198

6ApJ.

.

.SOIL.

.35K

The

Astrophysical

Journal,

301:L35-L38,

1986

February

1

<

1986.

The

American

Astronomical

Society.

All

rights

reserved.

Printed

in

U.S.A.

VARIABLE

POLARIZATION

AND

ACTIVITY

IN

ARCTURUS

J.

C.

Kemp,

G.

D.

Henson,

D.

J.

Kraus,

I.

S.

Beardsley,

and

L.

C.

Carroll

Department

of

Physics,

University

of

Oregon

AND

D.

K.

Duncan

Mount

Wilson

and

Las

Campanas

Observatories

Received

1985

October

11;

accepted

1985

November

15

ABSTRACT

High-sensitivity

measurements

of

the

blue

light

(B)

polarization

of

this

bright,

nearby

star

on

65

nights

have

led

to

the

discovery

of

intrinsic

variable

polarization,

with

amplitude

about

0.005%.

There

may

be

a

period

or

semiperiod

of

around

45

days,

and

there

is

also

more

rapid

variation.

Concurrent

Ca

n

H

and

K

line

emission

data

clearly

show

variability,

indicating

activity,

during

the

time

interval

represented.

Intensive

further

observa-

tions

including

photometry

are

imperative.

We

consider

three

mechanisms

for

the

polarization.

Subject

headings:

polarization—

stars:

individual

—

stars:

variables

I.

BACKGROUND

In

early

1985

a

program

of

intensive

polarimetry

of

bright

nearby

stars

was

begun

at

Pine

Mountain

Observatory,

Oregon.

A

long-term

aim

of

this

program

is

the

possible

detection

of

dark

orbiting

bodies,

e.g.,

planets,

around

such

stars,

making

use

of

the

fact

that

reflected

light

from

these

bodies

should

be

polarized.

For

a

Jupiter-size

body

0.3

AU

from

a

star,

a

net

polarization

of

at

least

10~

6

,

i.e.,

10~

4

%

,

could

be

expected

in

the

integrated

light.

Differentially,

making

use

of

the

orbital

time

variation,

we

can

reach

such

sensitivity

levels

with

pres-

ent

instruments,

limited

only

by

the

statistics

of

photon

collec-

tion.

We

realized

that

other

effects,

such

as

pulsation

and

stellar

activity,

might

well

cause

apparently

similar

polariza-

tion,

but

those

effects

are

also

interesting.

Tinbergen

(1982)

studied

the

polarization

of

180

stars

within

35

pc

down

to

the

level

0.01%,

but

he

did

not

report

signifi-

cant

effects,

e.g.,

time

variation,

in

such

stars

as

Vega

and

Arcturus.

Measurements

of

stellar

polarizations

an

order

of

magni-

tude

below

the

0.01%

level

have

become

possible

at

Pine

Mountain

Observatory

(PMO).

In

the

eclipsing

binary

Algol

(Kemp

et

al.

1983),

differential

effects

of

0.001%

were

de-

tected.

In

a

solar

polarimetry

program,

observations

at

the

10

6

fractional

polarization

level

(0.0001%)

were

achieved

(Kemp

and

Henson

1983;

Henson

and

Kemp

1984),

princi-

pally

in

circular

polarimetry

but

with

comparable

sensitivity

in

linear

polarimetry.

Making

use

of

this

experience,

we

began

the

present

effort.

Five

stars

have

been

observed

so

far

in

this

program:

Vega,

Arcturus,

Regulus,

Altair,

and

Procyon.

Our

data

on

the

first

two

of

these

are

the

most

numerous.

Some

surprising

results

are

reported

here

on

Arcturus.

Arcturus

is

a

zeroth

magnitude

(V

=

-0.04)

K2

III

giant

at

a

distance

of

about

10

pc.

In

Kukarkin

(1982)

there

is

an

extremely

obscure

reference

to

a

possible

brightness

variation

of

~

0.10

mag,

but

we

have

found

no

reference

to

modem

photometric

studies.

The

star

is

known

to

have

variable

Ca

n

H

and

K

emission,

and

it

has

been

included

in

a

long-term

survey

of

various

stars

for

chromospheric

activity

carried

out

at

Mount

Wilson

(Vaughan,

Preston,

and

Wilson

1978;

Noyes

et

al

1984).

In

this

Letter

we

will

include

some

results

on

Arctums

from

that

program,

for

comparison

with

the

polar-

ization

data.

II.

INSTRUMENTATION

AND

OBSERVATIONS

The

polarization

data

presented

here

were

obtained

with

the

photoelastic-modulator

polarimeter

on

the

61

cm

telescope

at

PMO

(Kemp

and

Barbour

1981).

The

system

has

an

instru-

mental

polarization

in

the

B

band

of

about

0.007%

at

a

certain

position

angle.

Tests

and

results

from

many

programs

over

the

past

8

yr

indicate

this

instrumental

offset

to

be

stable

within

0.002%

or

better.

The

offset

has

recently

been

defined

accurately

by

comparison

measurements

with

another

polar-

imeter,

used

on

the

81

cm

telescope

at

PMO,

as

follows.

The

81

cm

telescope

system

has

arrangements

which

permit

both

solar

and

stellar

measurements.

For

linear

polarimetry,

the

polarimeter

in

that

system

is

operated

in

a

second-harmonic

mode

(Stokes,

Ekstrom,

and

Swedlund

1976).

No

auxiliary

X/4

plate,

which

is

a

source

of

spurious

polarization

(Kemp

and

Barbour

1981;

Kemp

1981),

is

used.

Manual

rotation

of

the

modulator

is

necessary

to

measure

both

linear

Q

and

U

parameters.

That

is

inefficient,

and

we

thus

do

not

use

that

system

for

routine

stellar

polarimetry.

However,

studies

of

inactive

regions

in

the

center

of

the

Sun’s

disk,

with

this

set-up,

showed

near-zero

polarizations

oí

p

<

0.001%.

On

seven

nights

in

1985

June

we

performed

parallel

ob-

servations

of

Vega

and

Arcturus,

using

both

the

61

cm

and

81

cm

telescopes

and

systems.

Comparing

the

data

and

assuming

zero

instrumental

polarization

for

the

81

cm

system,

we

could

then

define

the

instrumental

offset

of

the

61

cm

system,

finding

in

the

B

band:

g

i

nst

=

+0.0054%

and

U

inst

=

-0.0034%.

We

now

use

these

offsets

to

correct

the

61

cm

telescope

data.

In

Figure

1

we

show

the

B

band

polarization

of

Arcturus

from

65

nights

in

early

1985.

The

star

was

measured

for

30-90

©

American

Astronomical

Society

•

Provided

by

the

NASA

Astrophysics

Data

System

198

6ApJ.

.

.SOIL.

.35K

L36

KEMP

ETAL.

Vol.

301

Fig.

1.—Polarization

variations

in

B

band

in

Arcturus

during

1985

May-August

{upper

Wo

panels).

Normalized

equatorial

Stokes

parameters

are

used:

Q

=

p

cos

(20)

and

U

=

p

sin(20).

Dashed

horizontal

lines

indicate

approximate

instrumental

polarization

levels

(see

text).

Dotted

curves

are

from

least-mean-squares

fit

to

44.5

day

sinusoids.

Polarization

of

Vega

is

also

shown

for

comparison,

using

87

contemporaneous

data

points

connected

by

continuous

lines.

Lower

panel

shows

Mount

Wilson

measurements

of

the

Ca

il

H

and

K

emission

in

Arcturus

over

the

same

time

span.

The

rapid

variability

on

time

scales

of

1-5

days

tends

to

obscure

the

longer

period

effects,

indicating

need

for

dense

coverage

in

future

observations.

minutes

each

night,

including

time

for

sky

sampling

and

calibration.

The

data

are

given

in

terms

of

normalized

equa-

torial

Stokes

parameters

Q

=

p

cos

(20)

and

U

=

p

sin

(20).

Errors

were

computed

from

the

scatter

among

independent

4

minute

measures

and

include

both

photon

statistics

and

other

error

sources.

The

vertical

Q

and

U

scales

are

the

direct

or

uncorrected

ones;

we

show

the

estimated

instrumental

offset

levels

(see

above)

with

dashed

lines.

The

star

Vega

was

also

measured

throughout

the

time

interval

of

Figure

1,

and

its

B

band

polarization

on

87

nights

is

also

shown

in

the

figure,

for

simplicity

with

connecting

fines

between

nightly

points.

The

Vega

curves

have

been

shifted

vertically,

to

separate

them

from

the

Arcturus

points.

The

actual

mean

observed

Vega

polarization

(on

the

61

cm

tele-

scope

polarimeter

scale)

was

Q

=

+0.0088%,

U

=

—0.0014%;

the

values

corrected

for

instrumental

offsets

can

be

given

as

Q

0

=

+(0.0034

+

0.0007)%

and

U

0

=

-(0.0048

+

0.0006)%.

Corresponding

corrected

mean

values

for

Arcturus

are

Q

0

=

-0.0007%

and

U

0

=

+0.0001%.

The

broad-band

circular

polarization

of

Arcturus

was

also

measured

on

three

nights,

namely

JD

2,446,246.8-2,446,249.8.

This

was

done

in

unfiltered

fight

(5-20

photomultiplier)

using

the

81

cm

telescope

and

polarimeter.

The

mean

result

was

q

=

V/I

=

(

+

0.00030

+

0.00020)%,

which

is

essentially

null.

It

was

desired

to

compare

the

variable

polarization

in

Arcturus

with

other

forms

of

variability.

Unfortunately

we

did

not

do

simultaneous

photometry

in

this

case.

1

The

only

con-

the

case

of

Vega,

which

is

also

under

study

at

PMO,

both

photometry

and

polarimetry

are

being

carried

out.

©

American

Astronomical

Society

•

Provided

by

the

NASA

Astrophysics

Data

System

198

6ApJ.

.

.SOIL.

.35K

No

1

1986

VARIABLE

POLARIZATION

AND

ACTIVITY

IN

ARCTURUS

current

set

of

other

kinds

of

observations

was

on

the

Ca

n

H

and

K

emission,

referred

to

above.

In

the

lower

panel

of

Figure

1

we

show

the

parallel

record

of

the

H

and

K

emission

index

S,

furnished

by

one

of

us

(Duncan).

Approximately,

S

is

the

ratio

of

fluxes

in

1

À

bandpasses,

in

the

line

cores

relative

to

the

continuum.

The

errors

shown

are

computed

from

the

scatter

among

three

independent

S

value

measures

per

night.

Instrumental

details

will

be

found

in

Vaughan,

Preston,

and

Wilson

(1978).

The

variability.—The

polarization

clearly

varies

on

at

least

two

time

scales.

We

observe

(1)

a

roughly

50

day

variation

and

(2)

cases

of

definite

changes

over

1-5

days.

We

do

not

claim

to

have

discovered

a

periodicity,

but

the

slow

variation

looks

sinusoidal

(especially

in

the

U

parameter),

and

in

Figure

1

we

show

best-fit

sine

waves

with

a

period

of

44.5

days.

The

Vega

polarization,

which

in

any

case

has

a

much

lower

amplitude

variability

than

Arcturus,

shows

no

trace

of

the

~

50

day

variation;

thus,

this

variation

in

Arcturus

cannot

be

spurious.

The

Ca

u

emission

points

show

decidedly

variable

activity,

but

the

points

are

too

sparse

to

permit

a

detailed

test

for

correlation

with

the

polarization

over

most

of

the

time

inter-

val.

In

the

last

part

of

the

interval,

where

the

points

are

denser,

there

is

a

suggestion

of

correlation—note

the

down-

slopes

in

both

the

U

parameter

and

S

curves.

It

is

evident

that

the

rapid

variability

(time

scales

of

perhaps

hours

to

a

few

days)

tends

to

mask

the

longer

period

effects.

A

power

spec-

trum

using

the

entire

H

and

K

emission

data

train

spanning

2

yr

shows

a

highest

peak

at

a

period

of

71

±

3

days.

However,

other

peaks

appear

with

half

the

amplitude

of

that

peak,

and

no

discovery

of

a

real

period

was

possible

from

the

emission

data

alone.

HI.

DISCUSSION

In

view

of

both

the

polarization

and

Ca

n

emission

variabil-

ities,

Arcturus

may

surely

now

be

called

a

variable

star.

Part

of

the

variability

seems

to

be

chaotic

or

flarelike

on

time

scales

at

least

as

short

as

1-5

days.

Whether

the

~

50

day

polarization

variation

is

in

fact

periodic,

and

whether

there

is

some

connection

with

a

candidate

period

of

~

70

days

in

the

emission,

will

be

answered

in

future

seasons.

Only

three

sorts

of

mechanisms

can

be

suggested

for

cyclic

polarization

variation

in

(nominally

nonbinary)

stars:

(1)

non-

radial

pulsation

(Serkowski

1970;

Henson,

Kemp,

and

Kraus

1985);

(2)

rotating

processes,

involving,

e.g.,

spots

or

oblique

magnetic

fields

(Kemp

and

Wolstencroft

1974);

and

(3)

orbit-

ing

bodies

(planets

or

clouds),

which

cause

polarization

by

reflection.

Fundamental

pulsation

periods

of

stars

scale

according

to

P

=

6/(p/Po)

1

/

2

»

where

the

factor

Q

=

0.05

±

0.02

and

p/p

0

is

the

mean

density

relative

to

that

of

the

Sun

(Cox

and

Giuli

1968).

Adopting

R

=

21R

Q

and

M

=

1.1

Mq

for

Arcturus

(Ayres

and

Johnson

1977),

we

find

án

upper

limit

of

about

7

days

for

the

fundamental-mode

period.

A

nonra-

dial

mode

would

have

a

shorter

period.

Thus

it

seems

that

pulsation

cannot

account

for

the

50

day

process.

As

for

a

rotating

process,

Gray

(1981)

gives

for

the

rotation

velocity

ü

sin/=

2.4

km

s

-

1

.

Taking

a

statistical

mean

inclination

of

/

=

60°,

the

rotation

period

would

be

some

300

days,

which

again

does

not

fit

a

50

day

time

scale.

However,

either

rotating

or

orbiting

processes

tend

to

produce

half-

period

(second-harmonic)

polarization

variations

(see,

e.g.,

Rudy

and

Kemp

1978).

Thus

the

50

day

variation

here

could

mean

a

100

day

physical

cycle.

Since

the

spectroscopically

determined

surface

velocity

of

Arcturus

may

be

uncertain

by

a

factor

of

2,

and

since

the

inclination

is

not

known

indepen-

dently,

we

cannot

rule

out

stellar

rotation

as

the

clock

causing

the

50

day

effect.

Regarding

the

inclination,

of

the

star’s

spin

axis

or

an

orbit

axis,

the

50

day

polarization

pattern

itself

suggests

a

large

/,

probably

>

80°.

This

has

to

do

with

the

fact

that

the

cyclic

pattern

of

the

variation

on

the

QU

plane

is

basically

rectilin-

ear

rather

than

elliptical

(Rudy

and

Kemp

1978):

The

Q

and

U

sine

waves

in

Figure

1

are

essentially

in

phase.

Thus

we

could

not

have

a

small

/,

with

thus

a

larger

surface

velocity

and

a

shorter

rotation

period

which

might

lead

to

better

agreement

here.

As

for

mechanism

(3),

taking

the

Arcturus

mass

as

1

M

0

we

find

the

Keplerian

period

at

the

star’s

surface

to

be

~

10

days.

Polarization

variation

by

binary-type

reflection

is

usually

at

the

half-period,

meaning

here

(as

with

the

rotation

case)

a

physical

period

of

around

100

days.

The

orbit

radius

would

be

some

four

stellar

radii,

or

0.4

AU.

An

object

large

enough

to

account

for

the

observed

polarization

amplitude

of

~

0.003%

would

need

to

have

a

radius

of

at

least

10

5

km,

at

that

distance.

Intensive

study

of

Arcturus

is

planned

at

PMO

in

the

coming

season,

including

both

polarimetry

and

photometry.

Other

observations,

such

as

high-resolution

radial

velocity

measurements,

are

strongly

encouraged.

Research

programs

at

Pine

Mountain

Observatory

are

sup-

ported

by

National

Geographic

Society

grant

3003-84,

and

by

NSF

grants

AST-8405542

and

ATM-841176.

The

Mount

Wilson

calcium-line

emission

program

is

supported

by

Na-

tional

Geographic

Society

grant

2548-82

and

by

NSF

grant

AST-817226.

D.

K.

D.

wishes

to

thank

Jim

Frazer,

Sister

Mary

Matthew,

Jean

Mueller,

Don

Poppe,

and

Laura

Woodard

for

assistance

in

taking

and

analyzing

the

Ca

n

data.

REFERENCES

Ayres,

T.

R.,

and

Johnson,

H.

R.

1977,

Ap.

J.,

214,

410.

Cox,

J.

P.,

and

Giuli,

R.

T.

1968,

p.

1029

in

Principles

of

Stellar

Structure,

Vol.

2

(New

York:

Gordon

&

Breach),

p.

1029.

Gray,

D.

F.

1981,

Ap.

J.,

245,

992.

Henson,

G.

D.,

and

Kemp,

J.

C.

1984,

Solar

Phys.,

93,

289.

Henson,

G.

D.,

Kemp,

J.

C,

and

Kraus,

D.

J.

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