“General Model for Light Curves of Chromospherically
Active Binary Stars”
Jetsu, Henry & Lehtinen
2017, ApJ 838: 122 (20pp)
Lauri Jetsu
June 2nd, 2017
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Pink elephant
“We saw a flying elephant.
We were not quite sure that it was pink
and spent a lot of time to prove that it was pink.
This colour problem puzzled us so much
that we never reported to anybody of
having seen a flying elephant.”
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Sunspots
Sunspots
I
Darker (colder areas) on solar surface
I
Magnetic field strongest in sunspots
I
Lifetimes: one or two rotations
I
Brightness effect ≈ ±0.1 %
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Solar cycle
Sunspot cycle (≈ 11 years)
Butterfly diagram (regular latitudinal migration)
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Solar surface differential rotation (SDR)
hereafter SDR
“Law” of SDR
– Equator faster
– Poles slower
– Latitudinal means: not individual
– Next figure: 36 000 sunspot groups
– “Sobering reminder” of “Solar-stellar
connection”
P(b) =
Peq
,
1 − k sin2 b
b = latitude, Peq period at equator and
SDR coefficient k = 0.186
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Dynamo theory
Dynamo theory
– Differential rotation and convection ⇒ Magnetic field
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Starspots
– Rapid rotation: young, binary, coalesced
“No Sun-like dynamo on the active
star Zeta Andromedae...”
(Roettenbacher et al. 2016, Nature
533, 217: Interfrometry)
– Starspots larger than sunspots
– Brightness variation “record” 30-40 %
– Polar spots (not in the Sun)
– Active longitudes (not in the Sun)
– Activity cycles (also in the Sun)
– Differential rotation (also in the Sun)
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
FK Com: “Flip flop” in light curve
FK Com
– Jetsu et el (1993: A&A, 278, 449)
– Single G4 giant
– Rapid rotation: 2.4 days
– Coalesced W UMa binary?
– Photometry: Quarter of a century
– 180 degrees jumps: “flip-flop”
– Three such events
– Two long-lived active longitudes
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
FK Com: “Flip flop” in time
– Another illustration of“flip-flop” events
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
σ Gem: “Flip flop”
σ Gem
– Jetsu et el (1996: A&A, 314, 153)
– Binary K1 giant
– Rapid rotation: 19.6 days
– Photometry: About 20 years
– Two long-lived active longitudes
– “flip-flop” events
– Activity simultaneously at both
longitudes
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
σ Gem: Ellipticity
σ Gem
– Synchronized: Porb = Prot
– Roettenbacher et al.
(2015: ApJ, 807, 23)
– Interferometry:
low mass companion
– Double peaked
Mean Light Curve
hereafter MLC
– Ellipticity
Reason for
“flip-flop” events?
Reason for
active longitudes?
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
BM CVn: MLC=What?
BM CVn
– Synchronized: Porb = Prot
– Siltala et al.
(2017: AN, 338, 453)
– Single peaked
mean light curve: MLC
– Reason: Can not
be ellipticity
– 1st half (dashed)
– 2nd half (dotted)
– Both (continuous)
– (b) Double period correct?
– (c) Radial velocity
– Evolves?
– We subtracted MLC ...
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
MLC model
– Model for these data is
– Orbital phase
g(x, β̄) = a0 +
φorb = FRAC[(t − t0 )/Porb ]
K
X
ak cos(kx) + bk sin(kx),
k=1
FRAC removes the integral part
where β̄ = [a0 , a1 , ..., aK , b1 , ..., bK ] are
the free parameters.
– Bins in orbital phase: N = 20
– Limits for j:th bin are
(j − 1)/N ≤ φorb,i < j/N
– Model is g(x, β̄) = a0 , if K = 0.
– Binned data for the nj values of mi in
the j:th bin are
nj
X
xj = (j/N) − 1/(2N), yj = n−1
mi ,
j
– What is correct K value?
– K = 0 = No periodicity
i=1
−1/2
σj = nj
[n−1
j
nj
X
– Criterion: K = 1 or K = 2, i.e. K 6= 0
Jetsu et a. 2017 (ApJ 838: 122)
(mi − yj )2 ]1/2 =
– Fourteen Chromospherically Active
Binary Stars = hereafter CABS
nj
X
– A component → Light curve
i=1
n−1
j [
– Lehtinen et al. (2011) criterion
i=1
(mi − yj )2 ]1/2
– B component → Unseen
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Mean Light Curves = MLCs
DM UMa
– All CABS synchronized: Porb = Prot
– MLC: All data =thick curve
– 1st part & 2nd part = dotted curves
– This star: Long M cycle
XX Tri
Aa=φrot = 0.25 = A (active) in front of B
Ac=φrot = 0.75 = B in front of A (active)
– This star: From high to low A
– This star: From low to high M
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Mean Light Curves = MLCs
EL Eri
V711 Tau
– MLC changes: dark spots
– This star: Shorter M cycle
– MLC single peaked: high and low A
– This star: Minimum at Aa
– MLC double peaked: only low A
– This star: Other minimum at Ac
– This star: M up → A down
– This star: MLC shape unchanged
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Mean Light Curves = MLCs
EI Eri
V1149 Ori
– Shorter M cycle
– Long M cycle
– Minimum at Ac
– Single peak MLC
– Other minimum at Aa
– Minimum near Ac
– MLC shape unchanged
– MLC shape unchanged
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Mean Light Curves = MLCs
σ Gem
FG UMa
– Stable MLC
– Shorter M cycle
– Double peaked
– MLC level changes
– Ellipticity?
– MLC shape same
– Minima: Aa and Ac
– Minima: Aa and Ac
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Mean Light Curves = MLCs
HU Vir
BM CVn
– From low to high A
– Shorter M cycle
– From high to low M
– Single peaked MLC
– Minima: Aa and Ac
– Small changes
– MLC shape same
– Minimum near Ac
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Mean Light Curves = MLCs
V478 Lyr
V1762 Cyg
– Double peaked
– Double peaked
– Low MLC amplitude
– Low MLC amplitude
– Minima switch (e versus g)
– Minima switch (e versus g)
– Minima: near Aa and Ac
– Ephemeris inaccurate
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Mean Light Curves = MLCs
HK Lac
II Peg
– Single peaked
– Single peaked
– High MLC amplitude
– High MLC amplitude
– Changes on one side
– Minimum near Aa (Ephemeris
accurate)
– Ephemeris inaccurate
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Stationary part of light curve
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Synchronized stationary part
– MLC: Where starspots concentrate
– Stationary “flip-flop” mode changes
– MLC: 1st and 2nd part → changes
Type I: S1f ↔ S1b
– Always: Same side towards each other
Type II: S12fb ↔ S12bf
– Line connecting A and B centres:
Spots always at longitudes of this line
Type III: S1f ↔ S12bf
– Spot S1 larger on this line
Type IV: S1b ↔ S12fb
– Spot S2 smaller on this line
– Another alternative
S1f ↔ S12fb ↔ S12bf ↔ S1b.
– M low A high → Dark starspots
– MLC = Stationary part f2 (t, β̄2 ) =
– M high A low → Dark starspots
– Double peak MLC: low amplitudes
→ Two dark starspots
– Single peak MLC: low and high
amplitudes
→ One dark starspot
– Ellipticity “fits in”: →
increases double peaked
weakens/shifts single peaked
M2 +
K2
X
k=1
Ck cos(
2πkt
2πkt
) + Dk sin(
)
Porb
Porb
(1)
– Free parameters:
β̄2 = [M2 , C1 , ..., CK2 , D1 , ..., DK2 ]
– Order: K2 = 1 or 2
– Stationary on surface of A component, i.e. in
corotating frame (Porb = Porb )
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
– MLC from all data,
or 1st and 2nd parts of data
– Detected Pact in thirteen CABS
– Continuous Period Search = CPS
– Lap cycle period
– Formulated in Lehtinen et al. (2011)
– Seasonal light curves (∆T = 30 days)
K = 0 ≡ Constant line = ≡ No periodicity
K = 1 ≡ Sinusoid ≡ Periodicity
K = 2 ≡ Single or double sinusoid ≡ Periodicity
MCPS = Mean brightess → Activity
cycles
ACPS = Amplitude → Activity cycles
PCPS = Rotation period → SDR
tCPS,min,1 = Primary minimum epoch
tCPS,min,2 = Secondary minimum epoch
– Kuiper test of tCPS,min,1 and tCPS,min,2 reveals
Active longitude period Pact
– Too few tCPS,min,1 for V478 Lyr
−1 −1
Pcyc = |[P−1
|.
orb − Pact ]
– Active longitude phases
φact = FRAC[(t − tcyc,0 )/Pact ],
where first tCPS,min,1 is tcyc,0
– Lap cycle phases
φcyc = FRAC[(t − tcyc,0 )/Pcyc ]
– Individual amplitudes ACPS studied as
function of φorb and φcyc
– Binned amplitudes ACPS studied as
function of φorb and φcyc
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
DM UMa
XX Tri
– Minima follow active longitudes (a:
tilted lines)
– Minima mostly follow active longitudes
(a: tilted lines)
– Lap cycle period
Pcyc = 25506 ± 104725 days (69.8 y)
– Migration direction only relevant
– Inaccurate, poor φcyc coverage
– Amplitude φcyc and φorb connection
– Amplitude orbital phase connection
– Amplitude scatter connection to both
– Pcyc = 2860 ± 145 days (7.8 y)
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
EL Eri
V711 Tau
– Minima follow both φorb (a: horizontal
lines) and φact (a: tilted lines)
– Minima follow both φorb (a: horizontal
lines) and φact (a: tilted lines)
– Pcyc = 4017 ± 1434 days (11.0 y)
– Fast Pcyc = 150 ± 11 days (0.4 y)
– Amplitude φcyc connection
– Weak amplitude φcyc connection
– Amplitude scatter connection to φorb
– Amplitude scatter connection to φorb
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
EI Eri
V1149 Ori
– Minima mostly follow φorb (a: horiz. lines)
– Minima mostly follow φact (a: tilted lines)
– Fast Pcyc = 526 ± 58 days (1.4 y)
– Pcyc = 6550 ± 912 days (17.9 y)
– Amplitude φcyc : too few points
– Amplitude: φcyc and φorb connection
– Amplitude connection to φorb
– Scatter: φcyc and φorb connection
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
σ Gem
FG UMa
– Minima follow either φact (a: tilted lines)
or φrot (a: horizontal lines)
– Minima follow either φact (a: tilted lines)
or φrot (a: horizontal lines)
– Pcyc = 3557 ± 116 days (9.7 y)
– Pcyc = 1883 ± 80 days (5.2 y)
– Amplitude & scatter: φcyc and φorb
connections “perfect”
– Amplitude & scatter: φcyc and φorb
connections “perfect”
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
HU Vir
– Similar phenomena 9.4 years ...
BM CVn
– Similar phenomena 10.3 years ...
– Inaccurate ephemeris ...
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
V1762 Cyg
– Similar phenomena 5.3 years ...
HK Lac
– Very long Pcyc = 57.5 years
– Similar phenomena ...
– Inaccurate ephemeris ...
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Continuous Period Search = CPS
II Peg
CABS light curves contain a
nonstationary part f1 (t, β̄1 ) =
M1 +
K1
X
k=1
Ak cos(
2πkt
2πkt
) + Bk sin(
)
Pact
Pact
(2)
– Free parameters:
β̄1 = [M1 , A1 , ..., AK1 , B1 , ..., BK1 ]
– Nonstationary tCPS,min,1 changes linear in
φorb → K1 = 1 perhaps sufficient
– Suitable general CABS light curve
model
– Similar phenomena 9.9 years ...
– Stationary dominates before 1997
f (t, β̄) = f1 (t, β̄1 ) + f2 (t, β̄2 )
(3)
is a sum stationary and nonstationary part
– Nonstationary dominates after 1997
– No “flip-flop” events
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
One complete Pcyc lap cycle
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Slice of σ Gem photometry
– Detailed analysis of
individual stars
elsewhere
– Test just three slices
– ∆T = 589 days of
σ Gem photometry
– K1 = 1 and K2 = 2
model
– Linear model =
Unique solution
– Earlier models
∆T ≤ 30 days
– Goes through gaps
– Light curve shape
and amplitude can
change
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Another slice of σ Gem photometry
– ∆T = 230 days of
σ Gem photometry
– K1 = 1 and K2 = 2
model
– K1 = 2 and K2 = 2
model
– Solutions similar
– Stationary and
nonstationary parts
change between
seasons
– Assumption:
Stationary and
nonstationary parts
do not change inside
seasons: NOT TRUE
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
ApJ: Slice of FK Com photometry
– ∆T = 126 days of
FK Com photometry
– Single star →
Prot ≡ Porb unknown
– Solve Prot by using
the model with
known Pact value
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)
Conclusions
– Draw and explain
– Two structures (magnetic field waves?)
rotating with constant periods Prot
(stationary) and Pact (nonstationary)
– If Prot dominates (horizontal in φorb )
– If Pact dominates (tilted linear in φorb )
– Except for filling factor changes:
“Nothing ever happens” (Giant clock)
– Magnetic fields in all spectral types?
1. Differential rotation and convection
(dynamo) in late-type stars
2. Fossil fields (oblique rotator) in
early-type stars
– Third alternative
3. Rotation and interference in all
spectral types? Convection
complicates things in late-type
– Two constant periods Prot (stationary)
and Pact → What happens to SDR?
– Kron (1947, PASP 59, 261) first
observations of starspots
– For 70 years we have been observing
interference: observed light curve
– Real light curves hidden behind this
“veil of interference”
– Draw: Example of constant light curve
– Earlier models worked for ∆T = 30
days → New model works for
∆T = 100 − 600 days (three slices)
– Pcyc : explains observed amplitudes!
– “Real Light Curves of FK Comae
Berenices”, Jetsu (2017, A&A,
submitted)
– Referee is a true believer in SDR →
I will elaborate in my next seminar
lecture → I can promise: “Things will
never be the same.”
– What was the elephant?
Lauri Jetsu
“General Model for Light Curves of Chromospherically Active Binary Stars” Jetsu, Henry & Lehtinen 2017, ApJ 838: 122 (20pp)