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21: Formation of Low

James R. Graham UC, Berkeley

AY216 1 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 2 Outline

• Nearby regions of Galactic formation • General properties of young, low mass stars – T Tauri stars (solar type stars) – Herbig Ae/Be stars • Massive stars (OB) covered later

AY216 3 Local Star Forming Regions

• Much of our knowledge of comes from a few nearby regions – Taurus-Auriga & Perseus • Low mass (solar type stars) • 150 pc – Orion • Massive stars (OB stars) in Orion • 500 pc • How representative are these regions of the as a whole?

Stahler & Palla Fig. 1.1 AY216 4 Taurus, Auriga & Perseus

• Nearest region of current star formation – Grey=Milky Way – Black = MC

AY216 5 Taurus, Auriga & Perseus

• Principal regions include – NGC 1333/ NGC 1579 IC348 – B5 • Bok globule IC 348 – Pleiades – TMC-1 TMC-2

• NH3 cores – T Tauri • Prototype – L 1551 • Young stellar outflow source

AY216 6 Taurus, Auriga & Perseus

• The Taurus clouds are rich in dense cores and young stellar objects • Traditionally, T Tauri stars are a class of variable stars – Found near molecular clouds & identified by their optical variability and strong chromospheric lines & associated X-ray emission – Youngest of optically visible stars: the presence of Li 6707 Å in absorption testifies to youth AY216 7 Ophiuchus Wilking et al. 1987 AJ 94 106 CO

• Three views of a star forming cloud – Optical – CO J=1-0 – 1.3 mm continuum Andre PP IV AY216 8 Orion

4 + MH2(L1630) ~ 8x10 M

+ 5 massive CS 2-1 cores with M > 200 M & associated stellar clusters 393 25) ApJL 1992 Lada ( AY216 9 Orion

4 + MH2(L1630) ~ 8x10 M

+ 5 massive CS 2-1 cores with M > 200 M & associated stellar clusters 393 25) ApJL 1992 Lada ( AY216 10 Orion

4 + MH2(L1630) ~ 8x10 M

+ 5 massive CS 2-1 cores with M > 200 M & associated stellar clusters 393 25) ApJL 1992 Lada ( AY216 11 Orion: Not Just OB Stars…

• Although the appearance of Orion is dominated by high mass (OB stars) but ~ 50% of low mass stars are formed in such regions

AY216 12 General Properties

• Young stars are associated with molecular clouds – Observations are affected by , 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 particularly interesting is circumstellar gas and dust–both flowing in as well as out, e.g., jets, winds, & disks AY216 13 Young Stars & Outflows

• Snell, Loren, & Plambeck 1980 ApJL 239 17

AY216 14 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 & Guilloteau 1999 A&A 343 571

AY216 15 The HH 211 Outflow in IC348

(a) Contours: CO 3-2 emission Palau integrated for low velocities -1 et

(2–8 km s [blue] and 10–18 al. -1

km s [red]). The cross marks 2006 the position of the submm

continuum source ApJL (b) Color contours: CO (32) emission integrated from - 636 L137 14–0 km s-1 (blue) and from 20–40 km s-1 (red). Black contours: submm continuum

emission. Gray contours: NH3 (1,1) (c) Contours: SiO (8-7) emission integrated from -20–0 km s-1 (blue) & from 20–42 km s-1 (red). In all panels, the gray scale is

the H2 emission at 2.12 µm (1” = 300 AU) AY216 16 HH 111 Jet in L1617

Star Jet

NICMOS WFPC2

AY216 17 Disks & Jets Around Young Stars

AY216 18 Basic Scenarios & Terminology

Star 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 outer layers (inside out collapse) 2. Matter originating far from the rotation axis has too much angular momentum to fall onto the deeply embedded proto- star and settles in a circumstellar disk • is powered 3. perpendicular to the disk • Deuterium burning ignites in central regions 4. Both infall & outflow decline & a newly formed star with a circumstellar disk emerges

AY216 19 The Four Stages of Star Formation

Molecular cloud core Embedded

1 2

4 Shu et al. 3 (1987 ARAA ← Classical/WTTS → 25 23) AY216 20 From Core to

AY216 21 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 the sub-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 22 SED Classification

Class I Infall with simultaneous bipolar outflow

Class II Visible T Tauri stars with disks & winds

Class III Circumstellar material accreted or dissipated, leaving a pre-main-sequence star, possibly with

AY216 23 T Tauri Stars

• Optical detection of young stars or of pre-main- sequence stars (YSOs) by A. H. Joy (1945 ApJ 102 168) – 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 patterns resemble those seen in the solar , but much stronger compared to the stellar photospheric emission • Ambartsumian proposed T Tauri stars were YSOs (~1957)

T Tauri stars are optically revealed YSOs AY216 24 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 to be 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 it does not mean that they always are that way – Accretion is episodic – It is likely that even the WTTS still have disks around them

AY216 25 The T Tauri Star Eye Chart

• Reviews that cover all aspects of T Tauri stars can • T Tauri stars are the link between deeply be found in Appenzeller & Mundt (1989) and embedded (class 1 objects) and low Bertout (1989) mass stars (M < 3 M ) (Lada • T Tauri stars are among the youngest objects 1986) directly observed –SEDs are characterized by both UV and IR excesses relative to a main sequence star of the same effective – Kinematic association of many T Tauri stars with dark temperature. clouds where stars are formed (Herbig 1977) – Li I 6707 Å in absorption shows T Tauri stars are young • According to the strength of the Hα emission line – Comparing the position of these stars in the HR diagram –T Tauri stars are Weak Line T Tauri Stars'' (WTTS) or with theoretical evolutionary tracks gives ages < 10Myr. ``Classical T Tauri Stars'' (CTTS) Evolutionary tracks ignore on-going accretion and may –WTTS have EW(Hα)<10 Å. underestimate ages by x2-3 (D'Antona & Mazitelli 1994; –This is not a rigid division: T Tauri stars can change Swenson et al. 1994; Siess, Forestini & Bertout 1997) spectroscopically such that the border is crossed • Observationally, T Tauri stars are identified as –When compared to CTTS, WTTS display no – Stellar objects associated with regions of obscuration ultraviolet excess, little or no excess and they show very weak, if any emission lines (Montmerle et al. – Spectra show emission in Balmer lines and Ca H & K 1993) – The photospheric spectra are similar to those of stars with spectral-type later than late F • The IR excess in T Tauri stars is attributed to the presence of a circumstellar disk (Beckwith & • Variability is a defining characteristic Sargent 1993,Strom et al. 1993) – Photometric variations occur at all wavebands, from the X-ray to the IR –This excess results both from reprocessing photospheric radiation and from heating of gas and – Variability range from a few minutes to > 100 yr dust by accretion (Kenyon & Hartmann 1987,Adams et – Usually variations are irregular, although some T Tauri al. 1987,Bertout et al. 1988, stars show a quasi-periodic behavior (of a few days), –The and sizes between 0.001-1M and likely due to the rotation of spots at the stellar surface 100-1000 AU (Beckwith et al. 1990) – Emission lines also change in intensity and shape as do degree and PA of polarization (Johns & Basri 1995; Lago & Gameiro 1998) AY216 26 Optical Spectra of T Tauri Stars

• T Tauri stars exhibit a range of emission line strengths – Clockwise from upper left the lines get stronger – LkCa3 is a weak-line T Tauri star ⊕ – BP Tau & DP Tau are classical T Tauri stars [OI] Hα – DG Tau has very strong emission lines [SII]

Kenyon et al. 1998 AJ 115 2491

AY216 27 T Tauri stars in Taurus-Auriga

• Spectra of Class I YSOs in Taurus-Auriga – Discovered from IR continuum emission (some the IRAS survey) – All show strong emission lines – HH30 IRS shows strong [OI] 6300, 6364 Å & [SII] 6717, 6731Å – Three show the TiO band at 7200–7500 Å of M-type stellar – Spectra decline sharply between 7000–5800 Å

AY216 28 T Tauri stars in Taurus-Auriga • Some extreme Class I objects have emission lines that dominate the spectrum – Difficult to see any stellar continuum – [NII] 6548, 6584 Å tends to be strong – Emission-line equivalent widths are comparable to those in Herbig-Haro objects These data suggest that TTS have warm

AY216 ionized region and strong outflows/jets 29 Disk Accretion Rates

• 3200-5200 Å spectra trace excess hot continuum emission produced by accretion onto the central star • Classical T Tauri stars have appreciable Balmer jumps (not dips) and emission lines – K3-M4 stars as judged from the red part of the spectrum • LKCa7, V819 Tau & V836 Tau are WTTS • Accretion rate •   GM* M R* Lacc ≈ 1 −  R*  Rin  -9 -7 -1 10 - 10 M yr at most 20% of total luminosity € Gullbring et al. 1998 ApJ 492 323 AY216 30 Disk Accretion Rates

AY216 Gullbring et al. 1998 ApJ 492 323 31 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 without a disk or outflows • Even though WTTS are not now accreting, it does 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 32 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 type stars with associated bright nebulosity and which were in obscured 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 33 T Tauri Stars & Herbig Ae/Be Stars

• T Tauri stars have long PMS evolution HAeBes – 10-100 Myr • Herbig Ae/Be stars are 2-10 M – tPMS < 10 Myr

• For M > 5 M there is no PMS phase – Birthline indicates approximate location where YSOs become visible T Tauri

AY216 34 IR Excess of HAeBe Stars

• SEDs are indicative of Hillenbrand disks & envelopes Group I – AB Aur • Group I (Hillenbrand et al's 1992) – PV Cep • Group II – Note the onset of an IR excess already at 1-2 µm • Squares are, observed Hillenbrand fluxes, circles are Group II extinction corrected • Hillenbrand’s classification is the opposite of the TTS SED scheme

AY216 35 IR Properties of YSO

• IRAS/ISO data for of HAeBe stars illustrate how IR data give fundamental and at times the only information about embedded YSOs – IR spectral energy distribution classification S • λFλ ~ λ • s = - 3 star • s = - 4/3 – 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 36 IR Spectra of Class I Objects

• Sources where most of the energy is radiated in the IR – Cool dust continuum T ≈ 35 K – Many absorption features (d’Hendecourt et al. 1996 AA 315 L365) • Deep, broad 9.7 & 18 µm Si absorption

• 3 & 6µm H2O ice • 4.27 & 15.2 µm CO2 ice

• 7.7 µm CH4

AY216 37 IR Spectra of Class I Objects

• The 2.5-18 µm spectrum of RAFGL 7009S compared to the laboratory spectrum of a ultraviolet photolysed ice mixture H O:CO:CH :NH :O AY216 2 4 3 2 38 Embedded Massive YSO

AY216 39 IR Spectra of HAe/Be Stars

• ISO spectra of HAeBes show a rich variety of solid state bands – Silicates (amorphous & crystalline) • ISM silicates are amorphous – FeO – Polycyclic aromatic hydrocarbons (PAHs),

– Crystalline H2O ice

λ(µm) AY216 40 HD 100546 & Comet Hale-Bopp

• ISO-SWS spectrum of the Herbig Ae star HD 100546 (full line) compared to the spectrum of comet Hale-Bopp

AY216 41 Interplanetary & Interstellar Dust

AY216 42 HAeBes are Progenitors of Debris Disks Stars

• A stars host debris Vega disks – Vega, β Pic, Fomalhaut • Dust removed by P-R effect & replenished by erosion of planetisimals • Warps & blobs may be excited by planets Liou & Zook 1999

Neptune AY216 β Pic 43 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 are too cool for for H fusion • Energy lost must be balanced by the release of gravitational potential energy – The location of a YSO in the HR diagram is a clue to its age

AY216 44 Inside-Out Collapse in B335

Choi et al. 1995 ApJ 448 742

AY216 45 Pre-Main Sequence Evolution

• A reliable understanding of pre-main sequence evolution would reveal many details of star formation – 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 GMC and the ?

AY216 46 Stars Near the

• Color diagram for young stars in the solar neighborhood shows the main sequence and pre-main sequence stars – All stars have Hipparcos parallaxes – Isochrones for solar [Fe/H] from four groups plotted at 10 & 100 Myr – Hyades (600 Myr) and late-type Gliese indicate the main sequence

AY216 47 Evolving Circumstellar Environment

• Debris disk studies suggest that the quantity of circumstellar material declines rapidly with age: M ∝ t -2

AY216 48 Young Low Mass Stars in Orion

• Spectral type & luminosity for ~ 1700 stars within 2.5 pc of the Trapezium cluster (Hillenbrand 1997 AJ 112 1733) • Youthful population – Lies above the main sequence – Age < 1-2 Myr

AY216 49 HR Diagram for Low Mass Stars in Orion Hillenbrand 1997 AJ 113 1733

AY216 50 Age Spread in IC 348?

• 110 T Tauri stars in IC 348 Herbig 1998 ApJ 497 736  Hα + ROSAT • Apparent age ~ 1 - 12 Myr • Mean ~ 1.3 Myr o Reddening for stars of known spectral type

 AV = 2.8 mag. assumed / Astrometric nonmembers

AY216 51 Disk Lifetime?

• JHKL excess/disk fraction as a function of mean cluster age (Haisch et al. 2001 ApJL 553 153) • The decline in the disk fraction vs.age suggests a disk lifetime ~ 6 Myr – Vertical bars represent the √N errors in derived excess/disk fractions – Horizontal bars represent the error in the mean of the individual source ages derived from a single set of PMS tracks – Systematic uncertainty is estimated by comparing ages from using different PMS tracks

AY216 52 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 -7 -1 • Disk accretion during the T Tauri phase (10 M yr ) is insignificant – Low mass protostars may finish their primary accretion phase near 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 point for for T Tauri stars depends on factors such as how much thermal energy is added during protostellar accretion • The youngest low mass stars are observed near the birthline, but a definitive observational test does not yet exist

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

AY216 53 Pre-Main Sequence Evolution

• Before a YSO reaches the main sequence its interior 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 convective interiors and hence nearly isentropic Pρ-γ = K where n = 1/(γ-1) is the polytropic index • γ = 5/3 corresponds to n = 3/2 polytrope 1/3 • Mass radius relation R* M* = K • K is determined by the boundary condition between the convective interior and the radiative atmosphere

AY216 54 Hayashi Tracks

• Hayashi (1961 PASJ 13 450) discovered a “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-main sequence stars tends to be at approximately constant temperature

AY216 55 Hayashi Tracks

• Hayashi 1961 PASJ 13 450 • D’Antona & Mazzitelli 1994 ApJS 90 467

AY216 56 Theoretical (Dis)Agreement

• Variation between pre- main-sequence contraction tracks for masses – Swenson et al. 1994 ApJ 425 286 (solid) – D’Antona & Mazzitelli 1994 ApJS 90 467 (dotted) – Baraffe et al. 1998 A&A 337 403, (long-dash) – Palla & Stahler 1999 ApJ 525 772 (dotshort-dash) – Yi et al. 2001 ApJS 136 417 (long-dashshort-dash)

AY216 57 Evolution of Polytropes

• The gravitational potential energy of polytrope is 3 GM 2 6 GM 2 W = − = − 5 − n R 7 R For n = 3/2 By the Virial theorem 2T + W = 0 Total energy 3 GM 2 E = T + W = − 7 R dE 3 GM 2 dR L = = − dt 7 R2 dt AY216 58

€ Hayashi Contraction

• The negative sign indicates that a decrease in the total stellar energy results in positive luminosity – By the virial theorem half of the gravitational potential energy is converted into thermal energy and half is radiated • Negative specific heat capacity – Consider Hayashi evolution is described by 2 1/4 Teff = (L / 4σ R ) ≈ const.

AY216 59 Kelvin-Helmholtz Timescale

• Combining the contraction luminosity with Teff = const. yields

−2 / 3  3t  3 GM 2 L = L0  where τ KH =  τ KH  7 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 6 • τKH = 4.3 x 10 yr and Hayashi contraction time is 6 τKH /3 = 1.4 x 10 yr AY216 60 Hayashi Contraction

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

– A discrepancy with detailed models arises between 1-3 x 105 yr due to D-burning which occurs when central temperatures reach ≈ 106 K – D-burning slows stellar contraction, which continues when D is exhausted – Contraction is halted again by H fusion on the main sequence

AY216 61 Contraction of Low Mass Stars/Brown Dwarfs

50% Li burned 50% D burned Stars

L ~ t-2/3 491 856

Planets Brown ApJ dwarfs 1997 al. et

L ~ t-2/3 Burrows

AY216 62 Convective/Radiative Tracks • Low mass stars remain convective until they reach the main sequence (n = 3/2 polytrope) – Path is ~ vertical on the HR diagram

– More massive stars (> 0.7 M) develop a radiative core (Henyey et al. 1955 PASP 67 154) • Subsequent contraction is at L ~ constant • Radiative stars have a well defined mass- luminosity relation

– Stars < 0.3 M are completely convective on the main sequence AY216 63 Formation of Protostars

• Pre-main sequence tracks assume that low mass stars are formed high on convective Hayashi tracks ? –Why are there so few of these objects? –Perhaps stars evolve quickly through this region? 2 • τKH ~ M / LR • For a uniform star formation rate N(t) ~ L-3/2 when L ~ t-2/3 –Young stars are also likely to be the most heavily extincted • But class I and III sources have the same median luminosity (Keyon & Hartmann 1995 ApJS 101 117)

AY216 64 Formation Timescales

• Stars cannot form arbitrarily high on Hayashi tracks (arbitrarily large R) – Finite time is required to accumulate the stellar matter – Characteristic accretion rate is dM/dt ~ c3/G -6 -1 • 2 x 10 (T/10 K) M yr

• Time to assemble 1 M star from a 20 K NH3 core is 0.2 Myr • Where does the gravitational potential energy go?

AY216 65 Where Does the Energy Go?

• Stahler Shu & Tamm (ApJ 1980 241 637) conclude efficient escape of accretion energy – Accretion energy is absorbed by the surrounding spherical dusty envelope

– A 1 M protostar emerges with a radius ~ 5 R

AY216 66 Where Does the Energy Go?

• Mo = 0.01 M Ro= 3.5 R -5 -1 5 • dM/dt = 10 M yr for 10 yr

– Accretion shut off at 1 M – Gas cools at constant R for ~ 1 day – Loiters for ~ 3000 yr on the D main-sequence 1 R – Followed by Hayashi  contraction 100 R • Accretion energy must be 5 R 1500 R trapped to produce a  protostellar core in   hydrostatic equilibrium • From the virial theorem computing the radius of a protostellar core reduces to finding the fraction of energy (including D-burning) trapped

AY216 67 The Birthline

• Schematically star formation consists of two steps – 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 68 The Birthline

• For large dM/dt deuterium is replenished and mixed into the convective core –Maintains significant D abundance • D burning rate is very sensitive to temperature, 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 relation defines the protostellar birthline AY216 69 Comparison with Observations

• Comparison with Taurus- Natta 2000 Auriga T Tauri stars suggests rough agreement with the positions of the most luminous optically- visible stars – A few objects may lie Hartmann et al. 1997 ApJ 475 770 above the birthline – Note—we have no way to estimate masses for class I objects

AY216 70 Comparison with Observations

• There is nothing in the birthline calculations which forbids accreting protostars to lie above the D-burning main sequence • By construction we have no details on core formation – The location of the Taurus-Auriga population implies a mass radius relation

R ≈ 6 (M / M ) R or an accretion luminosity -6 -1 L = 10 L (dM/dt / 2 x 10 M yr ) for our characteristic dM/dt

AY216 71 Comparison with Observations

• Comparison with the luminosity function for Class I objects implies very log mass accretion -7 rates—median dM/dt ~ 10 M – Episodic accretion? – FU Orionis phenomenon - 104 variation in L

B

AY216 72 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 first hydrostatic phase? • Stahler (1983 ApJ 274 822 ) suggested that the free-fall phase may end when deuterium burning is ignited • Theoretical models for young stars suggest that these reactions can remain active for of order 106 years in stars of approximately – The key question is whether the energy input from accretion can complete with the energy release due to the deuterium nuclear reactions—difficult to estimate • The original argument was that the radius of a deuterium burning star is tightly bound

AY216 73