CDP Workshop on Magnetic Fields and Structures Magnetic fields on Normal i'e', nondegenerate Stars

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CDP Workshop on Magnetic Fields and
StructuresMagnetic fields on Normal (i.e.,
nondegenerate) Stars

• Jeffrey Linsky
• University of Colorado
• February 11, 2008
• File CDP_stellarmagfields.ppt

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Solar magnetograms obtained with the Michelson
Doppler Imager (MDI) instrument on SOHO
Magnetic flux/aperture is the spatially averaged
magnetic field strength
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What are the true magnetic field strengths in the
solar photosphere? (Rabin ApJ 390, L103 (1992))

• Stokes V spectra of FeI 6388 cm-1 line (g3.00)
  and FeI 6386 line (g1.53 cm-1) (1.565 µm).

??B ?² geff B
fareal filling factor for magnetic flux tubes
can be as large as 0.5 at 2 arcseconds resolution
for plages.
ßPg/Pm8pPg/B²0.6 for B1300G in solar
photosphere at 150 km.
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Magnetic field strengths in sunspots (Kopp
Rabin (Solar Physics 141, 253 (1992))
Stokes I spectra of the Fe I 1.5651 µm (g3.00)
line in sunspots. Left plot shows Fe I line split
by B2600 G. ß0.1 for B3500 G.
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Solar image taken in the core of the Ca II H line

• Photographic solar image obtained by Hale and
  Ellerman (ApJ 19, 41 (1904)) at Yerkes
  observatory
• They recognized that the CaII emission was formed
  in a layer above the photosphere.
• The term plage or active region is now used
  instead of flocculi.

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CaII K line fluxes for dwarf stars. Emission in
the line cores is produced by magnetically heated
gas in their chromospheres
Linsky et al. (ApJS 41, 47 (1979))
Kelch et al. (ApJ 229, 700 (1979))
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Flux in a 1Å band centered on the solar CaII K
line (3933Å) core (from the National Solar
Observatory K line monitoring program)
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Sunspot cycle since 1600

• 11 year period except for the Maunder minimum
  (1645-1715) when no sunspots seen when Europe had
  colder temperatures (little ice age)
• Stars could also go through similar episodes of
  minimal magnetic activity

From Lockheed Martin Advanced Technology Center
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Evidence for stellar magnetic cycles from the Mt.
Wilson Ca II index program (Baliunas et al. ApJ
438, 269 (1995)
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Comparison of chromospheric and photospheric
variability for Sun and cool dwarf stars
(Lockwood et al. ApJS 171, 260 (2007))
S index measures the flux in 1Å bands centered on
the Ca II H and K lines
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Relation of chromospheric and photospheric
variability (Lockwood et al. ApJS 171, 260 (2007))

• For stars more active than the Sun, chromospheric
  and photospheric variability anticorrelated
  (i.e., active regions lie over starspots)
• For stars less active than the Sun, a positive
  correlation (i.e., active regions lie over
  faculae)
• Sample of 32 main sequence stars

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Yohkoh X-ray images of the Sun taken every 120
days for 4 years beginning at the 1991 maximum
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Measuring magnetic fields using the Zeeman
broadening technique proposed by Robinson (ApJ
239, 961 (1980))

• Spectral lines consist of an unsplit p component
  and s components shifted by ??4.67x10-13?²gB Å
  in magnetic regions and no shift in nonmagnetic
  regions.
• Compare the shapes of line pairs (high g and low
  g) in Fourier space.
• The two lines must have the same intrinsic shape
  and be formed in the same layer in the
  atmosphere.
• Figure shows inverse profiles of line pairs for
  active region (1600G, f0.1), sunspot (3000G,
  f0.6), and quiet region on Sun

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Measuring magnetic fields using Zeeman line
broadening (unpolarized light) Assumptions

• Excess broadening of high Landé g factor lines
  compared to low Landé g factor lines measures the
  unsigned magnetic field (B) and filling factor
  (f) in the photosphere. ??B4.7x10-13 g?2B Å
• Magnetic regions are assumed to have a single
  value of B (or a few values) and nonmagnetic
  regions have B0.
• Field are lines oriented radially in the
  photosphere. What if not true?
• Thermal structure of the magnetic and nonmagnetic
  regions is assumed to be the same. Unlikely to
  be true. Leads to errors in f but not in B. What
  effect on f if magnetic regions cooler/hotter?
• This technique avoids severe cancellation. At
  solar maximum, the net polarization signal would
  give B2 G amplitude.
• Best to observe in the IR because ??B/? ?D ?.
  For large B see the Zeeman spliting. For small B
  see only broadening.

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Zeeman broadening of an Fe I line in a Pleiades
K3 V star and an inactive K3 V star (Valenti
Johns-Krull, ASP Conf. Ser. 248, 179 (2001))
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Zeeman broadening of the flare star EV Lac (from
Johns-Krull and Valenti (1996)). Bf2.3 kG
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Zeeman broadening of the T Tauri star TW Hya (K7)
assuming 4 regions of different B (From Valenti
and Johns-Krull (2001))
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Magnetic parameters and relations (Valenti and
Johns-Krull ASPCS 248, 179(2001))

• Equipartition (magnetic pressure gas pressure)
  B²eq8pPg.
• B/Beq 1 in photosphere of normal dwarfs, but
  larger for very active stars (starspots?) Wilson
  depression?
• fmagnetic field filling factor is small for
  inactive slowly rotating stars, but large for
  rapid rotators. Magnetic coverage saturation
  (f1) when Plt1 day.
• Bf (1.5kG)(0.01) 15G for Sun to (4kG)(1.0)
  4 kG for very active stars (a factor of 270 in
  magnetic flux).

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Activity saturation (measured by UV or X-ray
emission) is related to the Rossby number Ro
Prot/?conv (from Sterzik and Schmitt (1997))
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Coronal activity regimes based on stars in
clusters (Pleiades, IC 2602, IC 2391, a Persei,
Hyades and the field) (Randich ASP 198, 401
(2000))

• Ro Prot/?c (Rossby number)
• Linear regime log R0 0.6 to -0.8 (for
  sun-like stars Prot 50 to 2 days).
• Saturation regime log R0 -0.8 to -2.0 (Prot
  2 to 0.1 days).
• Supersaturation regime log R0 lt -2.0.
• Sun log R0 0.6

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Other methods for determining that stars have
magnetic fields

• Radio emission gyroresonance (TB 107 K),
  gyrosynchrotron (TBgt109 K), or coherent (TBgt1012
  K)
• Channeled flows (accretion from disk to star)
• Very strong X-ray and UV emission lines
• Starspots (rotational modulation signal)
• Flares (radio to gamma rays)
• Stellar cycles (UV and X-ray)

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Essence of Doppler imaging technique (Vogt
Penrod PASP 95, 565 (1983))
Doppler imaging first proposed by Khokhlova
Ryabchikova (Astrophysics and Space Science 34,
403 (1975))
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Requirements for successful Doppler imaging

• Nvrotsini/FWHMnumber of resolution elements
  across the disk. Need vrotgt30 km/s and spectral
  resolution lt10 km/s.
• Need high S/Ngt500, especially for
  rapidly-rotating stars with shallow absorption
  lines or use many absorption lines.
• If inclination of rotational axis to line of
  sight, i90 then no Doppler effect. If i0 then
  N-S ambiguity. i20-70 best. Should know i to
  20.
• Need observations at many rotational phases.
  Preferably over many cycles to separate
  rotational modulations from intrinsic variability
  (in particular flares).
• Need unblended lines. Preferably many lines to
  enhance S/N of the Doppler image.
• Need a robust image reconstruction procedure. Why?

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Why is there a problem in reconstructing the
stellar image? (cf. Kürster AA 274, 851 (1993))
Doppler imaging requires the solution of a
Fredholm equation of the first kind.
D(y) is the observed function (i.e., the observed
flux as a function of the variable y representing
wavelength and rotational phase.
I(x) is the image of the star to be
reconstructed, where x represents the spatial
coordinates of the image (star) longitude and
latitude.
R(x,y) is the response function that maps I(x) to
D(y). R(x,y) contains the information on
geometry, local line formation, stellar limb
darkening, instrumental response, etc.
The problem is ill-posed. There are an infinite
number of I(x) solutions that will result in the
same D(y). Data noise makes the problem worse.
Need to impose additional constraints to produce
a unique solution (regularization).
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Image reconstruction techniques

• Inversion of a time-series of spectral line
  profiles is an ill-posed problem (i.e., not
  unique). Especially when insufficient spectral
  resolution, few rotational phases, low S/N data.
  Need to add constraints on the inversion process
  (regularization).
• For example, require that all pixels in the image
  have positive intensity.
• Maximum entropy method (e.g., Skilling Bryan
  1984) requires the image to have the minimum
  content consistent with the data. Produces the
  smoothest image with the least information.
• Tikhonov method (Tikhonov Goncharsky 1987)
  searches for the smoothest image consistent with
  the data by requiring strong correlation between
  neighboring image pixels. (Supresses noise)
• Two temperature method (spots and photosphere).
  Minimizes possibilities but does not lead to a
  unique solution by itself.
• CLEAN algorithm (e.g., Kürster 1993) used by
  radio astronomers. An iterative approach that
  ends when proceedure stops converging.

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Reconstuction using Doppler imaging under near
ideal conditions

• High signal/noise, good coverage of rotational
  phases, and known orientation of rotational axis
• Doppler imaging using maximum entropy image
  reconstruction
• Vogt et al. (ApJ 321, 496 (1987))

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Doppler images (intensity maps) of three young
active stars
Güdel The Sun in Time Activity and
Environment Living Reviews in Solar Physics (in
press)
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Some results concerning magnetic fields in active
stars from Doppler imaging (cf. Hussain AN 325,
216 (2004))

• Large polar starspots are real. Unlike Sun but
  predicted in simulations (e.g. Schrijver Title
  2001).
• Spots have lifetimes of years in RS CVn systems
  (e.g., HR 1099, Vogt et al. 1999) or vary on
  short timescales in PMS stars (e.g., He699 Barnes
  et al. 1998)
• Evidence for differential rotation (AB Dor,
  Donati Collier Cameron 1997)

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Doppler imaging study of the RS CVn-type system
HR 1099 (K1 IV G5 V) by Vogt et al. (ApJS 121,
547 (1999))
Polar projection of spots in 1981.70
Polar projection of spots in 1992.95
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Migration tracks of spots and inferred rotational
periods with latitude
Differential rotation
a-0.00350.0004 for HR 1099, opposite in sign
and 56 times smaller than for Sun
X is the orbital period. Why is the equator
rotating more slowly? Poleward migration 6-30 m/s.
a0.197 for the Sun
Polar spots live for many years
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What has been learned from 25 years of Doppler
imaging of stars with convection (Hussain AN 325,
216 (2004))

• http//www.aip.de/groups/activity website with
  maps of the gt60 stars that have been imaged.
• Spectral types late-F to early-M. Prot between
  0.26 and 27 days. Pre-MS (T Tauri stars) to
  evolved giants and tidally-locked binaries (e.g.,
  RS CVn binaries).
• Rapid rotating stars typically have large spots
  (up to 40 of surface) including polar or circum
  polar (unlike Sun).
• Solar-type differential rotation (equator rotates
  faster than poles).
• Large spots can last for years.
• Spot magnetic fields have not yet been measured
  (spots are dark). To be done with new IR
  spectrographs on large telescopes.

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Stokes representation of polarized light in the
presence of a magnetic field
Solar off-limb spectra of the Na I D
line Trujillo Bueno Manso Sainz (2001)
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Simulations of ZDI signals for radial and
azimuthal components Hussain (AN 325, 216 (2004))

• V is proportional to the line of sight component
  of B
• V/I line profiles are plotted.
• Redshifted and blueshifted ions spiral field
  lines in opposite directions producing opposite
  V/I signals.
• Radial component decreases and azimuthal
  component increases to limb due to projection of
  field lines along the line of sight.

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Simulations for achievable noise levels in 3 km/s
bins on 9th magnitude stars (Donati Brown
(1989))
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Zeeman-Doppler imaging of AB Dor (Donati et al.
1999)

• K0 V, 20-30 Myr, Prot0.51 d.
• ZDI with Stokes I and V.
• Spots mostly at pole (area 9, B400 G, f0.5).
• Radial field (Bfgt1 kG) in 12-16 regions of
  opposite polarity.
• Azimuthal field (Bfgt1 kG). Belt surrounding
  rotational pole at 70-80 deg. (Also HR 1099)
• Differential rotation like Sun (equator faster
  than pole).
• Evidence for a distributed magnetic dynamo in the
  convective zone.
• Log Fx 8.0 (very active).

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AB Dor in 2002 (Hussain et al. MNRAS 377, 1488
(2007)) I (top), Bradial (middle), Bazimuth
(bottom)
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Zeeman Doppler Imaging using all 4 Stokes
parameters (Kovhukhov et al. AA 414, 613 (2004))

• First application of ZDI with all 4 Stokes
  parameters. Inclusion of linear polarization data
  permits specifying magnetic vectors in 3
  dimensions.
• Applied to the chemically peculiar star 53 Cam.
• Magnetic field topology is complex not
  multipoles.
• Figure shows field strength (top) and
  orientations (bottom) at rotational phases, 0.0,
  0.2, 0.4, 0.6, and 0.8.

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Simulations of photospheric magnetic fields for a
sun-like star with different rotational periods
(activity levels)

• Schrijver Title (ApJ 551, 1099 (2001)).
• Models with solar parameters (granulation,
  supergranulation, meridional flow, differential
  rotation, 11 year cycle, etc.)
• Only change is number of magnetic bipoles
  emerging per day A01 (Sun) to 30 (active).
• When A030, Bf10xsolar max, Prot6 days.
• For A030 model, magnetic flux densities near
  pole would make large spot areas (opening angle
  25 degrees, B2 kG, and f 1.
• Rings of opposite magnetic polarity near pole
  could easily produce large prominences, flares,
  and coronal mass ejections.
• These phenomena observed on AB Dor (Collier
  Cameron, Donati, Hussain, Jardine).

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Magnetograms of the observed Sun and simulated
active Sun vs. cycle phase

• Active Sun shows polar spot (magnetic field
  strength 2 kG like a sunspot supresses
  convection) and ring of opposite polarity
• Grey scale saturates at 700 Mx/cm-2 for active
  Sun and 70 for observed Sun
• Active Sun predicted to have Prot6 days
• From Schrijver and Title (2001)

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Longitudinally averaged field for the Sun and a
30 times more magnetically active Sun from
Schrijver and Title (ApJ 551, 1099 (2001))

• Top observed Sun (magnetic cycle 21)
• Bottom Simulated active Sun with only the rate
  of emerging magnetic bipoles increased by factor
  of 30
• All else is like Sun (flux dispersion,
  differential rotation, meridional flow pattern,
  field cancellation rates, and cycle length)

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The effects of rotation on magnetic fields,
heating, and coronal magnetic structures for
solar mass stars
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Stellar wind mass flux vs. activity (measured by
X-ray surface flux)

• Wood et al. (ApJL 628, L146 (2005)).
• From analysis of Lyman-a astrospheric absorption.
• Power law correlation until Fx 8x105, then a
  sharp drop.
• e Eri Prot 11.7 days, f 0.1.
• ? Boo A Prot6.43 days, f0.2.
• Transition corresponds to activity level where
  polar spots become prominent.
• Large-scale magnetic geometry changes from
  solar-like (isolated active regions) to a more
  dipolar-like field with f 0.1 and a toroidal
  component.

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Magnetic field structure of the moderately active
star ? Boo A (Petit et al. MNRAS 361 (2005))

• G8 V star Prot6.43 days, log fX6.1 (just to
  the right of the wind/X-ray boundary.
• Stokes I and V spectrophotometry
• Large-scale dipole component Bp40 G inclined
  35 to rotational pole.
• Large-scale torroidal component Bt120 G
  probably surrounding the magnetic pole.
• Small scale magnetic structure unresolved.
• Large-scale magnetic structure is very different
  from the Sun. Rotation 4 times faster than Sun.

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Nonpotential magnetic field of young rapid
rotator AB Dor (Hussain et al. ApJ 575, 1078
(2002))

• ZDI analysis with a code that includes
  nonpotential fields.
• Free energy 14 of potential field in corona (20
  at base).
• Nonpotential component of azimuthal field (right)
  due to electric currents in polar spot penumbra
  (70-80 deg latitude).
• Predicts large slingshot prominences with high
  latitude footpoints (mixed polarity).
• Consistent with flares and strong X-ray emission
  from polar regions of rapid rotators (e.g., 44i
  Boo, Algol).

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AB Dor prominences and magnetic geometry

• Time drifts of absorption features across disk
  indicate 16 slingshot prominences (Donati et al
  1999).
• 4 prominences seen twice show magnetically
  enforced corotation with photosphere. Absorbing
  gas at 2.5-4.7 Rstar. (corotation radius 3
  Rstar)
• Anchored at high latitude.
• Lifetimes short in indicating reorganization of
  coronal magnetic fields.

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Magnetic field structure for simulated Sun and
active Suns from Schrijver and Aschwanden ApJ
566, 1147 (2002)

• Potential field lines for simulated Sun and
  active suns with 10 and 30 times emerging flux
  rates vs. cycle phase
• Only field lines with base B600 G
• Red and green field lines have small expansion
  with height
• Coronal heating flux density (and soft X-ray
  flux) PH B1.00.5

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Magnetic loops in the solar corona seen in by the
TRACE (Transition Region and Coronal Explorer)
satellite in the Fe IX/X 171 Å line (T1x106 K)
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Conclusions and suggestions for future research
on Magnetic coupling in solar and stellar
atmospheres

• Active stars are not scaled-up Suns. Their
  magnetic properties are qualitatively different.
• Rotation (not age) controls the input rate of
  magnetic bipoles (A0) which controls the magnetic
  geometry and magnetic energy input, fXA0.
• Magnetic field filling factor controls the
  spreading of flux tubes in the chromosphere and
  thus wave heating.
• Magnetic field geometry and filling factor in the
  corona likely control the wind, X-ray emission,
  flaring, etc.
• Important thresholds log fX5.9, 7.7 (Prot 12,
  2 days).
• Saturation is unexplained but may involves
  negative feedback of the magnetic field on the
  internal velocities that amplify the field via
  the dynamo mechanism.

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X-wind model of magnetic fields and gas flow of
embedded protostars with disks (Shu et al.
Science 277, 1475 (1997))

• Helmut streamer and reconnection ring are null
  surfaces with electric currents out of the
  diagram. Due to sharp reversal of poloidal
  magnetic field. Produces nonthermal particles.
• Near balance of O and Ox (Keplerian rate) at
  inner edge of gaseous disk due to magnetic
  torques on star.
• When O ? Ox field line wrap ? shear and sporadic
  reconnection events (flares) with hard X-ray
  emission (3x1030 erg/s). Flares can heat inner
  disk driving flows and changing inner radius and
  Ox.
• Observed funnel flows (accretion) are variable
  and torque the star. This slows the stellar
  rotation rate.
• There are additional complications when the
  stellar magnetic field axis is not aligned with
  the stellar rotation axis.

The X-wind model assumes that the star and disk
both have magnetic fields and thermally-driven
winds.
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More interesting phenomena when magnetic fields
of protostars and accretion disks interact

• Bright UV and X-ray emission from the star heat
  and ionize the inner layers of the disk driving
  the disk wind and accretion
• Collimated bipolar jets from star (many theories)
• Dust particles in inner disk are melted by flare
  heating ? CaAl-rich inclusions seen in solar
  system meteorites
• Disks (observed in the IR) dissipate in 5Myr

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Evidence for disk locking in young stars (Rebull
et al. ApJ 646, 297 (2006))

• Spitzer satellite observations of IR emission
  from premain sequence stars in the Orion Nebula
  Cluster (age1Myr).
• Stars with IR excesses (m3.6µ-m8µ)gt1 indicating
  disks are slow rotators.
• Slow rotation requires loss of angular momentum.
• Most plausible mechanism is the momentum carried
  by plasma from the more rapidly rotating star
  flowing along spiral field lines connecting the
  star to the disk.

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Jets and bow shocks from a PMS star in Orion
(V0421 Ori) observed with HST/ACS (Bally et al.
AJ 131, 573 (2006))
Vectors indicate proper motion in 100 years.
BlueOIII, greenHa, redNII, Arrow points to
?1 Ori C.
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Jets and bow shocks from another PMS star (IX
Ori, G-K) in Orion (Bally et al. (2006))
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Some conclusions from the HST/ACS study of flows
from PMS stars in Orion (Bally et al. (2006))

• Collimated bipolar outflows from PMS stars are
  often seen (jets and counter jets)
• Flow speeds up to 300 km/s.
• Collisions with interstellar matter produce
  shocks (Herbig-Haro objects) along the flow. In a
  few cases X-rays detected.
• Mass loss rates 10-9 to 10-6 Msun/yr in bipolar
  flows.
• Bipolar outflows bent by gas flows from nearby
  massive stars (e.g., ?1 Ori C).
• Ionization by Lyman continuum photons from hot
  stars in nebular.

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Magnetocentrifugal winds from disks and PMS stars
(Anderson Lee Protostars Planets V (2005))
and Krasnopolsky et al. ApJ 595, 631 (2003))

• First proposed by Blandford Payne (MNRAS 199,
  883 (1982)).
• Winds initiated by thermal pressure.
• Magnetic fields wound up by rotation becoming
  toroidal.
• Gas flows along field lines and accelerated
  centrifugally (slingshot).

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More on magnetocentrifugal winds

• At large vertical distances from the star the
  toroidal field collimates the flow into a jet.

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Models of magnetocentrifugally winds launched
from accretion disks (Krasnopolsky et al. ApJ
595, 631 (2003))

• X-type winds launched from near corotatation
  radius (Shu model).
• disk type winds launched from inner disk
  (RltRL).
• Injection by thermal pressure (hot inner disk)
  and acceleration along wound-up open magnetic
  field lines.
• Flow becomes superalfvenic and then a ballistic
  kinetic flow.

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Streamlines and poloidal velocities in the
Krasnopolsky et al. model

• Note high speed poloidal flow near rotational
  axis (self-collimating flow).
• High density along rotational axis (jet).
• Dashed line is superfast-alfvenic surface.
• Lighter colors show decreasing density.
• Models with increasing mass loading are more
  highly collimated.

Units are AU
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Transition from magnetically dominated to
kinetically dominated flow in Krasnopolsky et al.
model

• Model computed for 10-8 Msun/yr, RL1 AU,
  vinitial80 km/s at inner disk.
• At inner disk B1.1G assuming equipartition with
  wind flow mass flux.
• Mfvpol/vf, vffast magnetosonic speed.
• In distant jet, EKE/Emagfew so flow is kinetic.

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A unified model for bipolar outflows from PMS
stars Shang et al. (ApJ 649, 845 (2006))

• Numerical simulations of magnetocentrifugal winds
  with cylindrical density stratification
  interacting with density toroids with different
  degrees of flattening.
• As gas collapses to a protostar, the ambient
  magnetic field is pulled in and density stucture
  is toroidal with a small opening angle (Class 0)
  that flattens with time creating a larger opening
  angle (Class I and II).
• Models characterized by a parameter n4H0. H0
  represents the fractional overdensity supported
  by the magnetic field above that supported only
  by gas pressure. Ho increases with time leading
  to flattening of density toroid and disk
  formation.

n? from 1 to 6, t?
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Density (top panels) and velocity (bottom panels)
of wind for n4 model at 30, 100, 300, 1000
years. Jet and shell (swept up gas) structure
(both dense) coast freely with time until collide
with dense ISM producing shocks (HH objects)
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Summary of the roles played by magnetic field in
the unified outflow model of Shang et al. (2006)

• Wide angle wind and jets are launched by the same
  magnetic acceleration process.
• Density confinement at magnetic poles
  (consequence of magnetic overpressure) produces
  jets.
• Stronger magnetic fields (lower Alfven Mach
  number, MAvwind/vAlfven) create narrower jets.
• Without an ambient magnetic field, the jet would
  spread out and disappear.

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END OF PREPARED SLIDES
69
Twisted magnetosphere model assumptions

• Magnetic field inside the star is twisted with
  B10xBsurface. Neutron star likely born with
  strong differential rotation
• Twisted field means strong electric currents that
  extend to crust.
• Construct axisymmetric, self-similar solutions to
  force-free equation JxB0 to compute structure of
  magnetic field curl B a B.

Thompson et al. (ApJ 574, 332 (2002))
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Origin of the twisted magnetosphere

• If the magnetosphere magnetic field is locally
  radial, then the current flows along the highly
  conducting crust.
• Lorentz force (1/c)JxB twists the magnetosphere
  field with currents.
• Dissipation and heating in magnetosphere.
• Magnetosphere rotates rigidly out to light
  cylinder RlccPspin/2?.
• Star surface heated by current dissipation and
  impact of accelerated particles from magnetosphere

Electrons and protons that carry the currents in
the magnetosphere scatter X-rays at the local
cyclotron frequency with Doppler redistribution.
Multiple scattering at different resonant
frequencies leads to power law tails to thermal
spectra.
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New imformation on magnetic fields in PMS star
disks

• First models by Pudritz and Norman (ApJ 274, 677,
  1983). Cf Livio (IAU Colloquium 163, ASP 121,
  845, 1997).
• Rotation of flows seen by HST in Baccioti et al.
  ApJ 576, 222, 2002).
• Ray et al. (Protostars and Planets V, 231, 2007)
• Anderson et al. (ApJ 590, L107, 2003)
• Jet instabilities in Hardee (ApSS 293, 2004)
• Internal shocks in jets (Bally and Reipurth 2001)
• Theory in Matsner and McKee (ApJ 545, 364, 2000)

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Magnetorotational instability in stars

• Magnetic wind breaking of the Sun by Sofia et al.
  (Solar Interior and Atmosphere 140, 1991)
• Magnetorotational instability by Balbus and
  Hawley (ApJ 376, 214, 1991 and Rev Mod Phys. 70,
  1, 1998)
• Alpha parameter Frank et al. (2002)
• Magnetic processes and instabilities in radiative
  zones see Spruit (AA 349, 189, 1999 and AA 381,
  923, 2002)
• MRI gt solid body rotation Menou et al. (ApJ 607,
  564, 2004) and Menou and Le Mer (ApJ 650, 1208,
  2006)
• Figure in Hirschi et al (AA 425, 649, 2004)

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New information on magnetic fields in PMS star
disks (continued)

• Enhancing the magnetic accretion rate in Konigl
  and Pudritz (Planets and Protostars IV, 759,
  2000)
• Basic principle in Blandford and Payne (MNRAS
  199, 883, 1982)
• 3D simulations by Edwards et al. (ApJ 646, 319,
  2006)
• Stability by Shu et al. (ApJ 455, L155, 1995)
• Jet driving by Shu et al. (Planets and Protostars
  IV, 789, 2000)
• Magnetorotational instability by Balbus and
  Hawley (RvMP 70, 1, 1998)

74
More information on magnetic fields in PMS stars
continued

• Disk locking and angular momentum loss
  observations see Stassun et al. (AJ 117, 2941,
  1999) and Rebull et al. (ApJ 646, 297, 2006) and
  Holzwarth and Jardine (AA 444, 661, 2005)
• Magnetic buoyancy instability Charbonneau and
  MacGregor (ApJ 417, 762, 1993) and Dikpati et al.
  (ApJ 638, 2006)

75
Model of a protostar with an accretion disk
(Camenzind Rev. Mod. Astr. 3, 234 (1990))

• Central stars not rapid rotators so accretion
  flow torque must be balanced by ang. momentum
  loss through currents from star to disk (magnetic
  field is not force-free)
• Field lines beyond the corotation radius drive a
  disk wind centrifugally
• Disk winds are collimated into bipolar jets with
  radius500 AU

76
Error analysis for the Zeeman broadening
technique (Saar (ApJ 324, 441 (1988))

• Typical random and systematic errors when perfect
  data are degraded in different ways.
• ?line/continuum opacity ratio
• ?microturbulence
• Some types of error cancel each other

77
Zeeman Doppler imaging simulating the V/I signal
(Donati and Brown AA 326 (1997))

• ZDI first proposed by Semel (AA 225, 456 (1989))
• Plot shows V/I signal for a circular spot at
  phase 0.5 with 500G oriented radially, and
  transverse (meridional and azimuthal).
• i30 and spot at latitude 20 (left) or 70
  (right).
• Different signatures with phase mean little
  crosstalk

78
Differential rotation from ZDI time series
analysis

• Beat period is time for the equator to lap the
  pole by one complete rotation cycle.
• AB Dor (K0 V, Prot0.51days).
• Spot tracking (dark squares).
• Parametric imaging spot tracking (white
  squares), magnetic field tracing (white circles).
  
• Differential rotation always positive. Why are
  spots slower than magnetic field?
• Beat period for HR 1099 K1 IV star 400 days. Why
  so slow?

Petit et al. (AN 325, 221 (2004))
79
The solar wind structure is controlled by the
magnetic field

• Coronal hole regions have open magnetic fields,
  high speed (800 km/s) flows and low densities.
• Near the equator complex field structures
  dominate with low speed (400 km/s) flows and
  high densities.
• ?vconstant
• dM/dt2x10-14 Msun /yr
• 1x109 kg/s