Lecture notes 13: Interstellar material & the formation ofstellar systems

The space between the stars is not empty. Rather it contains vast quantities ofgas and dust; our own galaxy the Milky Way has some tens of percent of itsmass in the form of gas (90 − 99%) and dust (1 − −10%). This material wasfirst commented by Herschel as “holes in the sky” more than 200 years ago. It’snature was deduced by Trumpler in the 1930’s through an analysis open clustersizes D.

The idea behind the analysis was that if D was independent of distance rfrom the sun then θ = D/r should decrease with distance as

θ2 = (D/r)2 ∝ 1/r2. (1)

When plotted against the summed flux from the open clusters f = L/rπr2 oneshould expect a straight line. This was not observed, rather the radiative fluxfell off much more rapidly than expected at small θ2. The explanation for thiseffect could be

1. That the Earth is in some special location.

2. An observational selection effect.

3. That far away clusters are fainter.

4. Dimming by interstellar dust.

The latter explanation is the correct one. Interstellar dust, consisting of silicates(sand), graphite, and silicon carbide, can dim starlight from stars far away.

Dust and Gas

Dust can have other effects than dimming (extinction), among these being

1. Reddening. The size of dust grains is such that blue light is more easilyscattered (by Rayleigh scattering ∝ 1/λ4) than red light. The net effectis to make light redder as it passes through dust.

2. Polarization. Oval dust grains will orient themselves such that they arealigned with the interstellar magnetic field. This causes linear polarizationof starlight passing through such aligned dust grains. Measurements ofthe degree of polarization can therefore be used to measure the galacticmagnetic field.

3. (Reflection). Dust clouds around newly formed star clusters and stars willreflect (mainly) the blue light towards an observer. The result is blueish“reflection nebulae”, such as those around the Pleiades.

1

Figure 1: The emission nebulae NGC 3603 (left) 7200 pc away, and NGC 3576which is 2400 pc away. Note that NGC 3603 is much redder than NGC 3576even though the light they send out originally is from the same spectral lines,i.e. has the same colour.

Insterstellar gas was discovered much earlier than dust through stationary ab-sorption lines by Hartmann in 1904. These lines are very narrow, indicatinglow temperatures and at line shifts indicative of the velocities of interstellargas clouds, which also helped separate them from eventual circumstellar cloudswhich presumably would have the same line shifts as the stars they surround.

Gas and dust are mixed and gaseous nebulae are evident in a wide varietyof astrophysical contexts:

1. Reflection nebulae. Already mentioned above.

2. H ii regions. Gas clouds that are ionized by near lying O and B stars —these send out enough UV radiation at wavelengths < 91.2 nm requiredto ionize hydrogen. When protons recombine with electrons some of thisenergy is re-radiated in spectral lines visible to the naked eye giving char-acteristic red Balmer lines as well as green lines from twice ionized oxygen(O iii) at 500.7 nm and 495.9 nm. The region that is ionized is sometimesnamed the Strømgren sphere.

3. Planetary Nebulae. As discussed before the remains of the stellar envelopethrown off during the last stages of a low to medium mass stars’ life. Pow-ered by the remnant stellar core, a still very hot (105 K) carbon/oxygenwhite dwarf which will emit copius UV-radiation.

2

Figure 2: A reflection nebulae.

4. Supernova remnants. Powered by the pulsar in their midsts.

5. Dark nebulae. Barnard objects and Bok globules. Dense, cold regionswith densities on the order 1010 − 1015 /m3 and temperatures 10− 100 K.Barnard objects can have masses on the order of thousands of solar massesand diameters of, say, 10 pc. The Horsehead Nebula is a Bernard Object33. Bok globules constitute the inner core of a Barnard object, their outerless dense parts often rinsed away by stellar radiation and winds. Thevolumes of Bok globules are on the order of 1/10 of Barnard objects. Itis in Bok globules one finds protostars; stars in the act of being born.

6. Molecular clouds. Much of the hydrogen in interstellar space is in molec-ular form, H2 does not radiate and is difficult to observe. On the otherhand asymmetric molecules such as CO do radiate with both vibrationaland rotational lines in wavelengths between 1 − 10 mm. Over 100 differ-ent molecules have been found in interstellar space. Such radiation is amarker for large cloud complexes of which there are more than 5000 inthe galaxy. These have masses on the order 105 − 2 × 106 MS , diameterson the order 15 − 100 pc and densities of roughly 2 × 108 H atoms/m3.Embedded in these cloud complexes are the H ii regions and dark nebulaedescribed above. The molecular clouds lie as pearls on a string along the

3

spiral arms of the Milky Way at a separation of roughly 1000 pc as theydo in other disc galaxies. The Orion nebula, and the Horsehead Nebula25 pc away, both lie in an enormous molecular cloud with an estimatedmass of 5 × 105 MS .

Stellar birth

Embedded in the densest region of instellar clouds we find protostars. Thesenewly forming stars; the observational manifistation of which are called T-Tauri stars are due their location often invisible to visible radiation and mustbe observed in IR which has a greater probability of traversing the gas anddust clouds. T-Tauri star spectra are dominated by strong emission lines, in-dicative of strong chromospheric activity. They have strong stellar winds, upto 10−7 MS/yr, and their luminosity is highly variable on timescales of days.T-Tauri stars have masses on the order of 3 MS . The abundance of lithium inthese stars is also high,indicative of a young age since Li is quite easily fused toheavier elements even at fairly low temperatures and has essentially dissapearedfrom the solar spectrum. T-Tauri stars’ location in the HR-diagram, high lumi-nosities with low effective temperatues, is as predicted from the calculations ofHenyey and Hyashi.

It seems that at the densities found in the Milky Way at present are not greatenough that star formation can start on its own. Among agents for initiatingcloud contraction and stellar birth are considered:

1. The shock wave associated with spiral arms. There are indications thatthis process leads to an overabundance of O and B stars.

2. Shock waves from super nova explosions. Simulations indicate that supernova shocks produce a larger spread in the spectral classes of the starsinitiated. It is believed that the formation of the Sun was initiated bya super nova shock, due in part to analysis of the Allende meteorite, acarbonaceus chondrite.

3. Strong stellar winds from O and B stars.

Hyashi - Henye tracksTracks such as those shown in figure 3 are based on numerical calculations

and show the latter stages of cloud collapse and stellar birth before stars settledown on the hydrogen burning main sequence. Convection ensues when thestellar material becomes too opaque for energytransport by radiation, as suchthe stars move along Hyashi tracks vertically in the HR diagram with effetivetemperatures of roughly 2 500 K. As the stellar interiors heat up radiation isable to carry energy from the stellar interior and the stars follow the radiativeHenyey tracks that go horizontally towards the main sequence.

Notice that heavier stars develop much more rapidly than the lighter stars.Notice also that stars lose much material during their formation (in the form ofwinds).

4

Figure 3: Hyashi—Henyey tracks along with isochrones for stellar birth.

ProtostarsProtostars have large luminosities but are invisible in the visible region of

the spectrum. Their energy comes from the gravitational energy released inthe collapse of the cloud half of which goes into heating the gas, half of whichis radiated as dictated by the virial theorem. Protostars with masses of <3 MSshow accretion disks, the disks planetary systems are thought to beconstructed from. Protostars (T-Tauri stars) also often show jets — Herbig-Haro objects — that perhaps assist in carrying away excess angular momentumfrom the collapsing cloud.

Formation of the Solar System

The fossil record as known towards the end of the 19th century gave a goodrelative timescale for the age of the Earth and various geological epochs, butthe absolute scale was not known. The archbishop of Usher calculated that theEarth was 6000 years old in 1664. Kelvin and Helmholz estimated 20− 30 Myrbased on their theory of gravitational contraction as the energy source of theSun. It was first with the radioactive dating introduced by Rutherford at thebeginning of the 20th century that the age of the Earth become known with anycertainty.

Radioactive dating takes advantage of the radioctive decay of certain ele-

5

Figure 4: A protostar with disk and jet.

ments with known half lives:

n(t) = n(t = t0) exp [−t/te] = n(t = t0)(1/2t/τ (2)

where τ = te/ ln 2 is defined as the half life. The isotope 23892 U decays by α and

β decay to the stable 20682 Pb with a half life of 4.47 Gyr. The priciple of dating is

based on identifying the total number, in this case of uranium and lead isotopesand noting that

n(238U) + n(206Pb) = constant. (3)

It is then clear that the ratio of these isotopes gives the date of the material theywere found in. There are many complications in this procedure: i.e. how many206Pb where there originally, so the procedure is far from as straightforward asit seems here. Another isotype pair often used in dating is 40K → 40Ar whichhas a half life of 1.3 Gyr.

Another thing that may be done with this sort of procedure is to date theelements themselves. It is found that heavy elements are of order 7− 15 Gyr ascompared to the Earth’s 4.4 Gyr.

Kant’s hypothesisA theory of the formation of the solar system should explain the following:

• Planetary orbits lie in the same plane and resolve in the same direction.

• The Sun’s rotation (spin) is in the same direction.

• The plantets spin are also in the same direction (except Uranus)

6

• The eccentricity of planetary orbits is e << 1 for all planets except Mer-cury and Pluto.

• The satellite systems of the major planets mimic the solar system.

• The chemical differentiation and physical properties of the planets.

Serious scientific work on this problem was first done by Descartes, Kant andLaplace. The latter two’s nebular hypothesis is a direct ancestor of today’sformation theory.

1. A rotating nebula forms from a contracting/collapsing cloud. Conserva-tion of angular momentum L leads to flattening. There is a high proba-bility two lumps develop, eventually forming a double star system.

2. The rotating disk condenses into small pieces whcih grow into planets bycollisions. Planets have 99% of the solar systems angular momentum whilethe Sun has 99.9% of the total mass. The magnetic field may have beenimportant in transporting angular momentum outward in the protoplan-etary disk.

3. Insofar as planets grow by accretion, Jovian planets have a head start sincethey form in cooler regions. Jovian masses are large enough to gathergases. Terrestial planets have a later start, never gather large mass beforethe solar wind (during the Sun’s T-Tauri phase) sweeps the solar systemclean of material. The asteroid belt is all that remains of the debris fromplanetary formation in the inner solar system, in the outer solar systemthe Kuiper belt still remains and carries important information on theearly solar system and its later evolution.

4. A scaled down version of this formation scenario could be responsible forthe formation of the satellite systems of the gas giant planets.

Among the most difficult properties to explain lies in the difference betweenthe inner and outer solar system. The terrestial planets have densities on theorder of 4 − 5 × 103 kg/m3, while the Jovian are 1 − 2 × 103 kg/m3. Thedifferences mean that gravity is not the only active agent in planetary formation.The temperature in the disk was higher towards the center. At low enoughtemperatures solids can condense via molecular forces. It was probably nevercool enough — less than 200 K — in the inner solar system to allow ices ofwater, methane, and ammonia to form. (Where did the Earth’s water comefrom? Perturbed bodies from the outer solar system?) While on the other hand,silicates, magnesium silicates and iron-nickel alloys can form at temperaturesbelow 1800 K.

The outer planets thus presumably become large enough to to gather gas bygravity while the inner planets did not before the solar wind turns on at some106 yr.

One must also consider the role of presolar grains. At low enough disk tem-peratures it has been shown that a gravitational instability in the disk rapidly

7

Figure 5: A schematic illustration of the outer solar system and the processesthat occur there that drive its evolution.

can form asteroid sized objects from preexisting grains sized from mm to cm (likethose found in the rings of Saturn). The question is whether the temperatureever was low enough for this instability to develop.

Asteroid sized objects collide to form planetisimals and later planets.

8