Testing Models of Coronal Heating,
X-Ray Emission, and Winds . . .
. . . From Classical T Tauri Stars
Steven R. Cranmer
Harvard-Smithsonian Center for Astrophysics
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Testing Models of Coronal Heating,
X-Ray Emission, and Winds . . .
Outline:
1. Brief overview of T Tauri star & solar activity
2. Impact-driven turbulence: a plausible chain of events?
3. Testing the hypothesis: • Accretion shocks
• Coronal loops
• Stellar winds
. . . From Classical T Tauri Stars
Steven R. Cranmer
Harvard-Smithsonian Center for Astrophysics
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
T Tauri stars: complex geometry & activity
• T Tauri stars show signatures of disk accretion, “magnetospheric accretion streams,”
an X-ray corona, and polar (?) outflows from some combination of star & disk.
• Nearly every observational diagnostic varies in time, sometimes with stellar rotation,
but often more irregularly.
(Rucinski et al. 2008)
(Romanova et
al. 2007)
(Matt & Pudritz 2005, 2008)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Context from the Sun’s corona & wind
• Photospheric flux tubes are shaken by an observed spectrum of convective motions.
• Alfvén waves propagate along the field, and partly reflect back down (non-WKB).
• Nonlinear couplings allow MHD turbulence to occur: cascade produces dissipation.
Closed field lines experience strong turbulent heating
Open field lines see weaker turbulent heating & “wave pressure” acceleration
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Ansatz: accretion stream impacts make waves
• The impact of inhomogeneous “clumps” on the stellar surface can generate MHD
waves that propagate out horizontally and enhance existing surface turbulence.
• Scheurwater & Kuijpers (1988) computed the fraction of a blob’s kinetic energy
that is released in the form of far-field wave energy.
• Cranmer (2008, 2009) estimated wave power emitted by a steady stream of blobs.
similar to solar flare generated
Moreton/EUV waves?
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Testing the ansatz… with real stars
• Classical T Tauri stars in the Taurus-Auriga
star forming region are well-observed:
AA Tau
BP Tau
CY Tau
DE Tau
DF Tau
DK Tau
DN Tau
DO Tau
DS Tau
GG Tau
GI Tau
GM Aur
HN Tau
UY Aur
• Cranmer (2009) used two independent sets of M*, L*, R*, ages, & accretion rates,
from Hartigan et al. (1995) and Hartmann et al. (1998).
• Accretion spot “filling factors” δ taken from Calvet & Gullbring (1998)
measurements of Balmer & Paschen continua → accretion energy fluxes & areas.
• Surface magnetic field strengths B* for 10/14 stars taken from Johns-Krull (2007)
measurements of Ti-line Zeeman broadening; other 4 from empirical <B* / Bequi>.
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Start with the simplest geometry
• Königl (1991) showed how inner-disk edge
can scale with stellar parameters:
• Measured filling factor δ gives router, as well
as size of blobs at stellar surface.
• Assume ballistic (free-fall) velocity to
compute ram pressure; this gives ρshock/ρphoto.
The streams are inhomogeneous:
L. Hartmann, lecture notes
• 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)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Accretion shock models
• Temporarily ignoring the existence of “blobs” allows a straightforward 1D
calculation of time-steady shock conditions & the post-shock cooling zone.
• Typical post-shock conditions: log Te ~ 5–6, log ne ~ 13.5–15
• Cranmer (2009) synthesized X-ray luminosities: ROSAT (PSPC), XMM (EPIC-pn).
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Results: accretion shock X-rays
• Blah…
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Coronal loops: MHD turbulent heating
• Cranmer (2009) modeled equatorial zones of T Tauri stars as a collection of closed
loops, energized by “footpoint shaking” (via blob-impact surface turbulence).
• Coronal loops are always in motion, with
waves & bulk flows propagating back and
forth along the field lines.
• Traditional Kolmogorov (1941) dissipation
must be modified because counter-propagating
Alfvén waves aren’t simple “eddies.”
n = 0 (Kolmogorov), 3/2 (Gomez), 5/3 (Kraichnan),
2 (van Ballegooijen), f (VA/veddy) (Rappazzo)
• T, ρ along loops computed via Martens (2010) scaling laws: log Tmax ~ 6.6–7.
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Results: coronal loop X-rays
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Stellar winds from polar regions
• The Scheurwater & Kuijpers (1988) wave generation mechanism allows us to
compute the Alfvén wave velocity amplitude on the “polar cap” photosphere . . .
• Waves propagate up the flux tubes &
photosph.
sound speed
accelerate the flow via “wave pressure.”
• If densities are low, waves cascade and
dissipate, giving rise to T > 106 K.
• If densities are high, radiative cooling is
too strong to allow coronal heating.
• Cranmer (2009) used the “cold” wavedriven wind theory of Holzer et al. (1983)
to solve for stellar mass loss rates.
v┴ from accretion v┴ from interior
impacts
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
convection
( )
1 solar
mass
model
S. R. Cranmer, July 14, 2010
Results: wind mass loss rates
O
O II 6300
6300 blueshifts
blueshifts (yellow)
(yellow)
(Hartigan
(Hartigan et
et al.
al. 1995)
1995)
Model
Model predictions
predictions
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Conclusions
• Insights from solar MHD have led to models that demonstrate how the accretion
energy can contribute significantly to driving T Tauri outflows & X-ray emission.
.
• Is M
enough to solve the T Tauri angular momentum problem?
• Why do (non-accreting) weak-lined T Tauri stars show stronger X-rays?
wind
• More realistic models must include: (1) more complex magnetic fields, and
(2) the effects of rapid rotation on convective dynamo “activity.”
Cohen et al.
(2010)
Brown et al.
(2010)
For more information: http://www.cfa.harvard.edu/~scranmer/
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Extra slides . . .
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
How did we get here?
The Young Sun:
• Kelvin-Helmholz contraction:
An ISM cloud fragment becomes a
“protostar;” gravitational energy is
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 begins to
dominate → ZAMS.
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Mass loss: where does it originate?
• YSOs (Class I & II) show jets that remain
collimated far away (AU → pc!) from the
central star. Outflows anchored in disk?
• However, EUV emission lines and He I
10830 Å P Cygni profiles indicate that
blueshifted outflows are close to the star.
• Stellar winds & disk winds may co-exist.
(Ferreira et al. 2006)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Mass loss
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)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Ansatz: accretion stream impacts make waves
similar to solar flare generated
Moreton/EUV waves?
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
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)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
Wu et al. (2001)
S. R. Cranmer, July 14, 2010
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)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Accretion-driven T Tauri winds
• Results: wind mass loss rate increases
~similarly with the accretion rate.
• For high enough densities, radiative
cooling “kills” the coronal heating!
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Cool-star rotation → mass loss?
• There is a well-known “rotation-age-activity”
relationship that shows how coronal heating
weakens as young (solar-type) stars age and
spin down (Noyes et al. 1984).
• X-ray fluxes also scale with mean magnetic
fields of dwarf stars (Saar 2001).
• For solar-type stars, mass loss rates scale
with coronal heating & field strength.
• What’s the cause? With more rapid rotation,
(Mamajek 2009)
 Convection may get more vigorous
(Brown et al. 2008, 2010) ?
 Lower effective gravity allows more
magnetic flux to emerge, thus giving
a higher filling factor of flux tubes
on the surface (Holzwarth 2007)?
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Evolved cool stars: RG, HB, AGB, Mira
• The extended atmospheres of red giants and
supergiants are likely to be cool (i.e., not highly
ionized or “coronal” like the Sun).
• High-luminosity: radiative driving... of dust?
• Shock-heated “calorispheres” (Willson 2000) ?
• Numerical models show that pulsations couple
with radiation/dust formation to be able to drive
mass loss rates up to 10 –5 to 10 –4 Ms/yr.
(Struck et al. 2004)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
The extended “solar atmosphere”
Everywhere one looks,
the plasma is
“out of equilibrium”
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
The solar corona
• Plasma at 106 K emits most of its spectrum in the UV and X-ray.
• The “coronal heating problem” remains unsolved . . . .
Coronal hole
(open)
“Quiet”
regions
Active
regions
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
What sets the Sun’s mass loss?
• Coronal heating must be
ultimately responsible.
• Hammer (1982) & Withbroe (1988) suggested a steady-state energy balance:
• Only a fraction of total coronal
heat conduction
heat flux conducts down, but in
general, we expect something
close to
. . . along open flux tubes!
radiation
losses
5
— ρvkT
2
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Solar wind: connectivity to the corona
• 1958: Eugene Parker proposed that the hot corona provides enough gas pressure
to counteract gravity and accelerate a “solar wind.” 1962: Mariner 2 saw it!
• High-speed wind (600–800 km/s): strong connections to largest coronal holes.
• Low-speed wind (300-500 km/s): no agreement on full range of source regions
in the corona: “helmet streamers,” small coronal holes, active regions . . .
Fisk
(2005)
Wang et al. (2000)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
In situ fluctuations & turbulence
• Fourier transform of B(t), v(t), etc., into frequency:
Magnetic Power
f -1 “energy containing range”
f -5/3
“inertial range”
The inertial range is a
“pipeline” for transporting
magnetic energy from the
large scales to the small
scales, where dissipation
can occur.
few hours
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
f -3
“dissipation
range”
0.5 Hz
S. R. Cranmer, July 14, 2010
What processes drive solar wind acceleration?
Two broad paradigms have emerged . . .
• Wave/Turbulence-Driven (WTD)
models, in which flux tubes “stay open”
• Reconnection/Loop-Opening (RLO)
models, in which mass/energy is
injected from closed-field regions.
vs.
• There’s a natural appeal to the RLO idea,
since only a small fraction of the Sun’s
magnetic flux is open. Open flux tubes are
always near closed loops!
• The “magnetic carpet” is continuously
churning.
• Open-field regions show frequent coronal
jets (SOHO, Hinode/XRT).
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Waves & turbulence in open flux tubes
• Photospheric flux tubes are shaken by an observed spectrum of horizontal motions.
• Alfvén waves propagate along the field, and partly reflect back down (non-WKB).
• Nonlinear couplings allow a (mainly perpendicular) cascade, terminated by damping.
(Heinemann & Olbert 1980; Hollweg 1981, 1986; Velli 1993; Matthaeus et al. 1999; Dmitruk et al. 2001,
2002; Cranmer & van Ballegooijen 2003, 2005; Verdini et al. 2005; Oughton et al. 2006; many others)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Waves & turbulence in the photosphere
• Helioseismology: direct probe of wave
oscillations below the photosphere (via
modulations in intensity & Doppler velocity)
• How much of that wave energy “leaks” up
into the corona & solar wind?
Still a topic of vigorous debate!
• Measuring horizontal motions of magnetic
flux tubes is more difficult . . . but may be
more important?
splitting/merging
torsion
0.1″
bending
(kink-mode wave)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
longitudinal
flow/wave
S. R. Cranmer, July 14, 2010
Dissipation of MHD turbulence
• Standard nonlinear terms have a cascade energy flux that
gives phenomenologically simple heating:
• We used a generalization based on unequal wave fluxes along the field . . .
(“cascade
efficiency”)
Z–
Z+
• n = 1: usual “golden rule;” we also tried n = 2.
(e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou & Matthaeus
1990; Hossain et al. 1995; Dmitruk et al. 2002; Oughton et al. 2006)
• Caution: this is an order-of-magnitude scaling!
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
Z–
S. R. Cranmer, July 14, 2010
The solar wind acceleration debate
• What determines how much energy and
momentum goes into the solar wind?
Waves & turbulence input from below?
vs.
Reconnection & mass input from loops?
• Cranmer et al. (2007) explored
the wave/turbulence paradigm
with self-consistent 1D models
of individual open flux tubes.
• Boundary conditions imposed
only at the photosphere (no
arbitrary “heating functions”).
• Wind acceleration determined by a combination of
magnetic flux-tube geometry, gradual Alfvén-wave
reflection, and outward wave pressure.
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010
Understanding physics reaps practical benefits
Self-consistent WTD models
Z–
3D global MHD
models
Real-time
“space weather”
predictions?
Z+
Z–
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds
S. R. Cranmer, July 14, 2010