Stellar Magnetic Fields and
Signatures of Heating
Jeffrey Linsky
JILA, University of Colorado and National Institute
of Standards and Technology (NIST)
Boulder Colorado USA
COSPAR Session D2.2/E3.2
Beijing China
17 July 2006
Important questions concerning
magnetic fields and heating
• What can be learned empirically about stellar
magnetic fields and large-scale structure?
• Are there useful scaling laws that relate
magnetic properties to heating?
• Are there thresholds where the magnetic
structure and heating change character?
• Are active stars scaled up versions of the Sun?
• What is the most useful independent variable for
relating magnetic fields to heating?
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.
• Magnetic regions are assumed to have a single value of B (or a few
values) and nonmagnetic regions have B=0.
• Field are lines oriented radially in the photosphere.
• 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.]
• This technique avoids severe cancellation. [At solar maximum, the
net polarization signal would give B=2 G amplitude.]
• Best to observe in the IR because λB/ λD ~ λ. For large B see the
Zeeman spliting. For small B see only broadening.
Zeeman broadening of the T Tauri star TW Hya
(K7) assuming 4 regions of different B (From
Valenti and Johns-Krull (2001))
Zeeman broadening of the flare star EV Lac (from
Johns-Krull and Valenti (1996)). Bf=2.3 kG
Magnetic parameters and relations (Valenti
and Johns-Krull ASP 248, 179(2001))
•
•
•
•
Equipartition (magnetic pressure =
gas pressure): B²eq=8πPg.
B/Beq ≈1 for normal dwarfs but
larger for very active stars
(starspots?) [Wilson depression]
f small for inactive, slowly rotating
stars but large for rapid rotators.
Magnetic coverage “saturation”
(f≈1) when P<1 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).
Activity “saturation” (measured by UV or X-ray emission) is
related to the Rossby number Ro = Prot/тconv
(from Sterzik and Schmitt (1997))
Other methods for determining that
stars have magnetic fields
• Radio emission [gyroresonance (T ≈ 10^7 K), gyrosynchrotron
(T>10^9 K), or coherent (T>10^12 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)
Maps of H I density in the astrospheres of stars due to
interaction of the ISM and stellar wind (Wood et al. ApJ,
628, L143 (2005))
Blue side of Lyα absorption showing effects of
increasing mass loss (Wood et al ApJ 628 (2005))
Stellar wind mass flux vs. activity
(measured by X-ray surface flux)
• Wood et al. ApJL 628, L146
(2005).
• From analysis of Lyman-α
astrospheric absorption.
• Power law correlation until Fx =
8x10^5, then a sharp drop.
• ε Eri: Prot ≈ 11.7 days, f ≈ 0.1.
• ξ Boo A: Prot=6.43 days, f≈0.2.
• Transition corresponds to
activity level where polar spots
become prominent.
• Large-scale magnetic
geometry changes from solarlike (isolated active regions) to
a more dipolar-like field with f ≈
0.1 and a torroidal component.
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: A0=1 (Sun) to 30 (active).
• When A0=30, Bf≈10xsolar max, Prot≈6 days.
• For A0=30 model, magnetic flux densities near
pole would make large spot areas (opening
angle 25 degrees, B≈2 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).
Zeeman-Doppler imaging of AB Dor (Donati et al. 1999)
• K0 V, 20-30 Myr, Prot=0.51 d.
• ZDI with Stokes I and V.
• Spots mostly at pole (area
9%, B=400 G, f=0.5).
• Radial field (Bf>1 kG) in 12-16
regions of opposite polarity.
• Azimuthal field (Bf>1 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).
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.
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).
Magnetic field structure of the moderately active
star ξ Boo A (Petit et al. MNRAS 361 (2005))
• G8 V star: Prot=6.43 days, log fX=6.1 (just to the
right of the wind/X-ray boundary.
• Stokes I and V spectrophotometry
• Large-scale dipole component: Bp~40 G inclined
~35° to rotational pole.
• Large-scale torroidal component: Bt~120 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.
Coronal activity regimes based on stars in clusters
(Pleiades, IC 2602, IC 2391, α Persei, Hyades and
the field) (Randich ASP 198, 401 (2000))
• Ro = Prot/тc (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 < -2.0.
• Sun: log R0 = +0.6
Theoretical chromosphere models of K2 dwarfs with two components
(nonmagnetic regions heated by acoustic waves and magnetic flux tubes
heated by longitudinal MHD waves). B0=2100 G, f0 determined empirically from
Prot. Increasing f0 means less flux tube spreading with height, stronger shocks
and more chromospheric heating. (Cuntz et al. ApJ 522, 1053 (1999)). Relation
of Ca II emission to Prot from theoretical models is consistent with observations.
The effects of rotation on magnetic fields, heating, and
coronal magnetic structures for solar mass stars
Prot
Log fX
f
fB(G)
Log R0
A0
Comments
(days)
25
4.9
0.01 15
+0.6 1
12
5.9
0.10 150
+0.1 10
6
6.5
0.25 380
-0.3
2
7.7
0.70 1050 -0.8
0.5 7.7
0.90 4000 -1.4
Quiet Sun, few
active regions
Change in wind
vs. X-ray plot
Azimuthal polar
belt. Polar spots
500? Saturation begins
(log LX/Lbol = -3)
500? AB Dor. Coronal
free energy 14%
30
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, fX~A0.
• 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 fX=5.9, 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.