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 . . . Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics . . . From Classical T Tauri Stars
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Testing Models of Coronal Heating, X-Ray Emission, and Winds . . .
Testing Models of Coronal Heating, X-Ray Emission, and Winds. . . . From Classical T Tauri Stars. Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics. Outline: Brief overview of T Tauri star & solar activity Impact-driven turbulence: a plausible chain of events? - PowerPoint PPT Presentation
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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 . . .
Steven R. CranmerHarvard-Smithsonian Center for Astrophysics
. . . From Classical T Tauri Stars
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 . . .
Steven R. CranmerHarvard-Smithsonian Center for Astrophysics
. . . From Classical T Tauri Stars
Outline:
1. Brief overview of T Tauri star & solar activity
2. Impact-driven turbulence: a plausible chain of events?
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds S. R. Cranmer, July 14, 2010
T Tauri stars: complex geometry & activity
(Matt & Pudritz 2005, 2008)
(Romanova et al. 2007)
• 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)
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.
Open field lines see weaker turbulent heating & “wave pressure” acceleration
Closed field lines experience strong turbulent heating
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 TauCY TauDE TauDF TauDK TauDN Tau
DO TauDS TauGG TauGI Tau
GM AurHN TauUY 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:
• Need to assume “contrast:” ρblob / <ρ> ≈ 3.
• This allows us to compute:
L. Hartmann, lecture notes
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
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).
n = 0 (Kolmogorov), 3/2 (Gomez), 5/3 (Kraichnan),
2 (van Ballegooijen), f (VA/veddy) (Rappazzo)
• 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.”
• 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 & 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” wave-driven wind theory of Holzer et al. (1983) to solve for stellar mass loss rates.
v┴ from accretion
impacts
photosph. sound speed
v┴ from interior
convection
1 solar mass
model)(
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds S. R. Cranmer, July 14, 2010
O I 6300 blueshifts (yellow)(Hartigan et al. 1995)
Model predictions
Results: wind mass loss rates
O I 6300 blueshifts (yellow)(Hartigan et al. 1995)
Model predictions
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds S. R. Cranmer, July 14, 2010
Conclusions
For more information: http://www.cfa.harvard.edu/~scranmer/
• 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.
Brown et al. (2010)
• Is Mwind enough to solve the T Tauri angular momentum problem?
• Why do (non-accreting) weak-lined T Tauri stars show stronger X-rays?
.
• 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)
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
• Mwind is obtained from signatures of blueshifted opacity (~few 100 km/s).
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:
heat conduction
radiation losses
— ρvkT52
• Only a fraction of total coronal heat flux conducts down, but in general, we expect something close to
. . . along open flux tubes!
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 . . .
Wang et al. (2000)
Fisk (2005)
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:
The inertial range is a “pipeline” for transporting magnetic energy from the large scales to the small scales, where dissipation can occur.
f -1 “energy containing range”
f -5/3
“inertial range”
f -3
“dissipation range”
0.5 Hzfew hours
Mag
net
ic P
ower
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds S. R. Cranmer, July 14, 2010
What processes drive solar wind acceleration?
vs.
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.
• 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!
splitting/mergingtorsion
longitudinal flow/wave
bending(kink-mode wave)
0.1″
•Measuring horizontal motions of magnetic flux tubes is more difficult . . . but may be more important?
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds S. R. Cranmer, July 14, 2010
Dissipation of MHD turbulence
• Standard nonlinear terms have a cascade energy flux that gives phenomenologically simple heating:
Z+Z–
Z–
• We used a generalization based on unequal wave fluxes along the field . . .
• n = 1: usual “golden rule;” we also tried n = 2.
• Caution: this is an order-of-magnitude scaling!
(“cascade efficiency”)
(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)
Testing Models of CTTS Coronal Heating, X-Ray Emission, & Winds S. R. Cranmer, July 14, 2010
The solar wind acceleration debate
vs.
• What determines how much energy and momentum goes into the solar wind?
Waves & turbulence input from below?
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