Photometric Monitoring of the Field Photometric Monitoring of the Field ofof

Open Star Cluster M23Open Star Cluster M23

Jeff WilkersonJeff WilkersonIowa Academy of Iowa Academy of

ScienceScience

April 21, 2012April 21, 2012

Sensitive to Variability on a Wide Range of Timescales:

I. Tenths of seconds to seconds Occultation and microlensing events Brief flares

II. Tenths of hours to a few days Flares in long period variables Delta Scuti stars Traditional flare stars Eclipsing binaries Transiting planets

III. Days to hundreds of days Long period pulsating variable stars Eclipsing binary stars Cataclysmic variable stars Cepheid variables Period-to-period variability in long

period variables Rotating variable stars in young clusters

IV. Years to decades Luminosity stability Solar-like cycles Period-to-period variability in long

period variables Proper motions of stars

Have observed 61“classical” variable stars to date, 59 of them newly discovered

Student Participation:

Ujjwal Joshi

Nathan Rengstorf

Andrea SchiefelbeinTodd BrownBrajesh Lacoul

Kari Frank

Alex Nugent

Drew Doescher

Alex Sperry

Jennifer Schulz

Clara Olson

Robyn Siedschlag

Siri Thompson

Matt Fitzgerald

Heather Lehmann

Amalia Anderson

Hilary Teslow

Steve Dignan

Kirsten Strandjord

Donald Lee-Brown

Andrew Becklin

Zebadiah HowesBuena Vista Univ.

Travis DeJongDordt College

Forrest BishopDecorah High School

Support: Roy J. Carver Charitable Trust (Grant #00-50)Luther CollegeR.J. McElroy Trust/Iowa College FoundationAmerican Astronomical Society

OUR DATA SETS

Cluster Dur. (s) # Nights Total Images

Date Range

NGC 6531 (M21) 3.5 21 30,000 26 June 2002 – 8 Sept 2002

NGC 6514 (M23) 3.5 25 45,000 19 June 2003 – 8 Sep. 2003

NGC 129 10.5 9 15,000 11 Aug. 2003 – 8 Sep. 2003

NGC 2682 (M67) 2.0 14 35,000 25 Feb. 2004 – 26 April 2004

NGC 6694 (M26) 9.0 20 28,000 24 June 2004 – 9 Sep. 2004

NGC 6514 (M23) 2.5 20 45,000 23 June 2005 – 30 Aug. 2005

NGC 2286 7.5 22 28,000 24 Jan. 2006 – 10 April 2006

NGC 6514 (M23) 5.0 37 49,000 28 Mar. 2006 – 25 Sep. 2006

NGC 7380 10.0 40 44,000 12 Jul. 2006 – 9 Jan. 2007

NGC 2286 7.5 29 44,000 31 Oct. 2006 – 5 Apr. 2007

NGC 6514 (M23) 2.8 49 91,000 9 Mar. 2007 – 27 Sep. 2007

NGC 7380 10.0 42 48,000 5 Jul. 2007 – 14 Jan. 2008

NGC 2286 5.0 35 65,000 3 Oct. 2007 – 12 Apr. 2008

NGC 6514 (M23) 3.5 53 82,000 3 Mar. 2008 – 16 Sep. 2008

NGC 6514 (M23) 3.5 45 50,000 11 Mar. 2009 – 17 Sep. 2009

NGC 6514 (M23) 3.5 63 59,000 27 Feb. 2010 – 8 Oct. 2010

NGC 6514 (M23) 3.5 57 46,000 1 Mar. 2011 – 11 Oct. 2011

NGC 6514 (M23) 7.0 ? ? 11 Feb. 2012 – present

Short (II) Timescales: (tenths of hours to a few days)

Primarily two types of objects here:

(a)Flare stars

(a)Eclipsing binaries

From Contemporary Activities in Astronomy, by Hoff and Wilkerson

14

14.1

14.2

14.3

14.4

14.52450 2500 2550 2600 2650 2700

Star 723 Summer 2010 Lightcurve

ma

gn

itud

e

CJD-2452800

12.8

12.9

13

13.1

13.2

13.3

13.4

13.50 50 100 150 200 250 300

Star 924 Lightcurve May24, 2010

ma

gn

itud

e

Time (minutes)

How do we find these? WSVI-statistic test

1. Fit a second-order polynomial to signalas a function of normalization factor

2. Define the WSVI* statistic to measure the deviation of a star’s signal from the polynomial fit using paired observations

3. Find the mean WSVI for a subset of stars

4. Measure each star’s WSVI deviation from the mean of its subset

* Based on a variability index developed by Welch and Stetson (AJ, 105, 1993)

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

0 20 40 60 80 100 120 140

NGC 129 August 26, 2003

Image Number

95000

100000

105000

110000

115000

120000

125000

0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08

NGC 129 Star 35 8/26/03

Normalization Factor

Eclipsing Binaries

Period = 0.32866 days Period = 0.5455059(2) days Period = 0.20730 days

10.15

10.2

10.25

10.3

10.35

10.40 0.5 1 1.5 2 2.5 3 3.5 4

Star 16 July 5, 2007

ma

gn

itud

e

Time After Start (Hrs)

Period = 5.5 days Period = 1.883360(2) days

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16

16.10 50 100 150 200 250 300

Star 1267 Lightcurve June 1, 2006

ma

gn

itu

de

Time (minutes)

10.45

10.5

10.55

10.6

10.65

10.70 50 100 150 200 250 300

Star 41 Light Curve June 27, 2011

ma

gn

itud

e

Time (min.)

Period = 9.48665 days

Eclipsing Binaries: April 17, 2012

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0 500 1000 1500 2000 2500

Star 1267 P =.94168030 d

O-C EvenO-C Odd

O-C

(d

ays)

CycleP = 1.883360(2)d O-C, even = 0.00024±.0009d (unc. ≈ 0.2 sec.) O-C, odd = -0.00025±.0009d

3 limit on any variations ≈ 0.012d 3 limit on projection of eccentricity ≈ 0.001

<T2-T1>odd = 0.710±.053 hr

<T2-T1>even = 0.782±.045 hr

<T3-T2>odd = 0.683±.042 hr

<T3-T2>even = 0.703±.068 hr

<T4-T3>odd = 0.865±.041 hr

<T4-T3>even = 0.785±.075 hr

3 limit on LoS eccentricity ≈ 0.007

In general:

(dP/dt)/P = 2(dm/dt)/(m1+m2) + 3(dm1/dt)(m1-m2)/m1m2 + 3K

For us, 3 limit on dP/dt comes from 3 limit on O-C in 2011 vs. 2005 of 0.012d

Pavg – Pobs = 5.2x10-6d P = 1.04x10-5d in 2200 days (dP/dt)max = 4.5x10-9

Use sizes from eclipse timing and color to estimate m1 = 0.7Mʘ and m2 = 0.3Mʘ.

dm1/dt < [(0.7Mʘ)(0.3Mʘ)/3Mʘ](4.5x10-9)/1.88d = 6x10-8 Mʘ/year

(Ta/Tb)4 = Depth1/Depth2

odd = 71.3 ADU

even = 206.6 ADU

If the standard deviations are distributed normally then the variance of the of the standard deviation is:

Var() = 1/N[N-1-22(N/2)/2((N-1)/2)]N2/(N-1)

Yields one standard deviation uncertainties:

odd = 71.3 +/-12.9ADU

even = 206.6+/-33.3 ADU

One last check for a third star

About 40% of the light goes away in either primary or secondary eclipse

<T2-T1> = 0.746±.035 hr

<T4-T3> = 0.825±.042 hr

<T4-T2> = 1.494±.038 hr

<T3-T1> = 1.437±.037 hr

Total Light = C’(d12 +d2

2) = C[(.786)2 + (1.466)2] = C(.618 + 2.149) = C2.77

Fraction of total area from smaller object= 0.618/2.77 = 0.22

Eclipse timing actually gives minimum large object radius due to orbital inclination.

What if the secondary object is dark?

B-V = 1.415; V = 15.55

Assume reddening of cluster, = .356; (B-V)0= 1.059

Rstar≈0.80Rʘ

Now need (Rdark/Rstar)2=0.40

Rdark ≈0.80Rstar ≈0.50Rʘ

But we know brown dwarf stars have R ≈0.10Rʘ

Assuming Rstar actually 2 below mean measured value and Rdark 2 above mean measured value yields fractional areal coverage of 0.355.

If actual eclipse depth is 2 below mean measured value it would be 0.381.

4

4.5

5

5.5

6

6.5

7

7.5

8

May/1 May/1 May/1 May/1 May/1 May/1 May/1 May/1

Avg Depth vs. timeA

vg.

An

nu

al D

ep

th (

%)

Date

Star 166

-0.01

-0.005

0

0.005

0.01

Apr/1 Apr/1 Apr/1 Apr/1 Apr/1 Apr/1 Apr/1 Apr/1

Mean O-C Primary and Seconday Eclipses

Mean O-C OddMean O-C Even

Me

an

O-C

(d

ays

)

Date

-0.004

-0.002

0

0.002

0.004

May/1 May/1 May/1 May/1 May/1 May/1 May/1

Avg O-C vs. time

Me

an

O-C

(d

ays

)

Date

0

2

4

6

8

10

0.02 0.04 0.06 0.08 0.1 0.12

Minima Depth Histogram Star 166

Odd depthEven depth

# e

clip

ses

Depth (%)

Even Numbered Minima Depth:mean = 6.47+/-0.24 %

Odd Numbered Minima:mean = 5.84+/-0.18 %

0

50

100

150

200

250

300

-5 0 5 10 15

F-Stat Distribution

Num

ber

of S

tars

F-Stat

stars with F-Stat > 4.70 are variable

+20 stars →

We claim stars with F-Stat > 4.70 are intrinsically variable

High cutoff chosen so <FAP> ~0

Removed 7 stars with artificially high F-Stats:

- 6 due to close neighbor interference- 1 due to transiting asteroid

55 remaining stars with F-Stat>4.70

Long (IV) Timescales: a variance test

2

2

sec

nightsutivecon

longterm

Pulsating Variables in the M23 Field

Properties:

Period: DCDFTColor: R-IAmplitude: 4-96%Asymmetry: Risetime/PeriodMean Magnitude: (96+4)/2

15

16

17

18

19

200 500 1000 1500 2000 2500 3000

Star 1654

ma

gn

itud

e

MJD-2452800

15

16

17

18

19

200 0.2 0.4 0.6 0.8 1

Star 1654

20032005200620072008200920102011

mag

nitu

de

MJD/154.29 - X

Populations of Pulsating Stars

11

11.2

11.4

11.6

11.8

12

12.20 0.2 0.4 0.6 0.8 1

Star 82 Phase Diagram; 1 = 24.2

ma

gn

itud

e

MJD/118.03-X

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100

Power Spectrum Lead Term Amplitude Histogram

# s

tars

DCDFT Theta One

13

13.5

14

14.5

15

15.5

16

16.50 0.2 0.4 0.6 0.8 1

Star 356 Phase Diagram; 1 = 96.3

ma

gn

itud

e

MJD/321.42 - X

14.5

14.6

14.7

14.8

14.9

15

15.1

15.2

15.30 0.2 0.4 0.6 0.8 1

Star 981 Phase Diagram; 1 = 42.3

mag

nitu

de

MJD/193.32 - X

Populations of Pulsating StarsWe see many more lower A stars than higher A stars.

Recognize that detection efficiency is lower for lower A stars as well.

Fit a power law; extrapolate to threshold; use scatter to determine detection efficiency as a function of both magnitude and amplitude.

Estimate the percentage of stars with A>0.22 mag. and P>10 days as : 3.6±0.6%. With cluster members removed the number is: 7.2±1.2%.

0

5

10

15

20

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

Amplitude Distribution (F-Stat > 4.70)

Num

be

r o

f S

tars

Amplitude (Magnitude)

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Detection Efficiencies

Deteff m<13.85Deteff 13.85<m<14.85

Deteff 14.85<m<15.50Deteff m>15.50

Eff

icie

ncy

Amplitude of Variation (Magnitude)

0

0.1

0.2

0.3

0.4

0 0.5 1 1.5 2 2.5 3

Estimated Fraction of Stars Variable per Magnitude of Amplitude

Est

imat

ed F

ract

ion

Var

iab

le p

er

Ma

g of

Am

p

Amplitude of Variation

1

10

100

0.1 1

13.85<m<14.85

y = 54.608 * x^(1.6583) R= 0.70793

F-S

tat

Amplitude (mag)

Populations of Pulsating Stars

10

100

0.1 1

PS Lead Term Amplitude Vs. Varaibility Amplitude

y = 70.573 * x^(0.24606) R= 0.4897

y = 84.718 * x^(0.99436) R= 0.52016

DC

DF

T T

he

ta O

ne

Amplitude (mag)

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7

Amplitude vs. Color

Am

plit

ude

R-I

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500

Amplitude Vs. Best Period

Am

plitu

de

Period (days)

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500

Amplitude Vs. Period

Am

plitu

de

Period (days)

Interesting Stars: The Yellow Stars

A likely Cepheid variable

A likely RV Tau variable

12.5

13

13.5

14

14.5

15

15.5

160 0.2 0.4 0.6 0.8 1

Star 338 Phase Diagram

ma

gn

itud

e

MJD-2452800/77.9

13.3

13.4

13.5

13.6

13.7

13.8

13.9

140 0.2 0.4 0.6 0.8 1

Star 357 Phase Diagram

ma

gn

itud

e

MJD/14.898-X

Interesting Stars: Plateau Stars12.5

13

13.5

14

14.5

150 0.2 0.4 0.6 0.8 1

Star 317 Phase Diagram

ma

gn

itud

e

MJD/367.64 - X

13

13.5

14

14.5

15

15.5

160 0.2 0.4 0.6 0.8 1

Star 1223 Phase Diagram

ma

gn

itud

e

MJD/389.61 - X

13.5

14

14.5

15

15.5

160 0.2 0.4 0.6 0.8 1

Star 1495 Phase Diagram

ma

gn

itud

e

MJD/394.73 - X

15

16

17

18

19

202500 2600 2700 2800 2900 3000

Star 1654 Lightcurve

ma

gn

itud

e

MJD-2452800

Interesting Stars: SAS Stars14.6

14.8

15

15.2

15.4

15.6

15.8

16

16.20 500 1000 1500 2000 2500 3000

Star 1007 Lightcurvem

ag

nitud

e

MJD-2452800

11

11.2

11.4

11.6

11.8

12

12.20 500 1000 1500 2000 2500 3000

Star 82 Lightcurve

ma

gn

itud

e

MJD-2452800

Define Short-term Photometric Resolution (STPR) as for a Gaussian fit to a histogram of several hundred signal measurements for a given star and Long-term Photometric Resolution (LTPR) as for the nightly average signal measure of a given star over an entire campaign.

0.01

0.1

100 1000 104

105

M23 Data

Stellar Signal (ADU)

At large signal values STPR approaches a constant (plateau) value determined by our frame normalization, itself limited by scintillation. For faint stars STPR increases as signal-1. In between STPR increases as signal-1/2. Counting statistics of the stellar signal measurement dominate STPR in this region.

Functional fits shown of form: STPR=[(C1)² + (C2signal-1/2)² + (C3signal)2]1/2

0.01

0.1

1

100 1000 104

105

106

107

LTPR vs Mean Stellar Signal (M23)

Mean Signal (ADU)

0

2

4

6

8

10

12

14

16

0 0.05 0.1 0.15

M23 Summer 2011

Standard deviation of nightly signal over mean signal

0.001

0.01

0.1

10 100

Flux Resolution vs. Altitude

Altitude (degrees)

8

10

12

14

16

0 1 2 3 4 5 6 7

M23 Color-Magnitude Diagram

Non-VariableHA Pulsating StarsLA Pulsating StarsEclipsing Binaries

I

AVG R-I

8

10

12

14

16

0 1 2 3 4 5 6 7

M23 Color-Magnitude Diagram

Non-VariableHA Pulsating StarsLA Pulsating StarsEclipsing Binaries

I

AVG R-I

Star 16

Star 41Star 69

Star 519

Star 166

Star 1267

Oddities

CONCLUSION

We have a unique data set that offers unprecedented temporal coverage of >1600 stars down to 19th magnitude, yielding a detection of variability in about 8% of the field stars.

Have measured eclipsing binary periods down to tenths or hundredths of a second. Variation in orbital parameters gives information on perturbations in the system. Expect detections or stringent upper limits to appear in the next few years.

Strong evidence of two classes of pulsating stars (high and low amplitude) with different pulsation behavior

Distinct classes of pulsational behavior have emerged. Any model or models of these stars must account for the observed intra-group and inter-group homogeneity and heterogeneity.

Brief, rare events in these stars and others are still being sought.