Testing a New Astronomical Data Reduction Technique on ER CEPHEIUS

Robert ParishStephen F. Austin State University

Department of Physics and AstronomyParishrj@titan.sfasu.edu

Different Types of Eclipsing Binaries

Telescope

Obtaining Data

V(t)

Variable Star

D(t) = A(t)V(t)

Variable StarObtaining Data

Telescope

D(t) = A(t)V(t)+S(t)

Obtaining Data

Telescope

D(t) = A(t)V(t)

Telescope

D(x,y,t)=F(x,y) [A(t)V(t)+S(t)]

D(x,y,t)=N(x,y) + F(x,y) [A(t)V(t)+S(t)]

Noise

Obtaining Data

Current Technique

ND(x,y) F(x,y)

NB(x,y)D(x,y,t)

D

Dp

Current Technique

CComparison Star

SSky Brightness

𝑉 (𝑡 )𝐶 =

𝐷𝑃 (𝑥 , 𝑦 , 𝑡 )−S (𝑥3 , 𝑦 3 ,𝑡 )C (𝑥2 , 𝑦2 ,𝑡 )−S (𝑥3 , 𝑦 3, 𝑡 )

Variable StarDp

Current Technique – Problems

• Obtaining a Proper Flat Field– Sky Flats, Box Flats, “Shirt Flats”

• Maintaining CCD temperature Between Dark and Light Frames

• Variable System Noise• Incorrect Calibration Procedures

A New Approach

• Fix Current Technique Problems by– Eliminating the need for dark, flat and bias frames– Removing user error by automating the calibration

process

A New Approach

@ time t @ time t+Δt

A New Approach

D

C

S

A New Approach

D

C

S

A New Approach - Derivation

𝑉 (𝑡 )𝐶 =

𝐷 (𝑥 , 𝑦 , 𝑡 )−𝐷 (𝑥 , 𝑦 , 𝑡2 )+𝑆 (𝑥3 , 𝑦3 ,𝑡 2 )−𝑆 (𝑥3 , 𝑦3 , 𝑡 )𝐶 (𝑥2 , 𝑦2 , 𝑡 )−𝐶 (𝑥2 , 𝑦2 , 𝑡2 )+𝑆 (𝑥3 , 𝑦3 ,𝑡 2 )−𝑆 (𝑥3 , 𝑦3 , 𝑡 )

D

D

S

S

C

C

ER CEP. in NGC188

Testing – Check Star

0 50 100 150 200 250 300 350 400 4500

0.5

1

1.5

2

2.5

3

3.5

New Approach

Image Number

Rela

tive

Inte

nsity

0 50 100 150 200 250 300 350 400 4500

0.5

1

1.5

2

2.5

3

3.5

Conventional Method

Image Number

Rela

tive

Inte

nsity

Testing – Variable 3

0 50 100 150 200 250 300 350 400 450 5000

5000

10000

15000

20000

25000

30000

Raw Star Intensity

Image Number

Inte

nsity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Conventional Method - Variable 3 in NGC188

Phase

Rela

tive

Inte

nsity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

New Approach - Variable 3 in NGC188

Phase

Rela

tve

Inte

nsity

• Visual Band• Published Period1 P = .30652d

Approximate Period Calculations:• Conventional Method

P = .2857d• New Approach

P = .2860d• Percent Difference

.11% or 25.92seconds

Running Average

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Phase

Diff

eren

tial M

agni

tude

Screen Shot of Application

Running Average with Theory

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Phase

Diff

eren

tial M

agni

tude

Convergent Solutions

• Using Starlight Pro and Excel• Recalculate the solution based on minute

changes in chosen parameters• Linear Least Squares formula used to calculate

the error between the Average Light Curve and Theoretical Solution

• 3D Plots of Parameter 1, Parameter 2, and Error

0.00E+00

8.00E-03

1.60E-02

2.40E-02

3.20E-02

4.00E-02

4.80E-02

5.60E-02

6.40E-02

7.20E-02

8.00E-02

8.80E-02

9.60E-02

1.04E-01

1.12E-01

1.20E-011.28E-01

1.36E-011.44E-01

1.52E-01

Mass Ratio

Erro

r

Inclination

i = 81°Error = .0406

4500

4700

4900

5100

5300

5500

5700

5900

6100

6300

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

4500

4600

4700

4800

4900

5000

5100

5200

5300

5400

5500

5600

5700

5800

5900

6000

6100

6200

6300

Star2 Temperature

Erro

r

Star1 Temperature

T1 >100k + T2Error = .0391

0.4170.42

0.4230.4260.4290.4320.4350.4380.4410.4440.447

0.450.4530.456

3.80E-02

4.00E-02

4.20E-02

4.40E-02

4.60E-02

4.80E-02

5.00E-02

45004530

45604590

46204650

46804710

47404770

4800

Star2 Radius

Erro

r

Star2 TemperatureR2 = .328T2 = 4640KError = .0380

0.030.03180.03360.03540.0372

0.0390.04080.04260.04440.0462

0.0480.0498

0.05160000000000010.0534

0.05520000000000010.05700000000000010.05880000000000010.06060000000000010.06240000000000010.06420000000000010.0660000000000001

4500 4520 4540 4560 4580 4600 4620 46404660 4680 4700 4720 4740 4760 4780 4800

Mass Ratio

Erro

r

Star2 Temperatureq = .506T2 = 4640KError = .0374

ER Cepheius Starlight Pro Model

Animation Created with StarLight Pro http://www.midnightkite.com/binstar.html

i = 81°q = .506R1= .439T1= 4740KR2 = .328T2 = 4640KError = .0334

References (UPDATE THIS PAGE)1. X.B. Zhang, “A CCD Photometric Survey of Variable Stars in the

Field of NGC188,” Astron. J. 123, pp.1548, 2002.2. R.M. Branly, “Light Curve Solutions for Eclipsing Binaries

in NGC 188,” Astro. Sp. Sci 235, pp.149-160, 1996.3. W.H. Richardson, “Bayesian-based iterative method of image

restoration,” J. Opt. Soc. Amer. 62, pp.55-59, 1972.4. L.B. Lucy, “An iterative technique for the rectification of observed

distribution,” Astron. J. 79, pp.745-754, 1974.5. J.L. Starck, Astronomical Image and Data Analysis, Springer, 2002.6. R. Wodaski, The New CCD Astronomy, New Astronomy Press, 2002.