○ Using Cassiopeia: Connect the intersection of extension lines 1 and 2 with extension lines 4 and 5, meeting at point 3, extending the distance by 5 times.

④ Other

○ The Big Dipper is essentially composed of 8 stars.

Figure 3. Composition of the Big Dipper

⑶ Seasons and Celestial Positions

① Motion of Stars

○ Diurnal Motion: Earth’s rotation.

○ Annual Motion: Earth’s revolution.

○ Seasonal Constellations: Due to Earth’s revolution.

② Spring Constellations

○ Boötes, Virgo, Leo, etc.

○ Spring Triangle: Arcturus (Boötes), Denebola (Leo), Spica (Virgo).

○ Spring Curve: Handle end of the Big Dipper, Arcturus, Spica.

③ Summer Constellations

○ Cygnus, Lyra, Aquila, Hercules, etc.

○ Summer Triangle: Deneb (Cygnus), Vega (Lyra), Altair (Aquila).

○ (Note) July 7th in the lunar calendar is the day when Altair and Vega meet, known as Qixi.

④ Autumn Constellations

○ Pegasus, Andromeda, Pisces, Aries, etc.

○ Autumn Square: Four stars forming Pegasus.

⑤ Winter Constellations

○ Orion, Canis Major, Canis Minor, Gemini, Auriga, Taurus, etc.

○ Winter Triangle: Procyon (Canis Minor), Betelgeuse (Orion), Sirius (Canis Major).

○ Winter Hexagon: Sirius (Canis Major), Procyon (Canis Minor), Pollux (Gemini), Capella (Auriga), Aldebaran (Taurus), Rigel (Orion).

⑥ Major Stars

○ North Star (Polaris): Apparent magnitude 2.0, Absolute magnitude -3.7.

○ Betelgeuse: Apparent magnitude 0.8, Absolute magnitude -5.5.

○ Capella: Auriga, Apparent magnitude 0.0, Absolute magnitude -0.7.

○ Sirius: Canis Major, Apparent magnitude -1.5, Absolute magnitude 1.4.

○ Deneb: Apparent magnitude 1.3, Absolute magnitude -6.9.

3. Types

⑴ Variable stars are divided into intrinsic variables and extrinsic variables.

Figure 4. Types of Variable Stars

(a): Extrinsic Variables, (b): Intrinsic Variables

⑵ Type 1. Intrinsic Variables

① Binary Stars: A pair of stars orbiting each other.

Figure 5. Binary stars

② Intrinsic Variables: Variables where the brightness changes regularly due to mutual eclipses in binary stars.

⑶ Type 2. Cepheid Variables (Intrinsic Variables)

① Overview

○ These variables were first discovered in the star Delta Cephei in the constellation Cepheus.

○ Mechanism was first reported by female scientist Henrietta Leavitt in a 1912 paper.

② Light Curve: Graph representing changes in brightness.

Figure 6. Relationship between Period and Absolute Magnitude for Type I and Type II Cepheid Variables

○ Larger periods correspond to larger stars and smaller absolute magnitudes.

○ Type I: Heavier elements, young stars.

○ Type II: Lighter elements, older stars.

○ Period-Luminosity relationship derived from Cepheid variables with known distances.

③ Classification by Period

○ Short-Period Variables: Period less than 100 days.

○ Long-Period Variables: Period greater than 100 days.

④ Classification by Type

○ Pulsating Variables: Brightness pulsates like a heartbeat, often in older stars.

○ Expanding state → Contraction begins → Hydrogen fusion reaction outside the core → Expansion begins, becoming brighter → (Repeat)

○ Exploding Variables

⑷ Celestial Bodies

⑸ MACHO (Massive Astronomical Compact Halo Object): Celestial objects that emit no light.

4. Brightness and Magnitude

⑴ Luminosity (L): Brightness

⑵ Magnitude: Scale that represents brightness on a logarithmic scale.

① Absolute Magnitude (M): Magnitude determined assuming the star is 10 parsecs away.

○ Defined such that a first-magnitude star is 100 times brighter than a sixth-magnitude star.

○ 6th-magnitude star: The dimmest star visible to the naked eye.

② Apparent Magnitude (m): Magnitude determined by an observer on Earth for all brightness.

⑶ Important Relationships

① Relationship between Luminosity and Absolute Magnitude

○ Derived from the fact that a first-magnitude star is 100 times brighter than a sixth-magnitude star.

○ Used for comparing different stars.

② Relationship between Apparent Magnitude (m) and Absolute Magnitude (M) (Distances formula)

○ Derived from the inverse square law of luminosity with distance.

○ Used for comparing the same star.

5. Distance

⑴ Distance of nearby stars: Parallax method

Figure 7. Parallax Method

① Discovered by German astronomer Bessel in 1838.

② 1 parsec (pc): Distance when parallax is 1 second of arc (“).

③ Distance (pc) = 1 / Parallax (“).

④ Additional

○ If the angle is very small, θ ≒ tan θ ∝ 1 / distance.

○ θ = 1 AU ÷ 1 pc = 1/3600 × π/180 (where 1 AU = 1.5 × 10^8 km)

○ 1 pc = 3.09 × 10^16 m = 3.26 light-years

⑵ Distance of distant stars

① Using Cepheid Variables, a type of intrinsic variable.

② Step 1: Measure the period.

③ Step 2: Measure brightness through the period-luminosity relationship.

④ Step 3: Determine absolute magnitude and apparent magnitude through the assumption that at 10 pc, absolute magnitude equals apparent magnitude.

○ Assumption 1: At a distance of 10 pc, absolute magnitude equals apparent magnitude.

○ Assumption 2: A 100-fold increase in brightness results in a decrease of 5 magnitudes.

○ Assumption 3: A distance x-fold increase leads to a 2-fold decrease in brightness.

○ Conclusion: When distance increases by 10 times, brightness decreases by 100 times, and apparent magnitude increases by 5.

○ Main Conclusion: Pogson’s Formula

Observed magnitude (m) - Absolute magnitude (M) = 5 log(distance) - 5

○ Mnemonic Tip: Distances formula

⑤ Using this, Hubble determined the distance of the Andromeda galaxy, resolving the Shapley-Curtis debate (1920) on extragalactic nature.

⑶ Number and Distribution

① Parallax method

6. Temperature

⑴ Effective Temperature: Surface temperature of a star as seen from Earth.

① Spectral Type: Categorized into 7 types (O - B - A - F - G - K - M) based on surface temperature.

○ Also known as spectral classification or color index.

○ Sun’s spectral type is G2V (V indicates luminosity).

② As color index increases, surface temperature decreases. O-type stars have the smallest color index.

○ Color Index: Photographic magnitude - Visual magnitude, or B - V in UBV filters.

○ U (ultraviolet), B (blue), V (visual)

③ Mnemonic Tip: Oh, Be A Fine Girl, Kiss Me

⑵ H-R Diagram: Meaningful correlation between absolute magnitude and spectral type for main-sequence stars.

Figure 8. H-R Diagram (a: Supergiants, b: Giants, c: Main-sequence stars, d: White dwarfs)

① I: Proto Star

② II: T Tauri Star

③ III: Main Sequence Star

④ IV: Subgiant Star

⑤ V: Giant Star

⑶ Source of Stellar Energy

① Contraction Theory

② Mass Transfer Theory

③ Fusion Reaction Theory

7. Size, Mass, Density

⑴ Size of Stars

① Gravity: Acts towards the center of the star

② Internal Pressure: Generated by hydrogen fusion reactions, acting outward

③ Equilibrium between gravity and internal pressure maintains the star’s size

⑵ Mass of Stars

① Main Sequence, Giant, Supergiant

② Mass-Luminosity Relationship

⑶ Density of Stars

8. Motion

⑴ Radial Velocity: Measurable by observing spectral shifts of starlight

① Formulation: In terms of the speed of light, c,

② Using radial velocity to prove galactic rotation

⑵ Tangential Velocity: Calculated from distance and angular distance

① Tangential Velocity = 4.74 μr

○ μ: Proper motion (unit: “ / year)

○ r: Distance (unit: pc)

② Proper Motion: Angular distance a star moves in one year

⑶ Space Velocity: Calculated using Pythagoras’ theorem

① Space Velocity² = Radial Velocity² + Tangential Velocity²

9. Stellar Life Cycle

⑴ Nuclear Fusion Reaction

① Proton-Proton Reaction (p-p reaction): In the case of the Sun, most hydrogen fusion happens through proton-proton reactions

② CNO Cycle: Occurs in stars similar to the Sun, involving carbon, nitrogen, and oxygen cycling reactions

⑵ Stellar Birth: Birth caused by interstellar material and high-pressure, low-temperature dust

Figure 9. Stellar Life Cycle

① 1^st. Gas Cloud Formation: Interstellar material composed of hydrogen and helium forms gas clouds

② 2^nd. Nebula Formation: Gas clouds contract due to gravity, forming a nebula

○ Gravitational Contraction Energy: During contraction of interstellar material or protostars, gravitational potential energy decreases, generating heat

③ 3^rd. Protostar Formation: Protostars form in regions of high density within the nebula

○ Multiple protostars can form within one nebula

○ Protostars contract due to gravity, leading to higher temperatures and pressures

④ 4^th. Star Birth: When internal temperature of a protostar exceeds 10 million K, hydrogen fusion reactions occur, emitting light

○ Protostars rely on gravitational contraction as an energy source, not hydrogen fusion

⑶ Evolution of Stars with Smaller Mass than the Sun: Evolve directly into white dwarfs without transitioning to red giants or supergiants

⑷ Stars with Similar Mass to the Sun: Dominant p-p reactions in the core, no CNO cycle

① 5^th - 1^st. Main Sequence: Stage of hydrogen fusion reactions

○ Main Sequence: Stars emitting energy through hydrogen fusion reactions

○ Feature 1: Stable state: Equilibrium between outward pressure from nuclear explosions and inward gravitational forces maintains constant star size

○ Feature 2: Stars spend most of their lifetimes as main sequence stars (because hydrogen is the most abundant element in stars)

② 5^th - 2^nd. Red Giant: Stage of helium fusion reactions

○ 5^th - 2^nd - 1^st. Hydrogen depletion in the core after main sequence

○ 5^th - 2^nd - 2^nd. Core contraction: Increased density, temperature. Helium fusion reactions produce carbon and oxygen

○ 5^th - 2^nd - 3^rd. Outer hydrogen shell heats due to core contraction

○ 5^th - 2^nd - 4^th. Hydrogen fusion reactions in outer shell lead to increased internal pressure, causing star expansion

○ 5^th - 2^nd - 5^th. Star expands, surface temperature drops, becoming a red giant

○ Characteristics: Produces heavier nuclei, high luminosity, low outer density

○ Produced Elements: Helium, carbon, oxygen, elements lighter than iron

○ Stellar Structure: From outer to inner layers: hydrogen, helium, oxygen, carbon

○ Reason for stopping at carbon fusion: Stars with masses similar to the Sun only reach temperatures required for carbon fusion

③ 5^th - 3^rd. Planetary Nebula, White Dwarf: Stage with no ongoing fusion reactions

○ 5^th - 3^rd - 1^st. Helium depletion in the core halts helium fusion reactions

○ 5^th - 3^rd - 2^nd. Outer layers expand, forming a planetary nebula

○ 5^th - 3^rd - 3^rd. Core contracts, forming a white dwarf

○ Loss of outer envelope to form a planetary nebula

○ Core composed of heavier materials like carbon and oxygen: Contracted state

○ Example: Sirius B

⑸ Stars with about 10 times the mass of the Sun

① 6^th - 1^st. Main Sequence: Similar to stars with about 10 times the mass of the Sun

② 6^th - 2^nd. Supergiant: Fusion reactions of elements prior to iron, like helium, oxygen, silicon

○ 6^th - 2^nd - 1^st. Expands significantly after the main sequence to become a supergiant

○ 6^th - 2^nd - 2^nd. Core temperatures rise, leading to fusion reactions of helium, carbon, oxygen, silicon, producing iron

○ Produced Elements: Helium, carbon, oxygen, elements lighter than iron, iron

○ Reason for stopping at iron fusion: Iron nuclei are very stable

Figure 10. Graph of Mass Number and Nuclear Binding Energy

③ 6^th - 3^rd. Supernova: Enormous release of energy

○ 6^th - 3^rd - 1^st. Iron formation in the core, fusion reactions cease

○ 6^th - 3^rd - 2^nd. Rapid contraction, significant temperature increase

○ 6^th - 3^rd - 3^rd. Explosive release of energy due to sudden temperature increase

○ 6^th - 3^rd - 4^th. Heavier elements than iron are created by the supernova

○ Characteristics

○ Supernova emits light comparable to an entire galaxy

○ All type 1a supernovae have the same absolute brightness

○ Produced Elements: Gold, uranium, elements heavier than iron

○ Supernova and Life

○ Supernova at 50 light-years: Causes mass extinction of all life forms

○ Supernova at 100 light-years: Drastically increases radiation levels in the atmosphere

○ Supernova at 120 light-years: Causes mass extinction of marine life

⑹ Stars with mass about 10 times that of the Sun

① 7^th - 1^st. Main Sequence: Similar to stars with mass about 10 times that of the Sun

② 7^th - 2^nd. Supergiant: Similar to stars with mass about 10 times that of the Sun

③ 7^th - 3^rd. Supernova: Similar to stars with mass about 10 times that of the Sun

④ 7^th - 4^th. Black Hole

○ Celestial bodies heavier than neutron stars: Absorb all energy and mass

○ Named black holes because they do not even let light escape

○ Emit X-rays perpendicular to the accretion disk

○ First observed in 2019

Figure 11. Image of the First Observed Black Hole

⑺ Type I, Type II

⑻ Methods to Determine a Star’s Evolutionary Stage

Figure 12. Methods to Determine a Star’s Evolutionary Stage

Input: 2019.04.07 10:17

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Chapter 3. Stars

1. Nomenclature and Stellar Catalog

2. Constellations