1. Chiu Ngai Han
Lai San Yu
Lau Tsz Tung Sammy
Wong Ching Yau
Wu Hiu Sze
1

2. What are Cepheid Variables?
• They are a kind of very luminous variable
• They are yellow supergiants
• There is a strong direct relationship between
the its luminosity and period
(brightness-period relationship)
 important standard candles for establishing the
Galactic and extragalactic distance scales.
• They are a kind of very luminous variable
• They are yellow supergiants
• There is a strong direct relationship between
the its luminosity and period
(brightness-period relationship)
 important standard candles for establishing the
Galactic and extragalactic distance scales.
2

3. Brightness-period Relationship
3

4. The StudyThe Study
4

5. Criteria of Choosing the Candidates
1. Mainly their period (< 4 days)
Limited time for observation
• Tools/Catalog using: (website) VizieR
• Candidates chosen:
Su Cas (1.949d) DT Cyg (2.499d)
TU Cas (2.139d) IR Cep (2.114d)
V351 Cep (2.806d) EU Tau (2.102d)
BP Cir (2.398d) V504 Mon (2.77d)
EV Sct (3.09d) BE Cra (3.337d)
BB Gem (2.308d) BF Oph (4.08d)
5

6. Criteria of Choosing the Candidates
6

7. Criteria of Choosing the Candidates
7

8. Hypothesis
Our results(distance) are similar to those done
by Astronomy org.:
• BE CrA cannot be found
• BF Oph 0.789 kiloparsec(kpc) ≈ 2574
• EV Sct cannot be found
• IR Cep 0.524 ≈ 1709
• BP Cir cannot be found
1 kpc ( a unit of length used in astronomy)
= 3262 ly
8

9. Procedures
1. Making observation by photographic image
(skynet) and using aperture photometry (iris)
to find out the V-magnitude of each Cepheid
variables.
BE CrA
9

10. Procedures
2. Entre the data in to Excel and plot the light
curve of each Cepheid variables
10

11. Procedures
3. From the light curve and the photometric
data, two values can be determined:
 the average apparent magnitude, m, of the star
 its period in days.
11

12. 56513.9854166666
56517.33833
12

13. 56513.9854166666
56517.33833
13

14. Procedures
• Name : BE CrA
• m : take average of the variable magnitude
= 13.930
data from the internet = 14.235
• period (d) : 56517.33833 - 56513.9854166666
= 3.353
data from internet = 3.3365
14

15. 15

16. 16

17. Procedures
• Name : BF Oph
• m : take average of the variable magnitude
= 7.682
data from the internet = 7.37
• period (d) : 4.067(data from internet)
17

18. 56515.26985 56518.16832
18

19. 56515.26985 56518.16832
19

20. Procedures
• Name : EV Sct
• m : take average of the variable magnitude
= 10.097
data from the internet = 10.2
• period (d) : 56518.16832 - 56515.26985
= 2.898
data from internet = 3.09
20

21. 56519.31876
56517.3661226853
21

22. 56519.31876
56517.3661226853
22

23. Procedures
• Name : IR Cep
• m : take average of the variable magnitude
= 8.059
data from the internet = 7.86
• period (d) : 56519.31876 - 56517.3661226853
= 1.953
data from internet = 2.114
23

24. 56518.03572
56515.60242
24

25. 56518.03572
56515.60242
25

26. Procedures
• Name : BP Cir
• m : take average of the variable magnitude
= 7.758
data from the internet = 7.52
• period (d) : 56518.03572 - 56515.60242
= 2.433
data from internet = 2.3984
26

27. Procedures
4. Knowing the period of the Cepheid we can
determine its mean absolute magnitude, M, by
interpolating on the brightness-period plot
using formula:
M= -2.43(logP - 1) – 4.05 (Approx.)
M = -0.2-2.1(logP)
OR
Method used
27

28. Procedures
4.
Classical type: M= -2.43(logP - 1) – 4.05
Include: BF Oph
EV Sct
BP Cir
W Virginis type: M = -0.2-2.1(logP)
Include: BE CrA
IR Cep
28

29. Procedures
 BE CrA: -0.2-2.1(log3.353)
= -1.3034 (cor. to 5 sig. fig.)
 BF Oph: -2.43 log (4.067 ) – 1 – 4.05
= -3.1005 (cor. to 5 sig. fig.)
 EV Sct: -2.43 log ( 2.898 ) – 1 – 4.05
= -2.7429 (cor. to 5 sig. fig.)
 IR Cep: - 0.2 - 2.1 (log1.953)
= -0.80105(cor. to 5 sig. fig.)
 BP Cir: -2.43 log ( 2.433 ) – 1 – 4.05
= -2.5593 (cor. to 5 sig. fig.)
29

30. Procedures
5. After finding the apparent magnitude, m, and
absolute magnitude, M
We these two value into the distance-modulus
formula
And calculate the distance to the Cepheid, d.
 m - M = 5 log(d/10)
30

31. Results
• BE CrA: 13.930 - (-1.3034) = 5 log(d/10)
d = 11135 pc
• BF Oph: 7.682 - (-3.1005) = 5 log(d/10)
d = 1433.8 pc (789 pc)
• EV Sct: 10.097 - (-2.7429) = 5 log(d/10)
d = 3698.1 pc
• IR Cep: 8.059 - (-0.80105)= 5 log(d/10)
d = 591 pc (524 pc)
• BP Cir: 7.758 - (-2.5593) = 5 log(d/10)
d = 1157.3 pc
31

32. Results (Discussion)
• Errors were made and thus the calculations
were not accurate.
• Fluctuation of atmosphere affects the results.
• The Cepheid variables are very far away from
us.
• Though they are very far away from us, it still
has a quite high visual magnitude and negative
absolute magnitude. Hence, they are a kind of
very luminous variable!
32

33. Difficulties and Solutions
1. The time for research is limited and so we cannot
carry out a longer observation on the Cepheid
variables
=> the number of photos taken are not enough to
show the whole period of the variables
 Solution: Find those Cepheid variables with
shorter period (less than 3 days).
1. Difficult to determine the companion star
Some companion stars also have fluctuating
magnitude
 Solution: try some other companion stars.
33

34. Difficulties and Solutions
3. Due to bad weather and limited time, the
number of photos taken are not enough to
show the whole period of the stars
Also, the telescopes cannot observe the
Cepheid variables at day time.
=> cannot get a complete light curve
 Solutions:
Reasoning the parts we don’t have by
looking at the slope before and after.
Searching the data from internet to justify
our results
34

35. Difficulties and Solutions
4. Not sure which 5 Cepheid variables to
choose to find their distances
 Solutions:
Use different criteria to select.
Observe more than 5 Cepheid variables
and then choose 5 with good results
35

36. Errors and Improvements
• Major error:
we were not able to observe the stars for a long
enough time to overcome
observational errors (at least 2 periods),
not complete curve.
• Improvements:
start off the observation as soon as possible
find the data on the internet carefully, prevent
getting wrong interpretation on the
information
36

37. The things we’ve learnt:
• How to find stars with certain criteria (such as
the period of variables) using the online
catalog (VizieR etc.).
• How to convert and arrange the observation
into a systematic document for a easier and
more accurate interpretation of observation.
• The method and procedures of finding the
distance of Cepheid variables.
• How to use Iris and find the companion star of
a variable star using Simplay.
37

38. This is the end of our presentation
Thank you for your kind attention
38

39. Q & A section
39