Galaxies as Ecosystems

Show explicit units, and run a sanity check on every result. A scaling answer is judged by its exponents, not its coefficient. Worked solutions are released after the homework due date.

Useful constants (CGS):

Constant	Value
$G$	$6.67 \times 10^{-8}~\mathrm{cm^3\,g^{-1}\,s^{-2}}$
$m_H$	$1.67 \times 10^{-24}~\mathrm{g}$
$M_\odot$	$1.99 \times 10^{33}~\mathrm{g}$
$1~\mathrm{yr}$	$3.16 \times 10^{7}~\mathrm{s}$
$1~\mathrm{pc}$	$3.09 \times 10^{18}~\mathrm{cm}$
Typical molecular-cloud density	$n \sim 10^{2}$ – $10^{4}~\mathrm{cm^{-3}}$

Useful ideas from the reading: the dynamical timescale $\tau_\mathrm{dyn} \sim 1/\sqrt{G\bar\rho}$ with $\bar\rho = n\,m_H$ ; cold dense gas is the raw material for star formation; a wavelength is a physical filter; feedback both triggers and suppresses star formation.

Conceptual

Problem

⭐⭐ Rank three galaxies by current star formation. You observe three galaxies: (A) smooth, red, no dust lanes; (B) blue and patchy with prominent dust lanes and bright far-infrared emission; (C) red overall but with a few blue knots and a faint reservoir of neutral hydrogen.

(a) Rank A, B, C from most to least actively forming stars now.
(b) For your top choice, write the observable → model → inference chain explicitly.
(c) Which single waveband would best confirm where the cold star-forming fuel sits, and why?

Problem

⭐⭐ The tuning-fork trap. A student claims: “The Hubble tuning fork is an evolutionary sequence — ellipticals are young galaxies that grow spiral arms as they age.”

(a) Identify what is wrong with reading the tuning fork as a time sequence.
(b) State what the tuning fork actually organizes.
(c) Name three specific pieces of physical evidence you would need before making any evolutionary claim about a galaxy.

Problem

⭐ A wavelength is a physical filter. For each band, name the galaxy component it best isolates and one component it largely misses:

(a) 21-cm radio
(b) mid/far-infrared
(c) X-ray
(d) In one sentence, explain why no single band gives “the” picture of a galaxy.

Calculation

Problem

⭐⭐ The gravity clock. A molecular cloud has mean number density $n = 10^{3}~\mathrm{cm^{-3}}$ of hydrogen, so $\bar\rho = n\,m_H$ .

(a) Compute $\tau_\mathrm{dyn} \sim 1/\sqrt{G\bar\rho}$ in seconds, then convert to years. Show the unit check.
(b) Compare your $\tau_\mathrm{dyn}$ to the few-Myr lifetime of a massive star. How does the cloud’s collapse time compare with the timescale on which massive stars deliver feedback?
(c) A denser clump has $n = 10^{5}~\mathrm{cm^{-3}}$ . Without recomputing from scratch, by what factor is its $\tau_\mathrm{dyn}$ shorter?

Problem

⭐⭐ How long can it last? A galaxy holds $M_\mathrm{gas} = 5\times10^{9}\,M_\odot$ of cold gas and forms stars at $\mathrm{SFR} = 2\,M_\odot\,\mathrm{yr^{-1}}$ .

(a) Estimate the gas-depletion time $t_\mathrm{dep} = M_\mathrm{gas}/\mathrm{SFR}$ in years.
(b) Compare $t_\mathrm{dep}$ to the $\sim$ 10-Gyr age of the galactic disk. Can the galaxy sustain this rate from its current gas alone?
(c) Name two baryon-cycle processes that could make the real star-forming history longer than this simple estimate.

Problem

⭐⭐ The universe’s star-formation history. The cosmic star-formation-rate density peaked at “cosmic noon” ( $z \sim 2$ , about 10 billion years ago) at roughly $10\times$ its present value, then declined.

(a) From the shape of that history, is most of today’s stellar mass young or old? Reason it out.
(b) What does the decline since cosmic noon imply about the average cold-gas supply in galaxies then versus now?
(c) Tie this to the previous problem: why can’t the high early rates simply continue forever?

Synthesis

Problem

⭐⭐ Reading a merger. You observe a galaxy pair with long tidal tails, compressed dust lanes in the bridge between them, bright far-infrared emission, and many young blue star clusters near the contact region.

(a) Identify two direct observables and what each traces.
(b) Build an observe → model → infer chain for why the interaction is triggering star formation.
(c) Individual stars almost never collide during a merger, yet star formation surges. Resolve that apparent paradox.

Problem

⭐⭐ Feedback runs both directions. A central starburst drives a galactic wind (as in M82), launching gas out of the disk.

(a) Describe one way this same feedback can suppress future star formation.
(b) Describe one way feedback can trigger star formation elsewhere in the galaxy.
(c) Predict what happens to the galaxy’s star-formation rate over the next several hundred million years if the wind expels much of the cold gas and little fresh gas accretes.

Problem

⭐⭐⭐ Closing the loop. Follow one parcel of gas through the baryon cycle, then close the loop to the next generation of stars.

(a) Trace the parcel through its stages, from cold gas to the moment stellar feedback acts.
(b) The first generation of stars changes both the composition and the supply of the gas the next generation forms from. Explain each change and name the physical process responsible.
(c) Argue in two or three sentences why a galaxy is therefore better described as a self-regulating ecosystem than as a fixed container of stars.