Stellar Evolution

Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA)

Interstellar extinction

dust in the milky way — View of the Milky Way over Cathedral Rock, seen from the Cathedral Rock Trailhead on Back O' Beyond Road, Sedona, Arizona. The dark parts of the milky way are there because dust is occluding the light, not because there are no stars there.

In between the stars

dust scattering light — Light from stars passes into a dust cloud. Inside the cloud the light interacts with particles. Some light gets transmitted, some reflected.

Credit: NASA, ESA, AURA/Caltech, Palomar Observatory

Mie Scattering

What is the stuff?

Some polycyclic aromatic hydrocarbons: C₁₄H₁₀ (anthracene), C₂₄H₁₂ (coroene), and C₄₂H₁₈ (hexabenzocoronene)

Gasses

21-cm line

hydrogen hyperfine drawing — When the electron spin flips and becomes anti-aligned with the proton, a photon is released. The energy is small, 5.9 × 10^-6 eV, which correlates to wavelength of about 21 cm.

For more see Feynman Lectures III - 12

View of the milky way galaxy taken at 1420 MHz (i.e. 21 cm) Neutral Hydrogen exists in the gas clouds shown in this false color image.

Credit: J. Dickey (UMn), F. Lockman (NRAO), SkyView

This image shows a color composite of visible and near-infrared images of the dark cloud Barnard 68. It was obtained with the 8.2-m VLT ANTU telescope and the multimode FORS1 instrument in March 1999. At these wavelengths, the small cloud is completely opaque because of the obscuring effect of dust particles in its interior.

Credit: ESO

Protostars

When will gravitational collapse occur? There are two main sources of energy: gravitational and kinetic. Gravitational will lead to contractions, kinetic creates expansion through gas pressure.

Take a cloud with mass $M_c$ and radius $R_c$. The gravitational potential energy is approximately: $$\begin{equation} U \sim -\frac{3}{5}\frac{G M_c^2}{R_c} \end{equation}$$ The kinetic energy of $N$ particles will be approximately: $$\begin{equation} K = \frac{3}{2}N k T \end{equation}$$ Recasting this in terms of the mean molecular weight, $\mu$, $$\begin{equation*} N = \frac{M_c}{\mu m_H} \end{equation*}$$

If the kinetic energy is than half the gravitational energy, then collapse will be possible. $$\begin{equation} \frac{3 M_c k T}{\mu m_H} \lt \frac{3}{5}\frac{G M_c^2}{R_c} \label{eq:conditionforcollapse} \end{equation}$$ The radius of the cloud $R_c$ can be expressed in terms of the initial mass density: $$\begin{equation*} R_c = \left( \frac{3 M_c}{4 \pi \rho_0} \right)^{1/3} \end{equation*}$$ Which when substituted back into \eqref{eq:conditionforcollapse}, we get: $$\begin{equation} M_J \simeq \left( \frac{5 kT}{G \mu m_H}\right)^{3/2} \left( \frac{3}{4 \pi \rho_0} \right)^{1/2} \end{equation}$$ This is the Jeans mass. Or, in terms of a Jeans length, $$\begin{equation} R_J \simeq \left( \frac{15 k T}{4 \pi G \mu m_H \rho_0} \right)^{1/2} \end{equation}$$

A more thorough treatment would have to include the pressure from the surrounding ISM. The Bonner-Ebert mass captures the physics of this added complexity: $$\begin{equation} M_{\textrm{BE}} = \frac{c_{\textrm{BE}} v_T^4}{P_0^{1/2} G^{3/2}} \end{equation}$$ where $v_T \equiv \sqrt{\frac{kT}{\mu m_H}}$ is the isothermal speed of sound. $c_{\textrm{BE}}$ is a dimensionless constant approximately equal to 1.18.

Star formation simulation

Image copyright Matthew Bate.

Free fall collapse

The basic equation of motion for a gravitational system: $$\begin{equation} \frac{d^2 r}{dt^2} = - G\frac{M_r}{r^2} \end{equation}$$ Some differential equations leads to: $$\begin{equation} t_\textrm{ff} = \left(\frac{3 \pi}{32}\frac{1}{G \rho_0} \right)^{1/2} \end{equation}$$

Speed of sound

$$\begin{equation} t_\textrm{pressure} = \frac{r_0}{c_s} \end{equation}$$ and the speed of sound is: $$\begin{equation} c_s = \left( \frac{\gamma k T}{\mu m_p}\right)^{1/2} \end{equation}$$

Compare these two times

$$\begin{equation*} t_\textrm{ff} < t_\textrm{pressure} \end{equation*}$$

$$\begin{equation} \left( \frac{3 \pi}{32 G \rho_0}\right)^{1/2} < r_0 \left(\frac{\mu m_p}{\gamma k T} \right)^{1/2} \end{equation}$$

Jeans Length

$$\begin{equation} r_J = \left( \frac{3 \pi \gamma k T}{32 G \rho_0 \mu m_p}\right)^{1/2} \end{equation}$$

Star Formation

Perturbation

A shockwave from a nearby supernova can trigger the gravitational collapse. The molecular cloud collapses.

Collapse

However, it cannot collapse for ever, since the angular momentum will be conserved, and as it gets smaller, its rotates faster. $$\begin{equation} \frac{GM}{r_f^2} = \frac{v_f^2}{r_f} \end{equation}$$

An edge-on protoplanetary disk in the Orion Nebula

https://www.science.org/doi/10.1126/science.1059093

A pre-main-sequence star: HBC 1

ESA/Hubble

"Surrounded by an envelope of dust, the subject of this NASA/ESA Hubble Space Telescope image is a young pre-main-sequence star known as HBC 1. The star is in an immature and adolescent phase of life, hence its classification — most of a Sun-like star’s life is spent in a stage comparable to human adulthood dubbed the main sequence.

In this view, HBC 1 illuminates a wispy reflection nebula known as IRAS 00044+6521. Formed from clouds of interstellar dust, reflection nebulae do not emit any visible light of their own and instead — like fog encompassing a lamppost — shine via the light from the stars embedded within. Though nearby stars cannot ionise the nebula’s non-gaseous contents, as with brighter emission nebulae, scattered starlight can make the dust visible.

What makes this seemingly ordinary reflection nebula more interesting are three nearby Herbig–Haro objects known as HH 943, HH 943B and HH 943A — which are not visible in this image — located within IRAS 00044+6521 itself. Herbig–Haro objects are small patches of dust, hydrogen, helium and other gases that form when narrow jets of gas ejected by young stars such as HBC 1 collide with clouds of gas and dust. Lasting just a few thousand years, these objects rapidly move away from their parent star before dissipating into space.""

Hot gas moves out

Nuclear Fusion Begins

A star (like our sun) is born

Main sequence life

Leaving the Main sequence

main sequence to sub giant branch — Leaving the main sequence

Sub giant to Red Giant

Red Giants

He Flash

Asymptotic Branch

agb — Now, another shell of forms around the core. He will begin to fuse into carbon.

An asymptotic Red giant

Planetary Nebula

X-ray/optical composite image of the Cat's Eye Nebula (NGC 6543)

J.P. Harrington and K.J. Borkowski (University of Maryland), and NASA (HST)

White Dwarf

The white dwarf on the HR Diagram

The final form of a sun like star is a white dwarf. Our sun will eventually loose about 40% of its mass, and will spend the next trillion years just cooling down - no more fusion.

What	Time	Activity
Protostar	50 Myr	Gravitational Attraction
Main Sequence	10 Gyr	Fusion of H to He in the core
Red Giant Branch	1 Gyr	Fusion of H to He in shell
Horizontal Branch	100 Myr	Fusion of H to He in shell, He to C in core
Asymptotic Giant Branch	20 Myr	Fusion of H to He in outer shell, He to C in inner shell
Planetary Nebula	50 kyr	hot core emits UV radiation, gas flouresces
White Dwarf	→ ∞	No fusion - cool down

stars leaving ms — Main sequence and post main sequence evolution of stars.

Carrol and Ostlie Fig 13.1