dr.rupnathji( dr.rupak nath ) · ooo m o o o o 1 1 bl 6 3 bl 1 34 10 8 1 bl 2 bl 3 ii....

Jets and OutflowsPART IV

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

I. INTRODUCTION

o o o o oo o o

o o o oo o o

o o o o o oo o o o

o o

We review recent bservati nal and the retical results n the relati nship betweencircumstellar accreti n disks and jets in y ung stellar bjects. We then presenta the retical framew rk that interprets jets as accreti n-p wered, centrifugallydriven winds fr m magnetized accreti n disks. Recent pr gress in the numericalsimulati n f such utfl ws is described. We als discuss the structure f the un-derlying magnetized pr t stellar disks, emphasizing the r le that large-scale, penmagnetic fields can play in angular m mentum transp rt.

[759]

v

v

Uni ersity of Chicago

McMaster Uni ersity

Protostars and Planets III

DISK WINDS AND THEACCRETION-OUTFLOW CONNECTION

o o o o o oo o o o o

o o o o o o o oo o o o o

o o o o oo o o o o o

o o oo o o o

o oo o o

o o oo o o o o o

o o oo o o o

o oo o o o oo o o o o

o o o o o

¨ARIEH KONIGL

and

RALPH E. PUDRITZ

Tw f the m st remarkable aspects f star f rmati n are the presencef disks and f energetic utfl ws already during the earliest phases f

pr t stellar ev luti n. There is n w str ng evidence f r an apparent c r-relati n between the presence f utfl ws and f actively accreting disks,which suggests that there is a physical link between them. The prevalentinterpretati n is that the utfl ws are p wered by accreti n and that mag-netic stresses mediate the infl w and utfl w pr cesses and eject s me fthe infl wing matter fr m the disk surfaces. If disks are threaded by penmagnetic field lines, then the utfl ws can take the f rm f centrifugallydriven winds. Such highly c llimated winds carry angular m mentum andmay, in principle, play an imp rtant r le in the angular m mentum budgetf disks and their central pr t stars.

This review c ncentrates n the devel pments in the study f utfl wsand their relati nship t circumstellar disks that have ccurred since the

¨publicati n f . The reader may c nsult K nigland Ruden (1993) in that v lume and Pudritz et al. (1991) f r reviewsf earlier w rk. In secti n II we summarize the bservati nal findingsn utfl ws, disks, and magnetic fields, and their implicati ns. Secti n

III deals with the general the ry f magnetized utfl ws, and secti n IV

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

�

� �

o

o

o

o

1

1

b l6

3b l

1

3 4

10 8 1

b l

2

b l

3

II. OBSERVATIONAL BACKGROUND

A. Bipolar Outflows and Jets

¨760 A. KONIGL AND R. E. PUDRITZ

�

L

L

M

L

L c

c

�

�

�

�

�

�

��

�

� �

�

�

�

�

�

� � �

�

�

�

��

o o o oo o o o o o

o o o

o o o o o o oo o o o o o o

o oo o o o o

o o o o oo o o o



o o o o oo

o o oo oo

o oo o o

o o o oo

o o oo o

o o o o o o oo o

o o o oo o

o o o oo o o o


o o oo o

o o o

o o o o o oo o o

o o oo o o o o o o

o o o o oo o o o o o o o o

describes numerical simulati ns f disk-driven magnet hydr dynamic(MHD) winds. In secti n V we c nsider the the ry f magnetized pr t -stellar disks. Our c nclusi ns are presented in secti n VI.

Bip lar m lecular utfl ws and narr w at mic jets are ubiquit us phe-n mena in pr t stars. There are n w m re than 200 bip lar CO s urceskn wn (see the chapter by Richer et al., this v lume); they typically appearas c mparatively l w-vel city ( 25 km s ) and m derately c llimated(length-t -width rati s 3–10) l bes, alth ugh several highly c llimatedCO utfl ws that exhibit high vel cities ( 40 km s ) near the fl w axishave n w been detected. The mass utfl w rate exhibits a c ntinu us in-crease with the b l metric lumin sity f the driving s urce f r in therange 1–10 L . M lecular utfl ws are present thr ugh much f theembedded phase f pr t stars and, in fact, appear t be m st p werfuland best c llimated during the earliest (Class 0) pr t stellar ev luti naryphase (B ntemps et al. 1996).

The bip lar l bes are generally underst d t represent ambientm lecular material that has been swept up by the much faster, highlysupers nic jets that emanate fr m the central star/disk system (see the

¨chapters by Eisl ffel et al. and by Hartigan et al., this v lume). Jets ass -ciated with l w-lumin sity ( 10 L ) y ung stellar bjects (YSOs)have vel cities in the range 150–400 km s , large ( 20) Mach num-bers, and pening angles as small as 3–5 n scales f 10 –10 AU.The inferred mass utfl w rates are 10 –10 M yr . A signifi-cant number f utfl ws has als been detected by ptical bservati nsf intermediate-mass (2 /M 10) Herbig Ae/Be stars and ther

high-lumin sity s urces (Mundt and Ray 1994; C rc ran and Ray 1997).The jet speeds and mass utfl w rates in these YSOs are, respectively,a fact r 2–3 and 10–100 higher than in l w- bjects. The t talm mentum delivered by the jets, taking int acc unt b th the densityc rrecti ns implied by their partial i nizati n state and the l ng lifetimesindicated by the detecti n f parsec-scale utfl ws, appears t be c n-sistent with that measured in the ass ciated CO utfl ws (e.g., Hartigan

¨et al. 1994; Eisl ffel and Mundt 1997). A critical review f the physicalmechanisms f c upling the jets and the surr unding gas is given in Cabritet al. (1997).

The m mentum discharge deduced fr m the bip lar utfl w bserva-ti ns is typically a fact r 10 higher than the radiati n pressure thrust

/ pr duced by the central s urce (e.g., Lada 1985), which rules utradiative accelerati n f the jets. Because the b l metric lumin sity f pr -t stars is by and large due t accreti n, and because the rati f jet kineticlumin sity t thrust is f the rder f the utfl w speed ( 10 ), it f ll ws

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

�

�

4

B. Connection with Accretion Disks

DISK WINDS AND THE ACCRETION-OUTFLOW CONNECTION 761

.

Hubble Space Telescope

�

�

�

�

o o o oo o o

o ooo o o

oo o o o o o

o o oo o o

o o o o o oo o o o

o oo o o

o oo o o o o o o

o o o oo o o o o o o

o o o o o oo o o

o o oo o o o

o o oo o o o

o o o o oo o o

oo

o o oo o o

o o o o o

o o o o oo o o o o o oo o o

o o oo o o o

o oo

o oo o o o o o

o o o o oo o o o o

o o o oo o o o

that the jet kinetic lumin sity is n average a fracti n 0 1 f the rateat which gravitati nal energy is liberated by accreti n. This high ejecti nefficiency is m st naturally underst d if the jets are driven magnetically.

Magnetic fields have als been implicated in jet c llimati n. A par-ticularly instructive case is pr vided by (HST)bservati ns f the pr t typical disk/jet system HH 30 (Burr ws et al.

1996). The jet in this s urce can be traced t within 30 AU fr m thestar and appears as a c ne with an pening angle f 3 between 70 and700 AU. The narr wness f the jet indicates s me f rm f intrinsic c l-limati n, because external density gradients w uld n t act effectively nthese small scales. Magnetic c llimati n is a likely candidate, made evenm re plausible by the fact that the jet appears t rec llimate: its apparentpening angle decreases t 1.9 between 350 and 10 AU. Similar indi-

cati ns f rec llimati n have als been f und in ther jets. Given that anyinertial c nfinement w uld be expected t diminish with distance fr m thes urce, this p ints t the likely r le f intrinsic magnetic c llimati n.

The evidence f r disks ar und YSOs and f r their link t utfl ws has beenstrengthened by a variety f recent bservati ns. These include systematicstudies f the frequency f disks by means f infrared and millimeter sur-veys and further interfer metric mappings (n w c mprising als the sub-millimeter range), which have res lved the structure and vel city field fdisks d wn t scales f a few tens f AU (see the chapter by Wilner andLay, this v lume). High-res luti n images f disks in several jet s urceshave als been btained in the near infrared using adaptive ptics and inthe ptical using the HST (see the chapter by McCaughrean et al., thisv lume).

Stellar jets are believed t be p wered by the gravitati nal energy lib-erated in the accreti n pr cess and t be fed by disk material. This pictureis supp rted by the str ng apparent c rrelati n that is f und (e.g., Cabrit

´et al. 1990; Cabrit and Andre 1991; Hartigan et al. 1995) between thepresence f utfl w signatures (such as P Cygni line pr files, f rbidden-line emissi n, thermal radi radiati n, r well-devel ped m lecular l bes)and accreti n diagn stics (such as ultravi let, infrared, and millimeter-wavelength emissi n excesses, r inverse P Cygni line pr files). Furthersupp rt is pr vided by the apparent decline in utfl w activity with stellarage, which f ll ws the similar trend exhibited by the disk frequency (see

´the chapters by Andre et al. and by Mundy et al., this v lume) and massaccreti n rate (see the chapter by Calvet et al., this v lume). Whereas vir-tually every Class 0 s urce has an ass ciated utfl w, a survey f pticaland m lecular utfl ws in the Taurus-Auriga cl ud (G mez et al. 1997)f und an incidence rate f 60 % am ng Class I bjects but nly 10%am ng Class II nes (and n ne in Class III bjects). The inference that jetsare p wered by accreti n and riginate in accreti n disks is strengthened

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

o0 6b l

2

4 1

wind

accwind

3 4

�

.

.. .


M Laccre-

tion

ionized outflowmolec-

ular outflow

MM M .

�

�

�

�

��

�

�

�

� �

�

o o o oo o o o o

o o o o o oo

o o o o oo o o

o o o o o ooo o o o o

o o o o o o oo o o o o

oo o

o o oo o o o

o oo o o o o

oo o o o

o o oo o o

o o o o oo o o o o

o o oo o o

o o o oo o

o o o oo o o o

o oo o o

o o oo o o o

o o o o o oo o o o o o o

o oo o

o o oo

o o o oo o

o oo o o

o o o o o

by the evidence f r disks in the y ungest YSOs in which utfl ws aredetected. F r example, submillimeter interfer metric bservati ns f VLA1623, ne f the y ungest kn wn Class 0 s urces, imply the presence fa circumstellar disk f radius 175 AU and mass 0.03 M (Pudritz etal. 1996).

C rc ran and Ray (1998) dem nstrated that the c rrelati n between[O I] 6300 Å line lumin sity (an utfl w signature) and excess infraredlumin sity (an accreti n diagn stic) riginally f und in Class II s urcesextends sm thly t YSOs with masses f up t 10 M and spans 5 rdersf magnitude in lumin sity. It is n tew rthy that c rrelati ns f the type

that apply t b th l w-lumin sity and high-lumin sity YSOshave been established in several independent studies f r the mass

rate (fr m IR c ntinuum measurements; Hillenbrand et al. 1992; see,h wever, Hartmann et al. 1993; Bell 1994; Mir shnichenk et al. 1997;and Pezzut et al. 1997 f r alternative interpretati ns f the infrared emis-si n in Herbig Ae/Be stars), the mass rate in the jets (fr mradi c ntinuum bservati ns; Skinner et al. 1993), and the bip lar

rate (fr m CO line measurements; Levreault 1988). Takent gether, these relati nships suggest that a str ng link between accreti nand utfl w exists als in high-mass YSOs and that the underlying phys-

¨ical mechanism is basically the same as in l w-mass bjects (see K nigl1999).

Str ng evidence f r a disk rigin f jets is available f r the energeticutfl ws ass ciated with FU Ori nis utbursts (see the chapters by Bell et

al. and by Calvet et al., this v lume). The utbursts have been inferred tarise in y ung YSOs that are still rapidly accreting, alth ugh it is p ssiblethat they last int the Class II phase. The durati n f a typical utburst is

10 yr, and during that time the mass accreti n rate (as inferred fr mthe b l metric lumin sity) is 10 M yr , with the deduced mass ut-fl w rate (at least in the m st p werful s urces like FU Ori andZ CMa) being a tenth as large. The rati / 0 1 is similar tthat inferred in Class II YSOs and again p ints t a rather efficient ut-fl w mechanism. Detailed spectral m deling dem nstrates that virtuallyall the emissi n during an utburst is pr duced in a r tating disk. Further-m re, the c rrelati n f und in the pr t type FU Ori between the strengthand the vel city shift f vari us ph t spheric abs rpti n lines can be nat-urally interpreted in terms f a wind accelerating fr m the disk surface(Calvet et al. 1993; Hartmann and Calvet 1995). Because f the c mpara-tively l w temperatures ( 6000 K) in the wind accelerati n z ne, thermalpressure and radiative driving are unimp rtant; magnetic driving is thusstr ngly indicated. The recurrence time f utbursts has been estimated tlie in the range 10 –10 yr, and if these utbursts are ass ciated with thelarge-scale b w sh cks detected in parsec-scale jets (e.g., Reipurth 1991),then a value near the l wer end f the range is implied. In that case m stf the stellar mass w uld be accumulated thr ugh this pr cess, and, c r-

.

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

C. Magnetic Fields in Outflow Sources

III. MHD WINDS FROM ACCRETION DISKS

A. Basic MHD Wind Theory



o o o o o o o o oo o o o o o o

o oo o o

o o o o o oo

o oo o o o o o

o o o o

o o oo o o o o o

o o oo o o o

oo o o o o

oo o o

o o oo o o o

o o o o o oo

o oo o o o o

o o o o oo o

o o o oo o

o oo o o o

o oo o o

o o o oo o o o o

o o o o o oo o o o

resp ndingly, m st f the mass and m mentum ejected ver the lifetimef the YSO w uld riginate in a disk-driven utfl w during the utburst

phases (Hartmann 1997).

The c mm nly accepted scenari f r the rigin f l w-mass pr t stars isthat they are pr duced fr m the c llapse f the inner regi ns f m lec-ular cl uds that are supp rted by large-scale magnetic fields (and likelyals hydr magnetic waves). In this picture, a gravitati nally unstable in-ner c re f rms as a result f mass redistributi n by ambip lar diffusi n andsubsequently c llapses dynamically (see review by McKee et al. 1993).The mass accreti n rates predicted by this picture are c nsistent with the

¨inferred ev luti n f y ung YSOs (e.g., Ci lek and K nigl 1998). Basicsupp rt f r this scenari is pr vided by far-infrared (e.g., Hildebrand etal. 1995) and submillimeter (e.g., Greaves et al. 1994, 1995; Schleuning1998; Greaves and H lland 1998) p larizati n measurements, which re-veal an rdered, h urglass-shaped field m rph l gy n subparsec scales,c nsistent with the field lines being pulled in at the equat rial plane fthe c ntracting c re. M re ver, H I and OH Zeeman measurements (e.g.,Crutcher et al. 1993, 1994, 1996) are c nsistent with the magnetic fieldhaving the strength t supp rt the bulk f the cl ud against gravitati nalc llapse.

There n w exist measurements f magnetic fields in the fl ws them-¨selves at large distances fr m the rigin (see the chapter by Eisl ffel et al.,

this v lume). In particular, the str ng circular p larizati n detected in TTau S in tw pp sitely directed n nthermal emissi n kn ts separated by20 AU indicates a field strength f at least several gauss (Ray et al. 1997).This high value can be attributed t a magnetic field that is advected fr mthe rigin by the ass ciated stellar utfl w and that d minates the internalenergy f the jet. This bservati n thus pr vides direct evidence f r theessentially hydr magnetic character f jets.

The the ry f centrifugally driven winds was first f rmulated in the c n-text f r tating, magnetized stars (Schatzman 1962; Weber and Davis1967; Mestel 1968). Using 1D, axisymmetric m dels, it was sh wn thatsuch stars c uld l se angular m mentum by driving winds f this type.This idea was applied t magnetized accreti n disks in the seminal paperf Blandf rd and Payne (1982). Every annulus f a Keplerian disk may be

regarded as r tating cl se t its “breakup” speed, s disks are ideal driversf utfl ws when sufficiently well magnetized. The rem val f disk angu-

lar m mentum all ws matter t m ve inward and pr duces an accreti nfl w. In a steady state, field lines must als slip radially ut f the accreting

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

pp

p p

p p

p p

�

�

�

�

� �

�

�

�

�

��

�

BB

V

V V B B

V B

B

angular momentum equation

BV

ˆ ˆB B e V V e

V B

V B

V B


�

�

� �

�

�

�

� � � �

�

�

�

z

p

p

rV rB

B V

k

k

��

� �

� � ��

��

� �

� � � �

� �

� �

� � � �

o o oo o o

o o o o o oo o o o o o

o oo o o o o o

o oo o o o


o o o o oo o o o


o o oo o o o o

o o o oo o

o o o o oo o o o

o oo o o o o o

o o o oo o o o o

o o o o oo o o o o o o


o o o

gas and maintain their fixed p siti n in space; this c nstraint necessitatesdiffusive pr cesses. As we discuss in Secti n V.B, str ng field diffusivityis a natural attribute f the partially i nized regi ns f pr t stellar disks,and it c uld c unter b th the advecti n f the field lines by the radial infl wand their winding-up by the differential r tati n in the disk.

C nsider, f r the m ment, the simplest p ssible descripti n f a mag-netized, r tating gas threaded by a large-scale, pen field (characterized byan even symmetry ab ut the midplane 0). The equati ns f stati n-ary, axisymmetric, ideal MHD are the c nservati n f mass (c ntinuityequati n); the equati n f m ti n with c nducting gas f density sub-ject t f rces ass ciated with the pressure, , the gravitati nal field (fr mthe central bject, wh se gravitati nal p tential is ), and the magneticfield ; the inducti n equati n f r the ev luti n f the magnetic field inthe m ving fluid; and the s len idal c nditi n n :

( ) 0 (1)

1( ) (2)

4

( ) 0 (3)

0 (4)

C nsider the f r axisymmetric fl ws.This is described by the c mp nent f equati n (2). Ign ring stressesthat w uld arise fr m turbulence, and n ting that neither the pressure n rthe gravitati nal term c ntributes, we find

( ) ( ) (5)4

where we have br ken the magnetic and vel city fields int p l idal andt r idal c mp nents: and .

Imp rtant links between the vel city field and the magnetic field arec ntained in the inducti n equati n (3), wh se s luti n is

(6)

where is s me scalar p tential. This sh ws that the electric field due tthe bulk m ti n f c nducting gas in the magnetic field is derivable fr man electr static p tential. This has tw imp rtant ramificati ns. The firstis that, because f axisymmetry, the t r idal c mp nent f this equati nmust vanish ( / 0). This f rces the p l idal vel city vect r t beparallel t the p l idal c mp nent f the magnetic field, . This, inturn, implies that there is a functi n , the mass l ad f the wind, such that

(7)

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

p

p

p

p

p

0

0

p

2 2

2

�

�

� �

�

� �

�

�

�

��

��

�

B

B

.

.


��

� �

��

�

�

�

�

�

k

dAd M V dA

d B dA

V d Mk

B d

kB r V rB

rB

k

k

rBrV

k

rBl rV

k

l

lm rrV

m

� �

�

�

� � �

�

�

�

� �

�

�

��

��

�


o o o oo o o


oo

o o o

o o o oo

o o o o o o o o oo o o o o o o

o o oo o o

o o oo o

o o oo o o o o o

o o o oo o o o o

o

o

o o o oo o o o

o o oo o o o o

o o o o

Substituti n f this result int the c ntinuity equati n (1), and then use fthe s len idal c nditi n [equati n (4)], reveals that is a c nstant al nga surface f c nstant magnetic flux; that is, it is c nserved al ng fieldlines. This functi n can be m re revealingly cast by n ting that the windmass l ss rate passing thr ugh an annular secti n f the fl w f areais , whereas the am unt f p l idal magnetic flux thr ughthis same annulus is . Thus, the mass l ad per unit time andper unit magnetic flux, which is preserved al ng each streamline emanat-ing fr m the r t r (a disk in this case), is

(8)

The mass l ad is determined by the physics f the underlying r t r, whichis its s urce.

A sec nd maj r c nsequence f the inducti n equati n f ll ws fr mthe p l idal part f equati n (6). Taking the d t pr duct f it withand using equati n (7), it can be easily pr ved that the functi n

( / ), where / , is als a c nstant al ng a magnetic fluxsurface. In rder t evaluate , n te that 0 at the disk midplane bythe assumed even symmetry. Thus, equals , the angular vel city fthe disk at the midplane. We thus have a relati n between the t r idal fieldin a r tating fl w and the r tati n f that fl w,

( ) (9)

Let us n w examine the angular m mentum equati n. Returning t thefull equati n (5) and applying equati n (7) and the c nstancy f al ng afield line, we btain

0 (10)4

Hence the angular m mentum per unit mass,

(11)4

is c nstant al ng a streamline. This sh ws that the specific angular m -mentum f a magnetized fl w is carried by b th the r tating gas (first term)and the twisted field (sec nd term). The value f may be f und by elim-inating the t r idal field between equati ns (9) and (11) and s lving f rthe r tati n speed f the fl w

(12)1

w

w

o

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

2 2 2p Ap

1/2pAp

A

20 A

0

A 0

p

p

2 2 2 2 20 0p A

p

1/20 A

1/20 0 A 0

r

0 0r r z

0 0 0 0

�

� � � � �

�

�

�

� � ��

� � �

B

B. Connection with Underlying Accretion Disk


�

��

�

�

� � � � �

�

� �

m m V VV B

r rm

l r

rr r

V

E V r h r r

hV V

V r

V r r r

V V

r V r B BV B Br r r r z

�

�

�

�

�

�

�

� � �

o oo o o o

o o o o o oo o o o

o o o o o oo o o o o o oo o

o o o oo oo o o o


o o o o o o o


o oo o o o

o o o o o oo o o o

o o

o o o oo o o o

o o o oo o o o oo o

o o o o o oo o o

o o oo o o o o

o oo o o o

´where the Alfven Mach number f the fl w is defined as / ,´with /(4 ) being the p l idal Alfven speed f the fl w. The

´Alfven surface is the l cus f the p ints n the utfl w field lineswhere 1. The fl w al ng any field line essentially c r tates with the

´r t r until this p int is reached. Fr m the regularity c nditi n at the Alfvencritical p int [where the den minat r f equati n (12) vanishes], it f ll wsthat the c nserved specific angular m mentum satisfies

(13)

If we imagine f ll wing a field line fr m its f tp int at a radius , the´Alfven radius is at a distance ( ) fr m the r tati n axis and c nstitutes

the lever arm f r the back t rque that this fl w exerts n the disk. Thether critical p ints f the utfl w are where the utfl w speed equals

the speed f the sl w and fast magnet s nic m des in the fl w (at the s -called SM and FM surfaces).

Finally, a generalized versi n f Bern ulli’s equati n may be derivedby taking the d t pr duct f the equati n f m ti n with . We then findthat the specific energy

1( ) ( ) (14)

2

where is the enthalpy per unit mass, is als a field-line c nstant.The terminal speed c rresp nds t the regi n where the

gravitati nal p tential and the r tati nal energy f the fl w are negligi-ble. Since f r c ld fl ws the specific enthalpy may be ign red, we caninfer fr m equati n (14) that

2 (15)

a result first btained by Michel (1969) f r 1D fl ws. The imp rtantp int regarding utfl w speeds fr m disks is that / 2 / :The asympt tic speed is larger than the r t r speed by a fact r that isappr ximately the rati f the lever arm t the f tp int radius.

We n w apply the angular m mentum c nservati n relati n (5) t calcu-late the t rque exerted n a thin accreti n disk by the external magneticfield. The vertical fl w speed in the disk is negligible, s nly the radialinfl w speed and the r tati n speed (Keplerian f r thin disks) c n-tribute. On the righthand side, b th the radial and vertical magnetic c n-tributi ns c me int play, s

( ) ( )(16)

4 4

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

r

acc r 0

0 2acc zs0

0

220 wind 020

acc 0 A0 0 A

2acc A 0 wind

2acc 0 0

2wind 0 A

A 0

accwind

�

��

��

C. Flow Initiation and Collimation

.

.

..

. .

. .. .

. .


�

�

�

�

�

��

B

M V r

d r VM r B B

dr

rB k rV lk l

d r d M rM r

dr dr r

M r r M

J M rJ M r

r rM M .

�

��

� ��

�

�

�

�

�

�

�

��

� �


o o oo o o o

o o o o o oo o o o

o o oo o o o

o oo o

o o o oo o

o o oo

o o oo o o o

o

o o o oo o

o o o oo o o

o o

o o o o oo o

o o o oo o o o

o o o oo o o o

o oo o oo o

o o o o o o oo o o o

In ther w rds, specific angular m mentum is rem ved fr m the inwardaccreti n fl w by the acti n f tw types f magnetic t rque. The first termn the righthand side represents radial angular m mentum ass ciated with

the radial shear f the t r idal field, whereas the sec nd term is verticaltransp rt due t the vertical shear f the t r idal field. In a thin disk, and f rtypical field inclinati ns, the sec nd term will d minate. N te that the firstterm vanishes at the disk midplane, because 0 there. N w, f ll w-ing standard thin-disk the ry, vertical integrati n f the resulting equati ngives a relati n between the disk accreti n rate, 2 , andthe magnetic t rques acting n its surfaces (subscript s):

( )(17)

Angular m mentum is thus extracted ut f disks threaded by pen mag-netic fields. The angular m mentum can be carried away either by t r-

´si nal Alfven waves r, when the magnetic field lines are inclined by m rethan 30 fr m the vertical, by a centrifugally driven wind. By rewritingequati n (11) as 4 ( ) and using the derived relati ns f r

and , the disk angular m mentum equati n can be cast int its m stfundamental f rm,

( )1 (18)

This equati n sh ws that there is a crucial link between the mass utfl win the wind and the mass accreti n rate thr ugh the disk:

( / ) (19)

We have arrived at the pr f undly useful expressi n f the idea that, ifvisc us t rques in the disk are relatively unimp rtant, the rate at whichthe disk l ses angular m mentum ( ) is exactly the rate atwhich it is carried away by the wind ( ).

The value f the rati / is 3 f r typical parameters, s ne finds/ 0 1, which is in excellent agreement with the bservati ns

(secti n II). The explanati n f this relati nship is thus intimately linkedt the disk’s angular m mentum l ss t the wind.

Stellar winds usually require h t c r nae t get started, whereas windsfr m disks, which effectively r tate near “breakup,” d n t. In the casef a thin disk, even a c l atm sphere will suffice as l ng as the field

lines emerging fr m the disk make an angle 60 t the surface. Thisf ll ws fr m Bern ulli’s equati n by c mparing the variati ns in the effec-tive gravitati nal p tential and the kinetic energy f a particle that m ves

,

d

w

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

p

A

p A

A

z

1/2s rA K

s K1

r K

acc r3/2

A K

3/45/40 0

wind 0 0

acc

0

��

� �

j B j

.

.

.


�

�

B Br r

B B r rr

z

H rr

V c V V V r

c VT r V V H r

M H V rr V V

B r k rM r r

M r rB r r

.

� � �

� � �

��

�

�

��

�

�

��

�

�

�

�

�

�

�

�

�

o o oo

o o o o o oo o oo o o o o o

o o oo o o


o o

o o oo o o

o o o o o oo o o o

o o oo o o

o oo o o o o o

o o o oo o o o o

o oo o

o o o oo o o

o oo o o

o oo

o o oo

o oo o o o o o

o oo

o o oo o

o oo o

o o oo o o o o

o o o o oo oo o


¨al ng a field line near the disk surface (Blandf rd and Payne 1982; K nigland Ruden 1993; Spruit 1996; but see Ogilvie and Livi 1998).

The c llimati n f an utfl w, as it accelerates away fr m the disk,arises t a large extent fr m the h p stress f the t r idal field c mp nent.

´Fr m equati ns (9) and (15) ne sees that at the Alfven surfaceand that in the far field (assuming that the fl w pens up t radii )

/ / . Thus, the inertia f the gas, f rced t c r tate with theutfl w ut t , eventually causes the jet t self-c llimate thr ugh the

f rce (with being the current density), which is kn wn as the-pinch in the plasma physics literature.

The detailed radial structure f the utfl w is deduced by balancingall f rces perpendicular t the field lines and is described by the s -calledGrad-Shafran v equati n. This is a c mplicated n nlinear equati n f rwhich n general s luti ns are available. Because f the mathematicaldifficulties (e.g., Heinemann and Olbert 1978), the analytic studies havebeen characterized by simplified appr aches, including separati n f vari-ables (e.g., Tsingan s and Truss ni 1990; Sauty and Tsingan s 1994), self-similarity (e.g., Blandf rd and Payne, 1982; Bacci tti and Chiuderi 1992;C nt p ul s and L velace 1994; Lynden-Bell and B ily 1994), and previ-usly “guessed” magnetic c nfigurati ns (e.g., Pudritz and N rman 1983;

Lery et al. 1998), as well as examinati ns f vari us asympt tic limits tthe the ry (e.g., Heyvaerts and N rman 1989; Appl and Camenzind 1993;Ostriker 1997). Pelletier and Pudritz (1992) c nstructed n n-self-similarm dels f disk winds, including cases where the wind emerges nly fr ma finite p rti n f the disk.

Self-similarity imp ses a specific structure n the underlying disk. Inthe Blandf rd and Payne (1982) m del, all quantities scale as p wer lawsf spherical radius al ng a given radial ray. This directly implies that the

´Alfven surface is c nical and, similarly, that the disk’s scale height ( )scales linearly with . Furtherm re, inasmuch as the pr blem c ntains acharacteristic speed, namely the Kepler speed in the disk, ne infers that

´, i.e., that the Alfven, s und, radial infl w,terminal utfl w, and Kepler speeds, respectively, are all pr p rti nal tne an ther. The scaling implies that the disk temperature has the

virial scaling . The scaling as well as the ( ) relati nimply that, f r a c nstant mass accreti n rate 2 (2 ) , the

´density . Next, the scaling f the disk Alfven speed t -gether with the density result imply that the disk p l idal field (and henceals ) scales as . In turn, the mass l ad and the windmass l ss rate ( ) ln . M re general self-similar m dels may bec nstructed by making the m re realistic assumpti n that mass is l st fr mthe disk s that the accreti n rate is n t c nstant; ( ) . Ad ptingthe radial scaling f the disk magnetic field, ( ) , ne finds thatself-similarity imp ses the scaling 2( 1 25) [see equati n (17)].

The w rk f Heyvaerts and N rman (1989, 1997) and thers hassh wn that in general tw types f c llimati n are p ssible, depending n

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

y y

20

2

sA

��

� �

IV. NUMERICAL SIMULATIONS OF DISK WINDS

A. Dynamic Disks and Winds


�I c rB rI r

Protostars and PlanetsIII

B z

V c

�

�

�

�

o o oo o

o o oo o o o o oo o

o o o oo o oo o o

o o o oo o o o

o o o oo o o o


oo o o

o o o o o oo o o o

o o o o o o o o

o oo

o o o oo o o oo o o o

oo o o

o o o o o oo o o

o o oo o o

o o o oo


o o oo o o o o

o oo o o o

the asympt tic behavi r f the electric current ( /2) .If 0 as , then the field lines are space-filling parab l ids,whereas if this limit f r the current is finite, then the fl w is c llimatedt cylinders. The character f the fl w theref re depends n the b undaryc nditi ns at the disk.

Finally, we n te that the stability f magnetized jets with t r idal mag-netic fields is str ngly assisted by the jet’s p l idal magnetic field, whichacts as a spinal c lumn f r the jet (e.g., Appl and Camenzind 1992). H w-ever, the questi n f whether such jets w uld devel p a kink instability,and whether this w uld affect their c llimati n pr perties, is still beingdebated (e.g., Spruit et al. 1997).

The advent f numerical simulati ns has finally made it p ssible t studythe rich, time-dependent behavi r f MHD disk winds. This all ws net test the stati nary the ry presented ab ve as well as t search f r thec nditi ns that give rise t epis dic utfl ws. These simulati ns repre-sent perhaps the main advance in the subject since

. The published simulati ns generally assume ideal MHD and may begr uped int tw classes: (1) dynamic MHD disks, in which the structureand ev luti n f the magnetized disk is als part f the simulati n, and(2) stati nary MHD disks, in which the underlying accreti n disk d es n tchange and pr vides fixed b undary c nditi ns f r the utfl w pr blem.

The first numerical calculati ns f disk winds were published by Uchidaand Shibata (1985) and Shibata and Uchida (1986). These simulati nsm deled a magnetized disk in sub-Keplerian r tati n and sh wed that arapid radial c llapse devel ps in which the initially p l idal field threading

´the disk is w und up due t the differential r tati n. The vertical Alfvenspeed, being smaller than the free-fall speed, implies that a str ng, verticalt r idal field pressure gradient / must rapidly build up. This f rceresults in the transient ejecti n f c r nal material ab ve and bel w thedisk as the spring unc ils. The w rk f Uchida and Shibata (1985) wasc nfirmed by St ne and N rman (1994) using their ZEUS-2D ideal MHDc de (St ne and N rman 1992).

If the mean magnetic field energy density is less than the thermalpressure in the disk ( ), then a str ng magnet r tati nal (Balbus-Hawley, BH) instability will devel p (e.g., Balbus and Hawley 1991). In2D, this leads t a vig r us radial channel fl w and rapid utward transp rtf angular m mentum. St ne and N rman (1994) ran a series f ZEUS-

2D simulati ns f r a unif rm magnetic field threading a wedge-shapeddisk and a surr unding c r na (m dels defined by f ur parameters). Theirsimulati ns investigated three cases (see als Bell and Lucek 1995 andMatsum t et al. 1996): (a) sub-Keplerian r tati n, (b) a Kepler disk with

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

gas mag�

�

�

B. Stationary Disks and Winds

j


�

a,b

P P

a,b

��

�

oo o o

o oo o o o

o o o oo o o o

o o o oo o o o

o o


o o o o oo o o o


oo o

o o oo o o

o o o oo o o o

o o oo o o

o o o o oo

o o o oo o o o o

o o o oo o o o o o


o o o oo o o

oo o o

o o o o oo o o

o o oo o o o o o o o

o o o o oo o o o o

o o o

str ng disk field, and (c) a Kepler disk with a weak field. In case (a), rapidc llapse immediately ensues with an expanding, transient utfl w appear-ing in 2.5 rbits (repr ducing Uchida and Shibata 1985). In case (b), thedisk is BH stable, but c llapse ccurs anyway, because f the very str ngbraking f the disk due t the external MHD t rque. In case (c) ne againsees rapid radial c llapse f the disk, this time because f a str ng BHinstability.

The 2D channel fl w d es n t, h wever, persist in 3D. In that case theBH instability devel ps int a fully turbulent fl w, and the infl w rate issignificantly reduced (see the chapter by St ne et al., this v lume).

The utfl w pr blem can be clarified by f cusing n the m re restrictedquesti n f h w a wind is accelerated and c llimated f r a prescribed setf fixed b undary c nditi ns n the disk. Keplerian disks in 3D are stablen many tens f rbital times, and this justifies the stati nary disk ap-

pr ach: The launch and c llimati n f jets fr m their surfaces ccurs innly a few inner-disk r tati n times. Gr ups that have taken this r ute

include Ustyug va et al. (1995), Ouyed et al. (1997), Ouyed and Pudritz(1997 ), R man va et al. (1997), and Meier et al. (1997). The publishedsimulati ns differ in their assumed initial c nditi ns, such as the magneticfield distributi n n the disk, the plasma ( / ) just ab ve thedisk surfaces, the state f the initial disk c r na, and the handling f thegravity f the central star. Br adly speaking, all f the existing calculati nssh w that winds fr m accreti n disks can indeed be launched and accel-erated, much al ng the lines suggested by the the ry presented in secti nIII. The results differ, h wever, in the degree t which fl w c llimati nccurs.

Ustyug va et al. (1995) and R man va et al. (1997) empl yed amagnetic c nfigurati n described by a m n p le field centered beneaththe disk surface. N nequilibrium initial c nditi ns, as well as a s ftenedgravitati nal p tential, were used. Relatively l w res luti n simulati nsf fl ws with 1 (Ustyug va et al. 1995) sh wed that c llimated,

n nstati nary utfl ws devel p. Similar simulati ns in the str ng-field( 1) regime (R man va et al. 1997) resulted in stati nary, but unc l-limated utfl ws n these scales.

Simulati ns by Ouyed et al. (1997) and Ouyed and Pudritz (1997 )(see Pudritz and Ouyed 1997 f r a review) empl yed the ZEUS-2D c deand studied tw different magnetic c nfigurati ns. The c r nal gas wasinitially taken t be in hydr static equilibrium with the central bject aswell as in pressure balance with the t p f the disk. Tw initial magneticc nfigurati ns were ad pted, each ch sen s that n L rentz f rce is ex-erted n the hydr static c r na (i.e., such that 0). These are the p -tential field c nfigurati n f Ca and Spruit (1994) and a unif rm, verticalfield that is everywhere parallel t the disk r tati n axis. The gravity was

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

o

i i

i

i i

inj

3K

i

i

2

kn t jet A

�

� ��

�


�

�

�

t tr

r .V

t

V

z r

tb

B r

r V

�

��

�

�

�

�

�

o o oo o o o

o oo o o o

o o oo o o o o o o

o o o o o o o

o o oo o o o o


o o o o oo o o o o

o o o o o oo o

o o o o oo o o o o

o o o o o o oo o o o oo o o o

o o oo o o

o o o o oo o o

oo o o o

o o o ooo o o o o o o o

o o o o oo o o

o o o o o ooo o o o o


o o oo o o o o

o o o o o o o o oo o o o o

o o oo o o

o o o oo o o o

o o o o o oo o o

o o o

uns ftened in these calculati ns, (500 200) spatial z nes were used, andsimulati ns were run up t 400 (where is the Kepler time f r an rbit atthe inner edge f the disk, ). This m del is described by five parametersset at : three t describe the initial c r na (e.g., 1 0), as well as twparameters t describe the disk physics (e.g., the injecti n speed f thematerial fr m the disk int the base f the c r na). The initial c nditi nsc rresp nd t turning n the r tati n f the underlying Keplerian disk at

0.The first thing that happens is the launch and pr pagati n f a brief,

´transient, t rsi nal Alfven wave fr nt, which sweeps ut fr m the disksurface but leaves the c r na largely undisturbed. An utfl w als beginsalm st immediately and devel ps int a stati nary r an epis dic jet. Thesejetlike utfl ws are highly c llimated and terminate in a jet sh ck. A b wsh ck, driven by the jet, pushes thr ugh the c r na. A n ticeably emptycavity d minates m st f the v lume behind the b w sh ck: the cavity isfilled with the t r idal magnetic field that is generated by the jet itself. Thismay pr vide an explanati n f the extended bip lar cavities that surr undhighly c llimated jets. F r a fiducial injecti n speed f 10 , the p ten-tial field c nfigurati n devel ps int a stati nary utfl w with many (butn t all, since the fl w is n t self-similar) f the characteristics f the Bland-

´f rd and Payne (1982) s luti n. The Alfven surface is c rrectly predicted´by the analysis in secti n III. The Alfven and fast-magnet s nic Mach

numbers reach 5 and 1.6, respectively, at 10 , with the t r idal-t -p l idal field strength rati being 3 n this scale. Outfl w takes placenly n field lines that are inclined by less than 60 with respect t the

disk surface, as predicted by Blandf rd and Payne (1982).Figure 1 (adapted fr m Ouyed et al. 1997) sh ws that the p l idal

field lines in the initial state are c llimated t ward the r tati n axis by theh p stress f the jet’s t r idal field. The figure als sh ws the pr pagati nf the jet-driven b w sh ck and the eventual creati n f a cylindrically

´c llimated jet with well-determined Alfven and fast-magnet s nic criticalsurfaces in the accelerati n regi n ab ve the disk (the sl w-magnet s nicsurface is t cl se t the disk t be res lved in this figure).

F r the same b undary and initial c nditi ns, the initially vertical fieldc nfigurati n leads t the devel pment f a jet that is epis dic ver the400 durati n f the simulati n (Ouyed et al. 1997; Ouyed and Pudritz1997 ). Even th ugh the initial c nfigurati n is highly unfav rable t jetf rmati n, jet pr ducti n ccurs. The reas n is the effect f the t r idalfield in the c r na, which is c ncentrated t ward the inner edge f thedisk (where the Kepler r tati n is the greatest). It theref re exerts a radialpressure f rce ( /8 )/ that pens up field lines at larger radii. As l ngas 1 in this regi n, field lines are pliable en ugh t m ve, and a jetis launched. Epis dic kn ts are pr duced n a timescale / ,which is reminiscent f a type f kink instability. Regi ns f high t r idalfield strength and l w density separate and c nfine the kn ts, which in turnhave high density and l w t r idal field strength.

,

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

0 20 40 6005

1015

0 20 40 6005

1015

0 20 40 6005

1015

0 20 40 6005

1015

0 20 40 6005

1015

0 20 40 6005

1015

0 20 40 6005

1015

0 20 40 6005

1015

0 20 40 6005

1015

0 2 4 6 8 10

1

1.5

2

3inj K

A 0

0

5inj K

o o o o oo o

o o o o o o oo o o o o o o o

o o o o

o o o oo o o

o o o oo o o o o oo o o o

o o o o o o o


Figure 1. Numerical simulati ns f disk-driven MHD utfl ws (adapted fr mOuyed et al. 1997). In frame (a), the left panel sh ws the initial magnetic c n-figurati n c rresp nding t the “p tential field” s luti n, whereas the right paneldisplays the initial is density c nt urs f the c r na. The fl w injecti n speedis 10 . Frames (b) and (c) sh w the ev luti n f the initial magneticand density structures (the left and right panels, respectively) at 100 and 400

´inner time units. Frame (c) als displays the l cati ns f the Alfven critical sur-face (filled hexag ns) and the fast-magnet s nic surface (stars). In frame (d),

´the Alfven lever arm ( / ) f und in the simulati n is sh wn (filled hexag ns)as a functi n f the l cati n ( ) f the f tp ints f the field lines n the diskand is c mpared t the predicti n fr m the steady-state the ry f secti n III.A(squares).

�

�

V V

V V

r rr

�

o o oo o o


o o oo o o o o

o

Based n an extensive set f simulati ns, Ouyed and Pudritz (1999)c ncluded that the main fact r that determines whether jets are stati naryr epis dic is n t the initial field c nfigurati n, but rather the mass l adingf the wind. Figure 2 sh ws a simulati n with the same p tential c nfig-

urati n parameters as in Fig. 1 except f r a reduced injecti n speed (andhence mass l ad) f 10 . Clear epis dic behavi r is n w seenin this fl w.

�

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

0 5 10 1502468

0 5 10 1502468

0 5 10 1502468

0 5 10 1502468

2 4 6 80

20406080

100

2 4 6 80

20406080

100

2 4 6 80

20406080

100

2 4 6 80

20406080

100

5inj K

i 0

0

C. Far-field Behavior of MHD Jets

o o o oo o

o o o oo

oo o o o


Figure 2. MHD utfl w simulati ns with the same parameters and magnetic c n-figurati n as in Fig. 1, except 10 (adapted fr m Ouyed and Pudritz1999). The left panels sh w the magnetic field structure and kn t f rmati n attimes 0.0, 75.0, 112.5, and 150.0 . The right panels sh w the angle betweenthe field lines and the disk surface at these 4 times. Only field lines that pen upt an angle 60 are seen t drive an utfl w.

�

B

V V

t

�

� ��

o o o o o o oo o

o o o o o o

o o o o o oo o

o oo o o o o oo o

o o o o o oo o o o oo

N nsteady utfl ws c uld c nceivably als arise in highly c nduct-ing disk regi ns, where the winding-up f the field lines might eject gasthr ugh a str ng pressure gradient (e.g., C nt p ul s 1995).

Simulati ns f MHD jets pr pagating int a unif rm medium sh w that, incertain respects, they differ dramatically fr m hydr dynamic jets. Clarke

¨et al. (1986), Lind et al. (1989), and K ssel et al. (1990) sh wed that thestr ng t r idal field f a jet prevents matter fr m spraying sideways nenc untering the jet sh ck. Rather, jet material decelerated by a Machdisk and a str ng annular sh ck is f cused mainly f rward int a n sec ne. This c ntrasts with the backfl wing c c n that characterizes purely

�

�

�

�

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

2gas Az

A

5/2 1/2acc z s

�

�

V. MAGNETIZED PROTOSTELLAR ACCRETION DISKS

A. Magnetic Angular Momentum Transport

.


� �

.

B P r H

rH

M r B B GM

�

� ��

o o oo o o o o

o o o oo o o o

o o o o oo

o o o o oo

o o o o o oo o

o o o o oo o

o o o o o o o oo o o o

o o o o oo o

o o oo o o

o o o o oo o

o o o oo o

oo o o

o o o o o o oo o o

o o o oo o o o o

o oo

o oo o o o

oo o

o o o

oo oo o

o oo o

hydr dynamic, l w-density jets. Hydr magnetic jets are generally pre-ceded by str nger, m re blique sh cks and advance far m re quicklyint the surr unding medium than their hydr dynamic c unterparts (see

¨K ssel et al. 1990 f r m re detail). MHD jets may thus explain why str ngtransverse expansi ns have n t been measured in bip lar m lecular l bes(e.g., Mass n and Chernin 1993; Cabrit et al. 1997).

One f the primary reas ns why pen, rdered magnetic fields are imp r-tant in accreting astr physical systems is that they can mediate a verticaltransp rt f angular m mentum fr m accreti n disks. In secti n III we dis-cussed the angular m mentum transp rt by centrifugally driven winds, butit is imp rtant t realize that angular m mentum can be rem ved fr m thedisk surfaces even if the field line inclinati n with respect t the vertical isn t large en ugh f r the wind-launching c nditi n t be satisfied, s l ng asthe field is attached t a “l ad” that exerts a back t rque n the disk. In that

´case the disk can l se angular m mentum thr ugh t rsi nal Alfven wavespr pagating away fr m the disk surfaces (the “magnetic braking” mecha-nism; see M usch vias 1991 f r a review). When the magnetic fields arewell bel w equipartiti n with the gas pressure in a differentially r tatingdisk, the magnet r tati nal (BH) instability devel ps n a dynamical timescale and pr duces a magnetic stress-d minated turbulence that gives riset radial transp rt f angular m mentum characterized by an effective vis-c sity parameter in the range 0 005–0.5 (see the chapter by St ne etal., this v lume).

Numerical simulati ns (see secti n IV.A) have dem nstrated that allf the ab ve pr cesses c uld c ntribute t the angular m mentum trans-

p rt in magnetized disks. One can estimate the relative r les f verti-cal wind transp rt and radial turbulent transp rt by taking the rati fthe external wind t rque, c mputed in secti n III, and the visc us t rqueass ciated with magnet centrifugal turbulence, which can be written as( /4 ) ( / ) (Pelletier and Pudritz 1992). Thus, even if the r-dered field threading the disk were far bel w equipartiti n with the diskgas pressure, a wind t rque c uld still d minate a turbulent t rque simply

´because f its large lever arm (the Alfven radius , which greatly ex-ceeds the disk scale height ). We n te in passing that a l ng effectivelever arm als characterizes angular m mentum transp rt by spiral wavesin the disk.

The requirement that, in a steady state, the t rque exerted by a large-scale magnetic field at the surface f a thin and nearly Keplerian accreti ndisk balances the inward angular m mentum advecti n rate can be writtenas 2 /( ) [see equati n (17)]. Assuming a r ughequality between the vertical and azimuthal surface field c mp nents, this

,

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

�

�

6

1

B. Wind-Driving Protostellar Disk Models

B


a,b,

r

r

��

� �

�

��


o o o oo o

o o o o o oo o o o

o o oo o o o o

o o o o o oo o

o o o o o oo

o oo o oo

o o oo o o o o

o o o oo o o o o o o o

o o


o oo o o

o o o o oo

o o o oo o o o o o

oo o

o o o o o o oo o


o o o o oo oo o o o o

o o oo o o o o

o o o oo o o o

o o o

relati n implies that, at a distance f 1 AU fr m a s lar-mass pr t star, a1-G field (the value indicated by mete ritic data f r the pr t s lar nebula;Levy and S nnett 1978) c uld induce accreti n at a rate f 2 10 Myr , which is c mpatible with the mean values inferred in embedded pr -t stars. F r c mparis n, the minimum-mass s lar nebula m del implies athermal pressure at 1 AU that c rresp nds t an equipartiti n magneticfield f 18 G, which implies that a 1-G field c uld be readily anch redin the pr t s lar disk at that l cati n.

The pr perties f pr t stellar accreti n disks and f integrated disk/windsystems have, s far, been derived nly under highly simplified assump-

¨ti ns. Am ng the papers that can be c nsulted n this t pic are K nigl¨(1989, 1997), Wardle and K nigl (1993), Ferreira and Pelletier (1993

1995; als Ferreira 1997), Lub w et al. (1994), Li (1995, 1996), andReyes-Ruiz and Stepinski (1996). A plausible rigin f r an pen diskmagnetic field is the interstellar field that had riginally threaded themagnetically supp rted m lecular cl ud and that was subsequently car-ried in by the c llapsing c re. This picture is fav red ver disk-dynaminterpretati ns because the latter typically pr duce cl sed (quadrup lar)field c nfigurati ns, alth ugh we n te that scenari s f r pening dynam -generated field lines have been c nsidered in the literature (e.g., T ut andPringle 1996; Curry et al. 1994).

The the ry and simulati ns f the previ us secti ns assumed idealMHD. This appr ximati n is adequate f r the surface layers f pr t stel-lar disks, but the disk interi rs are typically weakly i nized, and theirstudy entails the applicati n f multifluid MHD. F r typical parametersf disks ar und s lar-mass YSOs, ne can distinguish between the l w-

density regime ( n scales 100 AU), in which the current in the disk iscarried by metal i ns and electr ns (wh se densities are determined fr mthe balance between i nizati ns by c smic rays and rec mbinati ns ngrain surfaces), and the high-density regime ( n scales 1–10 AU),where the current is carried by small charged grains r by i ns and elec-tr ns that rec mbine with ut grains. We restrict ur attenti n t the l w-density regime and c ncentrate n the case in which the magnetic fieldis “fr zen” int the electr ns and diffuses relative t the d minant neutralc mp nent as a result f an i n–neutral drift (ambip lar diffusi n).

T derive a self-c nsistent steady-state disk/wind c nfigurati n, nec mbines the mass, m mentum (radial, vertical, and angular), and energyc nservati n relati ns, t gether with Maxwell’s equati ns and the gen-eralized Ohm’s law, and imp ses the requirements that the utfl w passthr ugh the relevant critical p ints (see secti n IV). S far, nly simpleprescripti ns f r the disk thermal structure (is thermal r adiabatic) andc nductivity (ambip lar diffusi n in the density regime where the i n den-sity is c nstant, r hmic diffusivity parametrized using a “turbulence”

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

ionsneutrals

iφ

z = 0

φ K

B

Z

Z

Zs

b

h

V < V < Vφi

φ KV > V > V

b

K

i

r z

o o o oo o o o o

o o o o o o oo o o o o o o

o o oo o o


Figure 3. Schematic diagram f the vertical structure f an ambip lar diffusi n-d minated disk, sh wing a representative field line and the p l idal vel citiesf the neutral (s lid arr wheads) and the i nized ( pen arr wheads) fluid c m-

p nents. N te that the p l idal vel city f the i ns vanishes at the midplane( 0) and is small f r b th fluids at the base f the wind ( ). The rela-ti nship between the azimuthal vel cities is als indicated.

� �

V V

V Vi

B

B B

z z Z

� �

�

�

�

�

� �

�

o o o o oo o o

o o o o o

o oo o

o o o oo o o o

o o oo o o o o o o

o o oo o o o o

o o o o oo o o o o

oo o

o o oo o o

o oo o o

o o o o oo o o o

o o o oo o o o o o

o o o oo

o o o o oo o

prescripti n) have been c nsidered. These are pr bably adequate f r b-taining the basic structure f the disk, but m re realistic calculati ns areneeded t m del the transiti n regi n between the disk and the wind c r-rectly.

The vertical structure f a generic centrifugal wind-driving disk ( r“active” surface layer; see secti n V.C) can be divided int three distinctz nes (see Fig. 3): a quasihydr static regi n near the midplane f the disk,where the bulk f the matter is c ncentrated and m st f the field-linebending takes place; a transiti n z ne, where the infl w gradually dimin-ishes with height; and an utfl w regi n that c rresp nds t the base fthe wind. The first tw regi ns are characterized by a radial infl w andsub-Keplerian r tati n, whereas the gas at the base f the wind fl ws utwith . The b undary c nditi ns f r the stati nary disk simula-ti ns discussed in secti n IV.B arise fr m the physical pr perties f thislatter regi n.

What determines the disk structure, and h w d es the magnetic fieldextract the angular m mentum f the accreting gas? The quasihydr staticregi n is matter d minated, with the i nized plasma and magnetic fieldbeing carried ar und by the neutral material. The i ns are braked by amagnetic t rque, which is transmitted t the neutral gas thr ugh the fric-ti nal (ambip lar diffusi n) drag; theref re in this regi n (withthe subscript den ting i ns). The neutrals thus l se angular m mentumt the field, and their back reacti n leads t a buildup f the azimuthalfield c mp nent away fr m the midplane. The l ss f angular m -mentum enables the neutrals t drift t ward the center, and in d ing sthey exert a radial drag n the field lines. This drag must be balancedby magnetic tensi n, s the field lines bend away fr m the r tati n axis.This bending builds up the rati / , which needs t exceed 1/ 3 atDR.R

UPNAT

HJI( D

R.RUPA

K NAT

H )

h

zizi

i

i

i

b

s

13 3 1 1i

i K

�

�

�

! �

!

B B


�

�

z Z

r

V V B B rV r

r V V

V V

Z

Z

.

r V

��

�

� �

� � �

�

�

�

�

� �

�

� �

� �

oo o o o o o o o

o o o o

o o o o o oo

o o o o o

o oo o o o

o o oo o o oo o o o o o o

oo

o o o oo o o o

oo

o o o oo

o o oo o o

o o o oo o o

o o o oo o o o o

o o o o oo

o o oo o o o o oo o oo o o

o o o o oo o o o o

o o o o oo o o o

o o o o oo o o o o

o o o oo o o o

o oo o o

o o o

the disk surface t launch a centrifugally driven wind. The magnetic ten-si n f rce, transmitted thr ugh i n-neutral c llisi ns, c ntributes t theradial supp rt f the neutral gas and causes it t r tate at sub-Keplerianspeeds.

The gr wth f the radial and azimuthal field c mp nents n m vingaway fr m the midplane results in a magnetic pressure gradient that tendst c mpress the disk. The vertical c mpressi n by the c mbined magneticand tidal stresses is, in turn, balanced by the thermal pressure gradient. Themagnetic energy density bec mes d minant as the gas density decreases,marking the beginning f the transiti n z ne (at ). The field ab vethis p int is nearly f rce free [( ) 0], s the field lines, whichvary nly n a length scale , are l cally straight. This is the basis f rthe ad pti n f f rce-free initial field c nfigurati ns in the simulati ns re-viewed in secti n IV.B.

The field angular vel city, given by ( / )/ , is afield-line c nstant (see secti n III.A). The i n angular vel city / dif-fers s mewhat fr m but still changes nly slightly al ng the field. Be-cause the field lines bend away fr m the symmetry axis, the cylindrical ra-dius , and hence , increase al ng any particular field line, whereasdecreases because f the near-Keplerian r tati n law. Eventually a p intis reached where ( ) changes sign. At this p int, the magneticstresses n the neutral gas are small, and its angular vel city is alm st ex-actly Keplerian. Ab ve this p int, the field lines vertake the neutrals andtransfer angular m mentum back t the matter, and the i ns start t pushthe neutrals ut in b th the radial and the vertical directi ns. It is thus nat-ural t identify the base f the wind with the l cati n where the angularvel city f the field lines bec mes equal t the Keplerian angular vel city.The mass utfl w rate is fixed by the height f the effective s nic p intf the wind.

¨As was first rec gnized by Wardle and K nigl (1993), ne can derivekey c nstraints n a viable s luti n by neglecting the vertical c mp -nent f the neutral vel city, which is generally a g d appr ximati nthr ugh ut much f the disk c lumn. This simplifies the pr blem bytransf rming the radial and azimuthal c mp nents f the neutral m men-tum equati n int algebraic relati ns. One imp rtant c nstraint that canbe derived in this way expresses the intuitively bvi us c nditi n thatthe neutrals must be able t c uple t the magnetic field n an rbitaltimescale if magnetic t rques are t play a r le in the rem val f angu-lar m mentum fr m the disk. In the pure ambip lar diffusi n regime,this c nditi n is expressed by the requirement that the neutral-i n c u-pling time 1/ (where 3 5 10 cm g s is the c llisi nalc upling c efficient) be sh rter than the dynamical time. This is equiv-alent t requiring that the neutral-i n c upling parameter /satisfy

1 (20)

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

� � � �

�

��

1/2sK

1/2s0 0

s sr0

r b 0

0 r0 K

s K

accwind

!

! "!

�"

�"

"

. .


�

a V c

a B cc V c

B Z B

V V rc V

M M

a

� �

�

�

�

��

o o o o oo o

o o oo o

o o o o oo o o o

o oo o o o o o

o

o oo o o o

o o o oo o o

o oo o

o oo o o

o o o o o o o oo

o o oo o o

oo o o o

o o o o oo o o o

o oo o o o o

o o oo o o

o oo o

o o o o o o oo o o o o o


o o o o oo o o

o o o o o oo o o

o o o o oo o o

oo o o

This c nditi n is quite general and is als relevant t disk m dels in whichmagnetic t rques ass ciated with small-scale magnetic fields transfer an-gular m mentum radially thr ugh the disk [see the chapter by St ne et al.,this v lume; in the latter case equati n (20) identifies the linearly unsta-ble regime f the magnet r tati nal instability, alth ugh evidently a muchhigher minimum value f is required f r significant n nlinear gr wth].

Additi nal parameter c nstraints that can be derived by using the hy-dr static appr ximati n f r a wind-driving disk m del in the pure ambip -lar diffusi n regime are given by

(2 ) 2 /2 (21)

´where /(4 ) is the rati f the midplane (subscript 0) Alfvenspeed t the is thermal s und speed and / is the n rmalizedmidplane infl w speed. The first inequality c rresp nds t the requirementthat the disk remain sub-Keplerian, the sec nd t the wind-launching c n-diti n at the disk surface ( ) / 3, and the third t the requirementthat the base f the wind lie well ab ve a density scale height in the disk.The sec nd and third inequalities t gether imply that the vertical magneticstress d minates the gravitati nal tidal stress in c nfining the disk. This isa generic pr perty f this class f disk s luti ns that d es n t depend nthe nature f the magnetic diffusivity. The last inequality expresses therequirement that the ambip lar diffusi n heating rate at the midplane n texceed the rate /2 f gravitati nal p tential energy release. Inturn, / must be 1/(1 ) t guarantee that the disk is in near-Keplerian m ti n and ge metrically thin. Upper limits can als be placedn the density at the s nic p int t ensure that the bulk f the disk material

is hydr static and that d es n t exceed . Similar c nstraints arederived by applying this analysis t the ther diffusivity regimes identi-fied ab ve. The s luti ns that satisfy these c nstraints tend t have 1and 1. Furtherm re, the magnetic field in these m dels, wh se mag-nitude is essentially determined fr m the c nditi n that all the angularm mentum liberated by the accreting matter is transp rted by a centrifu-gally driven wind, aut matically lies in a “stability wind w,” where it isstr ng en ugh n t t be affected by the magnet r tati nal instability but

¨n t s str ng as t be subject t the radial interchange instability (K nigland Wardle 1996).

As we have n ted, the steady-state disk m dels are useful f r guidingthe ch ice f b undary c nditi ns at the base f the utfl w in numericalsimulati ns f winds fr m quasistati nary disks. In a c mplementary ap-pr ach (which typically empl ys a highly simplified treatment f the diskutfl w and theref re is n t suitable f r a detailed study f the disk wind),ne can generalize the steady-state m dels and investigate the time ev -

¨luti n f wind-driving accreti n disks (e.g., L velace et al. 1994; K nigl1997). The time-dependent m dels can be utilized t expl re the feed-back effect between the magnetic flux distributi n, which affects the an-gular m mentum transp rt in the disk, and the radial infl w induced by

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

�

�

�

�

�

2

3 2

26 40

2

3

5 1

3

2

4

!

C. Outflows from the Protostellar Vicinity


.

r .

T

�

�

�

�

�

�

�

�

� �

�

�

o o o oo o o

o o o o o o oo o o o

o o o o oo o

o o o o o oo

o oo o oo o o o o o

o o o oo o o o

o o o oo o

o oo o o

o o o o oo o o o o

o oo

o o o o o o o o oo

o oo o o o o o o

o o o oo o o

o o oo o o o o o

o o o o oo o o o

o o o o o oo o o

o o o o o

o o o oo o o o

o o o o o oo o o o

o o o o oo o o

o o o oo

o o o o

the magnetic rem val f angular m mentum, which can m dify the fluxdistributi n thr ugh field line advecti n.

As ne m ves t within a few AU fr m the pr t star, the disk hydr -gen c lumn density can bec me s large ( 192 g cm ) that c smic raysare excluded fr m the disk interi r. (F r reference, the c lumn density fthe minimum-mass s lar nebula m del is 1 7 10 g cm at 1 AU.) Atlarger c lumns the i nizati n rate is d minated by the decay f radi ac-tive elements (n tably Al, if it is present, and K; Stepinski 1992),but the charge density generally bec mes t l w f r the magnetic fieldt be effectively c upled t the matter. C nsequently, the interi r f thedisk bec mes inert, and magnetically mediated accreti n can pr ceed nlythr ugh “active” surface layers that extend t a depth f 96 g cm neach side f the disk. This scenari applies b th t a wind-driving disk(Wardle 1997) and t the case where small-scale magnetic fields pr ducean effective visc sity within the disk (Gammie 1996). Galactic c smicrays c uld reach the disk al ng the pen magnetic field lines that thread

´it, but a super-Alfvenic utfl w al ng these field lines w uld tend t ex-clude them. External i nizati n c uld, h wever, als be effected by stellarX-rays (see the chapter by Glassg ld et al., this v lume) as well as by fastparticles accelerated in stellar flares. In additi n, heating by stellar irra-diati n c uld c ntribute t the c llisi nal i nizati n f the surface layers(e.g., D’Alessi et al. 1998).

The entire disk can rec ver an adequate c upling with the magneticfield nce the interi r temperature bec mes high en ugh f r c llisi nali nizati n t be effective. This first ccurs when the temperature increasesab ve 10 K and p tassium is rapidly i nized (e.g., Umebayashi andNakan 1981). F r disks in which magnetic fields d minate the angu-lar m mentum transp rt, it may be p ssible that J ule dissipati n c uldmaintain the requisite degree f i nizati n f r efficient gas–field c upling[ 1; see equati n (20)]. Li (1996) first expl red this p ssibility f r theinner regi ns f wind-driving pr t stellar disks and c ncluded that, f r adisk that is in the ambip lar diffusi n regime n scales 1 AU, a self-c nsistent m del can be c nstructed nly if the accreti n rate is very high( 10 M yr ).

A p ssible mechanism f r rec upling the gas t the field in the vicin-ity f the YSO is the thermal i nizati n instability riginally discussed inthe c ntext f dwarf n vae and m re recently inv ked as a p ssible expla-nati n f FU Ori nis utbursts (e.g., Bell and Lin 1994). In this picture,accreti n in the innerm st disk pr ceeds in a n nsteady fashi n, with a“gate” at 0 25 AU pening every 10 yr r s after the accumulatedc lumn density has bec me large en ugh t trigger the instability. Dur-ing the “high” phase f the instability (which lasts 10 yr and is identi-fied with an utburst), the gas is h t ( 10 K) and alm st c mpletely

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

5 1

8 1

acc

accwind

.

. .


M

. M M

�

�

�

�

�

� �

� �

�

�

oo o o o

o o oo o o o

o o oo oo o oo o o o oo o o o o o

o o oo o o o

o o o oo o o

o o oo o o o o o

o oo o

o o o o o o o oo o o oo

o o oo o

o o o o o o oo o

o o oo o o o

oo o oo o

o o oo o o o o

o o o o oo o o

o o oo o o

o o o o o oo o o

o o o o oo o

o oo o o o o oo

o o oo o o

o o o oo o o o o


i nized, and mass rains in at a rate (1–30) 10 M yr , whereasduring the “l w” phase the temperature and degree f i nizati n declinesharply and the accreti n rate dr ps t (1–30) 10 M yr . In thec ntext f the magnetized disk m del, the increase in the accreti n rate asthe gas bec mes highly i nized can be attributed t the reestablishmentf g d c upling between the field and the matter, which all ws the field

t extract the angular m mentum f the accreting gas. This c uld acc untb th f r the marked increase in and f r the str ng disk utfl w thatacc mpanies it (see secti n II.B). The magnetic rec upling idea may berelevant t these utbursts even if the wind is n t the d minant angularm mentum transp rt mechanism in the disk pr vided that the visc sityhas a magnetic rigin (see the chapter by St ne et al., this v lume). Wen te, h wever, that the relatively large ( 0 1) / rati indicatedin s me f the utburst s urces is c nsistent with the bulk f the disk an-gular m mentum being rem ved by the wind.

At distances f a few stellar radii, the stellar magnetic field c uldbe str ng en ugh t drive utfl ws fr m the disk. Vari us scenari s havebeen c nsidered in this c nnecti n, including individual magnetic l psejecting diamagnetic bl bs thr ugh a magnetic surface drag f rce (Kingand Regev 1994); a steady-state c nfigurati n in which mass is trans-ferred t the star near the c r tati n radius and an utfl w is driven al ngadjacent (but disc nnected fr m the star) field lines (Shu et al. 1994);and time-dependent ejecti n ass ciated with the twisting, expansi n, andsubsequent rec nnecti n f field lines that c nnect the star with the disk(Hayashi et al. 1996; G ds n et al. 1997). Numerical simulati ns arerapidly reaching a stage at which they c uld be utilized t identify therelevant mechanisms and settle many f the utstanding questi ns. Thereare already indicati ns fr m s me f the existing simulati ns that mag-netically channeled accreti n fr m the disk t the star is m st likely tccur when the disk carries a str ng axial magnetic field that rec nnects

with the stellar field at an equat rial x-p int; the resulting field c nfigura-ti n appears t be quasisteady and gives rise t sturdy centrifugally drivenutfl ws al ng pen field lines (Hir se et al. 1997; Miller and St ne 1997).

Stellar field-driven utfl ws are the subject f the chapter by Shu etal., this v lume. This class f m dels is based n the realizati n that stel-lar magnetic field lines can be inflated and pened up thr ugh an inter-acti n with a surr unding disk, and that a centrifugal wind can be drivenut al ng the pened field lines. In these scenari s, the utfl w typicallyriginates near the inner disk radius, where the disk is truncated by the

stellar magnetic stresses. This c ntrasts with the scenari s c nsidered inthis chapter, wherein a disk-driven wind riginates (and can c ntribute tthe disk angular m mentum transp rt) ver a significant range f radii. It isw rth n ting in this c nnecti n that the massive infl ws that characterizeFU Ori nis utbursts are expected t crush the respective stellar magne-t spheres, s the str ng utfl ws that are inferred t riginate fr m the

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

VI. CONCLUSIONS


Acknowledgments

o o oo o

oo o o o o o


o o o oo o o o oo o o o

o o oo o o o

o o o o oo o o o

o

o oo o o o o

o o o o o oo o

o o o o oo o o o


o o o oo o o o o



o o o o oo o o o

o o o o o o o oo o o o o o

o o o oo o o

o o o o o oo o o oo o o o o o

o o o

o o o o oo o

circumstellar disks during these utbursts are unlikely t be driven al ngstellar field lines (Hartmann and Keny n 1996). C upled with the appar-ent inadequacy f thermal pressure and radiative driving, this argumentpr vides str ng supp rt f r the relevance f disk-driven hydr magneticwinds that are n t ass ciated with a stellar magnetic field t the bservedutfl ws fr m FU Ori nis utburst s urces. The ramificati ns f this ar-

gument bec me even str nger if a significant fracti n f the mass accu-mulati n in s lar-type stars ccurs thr ugh such utbursts during the earlyphases f their ev luti n (Hartmann 1997). T be sure, the “distributed”disk-wind m dels discussed in this chapter are meant t apply t YSOsin general and n t just when they underg an utburst, but nly duringan FU Ori nis utburst d es the disk bec me sufficiently lumin us thatan unambigu us bservati nal signature f an extended disk wind can bebtained.

Centrifugally driven winds fr m disks threaded by pen magnetic fieldlines pr vide the m st efficient way f tapping the gravitati nal p tentialenergy liberated in the accreti n pr cess t p wer an utfl w. The fact thatsuch winds “aut matically” carry away angular m mentum and thus fa-cilitate (and p ssibly even c ntr l) the accreti n pr cess makes them anattractive explanati n f r the ubiquity f jets in YSOs and in a variety fther accreting astr n mical bjects. One f the key findings f recent nu-

merical simulati ns f MHD winds fr m disks is that such utfl ws areindeed easy t pr duce and maintain under a variety f surface b und-ary c nditi ns. These simulati ns have als verified the ability f suchutfl ws t self-c llimate and give rise t narr w jets, as well as a vari-

ety f ther characteristics that are c nsistent with YSO bservati ns. Inthe case f pr t stellar disks, the presence f pen field lines is a natu-ral c nsequence f their f rmati n fr m the c llapse f magnetically sup-p rted m lecular cl ud c res. Alth ugh a stellar magnetic field that threadsthe disk c uld in principle als play a similar r le, this p ssibility is un-likely t apply t the str ng utfl ws ass ciated with FU Ori nis utbursts.(M re generally, it is w rth n ting that, in c ntrast t disk field-driven ut-fl ws, a scenari that inv kes a stellar field may n t represent a universalmechanism, because many c smic jet s urces are ass ciated with a blackh le that d es n t pr vide an anch r f r a central magnetic field.) Muchpr gress has als been achieved in c nstructing gl bal MHD disk/windm dels, but the full elucidati n f this picture and f its c nsequences f rstar f rmati n remains a challenge f r the future.

We thank Eric Blackman, Vincent Mannings,Rachid Ouyed, and the an nym us referee f r helpful c mments n themanuscript. This w rk was supp rted in part by NASA grant NAG 5-3687

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

REFERENCES

o

o o o oo o oo o oo o o o o o o

o oo o o

o o o o

o o o o

oo o o o o

o o o oo o o

o o o o oo o o o

o o o o o oo o o o

o o

o o o oo o o o

oo o o o

o o oo o o

o o oo

o o o o o o

o oo o o

o o o

o o oo o

o o o o o oo o o o o o o o o


Appl, S., and Camenzind, M. 1992. The stability f current carrying jets.256:354–370.

Appl, S., and Camenzind, M. 1993. The structure f MHD jets: A s luti n t then n-linear Grad-Shafran v equati n. 274:699–706.

Bacci tti, F., and Chiuderi, C. 1992. Axisymmetric magnet hydr dynamic equa-ti ns: Exact s luti ns f r stati nary inc mpressible fl ws.4:35–43.

Balbus, S. A., and Hawley, J. F. 1991. A p werful l cal shear instability in weaklymagnetized disks. I. Linear analysis. II. N nlinear ev luti n.376: 214–233.

Bell, A. R., and Lucek, S. G. 1995. Magnet hydr dynamic jet f rmati n.277:1327–1340.

Bell, K. R. 1994. Rec nciling accreti n scenari s with inner h les: The ther-mal instability and the 2 m gap. In

´ ´, ASP C nf. Ser. 62, ed. P. S. The, M. R. Perez, and E. P. J.van den Heuvel (San Francisc : Astr n mical S ciety f the Pacific), pp.215–218.

Bell, K. R., and Lin, D. N. C. 1994. Using FU Ori nis utbursts t c nstrain self-regulated pr t stellar disk m dels. 427:987–1004.

Blandf rd, R. D., and Payne, D. G. 1982. Hydr magnetic fl ws fr m accreti ndiscs and the pr ducti n f radi jets. 199:883–903.

´B ntemps, S., Andre, P., Terebey, S., and Cabrit, S. 1996. Ev luti n f utfl wactivity ar und l w-mass embedded y ung stellar bjects.311:858–872.

Burr ws, C. J., Stapelfeldt, K. R., Wats n, A. M., Krist, J. E., Ballester, G. E.,Clarke, J. T., Crisp, D., Gallagher, J. S., III, Griffiths, R. E., Hester, J. J.,H essel, J. G., H ltzman, J. A., M uld, J. R., Sc wen, P. A., Trauger, J. T.,and Westphal, J. A. 1996. Hubble Space Telesc pe bservati ns f the diskand jet f HH 30. 473:437–451.

´Cabrit, S., and Andre, P. 1991. An bservati nal c nnecti n between circumstellardisk mass and m lecular utfl ws. 379:L25–L28.

Cabrit, S., Edwards, S., Str m, S. E., and Str m, K. M. 1990. F rbidden line emis-si n and infrared excesses in T Tauri stars—Evidence f r accreti n-drivenmass l ss? 354:687–700.

Cabrit, S., Raga, A. C., and Gueth, F. 1997. M dels f bip lar m lecular utfl ws.In , IAU Symp. 182, ed.B. Reipurth and C. Bert ut (D rdrecht: Kluwer), pp. 163–180.

Calvet, N., Hartmann, L., and Keny n, S. J. 1993. Mass l ss fr m pre-main-sequence accreti n disks. I. The accelerating wind f FU Ori nis.

402:623–634.Ca , X., and Spruit, H. C. 1994. Magnetically driven wind fr m an accreti n disk

with l w-inclinati n field lines. 287:80–86.¨Ci lek, G. E., and K nigl, A. 1998. Dynamical c llapse f n nr tating magnetic

m lecular cl ud c res: Ev luti n thr ugh p int-mass f rmati n.504:257–279.

Astron.Astrophys.

Astron. Astrophys.

Phys. Fluids B

Astrophys. J.

Mon.Not. Roy. Astron. Soc.

The Nature and E olution of HerbigAe/Be Stars

Astrophys. J.

Mon. Not. Roy. Astron. Soc.

Astron. Astrophys.

Astrophys. J.

Astrophys. J. Lett.

Astrophys. J.

Herbig-Haro Flows and the Birth of Low Mass Stars

Astrophys.J.

Astron. Astrophys.

Astrophys.J.

v

o oo o

(A. K.) and by an perating grant fr m the Natural Science and Engineer-ing Research C uncil f Canada (R. P.).

�

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

o o oo

o o o o o o

o o o o oo o

o o o o

o o o o o

o ooo o o o


o o oo o

o

o oo o

o o o o oo o

o o o

o o

o o

o oo o o

o oo o

o

o o o oo

oo o o oo o o

o o oo

oo o o o

o oo o o o

o o o o oo o o o

o o oo o


Clarke, D. A., N rman, M. L., and Burns, J. O. 1986. Numerical simulati ns f amagnetically c nfined jet. 311:L63–L67.

C nt p ul s, J. 1995. A simple type f magnetically driven jets: An astr physicalplasma gun. 450:616–627.

C nt p ul s, J., and L velace, R. V. E. 1994. Magnetically driven jets and winds:Exact s luti ns. 429:139–152.

C rc ran, M., and Ray, T. 1997. F rbidden emissi n lines in Herbig Ae/Be stars.321:189–201.

C rc ran, M., and Ray, T. 1998. Wind diagn stics and c rrelati ns with the near-infrared excess in Herbig Ae/Be stars. 331:147–61.

´Crutcher, R. M., Tr land, T. H., G dman, A. A., Heiles, C., Kazes, I., and Myers,P. C. 1993. OH Zeeman bservati ns f dark cl uds. 407:175–184.

Crutcher, R. M., M usch vias, T. C., Tr land, T. H., and Ci lek, G. E. 1994. Struc-ture and ev luti n f magnetically supp rted m lecular cl uds: Evidence f rambip lar diffusi n in the Barnard 1 cl ud. 427:839–847.

Crutcher, R. M., R berts, D. A., Mehringer, D. M., and Tr land, T. H. 1996. H IZeeman measurements f the magnetic field in Sagittarius B2.

462:L79–L82.Curry, C., Pudritz, R. E., and Sutherland, P. G. 1994. On the gl bal stability f

magnetized accreti n disks. I. Axisymmetric m des. 434:206–220.

´D’Alessi , P., Cant , J., Calvet, N., and Lizan , S. 1998. Accreti n disks ar undy ung bjects. I. The detailed vertical structure. 500:411–427.

¨Eisl ffel, J, and Mundt, R. 1997. Parsec-scale jets fr m y ung stars.114:280–287.

Ferreira, J. 1997. Magnetically-driven jets fr m Keplerian accreti n discs.319:340–359.

Ferreira, J., and Pelletier, G. 1993 . Magnetized accreti n-ejecti n structures. I.General statements. 276:625–636.

Ferreira, J., and Pelletier, G. 1993 . Magnetized accreti n-ejecti n structures. II.Magnetic channeling ar und c mpact bjects. 276:637–647.

Ferreira, J., and Pelletier, G. 1995. Magnetized accreti n-ejecti n structures. III.Stellar and extragalactic jets as weakly dissipative disk utfl ws.

295:807–832.Gammie, C. F. 1996. Layered accreti n in T Tauri disks. 457:355–

362.G mez, M., Whitney, B. A., and Keny n, S. J. 1997. A survey f ptical and

near-infrared jets in Taurus embedded s urces. 114:1138–1153.¨G ds n, A. P., Winglee, R. M., and B hm, K.-H. 1997. Time-dependent accreti n

by magnetic y ung stellar bjects as a launching mechanism f r stellar jets.489:199–209.

Greaves, J. S., and H lland, W. S. 1998. Twisted magnetic field lines ar und pr -t stars. 333:L23–L26.

Greaves, J. S., Murray, A. G., and H lland, W. S. 1994. Investigating the mag-netic field structure ar und star f rmati n c res.284:L19–L22.

Greaves, J. S., H lland, W. S., and Murray, A. G. 1995. Magnetic field c mpres-si n in the M n R2 cl ud c re. 297:L49–L52.

Hartigan, P., M rse, J., and Raym nd, J. 1994. Mass-l ss rates, i nizati n frac-ti ns, sh ck vel cities, and magnetic fields f stellar jets.136:124–143.

Hartigan, P., Edwards, S., and Ghand ur, L. 1995. Disk accreti n and mass l ssfr m y ung stars. 452:736–768.

Astrophys. J. Lett.

Astrophys. J.

Astrophys. J.

Astron. Astrophys.

Astron. Astrophys.

Astrophys. J.

Astrophys. J.

Astrophys. J.Lett.

Astrophys. J.

Astrophys. J.Astron. J.

Astron.Astrophys.

aAstron. Astrophys.

bAstron. Astrophys.

Astron. As-trophys.

Astrophys. J.

Astron. J.

Astrophys. J.

Astron. Astrophys. Lett.



Astrophys. J.

Astrophys. J.

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

o o o o

o oo o o

o o o o

o oo o o

o o oo o o o o

o

o o o o

o o o oo o o o o

o oo o o

o o oo

o o o o oo o

oo

oo o o o o o

o o o o

o

o o o o

o o o o o o oo

o o o oo o

o o o o o o o o o

o o o oo o o

o o o oo

o o o

o o o o oo

o o oo o

o o o o


Hartmann, L. 1997. The bservati nal evidence f r accreti n. In, IAU Symp. 182, ed. B. Reipurth and

C. Bert ut (D rdrecht: Kluwer), pp. 391–405.Hartmann, L., and Calvet, N. 1995. Observati nal c nstraints n FU Ori winds.

109:1846–1855.Hartmann, L., and Keny n, S. J. 1996. The FU Ori nis phen men n.

34:207–240.Hartmann, L., Keny n, S. J., and Calvet, N. 1993. The excess infrared emissi n

f Herbig Ae/Be stars: Disks r envel pes? 407:219–231.Hayashi, M. R., Shibata, K., and Matsum t , R. 1996. X-ray flares and mass ut-

fl ws driven by magnetic interacti n between a pr t star and its surr undingdisk. 468:L37–L40.

Heinemann, M., and Olbert, S. 1978. Axisymmetric ideal MHD stellar wind fl w.83:2457–2460.

Heyvaerts, J., and N rman, C. A. 1989. The c llimati n f magnetized winds.347:1055–1081.

Heyvaerts, J., and N rman, C. A. 1997. Asympt tic structure f r tating MHDwinds and its relati n t wind b undary c nditi ns. In

, IAU Symp. 182, ed. B. Reipurth and C.Bert ut (D rdrecht: Kluwer), pp. 275–290.

Hildebrand, R. H., D ts n, J. L., D well, C. D., Platt, S. R., Schleuning, D.,Davids n, J. A., and N vak, G. 1995. Far-infrared p larimetry. In

, ASP C nf. Ser. 73, ed.M. R. Haas, J. A. Davids n, and E. F. Ericks n (San Francisc : Astr n mi-cal S ciety f the Pacific), pp. 97–104.

Hillenbrand, L. A., Str m, S. E., Vrba, F. J., and Keene, J. 1992. Herbig Ae/Bestars—intermediate-mass stars surr unded by massive circumstellar accre-ti n disks. 397:613–643.

Hir se, S., Uchida, Y., Shibata, K., and Matsum t , R. 1997. Disk accreti n nt amagnetized y ung star and ass ciated jet f rmati n.49:193–205.

King, A. R., and Regev, O. 1994. Spin rates and mass l ss in accreting T Tauristars. 268:L69–L73.

¨K nigl, A. 1989. Self-similar m dels f magnetized accreti n disks.342:208–223.

¨K nigl, A. 1997. Magnetized accreti n disks and the rigin f bip lar utfl ws. In, ASP C nf. Ser. 121, ed. D. T.

Wickramasinghe, G. V. Bicknell, and L. Ferrari (San Francisc : Astr n m-ical S ciety f the Pacific), pp. 551–560.

¨K nigl, A. 1999. The ry f bip lar utfl ws fr m high-mass y ung stellar bjects.43:67–77.

¨K nigl, A., and Ruden, S. P. 1993. Origin f utfl ws and winds. In, ed. E. H. Levy and J. I. Lunine (Tucs n: University f Ariz na

Press), pp. 641–688.¨K nigl, A., and Wardle, M. 1996. A c mment n the stability f magnetic wind-

driving accreti n discs. 279:L61–L64.¨K ssel, D., Muller, E., and Hillebrandt, W. 1990. Numerical simulati ns f axially¨

symmetric magnetized jets. 229:401–415.Lada, C. J. 1985. C ld utfl ws, energetic winds, and enigmatic jets ar und y ung

stellar bjects. 23:267–317.Lery, T., Heyvaerts, J., Appl, S., and N rman, C. A. 1998. Outfl ws fr m magnetic

r tat rs. I. Inner structure. 337:603–624.Levreault, R. M. 1988. M lecular utfl ws and mass l ss in the pre-main-

sequence stars. 330:897–910.

Herbig-HaroFlows and the Birth of Low Mass Stars

Astron. J.Ann. Re .

Astron. Astrophys.

Astrophys. J.

Astrophys. J. Lett.

J. Geophys. Res.

Astrophys. J.

Herbig-Haro Flowsand the Birth of Low Mass Stars

AirborneAstronomy Symposium on the Galactic Ecosystem

Astrophys. J.

Pub. Astron. Soc. Japan

Mon. Not. Roy. Astron. Soc.Astrophys. J.

Accretion Phenomena and Related Outflows

New Astron. Re .Protostars and

Planets III


Astron. Astrophys.

Ann. Re . Astron. Astrophys.

Astron. Astrophys.

Astrophys. J.

v

v

v

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

o o oo

o oo o o o o

oo o o o o

o o o o o

oo o

o o o oo o o

o o oo

o o o o oo o

o o o o oo

o o oo o o o o o o

o o o o

ooo o o

o o oo o o

o o

o

o o o o oo o o

o o o o

o o o oo o o

oo o o

o o o oo

o o o o o

o o o o oo

oo

o o oo o o o

o o oo o o o o


Levy, E. H., and S nnett, C. P. 1978. Mete rite magnetism and early s lar systemmagnetic fields. In , ed. T. Gehrels (Tucs n: Univer-sity f Ariz na Press), pp. 516–532.

Li, Z.-Y. 1995. Magnet hydr dynamic disk-wind c nnecti n: Self-similar s lu-ti ns. 444:848–860.

Li, Z.-Y. 1996. Magnet hydr dynamic disk-wind c nnecti n: Magnet centrifu-gal winds fr m ambip lar diffusi n-d minated accreti n disks.465:855–868.

Lind, K. R., Payne, D. G., Meier, D. L., and Blandf rd, R. D. 1989. Numericalsimulati ns f magnetized jets. 344:89–103.

L velace, R. V. E., R man va, M. M., and Newman, W. I. 1994. Impl sive accre-ti n and utbursts f active galactic nuclei. 437:136–143.

Lub w, S. H., Papal iz u, J. C. B., and Pringle, J. 1994. Magnetic field draggingin accreti n discs. 267:235–240.

Lynden-Bell, D., and B ily, C. 1994. Self-similar s luti ns up t flashp int inhighly w und magnet statics. 267:146–152.

Mass n, C. R., and Chernin, L. M. 1993. Pr perties f jet-driven m lecular ut-fl ws. 414:230–241.

Matsum t , R., Uchida, Y., Hir se, S., Shibata, K., Hayashi, M. R., Ferrari, A.,B d , G., and N rman, C. 1996. Radi jets and the f rmati n f active galax-ies: Accreti n avalanches n the t rus by the effect f a large-scale magneticfield. 461:115–126.

McKee, C. F., Zweibel, E. G., G dman, A. A., and Heiles, C. 1993. Magneticfields in star-f rming regi ns: The ry. In , ed. E. H.Levy and J. I. Lunine (Tucs n: University f Ariz na Press), pp. 327–366.

Meier, D., Edgingt n, S., G d n, P., Payne, D., and Lind, K. 1997. A magneticswitch that determines the speed f astr physical jets. 388:350–352.

Mestel, L. 1968. Magnetic braking by a stellar wind.138:359–391.

Michel, F. C. 1969. Relativistic stellar-wind t rques. 158:727–738.

Miller, K. A., and St ne, J. M. 1997. Magnet hydr dynamic simulati ns f stellarmagnet sphere–accreti n disk interacti n. 489:890–902.

ˇ´Mir shnichenk , A., Ivezic, Z., and Elitzur, M. 1997. On pr t stellar disks in Her-big Ae/Be stars. 475:L41–L44.

M usch vias, T. C. 1991. C smic magnetism and the basic physics f the earlystages f star f rmati n. In

, ed. C. J. Lada and N. D. Kylafis (D rdrecht: Kluwer), pp. 61–122.Mundt, R., and Ray, T. M. 1994. Optical utfl ws fr m Herbig Ae/Be stars and

ther high lumin sity y ung stellar bjects. In´ ´, ASP C nf. Ser. 62, ed. P. S. The, M. R. Perez, and

E. P. J. van den Heuvel (San Francisc : Astr n mical S ciety f the Pacific),pp. 237–252.

Ogilvie, G. I., and Livi , M. 1998. On the difficulty f launching an utfl w fr man accreti n disk. 499:329–339.

Ostriker, E. 1997. Self-similar magnet centrifugal disk winds with cylindricalasympt tics. 486:291–306.

Ouyed, R., and Pudritz, R. E. 1997 . Numerical simulati ns f astr physical jetsfr m Keplerian accreti n disks. I. Stati nary m dels. 482:712–732.

Ouyed, R., and Pudritz, R. E. 1997 . Numerical simulati ns f astr physical jetsfr m Keplerian accreti n disks. II. Epis dic utfl ws. 484:794–809.

Protostars and Planets

Astrophys. J.

Astrophys. J.

Astrophys. J.

Astrophys. J.



Astrophys. J.

Astrophys. J.

Protostars and Planets III

Nature


Astrophys. J.

Astrophys. J.

Astrophys. J. Lett.

The Physics of Star Formation and Early StellarE olution

The Nature and E olutionof Herbig Ae/Be Stars

Astrophys. J.

Astrophys. J.a

Astrophys. J.

bAstrophys. J.

v

v

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

o o oo o o o

o o o oo o

o oo

o oo o

o o oo

o o o oo

o oo o o

oo o

o o o o o o o

o o o o o oo o o o

oo o o o

oo o

o o oo o o

o o o o oo o o o o o o oo o o

o o o o o o oo o o o o o

o o o o oo

o o oo o o

o o oo o o o o o o

o oo

o o o oo

oo o o o o

o o o o

o o

o o o o oo o


Ouyed, R., and Pudritz, R. E. 1999. Numerical simulati ns f astr physical jetsfr m Keplerian accreti n disks. III. The effects f mass l ading.

in press.Ouyed, R., Pudritz, R. E., and St ne, J. M. 1997. Epis dic jets fr m black h les

and pr t stars. 385:409–414.Pelletier, G., and Pudritz, R. E. 1992. Hydr magnetic disk winds in y ung stellar

bjects and active galactic nuclei. 394:117–138.Pezzut , S., Strafella, F., and L renzetti, D. 1997. On the circumstellar matter

distributi n ar und Herbig Ae/Be stars. 485:290–307.Pudritz, R. E., and N rman, C. A. 1983. Centrifugally driven winds fr m c n-

tracting m lecular disks. 274:677–697.Pudritz, R. E., and Ouyed, R. 1997. Numerical simulati ns f jets fr m accreti n

disks. In , IAU Symp -sium 182, ed. B. Reipurth and C. Bert ut (D rdrecht: Kluwer), pp. 259–274.

Pudritz, R. E., Pelletier, G., and G mez de Castr , A. I. 1991. The physics f diskwinds. In , ed.C. J. Lada and N. D. Kylafis (D rdrecht: Kluwer), pp. 539–564.

Pudritz, R. E., Wils n, C. D., Carlstr m, J. E., Lay, O. P., Hills, R. E., and Ward-Th mps n, D. 1996. Accreti n disks ar und class 0 pr t stars: The case fVLA 1623. 470:L123–L126.

Ray, T., Muxl w, T. W. B., Ax n, D. J., Br wn, A., C rc ran, D., Dys n, J., andMundt, R. 1997. Large-scale magnetic fields in the utfl w fr m the y ungstellar bject T Tauri S. 385:415–417.

Reipurth, B. 1991. Observati ns f Herbig-Har bjects. In, ed. B. Reipurth (Munich: Eur pean

S uthern Observat ry), pp. 247–279.Reyes-Ruiz, M., and Stepinski, T. F. 1996. Axisymmetric tw -dimensi nal c m-

putati n f magnetic field dragging in accreti n disks. 459:653–665.

R man va, M. M., Ustyug va, G. V., K ld ba, A. V., Chechetkin, V. M., andL velace, R. V. E. 1997. F rmati n f stati nary magnet hydr dynamic ut-fl ws fr m a disk by time-dependent simulati ns. 482:708–711.

Sauty, C., and Tsingan s, K. 1994. N nradial and n np lytr pic astr physical ut-fl ws. III. A criteri n f r the transiti n fr m jets t winds.287:893–926.

Schatzman, E. 1962. A the ry f the r le f magnetic activity during star f rma-ti n. 25:18–29.

Schleuning, D. A. 1998. Far-infrared and submillimeter p larizati n f OMC-1:Evidence f r magnetically regulated star f rmati n. 493:811–825.

Shibata, K., and Uchida, Y. 1986. A magnet hydr dynamical mechanism f r thef rmati n f astr physical jets. II. Dynamical pr cesses in the accreti n fmagnetized mass in r tati n. 38:631–660.

Shu, F. H., Najita, J., Ostriker, E., Wilkin, F., Ruden, S., and Lizan , S. 1994. Mag-net centrifugally driven fl ws fr m y ung stars and disks. I. A generalizedm del. 429:781–796.

Skinner, S. L., Br wn, A., and Stewart, R. T. 1993. A high-sensitivity surveyf radi c ntinuum emissi n fr m Herbig Ae/Be stars.

87:217–265.Spruit, H. C. 1996. Magnet hydr dynamic jets and winds fr m accreti n disks.

In NATO ASI Ser. C. 477, ed.R. A. M. J. Wijers, M. B. Davies, and C. A. T ut (D rdrecht: Kluwer), pp.249–286.

Spruit, H. C., F glizz , T., and Stehle, R. 1997. C llimati n f magnetically drivenjets fr m accreti n discs. 288:333–342.

Mon. Not.Roy. Astron. Soc.,

Nature

Astrophys. J.

Astrophys. J.

Astrophys. J.

Herbig-Haro Flows and the Birth of Low Mass Stars

The Physics of Star Formation and Early Stellar E olution

Astrophys. J. Lett.

NatureLow Mass Star For-

mation and Pre–Main Sequence Objects

Astrophys. J.

Astrophys. J.

Astron. Astrophys.

Ann. Astrophys.

Astrophys. J.


Astrophys. J.

Astrophys. J. Suppl.

E olutionary Processes in Binary Stars,


v

v

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

o o o o o


o o oo o o o

oo o



o o oo o

o o o o oo o o o o o o o

oo o oo

o o o o oo

o o o o oo o o o

o o o


Stepinski, T. F. 1992. Generati n f dynam magnetic fields in the prim rdial s larnebula. 97:130–141.

St ne, J. M., and N rman, M. L. 1992. ZEUS-2D: A radiati n magnet hydr dy-namics c de f r astr physical fl ws in tw space dimensi ns. II. The magne-t hydr dynamic alg rithms and tests. 80:791–818.

St ne, J. M., and N rman, M. L. 1994. Numerical simulati ns f magnetic accre-ti n disks. 433:746–756.

T ut, C. A., and Pringle, J. E. 1996. Can a disc dynam generate large-scale mag-netic fields? 281:219–225.

Tsingan s, K., and Truss ni, E. 1990. Analytic studies f c llimated winds. I.T p l gies f 2-D helic idal hydr dynamic s luti ns.231:270–276.

Uchida, Y., and Shibata, K. 1985. A magnet hydr dynamic mechanism f r thef rmati n f astr physical jets. I. Dynamical effects f the relaxati n f n n-linear magnetic twists. 37:31–46.

Umebayashi, T., and Nakan , T. 1981. Fluxes f energetic particles and the i n-izati n rate in very dense interstellar cl uds. 33:617–635.

Ustyug va, G. V., K ld ba, A. V., R man va, M. M., Chechetkin, V. M., andL velace, R. V. E. 1995. Magnet hydr dynamic simulati ns f utfl ws fr maccreti n disks. 439:L39–L42.

Wardle, M. 1997. Magnetically driven winds fr m pr t stellar disks. In, ASP C nf. Ser. 121, ed. D. T. Wickrama-

singhe, G. V. Bicknell, and L. Ferrari (San Francisc : Astr n mical S cietyf the Pacific), pp. 561–565.

¨Wardle, M., and K nigl, A. 1993. The structure f pr t stellar accreti n disks andthe rigin f bip lar fl ws. 410:218–238.

Weber, E. J., and Davis, L. 1967. The angular m mentum f the s lar wind.148:217–227.

Icarus

Astrophys. J. Suppl.

Astrophys. J.


Astron. Astrophys.



Astrophys. J. Lett.Accretion

Phenomena and Related Outflows

Astrophys. J.As-

trophys. J.

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

DR.RUPN

ATHJI(

DR.R

UPAK

NATH )

dr.rupnathji( dr.rupak nath ) · ooo m o o o o 1 1 bl 6 3 bl 1 34 10 8 1 bl 2 bl 3 ii....

Documents