Object: delta Cephei

Constellation
RA / DEC
Magnitude A / C
Separation A / C
Position angle
Spectral class A / C
Colour A / C
: Cepheus
: 22:29:12 / +58.25
: 4.2 /6.1
: 40.6”
: 191°
: F51b-G21b / B7V
: yellow-orange / blue-white
Details sketch
Date / Time
Observing Location
Seeing / Transparency
Telescope
Eye-piece
Magnification / Field of View '
: 21/08/10 / 1:10
: Landgraaf
: 3 / 3
: Orion Optics UK 300mm
: 22mm Nagler Type 4
: 73 / 68
Delta Cephei tag
Observing report
Delta Cephei AC is already split at the lowest magnification with the 35mm Panoptic (46x). The optimum magnification for observing this double star is 72x, which is achieved with the 22mm Nagler. The contrast of delta Cephei AC is simply beautiful. The bright A component looks yellow, almost orange, while the dimmer C component looks blue-white. The B component, which is a magnitude 13 G0 star at a position-angle of 284° and a separation of 21", is completely invisible.

I see a nice asterism of stars to the southwest of Delta Cephei. It looks almost like a part of a circle or a hook. I see no other interesting field stars, double stars or stars that show color. I cannot detect any nebulosity or background glow of unresolved stars.
Notes
Delta Cephei A is a variable star. Variable stars are stars which change in brightness. The variations can be due to various reasons: the rotation of a heavily spotted star, an eclipse by a companion star or a planet, vibrations of a star (pulsating), eruptions (flares) on a star, explosions (novae), an accretion disc around a star (dwarf novae) or complete destruction of a star, a supernova.

Delta Cephei A, is a pulsating star, which is the prototype of a whole group of yellow giant or supergiant pulsating variables. These stars vary in brightness in very exact periods, almost like a clockwork, varying from 1 to 50 days. They are called Cepheid's, after Delta Cephei, the first star of the cepheid type that was discovered. The Cepheid variables are very important because their distance can be calculated if you have measured the period. The period is the time the star takes to reach its maximum brightness and minimum brightness.

In the beginning of the twentieth century it was discovered that there is a relation
between the period of a Cepheid and its absolute magnitude. In other words, if you know a Cepheid's period, you know its absolute magnitude. You also know the relative or visual magnitude of a star by visual observation or photometry. If you have both the visual and the absolute magnitude, you can calculate the distance. So if you can identify a variable as a Cepheid, you always can calculate the distance.


Example of a distance calculation in 4 steps: Delta Cephei

Delta Cephei has a period of 5.3 days. According to the period-luminosity table (see for instance Burnhams Celestial Handbook page 591) the absolute magnitude corresponding with a Cepheid (population 1) star with a 5.3 days period is -2.9.

The visual or apparent magnitude of a variable star can be calculated as follows: take the visual magnitude at the minimum and the maximum. Add them together and divide them by two. This way you get a median (middle) apparent magnitude. In the case of Delta Cephei the maximum magnitude is 4.1 and the minimum is 5.2. The median magnitude is (4.1+5.2)/2 = 4.65.

The difference between the absolute magnitude and the median visible magnitude is 7.55 (this number is called distance modulus). This means that the difference in light intensity between the absolute magnitude and the visual, apparent magnitude is about a 1000 times: 2.512 x 2.512 x 2.512 x 2.512 x 2.512 x 2.512 x 2.512 x 1.58 (one magnitude is a brightness difference of 2.512, half a magnitude has a ratio of 1.58).

Remark:
The absolute magnitude of a star is defined as the apparent magnitude that it would have at a distance of 10 parsecs or 32.6 light-years. If we would place Delta Cephei at this distance, its absolute magnitude would be -2.9, the same as its apparent magnitude at this distance.

To calculate the actual distance to Delta Cephei, multiply the square root of 1000 (the difference in light intensity between the relative and absolute magnitude) by 32.6 and you will get the actual distance to Delta Cephei: 1030 light-years.

If you own Burnhams Celestial Handbook, you don't need to make all the calculations. Just figure out the distance modulus as mentioned before, and you can use table III on page 65 to find the ratio and/or table IV on page 67 to determine the distance.
hrpulsvartag
The Cepheid's on the Hertzsprung-Russell diagram (HRD)
The Instability strip is a nearly vertical region in the HRD which is occupied by pulsating variable stars, including the Cepheid variables. The instability strip intersects the main sequence in the region of A and F stars (1-2 solar mass) and extends upwards almost vertically (slightly inclined to the right) to the highest luminosities.

Credit for the image on the right: CSIRO

Resources:
Cepheid's Explained by Daniel Mounsey 04/17/03 on:
http://www.cloudynights.com/item.php?item_id=1133

Burnhams Celestial Handbook by Robert Burnham Jr.
Understanding Variable Stars by John R. Percy
Encyclopedia of Stars by James B. Kaler
Wikipedia
AAVSO