Astronomy 218 Gas, Dust & Starlight Five Phases Observations like these reveal 5 different phases for gas in the interstellar medium. 1) Cold Molecular Clouds (n > 109 m−3, T ~ 10 K) 2) Cold Neutral Medium (n ~ 108 m−3, T ~ 100 K) also called HI regions. 3) Warm Neutral Medium (n ~ 4 ×105 m−3, T ~ 7000 K) also called the Intercloud Medium. 4) Warm Ionized Medium (n ~ 106 m−3, T ~ 104 K) also called HII regions. 5) Hot Ionized Medium (n < 104 m−3, T ~ 106 K) also called coronal gas. Dark Nebulae Returning to our wider-angle view of the Milky Way, aside from the myriad of stars and glowing regions of gas, the most notable feature is the dark regions that blocking light from the stars beyond.

These regions have historically been called dark nebulae. The question is what is the composition of these nebulae and how to they affect starlight. Interstellar Extinction The general affect of opacity is a reduction in the flux determined by the optical depth. −τ F = F0 e where for simplicity τ ≈ nσr ≈ κρr Observationally, this affects the apparent magnitude.

−τ mobs = C − 2.5 log F = C − 2.5 log F0 − 2.5 log (e )

= m0 + 2.5τlog(e)

= m0 + 1.086τ

≡ m0 + A The extinction, A, is added to the apparent magnitude and is linearly proportional to τ, A = 1.086τ. Optical Opacity A critical clue to the nature of dark nebulae is how the opacity changes as a function of wavelength. For example, Barnard 68 is far more opaque to visible light than it is to infra-red light.

Ultraviolet light is even more strongly absorbed. Extinction & Wavelength The extinction and optical depth are clearly wavelength dependent, Aλ = 1.086τ λ ∝ nσλr. Thus the observed magnitude acquires an additional wavelength dependence.

mobs(λ) = m0 (λ) + A

This also affects the distance modulus. mobs−M = 5 log(r/10 pc) + A

Empirically Aλ, falls steadily with increasing wavelength, except for a prominent peak around 0.22 μm = 220 nm. Interstellar Reddening As a result of this wavelength dependence, observed light is systematically reddened, as blue light suffers greater extinction than red. The effect is not just a diminishment of the flux but an apparent change in the spectra, seeming to move the spectrum toward the red. However, spectral lines remain in their places. With care, this can allow an apparently reddened star to be distinguished from an intrinsically red star. Color Excess The wavelength dependence of extinction results in weaker extinction as one progress through the UBVRI filters,

AU > AV > AB > AR> AI . This differential effect skews the color indices.

For example, (B – V) = B0 + AB – V0 + AV

= (B – V)0 + (AB – AV)

(AB – AV) is called the color excess and is generally denoted E(B – V). E(B – V) can be expressed in terms of the opacity or optical depth.

For example, E(B – V) = (AB – AV) = 1.086 (τB – τV). Reddening One measure of the wavelength dependence of the extinction is the ratio of total to selective extinction, labeled R. While a similar ratio can be defined for any color index, the standard R applies to (B – V). The opacity is inversely proportional to the wavelength. −1 If τ ∝ λ

For λeff,B = 550 nm, λeff,V = 445 nm, R = 4.2. Empirically, R~3.1, but it varies from ~2.5 to 5.5 along different lines of sight. Dust Construction The form of the extinction curve provides important hints to the nature of the dust, which is only 1% of gas. Large dust particles with a size d >> λ would have a flat curve, implying that d ≲ λ. More detailed studies estimate a range d~5-200 nm (0.005 - .2 μm). This is the size of fine soot particles or less than the size of talcum powder. The feature at 220 nm is similar to a feature seen in graphite in terrestrial laboratories, suggesting that graphite is a significant constituent of grains. Fitting the shape of the curve implies d~20 nm. Polarization from grains

Starlight is polarized as it passes through the dust, with some orientations of the E field more strongly scattered than others. This suggests elongated grains, aligned preferentially. Most likely, the alignment is due to the interstellar magnetic field. Simulations of dust formation produce tangled arrays of line segments. Thermal Dust At long wavelengths, λ > 100 μm, absorption by dust turns to emission, revealing a blackbody spectrum with T ~ 20 K, and considerable radio emission in molecular bands. Shorter λ reveals absorption features of silicates and ices. Nebulae in Concert The frequent coincidence of emission nebulae, reflection nebulae and dark nebulae hints an interconnection. As an example, the Ophiuchus dust cloud is surrounded by emission nebulae. But how are they connected? Horsehead Nebula The Horsehead Nebula (Barnard 33) is one of the most famous of dark dust clouds, silhouetted against the bright background of an emission nebula.

The connection is the bright young stars, like Alnitak with spectral type O9I, powering the emission nebula. Destruction by Emission The strong interaction between the young stars and the nebulae are most famously seen in the Eagle Nebula. The fuzzy areas near the pillars are due to photo- evaporation.

UV photons are turning the dark nebula into an emission nebula, destroying the dust and ionizing the gas. Building an HII Region Like all stars, bright O and B stars begin their lives cocooned in their natal gas cloud. Being short lived, they do not stray far before their demise.

With T★ > 20,000 K for O and B stars, they emit a considerable amount of ultraviolet light. Surrounded by a dense gas cloud, the UV photons quickly ionize much of the gas. The structure and size of the nebula is determined by the balance between ionizing radiation and recombination building an equilibrium population of ionized gas and neutral atoms.

The radiation field is characterized by T★ which is quite different from the temperature of the gas, Te. Recombination Light Focusing on the main constituent, hydrogen, we see that each photon emitted by the star with λ < 91.2 nm will ionize an atom, since Eλ > 13.6 eV. For photons with λ > 91.2 nm, the combination of ionized gas and cold neutral gas is optically thin, except for Lyman photons. A Lyman photon will excite an atom to an state with n > 1. These excited atoms will emit a combination of Balmer, Paschen, etc. lines, which escape, and Lyman lines, which are absorbed. Repeating many times, the Lyman photons are all converted to Lα, which diffuse slowly. Recombination Rate A free electron will recombine with a proton after covering a typical distance of The time to travel this mean free path is

If each electron takes trec to recombine, the total rate is Averaging over the distribution of velocities gives the recombination coefficient. −2 −1 −½ Physically σrec ∝ ʋe , so α(Te) ∝ ʋe ∝ Te Strömgren Sphere The rate the star emits ionizing photons is where hν0 = 13.6 eV In steady state this is matched by the rate of recombinations within the HII region. RS is the Strömgren radius, delimiting the size of the HII region or Strömgren sphere. Typical values are 4 Te ≈ 10 K, −19 3 −1 α(Te) = 2.6 × 10 m s 7 −3 np ≈ ne ≈ 10 m 48 −1 For an O6V star, Q = 5 × 10 s 4 * Te ≈ 10 K is due to 17 yielding RS ≈ 3.4 × 10 m ≈ 10 pc. cooling by metals. Next Time Turning gas clouds into stars. Monday turn in Homework #4, which we will discuss in class on Wednesday. First Exam is Friday of next week.