unordered pattern witha much weaker polarization signal, P ⇡ 3% indicative for depolarization e↵ects (e.g., Brauer et al. 2016). Considering therseparation between these regions, uniformly ordered polariza4⇡
turbtion segments are not necessarily expected.
|BPOS | = ↵ ·⇢gas,
3
A spatial gap is seen between the sub-mm an near-IR S.poJorquera and G. H.-M. Bertrang: Magnetic fields in Bok globules across large spatial scales
larization segments, which of about 3.3 ⇥ 104 auTable(⇠2. Gas0.16pc).
It
densities, gas velocities, polarization, and magnetic field strengths of the regions of CB34 traced in the near-IR.
where ⇢gas is the gas density in units of g cm
originates in the sensitivity of SOFI/NTT, resp. SCUBA/JCMT
Region
n
⇢
4
N
¯
B
)
(g cm )(km s velocity) (km s )(rad)(rad)of(µG)(Bertrang et al. 2014). The near-IR polarization segments North-Westin the 3.76(cmrms
turbulenceinunits
cm s 1 , and⇥ 10
1.71 ⇥ 10
1.37
0.58
11
2.32 0.51
9.6South-East 3.76deviation⇥ 10
1.71 ⇥ 10 of the
1.37 polarization
0.58
12
2.35angles
0.54
9.1in radians. It
western part of this object are well-aligned距離
with
the
<200
pc most external polarization segments in the sub-mm wavelength
range.
the magnetic field is frozen in the cloud material.
for globules. For example, Stutz & Gould (2016) propose that
Fig. 4. Distribution of polarization degree, P for P

Fig. 1. (a) Near-IR polarization segments (red) and optical polarization segments (blue) are plotted over a 150 ⇥ 150 R-Band DSS image of the
field containing CB34. A 10% polarization segment is drawn as reference for both data sets into the lower left corner. Contours correspond to
JCMT/SCUBA 850 µm dust continuum emissions from 0.1 to 0.7 Jy beam 1 , with intervals of 0.1 Jy beam 1 (Das et al. 2016). (b) Zoom into thedense center of CB34. The near-IR polarization segments (red) and the archival sub-mm polarization segments (blue) are plotted over the total
continuum intensity map at 850 (Das et al. 2016). The sub-mm segments are binned over a 1000 ⇥ 1000 grid. The solid (dashed) black (gray) contour
lines correspond to blueshifted (redshifted) integrated CO emission. Contour levels are spaced at 0.1 K km s 1 intervals of 0.5 K km s 1 (black),
and 0.2 K km s 1 intervals of 0.8 K km s 1 (white), respectively (from Yun & Clemens (1994), beam size of 48"). A 5% polarization segment
is drawn as reference for both data sets into the lower rightwell-orderedpolarization pattern indicates dominant magnetic fields on
A&Acorner.
proofs:The
manuscript
no. mainscales of 103 106 au (⇠ 0.005 5pc).

3%, counts given by N(P), of CB34, CB56, and OMK[2002]18, observed in the near-IR.

Fig. 5. Distribution of polarization angle, , counts given by N( ) of CB34, CB56, and OMK[2002]18, observed in the near-IR. The dashed lines
represent the mean polarization angles, while dotted lines represent the corresponding 1 deviation.

ization degrees of mostly 5% 12% (Fig. 4). The polarization
structure of this globule in the near-IR is well-ordered and predominantly oriented towards North-North/West (Fig. 5).
The region of CB56 which is covered by our near-IR observations overlays with the archival optical data set (Chakraborty
et al. 2014). The globule discloses a weak polarization signal in
the optical wavelength range, with an average of P ⇡ 1%(seeSection 5.1 for a discussion about the Serkowsky relation).
The polarization segments obtained in both the optical andnear-IR wavelength ranges are very well aligned within themselves, and fit well to each other. We find a slight deviation of
the polarization orientation towards the dense center of the globules when switching from the optical to the near-IR wavelength
range.

6. Magnetic Fields

In our analysis we assume that the magnetic field is oriented perpendicular to the measured polarization segments in the sub-mm
most dense center (sub-mm) towards the less dense outer enve- 5.1. CB34
and parallel oriented to the measured polarization segments inlope (near-IR, optical).
the near-IR and in the optical. This widely applied concept is
The polarization maps of the Bok globule CB34 are shown inbased on the finding that, independently of the alignment mechFig. 1. CB34 disclose a strong polarization signal, P 1%, inanism, charged interstellar dust grains would have a substantial
For CB56, the data set is restricted to archival data in the op- the outer, less dense regions observed in the near-IR (Fig. 4, Fig.
magnetic moment leading to a rapid precession of the grain antical wavelength range (Paul et al. 2012; Chakraborty et al. 2014) 5). The polarization segments in the near-IR wavelength range
gular momentum around the magnetic field direction, implying a
net alignment of the grains with the magnetic field (e.g., Draine
in addition to the newly obtained near-IR data. However, those cover this Bok globule on scales of 104 105 au (⇠ 0.05 0.5pc).
& Weingartner 1997; Lazarian 2007). However, one has to keep
two wavelength ranges cover this object almost completely. For The polarization segments in the near-IR wavelength range arein mind that polarization observations strongly su↵er from prothis comparison, we make use of the optical polarization data well-ordered and oriented towards North-West with a mean orijectional e↵ects along the line-of-sight (LOS). Thus, for a compublished in Chakraborty et al. (2014), given that it is the more entation of 111 ± 6 .
prehensive understanding of the magnetic field structure addicomprehensive data set at this wavelength range.
Most of the outer regions of this globule are traced in bothtional 3D radiativeturb
transfer modelingH2
gas
vec is essential but beyond thenear-IR and optical polarization. Both data sets fit well in oriscope of1 this study. 1
5.3. OMK[2002]18
3
3
entation (within the errors). The mean value of the polarization
In general, a high polarization signal is connected to a magFor [OMK2002]18, archival data only in the sub-mm wave2
21 3. netic field strong enough to align the dust grains along the LOS.
The polarization maps of OMK[2002]18
is shown in Fig.
angle in the near-IR wavelength range in this regions is relatively
length range were available (Matthews et al. 2009), in addition
OMK[2002]18 shows a strong polarization
signal, 2 P 21
10%, In Section 5, we find well-ordered polarization segments on
consistent with the position angle of the galactic plane at the lat2
to the newly obtained near-IR polarization data. With these, anin all the regions observed in the near-IR (Fig. 4).
scales of 103 au to 105 au (⇠ 0.005 0.5pc) in all of the three
itude of CB34, ✓GP ⇡ 148.7 , which suggests that the magnetic
analysis of the polarization of the most dense center of the globTwo clearly divided regions of the globule can be observed in Bok globules, CB34, CB56, and OMK[2002]18. This implies
field is coupled to the Galactic magnetic field in the observed
ule is possible (sub-mm), as well as an analysis of the0 less0 densethenear-IR
wavelength
range.
The
western
regionoftheglobulethe presence of dominant large-scale magnetic fields in eachFig. 2. (a) Near-IR polarization segments plotted over a 15 ⇥ 15 R-Band DSS
field containing
CB56. A in
10%
segment
is
POS.imageThisofisthesimilar
to the findings
thepolarization
optical (Daset al.
outer(near-IR).
shows well-ordered polarization segments in North/North-West globule.
drawnregions
for referencein the lower left corner. Only the segments with P/ p 2016)
3 are plotted. (b) Optical polarization segments of CB56, plotted overorientation with strong polarization degrees of P ⇡ 8%. The
In addition to this analysis, we can further estimate the maga 100 ⇥ 100 R-Band DSS image (Chakraborty et al. 2014). A 1% polarization segment
is
drawn
for
reference
in
the
lower
left
corner.
The
near-IR
A puzzling finding is the relation between the polarization
eastern
regionunderof the theirglobuleown
showsgravity,
an unorderedpattern withmassive clouds
evolveinevitably
thennetic field strength in the POS by using a method first proposed
and optical polarization is strong and well-ordered, indicating dominant magnetic fields on scales of 104 105 au (⇠ 0.05 0.5pc).
In the following, we discuss the polarization maps separately, degrees in the near-IR and the optical. As opposed to the emathemuchweaker polarization
signal,P ⇡ 3% indicative
for cloudde- by Chandrasekhar & Fermi (1953) (CF method):concentrating
magnetic
fieldsinaninitially
turbulent
first focusing on the new near-IR data, and subsequently, com- pirical Serkowski relation (Serkowski et al. 1975), the near-IR
polarization e↵ects (e.g., Brauer et al. 2016). Considering thermedium (see separatione.g., thebetweendi↵erences
betweenthe ordered
ISF andL1641
these regions,
uniformly
polarizaparing it to the maps of the optical and sub-mm wavelength signal is stronger polarized than the optical. Similar discrepansegments are
not necessarily
expected.
within Orion,tionfilaments
whichboth havethe same large scale|BPOS | = ↵ · 4⇡ ⇢gas turb ,ranges.
cies have been found also in very few other globules, tentatively(1)
3
A
spatialgap
isseenbetweenthesub-mmannear-IR
pogravitational potential
but di↵erent inner gravity and density prolarization segments, which of about 3.3 ⇥ 104 au (⇠ 0.16pc). It
Article number, page 3 of 9
files). In any case,thisin ansatz
shouldbe tested,but
for the time where ⇢gas is the gas density in units of g cm 3 , turb is theoriginates
the sensitivityof SOFI/NTT,
resp.
SCUBA/JCMT(Bertrang
et al.observations.
2014). The near-IR
polarization segments
the rms turbulence velocity in units of cm s 1 , andthe standard
being is consistentwith
Irrespectiveof the indetails
western part of this object are well-aligned with the most exter- deviation of the polarization angles in radians. It is assumed thatof internal evolutionofindividual
systems,
the
role
of
magnetic
nal polarization segments in the sub-mm wavelength range.
the magnetic field is frozen in the cloud material.

fields in clouds spanning ⇠5 to 6 orders of magnitude in mass
has not been previously discussed, and thus must be tested with
future theoretical and observational work.

Article number, page 5 of 9

7. Conclusions

距離 140For
pcthe first time, we have obtained near-IR polarization data

and, in conjunction with archival optical and sub-mm data,
Fig. 3. (a) Near-IR polarization segments plotted over a ⇠ 200 ⇥ 200 R-Band DSS image of the field containing [OMK2002]18. A 10% polarizationcompiled
multi-wavelength polarization maps which allow forsegment is drawn for reference in the lower left corner. Only the segments with P/ p
3 were plotted. (b) Sub-mm polarization segmentsof00
00[OMK2002]18, plotted over a 20 ⇥ 20 grid. Contours correspond to JCMT/SCUBA 850 µm dust continuum emissions from 0.05 toJy
the0.25verificationof the magnetic field influence on scales ofbeam 1 , with intervals of 0.05 Jy beam 1 (Matthews et al. 2009, c AAS. Reproduced with permission). Only segments with P/ p 2 are plotted.
3
10western
106 (⇠ 0.005 5pc) in the Bok globules CB34, CB56,
The near-IR polarization is strong and well-ordered, indicating dominant magnetic fields on scales of 104 105 au (⇠ 0.05 0.5pc) in theregion of the globule.
and [OMK2002]18, covering optically thin and optically thickregions. The major results are:explained by either a limited location of origin of polarization or
the presence of two di↵erent dust populations (Clemens 2012;
Alves et al. 2014). Recently, it has been suggested that not only

wavelength range are located just in between the cores C1 andC2. In this region, the mean polarization angle in the 1.
near-IR
Our findings determine the distance of CB56 to  200 pc, forwavelength is ¯ near IR ⇡ 111.9 ± 11.5 , which suggest that in

16

Article num

Annu. Rev. Astron. Astrophys. 2015
Access provided by Kokuritsu-Tenmondai Libr.

AA53CH13-Andersson

usually assumed to consist of silicates, amorphous carbon, and small graphite particles composedof simple shapes (e.g., spheres, spheroids, or cylinders). In the dark, cold parts of molecular clouds
grain aggregates may form (e.g., Ysard et al. 2013) as well as mantles of volatile ice materials(Whittet 2003, Boogert et al. 2015 in this volume).
（参考）Polarizaconとその波長依存性
Andersson, Lazarian, Vaillancourt (2015)
Interstellar polarization in the UV/O/NIR shows a near-universal wavelength dependence
AA53CH13-Andersson
23 July 2015
(Figure 2a), with a maximum
typically inARI the
range16:20of λ = 0.4–0.7 µm that falls off steeply into
Opccal/NIR:
整列ダストによる選択減光
both theUV and IR. The spectral shape can be parameterized byFIR/Sub-mm:
the following整列ダストによる放射
relation:

ARI

23 July 201516:20

p(λ) = p max · exp[−K ln2 (λmax /λ)],Southern Coalsack (R band)6ab

NGC 891amount of
at pwavelength
λmax4 , and K parameterizes thewhere pmax is the maximum
3.5 polarization
HD 283701= 3.17±0.04%
W51
λ = 0.60±0.01 µm
width of the curve (Serkowski 1973). 3
3
K = 0.84±0.06
The relatively narrow width of the2.5 polarization curve indicates that only a limited numberDR21
of2
grain sizes contribute to the polarization. Detailed modeling (e.g., Mathis 1986, Kim & OMC-3
Martin21995) shows that the polarization curve can be reproduced from the total M17
grain size OMC-1
distribution
1.5
1
if a larger small-size cutoff (∼0.04–0.05 µm) is assumed for the aligned
grains (Section 3.2). As
1
shown by Kim & Martin (1995), the value for λmax is a sensitive probe40of this100small-size cutoff.
1,000
2,000
Wavelength (µm)
0.5AlthoughtheKparameterwas
originallyassumed
to
be
fixed
at
K
=
1.15
(Serkowski1973),A (mag.)subsequent work (Codina-Landaberry0 &0.5Magalhães
1976,
Wilking
et al. 1980) showed that the
Figure 11
1.52(a) The amount of polarization p as a function of extinction A is bounded by the relation p/A < 3% mag (solid line), indicating a
λ (µm)
correlation between polarization and dust. However, the broad distribution
indicates that value
not all environments
the samebest-fitvariedproduce
fromsource to source. Wilking et al. (1982) and Whittet et al. (1992) argued
amount of polarization. Reproduced from Andersson (2015) with permission of Springer Science+Business Media. (b) The orientation
Figure 2of the optical/near-IR polarization (blue bars) is systematically orthogonal to that of synchrotron radiation ( yellow bars), which itself is
As pointed out by Mathis (1986), such a relationshipthat λmax and K are likely linearly correlated.
known to be orthogonal to the projected magnetic field (courtesy T.J. Jones).
(a) The wavelength dependence of interstellar UV/optical/near-IR polarization follows a near-universal relation referred to as the
Serkowski relation (Equation 2), illustrated here for the star HD 283701, using data from Whittet et al. (1992). (b) The observed far-IR
between the center and width of thepolarization curve follows naturally if its shape is due solely
polarization spectra for a number of molecular clouds (medians for each cloud) show a marked minimum near 350 µm using data from2

Klare et al. (1972)

1

Andersson & Potter (2005)

0

0

1

2

3

4

H-band6.2 cm5

V

V

V

POLARIZATION REDUCTION FACTORS

504

Andersson·

Lazarian−1·

Vaillancourt

Several effects reduce the observed polarization from the ideal estimated from theory. One way to capture thisinformation is the polarization reduction factor (i.e., Lee & Draine 1985),! = RF cos2 γ ,where γ is the inclination of the magnetic field to the line of sight, R is the Rayleigh reduction factor (a function of
the angle between the magnetic field and the precession axis of the grain; Greenberg 1968), and F is the reduction
factor due to a turbulent part of the magnetic field. The measured polarization is then!
!
p meas (λ) = F · p intr dτ = F · [ε(λ)R cos2 γ p 0 (λ)] dτ ,where p0 (Equation 4) corresponds to the ideal case, and pintr is the polarization per unit column density. The
fraction of aligned grains, ε(λ), has an explicit wavelength dependence because the alignment may vary with grain
size and because the extinction and emission cross sections are functions of grain size. However, there is no suchdependence on !, as it depends only on the magnetic field geometry. Hence, multiwavelength observations provide
a natural way to remove the effects of the field geometry, both for O/NIR and FIR observations.

Polarization ratio

3

p (%)

p (%)

4

max

max

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Access provided by Kokuritsu-Tenmondai Libr. - National Observatory of Japan on 07/07/16. For personal use only.

5

Annu. Rev. Astron. Astrophys. 2015.53:501-539. Downloaded from www.annualreviews.org
Access provided by Kokuritsu-Tenmondai Libr. - National Observatory of Japan on 07/07/16. For personal use only.

a

b

(2)

eff

Vaillancourt & Matthews (2012) and Zeng et al. (2013). The dotted line is an illustrative two-temperature dust model. Adapted from
Vaillancourt et al. (2008) with permission of the AAS.

to a varying small-grain cutoff in the aligned grain size distribution. Andersson & Potter (2007)
showed that a correlation exists between λmax and AV for AV ≤ 4 mag in six different clouds(Section 3.2), indicating that the grain alignment is directly dependent on the visual extinction.
The FIR/millimeter wave polarization spectrum shows a broad minimum around 350 µm
for lines of sight in star-forming clouds off of the FIR intensity peak (Figure 2b). As shown byHildebrand et al. (1999), a single population of grains cannot produce this polarization spectrum.
At minimum, a two-component dust population is required with either significantly different
wavelength-dependent grain emissivities or temperatures (e.g., T hot ∼ 2T cold ; Vaillancourt 2002).
Their preferred model, yielding the drop in polarization from 60 to 350 µm, is one in which thecomponents (along the line of sight and within the telescope beam) differ in temperature, and thewarmer dust component is better aligned. Vaillancourt et al. (2008) showed that the rise in thepolarization spectrum beyond 350 µm can, in such a two-component model, be understood as
an effect of different grain emissivities. Hence, grain alignment is seen to vary with environment,
which can provide observational constraints to the underlying physics.

17

Spots, Flares, Accretion, and Obscuration in the Pre-main-sequence Binary DQ Tau
1

Á. Kóspál1,2 , P. Ábrahám1 , G. Zsidi1, K. Vida1 , R. Szabó1, A. Moór1, and A. Pál1

Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, Konkoly-Thege Miklós út 15-17, 1121 Budapest,
308
Spots, Flares, Accre4on, and Obscura4onin the Pre-main-sequence Binary DQ Tau
Hungary
2
Kóspál1,2 , P.Max
Ábrahám1, G. Zsidi1,
K. Vida1 , R.
Szabó1 ,17,
A. Moór1,
A. Pál1 Germany; kospal@konkoly.hu
Planck Institutefor Astronomy,
Königstuhl
D-69117and
Heidelberg,#28 Á.
ApJ 862, 44 (2018)
Received 2018 February 25; revised 2018 June 4; accepted 2018 June 4; published 2018 July 20

Abstract
DQ Tau is a young low-mass spectroscopic binary, consisting of two almost equal-mass stars on a 15.8 day period
surrounded by a circumbinary disk. Here, we analyze DQTau’s light curves obtained by Kepler K2, the Spitzer
Space Telescope, and ground-based facilities. We observed variability phenomena, including rotational modulation
by stellar spots, brief brightening events due to stellar ﬂares, long brightening events around periastron due toincreased accretion, and short dips due to brief circumstellar obscuration. The rotational modulation appears as asinusoidal variation with a period of 3.017 days. In our model, this is caused by extended stellar spots 400 K colder
than the stellar effective temperature. During our 80 day long monitoring, we detected 40 stellar ﬂares withenergies up to 1.2×1035 erg and duration of a few hours. The ﬂare proﬁles closely resemble those in older latetype stars, and their occurrence does not correlate with either the rotational or the orbital period. We observe
each
periastron. Our Spitzer data suggest that theelevated accretion rates of up to 5×10−8 Me yr−1 around The
Astrophysical Journal, 862:44 (16pp), 2018 July 20
increased accretion luminosity temporarily heats up the inner part of the circumbinary disk by about 100 K. We
supports our scenario
found an inner disk radius of 0.13 au, signiﬁcantly smaller than expected from dynamical modeling ofresult
ﬂux during the periastroncircumbinary disks. Interestingly, the inner edge of the disk corotates with the binary’s orbit. DQTau also showsirradiation of the inner edge
short dips of <0.1 mag in its light curve, reminiscent of the well-known “dipper phenomenon” observed in many0.13–0.16 au.
Finally, we checked whlow-mass young stars.
accreting material is consisteradius. Again placing both st
Key words: circumstellar matter – stars: individual (DQ Tau) – stars: pre-main sequencea free-fall time
0.13 au. This value is only hresult supports our scenario that the increasing mid-infrared apastron (when the stars are
during the periastron event was due to the increased and the perturbation of the
1. Introduction
calledﬂux“dipperphenomenon” (e.g., Cody et al. 2014 andirradiation of the inner edge of the circumbinary disk at about (when the brightness peak im
references
therein).
In these cases, clumps of dustythematerial
0.13–0.16
au.
stellar surface). Consid
Pre-main-sequence stars are intimately linked with their
Finally,
wecheckedthe free-fallettimeof the orlifted from the disk’s innerwhether
edge (Bodman
al. 2017)
a warpmaterial
may take from the incircumstellar material. This relationship manifests in a variety
accreting material is consistent with the computed inner disk components, it is not at all
in Figurethe radius.
inner
disk
(Bouvier
et Theal.
1999)
temporarily
obscure part
Again
placingstars
at plusthecenterforthesimplicity,
10. Sketchof theDQ Tauboth
system.
sign
marks
center of we would take as much time asof phenomena that make young stars highly variable at a wide
mass.
The
black ellipses
indicatetime
the twostars’days
orbitsfrom
using athedistanceorbital ofofthestarlight.
computeda free-fallof 2.7
periastron.
range of wavelengths. The photometric variability of young
parameters
inclinationfromet al.
(2016).
The differenceparts of the orbit
0.13 andau.pre-main-sequenceThis value
is Czekala
only halfofthe time
between
Finally,
stars
are
known
to
exhibitﬂares,
where elevated accretion typically happens (between phases 0.75 and 1.1) arestars can be traced back to four main origins: variable accretion,
apastron(when
thecurves.
starsThe
areorangeclosesttothe thedisk’sinneredge,highlighted
with
thick
black
dots
reﬂectactualsizesofpredominantlyin X-rays(Stelzer
et al.
2000; Feigelson
andusing
the aperturbation
theRedisk
is theexpected)and periastron, whiledotted orange
circlesthe stars
stellar radius ofof 1.6rotational modulation due to hot or cold stellar spots, variable
5.5. Dipper Phe
highlight
the
size
of
the
magnetosphereforatypicalTTauristar(5×Ret al. (when2002;theFavata
et peakal. 2005),
but
in ofsomecasesbrightness
implies theinfallthe material*; onalso in theline-of-sight extinction, and stellar ﬂares.
Hartmannal. 1994).
The orange
ring around thethe
systemindicates the pathinner theOurVrba
results presented so fa
the etstellar
surface).
Considering
complicatedUV
optical/whitelight(Rydgren&Section
Vrbapart andof the circumbinary
disk, using 0.13
au as its
inner radius; see
5.4 1983;
According to the magnetospheric accretion model forthe accretion process, as wellmaterial
may
take
from
the
inner
edge
of
the
disk
to
the
binaryet foral.details.
1988;
Stassunet al.
2006;
Frascatoetassumeal. 2009).
structure in the DQTau bin
components,
it is notat allunreasonable
that thisAnalogous
T Tauri stars (e.g., Hartmannetal.
1994),
thecircumstellar
18
Figure 10. Sketch of the DQ Tau system. The plus sign marks the center toof solarwouldtake asthesemuch timeas thatelapsedbetweenthe
apastronand spot-related
ﬂares,
eventsareprobably
consequences
ofvariability from t
disk is truncated by themass.star’s
magneticﬁeld,the andmaterial
is the orbital
The black
ellipses indicate
two stars’
orbits usingfromtheand perias
periastron.
1.8–2.6 released
times largerinthan
semimajorreconnection
axis (Artymowiczevent&
parameters and inclination from Czekala et al. (2016). The parts of the orbit
energya themagnetic
above
anﬂareschanneled through accretion
columns
onto
the
star.
Unsteady
phenomenoncanbe seen: dwhere elevated accretion typically happens (between phases 0.75 and 1.1) are Lubow 1994). Another interesting fact is that the Keplerian
regiononthestellarsurface.
systemseems
tobefainterhighlightedaccretion
with thick blackrate,
curves. which
The orange may
dots reﬂect
the actual sizes activeof
accretion leads to a variable
cause
orbital period at 0.13 au is 15.56 days, essentially identical to
The Astrophysical Journal, 862:44 (16pp), 2018 July 20

Kóspál et al. computed

Centre for Star and Planet Formation, Niels Bohr Institute and Natural History Museum of Denmark, University of Copenhagen,Øster Voldgade 5-7, DK-1350 Copenhagen K, Denmark, e-mail: lars.kristensen@nbi.ku.dk
2
Department of Physics, State University of New York at Fredonia, 280 Central Ave, Fredonia, NY 14063, USA
3
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

308 Protostellar half-life: new methodology and es4mates

Submitted:
31, 2018;and
Accepted:
July 31,32018
Kristensen1
M.M. Dunham2,#29 L.E.July

Accepted by A&A h8ps://arxiv.org/pdf/1807.11262

807.11262v1 [astro-ph.SR] 30 Jul 2018

ABSTRACT

Protostellar systems evolve from prestellar cores, through the deeply embedded stage and then disk-dominated stage, before they
end up on the main sequence. Knowing how much time protostellar systems spend in each stage is crucial for understanding how
stars and associated planetary systems form, because a key constraint is the time available to form such systems. Equally importantis understanding what the spread or uncertainty in these inferred time scales is. The most commonly used method for inferring
protostellar ages is to assume the lifetime of one evolutionary stage, and then scale this lifetime to the relative number of protostars
in the other stages, i.e., the method assumes populations are in steady state. The number-counting method does not take into accountthe underlying age distribution and apparent stochasticity of star formation, nor that star formation is sequential, i.e., populations are
not in steady state. To overcome this, we propose a new scheme where the lifetime of each protostellar stage follows a distribution
based on the formalism of sequential nuclear decay. In this formalism, the main assumptions are: Class 0 sources follow a straightpath to Class III sources, the age distribution follows a binomial distribution, and the star-formation rate is constant throughout. The
results are that the half-life of Class 0, Class I, and Flat sources are (2.4±0.2)%, (4.4±0.3)%, and (4.3±0.4)% of the Class II half-life,
respectively, which translates to 47±4, 88±7, and 87±8 kyr, respectively, for a Class II half-life of 2 Myr for protostars in the Gould
Belt clouds with more than 100 protostars. The mean age of these clouds is 1.2±0.1 Myr, and the total inferred star formation rate is(8.3±0.5)⇥10 4 M yr 1 for a mean protostellar mass of 0.5 M . The critical parameters in arriving at these numbers are the assumed
half-life of the Class II stage, and the assumption that the star-formation rate and half-lives are constant. This method presents a firststep in moving from steady-state to non-steady-state solutions of protostellar populations.
Key words. Stars: formation — Stars: protostars — Stars: statistics — Methods: miscellaneous

1. Introduction
Protostellar systems evolve from prestellar cores, through the
deeply embedded stage and then disk-dominated stage, before
they end up on the main sequence. Knowing how long a time
protostellar systems spend in each stage is important for understanding how stars and associated planetary systems form (e.g.,
Hartmann et al. 2016), as well as understanding what the spreador uncertainty in these inferred lifetimes is. Any such measurement will naturally constrain current models and simulations of

The most commonly used method for inferring protostellar
lifetimes is to assume the lifetime of all protostars in a given
Class, often Class II, Class III, or combined Class II+III stage(see Dunham et al. 2015, for a full discussion). This lifetime isthen scaled to the relative number of protostars in other stages,
thereby providing a single number for the lifetime of each stage(e.g., Wilking et al. 1989, Kenyon et al. 1990, Evans et al. 2009),
but does not take into account that the di↵erent clouds
used in20
such studies may have di↵erent star-formation rates, nor what
the star-forming time of each cloud is, nor that star formation issequential, i.e., the current population of Class II sources comeFig. 1. Resulting decay rate distre flat t(8)butions for each evolutionary cl
t0).
( 0 Ntotflat(t)0() =I SFflat
P0estimate
probabilityof a decay
from Class
0 to I at
I (t) is the
Inwhereorder toprotostellar
half-lives,a numberof assumpcate theThenumberofprotostars
ineachevolutionary
Class
are
A&A
proofs:manuscript
no.meanpaperof each Class dec
time
t,
the
sum
is
over
all
Class
0
objects,
and
is
the
forSF
tions are made:SF
I flat II
I FlatII
III Total
1 adopted from Dunham et al. (2015),
e 0 t and they were observed as standard deviation. The x axis imation rate of Class 0 objects. If the probability is assumed to NII (t) =( Iof1. the( II in 0(c2d))
time, t0 , in units of Myr.
II0 ) (“Cores
flatof protostars0 ) Disks”
35
235
31
377 1.beEvolution
parttosurvey (Evanset al. whereis a continuous
process,i.e., Class
NumbervariousSpitzer
clouds (Dunham
et al. 2015).
constant (starover formation)
time and equal
for all Class
0 objects,
仮定
0 , theP0 I (t) is the probabili
観測 Table
0
flat
II
18
131 A&A
39 proofs:
222 manuscript2009).
To
separate
Class
0
and
I
protostars
fromthecommon0
objectsform
continuously
in
a
cloud
for
as
long
as
the
t
equation
becomes
I
no.
paper
time
t,
the sum is over all Ce65
327 63a538
Dunhamet al. (2015)
andrel- mation
cloud exists, and Class 0 objects form at some, constant star( 0 category
Cloud
0+I FlatII
III assign
Total
Table 2.rate
Decay
cla
I ) ( flatof 0+I,
I ) ( weII0 follow
I )Iof rates
Classfor0each
objectdN
873
15et al. 2015).
131
0
ative
fractions
of
35%
and
65%,
respectively(Enochetal.
2009).
formation(core-formation)
rate
over
the
star-forming
timeofPerseus
27
39
76
35
235
31
377
rious clouds(Dunham
0 I II
be constant over time and eq
where= P0SFI (t) is0 Ntheat
0 probability of a decay from Class 0 to I(2)e flat t
11
61
12
102
only9clouds
the cloud.
dt
tot > 100)
Serpens
25flatwith
131 (N39
222are equation becomes( 0 Furthermore,) 34many18protostars
flat ) ( Iflat ) ( II
time
t,
the
sum
is
over
all
Class
0
objects,
and
is
the
forSF
!
10
79
14
131 2. Protostellar half-lives only depend on time, not on mass, enincluded
preciseAquila to obtain the most 83
65numbers
327 possible
63a for
538anyCloud(My
I FlatII
III Total
mationrate
oforClass
objects. constantIf the probability
is assumedtowhere
0factors.
“decay”
and the associatedhalf0 is the
0 I cloud.
flat
tnumber8of Class
II35
43
174
32
277
vironment,otherindividual
Finally,theIII
objects
is un- dN0 Perseus
Auriga/CMC
73
15
131
e
.
(9)
15.1±
35
235
31
377
L.E.
Kristensen
andM.M.
Dunham:Protostellar
half-life:newmethodology
andestimatesbeconstant
over
time
and
equal
for
all
Class
0
objects,,
theis tevolution.a single protostar is sequential, that is,0 it= SF
1/2 = ln(2)/0 N0( 0 usually) ( flat Aquila.
3.lifeThe
Dunhamet al. (2015)
thatII ) ( IhighIItoward
II )
6 210
207
1988
Cepheus18
11
61 argues
12
102theno. becomes
paper theofnumber
dt Serpens
9.8±
18 1245
131 A&A
39 proofs:
222 manuscript
equation
Similarly,
of
Class
I,
flat,
and
Class
II
objects
will
start
in
Class
0,
then
go
to
Class
I,
Flat,
Class
II,
and
reasonisanunusuallyhighcontamination
by
AGB
stars,
since
IC514628
10D may79be 14
131
Aquila13.6±
65327 63a538
canbe
writteninaform
similar
to
Eq.
1,
which
becomestheMoregenerally,thesolutiontothepopulationinClass
equation
for
N
(t)
and
solve
it
on
equal
footing
with
Eq.s
6–9
III
finally Class III.
0 is the Class 0 “decay
thiscloud is locatedcon- where Auriga/CMC
ss III protostars
Ophiuchus
3 toward
25 the28 Galactic
43 Center,
174 where
32 the277
ariousclouds(Dunham2015).
dN
7.4±
873reported
15etbyal.Dunham
131
0
P0 underprobability
a decayfromClass
0 totheI(2)atfinalfollowing
the assumption
ofthatconstant
decay
rates:arewrittenas end centration
I (t) iswithout
assumingClassIII
sourcesstablelifeist= ln(2)/ .
4.where
The=star-formationand half-lives
are constant.
1/2
.
of
such
stars
will
be
naturally
higher.
We
here
adopt
a
SF
0 N0 rate
Total
326
210
1245
207
1988
Cepheus
12.6±
11
61
12
102 5.time
dt
t,
the
sum
is
over
all
Class
0
objects,
andisthe
forSF moment:
It is notdo soaatcertain
the0 contamination
1 rate of 90% following Dunham et al. (2015). The
The observedproduct.
populations
are possible
completetoabove
lumi- solving such an
Similarly, the number ofDX
I FlatII
III Total
IC5146
11.5±
dNI rate
BB
CCC
10
79
14
131
mationof equation
Class
0 objects.
If the leadprobability
is assumed
toinfinity because
SF B
for
would
to
the
solutionbeingtnositylimit.
canbe written in a form sim
III
i
=
N
N
(3)
(a)
B
C
numberofprotostars
in
each
cloud
and
in
each
Class
are
summawhere
is
the
Class
0
“decay”
constant
andtheassociatedhalfI I
0 0 0
ND (t) =(10)
90% of the Class III protostars
reported by Dunham
Ophiuchus
23.2±
35
235
31
377 6.beThere
43
174
32
277
@Bis1 Notes.ci e Assuming
AC ,constantovertime
and ofequal
for endallClass
0 objects,
dt
0 , thethenumberstableproducts,
themainsequencestars,
arenomain-sequence
stars
in
a
cloud
and
the
final
under the assumptioD
rized
in Table
Finally,
the total number of sources in all clouds following
is t1/2 = ln(2)/ .
etal. (2015)
are1.
AGB
contaminants.
i=1
18
131 nuclear
39 decay
222 is life
Total
14.7±
6since
210
1245
207
1988
any single
equation
becomesdN
zero
orIII.
unknown.
flat
stable
state
isthe
Class
are
consideredasasinglecloud.
aSimilarly,
number
of
Class
I,
flat,
and
Class
II
objects
D=N
N(4)
L.E. Kristensen and M.M. Dunham: Protostellar half-life:newmethodology 47±
andI I
flat flat
Y
65
327
63 cores538
t(kyr). Similarly,
prestellar“de1/2dN
Ifurthersolvetothese
the unknown
conj For each cloud, Equations 6–9 are solved numerically usdt be written in To
cana formsimilarEq.equations
1, which forbecomesthe decayClass=1/2 /t
dN
c
=
.
(11)
0N
0 II (%)
I NI
式II, Most
8to Class73reported
15 byClass131
0of these assumptions also apply to the number-counting
i
t
2.4±
decay
I, Flat,ss
III protostars
Dunhamstants,the boundary
conditions
are: rates:
1/2
dt
dNII= SFunder(2)0N
0 assumptioning
anfollowing
theof constantdecay
ji iterative bisector method, i.e., the decay rates are not aj=1,i, j equation
11 to the61final12
andflattheir
be discussed
below(Sect. 3.1). (5).decaysNflatvalidity
dt =stable 102
main- method,
for
NIII (t)andsolve it sinceon Theequal
footing
withdegenerate,
Eq.s
6–9
II NIIwill
intervalissolution
naturally
Poissonian,anysingle nuclear
decay
is dNflat
obs
fit
but
a
to
the
equations.
solutionsaredt
N0 (t0to) =solve
N0 is(12) without assuming that Class III sources are the final stable end
79
14the concept
131The
equation= I NI009) 10first introduced
flat Nflat
independentofthatallother decays.
Similarly,
dNI basic
where
the Class
0 “decay”
constant and the associated halfbecause
wetoareattempting
to constrain
sixprestellar
variablescores( SF ,“dedtThe solution is very
similarfoundby Bateman(1910)
for0 is N0,obs
43emphasize
174 that
32 protostars
277
=
N
(3)
ars to0 0NI, flat,II
product.
Itisnotpossible
to
do
so
at
the
moment:solving
such
an
where
indices
II
refer
to
Class
I,
Flat,
and
Class
II
sources,obs I, obs
obs
(13)
cay”
to Class
objects,
which
decay
to (N
Class
Class
II,,
0 NI (t. 0 ) = NI
X
, t0 )0throughobservables, NI Flat,, Nflat, NIIobs
dtis t1/2 = ln(2)/dNIIconsecutive
nuclearfromthefiveconstant
formation
I , decay,flat , IIapart
0rate
dNlife6etermined
210 lifespan,
1245 207
1988
0
but thatlifeequationforleadto thedecays
solutionbeing
infinity
becauseThis
set (t)of ,coupleddi↵erential
equationsmaybe= flat Nflat
Class
III
sources,which
finally
to
the
final
stablemainIII wouldobs
II NII
obs
since any single
nucleardecay
is respectively.
P(1)
Similarly,
thenumber
of
Class
I,
flat,
and
Class
II
objects
dN=
SF
0
I
of
Class
0
objects.
We
note
that
if
the
numberofmain-sequence
flat
N
(t
)
=
N
(14)
N
).
To
overcome
thisobstacle,
decay
rates
are
normalized
todtAn example is shown in F
flat
0
flat
IIInumberthanassociatedhalf-life.
theofstableend
products,
themainsequencestars,
isdt
solvedanalyticallyandsolutionswereobtained
using
the
free
=
N
N
(4)
sequence
stage.
Evansetal.
(2009)
first
introduced
theconcept
I
I
flat
flat
. Similarly, prestellar cores “de- canClass 0s
in a form similar
to Eq. 1, which becomes the stars in a cloud an
were
known,
it would
be possible
to setupln(2)/2
an Myr = 0.347 sulting distributions are typic
assumedClass
II half-lifeof 2 Myr,dt beatwritten
II =ss III protostars
reported by Dunhamollowing
nomenclature
will beor1 unknown.
solverhttp://www.wolframalpha.com.
Eachrates:of the equaNthe) = NIIobs of constant decay(15) zeroof half-life
as applied to protostars to emphasizethat protostars where
II (t0assumption
I, flat,values
II refer
decay to ClassI, Flat, ClassII, following
under
tendingindicesto higher
ofto
Myr
.
dN
. protostar has been in existence, tionsII 2–5 is solved with theobsinitial condition Ni (0) = 0. The soTo
furthersolvea single
these equations
for thelifespan,
unknownbut
decay
conare
not
born
with
pre-determinedthat
liferespectively.
This
set
of
coup
= flat page
Nflat
N
(5)
decays to the final stable main- Article number,
2
of
8
II
II
NIII (t0 ) = NIII
(16)
Tothe
estimate
the uncertainty
on the half-lives, we make use of tribution. This is not surprisi
dt I are:otostarin a given
Class. lutions
stants,boundary
conditionswith
are:times form
some distribution
an associated half-life.
dN
and solut009)
firstspends
introduced
the concept
toward analyticallythe Poisson distributio
境界条件
assumption
2,
that
time
is
the
only
factor in determining the evo- solved
=
N
N
(3)
0 0 whereI I superscript “obs” refers to the observed number of proears
over
which
half
the
protostars
To
avoid
confusion,
thefollowing
nomenclature will(12)be solver
obs
athttp://www.wolfr
to emphasize that protostars where⇣⌘
dt indices
I,
flat,
II
refer
to
Class
I,
Flat,
and
Class
II
sources,
N
(t
)
=
N
are
reportedinTable
2 and disstate of a protostar. If that is the case, the protostellar
0 0
SF tostars 0 tin each Class, and t is the unknown star-forming time lutionarynger) any
lifetime.
Finally,thestar0
adopted: age0 refers to the time a protostar has been in existence, tions
N0flat(t) =1 eset of coupled di↵erential
2–5
is solved
with
the
since
singlenucleardecay
is respectively.
etermined
lifespan,but that
life解
dN
This
equations may (6)
be
lives
for
Class
0,
I,
and
Flati
obs
distribution,i.e.,numberofprotostars
in
a
given
Class,
follows
theNcloud.
The total number! of protostars inhefirststar formedin acores
cloud.
NI (t01.) Resulting=refers
NI todecay(13)=analytically(4)a cloud is thus lifetime
Fig.
rate distributions
1000 inrandominput
distri- lutions are:the time
a protostar forspendsa givenClass.
I 0NI of flat
flat solutions.thSimilarly,
prestellar“de- solved
an associatedhalf-life.
andwere
obtained
using
the
free
dt
abutions
binomial
distribution
for eachClass(e.g., Huestis
2002).
We assumed Class II half-life, sofor
each
evolutionaryclass overin Perseus.
lines indielop
thetoconcept
half-life
obs toHalf-life
refersthe timescale
whichThe
halfvertical
the protostars
SF Ntot (t0 ) I= SF t00t.
0
decay
Class I,ofFlat,
Class
II, solver
ollowing
nomenclaturewill(disbe
I t Each of the equaN) =meanNrandom(14)athttp://www.wolframalpha.com.
⇣ a given⌘ Classofflat (t0the
dN
draw
1000
populationsforeach
cloud,
that
is,
we
draw
N
(t)
=
1
e
e
(7)
flat
II
I
cate
of
each
Class
decay
rate,
and
the
horizontalline
isthe the half-lifeSF
number of protostars in each evolutionary
Class are in a Class have a shorter (or longer) lifetime. Finally, the starpposedtovalue,
0t= is
Nflat The(5)
decaysto lifetime
the been
final(single
stablemain- tions 2–5
protostarhasinexistence,
flat
N
(t)
=
1 e half-lives
I solvedI II NII0the initial 0condition
I
with
N
(0)
=
0.
The
so0
reason,therelativeobs
iarandomnumberofprotostars
in
each
Class
where
the
distristandard
deviation.
x sinceaxis inthefirst
topstarleft formed
plot is thestar-forming
dt
N
NII is the The(15)
adopted from Dunham et al. (2015), and they were observed as forming
uationsforsequential
decay
and
II (t0 ) =time
time
the
in
a
cloud.
0009)
firstspends
introduced
theconcept
otostarin a given
Class.
lutions are:SF
randomtime, t0of
, inthese
units
of Myr. numbers follows a binomial distribution. star-formation times, t0 , areI flat“Coresto I,Disks”(c2d)
Spitzersurvey (Evans et al. bution
results
and underlying
assump- whereobsIn0 )thispaper,
we further develop the concept of half-life (disNflat (t) indices=1part
e 0 t andto whichemphasize
ears
overhalf thatthe protostars
SF mass of I0.5 M 0I,flat,ofIIthe
refer
to Class
Flat,
Class
II sources,
N
(t
=
N
(16)
III
This
distribution
is described by two numbers, the numberof meanIII⇣⌘( flattTo separate
NI (t)stellar=1e0 and I protostars from the common tribution, non steadynd
the lifetime.
conclusions
areflat 2009).
0 ) ( I Class
0)SF
state)
asopposedtolifetime(singlevalue,
etermined
lifespan,butpresented
that
life- respectively.
0 of coupled di↵erential equations may be
nger)
Finally,
the starThis
setinitialmass
C
N0 (t) =1categorye(6)and assign rel- where
I function
I (IMF,0draws superscript
and the probability.
In thistocase,the numberof draws
the“obs”
referstheobservednumberof isproof
0+I,
wefollow
Dunhametal.
(2015)
Table
2.
Decay
rates
for
each
class
of
protostars.
steadystate)
bysettinguptheequationsforsequential
decay
and
0
flat
th
an
associatedhalf-life.
t
obs
obs
obs
obs
obs
obs
he first star formed in a cloud.
0
solved analyticallyand solutions
were
obtained
using
the
free
I
結果
rate,
SFR,
may
also
be
inferretotal
numberofsources,
N
=
N
+
N
+
N
+
N
+
N
,
in eachClass,
and2).tot
t0The
is thestar-forming
time
SF
I fl
ative fractionsof) e35% and 65%,! Each
respectively(Enoch et al. 2009). tostars
0 unknownI
II assumpIII
flatthen solving
them(Sect.
results
andunderlying
ollowing
nomenclaturewill(disbe solver at http://www.wolframalpha.com.
elop
the conceptof half-lifeof the equaNflatThe(t) =results1are that the dec
I ) I( 0Iobs
obs protostars obs
SF( flat0!
0t
I t many protostars (Nofthecloud.
The
total
number
of
in
a
cloud
is
thus
and
the
probability
is
N
/
N
.
Here,
N
is
the
observed
Fig.
1.
Resulting
decay
rate
distr
Furthermore,
only
clouds
with
>
100)
are
(
N
(t)
=
1
e
e
(7)
tot
tot
i
i
tions are discussed in Sect. 3, andthe conclusions
areFlatpresented
flat
flat
0)
I 2–5 is solved with the initial condition Ni (0) = 0. The soprotostar
has been(single
in existence,0I
pposedto lifetime
value, tions
butions
for eachevolutionary
cla
N
(t
)
=
t
.
I
I 0 I to0 obtain the
0 flat t mostI
allclouds,
and
these
agree
wi
numberofprotostars
in
each
Class
1 i. Next, the1 modified Bateman
1
includedprecisenumbers
possible
for
any
tot
0
SF
0
in
Sect.
4.
e
(8)
Cloud
(Myr )(Myr )(Myr )
otostarin a given
Class.
uationsspends
for sequential
decay
and lutions are:0 flatthe mean ofTheeachhalf-lives
Class decf
The numberof protostars
in each evolutionaryClassare cateare solved
for each
population,
providing newvaluesof protostars.
flat ) ( I cloud.
flat ) Finally, the number of Class III objects is un- equations
I flatnumberassump- N (t) = SF( 01individual
ehalf-lives,
over whichhalf theofprotostars
Perseus15.1±3.0
8.1±1.6 11.8±3.10tresultsanda underlying(( axis
flat
I) x
0 and
e
standard
deviation.
The
i
⇣
⌘
flat
adoptedfrom
Dunhametal.
(2015),
and
they
were
observed
as
for
the
decay
rates.
1000
populations
is
a
good
compromisebe(2.4±0.2)%,(4.4±0.4)%,
usuallyhightowardAquila.
Dunhametal.
(2015)
argues
that
the
SF
0t
SF
nger)
Finally,
the starSerpens
9.8±2.4
5.3±1.2
6.6±2.1ndthe lifetime.
conclusions
are presented0 ) (I Iflat II0 )0t
NII0 (t)e( flat
(6)
time,
t
,
in
units
of
Myr.
0
N
(t) =
= flat 11reasone2.
Methods
andresultsof computing
the “Cores time
to Disks”(c2d) Spitzer
et al. life, respectively, which
tween
and
converging
on asurvey
mean (Evansand standard
0 I corre
an unusually high contamination
by AGB stars, since parthe first star formed in a cloud.
0
Aquila13.6±2.2
7.3±1.2
6.0±1.0( 0I is)IIflat 0 ) ( flat I t 0 ) ( II
!0Galactic
a continuous process, i.e., Class
2009).
To
separate
Class
0
and
I
protostars
fromthecommondeviation;
wetestedforconvergencebydrawing
2000
and
5000
87±8
kyr,
respectively,
this
cloud
is
locatedtowardtheCenter,
where
the
con(
)
( Ifor afle0
flat
elop the concept of half-life (dis7.4±2.2
4.0±1.2
13.1±8.5
In orderAuriga/CMC
toestimate
protostellar
half-lives,a numberofassumpSF(
I(0 flat 0IIt )0
IItt)y in a cloud for as long as thecategoryof
0+I,
wefollow
Dunhametal.
(2015)
andassignrelflatI
0I
populations
for
the
case
of
Perseus,andsaw
nosignificant
varicloudstar-formationtimes
acentration
of
such
stars
will
be
naturally
higher.
We
here
adopt
a
N
(t)
=
1
e
e
(7)
Table 2. Decay rates for each cla
Ipposed to lifetime (single value,! e
Cepheus6.8±2.5
7.7±3.8
tionsfractions
aremade:of 35% and12.6±4.4
SF1
I ( 0contamination
I ( flat00 90%I) following Dunham et al. (2015). The ativeects form at some, constant star))(65%,
respectively(Enochetal.
2009).
ationineitherparameter.
SFR
is830±50
M
Myr
fo
N
(t)
=
1
rate
of
I
I
II
I
II
0
I
t
uations for sequential decay andIC514611.5±3.8
6.1±2.0 12.2±6.9( I
e flat(8) are summa- Furthermore,II0) (ate over the star-forming time of
only
withismany
protostars(Ntot >i.e.,100) arenumberofI protostars
in each0 t cloudand in each Class
1. Evolution(starclouds
formation)a continuous
process,SF
0 I I flat
II )
(
)
(
0
results
andunderlying
assumpflat t
Ophiuchus23.2±6.2
12.5±3.3
5.2±1.2Class
0
flat
flat
N
(t)
=
1
e
e
half-lives, a number of assumpflat
includedtoobtainthemostprecisenumbers
possiblefor
any0
flat I
rized(flatin
1. Finally, the total number of sources in all clouds
0 objects
form continuously
in a cloud
for as8.0±0.7
long as the
Cloud
(Myr
) (Tablend the conclusions are presentedflat( 0flatI 0 ) (flatI) ( II0 ) flat )Total
14.7±1.1
7.9±0.6
SF are considered as
I flatII
epend on time, not on mass, enindividualcloud. andFinally,
numberformof Class
III objects
is una single
cloud.! e 0 t
cloudClassthe047±4
objects
at some,constant( 0I ) ( flat
NII (t) =1
Perseus15.1±
t1/2exists,
(kyr)
88±7
87±8 star0 flat0 I) (flatI t 0 ) ( II()
II t06–9
usuallyhightowardAquila.
Dunhametal.
(2015)
argues
that
the
II
I
0
flat
For
each
cloud,
Equationsaresolvednumericallyuseformation(core-formation)
rate
over
the
star-forming
time
of
e
.
(9)
Class
II
a continuous process, i.e., Class
Serpens
9.8±
0 I
t
/t
(%)
2.4±0.2
4.4±0.3
4.3±0.4
21
1/2( I 0 II )I )(bisector(( 0flat)rotostar is sequential, that is, it
an 1/2
unusually high contamination by AGB stars, sinceing IIan)I )(iterative
i.e., the decay rates are not a reason
the iscloud.
0 flat II flat
! IImethod,y in a cloud for as long as the
Aquila
13.6±
It
(
)
(
0
flat
I
e
o to Class I, Flat, Class II, andcloud is locatedtowardthedepend
Galactic
where
the con2. Protostellar
half-lives
only
onCenter,time, noton mass,
enbut
The solutions are degenerate, thisIflat t equations.
ects form at some, constant star- More generally,
Auriga/CMC
7.4±( 0fitthe(0a solution(toeIIthe
I )solution
flatI)toI )thepopulationin Class D may(8)be
0 I flacentration
of
such
stars
will
be
naturally
higher.
We
here
adopt
a
vironment,orother
factors.
becauseweareattempting
toconstrainsix
variables
(
,
,
(
)
(
)
SF
0
ate
over
the
star-forming
timeof
Cepheus
12.6±
0
flat
I
flat
0 I II
half-lives,area numberof assump- written as
obs
half-lives
constant.
( 0
rate of 90%
following
Dunhamet al. (2015).
Theit
3. The evolution
a single
protostaris sequential,that is,e flat t(N0obs , NIobs , Nflat, NIIobs , contamination
II ) ( I 11.5±
II
I , flat , II , t0 ) through five observables
IC5146SF(0 0 obs flat ) ( I 1 flatI )flat( IIII flat )e complete above a certain lumi0t

rious clouds (Dunham et al. 2015).

sequence stage. Evans et al. (2009) first introduced the conceptof half-life as applied to protostars to emphasize that protostars
are not born with a single pre-determined lifespan, but that lifetimes form some distribution with an associated half-life.
To avoid confusion, the following nomenclature will be
adopted: age refers to the time a protostar has been in existence,
lifetime refers to the time a protostar spends in a given Class.
Half-life refers to the timescale over which half the protostars
in a Class have a shorter (or longer) lifetime. Finally, the starforming time is the time since the first star formed in a cloud.
In this paper, we further develop the concept of half-life (distribution, non steady state) as opposed to lifetime (single value,
steady state) by setting up the equations for sequential decay andthen solving them (Sect. 2). The results and underlying assumptions are discussed in Sect. 3, and the conclusions are presented
in Sect. 4.

dt
where indices I, flat, II refer to Class I, Flat, and Class II sources,
respectively. This set of coupled di↵erential equations may besolved analytically and solutions were obtained using the freesolver at http://www.wolframalpha.com. Each of the equations 2–5 is solved with the initial condition Ni (0) = 0. The solutions are:⇣⌘SF
N0 (t) =1 e 0t
(6)
0
!
SF
I
0
NI (t) =
1
e 0t
e It
(7)
I

Nflat (t) =ISF( flatI) ( 02. Methods and results

1. Evolution (star formation) is a continuous process, i.e., Class
0 objects form continuously in a cloud for as long as thecloud exists, and Class 0 objects form at some, constant starformation (core-formation) rate over the star-forming time of
the cloud.
2. Protostellar half-lives only depend on time, not on mass, environment, or other factors.
3. The evolution of a single protostar is sequential, that is, itwill start in Class 0, then go to Class I, Flat, Class II, andfinally Class III.
4. The star-formation rate and half-lives are constant.
5. The observed populations are complete above a certain luminosity limit.
6. There are no main-sequence stars in a cloud and the final
stable state is Class III.
Most of these assumptions also apply to the number-counting
method, and their validity will be discussed below (Sect. 3.1).
The basic equation to solve isSF

P0 I (t) ,Class 0s

I)

(1)

( 0
NII (t) =

SF
II

I

flat ) ( I

0)flat )

0t

e

It

e

0 I

In order to estimate protostellar half-lives, a number of assumptions are made:

dN0
=
dt

0) ( I

0 flat( flatN0
X

0

I flat

1

flat

0

e

flat t!

(8)

I flat II1( I0 ) ( flat0 ) ( II

0 flat II( 0I ) ( flat

( 0

flat ) ( II ) ( III)e

0 I II
flat ) ( IIflat )

0 I flat( 0II ) ( I

II ) ( flat

II )

e

0)

e

0t

It

e
II t

flat t!

.

(9)More generally, the solution to the population in Class D may be
written as
0
1
D
X
BB
CC
SF B
t
i
ND (t) =ci e CCCA ,
(10)
BB@1
D

ci =

D
Y

j=1,i, j

i=1
j

j

i

.

(11)

The solution is very similar to that found by Bateman (1910) for
consecutive nuclear decay, apart from the constant formation rateof Class 0 objects. We note that if the number of main-sequencestars in a cloud were known, it would be possible to set up an

Article number, page 2 of 822

Carbon Chain Molecules toward Embedded Low-mass Protostars∗
Charles J. Law1, Karin I. Öberg1 , Jennifer B. Bergner2 , and Dawn Graninger1

Harvard-Smithsonian
Center for Astrophysics,
Garden Street, Cambridge,
MA 02138,
USA; charles.law@cfa.harvard.edu
308 Carbon
Chain
Molecules
toward60Embedded
Low-mass
Protostars
2
DepartmentofChemistryandChemical
Biology,
Harvard
University,
Cambridge,
MA 02138, USA
J. Law1, Karin I. Öberg1 , Jennifer B. Bergner2 , and Dawn Graninger1#30 Charles
Received 2017 September 15; revised 2018 June 10; accepted 2018 June 25; published 2018 August 13
ApJ 863, 88 (2018)
1

Abstract
Carbon chain molecules may be an important reservoir of reactive organics during star and planet formation.
Carbon chains have been observed toward several low-mass young stellar objects (YSOs), but their typicalabundances and chemical relationships in such sources are largely unconstrained. We present a carbon chain
survey toward 16 deeply embedded (Class 0/I) low-mass protostars made with the IRAM 30 m telescope. Carbon
chains are found to be common at this stage of protostellar evolution. We detect CCS, CCCS, HC3N, HC5N,
l-C3H, and C4H toward 88%, 38%, 75%, 31%, 81%, and 88% of sources, respectively. Derived column densities
for each molecule vary by one to two orders of magnitude across the sample. As derived from survival analysis,
median column densities range between 1.2×1011 cm−2 (CCCS) and 1.5×1013 cm−2 (C4H), and estimatedfractional abundances with respect to hydrogen range between 2×10−13 (CCCS) and 5×10−11 (C4H), which
are low compared to cold cloud cores, warm carbon chain chemistry (WCCC) sources, and protostellar model
predictions. We ﬁnd signiﬁcant correlations between molecules of the same carbon chain families, as well as
between the cyanopolyynes (HCnN) and the pure hydrocarbon chains (CnH). This latter correlation is explained bya closely related production chemistry of CnH and cyanopolyynes during low-mass star formation.
Key words: astrobiology – astrochemistry – ISM: abundances – ISM: molecules – stars: protostars
Supporting material: ﬁgure set
1. Introduction
Carbon chain molecules constitute an important reservoirof reactive organic material in interstellar clouds (e.g.,
Winnewisser & Walmsley 1979; Suzuki et al. 1992; Ohishi& Kaifu 1998) and in at least some protostellar envelopes(Sakai et al. 2008, 2009b; Sakai & Yamamoto 2013). Thesemolecules may eventually be incorporated into protoplanetarydisks (Visser et al. 2009, 2011) and then later intoplanetesimals and planets, seeding incipient planets withcomplex organic material. Carbon chains are thus expected to
be abundant throughout star formation and potentially during
planet formation as well (Qi et al. 2013; Bergin et al. 2016). In
this study, we present an inventory of such carbon chains

In light of the above observations and model predictions, thedetections of abundant gaseous carbon chains (e.g., CnH,
HCnN) in the lukewarm (T≈30 K) corino of low-mass
protostar L1527 in 2008 by Sakai et al. came as a surprise.
Detections toward a second source in the following year (Sakai
et al. 2009b) suggested that carbon chains may be common
toward some classes of protostars. The abundances could not
be accounted for by inheritance or cold, in situ ion chemistry,and Sakai et al. (2008) instead proposed that the observedcarbon chains form in the lukewarm protostellar envelopes
when methane, a common interstellar ice, sublimates
23 at 25 K(Öberg et al. 2008). This sublimation temperature is higher thanthat of CO (∼20 K) but is signiﬁcantly lower than that of H2O(∼100 K). Hence, CH4 can be abundant in a warm region that

The Astrophysical Journal, 863:88 (20pp), 2018 August 10

Law et al.

The Astrophysical Journal, 863:88 (20pp), 2018 August 10

Table 1
Source Information of the 16-object c2d Embedded Protostellar Sample with Ice Detections
SourceR.A.
(J2000.0)

Decl.
(J2000.0)

Cloud

Lbol
(L :)

Menv
(M:)

a
aIR

N(H2O)a(1018 cm-2)

Systemic Velocity (h)(km s-1)

L1448 IRS1
IRAS 03235+3004 (b)IRAS 03245+3002
L1455 SMM1
L1455 IRS3
IRAS 03254+3050
IRAS 03271+3013
B1-a (b)B1-c
B5 IRS1 (b)L1489 IRS (b)IRAS 04108+2803 (b)HH 300
SVS 4-5 (b)L1014 IRSIRAS 23238+7401

03:25:09.44
03:26:37.45
03:27:39.03
03:27:43.25
03:28:00.41
03:28:34.51
03:30:15.16
03:33:16.67
03:33:17.89
03:47:41.61
04:04:43.07
04:13:54.72
04:26:56.30
18:29:57.59
21:24:07.51
23:25:46.65

30:46:21.7
30:15:27.9
30:12:59.3
30:12:28.8
30:08:01.2
31:00:51.2
30:23:48.8
31:07:55.1
31:09:31.0
32:51:43.8
26:18:56.4
28:11:32.9
24:43:35.3
01:13:00.6
49:59:09.0
74:17:37.2

Perseus
Perseus
Perseus
Perseus
Perseus
Perseus
Perseus
Perseus
Perseus
Perseus
TaurusTaurusTaurusSerpens
L1014
CB244

17.0 (c)1.9 (c)7.0 (c)3.1 (c)0.32 (c)L
0.8 (c)1.3 (c)3.7 (c)4.7 (c)3.7 (e)0.62 (e)1.27 (e)38 (g)
LL

16.3 (c)2.4 (c)5.3 (c)5.3 (c)0.2 (d)0.3 (c)1.2 (c)2.8 (c)17.7 (c)4.2 (c)0.1 (f)
L
L
L
L
L

0.34
1.44
2.70
2.41
0.98
0.90
2.06
1.87
2.66
0.78
1.10
0.90
0.79
1.26
1.28
0.95

0.47±0.16
14.48±2.26
39.31±5.65
18.21±2.82
0.92±0.37
3.66±0.47
7.69±1.76
10.39±2.26
29.55±5.65
2.26±0.28
4.26±0.51
2.87±0.40
2.59±0.25
5.65±1.13
7.16±0.91
12.95±2.26

3.4
5.5
5.0
5.1
5.0
7.2
5.5
6.4
6.5
10.1
7.7
7.2
7.0
7.9
4.4
4.5

Carbon Chain
Molecule
C34S
C33S
CS
CCS

CCCS
HC3N
HC5N

Note.Adapted from Graninger et al. (2016) and Bergner et al. (2017).
References.
(a) 863:88
Boogert(20pp),
et al. (2008),
sources
et al.
(2008),The AstrophysicalJournal,2018 (b)August10were observed by Öberg et al. (2014), (c) Hatchell et al. (2007), (d) Enoch et al. (2009), (e) Furlan
Law
et al.
(f) Brinch et al. (2007), (g) Pontoppidan et al. (2004), (h) this study.

Table 2of carbon chains in their envelopes (e.g., de Gregorioto 21″Molecular
at 117 GHz.
reported
in Bergner
et al. (2017),
the rms
Carbon Chain
LinesAs
Observed
towardOur Protostellar
SampleMonsalvo et al. 2006; Graninger et al. 2016; Lindberg
values span 2–7 mK with the exception aof the highestEu (K)S
et al. 2016) and may present a more typical inventoryMoleculeoffrequencyTransition
spectral window. ν (MHz)
3
34
was
used
to
reducethespectra.
Globalbaselines
carbon chains during low-mass star formation. To assess Cthe
CLASSS
J=2–1
96412.950
2.00
6.25
were ﬁt toJ=2–1
each 4 GHz spectral
chunk using four
different possible organic inventories during planet formation,
C33S
97172.064
7.98 to seven
6.31linefree windows.
Individual scans
were baseline
it is clearly important to understand both of the extreme cases
CSJ=2–1
97980.953
2.00subtracted
7.05 andaveraged.JN=8
Ruze’sused to modify
thebeam
that the WCCCs present and the distribution of carbon chains
CCS
93870.107
7.97
19.89
7–76 equation was
efﬁciencyJN=7
with8–6a7 scaling factorof 0.861
around more “typical” protostars.
99866.521
6.87and sigma
28.14 of63.6 microns,
led to113410.186
beam efﬁciencies
In this paper, we present the results of a carbon chain survey
JN=89which–78
7.89 at the33.58ﬁrst,
middle, andlast channels of 0.81,
0.80, and17.00
0.78, respectively.
toward a sample of 16 embedded solar-type protostars using CCCS
theJ=17–16
98268.518
42.45
The scaling
factor and sigma
value are thesame as52.71
used in
IRAM 30 m telescope. In Section 2, we describe the observations
J=19–18
109828.293
19.00
Bergner J=11–10
et al. (2017). Witha forward efﬁciencyof 0.95,
and data reduction. In Section 3, we present column densities,
HC3N
100076.392
11.00
28.82
antenna J=12–11
temperature was 109173.634
then converted
to mainbeam
rotational temperatures, and estimated abundances for the observed
12.00
34.06
J=35–34
34.99 were 80.50
source velocities
initially
temperature,Tmb. Literature 93188.471
carbon chains, as well as sample statistics and correlations.HC
In5N
J=36–35
35.99frequency
85.10withused to convert
spectra to an 95850.714
approximate rest
Section 4, we discuss molecular formation pathways and compareJ=37–36
89.83
ﬁne-tuning
adjustments made98512.933
using the CS36.99
J=2–1 transition
our results with cold clouds and carbon-chain-rich protostars, andJ=41–40
40.99
110.02and are listed
in Table 1. 109161.555
then we summarize our conclusions in Section 5.
2. Observations

J=42–41
J=43–42
9
JF , l = e = 2 -

()
()
()
()

l-C3H

5

()
()
()
()

7
2 4

111823.643
114485.704
97995.166
3. Results

41.99
42.99
4.89

4

JF

J

J

J
C4H

b

Notes.Rest freq
JPL and CDMSaLine strength.
b
C4H transition

115.39120.88
12.54

Detailed information about source selection and observa9797995.913
12.54
JF , l = e = 2 - 3.1.
Molecule
Detections 3.89
2 3tional setup can be found in Graninger et al. (2016). In brief, 16
4
9
798011.611
4.87sources,
12.54
Class 0/I YSOs were chosen from the Spitzer c2d ice sample
JF , l =complete-spectrumThe
towardone of ourB1-a, Figure 1. Spectra at 93–101 and 109–117 GHz toward B1-a with key carbon
f = 2
2 4
5
of Boogert et al. (2008). All sources had an infrared spectralwith carbon 9chain identiﬁcations
is
shown
in
Figure1.
The chain lines highlighted. Most of the remaining lines have been previously
798012.524
3.87
12.54
JF , l = f = 2 - 2
index, αIR, deﬁned as the slope between 2 and 24 μm, in excess
spectrum
contains
a numberof carbon chain molecules that identiﬁed to methanol, complex organic molecules (COMs), CO isotopologues,
3
4
and CN and are the subject of previous studies (cf. Öberg et al. 2014; Graninger
C4Hb
NF=1095150.397
10.23
25.11
of 0.3, which designates Class 0/I sources (Wilking
have been
detectedhigh- or low-mass
protostars.
11–910toward other
NF=1095188.946
8.36
25.13
et al. 2001). Selections were based solely on their northern
We focuson sixchains,which are commonly
seen in et al. 2016; Bergner et al. 2017).
9–9carbon
8
NF=1212protostellar–1111
114182.512
11.17 chains
35.62CCS
hemisphere locations and ice abundances (Table 1). All sources
our low-mass
survey:sulfur-bearing
NF=1211–1110
114221.040
35.64pure
were observed with the IRAM 30 m telescope using the EMIR
HC5N, andand CCCS,
cyanopolyynes
HC3N and 10.23
nuclear spin in the S values and partition functions. In our case,
90 GHz receiver and the Fourier Transform Spectrometerhydrocarbons l-C3H and C4H. We also include CS and its
this affects the J=2–1 transition of C33S, whose CDMS S(FTS) backend, which contains two 8 GHz sidebands withNotes.Restanisotopologues
our analysis
to investigate
sulfurfrequency, line instrength,and upper-stateenergy arethe
takenfrom carbon
the8 GHz gap in between. Six of the sources (B1-a, B5 IRS1,
chaincatalogs.
chemistry. The frequencies, line strengths, and upper- value is fourfold that found in some other catalogs, e.g., the
JPL and CDMS
24
a
L1489 IRS, IRAS 04108+2803, IRAS 03235+3004, and SVS
state energies of the observed lines are summarized in Table 2. SLAIM catalog. Care, therefore, has to be taken to use
Line strength.
b454–5) were observed on 2013 June 12–16 at 93–101 GHz andC4H transitions
were reported income
Graninger
al. JPL(2016).
and CDMS catalogs. matching S values and partition functions; in this particularLine characteristics
frometthe
109–117 GHz. The remaining sources were observed on 2014
We note that catalogs sometime differ in their consideration ofcase, we took both from the CDMS catalog. A molecule isJuly 23–28 at 92–100 GHz and 108–116 GHz. The spectral
3
considered to be detected if (1) we observed at least one line
resolution for both sets of observations was 200 KHz
http://www.iram.fr/IRAMFR/GILDAS
−1

l-C3H

All detectedconsistent wiprotostars.
We detectin 16, 14, 6
correspond to
31%, 81%,detections of
two sources,
In Figure 2
CCS lines todiversity of lcontaining lin
ﬁgure set of

The Astrophysical Journal, 863:88 (20pp), 2018 August 10

Law et al.

The Astrophysical Journal, 863:88 (20pp), 2018 August 10

correlation (rbolometric lu

Table 6
Correlation Coefﬁcients for Molecular Abundance Correlations

C 4H
l-C3H
HC3N
CCS

CS

CCS

HC3N

l-C3H

0.36 [9]0.33 [9]0.39 [9]0.89 [10]0.52 [9]0.42 [9]0.42 [9]L

0.95 [8]0.98 [8]LL

0.98 [9]L
L
L

The observ
onthe chemis
Note.Brackets represent the number of sources with detections, including
chemistry
Fractional forabundances
plotted against Correlations
bolometric luminosity.
Upper limits
to non-detections
are indicated mu
by blthose thatFigure
are 7.
tentative,
both molecules.
that exceed
thedue90%
shown as open circles. Sources that are members of Perseus are shown as circles and all other sources arecarbon
represented by a star. S
conﬁdencelevel areshown inbold.sources
Correlations
coefﬁcients
CCCS
and For the sake of visual chains
all detected
and tentatively
detected
are shown inbrackets in thefor
lower
left corner.
clarity, theby omitted
0.1.
formation anddue to the small number (5) of mutual detections.
HC5N areto some asp
column densitythat is containeds
evolutionary
The Astrophysical Journal, 863:88 (20pp), 2018 August 10
densities, some correlation is expected regardless of chemicalorder-of-magnitude
estimate(macrossthe samdetailed models of each individu
relationships, as most molecules increase with an increasing
decreasing
scope
we usecol
extotal column density along a sight line. In fact, we seea of this study),
masses toward
the majority osulfur-bearing
positive correlation between column densities and envelope
spherically symmetricphysicalas is theincre
masses for all molecules, except CCCS (not shown). proﬁle:Wethese molecu⎛
therefore focus our correlation study on the derived
subsequentnH (r ) = n M ⎜d⎝abundances.
between the 1p
We calculate the Spearman’s rank correlation coefﬁcientwherefor n M ismolecules
a normalizingsug
conwhich we have eeach carbon chain with one another, as shown in Figure 6 envelopeand mass,carbon
chain
Table 1). We assume that all
Figure 6. Fractional abundances of each molecule plotted against one another. Detections are shown in black and upper limits as light gray arrows, while tentative
list the results in Table 6. Unlike Pearson’s correlation, which
composition
detections are shown as open circles. Sources that are members of Perseus are shown as circles and all other sources are represented by stars. Spearman correlation
molecular hydrogen.
From theincharacterizes linear relationships, Spearman’s correlation
coefﬁcients using all detected and tentatively detected sources are displayed in the bottom right corners of each scatter plot. As correlation coefﬁcients with 5 mutualWithintheradiative transfer
modeling
detections are not robust, these correlations, namely those involving the species CCCS and HC5N, are denoted by dashes (“−−”).
assesses monotonic relationships or, alternatively, the rank
Jørgensen et ﬁndal. (2002),
thatα=1.
the
value
of a free-fallingcore. Toorder
betweentwovariables.
Spearman’s
correlation
wasconsistent
witd
are often an order of magnitude in excess of the sample
Figure 8. Observed fractional abundances compared with cold cloud TMC-1.
nuclei within the beam for a
Table 5chosen
since
we
do
not
have
any
prior
expectationoflinearMedianfractional
abundances
are abundances
representedandbycolumn
red upwardandprevious
obse
medians. In contrast, L1448 IRS1 and L1489 IRS have zero
Figure10. Observed
fractional
densitiestriangles
comparedwith observations of two WCCC
sources. Left:med
Median Column Densities and Fractional Abundances
emitting
H(r) anderror represented
bars spanbytheﬁrst redandthird andquartiles
derivedupwardtriangles
error bars
span thebyﬁrstsurvival
and thirdanalysis.
quartiles derived density
by survivalproﬁleanalysis. n
Individual
sourcesare reand two carbon chain detections, respectively. While HH 300
correlation
andbecauseSpearman’s
correlationisless sensitivewitheven-numdetections
and downward
trianglesfor
upper
limits,while
open circles
indicate tentative detections.
Right: sameasthe leftpanel,
but w
Individual
sourcesarerepresentedbygraycirclesfordetections
anddownward
fromminimum(r)
tomaximumin
34
Median Column Densities
shows enhancement in sulfur-bearing molecules C S and CCS
abundances.
Median Abundances
triangles
for upper
limits.
Blue stars indicate
observed fractional
tovaluesthan
Pearson’s.
OnlyTMC-1
detections
were used forspecies witho
The Astrophysical Journal, 863:88 (20pp), 2018 August 10
Lawoutlier
et al.
rabundances from Gratier et al. (2016).
as well as carbon chain radical C4H, no cyanopolyynes are(1012 cm−2)
12h H = ò andA((10 )calculating
thecorrelations
withtheimplication
that
for
some
structureand then calculated mediansr via thobserved toward this source. L1489 IRS also displays an
Detections Only
Survival Analysis
Survival Analysis
Feigelson & Nelson
1985;1987;
BergnerKe
et al.
species, the relatively low number of mutual detections implies
enhancement in C34S and CCS along with HC3N, but lacks
3.48
For our
weinﬂate
assumermin
C34S
1.381.17
0.601.35
0.601.35
maysources,
artiﬁciallyestimate
0.35
0.35
while
l-C3H and C
by a factor areof ∼2.
Dueto method
4H quartiles differ
detections of the carbon chains l-C3H and C4H.
etal.
2010).
Bmthat
ourdeterminedcorrelation
coefﬁcientsnotrobust
to
the
3.4
6.95
of
r
=20,000
au,
which
believe
thisprocedure
still
providesa is1.73.4
1.7
CCS
4.08
max
0.90
0.90
2.01
the large fraction of non-detections for CCCS and HC5N, we
Since
only
upper
or
lower
limitscouldbeconstrained
for
all
0.19
0.66
0.54
is
also
presenthemedianthansimplyusing
detection
inclusion/exclusion
of
a
few
lowor
high-valued
data
points.
adoptedinJørgensen
et
al.
(20
0.12 0.0079
CCCS
0.200.17
0.160.037
are not able to reliably compare the distributions or quartile
molecules in L1448 IRS1, we have excluded this source in all
in terms
Figure of5 theandcylindrical
Table 5, there
is s
4.0
line
of
HC3N
3.41.6
2.33.84.068.00
gaseousenvel
theseifspecies.
0.32
2.18
We alsoranges
noteofthat,
we instead consider Pearson’s correlations,
between medians determined using on
subsequent analyses. It is possible that its lack of carbon chains
0.87
0.39
0.72
HC5N
0.390.32
0.250.100.410.28
form
whic⎧ 4panalysis,
all identiﬁed correlations are still found to be signiﬁcant.calculated with survival
could be related to its high mass. Carbon chain deﬁciencies
r 2efﬁcient,
l-C3H
0.350.41
0.230.40
0.601.61
of incorporating
prov
0.20
0.18
0.20
⎨ constraintstwo
A (r ) =the
3.4. Fractional
Abundance
have been previously observed in massive YSOs (Tercero
through
73.2
26.5
25.5
Correlations are foundat the 90%
conﬁdence level between
2
Note that we include
tentative
detectio
C 4H
46.016.2
17.014.0
15.010.7⎩ 2p [rb + (r et al. 2010; Pagani et al. 2017) and massive clumps in infrared(CanosaetaNtoestimate
their
mediancolumnHC
To
compareourobservational
resultswiththeoreticalsimilar families of carbon chains (e.g., CS/CCS, l-C3H/C54H)
dark clouds (Sakai et al. 2008). In both cases, these deﬁciencies
detections
not have
Equivalently,
thedoes
emittingsuT
predictions for low-mass YSO chemical abundances, we need of tentative
respectively.
Note.Lower and upper quartiles are shown to the right of the medians.
andbetween
HC
N
and
the
carbonchains
l-C
H
and
C
H.
This
columnhave been attributed to more advanced stages of chemical
than thebeamdensities
radius, (∼10%)ofbu
to calculate 3fractional abundances with respect3 to atomic 4 medianoddis thatnumb
medianfractional anabundance∼50%
evolution compared to their lower-mass counterparts. It islatter correlation
beneedexplainedby thea hydrogenclosely related
that particularradius. Forbyradiilahydrogen. Thus,could
we ﬁrstto determineMedian columnlow
densities
span threwith the caveat that we are certainly underestimating thetemperatu
unclear, however, whether this scenario can also explain the
production chemistry of l-C3H and C4H and that of HCFor
insulfur-bearing chains,
each
3Nthe
column density for L1448 IRS1 (however, this source is not
9leads to approximately
low abundances of unsaturated organics in L1448 IRS1
atoms
andof maCHan orderlow-mass protostars, as discussed in Section 4.1. This resultisused for further analysis). Using Equation (3) from Takano
compared to the sample median.
median column density.
Similarly,
theLoison&Be
independent of whether we only consider Perseus sources
or 3N to HC5N leads to a red
et al. (1998), we ﬁnd the highest value of optical depth for thefrom HC
The distributions of column densities and fractional
neutral–nemagnitude.
For thethecarbonchain radica
C34S line among our samples (excluding L1448 IRS1) was
abundances reveal variations in chemistry among sources andalso
includetheone
Taurussource
for
which
we
could
Figure 11. Observed fractional abundances compared with various modelto C4H l
of
one
C
atom
from
l-C
compared with observations of two WCCC sources. Left: median fractional abundances are
3H 1997,etal.
τ=0.072 for source B1-a.Figure 10. Observed fractional abundances and column densities
between different molecules. Figure 4(a) shows a histogram ofpredictions. Median fractional
abundancesthe
are represented
by upward
red
represented by upward red triangles and error bars span the ﬁrst and third quartiles derived by survival analysis. Individual sources are represented with graycalculate
circles forabundances.
However,correlation
could
also
be
magnitude increase in column density.
Across the sample, a detections
few sources
standoutfor foreachmolecule’s
columndensitytheleftsample.
triangles and error bars span the ﬁrst and third quartiles derived by survival
lukewarmpatand downward
triangles
upper theirlimits, while open
circles
indicate tentative
detections.
Right:acrosssame as thepanel, butThewith column
column densities instead ofMedianfractional
abundancescal
due to a analysis.
mutualdependence
onwithanunobserved
Individual
sources are represented
gray circles
for detections andunderlying
abundances.
especially rich or poor carbon
chain inventories, or because
densities of C34S, CCS, and HC3N span two orders ofin Figure 5(b).
correlation
bedownward triangles for upper limits, while open circles indicate tentative 25analysis are shown
they are enhanced in or lack speciﬁc molecules. The sources
variable. detections.
Without a clear mechanism or a multivariable
abundances also span three orders of mmagnitude or more. By comparison, the l-C3H and C4H
sharedoriginand thencalculated
mediansthequartiles
KM estimator (e.g.,same trends as found
for themedian
SVS 4–5 and B1-a have large carbon chain column densities
distributions are narrow.
Table
5 lists lower
and via
uppercorrelation
study,
thesetwo
explanations
cannotbe of abundances,distribution
reﬂected
Feigelson&
Nelson1985;
Bergneretal.
2017).
While
thissensitive
datainEquivalently,
every
positive
detectionwasweightedbythecompared to the other sources. All seven molecules arefor the column density of each molecule. For CCS and HC3N,
the lower and upper quartiles, is tighdistinguished.
method may artiﬁcially inﬂate estimates for median values,
wenumber of upper limits between it and the next largest positive
34as strong w
belower and upper quartile
valuesdifferbyafactorof∼3–4,
detected toward these sources and the derived column densities
and CCS tha
believe this procedure still provides a more realistic estimateofdetection.of abundances with physical propertiesbearing
Correlations
maymolecules C Scarbon
bearing chains and theFor
chaincy
ra
the
env

env

max

min

⎪
⎪

the median than simply using detections alone. As can be seen

To account for the discrete nature of the survival function,