Draft version August 11, 2020Typeset using LATEX twocolumn style in AASTeX62

13 Years of P Cygni Spectropolarimetry: Investigating Mass-loss Through Hα, Periodicity, and Ellipticity

Keyan Gootkin,1 Trevor Dorn-Wallenstein,1 Jamie R. Lomax,2 Gwendolyn Eadie,3, 4 Emily M. Levesque,1

Brian Babler,5 Jennifer L. Hoffman,6 Marilyn R. Meade,5 Kenneth Nordsieck,5 and John P. Wisniewski7

1Department of Astronomy, University of Washington, Seattle, WA, USA2Physics Department, United States Naval Academy, 572C Holloway Rd, Annapolis, MD, 21402, USA

3Department of Astronomy & Astrophysics, University of Toronto, Toronto, ON, Canada4Department of Statistical Sciences, University of Toronto, Toronto, ON, Canada

5Department of Astronomy, University of Wisconsin-Madison, 475 N. Charter St., Madison, WI 53706, USA6Department of Physics and Astronomy, University of Denver, 2112 East Wesley Ave., Denver, CO 80208, USA

7Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W Brooks Street, Norman, OK 73019, USA

ABSTRACT

We report on over 13 years of optical and near-ultraviolet spectropolarimetric observations of the

famous Luminous Blue Variable (LBV), P Cygni. LBVs are a critical transitional phase in the lives of

the most massive stars, and achieve the largest mass-loss rates of any group of stars. Using spectropo-

larimetry, we are able to learn about the geometry of the near circumstellar environment surrounding

P Cygni and gain insights into LBV mass-loss. Using data from the HPOL and WUPPE spectropo-

larimeters, we estimate the interstellar polarization contribution to P Cygni’s spectropolarimetric sig-

nal, analyze the variability of the polarization across the Hα emission line, search for periodic signals in

the data, and introduce a statistical method to search for preferred position angles in deviations from

spherical symmetry which is novel to astronomy. Our data are consistent with previous findings, show-

ing free-electron scattering off of clumps uniformly distributed around the star. This is complicated,

however, by structure in the percent-polarization of the Hα line and a series of previously undetected

periodicities.

1. INTRODUCTION

Luminous Blue Variables (LBVs)—also called S Do-

radus or S Dor variables—are incredibly rare, with less

than 20 confirmed members of this class in the Milky

Way (Richardson & Mehner 2018). Despite the short

lifetime of the LBV phase (∼ 105yr), these stars are

an important set of objects for understanding the post-

main sequence evolution of stars with initial masses

≥ 20M� (Groh et al. 2014). This eclectic group rep-

resents a critical transitional phase in the lives of the

most massive stars.

LBVs reside at the top of the Hertzsprung-Russell

diagram. This unique position—near the Humphreys-

Davidson limit (Humphreys & Davidson 1979), and on

the S Dor instability strip—produces strange behavior

in these stars. LBVs are highly unstable, losing large

amounts of mass, and dramatically varying both photo-

metrically and spectroscopically. In their quiescent, hot

state (12,000 to 30,000 K), LBVs resemble blue super-

Corresponding author: Keyan Gootkin

goot1024@uw.edu

giants. However, during an outburst they move horizon-

tally across the HR diagram to temperatures between

7500 K and 9000 K—maintaining a consistent bolomet-

ric luminosity even while V -band magnitudes fluctuate

(Humphreys & Davidson 1994).

Other than Wolf-Rayet stars, LBVs achieve the high-

est mass-loss rates of any group of stars, 10−5−10−4M�yr−1, and beyond the “typical” S Dor outbursts they

undergo catastrophic (but non-terminal) eruptions in

which significant mass is lost (Humphreys & Davidson

1994). The only observed eruptions in our galaxy were

from P Cygni (also known as P Cyg, 34 Cyg, or Nova

Cyg 1600), in which 0.1 M� was lost (Smith & Hartigan

2006), and η Car which is estimated to have lost over

10M� of material in its massive 19th century eruptions

(Smith et al. 2003). However, the physical mechanisms

behind the eruption, outburst, and quiescent modes of

mass loss are poorly understood.

The subject of this paper, P Cygni, was discovered

on August 18th, 1600. The Dutch cartographer, globe-

maker, and former student of Tycho Brahe, Willem Jan-

szoon Blaeu, observed a Nova Stella in the heart of

Cygnus (Blaeu 1602). He chronicled this discovery in

arX

iv:2

008.

0377

7v1

[as

tro-

ph.S

R]

9 A

ug 2

020

2 Gootkin et al.

an inscription on a celestial globe, made in his Amster-

dam workshop in 16021. This new star was P Cygni.

Although it was called a nova at the time, it was later

recognized as a Luminous Blue Variable (LBV).

During the 1600 eruption (the Nova Stella), P Cygni

brightened to the point of visibility (up to 3rd magni-

tude) for the first time, and remained visible for 26 years

before fading to ∼ 6th magnitude. It reached ∼ 3rd mag-

nitude again in 1654, experienced variability for a num-

ber of decades, but has been in a stage of quiescence

since the late 18th century (de Groot & Mart 1988).

Even in a rare, enigmatic class of objects, P Cygni is

unique. It does not exhibit all of the same photometric

behavior of other S Doradus variables. It has stayed in

its quiescent state, at roughly 18,700 K and 61,000 L�,

for several hundred years. The nebula surrounding P

Cyg is faint and morphologically different from those of

most LBVs (Nota et al. 1995). It has also been studied

for longer than any other LBV; an excellent summary

of work done in the 20th century can be found in Is-

raelian & de Groot (1999). Being such a singular and

well studied object, P Cygni is critically important to

our understanding of the evolution of the most massive

stars in the universe.

Additionally, since it has been so stable for the past

300 years, ejecta from the outbursts have had the time

to move far away from the star, and polarimetry can now

open a window into the less dramatic, quiescent mode

of mass-loss. There have been extensive studies of the

shells of material which were ejected in the 17th century

eruptions (Barlow et al. 1994; Nota et al. 1995; Meaburn

et al. 1996), first resolved by Leitherer & Zickgraf (1987),

but much less is known about the nature of the ambient

stellar wind.

In order to study the mass-loss in P Cygni’s current

state we turn to polarimetry. In the study of massive

stars, polarimetry is an invaluable tool. Due to these

stars’ enormous luminosities and optically thick nebu-

lae, it is difficult to observe the innermost regions of

their stellar winds. Polarimetry circumvents this prob-

lem, in fact, in certain geometries polarimetric signals

can be enhanced in the presence of an optically thick

nebula (Wood et al. 1996a,b). While P Cygni is in a

quiescent (hot) state, we expect electron scattering to

be the dominant mechanism causing any net polariza-

tion. This scattering is only efficient very near to the

star (Nordsieck et al. 2001; Taylor et al. 1991a; Davies

et al. 2005, 2006) and, as is discussed in the following sec-

1 The first edition of this globe, as of the writing of this paper,is in the collections of Skokloster Castle, a castle and museumnorth of Stockholm and can be viewed online here.

tion, is only sensitive to asymmetries when unresolved.

Therefore, polarimetry is a good way to probe asymme-

tries at the base of P Cygni’s stellar wind.

While P Cygni had long been known to be polarized

(Coyne & Gehrels 1967; Coyne et al. 1974; Serkowski

et al. 1975), the first extensive study of its polarization

was conducted by Hayes (1985). Taylor et al. (1991a)

and Nordsieck et al. (2001) (hereafter T91 and N01)

followed the results of Hayes (1985) using optical spec-

tropolarimetric observations. Spectropolarimetric ob-

servations measure the Stokes parameters q and u as

a function of wavelength, just as spectroscopic observa-

tions measure flux as a function of wavelength. The fol-

lowing conclusions were made by all three studies (Nord-

sieck et al. 2001; Taylor et al. 1991a; Hayes 1985):

• P Cygni is intrinsically polarized, indicating the

presence of asymmetries in the polarizing region.

• The polarization of P Cygni does not appear to

prefer a position angle. This implies that the

asymmetries which produce net polarization are

equally likely to emerge in any direction on the

plane of the sky.

• With previous data sets the polarization of P

Cygni did not appear to be periodic, although

there was evidence for a 10-15 day characteristic

timescale for polarimetric changes.

As presented in the discussion of T91, these results

seem to favor a roughly axisymmetric wind with re-

gions of enhanced electron density, referred to as inho-

mogeneities or clumps, which are ejected from the star

and travel outwards through the polarizing region within

its wind. We will use these terms in this work as well.

In this paper, we combine the previously published

data from T91 and N01 with unpublished observations

from the early 2000s, which were taken with the same

instrument as these archival data. In section 2, we dis-

cuss the details of these observations. We discuss our

attempts to remove the polarization due to the inter-

stellar medium in Section 3. We analyze the remaining

polarization signature, which is intrinsic to the P Cyg

system, with novel methods in Section 4. In Section 5,

we discuss our results in the larger context of what is

already known about the P Cyg system. Finally, we

summarize our conclusions in Section 6.

2. OBSERVATIONS

2.1. HPOL

Our data are comprised of spectropolarimetric obser-

vations taken on 80 nights, spanning 13 years, using the

University of Wisconsin’s Half-wave Spectropolarimeter

13 Years of P Cygni Spectropolarimetry 3

(HPOL) while it was mounted on the 36” telescope at

Pine Bluff Observatory. In 1995 HPOL switched from

using a Reticon dual channel photo-diode array to a

400 × 1200 pixel CCD. As a result our data are split

into the 46 observations taken before this switch (here-

after Reticon data) and the 34 taken after (CCD data).

The Reticon detector covered a wavelength range be-

tween 3200 and 7600 A at a 15 A resolution, while the

CCD recorded data using blue (3200-6000 A) and red

(6000-10,500 A) gratings in combination to obtain a full

observation. The blue grating had a spectral resolu-

tion of 7.5 A, while the red grating was 10 A. More

complete reviews of this instrument are in Nordsieck &

Harris (1996), Wolff et al. (1996), and Davidson et al.

(2014). Basic reduction steps were performed on all of

the HPOL observations using the custom built Fortran

software package REDUCE (Nook et al. 1990; Wolff et al.

1996; Davidson et al. 2014).

We downloaded these data from the Mikulski Archive

for Space Telescopes (MAST) archive2 and omitted 4

nights of data from our final data set. These four

nights of CCD observations only used the red grating

(27 September 1997, 27 August 1998, 30 May 2000, and

13 November 2002), which does not cover the full wave-

length range we were interested in analyzing. There-

fore, we omitted them from our final data set. Table 1

lists the civil and modified Julian dates of our remaining

HPOL observations (46 Reticon observations and 30 full

CCD observations). Of the full 80 nights of data, T91

used 20 of the Reticon observations and N01 used 15 of

the CCD observations.

From the normalized Stokes parameters, q and u, per-

cent polarization, P%, and position angle, Θ, are defined

as

P% =√q2 + u2 (1)

Θ =1

2arctan

u

q. (2)

2.1.1. Synthetic V Band Data

To characterize the optical broadband behavior of P

Cyg, we convolved each of our HPOL observations with

a synthetic Johnson V -band filter (Bessell 1990). We

report these values in Table 1 as our “observed” V band

values. Figure 1 shows a graphical representation of how

this convolution process works mathematically.

HPOL’s instrumental polarization was monitored on

an approximately monthly basis by observing polar-

ized and unpolarized standard stars. Davidson et al.

(2014) reported the instrument’s systematic uncertain-

ties in the Johnson UBVRI bands for the CCD detector,

which were calculated using those observations. In or-

der to match HPOL’s historically reported values, we

calculated one overall root-mean-square systematic un-

certainty for each CCD observation in the V band using

the individual q and u systematic uncertainties com-

piled by Davidson et al. (2014). Two observations (10

September 1998 and 16 September 1998) fell outside of

all of the date ranges for which Davidson et al. (2014) re-

ported systematic uncertainties. Therefore, we used the

values reported for the 14 June 1998-16 August 1998

range because it was closest in time to these observa-

tions. Systematic uncertainties for the Reticon detector

are less well known, but our previous experience with

HPOL data suggests they are less than 0.02%. In order

to characterize the uncertainty in the V band for a given

observation, we use the larger of its systematic and in-

ternal uncertainties, which are from photon statistics,

in our analysis. We report both these uncertainties in

Table 1.

Figure 1. Graphic illustrating how the V -band (§2.1.1) andHα pfew (§2.1.2) values tabulated in Table 1 are calculated.These data were taken from a representative observation af-ter ISP correction as described in §3. For the pfew side of thefigure (right) the dashed lines represent regions contributingto the continuum polarization and the color represents re-gions contributing to the line polarization.

2 The website for this archive is https://archive.stsci.edu

4 Gootkin et al.

Table

1.

HP

OL

Obse

rvati

ons

VBand

Hα

Continuum

Hα

Line

Dete

cto

rM

JD

Date

Obse

rved

Intr

insi

cIn

trin

sic

Obse

rved

Intr

insi

cO

bse

rved

%q

%u

%q

%u

Int

Err

Sys

Err

%q

%u

Err

or

%q

%u

Err

or

%q

%u

Err

or

%q

%u

Err

or

Ret

icon

47668

1989-0

5-2

20.3

05

0.9

97

-0.1

34

-0.1

35

0.0

20

0.0

04

-0.1

50

-0.1

71

0.0

65

0.2

40

0.8

77

0.0

65

0.0

46

0.0

27

0.1

72

0.4

35

1.0

75

0.1

72

—47672

1989-0

5-2

60.6

11

1.0

57

0.1

72

-0.0

76

0.0

20

0.0

04

0.2

14

-0.0

42

0.0

48

0.6

03

1.0

06

0.0

48

-0.1

10

0.1

15

0.1

08

0.2

79

1.1

62

0.1

08

—47697

1989-0

6-2

00.2

89

1.1

28

-0.1

50

-0.0

05

0.0

20

0.0

04

-0.0

58

0.0

42

0.0

53

0.3

32

1.0

90

0.0

53

-0.2

27

-0.1

43

0.1

01

0.1

63

0.9

05

0.1

01

—47714

1989-0

7-0

70.4

37

0.8

63

-0.0

02

-0.2

69

0.0

20

0.0

05

-0.0

77

-0.1

00

0.0

52

0.3

13

0.9

48

0.0

52

-0.1

38

-0.0

99

0.1

31

0.2

51

0.9

49

0.1

31

—47808

1989-1

0-0

90.5

27

1.1

06

0.0

88

-0.0

26

0.0

20

0.0

04

0.0

69

-0.0

28

0.0

55

0.4

58

1.0

19

0.0

55

-0.0

98

-0.0

99

0.0

99

0.2

92

0.9

49

0.0

99

—47822

1989-1

0-2

30.1

74

0.8

26

-0.2

65

-0.3

06

0.0

20

0.0

03

-0.1

93

-0.2

69

0.0

37

0.1

97

0.7

79

0.0

37

0.0

28

-0.1

68

0.0

64

0.4

17

0.8

79

0.0

64

—47913

1990-0

1-2

20.7

16

1.3

17

0.2

76

0.1

84

0.0

20

0.0

07

0.1

98

0.1

69

0.0

96

0.5

87

1.2

17

0.0

96

-0.0

64

-0.2

92

0.1

59

0.3

26

0.7

56

0.1

59

—47918

1990-0

1-2

70.5

47

1.0

56

0.1

08

-0.0

76

0.0

20

0.0

03

0.1

54

-0.1

48

0.0

35

0.5

44

0.9

01

0.0

35

0.0

20

-0.1

54

0.0

84

0.4

09

0.8

94

0.0

84

—47919

1990-0

1-2

80.6

75

1.1

11

0.2

36

-0.0

21

0.0

20

0.0

03

0.1

63

-0.0

51

0.0

40

0.5

53

0.9

97

0.0

40

-0.0

27

0.0

60

0.0

79

0.3

62

1.1

08

0.0

79

—47920

1990-0

1-2

90.7

62

1.0

27

0.3

23

-0.1

05

0.0

20

0.0

06

0.3

06

-0.0

98

0.0

78

0.6

96

0.9

51

0.0

78

0.0

50

0.1

01

0.1

33

0.4

40

1.1

49

0.1

33

—47942

1990-0

2-2

00.2

02

1.0

97

-0.2

37

-0.0

35

0.0

20

0.0

04

-0.2

24

-0.0

40

0.0

61

0.1

66

1.0

09

0.0

61

-0.0

81

-0.1

10

0.1

00

0.3

08

0.9

37

0.1

00

—47950

1990-0

2-2

80.3

53

1.3

87

-0.0

86

0.2

55

0.0

20

0.0

03

0.0

09

0.2

75

0.0

44

0.3

99

1.3

23

0.0

44

0.0

10

-0.0

55

0.0

91

0.3

99

0.9

92

0.0

91

—47987

1990-0

4-0

60.5

06

1.1

97

0.0

67

0.0

65

0.0

20

0.0

04

0.0

38

0.1

53

0.0

59

0.4

28

1.2

01

0.0

59

0.0

49

-0.0

82

0.1

14

0.4

38

0.9

66

0.1

14

—47988

1990-0

4-0

70.5

58

1.1

55

0.1

19

0.0

23

0.0

20

0.0

04

0.1

15

0.1

68

0.0

47

0.5

04

1.2

16

0.0

47

-0.0

93

-0.0

96

0.0

79

0.2

97

0.9

52

0.0

79

—47994

1990-0

4-1

30.3

55

0.9

55

-0.0

84

-0.1

78

0.0

20

0.0

03

-0.0

86

-0.1

19

0.0

31

0.3

03

0.9

29

0.0

31

0.0

07

0.0

28

0.0

64

0.3

97

1.0

75

0.0

64

—48003

1990-0

4-2

20.3

41

1.3

67

-0.0

98

0.2

34

0.0

20

0.0

06

-0.0

27

0.2

87

0.0

79

0.3

62

1.3

35

0.0

79

-0.0

03

-0.1

68

0.1

94

0.3

87

0.8

80

0.1

94

—48018

1990-0

5-0

70.2

82

0.9

65

-0.1

58

-0.1

67

0.0

20

0.0

07

-0.1

73

-0.2

07

0.0

99

0.2

17

0.8

41

0.0

99

0.1

69

-0.1

31

0.1

80

0.5

59

0.9

17

0.1

80

—48047

1990-0

6-0

50.5

56

0.9

77

0.1

16

-0.1

55

0.0

20

0.0

15

-0.0

28

-0.2

78

0.2

48

0.3

62

0.7

70

0.2

48

0.2

50

0.1

68

0.4

46

0.6

40

1.2

15

0.4

46

—48057

1990-0

6-1

50.3

00

1.2

23

-0.1

39

0.0

91

0.0

20

0.0

02

-0.1

90

0.0

74

0.0

25

0.1

99

1.1

21

0.0

25

0.1

04

-0.0

04

0.0

58

0.4

94

1.0

44

0.0

58

—48088

1990-0

7-1

60.3

31

1.2

03

-0.1

08

0.0

71

0.0

20

0.0

03

-0.0

94

0.0

57

0.0

37

0.2

96

1.1

05

0.0

37

-0.1

61

-0.0

77

0.0

69

0.2

29

0.9

70

0.0

69

—48133

1990-0

8-3

00.7

59

1.0

77

0.3

20

-0.0

56

0.0

20

0.0

03

0.1

93

-0.0

60

0.0

39

0.5

83

0.9

88

0.0

39

0.2

01

-0.1

21

0.0

67

0.5

90

0.9

26

0.0

67

—48150

1990-0

9-1

60.3

02

1.1

53

-0.1

37

0.0

20

0.0

20

0.0

02

-0.1

66

0.0

07

0.0

25

0.2

24

1.0

55

0.0

25

0.0

12

-0.0

76

0.0

58

0.4

02

0.9

72

0.0

58

—48159

1990-0

9-2

50.4

76

1.3

64

0.0

36

0.2

32

0.0

20

0.0

02

-0.0

46

0.2

13

0.0

27

0.3

44

1.2

61

0.0

27

0.0

58

-0.1

17

0.0

63

0.4

47

0.9

31

0.0

63

—48224

1990-1

1-2

90.4

72

0.9

62

0.0

33

-0.1

70

0.0

20

0.0

02

0.0

68

-0.1

23

0.0

23

0.4

58

0.9

25

0.0

23

-0.0

81

-0.1

14

0.0

63

0.3

09

0.9

35

0.0

63

—48231

1990-1

2-0

60.2

75

0.4

95

-0.1

64

-0.6

37

0.0

20

0.0

02

-0.1

18

-0.6

36

0.0

23

0.2

71

0.4

12

0.0

23

-0.0

66

0.0

89

0.0

47

0.3

24

1.1

37

0.0

47

—48235

1990-1

2-1

00.0

99

1.2

25

-0.3

40

0.0

92

0.0

20

0.0

02

-0.3

29

0.0

52

0.0

20

0.0

61

1.1

00

0.0

20

0.0

85

-0.2

25

0.0

46

0.4

74

0.8

22

0.0

46

Table1continued

13 Years of P Cygni Spectropolarimetry 5Table

1(continued)

VBand

Hα

Continuum

Hα

Line

Dete

cto

rM

JD

Date

Obse

rved

Intr

insi

cIn

trin

sic

Obse

rved

Intr

insi

cO

bse

rved

%q

%u

%q

%u

Int

Err

Sys

Err

%q

%u

Err

or

%q

%u

Err

or

%q

%u

Err

or

%q

%u

Err

or

Ret

icon

48320

1991-0

3-0

50.2

79

1.2

90

-0.1

61

0.1

58

0.0

20

0.0

03

-0.1

71

0.1

17

0.0

46

0.2

19

1.1

65

0.0

46

0.0

02

-0.0

90

0.0

88

0.3

92

0.9

58

0.0

88

—48444

1991-0

7-0

70.5

23

1.2

86

0.0

84

0.1

54

0.0

20

0.0

05

0.1

33

0.0

46

0.0

68

0.5

23

1.0

94

0.0

68

-0.0

86

0.0

07

0.1

28

0.3

03

1.0

55

0.1

28

—48473

1991-0

8-0

50.5

37

0.9

73

0.0

98

-0.1

59

0.0

20

0.0

14

0.3

48

-0.0

28

0.2

64

0.7

38

1.0

20

0.2

64

0.0

36

0.0

94

0.3

60

0.4

26

1.1

41

0.3

60

—48516

1991-0

9-1

70.5

96

1.1

50

0.1

56

0.0

18

0.0

20

0.0

02

0.1

28

0.0

05

0.0

28

0.5

18

1.0

53

0.0

28

-0.0

34

0.0

32

0.0

45

0.3

55

1.0

80

0.0

45

—48520

1991-0

9-2

10.1

35

0.8

17

-0.3

05

-0.3

15

0.0

20

0.0

02

-0.2

75

-0.3

69

0.0

27

0.1

15

0.6

79

0.0

27

0.0

22

-0.0

32

0.0

46

0.4

11

1.0

16

0.0

46

—48522

1991-0

9-2

30.0

24

1.0

21

-0.4

15

-0.1

11

0.0

20

0.0

02

-0.3

89

-0.1

87

0.0

25

0.0

01

0.8

61

0.0

25

0.0

16

-0.1

42

0.0

40

0.4

06

0.9

06

0.0

40

—48525

1991-0

9-2

60.7

99

1.3

36

0.3

60

0.2

03

0.0

20

0.0

04

0.2

77

0.1

97

0.0

60

0.6

66

1.2

45

0.0

60

-0.1

22

-0.0

36

0.0

98

0.2

68

1.0

12

0.0

98

—48526

1991-0

9-2

70.8

43

1.3

48

0.4

04

0.2

16

0.0

20

0.0

02

0.4

29

0.1

12

0.0

36

0.8

19

1.1

60

0.0

36

-0.1

37

-0.0

10

0.0

53

0.2

53

1.0

38

0.0

53

—48527

1991-0

9-2

80.7

96

1.2

26

0.3

57

0.0

94

0.0

20

0.0

02

0.3

67

0.0

62

0.0

25

0.7

57

1.1

10

0.0

25

-0.1

11

-0.0

85

0.0

40

0.2

78

0.9

63

0.0

40

—48528

1991-0

9-2

90.7

40

1.0

89

0.3

01

-0.0

44

0.0

20

0.0

02

0.2

95

-0.0

46

0.0

27

0.6

85

1.0

02

0.0

27

-0.0

39

0.0

58

0.0

41

0.3

51

1.1

05

0.0

41

—48529

1991-0

9-3

00.6

59

1.0

38

0.2

20

-0.0

94

0.0

20

0.0

03

0.1

71

-0.1

48

0.0

30

0.5

60

0.9

00

0.0

30

-0.0

43

0.0

06

0.0

55

0.3

46

1.0

53

0.0

55

—48530

1991-1

0-0

10.6

69

1.0

47

0.2

30

-0.0

86

0.0

20

0.0

02

0.1

95

-0.1

08

0.0

30

0.5

85

0.9

40

0.0

30

-0.0

17

-0.1

09

0.0

51

0.3

72

0.9

38

0.0

51

—49521

1994-0

6-1

80.4

32

0.7

32

-0.0

07

-0.4

00

0.0

20

0.0

08

-0.0

93

-0.3

68

0.1

03

0.2

96

0.6

80

0.1

03

0.0

92

-0.2

05

0.2

01

0.4

81

0.8

43

0.2

01

—49530

1994-0

6-2

70.5

51

0.7

90

0.1

12

-0.3

42

0.0

20

0.0

05

0.0

77

-0.2

36

0.0

64

0.4

67

0.8

12

0.0

64

0.1

69

-0.2

73

0.2

99

0.5

58

0.7

75

0.2

99

—49539

1994-0

7-0

60.7

70

0.6

94

0.3

31

-0.4

38

0.0

20

0.0

11

0.2

32

-0.4

91

0.1

27

0.6

21

0.5

57

0.1

27

0.1

91

0.3

25

0.6

84

0.5

80

1.3

73

0.6

84

—49573

1994-0

8-0

90.2

22

0.9

74

-0.2

17

-0.1

58

0.0

20

0.0

06

-0.1

34

-0.0

82

0.0

88

0.2

56

0.9

65

0.0

88

0.0

19

-0.2

48

0.1

54

0.4

09

0.7

99

0.1

54

—49606

1994-0

9-1

10.1

56

1.2

21

-0.2

83

0.0

89

0.0

20

0.0

04

-0.2

81

0.1

06

0.0

67

0.1

09

1.1

54

0.0

67

0.1

37

-0.1

88

0.1

56

0.5

27

0.8

60

0.1

56

—49636

1994-1

0-1

10.2

08

1.0

59

-0.2

32

-0.0

74

0.0

20

0.0

03

-0.3

07

-0.0

56

0.0

41

0.0

83

0.9

92

0.0

41

-0.0

77

-0.1

58

0.1

01

0.3

12

0.8

90

0.1

01

—49666

1994-1

1-1

00.1

59

1.0

47

-0.2

80

-0.0

85

0.0

20

0.0

03

-0.2

82

-0.0

66

0.0

41

0.1

08

0.9

82

0.0

41

-0.0

03

-0.2

63

0.1

33

0.3

87

0.7

84

0.1

33

—49690

1994-1

2-0

40.1

42

0.9

01

-0.2

97

-0.2

31

0.0

20

0.0

04

-0.3

52

-0.1

95

0.0

54

0.0

38

0.8

53

0.0

54

0.0

68

-0.2

27

0.1

34

0.4

57

0.8

20

0.1

34

CC

D49777

1995-0

3-0

10.2

91

1.2

41

-0.1

25

0.1

21

0.0

06

0.0

05

-0.0

84

0.1

70

0.0

32

0.3

04

1.2

13

0.0

32

0.0

37

0.0

02

0.0

58

0.4

27

1.0

53

0.0

58

—49779

1995-0

3-0

30.3

08

1.1

40

-0.1

09

0.0

18

0.0

06

0.0

03

-0.0

86

0.0

85

0.0

18

0.3

01

1.1

27

0.0

18

-0.0

44

-0.0

35

0.0

28

0.3

46

1.0

15

0.0

28

—49785

1995-0

3-0

90.0

51

1.1

69

-0.3

66

0.0

48

0.0

06

0.0

02

-0.3

58

0.0

41

0.0

19

0.0

29

1.0

84

0.0

19

-0.0

93

0.0

51

0.0

41

0.2

98

1.1

02

0.0

41

—49788

1995-0

3-1

20.2

85

1.5

77

-0.1

32

0.4

55

0.0

06

0.0

03

-0.1

14

0.3

63

0.0

35

0.2

73

1.4

06

0.0

35

-0.0

85

-0.0

41

0.0

53

0.3

05

1.0

10

0.0

53

—49891

1995-0

6-2

30.6

00

1.1

10

0.1

84

-0.0

10

0.0

06

0.0

03

0.2

26

0.0

49

0.0

21

0.6

14

1.0

92

0.0

21

-0.0

26

-0.0

25

0.0

67

0.3

65

1.0

27

0.0

67

—49913

1995-0

7-1

50.3

39

1.2

47

-0.0

77

0.1

27

0.0

10

0.0

03

-0.0

04

0.1

45

0.0

17

0.3

84

1.1

88

0.0

17

0.0

12

-0.0

59

0.0

42

0.4

03

0.9

93

0.0

42

—49940

1995-0

8-1

10.2

83

1.0

55

-0.1

33

-0.0

66

0.0

10

0.0

03

-0.0

72

0.0

23

0.0

17

0.3

16

1.0

66

0.0

17

-0.0

17

0.0

21

0.0

50

0.3

75

1.0

74

0.0

50

—49965

1995-0

9-0

50.4

82

1.3

81

0.0

66

0.2

61

0.0

10

0.0

03

0.0

30

0.2

49

0.0

19

0.4

18

1.2

93

0.0

19

-0.0

63

-0.0

32

0.0

76

0.3

28

1.0

19

0.0

76

—49977

1995-0

9-1

70.6

66

0.9

61

0.2

49

-0.1

60

0.0

10

0.0

02

0.2

62

-0.2

26

0.0

17

0.6

50

0.8

17

0.0

17

-0.1

38

-0.0

07

0.0

50

0.2

54

1.0

47

0.0

50

Table1continued

6 Gootkin et al.Table

1(continued)

VBand

Hα

Continuum

Hα

Line

Dete

cto

rM

JD

Date

Obse

rved

Intr

insi

cIn

trin

sic

Obse

rved

Intr

insi

cO

bse

rved

%q

%u

%q

%u

Int

Err

Sys

Err

%q

%u

Err

or

%q

%u

Err

or

%q

%u

Err

or

%q

%u

Err

or

CC

D49992

1995-1

0-0

20.2

10

1.0

49

-0.2

07

-0.0

71

0.0

10

0.0

02

-0.1

92

-0.0

98

0.0

13

0.1

96

0.9

44

0.0

13

-0.0

24

0.0

53

0.0

41

0.3

68

1.1

08

0.0

41

—50009

1995-1

0-1

90.2

42

1.0

08

-0.1

74

-0.1

12

0.0

10

0.0

04

-0.1

58

-0.0

52

0.0

18

0.2

30

0.9

91

0.0

18

0.0

10

0.0

14

0.0

52

0.4

02

1.0

68

0.0

52

—50036

1995-1

1-1

50.3

82

1.1

81

-0.0

34

0.0

60

0.0

10

0.0

02

-0.0

18

0.0

51

0.0

14

0.3

70

1.0

94

0.0

14

-0.0

83

-0.0

03

0.0

51

0.3

09

1.0

51

0.0

51

—50055

1995-1

2-0

40.2

89

1.2

22

-0.1

27

0.1

01

0.0

10

0.0

03

-0.1

32

0.1

48

0.0

16

0.2

56

1.1

90

0.0

16

-0.0

57

-0.0

89

0.0

61

0.3

34

0.9

64

0.0

61

—50733

1997-1

0-1

20.3

12

1.0

77

-0.1

05

-0.0

43

0.0

09

0.0

03

-0.0

94

-0.0

98

0.0

14

0.2

93

0.9

44

0.0

14

0.1

65

0.1

93

0.0

84

0.5

62

1.2

59

0.0

84

—50803

1997-1

2-2

10.4

76

1.1

73

0.0

59

0.0

52

0.0

09

0.0

02

0.0

74

0.0

70

0.0

14

0.4

61

1.1

11

0.0

14

-0.0

37

-0.3

04

0.0

73

0.3

59

0.7

60

0.0

73

—51010

1998-0

7-1

60.4

11

1.0

45

-0.0

06

-0.0

75

0.0

10

0.0

02

-0.0

15

-0.1

06

0.0

13

0.3

72

0.9

36

0.0

13

-0.0

93

-0.0

22

0.0

68

0.3

02

1.0

40

0.0

68

—51034

1998-0

8-0

90.7

11

0.9

66

0.2

94

-0.1

55

0.0

10

0.0

03

0.3

32

-0.1

46

0.0

15

0.7

19

0.8

96

0.0

15

-0.3

23

0.2

56

0.0

75

0.0

72

1.3

19

0.0

75

—51066

1998-0

9-1

00.4

70

1.1

70

0.0

53

0.0

49

0.0

10

0.0

02

0.0

72

0.0

18

0.0

13

0.4

60

1.0

60

0.0

13

0.0

43

0.1

51

0.0

67

0.4

38

1.2

11

0.0

67

—51072

1998-0

9-1

60.3

90

1.2

03

-0.0

27

0.0

82

0.0

10

0.0

02

0.0

18

0.0

73

0.0

15

0.4

05

1.1

15

0.0

15

0.0

23

-0.1

27

0.0

67

0.4

18

0.9

34

0.0

67

—51160

1998-1

2-1

30.5

18

1.2

77

0.1

01

0.1

56

0.0

08

0.0

03

0.0

79

0.1

50

0.0

14

0.4

67

1.1

93

0.0

14

-0.0

24

-0.0

52

0.0

48

0.3

69

1.0

02

0.0

48

—51177

1998-1

2-3

00.2

65

1.0

69

-0.1

52

-0.0

52

0.0

08

0.0

04

-0.1

71

-0.0

34

0.0

28

0.2

17

1.0

09

0.0

28

-0.0

12

0.0

85

0.0

59

0.3

78

1.1

36

0.0

59

—52533

2002-0

9-1

60.2

10

0.9

70

-0.2

06

-0.1

51

0.0

12

0.0

04

-0.2

19

-0.0

67

0.0

24

0.1

69

0.9

76

0.0

24

-0.1

51

-0.0

12

0.0

50

0.2

39

1.0

39

0.0

50

—52534

2002-0

9-1

70.0

89

0.9

49

-0.3

28

-0.1

71

0.0

12

0.0

04

-0.3

67

-0.1

11

0.0

30

0.0

21

0.9

32

0.0

30

0.1

26

0.0

56

0.0

56

0.5

17

1.1

07

0.0

56

—52541

2002-0

9-2

40.2

36

1.0

29

-0.1

81

-0.0

91

0.0

12

0.0

04

-0.2

19

-0.0

47

0.0

27

0.1

69

0.9

96

0.0

27

-0.1

53

-0.0

95

0.0

58

0.2

38

0.9

56

0.0

58

—52542

2002-0

9-2

50.2

37

1.0

31

-0.1

79

-0.0

90

0.0

12

0.0

06

-0.2

48

-0.0

33

0.0

30

0.1

40

1.0

10

0.0

30

-0.0

53

-0.0

18

0.0

75

0.3

38

1.0

34

0.0

75

—52561

2002-1

0-1

40.5

89

1.0

35

0.1

72

-0.0

85

0.0

12

0.0

04

0.1

50

-0.0

78

0.0

22

0.5

38

0.9

65

0.0

22

-0.1

81

-0.0

05

0.0

56

0.2

10

1.0

47

0.0

56

—52562

2002-1

0-1

50.4

87

1.1

17

0.0

70

-0.0

03

0.0

12

0.0

04

0.0

96

0.0

14

0.0

22

0.4

83

1.0

56

0.0

22

-0.0

78

-0.0

72

0.0

48

0.3

12

0.9

79

0.0

48

—52579

2002-1

1-0

10.2

93

0.9

19

-0.1

23

-0.2

01

0.0

12

0.0

04

-0.1

21

-0.1

37

0.0

25

0.2

67

0.9

06

0.0

25

-0.0

70

-0.1

12

0.0

55

0.3

21

0.9

39

0.0

55

—52583

2002-1

1-0

50.1

76

0.9

53

-0.2

41

-0.1

68

0.0

12

0.0

05

-0.2

81

-0.1

70

0.0

79

0.1

07

0.8

73

0.0

79

-0.0

82

0.0

31

0.1

47

0.3

09

1.0

83

0.1

47

—52586

2002-1

1-0

80.4

49

0.8

39

0.0

32

-0.2

82

0.0

12

0.0

04

-0.0

81

-0.2

04

0.0

25

0.3

07

0.8

39

0.0

25

0.0

23

-0.1

34

0.0

43

0.4

14

0.9

16

0.0

43

13 Years of P Cygni Spectropolarimetry 7

2.1.2. Hα: the pfew Method

In an attempt to quantify the overall behavior of the

Hα emission line, we calculated its polarized flux equiv-

alent width (pfew) (Lomax et al. 2015; Hoffman et al.

1998), which integrates the Stokes q and u values in the

emission line and removes underlying continuum polar-

ization (see Figure 1 for a graphical representation of

the mathematics used the pfew method). These values

are reported in Table 1. In order to do this, we identi-

fied two continuum regions on either side of the line that

the pfew method uses to determine the line’s underlying

continuum: 6400 to 6475 A on the blue side and 6750

to 6800 A on the red side. Additionally, we integrated

over the line between 6540 and 6600 A.

In the remainder of this work we use the term pfew to

refer to both this method and the values it produced—

listed under Hα Continuum and Hα Line columns in

Table 1.

2.2. WUPPE

We also used three ultraviolet (UV) spectropolari-

metric observations of P Cyg taken with the Wis-

consin UV Photo-Polarimeter Experiment (WUPPE).

WUPPE had a resolution of approximately 12 A and

recorded spectropolarimetric data between 1400 and

3200 A. P Cyg was observed on four separate occasions

with WUPPE, which flew aboard both the Space Shut-

tle Columbia as part of the STS-35 ASTRO-1 mission

and the Space Shuttle Endeavour as part of the STS-

67 ASTRO-2 mission. More information about this in-

strument can be found in Bjorkman et al. (1993) and

Nordsieck et al. (1994).

The ASTRO-1 data were taken on 5 December 1990

and originally published in Taylor et al. (1991b). The

three ASTRO-2 observations, taken on 3, 8, and 12

March 1995, show little to no variability suggesting P

Cyg has a constant UV polarimetric behavior. There-

fore, we did not include the ASTRO-1 observation in

our analysis.

3. INTERSTELLAR POLARIZATION

In general, we expect the light coming from spatially

unresolved stars to be unpolarized. It only becomes

polarized when those photons scatter off of something,

which is typically either circumstellar dust around a

star, free electrons in the circumstellar medium (CSM)

around a star, or dust in the interstellar medium. Be-

cause P Cyg is a hot star, its circumstellar material is

highly ionized. Therefore, the polarization we observe

is from a combination of electron scattering within P

Cyg’s CSM and scattering with dust in the interstellar

medium between P Cyg and Earth. Before analyzing

Figure 2. The stars within ∼ 3◦ of P Cygni found in Heiles(1999). The length of the line going through the positionof each star represents the relative strength of the star’s po-larization and the orientation of the line represents positionangle. The yellow star shows the position of P Cygni.

our spectropolarimetric observations of P Cyg, we sepa-

rate polarization which is intrinsic to the P Cyg system

due to electron scattering in the CSM (hereafter called

intrinsic polarization) from that which is produced by

the interstellar medium (hereafter called interstellar po-

larization or ISP).

Electron scattering is a gray process that produces a

constant polarization signal in both q and u (or P% and

Θ) with wavelength. However, a polarization signal from

electron scattering can change with time if the geome-

try of the scattering region (i.e. region where the free

electrons are located) is changing or the number of free

electrons for photons to scatter off of changes. There-

fore, the polarization signal due to electron scattering

from P Cyg may change location in the q vs. u plane

(i.e. Figure 3) with time, but the polarization signal at

different wavelengths will lie on the same point if they

were taken simultaneously.

Conversely, the ISP has a wavelength dependence, but

is generally thought to be constant over long periods of

time. In the q vs. u plane (i.e. Figure 3) the interstel-

lar polarization signal manifests itself as a vector that

changes with wavelength which adds to the constant

electron scattering signal from P Cyg. In particular, it is

the P% of the ISP that changes with wavelength, while

the Θ of the ISP is constant with wavelength (Serkowski

et al. 1975; Wilking et al. 1982). Thus one must con-

struct a model of the wavelength dependence of the P%

of the ISP along the line of sight to P Cygni—which

is caused by light scattering off of dust grains in the

8 Gootkin et al.

interstellar medium—to subtract from the observed po-

larization in order to determine P Cygni’s intrinsic po-

larization. The wavelength dependence of the ISP can

be modeled with the Serkowski law (Serkowski et al.

1975), as modified by Wilking et al. (1982):

Pλ = Pmaxe−K ln2 λmax/λ (3)

where Pmax is the largest value of P% due to the ISP,

λmax is the wavelength at which that peak occurs, and,

K = (0.01± 0.05) + (1.66± 0.09)λmax,

where λmax is measured in microns (Whittet et al.

1992).

Therefore, to determine the Serkowski law in the di-

rection of P Cygni, we must find:

1. at least one wavelength at which we know the mag-

nitude of the ISP—This allows us to solve for Pmaxin equation 3.

2. the wavelength of peak polarization, λmax

A summary of techniques and challenges relating to de-

termining the ISP can be found in Wisniewski et al.

(2010).

Traditionally, the most common method to find a

known ISP value is to observe stars near the science

target in the sky and find the average direction and

strength of their polarization and take this to be the

value of the ISP. Unfortunately, the Cygnus region is no-

toriously complex. This is illustrated in Figure 2, which

shows the relative strength and orientation of linear po-

larization for the stars in the Heiles (1999) polarimetric

catalog within ∼ 3◦ of P Cygni. Taking only the sub-

set of stars at a similar distance as P Cygni does not

help to establish a pattern. It is worth noting that the

Heiles (1999) catalogue does not provide the wavelength

at which polarization was measured. However, since we

do not expect a significant wavelength dependence in

the observed position angle of the ISP, it is generally

still valuable to compare nearby stars in this manner.

In the case of P Cygni, the large variations in the posi-

tion angles of its surrounding field stars (Figure 2) make

this method of determining the ISP less than ideal.

Alternatively, the line center method makes the as-

sumption that strong emission lines, such as Hα, are

intrinsically unpolarized. In P Cygni, these emission

lines are formed between 3.2 and 9.3 R? (Avcioglu 1984),

beyond the region where free-electron scattering is effi-

cient; i.e. the Hα line forms farther away from the star

than the region where electron scattering occurs (Nord-

sieck et al. 2001; Taylor et al. 1991a; Davies et al. 2005,

2006). Therefore, the observed polarization of these

Figure 3. 76 synthetic V -band HPOL observations (see§2.1.1), observed Hα line polarization (see §2.1.2), and ourestimate of the ISP at Hα (see §3; Table 1).

lines are likely a direct measurement of the ISP, which

we do not expect to vary on the timescales over which

our data were taken. We find evidence for this in Fig-

ure 3 which shows the distribution of the 76 synthetic

V -band observations and measurements of the polariza-

tion in the Hα emission line (§2.1.2) in q-u space. It can

be seen that Hα varies less than the V -band observa-

tions (σV ' 0.2 while σH ' 0.1), suggesting it is less

affected by a time-variable electron scattering compo-

nent (i.e. polarization intrinsic to P Cyg). This makes

Hα a better estimator of the ISP, which likely lies near

the center of both distributions.

Both T91 and N01 presented models for the ISP, con-

structed using different methods and data. To estimate

λmax, T91 made use of the relationship between the

ratio of total-to-selective extinction, RV , and λmax in

Serkowski et al. (1975):

RV = (5.6± 0.3)λmax (4)

and assumed the galactic average, Rv = 3.1 (Cardelli

et al. 1989), to find a peak polarization wavelength of

5500 A. They then employed the line center method and

assumed that Hα is intrinsically unpolarized to estimate

Pmax (1.06%) using their spectropolarimetric observa-

tions of P Cygni. With both Pmax and λmax they were

able to construct a model of the ISP in the direction of

P Cygni.

13 Years of P Cygni Spectropolarimetry 9

Figure 4. Comparison of ISP estimates from Nordsieck et al. (2001), Taylor et al. (1991a), and this paper. These modelsare plotted over the mean HPOL CCD data in black (see Section 3), and the mean of 3 UV observations from the WUPPEpolarimeter in grey. The zoom-in in the upper-righthand corner shows the region around Hα in greater detail.

N01 followed a method to similar to T91’s to estimate

the ISP. They also assumed the Hα was intrinsically

unpolarized and estimated the ISP at that wavelength.

They used UV data from the Wisconsin Ultraviolet

Photo-Polarimeter Experiment (WUPPE) and assumed

that the region between 1700-1900 A is also unpolar-

ized to get an estimate of the ISP at those wavelengths.

With the combination of those two data points (the Hα

and UV ISP) they were able to use the Serkowski law to

back out both a Pmax (1.17± 0.03%) and a λmax (5100A).

When we subtracted the ISP estimates from T91 and

N01 from our HPOL data, we found that the result-

ing polarization was strongly wavelength dependent for

most observations. Because P Cygni is a hot star, we

expect that its intrinsic polarization is due to electron

scattering, which is a ‘gray’ process that should have no

wavelength dependence. Therefore, we determined our

own ISP estimate to try to resolve this issue.

Using the line center method (despite the problems

discussed in §5) we initially performed a similar analysis,

using pfew measurements of Hα, eq. 4 and Rv = 3.1.

However, we found that the peak wavelength which best

describes our overall dataset is bluer than both T91’s

and N01’s previously used λmax estimates (5500A and

5100A). However, both T91 and N01 also noted that

they observed a persistent decrease of P Cygni’s intrin-

sic polarization into the infrared whose strength varies,

suggesting there might be a high amount of free-free

absorptive opacity due to clumps at the base of the sys-

tem’s wind.

To more rigorously determine λmax instead of assum-

ing that RV = 3.1, we first found the mean P% curve of

all our CCD observations. We calculated this by find-

ing the error-weighted mean Stokes q and u parameters

at every wavelength for which we have CCD data and

then combined those mean Stokes parameters into P%

(Figure 4). We then performed a least squares fit, using

equation 3 and SciPy’s curve fit function (Jones et al.

2001), to two sections of our mean P% curve (between

4000 and 5900 A and between 6200 and 9000 A) simulta-

neously, which were chosen to avoid including data that

fell near the edges of the CCD detector that typically

have higher uncertainties. As part of this process, we

allowed Pmax and λmax in equation 3 to vary and found

λmax = 4712± 51 A.

We then estimated the P% at Hα because that should

only be due to the ISP. We used the pfew Hα line val-

ues tabulated above, found the mean Hα Stokes q and

u value weighted inversely by variance, and converted

that into a mean P% at Hα. We used this value, equa-

tion 3, and our previously determined λmax (4712A) to

find P%,ISP = 1.06%. Because the ISP is not expected

to have a wavelength dependence in its position angle,

we found the average position angle of all of our obser-

vations and assumed that was representative of the ISP

(ΘISP = 34.4◦ ± 0.7◦).

We then use equation 4 to solve for RV in the direction

of P Cygni. Given our value of λmax and equation 4, we

find that RV = 2.638 ± 0.028. This lower, when com-

pared to T91, value of RV —corresponding to a smaller

size of dust grains in the interstellar medium—is in ex-

10 Gootkin et al.

cellent agreement with the value of RV = 2.73 ± 0.23

determined by Turner et al. (2001). This result can be

explained by the dust being processed by ionizing ra-

diation from P Cygni and other massive stars in the

OB association (Draine 2003), and suggests we have a

robust ISP estimate to subtract from our observations.

Our resulting ISP fit is plotted in yellow in Figure 4.

We also over plot the T91 and N01 ISP estimates for

comparison.

To be clear, our ISP model itself is not a fit to the

data. The fitting done above is only for determining

λmax. Using λmax and the polarization at Hα (which

we assume to be the same as the value of the ISP at

Hα) we solve for Pmax. Plugging λmax and Pmax into

equation 3 yeilds the wavelength dependence of the ISP

signal.

It is worth noting that even though we do not use the

WUPPE data, our ISP estimate agrees well with N01’s

assumption that the 1700-1900 A region of P Cygni is

intrinsically unpolarized (i.e. our estimate overlaps with

the WUPPE data in this wavelength regime). The small

vertical offset from our ISP fit can be explained by P

Cygni being a “super-Serkowski” object as discussed in

Anderson et al. (1996).

Figure 5. q vs. u, for 76 intrinsic synthetic V -band observa-tions of P Cygni after subtracting the ISP estimate describedin §3. The yellow square marks the center of the distribu-tion. The error of that mean location is smaller than themarker. While the separation between the mean of the V -band observations and the origin is statistically significant itis perhaps most notable how small this separation is. Thisindicates symmetry at the base of the wind in the P Cygsystem—at least over the timescale of these observations.

Figure 6. Mean intrinsic P%, q, and u taken at each λ binover time. Means of percent polarization and position anglewere calculated from the means of q and u. The grey back-ground indicates uncertainty of the mean measured at eachλ across all observations. Θ values are not included; sincemost P% values are near the origin, position angle becomeshighly uncertain.

4. RESULTS

We used our ISP estimate determined above (λmax =

4712 A) and P%,ISP = 1.06%) and equation 3 to cal-

culate the wavelength dependence of the ISP. We con-

verted that wavelength dependent P% and ΘISP = 34.4◦

into wavelength dependent q and u values for the ISP.

Subtracting those q and u components of the ISP from

each observation results in an estimate of the intrinsic

polarization of P Cygni. After we subtracted the ISP,

we applied synthetic V -band filters to our data (see

§2.1.1) to quantify P Cyg’s intrinsic continuum polar-

ization behavior (Table 1). After this subtraction, the

center of the distribution of the V -band data in q-u

space is shifted very near to the origin, as can be seen

in Figure 5. The distance between the center of that

distribution and the origin is 0.047± 0.002.

Additionally, we found the intrinsic polarization re-

maining in P Cyg’s Hα line and continuum (§2.1.2; Ta-

ble 1). As discussed in §3, polarization in the Hα line

appears to be at least partially suppressed when com-

pared to the V -band, making it a good estimator of the

ISP. However, we note that the Hα line does show some

variability with time, which suggests that not 100% of its

observed polarization is due to the ISP. Because we used

the mean Hα polarization to generate our ISP estimate,

the possibility that we have over or under subtracted the

ISP exists. Without a more reliable way to determine an

ISP estimate we cannot evaluate how much of an effect

13 Years of P Cygni Spectropolarimetry 11

Figure 7. Slopes of lines fit to the P% of each observation between 4000 and 7500 A plotted against time with 1σ uncertainties.The dashed horizontal line indicates a slope of 0. The dashed vertical line shows the cutoff between Reticon observations (onthe left) and CCD observations (on the right). The top panel shows the model (green) fit to the data (black) for the observationmarked with a green dot.

this has on our intrinsic polarization of P Cyg, but the

agreement of our Rv calculated from our ISP estimate

with Rv values for P Cyg in the literature suggests our

ISP estimate is robust and the temporal variability in

the Hα that remains after we performed ISP subtrac-

tion is due to changes in P Cyg’s intrinsic polarization;

i.e. on average the polarization in P Cyg’s Hα line is a

good estimator of the ISP, but night-to-night there can

be a variable, intrinsic polarization component to theHα line. Therefore, we still report intrinsic pfew Hα

line values in Table 1 for completeness and because the

remaining signal in the lines likely holds key information

about P Cyg’s winds.

Figure 6 shows the mean P%, q, u, and Θ spectra,

taken at each wavelength bin over time. Overall, these

mean spectra are quite flat—as is expected for polar-

ization caused by free electron scattering. We also see

sharp features, most noteably at Hα. The magnitude of

polarization is indistinguishable from zero unless aver-

aged over a wide wavelength bin, as is the case for the

V -band mean shown in Figure 5. This shows that—at

least when considered over a 13 year period—the ambi-

ent wind of P Cygni is nearly symmetrical on the plane

of the sky. Note that uncertainties become significantly

smaller at Hα, this is likely due to the increased num-

ber of photons received at the emission line. The region

around Hα is shown in more detail in Figure 8.

4.1. Intrinsic Polarization: the Search for Slope

Both N01 and T91 describe a decrease of polarization

levels moving into the infrared, which may be connected

to the free-free absorptive opacity—κff—in the wind of

P Cygni. This observed slope is used in N01 to estimate

the density of the inhomogeneities which are thought to

give rise to intrinsic polarization in P Cygni. In order

to investigate this previously discovered trend we fit a

straight line to our data, this serves as a proxy for the

true relation for the attenuation of polarization caused

by κff—P% ∝ eaλ2

. We perform this fit to our data

between 4000 and 7500 A, after subtracting the ISP

estimate found in §3, using SciPy’s curve fit function

(Jones et al. 2001). This function utilizes a least-squares

fit of the form y = mx+ b. One example of such a fit is

shown in the upper panel of Figure 7.

We report the results of this analysis in Figure 7 as

a slope (P%A−1) for each observation with 1 σ uncer-

tainties. Because the exact value of the slope for each

individual observation is highly dependent on our ISP

calculation, it is most useful to look for trends across our

observations. The slope of P% does appear to change

between individual observations at a statistically signif-

12 Gootkin et al.

Figure 8. The mean, calculated over all CCD observations,of intrinsic P%, Θ, Stokes q, and Stokes u across Hα. Thegrey bounded region, between 6540 and 6600 A shows theline core from which the ISP at Hα was calculated.

icant level. However, using Astropy’s (Robitaille et al.

2013; Price-Whelan et al. 2018) Lomb-Scargle analysis

software3 (Lomb 1976; Scargle 1982; Press & Rybicki

1989) on these slopes showed no statistically significant

periodicity, which is consistent with the stochastic vari-

ability displayed in Figure 7.

There do appear to be differences in the slopes of the

P% in our observations taken with HPOL’s CCD (to

the right of the vertical dashed line in Figure 7) when

compared to the Reticon detector (to the left of the ver-

tical dashed line). The CCD observations have a more

consistently negative slope, which corresponds to a per-

sistent trend of a decrease in the P% into the infrared

consistent with N01’s findings. However, the observa-

tions taken with HPOL’s Reticon detector have a larger

overall scatter in their slope, many of which are con-

sistent with no wavelength dependence at the 3σ uncer-

tainty level. Some of our Reticon observations also show

an increasing wavelength dependence into the infrared

3 All Lomb-Scargle analysis was done using the default normal-ization as of Astropy v. 4.0.1

Figure 9. Hα line-profile in percent polarization for 30 CCDobservations. Each observation has a constant value added.The observations are stacked in chronological order, withthe oldest being on the bottom. The grey bounded region,between 6540 and 6600 A shows the line core from which theISP at Hα was calculated. Note—the constant added doesnot scale linearly with time.

(positive slope). It is possible the overall polarization

behavior of P Cygni changed when HPOL’s detector was

upgraded, no major changes in the system have been re-

ported to be observed in other data sets corresponding

to this time frame. Still, it cannot be ruled out that the

difference in wavelength dependence between these two

13 Years of P Cygni Spectropolarimetry 13

detectors is due to instrumental differences, perhaps due

to differences in sensitivities between them.

4.2. Hα Polarization

While it is true that intrinsic polarization at Hα ap-

pears to be suppressed, as we show in Figure 3, there ap-

pear to be more complicated processes at work. Closer

inspection of the Hα line reveals a feature in the po-

larization spectrum of P Cygni. As shown in Figure

8—though taking the mean washes out some of this

feature—and Figure 9, there is clear structure at Hα

in both P% and Θ. While less easily seen in the Reti-

con data, this feature has an amplitude larger than the

mean level of uncertainty of the CCD observations, sug-

gesting that it is astrophysical in nature. The typical

uncertainty of the Reticon observations is large enough

that this feature is not clearly visible in many of those

observations.

Figure 8 paints a puzzling picture. The strongest po-

larization appears near to the peak of the Hα emission

line. Moving red-ward there is a strong and rapid rota-

tion, passing near to the origin in q vs. u space.

This feature shows temporal variations with no clear

periodicity with regard to amplitude or shape (Figure

9). There are no significant correlations between the

amplitude of the feature and the average percent polar-

ization or position angle across the line.

However, our Figure 7 shows possible night-to-night

changes in the wavelength dependence of P Cygni’s po-

larization, which was also noted by T91 and N01, sug-

gesting there are changes in P Cygni’s free-free absorp-

tive wind opacity. Because it is plausible that this ab-

sorption is also affecting the Hα line and varying with

time, we do not attempt to correct for it. Instead, we

attempt to quantify variability in the line—which may

be due to changes in its underlying absorption—using

the methods described below.

4.3. Periodicity

Over the past century observers have noted irregular

variability in P Cygni (de Groot 1969). As Kharadse

(1936) put it, “P Cygni — Nova of 1600 — is one of

the most remarkable stars of the Northern sky. It has

attracted the attention of astronomers by an unusual

character of light variation.” More recently, however,

evidence for periodicity in these unusual light varia-

tions has been presented by various authors (de Groot

et al. 2001a,b; van Genderen A.˜M. 2002; Michaelis et al.

2018; Kochiashvili et al. 2018). The periods found range

from ∼ 17 day microvariations (de Groot et al. 2001b,a)

to ∼ 4.7 years (Michaelis et al. 2018). As will be dis-

cussed in §5.1, there are many fascinating phenome-

nae that can cause periodic signals in polarimetric data.

Here we detail our search for such signals.

We use Astropy (Robitaille et al. 2013; Price-Whelan

et al. 2018) to calculate the Lomb-Scargle periodogram

(Lomb 1976; Scargle 1982; Press & Rybicki 1989) for all

available sets of P% data from Table 1. Some sets of Θ

data were found to have periodicities, these periods were

significantly less robust under the prewhitening proce-

dure described below.

We first search for peaks in the periodograms with low

false alarm probability (FAP) under the null hypothesis

of white noise (Horne & Baliunas 1986). This results

in multiple detected periods with FAP ≤ 11000 . How-

ever, not all of these periodicities may be the result of

astrophysical phenomena. As discussed extensively in

VanderPlas (2018), there are many subtleties in inter-

preting the Lomb-Scargle periodogram. Therefore, we

also conduct a prewhitening procedure, similar to that

described in Dorn-Wallenstein et al. (2019). In short, we

iteratively select the highest peak in the periodogram,

fit a sinusoid to the data (allowing the frequency to vary

within the resolution of the periodogram), subtract the

sinusoid, and recalculate the periodogram until we reach

a minimum in the Bayesian Information Content of the

fit (Schwarz 1978). Formal errors on the frequency, am-

plitude, and phase of the sinusoids extracted in each

stage of prewhitening are calculated following Lucy &

Sweeney (1971) and Montgomery & Odonoghue (1999).

This results in a list of frequencies that uniquely describe

the data to within the noise. Frequencies extracted via

prewhitening are listed—in the order that they were

detected by the prewhitening algorithm—in Table 11,

and the full periodograms are shown in Figure 10. We

additionally search for harmonic frequencies—fi = nf◦where n is an integer—and combination frequencies of

the form fi = f1 + f2.

These periodograms have relatively poor signal-to-

noise ratios (SNRs), and many of the extracted frequen-

cies have large false alarm probabilities, meaning that it

is difficult to say whether any particular period is “real”

or simply a statistical artefact. However, several peri-

ods are more convincing than others. For example, the

97 day period found in the pfew continuum P% data

has a small FAP (of order 10−4), is the base of multiple

harmonic/combination frequencies, and is also detected

in the intrinsic V -band P% data.

14 Gootkin et al.

Figure 10. Lomb-Scargle periodograms of P% data. Frequencies picked by the prewhitening procedure described in §4.3 aremarked by vertical lines. Fainter lines indicate locations of frequencies which are harmonics or linear combinations of the darker,base frequencies (marked with † in Table 11). Errorbars at the top of each vertical line indicate error in the frequency of thepeak selected.

Table 2.

Data Frequency [days−1] Frequency Error Period [days] SNR False Alarm Probability

Observed V -Band

0.001629† 0.000031 614.0 5.0 0.048

0.016990† 0.000038 58.9 5.6 0.129

Table 2 continued

13 Years of P Cygni Spectropolarimetry 15

Figure 11. Lomb-Scargle periodogram analyzing simulated data which has the same temporal spacing of observations in Table1, based on a sinusoidal model with a period of 475 days. The horizontal dashed line shows the 1

1,000false alarm level.

Table 2 (continued)

Data Frequency [days−1] Frequency Error Period [days] SNR False Alarm Probability

0.030053† 0.000055 33.3 3.7 ∼1

0.037419 0.000041 26.7 5.1 ∼1

0.036741 0.000061 27.2 4.9 ∼1

0.023797 0.000045 42.0 5.7 ∼1

0.004683† 0.000045 213.5 5.3 ∼1

0.034663 0.000040 28.8 4.6 ∼1

0.006739† 0.000067 148.4 4.9 0.874

0.031080† 0.000055 32.2 9.4 ∼1

0.029281† 0.000064 34.2 5.4 0.647

0.016665† 0.000074 60.0 5.5 0.083

0.034099† 0.000071 29.3 5.0 ∼1

Intrinsic V -Band

0.034717 0.000035 28.8 4.6 0.001

0.026951 0.000032 37.1 7.0 0.023

0.018596 0.000036 53.8 4.1 0.049

0.010299† 0.000038 97.1 6.9 0.206

0.020022 0.000049 49.9 4.7 0.927

0.031412 0.000042 31.8 5.1 0.117

0.035521 0.000047 28.2 6.0 0.025

0.032523 0.000069 30.7 5.5 ∼1

0.011359 0.000055 88.0 4.7 0.744

0.038363 0.000061 26.1 4.1 ∼1

0.030532 0.000058 32.8 7.4 ∼1

0.012354† 0.000045 80.9 6.4 ∼1

0.004669† 0.000039 214.2 4.9 ∼1

0.001084† 0.000044 922.9 5.6 ∼1

0.016677† 0.000059 60.0 5.0 0.811

0.018210 0.000061 54.9 6.1 0.455

Table 2 continued

16 Gootkin et al.

Table 2 (continued)

Data Frequency [days−1] Frequency Error Period [days] SNR False Alarm Probability

0.014242 0.000066 70.2 5.5 0.152

0.023261 0.000058 43.0 4.1 0.948

0.003896† 0.000200 256.6 5.2 ∼1

Observed pfew Continuum

0.021624† 0.000037 46.2 5.1 0.018

0.034627† 0.000038 28.9 5.4 0.280

0.027373† 0.000038 36.5 6.4 ∼1

0.034168† 0.000057 29.3 5.2 ∼1

0.006258† 0.000044 159.8 6.3 ∼1

0.033576 0.000052 29.8 8.4 ∼1

0.029280† 0.000083 34.2 4.6 ∼1

0.038049† 0.000085 26.3 4.4 ∼1

0.026358† 0.000053 37.9 6.0 ∼1

0.018158† 0.000064 55.1 7.1 ∼1

Intrinsic pfew Continuum

0.010285† 0.000035 97.2 5.0 0.0001

0.037901† 0.000045 26.4 5.5 0.0007

0.020591 0.000033 48.6 5.0 0.012

0.034052† 0.000053 29.4 4.3 0.591

Observed pfew Line 0.001637† 0.000041 611.0 6.2 0.965

Intrinsic pfew Line0.000720† 0.000025 1388.2 3.3 0.118

0.038670† 0.000039 25.9 7.7 0.162

Note—† mark base frequencies—which are not a harmonic or linear combination of other frequencies.

We also note that several of the base periods (those

marked with a † in Table 11) have multiple harmonics of

the same order. This could be a result of errors in either

the base or harmonic frequencies. In fact, the presence

of any harmonics may be evidence that any true periodic

oscillations are not sinusoidal. If the polarization in P

Cygni arises from the ejection of asymmetries into the

ambient stellar wind, as is described in T91 and N01,

we should not expect the time-series P% curve to be a

sinusoid. Under these conditions that curve would peak

sharply when such an asymmetry is ejected from the

photosphere.

4.3.1. Cadence Test

To determine if this observed periodicity is a result of

the temporal spacing of the observations, we perform

a Lomb-Scargle periodicity search on simulated data

which lacks any of the periods that we have found. We

claim that if we detect a similar period in this test, then

the periods found in Table 11 can be attributed to how

the data was sampled, not an astrophysical process.

To create a set of simulated data we used a series

of periodic functions with various periods (for example

sin( 2πt475 )), as well as flat distributions. We calculated

the values of these functions at the time values of our

observations (MJD) then added Gaussian noise defined

by errors at each observation in Table 1.

However, as is exemplified in Figure 11, all incor-

rect periods found in such data sets are either clustered

around the true period or a harmonic of the true period.

Based on this result, we conclude that the periodicities

must be either astrophysical in nature or a result of more

complicated instrumental/analytical effects. The likeli-

hood of our findings being due to HPOL is minimal as

HPOL is a well characterized instrument and spurious

periodicities have not been found in other HPOL data

sets. But, as can be seen in Table 11, there are differ-

ent periods found in intrinsic polarization as compared

to observed polarization. This could be a sign that the

process of subtracting out the interstellar polarization

signal (see §3) may either obscure or insert periodicities.

For example, in q-u space, the P% of a circle centered at

the origin would be constant, whereas one shifted away

13 Years of P Cygni Spectropolarimetry 17

from the origin would result in a sine wave pattern in

P%.

Additionally, converting the MJD values in Table 1

to barycentric Julian date had no effect on any of the

results discussed here.

4.3.2. pfew Periodicity

By searching for periodicity in pfew Hα line data, we

can test whether there is any non-stochastic variability

present in P Cyg’s Hα emission line itself, as opposed

to the V band continuum or the pfew continuum. Fig-

ure 10 shows our resulting Lomb-Scargle periodograms.

The evidence for any significant periods is much weaker

than in the continuum data. This suggests that any pe-

riodicities are not due to changes in the Hα emission

region of P Cygni.

4.4. Ellipticity in q-u Space: The Mauchly Test

The position angle of P Cygni’s intrinsic polarization

appears to move randomly, with no strong preference for

one orientation. In other words, whatever mechanism is

responsible for P Cygni’s mass loss appears to eject mass

asymmetries stochastically in all directions. This can be

seen from a q-u plot. A random distribution of position

angles will produce a circular distribution of points in q

vs. u space, as appears to be the case in Figures 3 and

5.

Here, we attempt to quantify the statistical signifi-

cance of ellipticity of the V band q-u distribution using

the Mauchly test (Mauchly 1940a) to determine if their

position angle is truly random (i.e. circular in q-u space)

or if there is a slightly preferred position angle (i.e. el-

liptical in q-u space). The Mauchly test has been used

extensively in the field of biostatistics (Davis 2003; My-

ers et al. 2010; Crowder & Hand 2017), but has thus far

not been used in the context of polarimetry.

In the original paper by Mauchly, he seeks to identify

significant ellipticity in a collection of two-dimensional

data points. A collection of data points in two dimen-

sions may appear elliptically distributed even when their

parent population is actually circular, simply due to ran-

dom sampling. Thus, Mauchly asks “What is the prob-

ability of obtaining, from a circular normal population,

a random sample of N points for which the ellipticity is

as great or greater than that actually obtained in the

given sample of N points?” (Mauchly 1940b).

To help answer this question, Mauchly defines the el-

lipticity statistic:

Le =2σqσu

√1− r2

σ2q + σ2

u

, (5)

where r is Pearson’s correlation coefficient between the

distribution in q and u, and where σ2q and σ2

u are the

sample variances. By using r, σ2q , and σ2

u, this test as-

sumes that the distribution can be described by a two

dimensional Gaussian, defined by the covariance matrix,

Kqu =

(σ2q r

r σ2u

).

Note that if the distribution of points is circular, then

σ2q = σ2

u, r = 0, and Le = 1. Conversely, if the distri-

bution of points is elliptical, then σ2q 6= σ2

u, r → 1, and

Le → 0.

Assuming that N points are drawn from a circular

distribution, the statistic Le has the distribution

f(Le) = (N − 2)LN−3e dLe. (6)

If the actual value of Le calculated from the data is Le,then the probability that a value as small or smaller than

Le is found from a random sample of N points is

P (Le) =

∫ Le

0

(N − 2)LN−3e dLe = LN−2e . (7)

When P (Le) is close to one, then the null hypothesis

cannot be rejected (i.e. the parent distribution is likely

circular) (Mauchly 1940b). We take the position that

a value of P (Le) which is less than α = 0.05 provides

sufficient evidence to reject the null hypothesis.

To illustrate how these numbers are interpreted, Ta-

ble 3 includes three general examples in the last three

rows. The first is a distribution which is very close to

being circular, however, the small amount of ellipticity

present is statistically significant. The next is an ex-

tremely elliptical distribution which would appear to be

a line. But, there is a 50% chance that points drawn

from a circular distribution would appear more ellipti-

cal. The last example is an elliptical distribution which

is very statistically significant; this example would be

similar to what we would see for a significant preferred

position angle.

Using all q-u data sets from Table 1 we apply this

Mauchly test. For the observed V -band values, plot-

ted in Figure 12, the sample standard deviations and

Pearson correlation coefficient are σq = 0.202; σu =

0.177; r = 0.115. Given these values we find that

Le = 0.985 and P (Le) = 0.320. This is not significant

evidence for a preferred position angle and is consistent

with the findings of T91 and N01. In fact, analyzing any

other data set in Table 1 in this manner yields similar

results. The fact that the observed pfew-line observa-

tions do not show evidence for a preferred position angle

actually strengthens the argument for using it as an ISP

probe, since deviations will then be evenly distributed

about the desired value.

18 Gootkin et al.

Figure 12. White crosses show the position of observedV -band observations of P Cygni in q vs. u space, with thesize of the cross indicating uncertainty. Underlying colormapshows the 2D Gaussian distribution derived from r, σq, andσu (discussed in §4.4). Contours show equally spaced slicesin likelihood, the lightest colors corresponding to a peak inthe probability distribution function.

4.4.1. A Test of the Mauchly Test

To see if the Mauchly Test is capable of finding a pre-

ferred position angle we use the method described above

on a system with a known preferred position angle. Here

we use HPOL data from Hoffman et al. (1998); Lomax

et al. (2012) of β Lyrae—a self-eclipsing binary with

mass transfer via an accretion disk. The presence of

this disk creates net linear polarization with a preferred

position angle perpendicular to the disk.

Using 69 non-ISP removed, V -band polarimetric ob-

servations from Lomax et al. (2012), we find the dis-

tribution shown in the left panel of Figure 13, with

σq = 0.089; σU = 0.099; r = −0.203. This corresponds

to Le = 0.975 and P (Le) = 0.178. This would seem to

suggest that the Mauchly test would not be capable of

detecting the present preferred position angle.

However, there is obviously a set of outliers towards

the bottom of the figure. These points are identified as

outliers by Lomax et al. (2012), and all three observa-

tions were taken on the same night. When these outliers

are discounted, the model of this distribution changes to

that of the right panel of Figure 13. Using this sub-

set of data, we derive the values σq = 0.089; σu =

0.074; r = −0.443. This corresponds to Le = 0.880

and P (Le) = 0.0003. which is significantly below our

Table 3. Ellipticity

Data Le P (Le)

P Cygni 0.986 0.354

β Lyrae 0.975 0.178

β Lyrae (adjusted) 0.880 0.0003

Significant Circle 0.95 1e-05

Insignificant Line 0.01 0.5

Significant Ellipse 0.5 1e-05

threshold of α = 0.05. Thus, we can reject the null

hypothesis that the distribution is circular.

This example outlines an important limitation of this

test. In small data-sets, the presence of even a small

number of outliers can have an impact on the estimated

value of Le and the results of the associated significance

test.

5. DISCUSSION

These results allow us to infer properties of the ma-

terial in the near circumstellar environment around P

Cygni. Reporting on 13 years of observations of P Cygni

we can revisit the findings of previous spectropolarimet-

ric studies.

This paper supports previous claims from T91, N01,

and Hayes (1985) that asymmetries in the system lack

a preferred polarimetric position angle. Not only is the

distribution of observations in q-u space nearly circular,

but the small amount of observed ellipticity is statisti-

cally insignificant as shown in Table 3. Previous studies

investigating the resolved nebula around P Cygni (Lei-therer & Zickgraf 1987; Barlow et al. 1994; Nota et al.

1995; Meaburn et al. 1996) have reported that this neb-

ula is roughly spherical in shape, with some clumping.

This is not entirely expected as more than 50% of re-

solved galactic LBVs have bipolar nebulae (Weis 2012).

Our findings suggest that this lack of observed direction-

ality in the circumstellar environment starts at the base

of the wind. This means that this mode of mass loss is

either truly lacking any directional preference, or that

the preferred direction is hidden by projection effects. It

is possible, for example, that the mass inhomogeneities

could be ejected solely from the equator of the star, but

if the equatorial plane is close to the plane of the sky

then it would be nearly impossible to tell.

It is more difficult to interpret the wavelength depen-

dent feature observed at Hα. This is troubling, partic-

ularly in light of the importance of using the line cen-

13 Years of P Cygni Spectropolarimetry 19

Figure 13. Stokes q-u data for a test system with a preferred position angle, β Lyr from Lomax et al. (2012), see §4.4.1.White crosses represent individual V -band observations, with the size of the cross indicating uncertainty, while the underlyingcolormap shows the distribution derived from r, σq, and σu (discussed in §4.4). Contours of the color map are equally spacedslices in likelihood, the lightest colors corresponding to a peak in the probability distribution function. The left panel shows thedistribution with the three outliers included, the right panel shows the distribution without those observations.

ter method for ISP estimates of early-type stars. The

higher levels of polarization in the line (shown in Figure

8) could potentially skew measurements of the ISP in

studies of P Cygni and other strong emission-line ob-

jects. While this feature has a relatively small ampli-

tude, and it likely does not have a significant impact on

the analysis in this work, we cannot be certain as to the

extent of its impact until it is explained.

5.1. Problematic Polarimetric Periodicities

The series of periodicities in the polarimetric data

poses a serious question. What could cause these pe-

riodicities? While it is unlikely that all instrumental

effects can be ruled out, HPOL was a well-characterized

instrument. Therefore, for the remainder of this sec-

tion we shall attempt to explain this result as a truly

astrophysical phenomenon.

We did not find strong evidence for periodicity in the

Hα emission line (using pfew as described in §2.1.2) or

in the slopes of the individual observations’ P% versus

wavelength data. This suggests that the cause of these

periods is likely not due to changes in the free-free ab-

sorptive opacity of P Cygni’s wind, which is thought to

cause a general decrease in its P% into the infrared.

These results could be explored with great depth, and

likely deserves their own paper, but here we will discuss

the major points, and possible explanations for the pe-

riodic effects observed in these data. In particular, we

focus the majority of this discussion on the 97 day pe-

riod in the continuum polarization found in §4.3, as that

is the period with the strongest false alarm probability

and has proven quite robust over different iterations of

analysis.

5.1.1. P Cygni Absorption

It is interesting to note that there are periodicities

which appear in the pfew Continuum P% that are not

present in the V -Band P% data. Given how close these

two regions of continuum are, this is somewhat unex-

pected. If these differences are astrophysical in nature

it points to a difference not in the Hα emission line, but

to a difference in what is happening at Hα in continuum

emission.

A possible explanation could be the eponymous P

Cygni absorption component of the Hα line. Since our

implementation of the pfew method does not account for

this absorption component, it should have some impact

on the continuum values tabulated in Table 1. There-

fore, it is possible that we are detecting periodicity in

the polarization of the absorption component itself.

5.1.2. Pulsations

The 97 day period listed in Table 11 lines up with

∼ 100-d type periods found by de Groot et al. (2001a)

in a study of the photometric behavior of P Cygni over

multiple decades. The authors attempt to explain this

mode of variability as being a result of radial pulsa-

tions. They find an anti-correlation between mV and

B − V ; the star becomes redder as it gets brighter, as

would be expected for radial pulsations where the in-

20 Gootkin et al.

creased brightness is the result of an increase in radius

and subsequent drop in effective temperature. While it

is not likely that radial pulsations would directly affect

the net polarization that we observe, inhomogeneities in

pulsation-driven mass loss from the star (expected when

the star is in its cool state, with a more extended atmo-

sphere and lower surface gravity) could lead to periodic

variations in polarization.

Hydrodynamic models of LBV pulsations by Jiang

et al. (2018) have also predicted pulsations with peri-

ods of order ∼day timescales. While it is less likely that

the data presented here would be sensitive to such short

periods, these fast pulsations may combine with other

effects to produce the periodicity which we see.

5.1.3. Rotation

It is possible that inhomogeneities are being sourced

from a stationary feature on the photosphere, such as

a hotspot, corotating interaction region, or some other

localized site of asymmetric mass loss. Using a radius of

76R� and v sin i = 35 kms−1 (Najarro et al. 1997), the

rotational period of P Cygni would be roughly 110 days.

Since free-electron scattering produces maximum polar-

ization for a 90◦ scattering angle, we would observe the

effect of asymmetries most strongly when this feature is

at the plane of the sky.

However, we would expect to see peaks in polariza-

tion twice per rotation period for this scenario to make

sense in the context of our data set—which is a higher

frequency than most of the base frequencies we have

found. Additionally, it is not certain that a feature such

as a hotspot or mass loss asymmetry can be stable over

a 13 year period.

5.1.4. A Companion

The potential binarity of LBVs is a contentious issue,

but one explanation for the period found in this data is

that P Cygni has a binary companion. Periodic variabil-

ity in polarimetric data arising from companions is not

new. For example, Wolf-Rayet-O-star and Roche-lobe

overflow binary systems show variability in this manner

(see Brown et al. 1978; Moffat & Piirola 1993; Hoffman

et al. 1998; Lomax et al. 2015).

Assuming the masses of P Cygni and its possible com-

panion are each between 20 and 60 M�, we can place

some rough limits on the geometry of the system. For

these masses, and a 97 day orbital period, we find a

semi-major axis of roughly 1-2 AU, or about 3-6 times

the radius of P Cygni (Najarro 2001).

However, the observations in q-u space do not behave

like typical binary systems. Figure 14 shows the some-

what erratic path that Hα continuum observations take

Figure 14. pfew Continuum q-u observations, phase foldedto a 97 day period, and re-binned to 10 phase bins. Solidline shows path between adjacent bins in phase-space.

as a function of phase when phase folded by a 97 day pe-

riod, which shows the most orderly path of all periods in

Table 11. Typically, polarization in binary systems cre-

ates elliptical patterns in q-u space (Brown et al. 1978).

The path in Fig. 14 is not obviously elliptical; this may

be due to the irregular cadence and very long-term data

set compared with this short period.

While this does not prove that P Cygni is not a binary,

it does cast doubt on a simple binary model of the P

Cygni system.

5.2. The Mauchly Test in Polarimetry

The shape of distributions in q-u space encodes im-

portant information about the geometry of objects with

time varying polarization. For example, N01 discusses

how polarimetric observations of Be stars are generally

constrained to a line in q-u space. The Mauchly Test

would find these systems quickly and computationally

efficiently.

It is important to note two strengths of the Mauchly

test:

• This test works even in the case of unresolved fea-

tures.

• Since this technique only measures the shape of a

distribution, as long as the data being analyzed is

at one wavelength, ISP-correction has no effect.

Additionally, for objects that are already known to

have a preferred position angle, this statistic can quan-

tify how “preferred” it really is. In the case of a star with

a circumstellar disk, ellipticity of polarimetric observa-

tions could yield the inclination angle of the disk with

13 Years of P Cygni Spectropolarimetry 21

respect to the line of sight. Here, Le = 0 corresponds to

viewing the disk edge on and Le = 1 corresponds to a

face on alignment.

The eagle-eyed readers may ask, “But what about

β Lyr? That is an eclipsing binary system (Hoffman

et al. 1998; Lomax et al. 2012), but your analysis found

Le = 0.88. Are you claiming that we are somehow see-

ing the β Lyr system face on?”. Thankfully we are not

making that claim. There is some nuance in how we

must interpret this statistical tool. β Lyr, for which we

found Le = 0.88 and P (Le) = 0.0003, is an excellent

example. These values are measurements of our data,

not of the parent distribution. What these values tell us

is that it is very unlikely the the ellipticity of the par-

ent distribution is greater than 0.88. We have placed an

upper bound on the true value of Le.

6. CONCLUSION

Using 76 observations taken over 13 years we have

been able to update and confirm the conclusions of past

work on the circumstellar environment around P Cygni.

• P Cygni produces intrinsic polarization, indicating

time varying asymmetries in the geometry of the

circumstellar material.

• Using the line center method at Hα and by fitting

the Serkowski law we find a λmax of 4595 A and

a Pmax of 1.23% for the ISP. This implies that in

the direction of P Cygni RV = 2.638± 0.028.

• We utilize the Mauchly ellipticity statistic to find

that the ellipticity of the distribution of observa-

tions in q-u space is small and statistically insignif-

icant. Thus we do not see evidence for a preferred

position angle.

• Hα, while being less polarized than the contin-

uum on average, contains a wavelength dependent

polarization feature. Given its appearance across

multiple HPOL observations, and in Davies et al.

(2005), this feature is most likely astrophysical in

nature.

• There are a set of statistically significant periods

in various aspects of our data. These periodicities

are in the V -Band, and Hα Continuum data, but

not in the Hα emission line polarization.

The feature found in Hα is particularly intriguing, for

many reasons. It provides a cautionary tale for those

wishing to use the line-center method. While we do

not believe this structure has had a significant impact

on the ISP estimate derived in §3, it exemplifies how the

base assumptions of the line-center method—that strong

emission lines in hot stars are intrinsically unpolarized—

can break down. This strange feature is also a reminder

of how much is left to discover, even about an object

like P Cygni which has been studied for more than 400

years, and even about its Hα line which has become

the prototype for an entire class of similar spectral fea-

tures. In this sense, this study joins a long and distin-

guished astronomical tradition, as Wilson (1936) wrote

after finding variability in multiple absorption features

in the spectra of P Cygni taken over the course of 20

years at Lick Observatory, “...although these variations

have hitherto escaped observation, they are by no means

minor, but constitute one of the major features of the

problem.”

More complete and detailed observations of P Cygni

will lead to a better understanding of its spectropo-

larimetric behaviour. The current available data on P

Cygni shows its long term behavior. However, it would

be incredibly valuable to obtain higher cadence data,

particularly, over the course of the longer periods dis-

cussed in §4.3. Such a campaign could reveal potential

correlations between the different aspects discussed here

and provide a more unified view of the mass-loss of P

Cygni. Additionally, observing the ejection of an inho-

mogeneity, and the ∼14 day period afterwards—which

Hayes (1985) called the characteristic timescale of po-

larimetric changes in P Cygni—could reveal much about

the nature of the mass-loss in this system.

We gratefully acknowledge the contributions of the

large team of HPOL and WUPPE observers from the

University of Wisconsin who helped to acquire and re-

duce these data. We also thank Inger Olovsson, curator

at the Collections of Skokloster Castle, for her timely

and enthusiastic assistance in locating and confirming

the existence of Blaeu’s globe chronicling the discovery

of P Cygni. This research has made use of the SIMBAD

database, operated at CDS, Strasbourg, France. Some

of the data presented in this paper were obtained from

the Mikulski Archive for Space Telescopes (MAST).

STScI is operated by the Association of Universities

for Research in Astronomy, Inc., under NASA contract

no. NAS5-26555. Support for MAST for non-HST data

is provided by the NASA Office of Space Science via

grant no. NNX09AF08G and by other grants and con-

tracts. This work was funded by Washington NASA

Space Grant Consortium, NASA Grant #NNX15AJ98H

and a Cottrell Scholar Award to EML by the Research

Corporation for Scientific Advancement.

The authors acknowledge that the work presented

was largely conducted on the traditional land of the

first people of Seattle, the Duwamish People past and

22 Gootkin et al.

present, and honor with gratitude the land itself and the

Duwamish Tribe.

Software: Python 3.7.4, Astropy v4.0.1 (Robitaille

et al. 2013; Price-Whelan et al. 2018), Scipy v.1.18.1

(Jones et al. 2001), Numpy v1.17.2 (van der Walt et al.

2011),Matplotlib v3.1.1 (Hunter 2007), REDUCE (Nook

et al. 1990; Wolff et al. 1996; Davidson et al. 2014)

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