Stellar Pulsations and Star Formation Quiz

Introduction to Astronomy: Evolution of Stars

• Stars emit vast energy, implying they evolve.
• Human timescales are small compared to stellar lifetimes (millions to billions of years), making it seem like stars don't change.
• Stellar evolution theories combine observations and theoretical models.
• Stars form in interstellar gas clouds, mature, age, and die, enriching space for future generations.

Stellar Evolution: Contents

• Stellar Evolution (Introduction)
• Birth of Stars
• Stellar Maturity and old age
• Deaths of Stars
• Neutron stars and black holes

Stellar Evolution: Introduction

• Interstellar space contains tenuous matter (gas and dust).
• Observations like photographs, spectroscopy, and interstellar extinction show this matter.
• Stars form from cold, dark interstellar clouds (dark nebulae).
• Typical dark nebulae have thousands of solar masses of gas and dust spread over volumes of 10³pc³.
• These clouds have low temperatures (∼10K), causing contraction under their own gravity.
• Star formation is often triggered by nearby supernovae or galaxy collisions.

The Jeans Instability

• Newton's concept of density fluctuations in gases.
• Regions with slightly higher densities attract nearby material and gain mass (contraction).
• Increased pressure in these regions causes them to expand and disperse.
• Conditions for a density fluctuation to grow: the inward gravitational forces exceed outward pressure forces(a > b).

The Jeans Instability: Further Details

• Consider a spherically symmetric mass distribution with density ρ and radius L.

• Two important times are: (i) free-fall time (T_ff) and (ii) sound wave crossing time (T_s), where Tff~ 1/√(Gp) and Ts~ L/Cs.

• Density perturbations are damped if sound wave crossing time is shorter than the free-fall time (T_s < T_ff).

• Density perturbations grow if sound wave crossing time is longer than the free-fall time (T_s > T_ff).

• The Jeans length is the distance a fluctuation must extend to overcome opposition from pressure forces:

  L_J = √(kT/m_pGρ)

The Birth of Stars

• Gravitational energy transforms to thermal energy when a cloud contracts.
• Few thousands of years into contraction, the surface temperature reaches 2000-3000K.
• Protostar contraction continues, increasing the core temperature up to millions of degrees to begin hydrogen fusion.
• Once hydrogen burning begins, the pressure increases, arresting contraction.
• Stars with masses >60M_☉ have too high a temperature that radiation pressure opposes contraction.
• Stars with masses <0.08M_☉ do not reach the high temperature necessary for hydrogen fusion (brown dwarfs).

The Main Sequence

• Stars primarily spend their lifetimes in the main sequence, fusing hydrogen into helium.
• The core reaction of 4H → He + energy leads to a loss of mass: 0.048x10^-27 kg.
• This mass is converted into energy according to Einstein's formula (E=mc²).
• The luminosity of a star is directly proportional to the mass raised to 3.5 power (L∝M^3.5)
• This means that a high mass star has high luminosity, but a short lifetime.

Stellar Maturity: From Main Sequence to Red Giant

• As hydrogen decreases, the core has difficulty supporting the outer layers.
• The core contracts and heats up, increasing the temperature required to initiate hydrogen fusion in a shell around the core.
• Increasingly, the luminosity of the star increases.
• Outer layers expand and cool (red giant phase).

Stellar Maturity: Red Giant Evolution

• Helium core contracts, reaching temperatures for helium fusion (∼100 million K).
• Reactions produce heavier elements (e.g., Carbon, Oxygen).
• The energy released stops further core contraction.
• The time spent burning helium is 20% that of the main sequence period.

Stellar Maturity: Asymptotic Giant Branch

• Helium and hydrogen shell fusions power the Asymptotic Giant Branch (AGB).
• Helium produced in the outer hydrogen shell falls towards the star center.
• Thermal pulses in the helium shell cause periodic expansion and contraction of the star.
• Mira Variable stars are AGB stars that vary significantly in brightness (period>100 days).

Stellar Maturity: Other Pulsating Stars

• Cepheids are very luminous and massive stars with pulsation periods of 1-70 days.
• RR Lyrae stars are old population stars in globular clusters with periods of 1.5 hours to days, respectively.
• RV Tauri stars are yellow supergiants with periods of 20-100 days.
• Mira-type stars are pulsating AGB stars with periods of a few hundred days.

Stellar Death: Stars with 0.4 to 8 Solar Masses

• Stars with masses between 0.4 and 8 solar masses become white dwarfs after exhausting their nuclear fuel.
• The core is approximately the size of Earth and the mass of the sun.
• The core is supported by electron degeneracy pressure.
• The outer layers are blown away, forming a planetary nebula.
• Final product is a white dwarf.

Stellar Death: Stars with >8 Solar Masses

• Stars with masses greater than 8 solar masses are not supported by electron degeneracy pressure.
• The core collapses, leading to a significant increase in temperature.
• This increase initiates a series of nuclear reactions, releasing extreme energy.
• The star undergoes a supernova explosion.
• The remaining core collapses forming a neutron star or a black hole.

White Dwarf Observations

• Observations: Sirius A and B.
• Sirius B is a massive star (∼1.0 solar mass) with a radius of ∼4200 km.
• The surface temperature is 26000 K.
• Period of orbit = 50 years

More on white dwarfs

• White dwarfs vary in spectral type as their temperature decreases.
• The radius decreases with increasing mass. R ~ M^−1/3
• The luminosity of a white dwarf decreases as it cools and gets older, possibly becoming "black dwarfs".
• White dwarf cooling timescales allow determination of age for globular clusters.

Other pulsating stars

Stellar Death: Neutron Stars

• Neutron stars are formed from the remnants of massive stars that have undergone supernova explosions.
• They have a radius around 10km.
• Supported by neutron degeneracy pressure.
• Strong magnetic fields (10⁸ to 10¹⁵ times the Earth's field.)
• High rotational velocity—pulsars.

Stellar Death: Neutron Star: Crab Nebula

• Crab Nebula is a supernova remnant in Taurus.
• It resulted from a supernova documented by Chinese astronomers in 1054.
• It is located in the Perseus arm of the Milky Way, with a distance of 2 kiloparsecs (∼6500 light-years).
• Rotation of neutron star emits radiation that becomes energy in the nebula.

Black Holes

• Black holes are extremely dense regions in space with gravitational fields so strong that nothing, including light, can escape.
• They are described by Einstein's general relativity.
• The singularity forms the central point of a black hole.
• The event horizon marks the boundary from within which nothing can escape.
• Black holes result from the collapse of very massive stars.
• Black holes can have mass, angular momentum, and charge.
• There are techniques to measure these.
• Quantum processes can lead to black hole evaporation.

Stellar Evolution Summary Chart

• A visualization chart summarizing the different phases of stellar evolution based on mass, showing protostars, main sequence stars, red giants, white dwarfs, and neutron stars.

Test your knowledge on the intriguing phenomena of stellar pulsations and the processes involved in star formation. This quiz covers various types of variable stars, their characteristics, and the stages of stellar evolution leading to the birth of new stars. Dive into the fascinating world of astrophysics and enhance your understanding.