I wonder if you can help me with this.
There is a database of cepheid variables called, The David Dunlap Observatory Database Of Galactic Classical Cepheids (DDOD)
http://www.astro.utoronto.ca/DDO/research/cepheids/cepheids.html#files
I have chosen a representative sample of cepheids from that database. I then looked them up in Stellarium, which as you know, is an awesome planetarium. I plotted the Stellarium Absolute Magnitude against the Stellarium Period of pulsation. I attach the resulting graph. My data points are the blue circles.
I was expecting to see data points form a pattern that corresponds with the Ferni relationship. But I cannot see any correlation at all.
I confirmed the validity of the Stellarium data as follows:
- Stellarium Apparent Mags data matches the data in the DDOD database.
- Stellarium Distance/parallax data matches the data in Simbad
- Stellarium Period data matches the data in the DDOD database.
- To check Stellarium's Absolute Magnitude, I used the formula M = m + 5(log10(p) and the results agreed with the data in Stellarium. (M=AbsoluteMag, m=ApparentMag, p=parallax)
I would be grateful if you could explain why is there no correlation? Am I making false assumptions or doing something else wrong?
Here is the data.
STAR
Period
Abs Mag
(d)
FF Aql
4.4709
-3.08
Eta Aql
7.1767
-4.29
RY CMa
4.6783
-0.72
WW Car
4.6768
2.89
GZ Car
4.159
0.92
l Car
35.5358
-4.75
SU Cas
1.9493
-2.08
V553 Cen
2.0605
-0.23
Del Cep
5.3663
-3.07
AD Cru
6.3979
4.67
BG Cru
3.3428
-2.71
DT Cyg
2.4992
-2.82
Beta Dor
9.8426
-3.7
Zeta Gem
10.1507
-4.13
V473 Lyr
1.4908
-2.01
S Mus
9.66
-2.51
RT Mus
3.0861
-1.18
RS Ori
7.5669
-2.06
RS Pup
41.3876
-1.64
W Sgr
7.595
-2.48
X Sgr
7.0128
-2.9
RY Sco
20.3132
3.26
SZ Tau
3.1487
-1.65
R TrA
3.3893
-3.46
Alp UMi
3.9696
-3.66
AP Vel
3.1278
-0.59
The Ferni relationship is a cornerstone in the study of variable stars.
I do hope that someone will step up and take this discussion forward.
Regards
Peter
.
Hi Peter,
I haven't thought about this problem in great depth, but here are a couple of quick reactions. First, have you taken into account interstellar extinction? I would expect it to be significant for many galactic Cepheids, and it can have a major impact on the computed absolute magnitude. Second, what are the uncertainties on the parallax measurements?
Also, I was unable to view the plot in your original post. I don't know why.
Colin
[quote=metham]
I have chosen a representative sample of cepheids from that database.
[/quote]
Wondering what this sample consisted of? All one type or a mix of Classical and Type II? There is about a 2 magnitude offset in the curves of the two types, so if you mixed them in the sample it could look pretty random.
Mike
Some of those absolute magnitudes look highly suspect. I was under the impression that cepheids were all roughly of the same M, round about -2 and brighter. Maybe some of the source material is inaccurate.
The suggestion that the parallaxes for some of the Cepheids may be uncertain seems likely to me. Most Cepheids in the Galaxy are too distant to have accurate parallaxes determined by the trigonometric method (although GAIA will much improve that). You might explore the sources of the Stellarium parallaxes and their uncertainties.
Horace Smith
The parallax data comes from the Hipparcos survey.
On reviewing this survey, I see that the accuracy was about 1 mas, which had seemed more than adequate to me at first sight.
However, one of my data items is RS Pup, for example, and its Hipparcos parallax distance is given as 0.49 mas. Clearly there is a huge uncertainly in that measurement.
(Incidentally I note that some of the measurements for parallax in that survey have negative values - which on reflection is acceptable within the limitations of accuracy.
The average parallax measurement in my data set is 2.8 mas - and so it seems that my data set included many parallax measurements having a high degree of uncertainty - explaining the lack of correlation.
Thanks for nudging me in the right direction.
Peter