Molecular clouds: general properties

Cosmic abundances of the elements
It's not so easy to see molecular H₂
Creating molecular hydrogen
Destroying molecular hydrogen
Dissociation regions at the edges of molecular clouds
For more information

Today, we'll move from the cold atomic (HI) phase of the ISM to the cold molecular (H₂) phase.

Table 1 taken from Ferriere, K. M., Reviews of Modern Physics, 73, 1031 (2001)

Cosmic abundances of the elements

As you will see shortly, clouds of gas in molecular form aren't just hydrogen; there are a number of heavier elements which play important roles in their creation. Sometimes, the trace elements can help us to study the clouds; other times, they just get in our way.

So, let's review the abundances of the elements in space. There are variations from place to place, and from long ago until recent times, but the graph below, based on observations in the Solar System, provides a useful general guide. Pay special attention to the labels on the Y-axis.

Figure courtesy of MHz`as and Wikipedia , based on data in Lodders, K., ApJ 591, 1220 (2003)



  Q:  How many hydrogen atoms are there for every single carbon atom?


  Q:  Do you notice a pattern in these abundances?  Can you explain it?


  Q:  Why is the value for hydrogen set to 12?

My answers.

It's not so easy to see molecular H₂

Clouds of cold atomic hydrogen are easy to find, since the atoms emit radio waves at a wavelength of 21 cm due to the hyperfine transition in the ground state. What about cold molecular hydrogen gas? What sort of radiation does it emit?

Alas, molecules of hydrogen do not radiate electromagnetic energy very efficiently. The problem is that the coupling between a molecule and the electromagnetic field -- which determines the probability that photons will be absorbed or emitted by the molecule -- depends in large part on the electric dipole moment of the molecule. The stronger the dipole moment, the more strongly the molecule interacts with electromagnetic radiation.

Diagram of electric dipole courtesy of Geek3 and Wikimedia.

Molecular hydrogen consists of two identical atoms joined together, yielding no electric dipole moment at all. The combination does have a quadrupole moment, but that yields only weak coupling to photons.

In order to detect clouds of molecular gas, we need to look for OTHER molecules, preferably those which

are common
have a strong electric dipole moment (asymmetry)



  Q:  Can you think of any molecules which might meet these conditions?

Among the best options are

carbon monoxide (CO)
hydroxyl ion (OH)

though radio astronomers have found many others (thanks to Karen Lee-Waddell's ICRAR/CASS Radio School 2018 presentation.) We will concentrate on the carbon monoxide molecule for the rest of today's discussion.

Inside clouds of molecular gas, the temperatures are very low, only 10 - 20 Kelvin. That means that only transitions between very low energy states are likely to produce significant amounts of radiation. Instead of considering the electronic energy states of these molecules, we should instead examine the vibrational and rotational energy states.

Let's start with VIBRATIONAL modes. You should remember the example of a block attached to a spring, sliding along a frictionless floor. If one pulls the block away from its rest position, it will start to oscillate back and forth in Simple Harmonic Motion (SHM).



  Q:  What determines the frequency of this oscillation?

The mass m of the block and the force constant k of the spring, of course.

One can build a similar model of a CO molecule as two masses attached by a spring:

Unlike the everyday block and spring, this molecule can oscillate at a number of different frequencies. A quantum mechanical analysis shows that the allowed frequencies follow a simple pattern (at least for the lowest energy states, which are the relevant ones inside a molecular cloud). The corresponding vibrational energies of the molecule are

In the case of CO, the combination ℏω₀ is equal to 0.269 eV. One of the strongest lines emitted by the molecule involves a transition from the vibrational state n = 1 to the ground state n = 0.



  Q:  What is the energy of a photon produced by this transition?

  Q:  What is the wavelength of the photon?

  Q:  In what region of the electromagnetic spectrum does this line appear?

My answers.

There is a second way that molecules can produce (or absorb) electromagnetic radiation: by making transitions between ROTATIONAL states.

Just as the vibrational states of these molecules are quantized, so are their rotational states: molecules may only have specific values of rotational angular momentum. As a result, their rotational energies are also quantized. One can express these rotational energy states as

where J is the rotational quantum number. It is common to replace the ℏ/2I term with a single constant B₀ for convenience, yielding

One can look up the rotational energy constant B₀ for any particular molecule of interest. In the case of CO, it has value B₀ = 2.3825 x 10^-4 eV.



  Q:  Compare the constants in front of the expressions for energy
      states in vibrational and rotational states for CO.

           vibrational:   E(n)  =  0.269 eV * (n + 1/2)

           rotational:    E(J)  =  0.00023825 eV * [ J(J+1) ]

 
      Which type of transition requires the molecules to have
      higher energies?

In the case of rotational transitions, quantum mechanical rules require that the rotational index J changes by one; in other words, J → J ± 1.



  Q:  Compute the energy of a photon emitted when a CO molecule
      drops from J = 1 to J = 0.


  Q:  What is the wavelength of this photon?

My answers.

Radio astronomers have adopted CO as a tracer of molecular hydrogen: if they detect CO in some region of space, they can assume safely that molecular hydrogen is there, too. But because both carbon and oxygen are less common in the ISM than hydrogen, the number of H₂ molecules will greatly exceed that of CO. As a rough guide, one can expect roughly 20,000 molecules of H₂ for every single CO.

The role of dust in the creation of molecular hydrogen

One might think that since hydrogen atoms are by far the most common denizens of space, the creation of hydrogen molecules would be a simple matter: whenever two H atoms bump into each other, they stick together and *poof* an H₂ molecule is formed.

Alas, no. The probability that two H atoms will actually combine during a collision is very, very, very small. While this can happen, and was the mechanism for creating molecular gas in the very early universe, it's just too slow to be important in the contemporary Milky Way.

Instead, the dominant mechanism for the creation of molecular hydrogen involves a catalyst: dust grains. The basic idea is that a grain provides a place for hydrogen atoms to meet and form pairs -- sort of like a celestial singles bar. The sequence of events runs like so:

first hydrogen atom collides with grain, adheres to the surface (adsorption)
first atom is free to migrate around the surface of the grain (diffusion)
second hydrogen atom collides with grain, adheres to the surface
second atom is free to migrate around the surface of the grain
the two atoms meet on the surface and combine to form a molecule
the energy released in the reaction pushes them off the surface of the grain (desorption)

Figure 7.4 from Ryden and Pogge, "Interstellar and Intergalactic Medium", Cambridge (2021) , after the original Fig 1 of Delieu et al., Scientific Reports, 3, 1338 (2013)

One of the reasons that this process is so efficient is that, under typical conditions in a molecular cloud, collisions between dust grains and H atoms are pretty frequent, providing many opportunities for molecules to form. How frequent are the collisions? Let's do a quick estimate.

In a typical atomic cloud, the gas has

density of hydrogen n = 50 atoms cm^-3 = 50 x 10⁶ m^-3
temperature T = 50 K

Dust grains (which we will discuss in detail shortly) have a wide range of properties, but a representative grain might have a radius of about a = 0.1 micron = 10^-7 m.


  Q:  What is the typical speed of hydrogen atoms?

  Q:  What is the mean free path of a dust grain?

  Q:  How long between each collision of an H atom and the grain?

My answers.

We'll talk more about dust in a week or two, but here's a quick introduction. Scientists don't have to rely upon theory and remote observations to figure out the properties of interstellar dust grains (though they do use these tools), because we have been able to collect some actual grains and bring them to labs on Earth.

Objects in space will always encounter the Earth with a large relative speed; recall that the Earth's orbital velocity is about 29 km/s, and other objects in the Solar System will move with similar speeds. When a large object -- such as whole asteroids or fragmented "rocks" created in collisions between asteroids -- encounters the Earth, it maintains its speed as it pushes through the air violently. We call the brief flashes of light caused by the heated gas surrounding the object a meteor.

Smaller objects, however, may have a much more gentle ride. Grains of dust can be small enough that just a few collisions with air molecules dissipate most of their relative speed, allowing them to float aimlessly in the upper atmosphere in the same way that pollen and volcanic dust particles sometimes do. One can simply spread out a white sheet on the ground on a windless summer day, wait for a few hours, and find some interplanetary material among the ordinary fluff.

Or, if one is in a hurry, one can fly up into the upper reaches of the atmosphere and grab them in situ. The picture below shows a grain of dust collected by a high-flying aircraft several decades ago. Chemical analysis of these grains reveals that some have extra-terrestrial origins.

Dust particle collected by U2 aircraft, courtesy of NASA