The Ap/Bp stars

The origin of magnetic fields in
massive and intermediate-mass stars
Jon Braithwaite
Bonn University
29th August 2013
Biarritz
The origin of magnetic fields in
massive and intermediate-mass stars
Subject of this talk
(and the next few)
Early-type
Subject of loads of talks
the last couple of days
late-type
Early-type stars: classification
spectral type
Subset (~10%)
Rest of population
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
Magnetic fields are:
200G - 30kG,
time-constant & large-scale
The Ap/Bp stars
α2 CVn
(Kochukhov et al 2002)
53 Cam
(Kochukhov et al 2004)
Early-type stars: classification
spectral type
Subset (~10%)
Rest of population
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
Early-type stars: classification
spectral type
Subset (~10%)
Rest of population
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
O and early B: magnetic subset

Fields similar to those in Ap/Bp stars

200G - 5kG?
Field topology of τ Sco, a B0 main-sequence star (MV=2.8)
(Donati et al. 2006, using Zeeman-Doppler imaging)‫‏‬
Early-type stars: classification
spectral type
Subset (~10%)
Rest of population
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Early-type stars: classification
spectral type
early F, A and late B
O and early B
(intermediate mass)
(massive)
Subset (~10%)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Rest of population
~1G fields found in two
brightest A stars
Probably present in all of
these stars........
The "non-magnetic" A and late B stars
Fields < 10 gauss
No stars with fields 10 to 200 G? (Aurière et al 2007)
Recent detection of weak fields in A stars Vega and
Sirius: 0.6 and 0.2 G
•
•
(Lignières et al 2009, Petit et al 2010, 2011)
• Time variability & geometry uncertain
(Very small-scale field would not be detected)
Go to Lignières' talk this afternoon
Early-type stars: classification
spectral type
early F, A and late B
O and early B
(intermediate mass)
(massive)
Subset (~10%)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Rest of population
~1G fields found in two
brightest A stars
Probably present in all of
these stars........
Early-type stars: classification
spectral type
early F, A and late B
O and early B
(intermediate mass)
(massive)
Subset (~10%)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
O and early B: rest of population

No large-scale field above 200G

Various observational phenomena


discrete absorption
components (DACs)

line profile variability (LPV)

wind clumping

solar-like oscillations

red noise

photometric variability

X-ray emission
Could be caused by



magnetic activity at surface
wind shocks, caused by
line-deshadowing instability
likely: both
(DACs: Kaper, Henrichs et al. 1999)
Huib's talk right after mine!
Early-type stars: classification
spectral type
early F, A and late B
O and early B
(intermediate mass)
(massive)
Subset (~10%)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
Early-type stars: classification
spectral type
Subset (~10%)
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
What theory?
What theory?
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
Nature of fields in magnetic subset

Core dynamo?

core is good location for dynamo
figure from MacGregor & Cassinelli 2002
16
Nature of fields in magnetic subset

Core dynamo?

core is good location for dynamo, but:

same fields seen in pre-MS stars
figure from MacGregor & Cassinelli 2002
17
Nature of fields in magnetic subset

Core dynamo?

core is good location for dynamo, but:

same fields seen in pre-MS stars

Subsurface convection? Not enough energy

Meridional circulation? Not enough energy
figure from MacGregor & Cassinelli 2002
18
Nature of fields in magnetic subset

Core dynamo?

core is good location for dynamo, but:

same fields seen in pre-MS stars

Subsurface convection? Not enough energy

Meridional circulation? Not enough energy

Fossil field?

Field is in stable equilibrium

"Fossil" remnant from some earlier time:
pre-MS convective dynamo

merger event

parent cloud
But do stable equilibria exist?


figure from MacGregor & Cassinelli 2002
19
Fossil fields - finding stable equilibria

Analytic studies 1950-1980:
(Prendergast 1956, Markey & Tayler 1973, 74, Wright 1973 inter alia)

two steps:
find equilibrium

check stability
simplifying assumptions, e.g. axisymmetry


Mixed poloidal-toroidal
axisymmetric equilibrium
probably stable
Unstable!
(e.g. Prendergast 1956 and
Wright 1973)
(Tayler 1973, Markey & Tayler 1973,
Flowers & Ruderman 1977)
20
Fossil fields - finding stable equilibria

Analytic studies 1950-1980:
(Prendergast 1956, Markey & Tayler 1973, 74, Wright 1973 inter alia)

two steps:
find equilibrium

check stability
simplifying assumptions, e.g. axisymmetry



Numerical methods (Braithwaite & Spruit 2004, +)

evolve arbitrary initial field

watch formation of stable equilibrium (note: one step)
21
Simulations of magnetic
relaxation to equilibrium
figures from Braithwaite 2008
Simulations of magnetic
relaxation to equilibrium
Axisymmetric and
non-axisymmetric
equilibria
Axisymmetric equilibria
Simulations
(Braithwaite 2008)
Braithwaite & Nordlund 2006
Axisymmetric equilibria
Simulations
(Braithwaite 2008)
Braithwaite & Nordlund 2006
α2 CVn
(Kochukhov et al 2002)
Non-axisymmetric equilibria
Simulations
(Braithwaite 2008)
Non-axisymmetric equilibria
Simulations
(Braithwaite 2008)
τ Sco
(Donati et al. 2006)‫‏‬
Fossil fields - finding stable equilibria

Analytic studies 1950-1980:
(Prendergast 1956, Markey & Tayler 1973, 74, Wright 1973 inter alia)

two steps:
find equilibrium

check stability
simplifying assumptions, e.g. axisymmetry





some types of equilibria found to be unstable
Numerical methods (Braithwaite & Spruit 2004, +)

evolve arbitrary initial field

watch formation of stable equilibrium (note: one step)
Analytic studies since 2000:

solve Grad-Shafranov equation (axisymmetric, barotropic EOS)

include neutron-star physics, e.g. Hall effect, general relativity
26
Fossil equilibria:
recent analytic work
Gourgouliatos et al 2013
Duez & Mathis 2009
1.5
Fossil equilibria:
recent analytic work
1
z
0.5
0
-0.5
-1
-1.5
0
0.5
1
1.5
2
R
2.5
3
3.5
4
Fujisawa & Eriguchi 2013
j0 = 2.5E-3
2
1.5
1.5
1
1
0.5
z
z
0.5
0
0
-0.5
-0.5
-1
-1
-1.5
-2
-1.5
0
0.5
1
1.5
2
R
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3 3.5 4
R
Early-type stars: classification
spectral type
Subset (~10%)
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Theory: fossil field (?)
Theory: fossil field
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
Early-type stars: classification
spectral type
Subset (~10%)
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Theory: fossil field (?)
Theory: fossil field
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
What theory?
Evolution of magnetic field in absence of driving
Vega and Sirius:
first need to think about how fossil fields form
Evolution of magnetic field in absence of driving
Equilibrium in a non-magnetic star:
0=
1
rP + g
⇢
Evolution of magnetic field in absence of driving
Adding a magnetic field:
du
=
dt
U2
1
1
rP + g +
(r ⇥ B) ⇥ B
⇢
4⇡⇢
c2s
v↵2
2
vA
Evolution of magnetic field in absence of driving
Comparing terms in radial direction:
du
=
dt
U2
1
1
rP + g +
(r ⇥ B) ⇥ B
⇢
4⇡⇢
c2s
v↵2
Balanced
2
vA
Evolution of magnetic field in absence of driving
Comparing terms on spherical shells:
du
=
dt
U2
1
1
rP + g +
(r ⇥ B) ⇥ B
⇢
4⇡⇢
c2s
v↵2
Balanced
2
vA
Magnetically-induced motion
happens on Alfvén timescale
Evolution of magnetic field in absence of driving
Comparing terms on spherical shells:
du
=
dt
U2
1
1
rP + g +
(r ⇥ B) ⇥ B
⇢
4⇡⇢
c2s
v↵2
Balanced
2
vA
Magnetically-induced motion
happens on Alfvén timescale
Equilibrium reached on Alfvén timescale:
e.g. 10 years if B~1kG
What happens if we add rotation?
Evolution of magnetic field in absence of driving
Comparing terms on spherical shells:
du
=
dt
U2
1
1
rP + g +
(r ⇥ B) ⇥ B
⇢
4⇡⇢
c2s
v↵2
2
vA
Balanced
In regime Ω << 1/τA , evolution on timescale τA
2⌦ ⇥ u
(L⌦)U
Evolution of magnetic field in absence of driving
Comparing terms on spherical shells:
du
=
dt
U2
1
1
rP + g +
(r ⇥ B) ⇥ B
⇢
4⇡⇢
c2s
v↵2
2
vA
2⌦ ⇥ u
(L⌦)U
Balanced
In regime Ω >> 1/τA , evolution on timescale τA2 Ω
Reference: Braithwaite & Cantiello 2013
Evolution of magnetic field in absence of driving
Comparing terms on spherical shells:
du
=
dt
U2
1
1
rP + g +
(r ⇥ B) ⇥ B
⇢
4⇡⇢
c2s
v↵2
2
vA
2⌦ ⇥ u
(L⌦)U
Balanced
In regime Ω >> 1/τA , evolution on timescale τA2 Ω
Equating age of star to evolution timescale gives
15 and 5 gauss, in cases of Vega and Sirius
Reference: Braithwaite & Cantiello 2013
Failed fossil theory

If field in Vega was ever greater than 15G,
impossible to decay below 15G in its lifetime

Pre-MS convective dynamo B>>15G

Field lower at surface than in interior
Reference: Braithwaite & Cantiello 2013
Early-type stars: classification
spectral type
Subset (~10%)
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Theory: fossil field (?)
Theory: fossil field
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
Theory: failed fossil?
Early-type stars: classification
spectral type
Subset (~10%)
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Theory: fossil field (?)
Theory: fossil field
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
What theory?
Theory: failed fossil?
Subsurface convection in massive stars


Convective layers near surface caused by iron opacity bump
(Langer's talk on Monday)
Dynamo activity?
Cantiello et al. 2008
Subsurface convection in massive stars
Dynamo-generated field reaches
surface via buoyancy
Subsurface convection: simulations

Pencil Code

Setup: piecewise
polytropic (stableunstable-stable)
Cartesian grid
128 x 128 x 256
Fcon/Frad ~ 0.3
Re ~ 80




(Brandenburg & Dobler 2002)
Shown is vertical
velocity field
(Cantiello, Braithwaite, Brandenburg et al. 2011)
Field strengths expected
Assuming equipartition in convective zone (B2/8π ~ ρu2/2)
B (G)
0
500
1500
2500
150 1000
0 500 0
1500
00
35 MSun
2000
2000
10
5.5
1000
120 MSun
6.0
500
5.0
Log L

1000
20 MSun
4.5
4.0
10 MSun
3.5
3.0
4.8
500
0
GAL
7 MSun
4.6
4.4
logTeff
Cantiello & Braithwaite 2011
4.2
4.0
Field strengths expected

Assuming equipartition in convective zone (B2/8π ~ ρu2/2)
B (G)
and B ~ ρ2/3 on
way to surface
0
6
But small-scale
fields not directly
detectable
10
120 MSun
20
40
80
320
160
40
160
> 320
1020 5
80

Effect on wind
35 MSun
40
5
20
Log L

5
20 MSun
10
4
5
10 MSun
3
4.8
GAL
7 MSun
4.6
4.4
logTeff
Cantiello & Braithwaite 2011
4.2
4.0
Spots on surface?
Magnetic features in a radiative star are brighter
than surrounding photosphere
Making simple assumptions:
B ~ 100 G causes a
temperature increase
ΔT ~ 1000 K
at photosphere
Spots on surface?
Spot in convective star
Spot in radiative star?
Spots in a O8V star?
HD 46149 (Degroote et al. 2010, using CoRoT)
Spots in a
B0.5IV star?
HD51756 (Pápics et al. 2011, using CoRoT)
Spots in a
B0.5IV star?
HD51756 (Pápics et al. 2011, using CoRoT)
Summary
spectral type
Subset (~10%)
early F, A and late B
O and early B
(intermediate mass)
(massive)
Ap/Bp stars
200G < B < 30kG
steady, large-scale
200G < B < 5kG
steady, large-scale
Theory: fossil field (?)
Theory: fossil field
Rest of population
~1G fields found in two
brightest A stars
No direct detection, but
indirect suggestions of
Probably present in all of magnetic activity
these stars........
Theory:
subsurface convection?
Theory: failed fossil?
(?) = probable
? = plausible, & absence of other theories