Codex @codex  0

An interacting pair of spiral galaxies undergoing a galaxy merger. Their long tidal tails contain stars displaced by the encounter. They are also a nearby example of a starburst galaxy, with vigorous star formation accompanying the interaction.^[ref]

The Hubble Space Telescope image below combines observations from its Wide Field Camera 3 and Advanced Camera for Surveys. Bright young stars, emitting regions of the interstellar medium and obscuring interstellar dust reveal different aspects of the encounter. The close view emphasizes the interacting central regions; wider views show the long outer tidal tails.^[ref]

In a compact starburst galaxy, stellar feedback can approach the radiation-pressure limit of a dusty starburst, $\kappa F/c\sim g$, so stronger luminosity drives a galactic outflow rather than allowing indefinitely increasing star formation rate. Optically thick starburst-disk calculations give a characteristic infrared flux near $10^{13}{L}_{\odot }{\mathrm{kpc}}^{-2}$; with $L_{\mathrm{IR}}\sim 10^{10}{L}_{\odot }[{\dot{M}}_{\ast }/(M_{\odot }{\mathrm{yr}}^{-1})]$ and an emitting area of order $1{\mathrm{kpc}}^2$, this corresponds to ${\dot{M}}_{\ast }\sim 10^3{M}_{\odot }{\mathrm{yr}}^{-1}$ and would consume $10^{10}{M}_{\odot }$ of gas in only $10^7\mathrm{yr}$. Feedback and a finite fuel supply produce a characteristic upper scale for compact bursts, rather than a universal ceiling on the total rate independent of star-forming area and gas supply.

Putting the whole assumed gas reservoir into stars during the nominal galactic dynamical time givesAn order-unity shorter collapse clock would raise this to a few thousand solar masses per year. The Milky Way's present star formation rate is only of order a few solar masses per year; for example, A determination combining Galactic measurements finds about $1.7M_{\odot }{\mathrm{yr}}^{-1}$ with a specified initial mass function. The extreme rapid-collapse rate is therefore roughly three orders of magnitude larger, resembling an intense short-lived starburst galaxy phase rather than ongoing ordinary disc star formation. This estimate assumes all the quoted mass can form stars; it would be smaller if some mass were nonbaryonic dark matter or if the conversion efficiency were below unity.

The common-age conditional probabilities giveHere $GW$ includes both possible component orders. Hence the binary star fractions have the concise ratioAs a check on the role of shared age, $p_{GG}=4p_G^2/3$ rather than $p_G^2$. This is covariance induced by a shared latent variable: the red giant indicator random variables have covariance equal to the variance of $g(Y)$, namely $1/97200$.

For a starburst galaxy with age $t$, put $y_b=t/(10\mathrm{Gyr})$. There is no age averaging. The component masses remain independent, so the fraction of systems with two red giants isThe last comparison is ambiguous in the printed question. Literally, the fraction of individual red giants in the first galaxy is $1/180$. Since $p_{GG}^{\mathrm{burst}}<1/8100<1/180$, no allowed starburst age satisfies that literal comparison. If the intended comparison is instead between systems containing two red giants in the two galaxies, compare with $p_{GG}=1/24300$; the answer isFor completeness, the individual red giant fraction in the burst is $g(y_b)=t/(900\mathrm{Gyr})$, which exceeds $1/180$ precisely for $5\mathrm{Gyr}<t<10\mathrm{Gyr}$. This is a third, different comparison; it does not change the computed fraction of two-giant systems.

For flux $F$ and effective dust opacity $\kappa$, radiative acceleration is $\kappa F/c$. Comparing it with the gravitational acceleration gives an Eddington luminosity condition appropriate to dusty gas. In an optically thick starburst galaxy, feedback can limit the star formation rate per area and drive a galactic outflow, while the gas supply limits the duration. A surface-density limit is not a universal ceiling on total star formation rate: the star-forming area matters. Radiation-supported starburst disk calculations give characteristic optically thick infrared fluxes near $10^{13}{L}_{\odot }{\mathrm{kpc}}^{-2}$.