testing models of coronal heating, x-ray emission, and winds .

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 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?

3. Testing the hypothesis: • Accretion shocks• Coronal loops• Stellar winds


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)


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


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 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>.


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)


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).


Results: accretion shock X-rays

• Blah…


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.


Results: coronal loop X-rays


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)(


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


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)


Extra slides . . .


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.


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)


Mass loss

• 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


Ansatz: accretion stream impacts make waves

similar to solar flare generated Moreton/EUV 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


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!


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.

(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)?

• What’s the cause? With more rapid rotation,


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)


The extended “solar atmosphere”

Everywhere one looks, the plasma is

“out of equilibrium”


The solar corona

“Quiet” regions

Active regions

Coronal hole (open)

• Plasma at 106 K emits most of its spectrum in the UV and X-ray.

• The “coronal heating problem” remains unsolved . . . .


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!


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)


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


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).


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)


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?


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)


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.


Understanding physics reaps practical benefits

3D global MHD models

Z+Z–

Z–

Real-time“space weather”

predictions?

Self-consistent WTD models

testing models of coronal heating, x-ray emission, and winds .

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