The Evolution of Stars

Содержание и основные понятия

The star maintains a balance between gravity and the pressure of a substance heated by thermonuclear reactions, and the initial mass determines the pace and the final stages of evolution.
GEF · 11 grade
PIF · Baseline
Interactive model
Main sequence
Red giant
Supernova
White dwarf
Black hole
01
The physical picture
What happens and what boundaries the model has.
Main message
The star maintains a balance between gravity and the pressure of a substance heated by thermonuclear reactions, and the initial mass determines the pace and the final stages of evolution.
In the main sequence, the main source of energy is the transformation of hydrogen into helium.
Once the fuel is exhausted, the kernel is compressed, and the outer layers expand.
Small stars end up with white dwarfs, massives can leave a neutron star or a black hole.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
L
=
4
π
R
2
σ
T
4
L=4\pi R^2\sigma T^4
L
=
4
π
R
2
σ
T
4
luminous intensity of the star
r
с
=
2
G
M
c
2
r_{\text{с}}=\frac{2GM}{c^2}
r
c
​
=
c
2
2
GM
​
Schwarzschild radius
Review of the situation
Massive stars live less: large mass increases the core temperature and fuel consumption increases faster than its stock.
04
Links and application
In the real world
Massive stars live less: large mass increases the core temperature and fuel consumption increases faster than its stock.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Evolution of the Stars" through the model, not just the formula.
Outcome 2
Distinguish and correctly use terms: main sequence, red giant, supernova.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Main sequence
The slope of the Herzshprunga-Rassel diagram, where the stars receive energy mainly from a synthesis of helium from hydrogen.
Red giant
A late stage of the evolution of a star with a high radius and a relatively low surface temperature.
Supernova
An explosive star phenomenon with a sharp increase in luminous intensity and a release of the substance.
White dwarf
A compact remnant of a star maintained by the pressure of a emitted electronic gas.
Black hole
A space-time area from which the horizon of events cannot even come out of light.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
L
=
4
π
R
2
σ
T
4
L=4\pi R^2\sigma T^4
L
=
4
π
R
2
σ
T
4
model effect
The luminance of the star.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
j
=
σ
T
4
j=\sigma T^4
j
=
σ
T
4
The law of Stefan — Boltzmann — sets the thermal radiation of a single area of a completely black body.
S
=
4
π
R
2
S=4\pi R^2
S
=
4
π
R
2
The area of the spherical surface of the star radius R is 4piR2.
L
=
j
S
=
4
π
R
2
σ
T
4
L=jS=4\pi R^2\sigma T^4
L
=
j
S
=
4
π
R
2
σ
T
4
The increase in surface flow to the area gives complete luminous intensity.
Conditions:
The star is spherical and emits like a black body with an effective temperature of T; R is a photospheric radius.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
r
с
=
2
G
M
c
2
r_{\text{с}}=\frac{2GM}{c^2}
r
c
​
=
c
2
2
GM
​
model effect
Schwarzschild Radio.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
d
s
2
=
−
(
1
−
2
G
M
r
c
2
)
c
2
d
t
2
+
(
1
−
2
G
M
r
c
2
)
−
1
d
r
2
+
⋯
ds^2=-\left(1-\frac{2GM}{rc^2}\right)c^2dt^2+\left(1-\frac{2GM}{rc^2}\right)^{-1}dr^2+\cdots
d
s
2
=
−
(
1
−
r
c
2
2
GM
​
)
c
2
d
t
2
+
(
1
−
r
c
2
2
GM
​
)
−
1
d
r
2
+
⋯
Schwarzschild's decision describes space-time outside the spherical-symmetric non-rotating mass.
1
−
2
G
M
r
c
2
=
0
1-\frac{2GM}{rc^2}=0
1
−
r
c
2
2
GM
​
=
0
The event horizon is where the decision coefficient is zero.
r
=
r
с
=
2
G
M
c
2
r=r_{\text{с}}=\frac{2GM}{c^2}
r
=
r
c
​
=
c
2
2
GM
​
The solution to the equation sets the radius of the horizon.
Conditions:
Non-rotational uncharged spherical symmetrical object of mass M in general relativity theory; for rotating or charged objects, the horizon is different.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't move the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that, on the main sequence, the main source of energy is to turn hydrogen into helium.
How to Check the Mind
Once the fuel is exhausted, the kernel is compressed, the outer layers are extended. Then check the units, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
The Evolution of Stars
The star maintains a balance between gravity and the pressure of a substance heated by thermonuclear reactions, and the initial mass determines the pace and the final stages of evolution.
In the main sequence, the main source of energy is the transformation of hydrogen into helium.
Once the fuel is exhausted, the kernel is compressed, and the outer layers expand.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.