South African Astronomical Observatory (SAAO), Cape Town

IST h:m:s
20:23:23
21:05:42
21:50:03
22:36:34
23:10:45
23:55:29
00:43:56
Data
Counts per unit time
23448
23988
25325
25030
24009
23859
23224
• Calculate Universal Time(UT) as following :
UT h = IST h - 5 h 30 m
IST = Indian Standard Time
• Calculate Magnitude :
m i
= -2.5 log(COUNTS)

Atmospheric Extinction
• Dimming of star light by Atmosphere.

Atmospheric Extinction
• Dimming of star light by Atmosphere.
• Loss of the star light characterized by Extinction
Coefficients k
λ
.

Atmospheric Extinction
• Major factors for extinction of star light :
Atmospheric and meteorological condition.
Altitude of the Observing place.
Wavelength of the incoming light.
• Airmass (X) :
Effective path length of air through which star light must pass to reach observer.
X = sec z where z = zenith angle

Atmospheric Extinction

Atmospheric Extinction
• Major factors for extinction of star light :
Atmospheric and meteorological condition.
Altitude of the Observing place.
Wavelength of the incoming light.
• Airmass (X) :
Effective path length of air through which star light must pass to reach observer.
X = sec z where z = zenith angle sec z = (sin ϕ
sin
δ
+ cos ϕ
cos
δ
cos H ) −1
where ϕ = latitude of observing place
δ = Declination of the star
H = Hour angle of star

Atmospheric Extinction
• Hour angle :
The distance from celestial meridian
HA = LST - RA where LST = Local Sidereal Time
RA = Right Ascension of star
• Local Sidereal Time :
1 . Defined as the instantaneous hour angle of vernal equinox.
2. It depends on observers location specifically longitude .
LST = 6.6460556+2400.0512617(JD-2415020)/36525 +1.0027379(UT)-
Longitude(hour)-24(Year-1900)
where JD = Julian date

Atmospheric Extinction
• Julian date
1. The number of days that have elapsed since noon on January
1, 4713 B.C.
2. Julian day begins at noon Greenwich time(12 h UT).
3. Julian date is used to calculate the time between events
which are separated by long intervals.
JD = 2415020+365(Year-1900)-0.5+(UT/24)
+(days starts from year)+(no. of leap year since 1900)
Example : 10 August 2007 at 10 h 30 m UT (16h00m IST) is
JD = 2454322.94

Atmospheric Extinction
Observations :
1. Using single star.
2. All sky photometry.

Atmospheric Extinction
• Plot of Airmass vs Magnitude will give extinction.
m i
 X

Atmospheric Extinction
• Typical values of extinction coefficients at IUCAA :
(observations carried with IUCAA 16" Meade telescope)
k v
= 0.44±0.18
k bv
= 0.18±0.05
k vr
= 0.10±0.05
• Extinction correction : m c
= m i
– k X where m i
= instrumental magnitude
m c
= extinction corrected magnitude

Transformation Coefficients
• To compare the observations taken by different observer using different photometric system, the observations must be transformed from instrumental system to standard system.
• There are many standard photometric system according to different physical requirements. Example :
UBVRI broad band system (900 A° )
uvby intermediate band system (200 A° )
H
α
,H
β
narrow band system (30 A° )

Transformation Coefficients
Filter Central Wavelength (A°)
Broad band system
U 3600
B 4400
V 5500
R 7000
I 9000
Intermediate band system
u 3500
v 4100
b 4700
y 5500
Narrow band system
H α 6567
H β 4868

Transformation Coefficients

Transformation Coefficients
• Observations :
1.
15-20 standard stars having standard magnitude and colors.
2.
Standard stars must cover all colors and wide ranges in magnitude.
3.
Relatively close together in the sky.
4.
They should be observed within an hour or so.
5.
Photometric night (a clear night when atmospheric transparency is almost constant) can be use for calibration observation.
• Transformation Relations :
V - v
0
= a v
(B-V) + b v
B-V = a b−v
(b-v)
0
+ b b−v
V-R = a v−r
(v-r)
0
+ b v−r where a’s are transformation coefficients and b’s are zero points
V, B-V and V-R are the magnitude and colors in standard system.
v
0
, (b-v)
0
and (v-r)
0
are the observed magnitude and colors.

Transformation Coefficients

Transformation Coefficients
• The typical values of a’s and b’s for observations carried with
IUCAA 16" Meade Telescope :
a v
= -0.040
± 0.005 b v
= 8.790
± 0.003
a b − v
= 1.334
± 0.055 b b − v
= -0.626
± 0.034
a v − r
= 1.147
± 0.023 b v − r
= 0.141
± 0.011
• What the values of the transformation coefficients can tell us?
• Reliability of transformation coefficients ?
V = 0.03
(B-V) = 0.039
(V-R) = 0.032

Transformation Coefficients
• The zero points may vary with time because :
1. variable atmospheric extinction
2. dust deposition on mirror, Schmidt corrector plate or filters
3. deterioration of telescope-photometer system

Differential Photometry
• Differential photometric technique is one of the most simplest technique to record photometric variability of the stars with very high accuracy.
• The basic idea of differential photometry is to record light variability of variable star with respect to a nearby constant stars called comparison star.
• Also we choose a third star, called check star gives accuracy of the observation and also used to check constancy of the Comparison star.

Differential Photometry
• The basic criteria to choose comparison and check stars are :
1. Should be as near as possible to the variable star
2. Preferably within a degree.
3. Nearly same magnitude and color as those of the variable star.

Differential Photometry
• Observing sequence :
Observing sequence of the Comparison(C), Variable(V) and
Check(Ch) star accompanied with observation for Sky(S) is :
C-S-V-S-Ch-C-S-V-S-Ch
repeat this sequence for different filters and according to nature of the variable star.
• Differential Magnitude : m v
= -2.5 log(C
V
/C
C
) where C
V
= Counts of Variable star, C
C
= Counts of Comparison star
m ch
= -2.5 log(C
C
/C
Ch
) where C
V
= Counts of Check star

Differential Photometry
• Calculate JD for time of observation.
• Plot of JD vs Differential Magnitude :

Differential Photometry
• Phase calculation :
fractional part of (JD - E) / P
Where E = Time of minimum light or JD at which minima of light curve occurs.
P = variability period (in days)
• For variable star photometry ephemeris for minimum light is given
JD = 2452646.96591 + 0 d .4231n
where 2452646.96591 is initial epoch
0 d .4231 is the Period
n is cycle number

Differential Photometry
• Plot of Phase vs Differential Magnitude :

Differential Photometry
• Advantages :
1. Error introduced by variable atmosphere is minimized.
2. Same color minimized the difference in wavelength response between the instrumental system and the standard system.
3. Similar brightness of both stars means you can use CCD or Photometer for same exposure/integration time.

References
• Astronomical Photometry :
Henden, A.A. and Kaitchuck, R.H.
• Photoelectric Photometry of Variable Stars :
Hall, D.S. and Genet, R.M.