Understanding stellar evolution
Students recognize the principal stellar observables (brightness and color) and the
relationships between them (Hertzsprung Russell diagram). After a short introduction to stellar
evolution theory, students verify the Main Sequence Mass Luminosity Relationship ( L M 3.5 )
and calculate Main Sequence Lifetimes.
The main items
At the beginning of the twentieth century two astronomers, the Danish E. Hertzsprung and
the American H. N. Russell, established a correlation between two important stellar parameters:
brightness and color.
Since ancient times, the brightness of a star is indicated by "magnitudes": I, II and so on,
dim stars having larger magnitudes. We don’t confuse the relative magnitude with absolute
magnitude. The relative magnitude measure the brightness of a star as so as it appears in the sky
and it depends on the brightness and on the distance; if we put a star at the distance of 10 Parsec (33
year light), its magnitude is called absolute magnitude: obviously it depends only on brightness of
According to color, stars are grouped in classes: O, B, A, F, G, K, and M. O stars are bleu
and M are red, see table 1. Classes are oddly sequenced because they were assigned long before we
understood their relationship to surface temperature: O stars are the hottest and M the coolest ones;
O and B stars are rare but very bright; M stars are numerous but dim.
Hertzsprung and Russell discovered that in a Color-Magnitude diagram (H-R diagram) stars
appear distributed in well defined groups, so that there is a correlation between temperature and
luminosity (Fig. 1).
We think that it is important the student appreciates the difference between a random
distribution of two variables and a correlated one.
The H-R diagram provides a full interpretation in terms of stellar evolution theory. With
reference to fig. 1, a short of stellar evolution says:
1. The star is just born: its temperature rises, but not its luminosity. During this phase stars the
thermonuclear reactions involving the burning of Hydrogen.
2. The star is into main sequence: this is a period of stability in which the star burns the Hydrogen
producing Helium. The star spend mostly time in the main sequence; we can calculate how long
does the star stay into main sequence, using this easy equation:
t m.s. 10 Sun Years
If we remember that the Sun’s mass is 8 10 30 Kg, knowing the stellar mass, we can calculate
the period in which the star burn the Hydrogen.
3. The star turn off: the star exhaust the Hydrogen in core and it continues to burn it in shells. to
Helium. For a ‘short’ period the stellar temperature decreases without a great change of
4. The star burns Hydrogen in shell (red giants) through the CNO cycle: as its radius increases so
its luminosity raises.
5. Helium flash: the star begins to burn Helium maintaining the combustion of Hydrogen in shells.
The stellar temperature increases very quickly, because the new reactions give a great quantity
6. The star crosses a fast period of luminosity’s variability (Horizontal branch) till to reach a new
configuration of equilibrium during which the star burns Helium in core and Hydrogen in shells.
7. If the stellar mass is not enough to light new thermonuclear reaction beyond the Helium
burning, it ‘died’ as a white dwarfs of Helium.
In Fig. 1 there aren’t stars with mass greater than 7-8 solar mass: the stars with this mass are
able to begin new fusion reactions involving the burning of Helium, Carbon, Oxygen, Magnesium
and Neon. A star with a mass greater than 10 solar mass can develop thermonuclear reaction until
the Iron, ending its life in a supernova type II.
The luminosity of a star is the energy radiated from all its surface in one second. The
absolute magnitude (M) is used usually to measure the luminosity of the stars; it is connected to the
stellar luminosity by an approximate relation:
M 2.5 log star 5
We don’t need students have familiarity with the logarithm, since we will use the inverse
100 10 5 [1.2]
We remember that Sun’s luminosity is: LSun 4 10 26 Watt. The stellar luminosity is
connected by the mass through this correlation:
LStar : LSun mStar : mSun
Using all these easy relationships and the HR diagram, if we know one parameter, we are
able to estimate the rest. For example, the absolute magnitude of Sirius (α Canis Majoris) is
M=+1.5. With this parameter, using [1.2] we can find Star 25 ; than using [1.3] we obtain its
mass: mCM 2.4 m Sun . Through a graph method, as illustrated in Fig. 2, the student can estimate
the spectral class of α Canis Majoris. At the end we can appreciate how long the star stay into main
sequence, using the [1.1] the value is 0.7 billions of years.
So if we have the absolute magnitude of a star, connecting all the equations, we are able to
estimate these parameter: luminosity, mass, spectral class (then temperature) and the time of
permanence in the main sequence of a star. This is a great result that represents a kind of revelation
for young student with fundamental basis of algebra.
The development in the classroom
This is only a suggestion about the modality with which is possible to introduce the
arguments: obviously much depends on the student’s background. A helpful instrument could be a
Power Point presentation as we present here.
The lesson can be divided in two part: the first one in which the teacher show some Power
Point slides, just to introduce the argument, and the second part in which the class is divided in four
groups for a ‘competition’ game.
The teacher shows the first Power Point slide and he asks: “What do you see?”. The students
are stimulate to answer developing their observational capacities. A good initial discussion helps the
teacher to understand the wrong ideas of students and to focus the main priors. A second good
question can be: “According to you, what are the main parameter with which we can study a star?”.
After the teacher has collect the classroom’s suggestions, he summarizes the fundamental
parameters in the second Power Point slide. It can be useful to present the third slide which shows
the values of these parameter for the Sun.
The fundamental question to ask the student is: “According to you is there a correlation
between the color and the luminosity of a star?”. The persons saying “yes” form a group: the
teacher gives them have two dies, one with numbered faces (-10, -5, 0, +5, +10, +15) and one with
colored faces (O, B, A, F, G, K) corresponding to spectral classes. After 30 throws they obtain a
random distribution on the plan (spectral class Vs absolute magnitude) (Fig. 3). On the other hand
the teacher give a singles die, such that each face contains both magnitude and color, to the students
that believe in a correlation between these two parameter. This game emphasizes as the correlation
between the two observable appears collecting on the plan an enough number of events.
Next the teachers presents the three slides about the spectral classification and HR diagram.
The teacher can freely expand the aspects which he thinks important about evolution, thermonuclear
burning (see a short movie), which are however not essential for our.
The final slide is about the relationship between the main parameters: after the previous
explanations, all the symbols must be evident. The formulas should not be presented in an ordered
way, so that the student has the time to reflect and to discover the relationships between them
The teacher divide the class in four parts, in order to form small groups of about 5 students.
He gives to every group the three carts with the three formulas, the HR diagram and the sheet with
the absolute magnitude of some important stars (see material for student). We have chose stars that
the boys can recognize in the sky every night. The challenge is to fill the sheet using the formulas
and HR diagram.
This little game stimulate the student to increase the connection ability and it help them to
become familiar with the sizes of the astrophysics; moreover it incite them to have a collaboration’s
spirit. The lesson end with a discussion about the found values, the used method and the student’s
curiosity about these arguments.
We suggest to not give them the right value of the star: about it, we will present a general
discussion in the fourth part. It’s important to stimulate the boys with the questions like:
What kind of relationship is there between the absolute magnitude and luminosity?
What kind of relationship is there between the luminosity and the stellar mass?
What kind of relationship is there between the mass and the time of permanence in the main
The ‘three carts’
Sheet to fill
100 10 5
LStar : LSun mStar : mSun
Absolute Lstar Main sequence
Star Mass Spectral class
Magnitude LSun lifetime
Sirius (α Canis
Vega(α Lyrae) +0.5
Capella (α Aurigae) -0.6
Rigel (β Orionis) -8.2
Procyon (α Canis
Altair (α Aquilae) +2.4
Aldebaran (α Tauri) -0.6
Antares (α Scorpii) -5.0
Spica (α Virginis) -2.9
Polaris (α Ursae
Deneb (α Cygni) -6.2
Regulus (α Leonis) -0.2