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Photometric Monitoring of the Field of
Open Star Cluster M23
Jeff Wilkerson
Iowa Academy of Science
April 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 Schiefelbein
Todd Brown
Brajesh 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 Howes
Buena Vista
Univ.
Travis DeJong
Dordt College
Forrest Bishop
Decorah High
School
Support:
Roy J. Carver Charitable
Trust (Grant #00-50)
Luther College
R.J. McElroy Trust/Iowa
College Foundation
American 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:
Star 723 Summer 2010 Lightcurve
Star 924 Lightcurve May24, 2010
14
12.8
(a) Flare stars
12.9
14.1
13
magnitude
magnitude
14.2
13.1
13.2
14.3
13.3
14.4
13.4
14.5
2450
13.5
0
50
100
150
200
250
2500
2550
2600
300
CJD-2452800
Time (minutes)
(a) Eclipsing binaries
From Contemporary Activities in
Astronomy, by Hoff and Wilkerson
2650
2700
How do we find these? WSVI-statistic test
NGC 129 August 26, 2003
1.08
1.
Fit a second-order polynomial to signalas
a function of normalization factor
1.06
1.04
1.02
2.
Define the WSVI* statistic to measure
the deviation of a star’s signal from the
polynomial fit using paired observations
1
0.98
0.96
0.94
0.92
3.
Find the mean WSVI for a subset of stars
4.
Measure each star’s WSVI deviation
from the mean of its subset
0
20
40
60
80
Image Number
100
120
140
NGC 129 Star 35 8/26/03
125000
120000
115000
* Based on a variability index developed by Welch and
Stetson (AJ, 105, 1993)
110000
105000
100000
95000
0.92
0.94
0.96
0.98
1
1.02
Normalization Factor
1.04
1.06
1.08
Eclipsing Binaries
Period = 0.32866 days
Star 16
Period = 0.5455059(2) days
Period = 0.20730 days
Star 41 Light Curve June 27, 2011
Star 1267 Lightcurve June 1, 2006
July 5, 2007
15.3
10.45
10.15
15.4
10.5
10.2
15.5
10.3
magnitude
magnitude
magnitude
15.6
10.25
15.7
15.8
10.55
10.6
15.9
10.65
10.35
16
16.1
10.4
0
0.5
1
1.5
2
2.5
3
Time After Start (Hrs)
Period = 5.5 days
3.5
4
10.7
0
50
100
150
200
250
300
Time (minutes)
Period = 1.883360(2) days
0
50
100
150
200
250
300
Time (min.)
Period = 9.48665 days
Eclipsing Binaries: April 17, 2012
<T2-T1>odd = 0.710±.053 hr
<T2-T1>even = 0.782±.045 hr
Star 1267 P =.94168030 d
0.02
<T3-T2>odd = 0.683±.042 hr
O-C Even
O-C Odd
0.015
<T3-T2>even = 0.703±.068 hr
O-C (days)
0.01
<T4-T3>odd = 0.865±.041 hr
0.005
<T4-T3>even = 0.785±.075 hr
0
-0.005
-0.01
3s limit on LoS eccentricity ≈
0.007
-0.015
-0.02
0
500
1000
1500
2000
2500
Cycle
P = 1.883360(2)d
(unc. ≈ 0.2 sec.)
mO-C, even = 0.00024±.0009d
mO-C, odd = -0.00025±.0009d
In general:
3s limit on any variations ≈ 0.012d
3s limit on projection of eccentricity ≈ 0.001
(dP/dt)/P = 2(dm/dt)/(m1+m2) +
3(dm1/dt)(m1-m2)/m1m2 + 3K
For us, 3s limit on dP/dt comes from 3s limit on O-C in 2011 vs. 2005 of 0.012d
Pavg – Pobs = 5.2x10-6d
DP = 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
sodd = 71.3 ADU
seven = 206.6 ADU
If the standard deviations are
distributed normally then the variance
of the of the standard deviation is:
Var(s) = 1/N[N-1-2G2(N/2)/G2((N-1)/2)]Ns2/(N-1)
Yields one standard deviation
uncertainties:
)4
(Ta/Tb = Depth1/Depth2
sodd = 71.3 +/-12.9ADU
seven = 206.6+/-33.3 ADU
One last check for a third star
<T2-T1> = 0.746±.035 hr
<T4-T3> = 0.825±.042 hr
<T4-T2> = 1.494±.038 hr
About 40% of the light goes away in
either primary or secondary eclipse
<T3-T1> = 1.437±.037 hr
Total Light = C’(d12 +d22) = 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
What if the secondary object is dark?
Eclipse timing
actually gives
minimum large
object radius due
to orbital
inclination.
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 2s below mean measured
value and Rdark 2s above mean measured value yields
fractional areal coverage of 0.355.
If actual eclipse depth is 2s below mean measured
value it would be 0.381.
Star 166
Avg Depth vs. time
8
Avg O-C vs. time
0.004
7.5
0.002
Mean O-C (days)
Avg. Annual Depth (%)
7
6.5
6
5.5
0
-0.002
5
4.5
4
May/1
-0.004
May/1
May/1
May/1
May/1
May/1
May/1
May/1
May/1
May/1
May/1
May/1
Date
May/1
May/1
May/1
Date
Mean O-C Primary and Seconday Eclipses
Minima Depth Histogram Star 166
10
0.01
Even Numbered Minima Depth:
mean = 6.47+/-0.24 %
Mean O-C Odd
Mean O-C Even
Odd Numbered Minima:
mean = 5.84+/-0.18 %
8
Odd depth
Even depth
6
4
Mean O-C (days)
# eclipses
0.005
0
-0.005
2
0
0.02
0.04
0.06
0.08
Depth (%)
0.1
0.12
-0.01
Apr/1
Apr/1
Apr/1
Apr/1
Apr/1
Date
Apr/1
Apr/1
Apr/1
Long (IV) Timescales: a variance test
s
2
s
F-Stat Distribution
2
300
longterm
250
con sec utive nights
We claim stars with F-Stat > 4.70
are intrinsically variable
Number of Stars
200
stars with
F-Stat > 4.70
are variable
150
100
High cutoff chosen so <FAP> ~0
+20 stars →
50
Removed 7 stars with artificially
high F-Stats:
0
-5
0
5
F-Stat
10
15
- 6 due to close neighbor
interference
- 1 due to transiting asteroid
55 remaining stars with F-Stat>4.70
Pulsating Variables in the M23 Field
Star 1654
15
magnitude
16
17
18
19
20
0
500
1000
1500
2000
2500
3000
MJD-2452800
Properties:
Star 1654
15
16
magnitude
Period: DCDFT
Color: R-I
Amplitude: 4-96%
Asymmetry: Risetime/Period
Mean Magnitude: (96+4)/2
17
18
2003
2005
2006
2007
2008
2009
2010
2011
19
20
0
0.2
0.4
0.6
MJD/154.29 - X
0.8
1
Populations of Pulsating Stars
Star 356 Phase Diagram;  = 96.3
Power Spectrum Lead Term Amplitude Histogram
8
13
7
13.5
6
1
14
magnitude
# stars
5
4
14.5
15
3
15.5
2
16
1
16.5
0
0
20
40
60
80
0
100
0.2
Star 82 Phase Diagram;  = 24.2
0.6
0.8
1
Star 981 Phase Diagram;  = 42.3
1
11
0.4
MJD/321.42 - X
DCDFT Theta One
1
14.5
14.6
11.2
14.7
magnitude
magnitude
11.4
11.6
14.8
14.9
15
11.8
15.1
12
15.2
12.2
15.3
0
0.2
0.4
0.6
MJD/118.03-X
0.8
1
0
0.2
0.4
0.6
MJD/193.32 - X
0.8
1
Populations of Pulsating Stars
Amplitude Distribution (F-Stat > 4.70)
20
y = 54.608 * x^(1.6583) R= 0.70793
We see many more lower A
stars than higher A stars.
15
Recognize that detection
efficiency is lower for lower
A stars as well.
10
F-Stat
Number of Stars
13.85<m<14.85
100
10
5
0
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
Amplitude (Magnitude)
Estimated Fraction Variable per Mag of Amp
Estimated Fraction of Stars Variable per Magnitude of Amplitude
0.4
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%.
0.3
0.2
0.1
1
0.1
1
Amplitude (mag)
Detection Efficiencies
Deteff m<13.85
Deteff 13.85<m<14.85
Deteff 14.85<m<15.50
Deteff m>15.50
1
0.8
Efficiency
0
Fit a power law; extrapolate
to threshold; use scatter to
determine detection
efficiency as a function of
both magnitude and
amplitude.
0.6
0.4
0.2
0
0
0
0
0.5
1
1.5
2
Amplitude of Variation
2.5
3
0.1
0.2
0.3
0.4
0.5
0.6
Amplitude of Variation (Magnitude)
0.7
0.8
Populations of Pulsating Stars
PS Lead Term Amplitude Vs. Varaibility Amplitude
Amplitude vs. Color
100
3
DCDFT Theta One
2.5
Amplitude
2
1.5
1
0.5
y = 70.573 * x^(0.24606) R= 0.4897
y = 84.718 * x^(0.99436) R= 0.52016
10
0
0.1
1
0
1
2
3
Amplitude (mag)
Amplitude Vs. Period
5
6
7
Amplitude Vs. Best Period
3
3
2.5
2.5
2
2
Amplitude
Amplitude
4
R-I
1.5
1.5
1
1
0.5
0.5
0
0
0
100
200
300
Period (days)
400
500
0
100
200
300
Period (days)
400
500
Interesting Stars: The Yellow Stars
Star 338 Phase Diagram
12.5
13
A likely RV Tau variable
magnitude
13.5
14
14.5
15
15.5
16
0
0.2
0.4
0.6
0.8
1
MJD-2452800/77.9
Star 357 Phase Diagram
13.3
13.4
magnitude
13.5
13.6
A likely Cepheid variable
13.7
13.8
13.9
14
0
0.2
0.4
0.6
MJD/14.898-X
0.8
1
Interesting Stars: Plateau Stars
Star 317 Phase Diagram
12.5
Star 1223 Phase Diagram
13
13.5
13
magnitude
magnitude
14
13.5
14
14.5
15
14.5
15.5
15
16
0
0.2
0.4
0.6
0.8
1
0
0.2
Star 1495 Phase Diagram
13.5
15
14
16
14.5
17
magnitude
magnitude
0.4
0.6
0.8
1
MJD/389.61 - X
MJD/367.64 - X
15
Star 1654 Lightcurve
18
19
15.5
20
16
0
0.2
0.4
0.6
MJD/394.73 - X
0.8
1
2500
2600
2700
2800
MJD-2452800
2900
3000
Interesting Stars: SAS Stars
Star 1007 Lightcurve
14.6
14.8
15
magnitude
15.2
15.4
15.6
15.8
16
16.2
0
500
1000
1500
2000
2500
3000
2500
3000
MJD-2452800
Star 82 Lightcurve
11
11.2
magnitude
11.4
11.6
11.8
12
12.2
0
500
1000
1500
2000
MJD-2452800
Define Short-term Photometric Resolution (STPR) as s/m for a Gaussian fit to a histogram
of several hundred signal measurements for a given star and Long-term Photometric
Resolution (LTPR) as s/m for the nightly average signal measure of a given star over an
entire campaign.
LTPR vs Mean Stellar Signal (M23)
M23 Data
1
0.1
0.1
0.01
0.01
100
1000
10
4
Stellar Signal (ADU)
10
5
100
1000
10
4
10
5
10
6
10
7
Mean 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.
M23 Summer 2011
16
14
12
10
8
6
4
2
Functional fits shown of form: STPR=[(C1)² + (C2
signal-1/2)²
+ (C3
signal)2]1/2
0
0
0.05
0.1
Standard deviation of nightly signal over mean signal
0.15
M23 Color-Magnitude
Color-Magnitude Diagram
Diagram
M23
Non-Variable
Non-Variable
HA Pulsating
Pulsating Stars
Stars
HA
LA Pulsating
Pulsating Stars
Stars
LA
Eclipsing Binaries
Binaries
Eclipsing
88
Star 16
10
10
Star 41
Star 69
II
Star 166
12
12
Star 519
14
14
Star 1267
16
16
00
11
22
33
44
AVG R-I
R-I
AVG
55
66
77
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.