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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