AY216 1

21: Formation of Low MassStars

James R. Graham

UC, Berkeley

AY216 2

Reading

• Adams, Lizano & Shu, 1987, AARA, 25,23

• Shahler & Palla, Chs. 17 & 18

• More detailed reviews in PPIV and PPV– Proceedings of PPV are available at:

http://www.ifa.hawaii.edu/UHNAI/ppv.htm

AY216 3

Outline

• Nearby regions of Galactic star formation

• General properties of young, low massstars– T Tauri stars (solar type stars)

– Herbig Ae/Be stars

• Massive stars (OB) covered later

AY216 4

Local Star Forming Regions• Much of our knowledge of

star formation comes froma few nearby regions– Taurus-Auriga & Perseus

• Low mass (solar type stars)

• 150 pc

– Orion• Massive stars (OB stars) in

Orion

• 500 pc

• How representative arethese regions of the Galaxyas a whole?

Stahler & Palla Fig. 1.1

AY216 5

Taurus,Auriga &Perseus

• Nearest regionof current starformation– Grey=Milky Way

– Black = MC

AY216 6

Taurus, Auriga & Perseus• Principal

regions include– NGC 1333/

IC348– B5

• Bok globule

– Pleiades– TMC-1 TMC-2

• NH3 cores

– T Tauri• Prototype T

Tauri star

– L 1551• Young stellar

outflow source

IC 348

NGC 1579

AY216 7

Taurus, Auriga & Perseus• The Taurus clouds

are rich in densecores and youngstellar objects

• Traditionally, T Tauristars are a class ofvariable stars

– Found nearmolecular clouds &identified by theiroptical variabilityand strongchromospheric lines& associated X-rayemission

– Youngest ofoptically visiblestars: the presenceof Li 6707 Å inabsorption testifiesto youth

AY216 8

CO

Wilking et al. 1987 AJ 94 106

Ophiuchus

Andre PP IV

• Three views of a star formingcloud– Optical

– CO J=1-0

– 1.3 mm continuum

AY216 9

Orion

+ 5 massive CS 2-1 coreswith M > 200 M

& associatedstellar clusters

+ MH2(L1630) ~ 8x104 M

(Lad

a 19

92 A

pJL

393

25)

AY216 10

Orion

+ 5 massive CS 2-1 coreswith M > 200 M

& associatedstellar clusters

+ MH2(L1630) ~ 8x104 M

(Lad

a 19

92 A

pJL

393

25)

AY216 11

Orion

+ 5 massive CS 2-1 coreswith M > 200 M

& associatedstellar clusters

+ MH2(L1630) ~ 8x104 M

(Lad

a 19

92 A

pJL

393

25)

AY216 12

Orion: Not Just OB Stars…

• Although theappearanceof Orion isdominated byhigh mass(OB stars)but ~ 50% oflow massstars areformed insuch regions

AY216 13

General Properties

• Young stars are associated with molecularclouds– Observations are affected by extinction, which

decreases with increasing wavelength

• Loosely speaking, we can distinguish two types:– Embedded stars-seen only at NIR or longer

wavelengths, usually presumed to be very young– Revealed stars–seen at optical wavelengths or

shorter, usually presumed to be older

• What makes young stars particularlyinteresting is circumstellar gas anddust–both flowing in as well as out, e.g., jets,winds, & disks

AY216 14

Young Stars & Outflows

• Snell, Loren, & Plambeck 1980 ApJL 239 17

AY216 15

The HH 211 Outflow in IC348

• 1.3 mm continuum• Circumstellar disk

• 12CO 2 – 1(contours)• Molecular outflow• Top: |v| < 10 km/s• Bottom: |v| > 10 km/s

• H2 2.12 µm• Shocks• Gueth & Guilloteau1999 A&A 343 571

AY216 16

The HH 211 Outflow in IC348P

alau et al. 2006 ApJL 636 L137

(a) Contours: CO 3-2 emissionintegrated for low velocities(2–8 km s-1 [blue] and 10–18km s-1 [red]). The cross marksthe position of the submmcontinuum source

(b) Color contours: CO (32)emission integrated from -14–0 km s-1 (blue) and from20–40 km s-1 (red). Blackcontours: submm continuumemission. Gray contours: NH3(1,1)

(c) Contours: SiO (8-7) emissionintegrated from -20–0 km s-1

(blue) & from 20–42 km s-1

(red).In all panels, the gray scale isthe H2

emission at 2.12 µm(1” = 300 AU)

AY216 17

HH 111 Jet in L1617

NICMOS WFPC2

Star Jet

AY216 18

Disks & Jets Around Young Stars

AY216 19

Basic Scenarios & TerminologyStar formation can be divided into four stages

1. Formation of dense cores in molecular clouds• Initially supported by turbulent & magnetic pressure, which

gradually decrease due to ambipolar diffusion.

• Rapid collapse (free-fall) at the center & less so in its outerlayers (inside out collapse)

2. Matter originating far from the rotation axis has too muchangular momentum to fall onto the deeply embedded proto-star and settles in a circumstellar disk

• Luminosity is accretion powered

3. Bipolar outflow perpendicular to the disk• Deuterium burning ignites in central regions

4. Both infall & outflow decline & a newly formed star with acircumstellar disk emerges

AY216 20

The Four Stages of Star Formation

1

43

2

Shu et al.(1987 ARAA25 23)

Molecular cloud core Embedded protostar

← Classical/WTTS →

AY216 21

From Molecular Cloud Core to Planetary System

AY216 22

YSO SED Classification• Lada & Wilking (1984 ApJ 287 610), Adams, Lada & Shu (1987

ApJ 312 788)– Based on the fact that, when YSOs emerge as optically visible stars,

they remain partially obscured

• Class I–(stage 2)– Completely embedded objects have SEDs with a positive spectral

index in the far-IR. Class II –(stage 2 & 3)– Older YSO with SEDs due to a reddened stellar component and an IR

excess

• Class III–(stage 3 & 4)– The IR excess disappears except for circumstellar gas which causes

atomic emission lines

The youngest sources (stage 1 emit the bulk of their energy in thesub-mm & mm: pre Class I– Class 0 (André et al. 1993 ApJ 406 122)– Class -I sources (Boss & Yorke 1995 ApJL 439 55), where the

collapse has just been initiated and which still await detection!

AY216 23

SED ClassificationClass I

Infall withsimultaneousbipolar outflow

Class IIVisible T Tauri starswith disks & winds

Class III Circumstellarmaterial accreted ordissipated, leaving apre-main-sequencestar, possibly withplanets

AY216 24

T Tauri Stars• Optical detection of young stars or of pre-main-

sequence stars (YSOs) by A. H. Joy (1945 ApJ 102168)– T Tauri stars were defined after the prototype T Tau

• Irregular variability by as much as 3 mag.• Spectral types F5 to G5 with strong CaII H & K 3933, 3968 Å

emission as well as H Balmer lines• Low luminosity• Association with either bright or dark nebulosity• Later extended to include any spectral types later than F5, and

requiring strong Li 6707 Å absorption (age indicator)

– It was recognized from the start that the emission line patternsresemble those seen in the solar chromosphere, but muchstronger compared to the stellar photospheric emission

• Ambartsumian proposed T Tauri stars were YSOs (~1957)

T Tauri stars are optically revealed YSOs

AY216 25

T Tauri Stars without Accretion• By definition weak-lined T Tauri stars have little or no

line emission– WTTS have no (current) disk accretion

• Prior to IR observations line emission was thought tobe vigorous chromospheric activity– YSOs must have very strong magnetic fields– YSO magnetic fields are probably not strong enough to directly

produce the line emission if there were no disk present

• Even though the WTTS are not currently accreting itdoes not mean that they always are that way– Accretion is episodic– It is likely that even the WTTS still have disks around them

AY216 26

The T Tauri Star Eye Chart• Reviews that cover all aspects of T Tauri stars can

be found in Appenzeller & Mundt (1989) andBertout (1989)

• T Tauri stars are among the youngest objectsdirectly observed

– Kinematic association of many T Tauri stars with darkclouds where stars are formed (Herbig 1977)

– Li I 6707 Å in absorption shows T Tauri stars are young– Comparing the position of these stars in the HR diagram

with theoretical evolutionary tracks gives ages < 10Myr.Evolutionary tracks ignore on-going accretion and mayunderestimate ages by x2-3 (D'Antona & Mazitelli 1994;Swenson et al. 1994; Siess, Forestini & Bertout 1997)

• Observationally, T Tauri stars are identified as– Stellar objects associated with regions of obscuration– Spectra show emission in Balmer lines and Ca H & K– The photospheric spectra are similar to those of stars

with spectral-type later than late F

• Variability is a defining characteristic– Photometric variations occur at all wavebands, from the

X-ray to the IR– Variability range from a few minutes to > 100 yr– Usually variations are irregular, although some T Tauri

stars show a quasi-periodic behavior (of a few days),likely due to the rotation of spots at the stellar surface

– Emission lines also change in intensity and shape as dodegree and PA of polarization (Johns & Basri 1995;Lago & Gameiro 1998)

• T Tauri stars are the link between deeplyembedded protostars (class 1 objects) and lowmass main sequence stars (M < 3 M ) (Lada1986)

–SEDs are characterized by both UV and IR excessesrelative to a main sequence star of the same effectivetemperature.

• According to the strength of the Hα emission line–T Tauri stars are Weak Line T Tauri Stars'' (WTTS) or``Classical T Tauri Stars'' (CTTS)

–WTTS have EW(Hα)<10 Å.–This is not a rigid division: T Tauri stars can changespectroscopically such that the border is crossed

–When compared to CTTS, WTTS display noultraviolet excess, little or no infrared excess and theyshow very weak, if any emission lines (Montmerle et al.1993)

• The IR excess in T Tauri stars is attributed to thepresence of a circumstellar disk (Beckwith &Sargent 1993,Strom et al. 1993)

–This excess results both from reprocessingphotospheric radiation and from heating of gas anddust by accretion (Kenyon & Hartmann 1987,Adams etal. 1987,Bertout et al. 1988,

–The masses and sizes between 0.001-1M and100-1000 AU (Beckwith et al. 1990)

AY216 27

Optical Spectra of T Tauri Stars• T Tauri stars exhibit a

range of emission linestrengths– Clockwise from upper left

the lines get stronger

– LkCa3 is a weak-line TTauri star

– BP Tau & DP Tau areclassical T Tauri stars

– DG Tau has very strongemission lines

Kenyon et al. 1998 AJ 115 2491

⊕

Hα

[SII]

[OI]

AY216 28

T Tauri stars in Taurus-Auriga• Spectra of Class I YSOs in

Taurus-Auriga– Discovered from IR

continuum emission (somethe IRAS survey)

– All show strong emissionlines

– HH30 IRS shows strong [OI]6300, 6364 Å & [SII] 6717,6731Å

– Three show the TiO band at7200–7500 Å of M-typestellar photospheres

– Spectra decline sharplybetween 7000–5800 Å

AY216 29

T Tauri stars in Taurus-Auriga• Some extreme Class I

objects have emissionlines that dominate thespectrum– Difficult to see any

stellar continuum– [NII] 6548, 6584 Å

tends to be strong– Emission-line

equivalent widths arecomparable to those inHerbig-Haro objects

These data suggest that TTS have warmionized region and strong outflows/jets

AY216 30

Disk Accretion Rates• 3200-5200 Å spectra trace excess hot

continuum emission produced byaccretion onto the central star

• Classical T Tauri stars haveappreciable Balmer jumps (not dips)and emission lines– K3-M4 stars as judged from the red

part of the spectrum

• LKCa7, V819 Tau & V836 Tau areWTTS

• Accretion rate

10-9 - 10-7 M yr-1

at most 20% of total luminosity

Gullbring et al. 1998 ApJ 492 323€

Lacc ≈GM* M

•

R*1− R*

Rin

AY216 31

Disk Accretion Rates

Gullbring et al. 1998 ApJ 492 323

AY216 32

T Tauri Stars without Accretion• WTTS have little or no [EW (Hα) < 10 Å] line

emission & are not accreting (by definition)• Prior to IR observations, line emission was

thought to be vigorous chromospheric activity– YSOs must (and do) have strong magnetic fields– However, YSO magnetic fields alone are not strong

enough to directly produce the line emission withouta disk or outflows

• Even though WTTS are not now accreting, itdoes not mean that always was the case– Accretion is episodic, as evidenced by the structure

of jets– WTTS probably still have disks around them

AY216 33

Herbig Ae/Be Stars• More massive YSO have earlier spectral types, and

begin to overlap with the A and B stars– Many of the A-type stars have emission lines and other

spectral peculiarities– To distinguish these stars from older emission line-stars,

Herbig (1960 ApJS 4 337) selected a group of Ae or Be typestars with associated bright nebulosity and which were inobscured regions

• These stars have IR excess due to circumstellar dust– Circumstellar dust distinguishes YSOs in this mass range from

classical Ae and Be type stars– Classical Ae and Be stars often have IR excesses

• Due to free-free emission from circumstellar gas disk (free-free)

AY216 34

T Tauri Stars & Herbig Ae/Be Stars

• T Tauri stars have longPMS evolution– 10-100 Myr

• Herbig Ae/Be stars are2-10 M– tPMS < 10 Myr

• For M > 5 M there isno PMS phase– Birthline indicates

approximate locationwhere YSOs becomevisible

HAeBes

T Tauri

AY216 35

IR Excess of HAeBe Stars• SEDs are indicative of

disks & envelopes– AB Aur

• Group I (Hillenbrand etal's 1992)

– PV Cep• Group II

– Note the onset of an IRexcess already at 1-2µm• Squares are, observed

fluxes, circles areextinction corrected

• Hillenbrand’sclassification is theopposite of the TTSSED scheme

HillenbrandGroup I

HillenbrandGroup II

AY216 36

IR Properties of YSO

• IRAS/ISO data for of HAeBe stars illustratehow IR data give fundamental and at times theonly information about embedded YSOs– IR spectral energy distribution classification

• λFλ ~ λS

• s = - 3 star

• s = - 4/3 accretion disk– s < - 4/3 Class III

– - 4/3 < s < 0 Class II

– s > 0 Class I

• IR properties of YSO cannot

be understood in terms of

spherical dust clouds

AY216 37

IR Spectra of Class I Objects• Sources where mostof the energy isradiated in the IR

– Cool dust continuum T≈ 35 K

– Many absorptionfeatures (d’Hendecourtet al. 1996 AA 315L365)• Deep, broad 9.7 & 18µm Si absorption

• 3 & 6µm H2O ice• 4.27 & 15.2 µm CO2

ice• 7.7 µm CH4

AY216 38

IR Spectra of Class I Objects

• The 2.5-18 µm spectrum of RAFGL 7009S compared to the laboratory spectrum of a ultravioletphotolysed ice mixture H2O:CO:CH4:NH3:O2

AY216 39

Embedded Massive YSO

AY216 40

IR Spectra of HAe/Be Stars• ISO spectra of

HAeBes show arich variety of solidstate bands– Silicates (amorphous

& crystalline)• ISM silicates are

amorphous

– FeO

– Polycyclic aromatichydrocarbons(PAHs),

– Crystalline H2O ice

λ(µm)

AY216 41

HD 100546 & Comet Hale-Bopp• ISO-SWS spectrum

of the Herbig Aestar HD 100546(full line) comparedto the spectrum ofcomet Hale-Bopp

AY216 42

Interplanetary & Interstellar Dust

AY216 43

HAeBes are Progenitors of Debris Disks Stars

• A stars host debrisdisks– Vega, β Pic,

Fomalhaut

• Dust removed by P-Reffect & replenished byerosion of planetisimals

• Warps & blobs may beexcited by planets

β Pic

Vega

Liou & Zook 1999

Neptune

AY216 44

Collapse & Accretion of Stars

• YSO are not on the main sequence– Main sequence?

• Hydrostatic equilibrium• Surface radiant energy loss balanced by

thermonuclear burning of H

– Initially the core temperatures of YSO aretoo cool for for H fusion

• Energy lost must be balanced by the release ofgravitational potential energy

– The location of a YSO in the HR diagram isa clue to its age

AY216 45

Inside-Out Collapse in B335

Choi et al. 1995 ApJ 448 742

AY216 46

Pre-Main Sequence Evolution• A reliable understanding of pre-main sequence

evolution would reveal many details of starformation– What is the star formation history?

• How long does star formation last?• Which stars form first?• What is the relation between young stars in adjacent

regions?• How long does circumstellar material persist?

– What is the evolutionary status of various YSO• CTTS vs. WTTS?• How quickly do planets form?

– What’s the connection between structure in GMCand the initial mass function?

AY216 47

Stars Near the Sun• Color magnitude

diagram for youngstars in the solarneighborhood showsthe main sequenceand pre-mainsequence stars– All stars have

Hipparcosparallaxes

– Isochrones for solar[Fe/H] from fourgroups plotted at 10& 100 Myr

– Hyades (600 Myr)and late-type Glieseindicate the mainsequence

AY216 48

Evolving Circumstellar Environment

• Debris diskstudiessuggest thatthe quantity ofcircumstellarmaterialdeclinesrapidly withage: M ∝ t -2

AY216 49

Young Low Mass Stars in Orion

• Spectral type & luminosity for ~ 1700stars within 2.5 pc of the Trapeziumcluster (Hillenbrand 1997 AJ 112 1733)

• Youthful population– Lies above the main

sequence

– Age < 1-2 Myr

AY216 50

HR Diagram for Low Mass Stars in OrionH

illenbrand 1997 AJ 113 1733

AY216 51

Age Spread in IC 348?• 110 T Tauri stars in IC

348 Hα

+ ROSAT

• Apparent age ~ 1 - 12Myr

• Mean ~ 1.3 Myr

o Reddening for starsof known spectraltype

AV = 2.8 mag.assumed

/ Astrometricnonmembers

Herbig 1998 ApJ 497 736

AY216 52

Disk Lifetime?• JHKL excess/disk fraction

as a function of meancluster age (Haisch et al.2001 ApJL 553 153)

• The decline in the diskfraction vs.age suggests adisk lifetime ~ 6 Myr

– Vertical bars represent the√N errors in derivedexcess/disk fractions

– Horizontal bars representthe error in the mean of theindividual source agesderived from a single set ofPMS tracks

– Systematic uncertainty isestimated by comparingages from using differentPMS tracks

AY216 53

Estimating Ages• Derived ages for T Tauri stars depend to some extent on

initial location in the HR diagram– L & Teff at the end of protostellar accretion

• Disk accretion during the T Tauri phase (10-7 M yr-1) is insignificant

– Low mass protostars may finish their primary accretion phasenear the birthline (Stahler 1983 ApJ 274 822)

• The birthline is generally near the D-burning main sequence

• Whether the D-burning main sequence defines an exact starting pointfor for T Tauri stars depends on factors such as how much thermalenergy is added during protostellar accretion

• The youngest low mass stars are observed near the birthline, but adefinitive observational test does not yet exist

– D-burning is insignificant for more massive stars (M > 5 M)

AY216 54

Pre-Main Sequence Evolution

• Before a YSO reaches the main sequence itsinterior is too cool for H fusion– The star contracts so that gravitational potential

energy makes up for energy lost from the surface

• Pre-main sequence stars have convectiveinteriors and hence nearly isentropic

Pρ-γ = Kwhere n = 1/(γ-1) is the polytropic index

• γ = 5/3 corresponds to n = 3/2 polytrope• Mass radius relation R* M*

1/3 = K• K is determined by the boundary condition between the

convective interior and the radiative atmosphere

AY216 55

Hayashi Tracks

• Hayashi (1961 PASJ 13 450) discovereda “forbidden zone” on the HR diagram– Opacity drops rapidly < 4000 K when H

recombines

– Photosphere must have large optical depth• Low opacity makes it impossible to match the

radiative atmosphere to the convective interior

– Initial contraction of low mass pre-mainsequence stars tends to be at approximatelyconstant temperature

AY216 56

Hayashi Tracks• Hayashi

1961 PASJ13 450

• D’Antona &Mazzitelli1994 ApJS90 467

AY216 57

Theoretical (Dis)Agreement• Variation between pre-

main-sequencecontraction tracks formasses– Swenson et al. 1994 ApJ

425 286 (solid)– D’Antona & Mazzitelli 1994

ApJS 90 467 (dotted)

– Baraffe et al. 1998 A&A337 403, (long-dash)

– Palla & Stahler 1999 ApJ525 772 (dotshort-dash)

– Yi et al. 2001 ApJS 136417 (long-dashshort-dash)

AY216 58

Evolution of Polytropes

• The gravitational potential energy of polytropeis

€

W = −3

5 − nGM 2

R= −

67GM 2

RFor n = 3/2By the Virial theorem2T +W = 0Total energy

E = T +W = −37GM 2

R

L =dEdt

= −37GM 2

R2dRdt

AY216 59

Hayashi Contraction

• The negative sign indicates that adecrease in the total stellar energyresults in positive luminosity– By the virial theorem half of the gravitational

potential energy is converted into thermalenergy and half is radiated

• Negative specific heat capacity

– Consider Hayashi evolution is described byTeff = (L / 4$σ R 2 )1/4 ≈ const.

AY216 60

Kelvin-Helmholtz Timescale

• Combining the contraction luminosity with Teff = const.yields

€

L = L03tτKH

−2 / 3

where τKH =37GM 2

L0R0

• τKH is the Kelvin-Helmholtz timescale ~ E/L• As the star ages it contracts and becomes fainter

• The rate of decrease in L (and R) slows with time

• For a PMS object 0.8 M, 2 R, & 1 L

• τKH = 4.3 x 106 yr and Hayashi contraction time isτKH /3 = 1.4 x 106 yr

AY216 61

Hayashi Contraction• A factor of 10 in age corresponds to a factor of 102/3 or 1.7 mag.

dimmer

– A discrepancy with detailedmodels arises between 1-3x 105 yr due to D-burningwhich occurs when centraltemperatures reach ≈ 106 K

– D-burning slows stellarcontraction, whichcontinues when D isexhausted

– Contraction is halted againby H fusion on the mainsequence

AY216 62

Contraction of Low Mass Stars/Brown Dwarfs

50% D burned50% Li burned

L ~ t-2/3

L ~ t-2/3

Stars

Browndwarfs

Planets

Bur

row

s et

al.

1997

ApJ

491

856

AY216 63

Convective/Radiative Tracks

• Low mass stars remain convective untilthey reach the main sequence (n = 3/2polytrope)– Path is ~ vertical on the HR diagram– More massive stars (> 0.7 M) develop a

radiative core (Henyey et al. 1955 PASP 67154)• Subsequent contraction is at L ~ constant• Radiative stars have a well defined mass-

luminosity relation

– Stars < 0.3 M are completely convective onthe main sequence

AY216 64

Formation of Protostars• Pre-main sequence tracksassume that low mass starsare formed high on convectiveHayashi tracks–Why are there so few of these

objects?–Perhaps stars evolve quickly

through this region?• τKH ~ M2 / LR• For a uniform star formation rate N(t)~ L-3/2 when L ~ t-2/3

–Young stars are also likely to bethe most heavily extincted• But class I and III sources have thesame median luminosity (Keyon &Hartmann 1995 ApJS 101 117)

?

AY216 65

Formation Timescales

• Stars cannot form arbitrarily high onHayashi tracks (arbitrarily large R)– Finite time is required to accumulate the

stellar matter

– Characteristic accretion rate is dM/dt ~ c3/G• 2 x 10-6 (T/10 K) M yr-1

• Time to assemble 1 M star from a 20 K NH3

core is 0.2 Myr

• Where does the gravitational potentialenergy go?

AY216 66

Where Does the Energy Go?

• Stahler Shu & Tamm(ApJ 1980 241 637)conclude efficientescape of accretionenergy– Accretion energy is

absorbed by thesurrounding sphericaldusty envelope

– A 1 M protostar emergeswith a radius ~ 5 R

AY216 67

Where Does the Energy Go?

• Mo = 0.01 M Ro= 3.5 R

• dM/dt = 10-5 M yr-1 for 105

yr–Accretion shut off at 1 M

–Gas photosphere cools atconstant R for ~ 1 day

–Loiters for ~ 3000 yr on theD main-sequence

–Followed by Hayashicontraction

• Accretion energy must betrapped to produce aprotostellar core inhydrostatic equilibrium

• From the virial theoremcomputing the radius of aprotostellar core reduces tofinding the fraction ofenergy (including D-burning)trapped

5 R

1 R

100 R

1500 R

AY216 68

The Birthline

• Schematically star formation consists of twosteps– Formation of a core in hydrostatic equilibrium

– Quasi-static contraction to the main sequence

• Step (1) is complex– 3-d Radiation-MHD

– Vast range of spatial scales R ~ 1011 - 1017 cm

• Stahler (1983 ApJ 274 822) says skip (1)– D-burning enforces a strong mass-radius relation

once accretion terminates

AY216 69

The Birthline

• For large dM/dt deuterium is replenishedand mixed into the convective core–Maintains significant D abundance

• D burning rate is very sensitive totemperature, ε ~ T 14.8

–In hydrostatic equilibrium Tcore ~ Mp/Rp• If the core temperature drops the protostar radius

contracts until D burning re-ignites• The increase in Lp causes the protostar to expand• D-burning enforces a constant Mp/Rp

• The D main-sequence mass-radius relationdefines the protostellar birthline

AY216 70

Comparison with Observations

• Comparison with Taurus-Auriga T Tauri starssuggests rough agreementwith the positions of themost luminous optically-visible stars– A few objects may lie

above the birthline

– Note—we have no way

to estimate masses for

class I objects

Natta 2000

Hartmann et al. 1997 ApJ 475 770

AY216 71

Comparison with Observations

• There is nothing in the birthline calculationswhich forbids accreting protostars to lieabove the D-burning main sequence

• By construction we have no details on coreformation– The location of the Taurus-Auriga population

implies a mass radius relation

R ≈ 6 (M / M ) R

or an accretion luminosity

L = 10 L (dM/dt / 2 x 10-6 M yr-1)

for our characteristic dM/dt

AY216 72

Comparison with Observations• Comparison with the luminosity

function for Class I objectsimplies very log mass accretionrates—median dM/dt ~ 10-7 M

– Episodic accretion?– FU Orionis phenomenon - 104

variation in L

B

AY216 73

Summary• Initial phase of evolution of a protostar is the infall of material

directly onto the core– At some point collapse is halted and the core achieves hydrostatical

equilibrium– Henceforth the protostar grows via accretion (directly or via a disk)

• When does this occur? What separates the free-fall phase from the firsthydrostatic phase?

• Stahler (1983 ApJ 274 822 ) suggested that the free-fall phasemay end when deuterium burning is ignited

• Theoretical models for young stars suggest that these reactionscan remain active for of order 106 years in stars of approximatelysolar mass– The key question is whether the energy input from accretion can

complete with the energy release due to the deuterium nuclearreactions—difficult to estimate

• The original argument was that the radius of a deuterium burningstar is tightly bound