# The Zeta-Ophiuchus HII Region

This HII region is particularly prominent because it is, unusually, surrounding a star that is well outside of the plane of the Milky Way galaxy. This star, zeta-Ophiuchi, is about 370 light years from Earth and has a very high velocity. It may have begun its life in a triple or quadruple system and undergone a close encounter with another star in the system, which accelerated it to this speed. Alternately, it may have originally been a binary whose companion exploded as a supernova and been shot out of the galaxy as a result of this violent explosion (Hubrig et al 2011). Zeta-Oph is a very bright, massive star that would be one of the brightest stars in the sky if much of its light weren’t blocked by dust. In the infrared image below, taken with Spitzer, the shock wave created by zeta-Oph’s motion through the surrounding dust is clearly visible.

The bubble of ionized gas surrounding this star is clearly visible in hydrogen-alpha emission, as is discussed in the tour. For a more detailed discussion of the hydrogen-alpha observations of this region, check out this webpage.

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# Shocks in the ISM

A shock is simply an abrupt change in the properties of a medium. In the ISM, shocks can originate from supernovae and other violent events, or from the interactions of stellar winds with the surrounding material. This second kind of shock is called a bow shock. In the Orion Nebula, many stars have prominent bow shocks, like the star pictured below. Another example of a bow shock can be seen by the star zeta ophiuchi.

For more details about shocks in the ISM, check out the module by Philip Mocz, which can be found here.

# Jeans Collapse

One of the reasons astronomers study the ISM is to learn how stars form. Broadly speaking, in order for a star to form, a cloud of material must collapse to high enough densities and temperatures that nuclear fusion can begin. Additionally, the cloud must collapse more quickly than it can be dispersed (by stellar winds and ionizing radiation from nearby stars, for example). We know that star formation begins in giant molecular clouds, which consist of cold, diffuse molecular hydrogen, some helium and other gases, and some dust. The lifetime of such clouds is thought to be about 10 million years. We would like a way of quantifying how and when such a cloud will collapse to form a star, and when it wont.

As a simplified case, we consider a spherical cloud of uniform temperature $T$ and density $\rho$ consisting of hydrogen and other elements, such that the average mass of a particle is $\mu m_H$ (where $m_H$ is the mass of a hydrogen atom and $\mu$ is an enrichment factor). Typically $\mu\approx2.33$ for interstellar clouds. There are two main forces acting on the cloud: its own self-gravity, pulling it inward, and the thermal kinetic energy of the particles, which supports the cloud and on average acts to prevent collapse. In order for collapse to occur — i.e. for the cloud to be a bound object — we must have $E_{grav}+E_{therm} \leq 0$, which gives

$\frac{3}{5} \frac{GM^2}{R} + \frac{3}{2} \frac{M}{\mu m_H} kT \leq 0$
$\frac{kT}{2 \mu m_H} \leq \frac{GM}{5R}$

using the assumption that the cloud has uniform density to write $M=\frac{4}{3}\pi \rho R^3$, we find:

$\frac{4}{15} \pi G \rho R^2 \geq \frac{kT}{2\mu m_H}$
$R \geq \left( \frac{15kT}{8\pi G\rho\mu m_H}\right)^{1/2}$

So the cloud will collapse if its radius is larger than the Jeans Radius, $R_J = \left( \frac{15kT}{8\pi G\rho\mu m_H}\right)^{1/2}$. We can also write this criterion in terms of the mass of the cloud; the cloud will collapse if its mass exceeds the Jeans Mass, $M_J=\left(\frac{3}{32\pi\rho}\right)^{1/2}\left(\frac{5kT}{G\mu m_H}\right)^{3/2}$. The constants are not exact, as we have made some glaringly wrong assumptions about the cloud. A more careful derivation from treating small perturbations to the equations of hydrostatic equilibrium (found here) produces a Jeans Length $\lambda_J$ of $\sqrt(2)$ times the Jeans radius I derived above.

There is a glaringly obvious flaw in the derivation of the Jeans mass, which is that it assumes that the gravitational potential gradient is zero everywhere. This implies that $\nabla^2\phi=0$, which can only be true if $\rho=0$ everywhere, which is obviously incorrect. Furthermore, once collapse begins our starting assumptions of uniform temperature no longer holds and the density is probably not strictly uniform throughout the entire cloud. Additionally, this analysis does not consider the effects of turbulence or magnetic fields, both of which are thought to play key roles in star formation. A slightly more accurate treatment accounting for the fact that there is typically a nonzero external pressure on a collapsing cloud tells us that a cloud will collapse if its mass exceeds the Bonnor Ebert mass,

$M_{BE} = \frac{c_{BE}v_T^4}{P_0^{1/2}G^{3/2}}$
where $c_BE \approx 1.18$ is a dimensionless constant, $v_T=\sqrt{\frac{kT}{\mu m_H}}$ is the average thermal speed of the particles in the cloud, $P_0$ is the external pressure, and $G$ is Newton’s gravitational constant. For more about Bonnor Ebert spheres and modified Bonnor Ebert spheres, see the module by Zachary Slepian [link].

Despite these flaws, observations have shown that the Jeans analysis produces approximately correct results. For a typical molecular cloud, we obtain $M_J \approx 70$ solar masses. We can approximate the time that it takes such a cloud to  collapse as the gravitational free-fall time for a pressureless gas, $t_{ff} \approx \left(\frac{3\pi}{32G\rho}\right)^{1/2}$. For densities of $n_H \approx 1000$ particles per cubic cm, typical of giant molecular clouds, $t_{ff} \approx 1.4$ Myr, which is less than the estimated lifetime of such clouds (about 10 Myr), so this is reasonable.

# HII Regions

HII regions are bubbles of ionized gas surrounded by denser, colder neutral material. They are created by hot young stars that produce high-energy electromagnetic radiation. Any photon with an energy of at least 13.6 eV is powerful enough to ionize a hydrogen atom; this corresponds to light with wavelengths of shorter than 19.2 nm (which is in the ultraviolet portion of the electromagnetic spectrum). Only massive stars emit significant quantities of such high-energy photons, so HII regions tend to form around one or more massive stars. Since massive stars don’t live very long, HII regions are often seen in regions of ongoing star formation with lots of young stars, still surrounded by neutral dust and gas. The energy expelled from a young massive star will spread out into the volume around it, ionizing any gas it encounters.

Eventually, the high-energy photons will be spread too thinly to continue to ionize the surrounding material faster than the newly ionized protons and electrons can recombine to reform neutral hydrogen atoms. Setting the rate at which a central star emits ionizing photons $N^*$ equal to the recombination rate of the surrounding gas defines a volume within which the gas is almost completely ionized. Outside this volume, the gas quickly becomes almost completely neutral. If the density of the surrounding material is roughly constant and we assume that the region contains only hydrogen gas, then the so-called HII region will be roughly spherical and the radius will be given by:

ionizing photon emission rate = recombination rate
$N^*=\frac{4}{3}\pi r^3\alpha n^2$
$r=\left(\frac{3N^*}{4\pi\alpha n^2}\right)^{1/3}$
where $\alpha$ is the recombination coefficient and $n$ is the number density of the gas.

Spherical HII regions are sometimes called “Stromgren spheres” after the scientist who first estimated what their radius should be (see Stromgren 1939). For typical values of $n, \alpha$ and $N^*$, we expect $r\approx$ 10-100 parsecs (about 30-300 light years, or 7-70 times the distance from the Sun to the nearest star). This is somewhat larger than the radius of the HII region in the Orion Nebula that we visit on the tour, which has a radius of only about 12 light years.

# The Orion Star-Forming Region

One of the closest star-forming regions to Earth is located in the constellation of Orion. When we go stargazing and look at this constellation, we can see some of the young, massive stars shining brightly, but the complex networks of turbulent dust and gas shaped by supernovae and ionizing stellar winds are all but invisible. Only by looking at infrared emission from the dust or hydrogen-alpha emission from the ionized gas does the full story begin to emerge.

One particularly beautiful and interesting part of the Orion Star-Forming Complex is the Orion Nebula. This nebula provides a particularly good laboratory for studying the ISM, as multiple phases coexist and the whole region is very active. Additionally, the nebula has been a popular target for amateur astronomers and professional scientists alike: beautiful high-resolution images taken with Spitzer (infrared), Hubble (visible), and Chandra (X-ray) have revealed the process of star formation in unprecedented detail. Some of these images are explored in the WorldWide Telescope tour.

# Energy in the ISM

As discussed on this page, the ISM has multiple components, all of which have different temperatures, densities, and ionization states. As the ISM is a very dynamic environment, clearly it contains nonzero amounts of energy. We are interested in the types of energy stored in the ISM and the relative importance of each component. This is outlined in the pie chart below, adapted from Bruce Draine’s book Physics of the Interstellar and Intergalactic Medium (2011).

A brief description of each component is as follows (ranked in decreasing order of importance to the total energy balance of the ISM):

• Cosmic Rays (light yellow slice): Cosmic rays are very high-energy particles that have been accelerated to relativistic speeds. The origin of these particles is still under debate, although a significant fraction are believed to have been accelerated by supernovae.
• Magnetic Fields (orange slice): Magnetic fields play an important role in shaping the ISM. Developing accurate models of interstellar magnetic fields is an area of ongoing research.
• Starlight (purple slice): This includes light from stars at all wavelengths.
• Thermal Energy, or “nkT” (red slice): This is the energy from the random thermal motions of individual particles in the ISM due to their temperature. The hotter the gas, the more thermal energy it has.
• Far Infrared (FIR) Emission from Dust (blue slice): Dust particles can be modeled as blackbodies, which absorb energy from starlight and other sources and re-emit it in the far infrared.
• CMB (dark yellow slice): Energy in light from the Cosmic Microwave Background, which is the afterglow of the Big Bang. The CMB is nearly perfect blackbody radiation with a temperature of 3K and contributes a small amount of energy to the ISM. CMB photons were emitted by the hot, dense, glowing plasma that filled the early Universe and have been propagating through space since the Universe was only a few hundred thousand years old. Studying the tiny fluctuations in the CMB spectrum observed at different locations on the sky can reveal what the Universe was like at these early times, which provides vital information to cosmologists seeking to understand how the Universe began and how it evolved to the state in which we find it today. Dust in the ISM can scatter or absorb CMB photons, so these effects must be taken into account before the CMB can be used to provide meaningful cosmological constraints. For more information about the role that the ISM plays as a foreground to CMB measurements, see the module by Kirit Karkare [link].
• Turbulence (green slice): Much of the ISM is not smooth but rather full of turbulent motions on a wide range of scales. Turbulence may play an important role in star formation.

# Supernovae

Stars will continue to forge elements into heavier elements in their cores via nuclear fusion until it is no longer energetically favorable for them to do so. The heaviest element that massive stars can create via nuclear fusion is iron. Once the core of a massive star has been entirely converted to iron, nuclear fusion cannot proceed further and there is no source of energy great enough to keep the star from collapsing under its own gravity. As a result, the outer layers of the star fall inward on the core and rebound, flying outward in a massive explosion called a supernova. Elements heavier than iron can be formed during this violent release of energy. The supernova generates huge shockwaves that propagate through the surrounding ISM, sweeping up material in front of them and heating and ionizing gas. Material from the outer layers of the star is also ejected into the ISM, enriching it in the heavier elements produced by nuclear fusion over the star’s lifetime. The next generation of stars to form in this region will therefore start out slightly richer in these heavy elements than their predecessors — so by measuring the amount of heavy elements present in stars, astronomers can infer the existence of prior generations of massive stars. All of the elements on Earth besides hydrogen (and some helium) were formed and released in this manner — so it is literally true that, as Carl Sagan said, “we are made of starstuff.”

# Nuclear Fusion

Stars are powered by nuclear fusion, which is the process of smashing atomic nuclei together to create heavier elements. Stars like our Sun produce most of their energy by converting hydrogen to helium in their cores. This process releases energy in the form of light, which causes the stars to shine brightly. Stars like our Sun have enough hydrogen fuel to burn for about 10 billion years.

Stars more massive than our Sun also undergo nuclear fusion, but since they have more mass their cores are hotter and denser, and nuclear fusion proceeds more rapidly. After they convert all of their hydrogen to helium they begin to fuse the helium into carbon and other heavier elements, and so on. Each successive phase of fusion requires a higher temperature to proceed, so only the most massive stars will produce all of the heavier elements. Fusing heavier elements produces less energy per reaction each time, and producing elements heavier than iron actually requires more energy than it produces. Therefore, no matter how massive the star is nuclear fusion stops once iron is produced, and the star will then collapse in a supernova explosion.

# Understanding Spectral Lines

The modern picture of the atom is a compact nucleus, containing protons and neutrons, surrounded by a cloud of electrons. These electrons can only occupy specific energy states. If a photon with exactly the right amount of energy hits an atom, it can push an electron from a lower energy state to a higher energy state, or even knock the atom free of the nucleus entirely (a process called ionization.) Electrons naturally like to be in the lowest possible energy state, so if an electron is bumped into a higher (“excited”) energy state it will eventually spontaneously fall back to a lower energy state on its own. When it does, it will emit a photon equal to the energy difference between its starting state and its final state. We can see evidence of both steps of this process: if we are looking through cool gas with stars behind it, the gas will absorb the starlight as electrons in the atoms in the gas are excited, so we see dark lines in the spectrum from the star corresponding to these transitions. If, instead, we are looking at a bright object we will see the emission released when the electrons fall back down to lower energy states, so we will see bright lines at the points in the spectrum corresponding to these transitions.

Since the energy levels of different elements are different, if astronomers see a specific spectral line coming from a certain region, they can infer what elements are present there. One particularly important line is the hydrogen-alpha line at 656.28 nm. This is caused by the transition of an electron in a hydrogen atom from the third lowest energy state to the second lowest. This transition frequently results when an ionized hydrogen atom recombines (i.e. recaptures an electron to become neutral), so H-alpha emission is characteristic of regions of ionized hydrogen. The H-alpha emission from the entire sky has been mapped in great detail, revealing a wealth of structure in our galaxy.

# Blackbody Radiation

A blackbody is an object that absorbs all electromagnetic radiation that hits it and re-emits it at a range of wavelengths determined solely by its temperature. The shape of a blackbody’s spectrum is always the same, but the peak of the spectrum shifts to shorter wavelengths (higher energies) as the blackbody’s temperature increases. (This is why a cold piece of metal at room temperature appears dark, but if heated in a fire it will begin to glow red, then orange, and then white as the peak of its emission shifts to shorter wavelengths.)

It turns out that stars are well-approximated as blackbodies. Our Sun, for example, has a temperature of 5800 K, which puts the peak of its spectrum at about 500 nm — which is the wavelength of green light. It makes sense that our eyes evolved to see a narrow range of wavelengths corresponding to the peak of the solar spectrum!

Since the peak wavelength of a blackbody spectrum is inversely proportional to its temperature, all astronomers have to do to obtain the temperature of a glowing object is to  measure its spectrum and determine the peak wavelength. This is incredibly useful for studying stars. Another tool that is important for stars and the ISM alike is the study of spectral lines.