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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