Transcript Turbulence-driven Polar Winds from T Tauri Stars Energized by

Turbulence-driven Polar Winds from
T Tauri Stars . . .
. . . Energized by
Magnetospheric Accretion
Steven R. Cranmer
Turbulence-driven
Polar Winds from T Tauri Stars
Harvard-Smithsonian
Center
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
for Astrophysics
SSP Seminar, Harvard-Smithsonian CfA
Turbulence-driven Polar Winds from
T Tauri Stars . . .
Outline:
1. Background: T Tauri accretion and outflows
2. Driving a wind: • convection → coronal heating
• accretion-stream impacts → waves
.
–9
3. Results: Mwind >
10
M/year !
~
. . . Energized by
Magnetospheric Accretion
Steven R. Cranmer
Turbulence-driven
Polar Winds from T Tauri Stars
Harvard-Smithsonian
Center
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
for Astrophysics
SSP Seminar, Harvard-Smithsonian CfA
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.
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Pre-Main-Sequence accretion phases
Feigelson &
Montmerle
(1999)
M. Burton
(UNSW)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Accretion geometry
• 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 . . .
(Romanova et al. 2007)
(Matt & Pudritz 2005, 2007)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Accretion rate vs. age
• Macc obtained from accretion luminosity (excess continuum > photospheric SED)
Hartigan et al. (1995);
Hartmann et al. (1998)
~ t –1.5
all T Tauri stars
“solar mass” (4000 < Teff < 4500 K)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Mass loss rates
M acc
• 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)
Hartigan et al. (1995)
• P Cygni absorption trough of He I
10830 (chromospheric diagnostic):
TW Hya:
Batalha et al. (2002)
Dupree et al. (2005)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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.,
CTTS
(accreting)
Bouvier et al. 1993; Edwards et al. 1993).
• How is angular momentum carried away?
 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.
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
WTTS
(non-accreting)
Rot. Period (days)
L. Hartmann,
lecture notes
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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
• ion opacity? (Teff ~> 15,000 K)
• free electron (Thomson) opacity? (goes as 1/r2 ; needs to be supplemented)
• dust opacity? (Teff <~ 3,500 K)
 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 . . .
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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 . . .
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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
5
— ρvkT
2
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Conservation equations solved by ZEPHYR (1/2)
• The only “free parameters:” wave properties at photosphere, and background Br(r)
(for more information, see Cranmer et al. 2007)
mass:
A(r)
momentum:
internal energy:
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Conservation equations solved by ZEPHYR (2/2)
• Waves/turbulence: modeled “statistically” rather than by following... Σ ei(ωt – kz)
• Energy density & flux:
• Static medium:
A(r)
• 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).
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Results: coronal heating and solar M
Ulysses
SWOOPS
T (K)
Goldstein et al.
(1996)
reflection
coefficient
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
But how do T Tauri stars generate
mass loss rates 1000 to a million
times solar?
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Ansatz: accretion streams make more waves
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
Wu et al. (2001)
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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.
L. Hartmann, lecture notes
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)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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
x
given by the power divided by
the wall area.
• The total wave flux at a given
2rblob
“target point” (i.e., the pole) is
N times the flux of one impact.
• 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.
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
(see Stein-Lighthill convection!)
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
The Sun in time . . .
• Eggleston’s STARS code was run for 1 M* evolution before and after ZAMS . . .
ρphoto
rinner
ρshock
rblob
R*
photosph.
scale ht.
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
δ
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Modifications to the solar ZEPHYR models
• Age-dependent R*, Teff , ρphoto
• Resulting Alfvén wave amplitude at
photosph.
sound speed
the photosphere, versus age
• Photospheric acoustic wave amplitude
is scaled similarly to Alfvén waves.
v┴
• 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).
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Results: mass flux
Macc
Mwind
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Results: speed, temperature, momentum flux
Vesc
Macc
u∞
ucrit
phot. cs
HH
phot. Teff
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
The “cold wave-driven wind” limit
• When the plasma becomes massive enough, radiative cooling (~ρ2) becomes more
efficient throughout the wind:
• 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.
• 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.
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Results: mass flux
Macc
Mwind
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Results: speed, temperature, momentum flux
Vesc
Macc
u∞
ucrit
phot. cs
HH
phot. Teff
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Preliminary Conclusions
• 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. Brown
et al. (2007)
For more information: http://www.cfa.harvard.edu/~scranmer/
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
extra slides
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Disk accretion is variable! (L. Hartmann)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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., JohnsKrull, Valenti, & Koresko
1999)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Cool-star winds: “traditional” diagnostics
• 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
• Radio: free-free emission from (partially
ionized?) components of the wind
(Bernat 1976)
• Continuum methods need V from
another diagnostic to get mass loss rate.
•
wind
star
• Clumping?
(van den Oord &
Doyle 1997)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Cool-star mass loss rates
Schröder & Cuntz (2005)
scaling for I, III, V
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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.
open or closed fields?
K, M stars
Sun
Judge, Güdel, Kürster, Garcia-Alvarez, Preibisch, Feigelson, Jeffries
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
Saar (2001, CS11)
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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 ~ LX1.3
M ~ LX1.0
M ~ LX0.4
M ~ LX0.1
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Supergranular “funnels”
Peter (2001)
Fisk
(2005)
Tu et al. (2005)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
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
Z–
Z+
field is far from isotropic:
Z–
(e.g., Dmitruk et al. 2002)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
A recipe for coronal heating?
Ingredients:
• “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.
refl. coeff =
|Z+|2/|Z–|2
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Fast/slow wind diagnostics
• Frozen-in charge states
• FIP effect
(using Laming’s 2004 theory)
Ulysses SWICS
Cranmer et al. (2007)
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Runaway to the transition region (TR)
• Whatever the mechanisms for heating, they must be balanced by radiative losses to
maintain chromospheric T.
• When shock strengths
“saturate,” heating depends
on density only:
• 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.
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Coronal heating mechanisms
• So many ideas, taxonomy is needed!
(Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
• How rapidly is this energy
coupled to the coronal
plasma?
waves
shocks
eddies
(“AC”)
interact with
inhomog./nonlin.
vs.
twisting
braiding
shear
(“DC”)
turbulence
reconnection
• How is the energy dissipated
and converted to heat?
collisions (visc, cond, resist, friction) or collisionless
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA
Alfvén wave pressure (“pummeling”)
• Just as E/M waves carry momentum and
Contours: wind speed at 1 AU (km/s)
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.
P
C
H
• 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.
Turbulence-driven Polar Winds from T Tauri Stars
Energized by Magnetospheric Accretion
S. R. Cranmer, January 28, 2008
SSP Seminar, Harvard-Smithsonian CfA