Turbulence-driven Polar Winds from T Tauri Stars Energized by Magnetospheric Accretion S. R....

Turbulence-driven Polar Winds from T Tauri Stars Energized by Magnetospheric Accretion

S. R. Cranmer, January 28, 2008SSP Seminar, Harvard-Smithsonian CfA

Turbulence-driven Polar Winds fromT Tauri Stars . . .

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

. . . Energized by Magnetospheric Accretion



Turbulence-driven Polar Winds fromT Tauri Stars . . .

Steven R. CranmerHarvard-Smithsonian Center for Astrophysics

. . . Energized by Magnetospheric Accretion

Outline:

1. Background: T Tauri accretion and outflows

2. Driving a wind:

3. Results: Mwind > 10–9 M/year !

• convection → coronal heating• accretion-stream impacts → waves

.~



Evolutionary overview

• Kelvin-Helmholz contraction: ISM cloud fragment becomes a protostar; gravitational energy converted to heat.

• Hayashi track: protostar reaches approx. hydrostatic equilibrium, but slower gravitational contraction continues. Observed as the T Tauri phase.

• Henyey track: Tcore reaches ~107 K and hydrogen burning dominates; some accretion and gravitational contraction remain, but both slow to a halt at ZAMS.



Pre-Main-Sequence accretion phases

Feigelson & Montmerle

(1999)

M. Burton (UNSW)



Accretion geometry

(Matt & Pudritz 2005, 2007)

(Romanova et al. 2007)

• Classical T Tauri stars exhibit signatures of disk accretion (outer parts), “magnetospheric accretion streams” (inner parts), and various (polar?) outflows.

• Nearly every observational diagnostic varies in time, sometimes with stellar rotation, but often more irregularly. The accretion flow is inhomogeneous . . .



Accretion rate vs. age

Hartigan et al. (1995); Hartmann et al. (1998)

~ t –1.5

• Macc obtained from accretion luminosity (excess continuum > photospheric SED)

all T Tauri stars

“solar mass” (4000 < Teff < 4500 K)



Mass loss rates

• Mwind is obtained from signatures of blueshifted opacity (~few 100 km/s).

For example . . .

• Forbidden emission lines [O I], [Si II], [N II], [Fe II] (Hartigan et al. 1995)

• P Cygni absorption trough of He I 10830 (chromospheric diagnostic):

TW Hya:

Batalha et al. (2002)

Dupree et al. (2005)

Hartigan et al. (1995)

M acc



What kind of outflow is it?

• YSOs (Class I & II) show jets that remain collimated far away (AU → pc!) from the central star.

• However, EUV emission lines and He I 10830 P Cygni profiles indicate the blueshifted outflow is close to the star.

• Stellar winds & disk winds may co-exist.

(Ferreira et al. 2006)



Angular momentum removal

• Many accreting T Tauri stars are slowly rotating, despite the fact that disk accretion adds angular momentum to the star (e.g., Bouvier et al. 1993; Edwards et al. 1993).

• How is angular momentum carried away?

CTTS

(accreting)

WTTS

(non-accreting)

Rot. Period (days)

By field lines that thread the disk? (“disk locking”) This would imply that magnetic reconnections (and X-rays!) scale with accretion rate. No...

By CME-like ejections from the tangled field in the disk?

By a stellar wind! Matt & Pudritz (2005, 2007) say Mwind ~ 0.1 Macc can do the job.

L. Hartmann, lecture notes



Driving a stellar wind

• Gravity must be counteracted above the photosphere (not below) by some continuously operating physical mechanism . . .

Gas pressure: needs T ~ 106 K (“coronal heating”)

Radiation pressure: possibly important when L* > 100 L

Wave pressure: can produce outward acceleration in a time-averaged sense

Magnetic buoyancy: plasmoids can be “pinched” like melon seeds and carry along some of the surrounding material . . .

• ion opacity? (Teff > 15,000 K)

• free electron (Thomson) opacity? (goes as 1/r2 ; needs to be supplemented)

• dust opacity? (Teff < 3,500 K)

~

~



The solar wind: very brief history• Mariner 2 (1962): first direct confirmation of continuous supersonic solar wind,

validating Parker’s (1958) model of a gas-pressure driven wind.

• Helios probed in to 0.3 AU, Voyager continues past 100+ AU.

• Ulysses (1990s) left the ecliptic; provided 3D view of the wind’s connection to the Sun’s magnetic geometry.

• SOHO gave us new views of “source regions” of solar wind and the physical processes that accelerate it . . .



The solar wind mass loss rate• The sphere-averaged “M” isn’t usually considered by solar physicists.

• Wang (1998, CS10) used empirical relationships between B-field, wind speed, and density to reconstruct M over two solar cycles.

ACE (in ecliptic)



What sets the Sun’s mass loss?

• Coronal heating must be ultimately responsible for the solar wind.

• A fraction of the “coronal heating” is channeled downward by conduction.

• Hammer (1982) & Withbroe (1988) suggested a balance between conduction (downward), enthalpy (upward), and radiation losses (local) that sets mass flux:

heat conduction

radiation losses

— ρvkT52



A recent “kitchen sink” model• Sub-photospheric convection generates acoustic & magnetic waves that reach the

photosphere. Their power spectra are observable.

• Photospheric flux tubes are shaken (mainly horizontally) by these waves.

• Alfvén waves propagate along the field, and partly reflect back down (non-WKB).

• Nonlinear couplings allow a turbulent cascade to develop, terminated by damping.

(Cranmer & van Ballegooijen 2005; Cranmer et al. 2007)



Conservation equations solved by ZEPHYR (1/2)

(for more information, see Cranmer et al. 2007)• The only “free parameters:” wave properties at photosphere, and background Br(r)

mass:

momentum:

internal energy:

A(r)



Conservation equations solved by ZEPHYR (2/2)

• Energy density & flux:

• Static medium:

• Non-zero wind speed (wave action conservation):

• Damping is included via “phenomenological” models of MHD turbulence (for Alfven waves), and shock formation & heat conduction (for acoustic waves).

A(r)

• Waves/turbulence: modeled “statistically” rather than by following... Σ ei(ωt – kz)



Results: coronal heating and solar M

T (K)

reflection coefficient

Goldstein et al.(1996)

Ulysses SWOOPS



But how do T Tauri stars generate mass loss rates 1000 to a million

times solar?



Ansatz: accretion streams make more waves



More solar precedents

• Solar flares and coronal mass ejections (CMEs) can set off wave-like “tsunamis” on the solar surface . . .

• Moreton waves propagate mainly as chromospheric Hα variations, at speeds of 400 to 2000 km/s and last for only ~10 min. Fast-mode MHD shock?

• “EIT waves” show up in EUV images, are slower (25–450 km/s), and can traverse the whole Sun over a few hours. Slow-mode MHD soliton??

NSO press release (Dec. 7, 2006) Wu et al. (2001)



Properties of accretion streams

• Königl (1991) showed how inner-disk edge scales with stellar parameters:

• Dipole geometry gives δ (fraction of stellar surface filled by columns) and rblob.

• Assume ballistic (free-fall) velocity to compute ram-pressure balance; gives ρshock / ρphoto.

The streams are inhomogeneous:

• Need to assume “contrast:” ρblob / <ρ> ≈ 3.

• This allows us to compute:N (number of flux tubes impacting the star)Δt (inter-blob intermittency time)

L. Hartmann, lecture notes



Wave “yield” from blob impacts

• Scheurwater & Kuijpers (1988) predicted the fraction of a blob’s kinetic energy that is released in the form of wave energy (mainly Alfvén, some fast-mode).

• The power emitted by a stream of blobs is the wave energy EA divided by Δt.

• The wave flux (into “walls”) is given by the power divided by the wall area.

• The total wave flux at a given “target point” (i.e., the pole) is N times the flux of one impact.

2rblob

x

• The Alfvén wave amplitude at the photosphere must be scaled from the amplitude at the shock impact, using ρshock versus ρphoto.

• We assume that “acoustic” waves are also generated at the base with the ~same energy density as the resulting Alfvén waves. (see Stein-Lighthill convection!)



The Sun in time . . .• Eggleston’s STARS code was run for 1 M* evolution before and after ZAMS . . .

R*

rinner

rblob

photosph. scale ht.

δ

ρshock

ρphoto



Modifications to the solar ZEPHYR models

• Age-dependent R*, Teff , ρphoto

• Resulting Alfvén wave amplitude at the photosphere, versus age

• Photospheric acoustic wave amplitude is scaled similarly to Alfvén waves.

• MHD turbulence “correlation length” is assumed to scale with the surface granule size, which in turn is assumed to scale with the vertical scale height.

• Photospheric magnetic field strength is kept fixed (~1500 G), but radial dependence in the lower atmosphere is “stretched” with the scale height.

• Because extended chromospheres may be optically thick, we modify the radiative cooling to account for Mg II opacity (Hartmann & Macgregor 1980).

v┴

photosph. sound speed



Results: mass flux

Macc

Mwind



Results: speed, temperature, momentum flux

Vesc

ucrit

HH

phot. cs

phot. Teff

Macc u∞



The “cold wave-driven wind” limit

• When the plasma becomes massive enough, radiative cooling (~ρ2) becomes more efficient throughout the wind:

• Why then isn’t a corona 109 K? Downward heat conduction smears out the “peaks,” and the solar wind also “carries” away some kinetic energy. Conduction also steepens the 105 K transition region to be as thin as it is.

• The high-density wind becomes an extended chromosphere supported by wave pressure.

• For this case, Holzer et al. (1983) showed the energy equation is ~irrelevant in determining mass flux! A simple analytic model (of the momentum equation) suffices.



Results: mass flux

Macc

Mwind



Results: speed, temperature, momentum flux

Vesc

ucrit

HH

phot. cs

phot. Teff

Macc u∞



Preliminary Conclusions

For more information: http://www.cfa.harvard.edu/~scranmer/

• Magnetospheric accretion streams seem to be energetic enough to drive waves that can greatly enhance polar wind mass loss rates.

• Is this enough to solve the T Tauri angular momentum problem?

• More realistic models must include: (1) more complex magnetic fields, and (2) the effects of more “active” convection . . .

B. Brownet al. (2007)



extra slides



Disk accretion is variable! (L. Hartmann)



Why magnetospheric accretion? (L. Hartmann)

• “Hole” in inner disk (Bertout, Basri, Bouvier 1988)

• Periodic modulation of light from “hot spots” (BBB)

• High-velocity infall (Calvet, Edwards, Hartigan, Hartmann)

• Stellar spindown through “disk locking” (Königl 1991) (?)

• Stellar magnetic fields ~ several kG, strong enough to disrupt disks (e.g., Johns-Krull, Valenti, & Koresko 1999)



Cool-star winds: “traditional” diagnostics

(Bernat 1976)

• Optical/UV spectroscopy: simple blueshifts or full “P Cygni” profiles

• IR continuum: circumstellar dust causes SED excess

• Molecular lines (mm, sub-mm): CO, OH maser

(van den Oord & Doyle 1997)

wind

star

• Radio: free-free emission from (partially ionized?) components of the wind

• Continuum methods need V from another diagnostic to get mass loss rate.

•

• Clumping?



Multi-line spectroscopy• 1990s: more self-consistent treatments of radiative transfer AND better data

(GHRS, FUSE, high-spectral-res ground-based) led to better stellar wind diagnostic techniques!

• A nice example: He I 10830 Å for TW Hya (pole-on T Tauri star) . . .

Dupree et al.

(2006)



Schröder & Cuntz (2005) scaling for I, III, V

Cool-star mass loss rates



Stellar coronal heating

• The well-known “rotation-age-activity” relationship shows how coronal heating weakens as young (solar-type) stars spin down.

• Heating rates also scale with mean magnetic field.

K, M stars

Sun

Saar (2001, CS11)Judge, Güdel, Kürster, Garcia-Alvarez, Preibisch, Feigelson, Jeffries

open or closed fields?



Sun’s mass loss history• Did liquid water exist on Earth 4 Gyr ago? If “standard” solar models are correct,

a strong greenhouse effect was needed.

• Sackmann & Boothroyd (2003) argued that a more massive (~1.07 M) young Sun could have been luminous enough to solve this problem, but it would have needed strong early mass loss . . .

Sackmann & Boothroyd (2003)

M ~ LX0.4

M ~ LX1.3

M ~ LX0.1

M ~ LX1.0



Supergranular “funnels”

Peter (2001)

Tu et al. (2005)

Fisk (2005)



MHD turbulence• It is highly likely that somewhere in the outer solar

atmosphere the fluctuations become turbulent and cascade from large to small scales:

• With a strong background field, it is easier to mix field lines (perp. to B) than it is to bend them (parallel to B).

• Also, the energy transport along the field is far from isotropic:

Z+Z–

Z–

(e.g., Dmitruk et al. 2002)



A recipe for coronal heating?

• “Outer scale” correlation length (L): flux tube width (Hollweg 1986), normalized to something like 100 km at the photosphere.

• Z+ and Z– : need to solve non-WKB Alfven wave reflection equations.

Ingredients:

refl. coeff =|Z+|2/|Z–|2



Fast/slow wind diagnostics

• Frozen-in charge states • FIP effect (using Laming’s 2004 theory)

Cranmer et al. (2007)

Ulysses SWICS



Runaway to the transition region (TR) • Whatever the mechanisms for heating, they must be balanced by radiative losses to

maintain chromospheric T.

• Why then isn’t the corona 109 K? Downward heat conduction smears out the “peaks,” and the solar wind also “carries” away some kinetic energy. Conduction also steepens the TR to be as thin as it is.

• When shock strengths “saturate,” heating depends on density only:



Coronal heating mechanisms• So many ideas, taxonomy is needed! (Mandrini et al. 2000; Aschwanden et al. 2001)

• Where does the mechanical energy come from?

• How rapidly is this energy coupled to the coronal plasma?

• How is the energy dissipated and converted to heat?

wavesshockseddies

(“AC”)

vs.

twistingbraiding

shear

(“DC”)vs.

reconnectionturbulenceinteract with

inhomog./nonlin.

collisions (visc, cond, resist, friction) or collisionless



Alfvén wave pressure (“pummeling”)Contours: wind speed at 1 AU (km/s)• Just as E/M waves carry momentum and

exert pressure on matter, acoustic and MHD waves do work on the gas via similar net stress terms:

• This works only for an inhomogeneous (radially varying) background plasma.

• Wave pressure & gas pressure work together to produce high-speed solar wind; each point in this grid represents a solution to the Parker critical pt. eqn.

PCH

Turbulence-driven Polar Winds from T Tauri Stars Energized by Magnetospheric Accretion S. R....

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