Binary Stars and the BVRI

Observations and Analysis of

Solar Type Dwarf Algol,

V2421 Cygni

By

Travis Shebs

1

Two stars that rotate around a

center of mass

2

But why do we care?

• Estimated that 50% of stars are in binary

systems

• Determine stellar masses, density,

composition, and size

• Best determination of distance in

astronomy

• Allows the study of stellar atmospheres.

• Applies to single stars

3

Studied via light curves

4

• History and Observations

• Location and Raw Results

• Period Study

• Possible Stream Trajectories

• Solution

• Conclusion

5

Outline

6 6

History and Observations

• V2421 Cyg is a faint detached eclipsing binary in the star cloud of Cygnus.

• Discovered by the MISAO project in 2005 they gave the following ephemeris.

HJD Tmin I = 2452873.9913 + 0.6331 d*E. [1]

(August 2003)

They also give two times of minimum light (See O-C table).

• Three times of minimum light are given in The Variable Star Bulletin No. 42.

• Appeared in 78th name list of variable stars.

7

History and Observations

• Observed as a part of our student/professional

collaborative studies of interacting binaries.

•The observations were taken by Dr. Ron Samec, Dr.

Danny Falkner, Adam Jaso, and Paul Smith.

• Reduction and analyses were mostly done by Travis

Shebs, Dr. Samec and Jesse White.

8

History and Observations

• Observed from September 30 to October 2, 2010 with

Lowell 0.81-m reflector in Flagstaff using standard BVRI filters.

•Individual observations included 140 in B, 149 in V, 139 in R, and 135 in I.

•Removing the areas of emission, the precision of a single observation are 12 mmags in B, 7 in V, 6 in R and 9 in I.

•The exposure time in B was 175s, in V 100s, in R 100s, and in I 100s.

9

Finding Chart

Positions V: V2421 Cyg [GSC 3159 1247, Mis V1105, (2000) = 20h 14m 38.57s, (2000) = +41

56’ 14.7” ICRS, V = 13.93] K: Check GSC 3159[(2000) = 20h 14m 14.575s, (2000) = +42

00’ 36.64” V=12.04, Guide 8] C: Comparison GSC 3159 1731 [(2000) = 20h 14m 14.575s, (2000) = 42

00’ 36.64” Guide 8]

10

Some Nightly Light Curves V2421 Cyg

HJD 69.5

69.60 69.65 69.70 69.75 69.80 69.85 69.90

B

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

V

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

(B-V)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

V2421 Cyg

HJD 70.5

70.60 70.65 70.70 70.75 70.80

B

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

V

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

(B-V)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

11

Period Study

• The three times of minimum light were calculated from our present observations (PO):

HJD I = 2455469.82375

0.00037,2455471.72232

0.0012

HJD II = 2455470.77149

0.0012

(September 30th – October 2nd 2010)

• The first, improved ephemeris below was calculated from all the available eclipse timings and the second ephemeris is from the Wilson code fitting to our recent modeled curves only.

HJD Tmin I = 2455469.8238

0.0047 + 0.6331290

0.0000015 d*E [1]

HJD Tmin I = 2455469.82342

0.00014 + 0.633030

0.000069 d*E [2]

12

Observations taken over some 4000 orbits seem to show a fairly

constant period over the 7 years it has been observed.

Period Study •O-C’s Calculated from equation [1]

V2421 Cyg

EPOCH (ORBITS)

-4000 -3000 -2000 -1000 0

O-C

(d

ay

s)

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

13

Table 1. O-C Linear Residuals for V2421 CYG from equation [1]

* http://www.aerith.net/misao/report/variable/MisV1105.html

No. Epochs Cycles Weight Residuals References

1 52856.248 -4128.0 0.1 -0.0181 Nakajima, K, et al. 2005

2 52858.188 -4125.0 0.1 0.0225 Nakajima, K, et al. 2005

3 53339.991 -3364.0 0.1 0.0143 *MISAO

4 52872.7177 0.5 0.5 -0.0097 *MISAO

5 52857.2195 -4126.5 1.0 0.0037 Nagai, 2004

6 52873.0459 -4101.5 1.0 0.0019 Nagai, 2004

7 52873.9913 -4100.0 1.0 -0.0024 Nagai, 2004

8 55469.82375 0.0 1.0 0.0008 Shebs 2010 SEPT 26 2010

9 55470.7715 1.5 1.0 -0.0011 Shebs 2010 SEPT 26 2010

10 55471.7223 3.0 1.0 0.0000 Shebs 2010 SEPT 27 2010

14

Phased Light Curves 2010

•Phases calculated from equation [1]

V2421 Cas

PHASE

-0.25 0.00 0.25 0.50 0.75

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

B

V

(B-V)

15

Phased Light Curves, cont.

V2421 Cas

PHASE

-0.25 0.00 0.25 0.50 0.75

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

R

I

(R-I)

16

V2421 Cygni has distinctive high amplitude Algol type light curve yet it is a dwarf, solar type binary. Very short period, some 0.63 days. The amplitudes are 1.35, 1.12, 0.98, and 0.87 mags in BVRI, respectively. The color curves dip sharply at the primary eclipse and rise at the secondary eclipse revealing that the binary is semidetached. The curves show high scatter about phases 0.15 and 0.55 (discussed next slide).

LIGHT CURVE CHARACTERISTICS

V2421 Cas

PHASE

-0.25 0.00 0.25 0.50 0.75

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

B

V

(B-V)

17

We find there are areas of raised emission at phases 0.15 and 0.55.

V2421 Cas

PHASE

-0.25 0.00 0.25 0.50 0.75

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

18 18

It is possible that the streams are causing the regions of noisy data

on the light curves.

19

MAX I, phase 0.25 MAX II, phase 0.75

Filter phase mag phase mag

B 0.2500 2.3240.008 0.7500 2.3310.004

V 2.1590.006 2.1340.004

R 2.0070.006 2.0030.003

I 1.7610.008 1.7710.002

MIN II, phase 0.5 MIN I, phase 0.0

Filter phase mag phase mag

B 0.5000 2.6390.018 0.0000 3.6350.087

V 2.5140.031 3.3630.035

R 2.3810.023 3.0790.005

I 2.4130.027 2.6050.047

Filter MIN I-MAX I MAX II-MAX I MIN I-MIN II

B 1.3110.091 0.0060.012 0.9950.105

V 1.2030.039 -0.0250.010 0.8490.065

R 1.0720.009 -0.0040.011 0.6980.028

I 0.8440.049 0.0080.010 0.1920.074

LIGHT CURVE CHARACTERISTICS: Table II

20

Temperature Determination

2MASS photometry, J = 12.549 and H = 12.160 yield a J-H of 0.389, a G7V spectral type which has a temperature of ~ 5500K . The photometry of the V, C and K combined with known values of B-V for the C and K give nearly the same mean value.

21

Pre-modeled with Binary Maker 3.0 (Bradstreet and Steelman 2002). The parameters were averaged and put into a 4-color simultaneous light curve calculation using the Wilson Code. Computed in Mode 0, the general mode. First solution was a non-spotted solution with a sum of square residual of ~0.98.

Light Curve Solution

Due to the fact the our light curves did not show total eclipses, we undertook a mass ratio search. The search minimized at 0.5.

22

Q-Search, V2124 Cyg

MASS RATIO

0.0 0.5 1.0 1.5 2.0 2.5

SU

M O

F S

QU

AR

E R

ES

ID

UA

LS

0.80

0.85

0.90

0.95

1.00

23

Opened up the mass ratio as well as all parameters for a final run. Converged to our present solution with the secondary near filling its Roche Lobe (98

2%) and its primary more massive component under filling its Roche lobe (82

1%).

The final mass ratio was 0.4997, inclination 86. Component temperature difference is ~900 K. Secondary component is about a K4 spectral type. Both spots are hot spots and positioned at the equator. This most likely makes them stream spots.

24

Final BVRI Solution

Parameters

Parameters Values

B,V ,R,I (nm) 440, 550, 640, 790

xbol1,2 , ybol1,2 0.649, 0.637, 0.193, 0.148

x1I,2I , y1I,2I 0.623, 0.656, 0.230, 0.160

x1R,2R , y1R,2R 0.708, 0.744, 0.229, 0.128

x1V,2V , y1V,2V 0.778, 0.799, 0.200, 0.054

x1B,2B , y1B,2B 0.847, 0.848, 0.098, -0.087

g1 , g2 0.320

A1 , A2 0.5

Inclination (°) 85.75±0.1

T1, T2 (K) 5500±500K, 4595±2*

1, 2 3.48±0.08, 2.944±0.003

q(m2/m1) 0.4997±0.001

Fill-outs: F1= F2 82.9%, 97.7%

L1/(L1+L2)I 0.7059±0.0046

L1/(L1+L2)R 0.7376±0.0032

L1/(L1+L2)V 0.7712±0.0041

L1/(L1+L2)B 0.8552±0.0050

JDo (days) 24 55469.823422±0. 000137

Period (days) 0. 633024±0.000069

r1, r2 (pole) 0. 3324±0. 0047, 0. 2883±0. 0058

r1, r2 (point) 0. 3422±0. 0053, 0. 2994±0. 0068

r1, r2 (side) 0. 3515±0. 0060, 0. 3256±0. 0103

r1, r2 (back) 0. 3589±0.0018, 0.3568±0.0120

Spot 1 On STAR 1 Hot Spot

Colatitude (°) 92.5±2.0

Longitude (°) 98.1±1.4

Spot radius (°) 10.0±0.3

Spot T-factor 1.173±0.01

Spot 2 On STAR 1 Hot Spot

Colatitude (°) 89.1±1.4

Longitude (°) 248.2±1.6

Spot radius (°) 8.9±0.5

Spot T-factor 1.162±0.010

25

B,V Light Curve Solution

PHASE

-0.25 0.00 0.25 0.50 0.750.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

26

R,I Light Curve Solution

Rflux

Iflux

PHASE

-0.25 0.00 0.25 0.50 0.750.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

(R-I)flux

V2421 Cyg

27

Surface

Geometry

Phase 0.25

28

Phase 0.50

29

Phase 0.75

30

Phase 0.00

31

Conclusion

• V2421 Cygni is a solar type dwarf Algol binary.

• Mass transfer is present, but the binary is coalescing due to magnetic braking.

• The system fits the theory for pre-contact binaries, except for the matter stream.

32

Future Work

• This system should be patrolled for the next 10 years or more to show us the orbital evolution of the system.

• Radial velocity curves are needed to obtain absolute (not relative) system parameters and spectral typing would give us sure temperatures.

33

• An Arizona Space Grant supported this observing run.

•We wish to thank the American Astronomical Society Small Research Grants for their continuing support of our undergraduate research programs.

• We wish to thank NURO for their allocation of observing time.

Acknowledgments

34

References

Bradstreet, D. H. and Steelman, D.P., 2002, BAAS, Vol. 34, 1224

Kazarovets E.V.; Samus N.N.; Durlevich O.V.; Kireeva N.N.; Pastukhova E.N. 2006, IBVS # 5721. Nagai, K. 2004 Variable Star Bulletin No.42 Nakajima, K., Yoshida, S., Ohkura, N., Kadota, K. 2005, IBVS #5600. Nagai, K. 2004 Variable Star Bulletin No.42 Wilson, R. E. & Devinney, E. J. 1971, ApJ, 166, 605

Wilson, R. E. 1990, ApJ, 356, 613

Wilson, R. E. 1994, PASP, 106, 921

Van Hamme, W.V. Wilson, R.E. 1998, BAAS, 30, 1402

http://cronodon.com/SpaceTech/BinaryStar.html