Measuring the mass of protostars
Nagayoshi Ohashi(Subaru Telescope, NAOJ)

アブストラクト• 星形成の研究にとって、原始星質量を測ることは極めて重要。
– 星形成過程は、M*(t)で基本的に記述できる– 原始星質量は、進化の指標として使用可能• 近年、原始星周囲のケプラー円盤の観測が可能となり、ケプラー回転から原始星のダイナミカル質量の測定が可能となった。
• 原始星周囲のケプラー円盤の観測へと至った背景を概観し、原始星周囲のケプラー円盤がどのように観測されるのか、また、原始星の質量測定から明らかとなってきた、星形成過程について、解説する。

キーワード１：原始星の質量測定

学研ウエッブサイトより

キーワード２:円盤形成

本日の話• 恒星質量の測定について• 星の形成と円盤形成• 原始星周囲の円盤の観測• 原始星の力学的質量の測定とそこから見えてくる星形成の新たな側面• まとめ

星の質量：現代天文学の基本的パラメータ• 星の質量が現代天文学の研究、あるいは星形成の研究において、基本的なパラメータであることは、言うまでもない– Initial Mass Function– 星の質量は何よって決まるのか？
– 星の質量により形成過程や進化過程が違う

星の質量の測定• 直接に質量が測定できるのは、連星系の場合のみ• 主系列星の場合、スペクトルの観測から、星の表面温度を測定し、その絶対等級を推定。質量光度関係を使って、質量を推定• YSOsの中でも、前主系列星に関しては、HR図上にプロットすることが可能。一方、質量ごとにHR図上の理論的な進化パスがわかるので、それと比較して質量が求められる。
• しかしながら、原始星に関しては、原始星を直接観測することができないため、HRダイアグラムを用いて質量を測定することは不可能

If we can measure mass of aprotstar….

Estimation of protostellar masses• Estimation from accretion luminosity– It is not trivial to measure mass accretion rate

• Estimation from mass infall velocity– It may not necessarily correct to assume free-fallPromising method to measureprotostellar masses• To measure dynamical masses of protstars
based on Kepler rotation of their circumstellar
disks would be the most promising method.

Disks are expected to be formed
around protostar?
Vinfall µ R -0.5
Vrotation µ R -1
Vinfall > Vrotation

Dynamical Infall region
Vinfall > Vrotation
If magnetic field iscoupled with infallingmaterials

Keplerian rotation region
Vinfall ~ Vrotation
Angular momentum-0.5
Vrotation µ R
is moved away, andno disk is formed (e.g.,RcMellon & Li ’08; see also
Li’s and Zhao’s talks )c. f. Terebey et al. 1984; Basu 1998

Protoplanetary disks around PMSs
• In the last two decades many studies havebeen done• They usually show Keplerian motions• Recent observations show a lot of varietyof disks around PMSs

“SEEDS” project carried out
by the Subaru Telescope andHiCIAO (PI: M. Tamura)Measurements ofdynamical masses of TTSs

Simon, Dutrey, Guilloteau 2000

• Measure dynamical masses ofTTSs and compare withtheoretical tracks on HR
diagram, calibrating PMSs
evolution.

How about disks aroundprotostars?
• Disks are also naturally expected aroundprotostars (e.g., Terebey, Shu, Cassen 84).
• As compared with PPDs, however, lessobservations of disks around protostars
have been done.
– It is difficult to distinguish extended envelopes
and disks embedded in the envelopes.
– Envelopes often show disklike structures androtation.

Early efforts to detect disks
around protostars• Continuum observations– Compact continuum sources (with disklikestructures) associated with protostars wereidentified as disks.
– No kinematical information, could be innermost
envelope• Line observations– Disklike structures around protostars with spin-up
rotation were identifies as Keplerian disks– Infalling envelopes, which often show disklike
structures, can also show spin-up rotation (Vr ∝1/r)

Lommen et al 2008
Compact continuum emission

Spin-up rotation is interpreted
as Keplerian rotation

Brinch et al. 2008

Brinch et al. 2008

Compared with only Kepler rotation curves

Disk evolution
from protostars to TTSs?
• Disk masses decrease as
protostars evolve into T
Tauri stars?
• We should note that
continuum emission fromprotostars arises fromenvelopes as well as
disks, suggesting thatdisk masses areoverestimated fromsingle dish observations.
Andrew et al. 2005

Envelopes around protostars• Disks are not easily identified around protostars
because they are surrounded by envelopes,
which are often flattened and rotating.
L1551 IRS5 C18O 1-0 with NMA
Mass ~0.08 M
Radius ~ 1200 AU

C18O (1-0) with NMA(Momose, Ohashi et al. 1998)

Envelopes around protostars• Disks are not easily identified around protostars
because they are surrounded by envelopes,
which are often flattened and rotating.
L1551 IRS5 C18O 1-0 with NMA

CS 7-6Mass ~0.08 M
Radius ~ 1200 AU

Chou et al. 2014

Envelopes around protostars• Disks are not easily identified around protostars
because they are surrounded by envelopes,
which are often flattened and rotating.
L1551 IRS5 C18O 1-0 with NMA

CS 7-6Mass ~0.08 M
Radius ~ 1200 AU

Chou et al. 2014

Envelopes around protostars• Disks are not easily identified around protostars
because they are surrounded by envelopes,
which are often flattened and rotating.
CS 7-6

Chou+ 2014 (see also Lommen+ 2008)

How about disks aroundprotostars?

• Disks are not easily identified aroundprotostars because they are surrounded byenvelopes.
• Observations of disks around protostars havebeen done in continuum emission in the earlydays– Compact structures were identified– It was difficult to unambiguously distinguish disks
and envelopes

How to unambiguously identify
disks around protostars?
• It is the best way to kinematicallydistinguish disks from envelopes– Envelopes rotates as r-1– (Keplerian) disks rotate as r-0.5– Estimate powers of rotation curves

Searching for Keplerian disks
around protostars I
HH111 C18O 2-1 with SMALee 2010

Searching for Keplerian disks
around protostars IIrotation curve with a logarithmic scale

Representative data points on a PV diagram is measured
based on Gaussian fittings along either the velocity axis or
the position axis of the PV diagram (Yen+ ‘13)

Searching for Keplerian disks
around protostars ISearching for Keplerian disks
around protostars III• Fit channel maps with models of Keplerian
disks– Low velocity channels are likely due to envelopes– Only high velocity channels should be fitted bysuch models
There would be some ambiguityof the estimated disk radius
Chou+2014

ALMA C18O 2-1 observations ofdisks around protostars
ObjectRegion

Class Tbol
(K)

Lbol(Lo)DALMA θ(pc) Cycle

IRAS 16253

Oph0VLA1623

OphB335
Lupus 3 MMS

reference

350.24

125

21.0” Yen+ 170352.612000.7” Murillo+ 13

Isolated0390.68

150

20.3” Yen+ 15

Lupus0400.41

20020.5” Yen+ 17

B228 (IRAS 15398) Lupus

0/I

611.2

150

20.5” Yen+ 17

L1527 IRS

Taurus0/I

67

1.7

14010.5” Aso+ 17†

TMC-1A

TaurusI

164

2.5

14000.9” Aso+ 15

L1489 IRS

TaurusI

226

3.5

14000.9” Yen+ 14

18
ALMA C O 2-1 observations ofdisks around protostars
IRAS 16253

IRAS 16253
Tbol = 35 K

D Dec.

B228

VLA1623

VLA1623
Tbol = 35 K

L1527 IRS

B228
Tbol = 61 K300 AU

D R.A.

L1527 IRS
Tbol = 67 K

B335

B335
Tbol = 39 KTMC-1A

TMC-1A
Tbol = 164 K

Lupus 3 MMS

Lupus 3 MMS
Tbol = 40 K

L1489 IRS

L1489 IRS
Tbol = 226 K

18
ALMA C O 2-1 observations ofdisks around protostars
4IRAS 16253

VLA1623

B335

Lupus 3 MMS

B228

L1527 IRS

TMC-1A

L1489 IRS

20-2

D Position (arcsec)-4

D Vel (km s–1)

Rotation Curves
VLA1623

Rotation Velocity (km s–1)

pin=–0.5 (fixed)
pout=–1.0 (fixed)
Rb=50 AU
Rkep ~74 AU

Lupus 3 MMS

p=-0.57±0.03
M* ~ 0.23 Mo

Radius (AU)p=-1.0 ± 0.06

TMC-1A

L1527 IRS

pin=–0.50±0.05
pout=–1.22±0.04
Rb=56 AU
Rkep ~74 AU

B228

Pin = – 0.54 ± 0.14
Pout = – 0.85 ± 0.04
Rb = 67 AU
Rkep ~ 90 AU

L1489 IRS

P = –0.57± 0.03
M* ~ 1.6 Mo

Evolutional Trend: Md and Rd
Rd (AU)

Widely spread?

Widely spread?

M* (Mo)Tbol (K)

Tbol (K)• If Tbol can be an evolutional indictor, M* and Rd increase as
the central star evolves• At the earliest evolutionary stage, M* and Rd increase
quickly by more than a factor of 10?
Distribution of M* and Rd at the earliest stage would be important.

Case Study: L1527 IRS•••••

Class 0/I object
Lbol ~ 1.7 Lo
Tbol ~ 67 K
Associated with an infallingenvelope (Ohashi+ 1997)
Associated with a Kepleriandisk (Tobin+ 2012; Ohashi+2014; Aso+ 2017)– Rk ~74 AU– M* ~0.45 Mo• Chemistry of the disk
forming region is alsostudied in detailed(Sakai+ ‘14, ‘17)

Case Study 1: L1527 IRS
 Infall motions in the envelope are free-fallyielded by the central star?
Vinfall ~ 0.3 km s-1 at 2000 AU in radius (measured)
Vfreefall ~ 0.6 km s-1 at 2000 AU in radius estimated from thedynamical mass
• Infall motions may befree-fall
0.2-0.5 of free-fall
suppressed by magnetic field?
• Infall motions may be reduced
before landing to the disk?
• Other protostars such as
L1551 IRS5 (Chou+ ’14),
TMC-1A (Aso+ ‘15), andHH111 (Lee+ ‘10) also show
Ohashi+ 2014
similar features.

Case Study: L1527 IRS
 What are disk structures?
220 GHz Continuum

UV plane

Deconvolved size:
0.53x0.15 (1.5°)

Contours: 3,6,12...σDisk structures areclearly resolved
even in theazimuthal direction.

 Visibility data should be analyzed without azimuthal averaging.

Case Study: L1527 IRS
 Model fitting w/o annulus averaging.
Vertical and radial information are notmerged in the edge-on case.
6 parameters: Mdisk, Rout, p, Sdamp, H1, h Temperature is fixed （T1=403.5 K, q=0.5; Tobin+13）.

Case Study: L1527 IRSObs. Modelbest model: reduced χ2=5.7
Mdisk
Rout p(1e–3M) (AU)

Sdamp H1(AU)h6.084

1.7

0.19

0.11

1.2+1.5–1.8+16–24+0.1–0.3+0.03– +0.02
0.09
–0.03

+0.1
–0.1

ResidualContours: 3,6,12,24,...σ Contours: 3,6,9,12,...σ Rout corresponds to thekinematic Rkep within
uncertainty.
 Scale height appears inhydrostatic equilibrium:H(84 AU)~1.3 HHSEQ.

A statistical study• Yen+ 2017 use 18 of protostars associated with
Keplerian disks to study disk formation andevolution of protostars, investigating;– evolutional trend of specific angular momentum– Md – Rd relation– evolutional trend of Macc and Rd

Keplerian disks areformed around class 0
within a timescale of~ 4e5 yr

For class 0td = 4e5 yr

Keplerian disks
Are not spatially resolved

Upper limit

Evolution?

Evolutional Trend: specific angularmomentum
HH111: 78 K
TMC-1A: 164K
L1551 IRS5: 106 K
HH212: <56 K
L1527: 67 K
IRAS 16253: 35 K
IRAS 15398: 67K
B335: 39 K
Younger (lower Tbol)
 Lower jj might increase
as YSOs evolve?

Disk Formation around Protostars
Infall region

Rotation region

B335, IRAS 16253
Younger YSOs

L1551 IRS5, L1527 IRS
More evolved YSOs

M* – Rd relation

Evolutional Trend: M* and Rd

Macc – tage relation

Evolutional Trend: M* and Rd

4 x 105 yr

Class 0Class I
100 AU disk is formed
within a timescale of 4 x 105 yr

Summary• Keplerian disks has been unambiguously identified
around protostars, including class 0 sources, providing
a strong method to estimate masses of protostars, andalso related physical parameters, such as ages ofprotostars and mass accretion rates to them.
• Physical parameters obtained from disk observations
could provide a new picture of star and disk formation,
giving important constraint on theories of star and diskformation.
• Further observations of disks around protostars arevery important to perform even better statistics.