5.3 Star formation rate

Star formation rate is a crucial metric for understanding galaxy evolution and cosmic history. It quantifies the mass of stars formed per unit time in a galaxy, typically expressed in solar masses per year.

Measuring star formation rates involves various techniques, each sensitive to different timescales and stellar populations. Factors influencing star formation include gas density, turbulence, and feedback effects from stellar winds and supernovae.

Star formation rate overview

• Star formation rate (SFR) is a crucial parameter in understanding galaxy evolution and the cosmic history of star formation
• SFR quantifies the mass of stars formed per unit time in a galaxy or region, typically expressed in solar masses per year ($M_{\odot}/yr$)
• Studying SFR across different galaxy types, redshifts, and environments provides insights into the physical processes governing star formation and galaxy growth

Measuring star formation rates

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• Various techniques are employed to measure SFR, each sensitive to different timescales and stellar populations
• Common SFR indicators include ultraviolet continuum emission, recombination lines (H$\alpha$), infrared emission, and radio emission
• Combining multiple SFR indicators helps mitigate biases and uncertainties associated with individual methods

Factors influencing star formation

• Star formation is regulated by a complex interplay of physical processes, including gas density, turbulence, and feedback effects
• Gas density plays a crucial role in star formation, with higher densities leading to increased SFR (Schmidt-Kennicutt law)
• Turbulence in the interstellar medium can both trigger and suppress star formation by creating overdensities and dispersing gas clouds
• Feedback from stellar winds, supernovae, and radiation can heat and expel gas, regulating the efficiency of star formation

Molecular clouds and star formation

• Star formation primarily occurs in dense, cold molecular clouds composed of molecular hydrogen (H$_2$)
• Molecular clouds undergo gravitational collapse, fragmentation, and accretion to form protostars and ultimately main-sequence stars
• The efficiency of star formation in molecular clouds is relatively low, with only a small fraction of the gas mass converted into stars

Star formation rate vs galaxy type

• SFR varies significantly across different galaxy types, reflecting their distinct physical properties and evolutionary stages

Elliptical galaxies

• Elliptical galaxies typically have low current SFRs, as they are dominated by older, redder stellar populations
• Most of the star formation in elliptical galaxies occurred in the past, with their gas reservoir depleted or heated, suppressing further star formation

Spiral galaxies

• Spiral galaxies exhibit a wide range of SFRs, with higher rates in gas-rich, late-type spirals compared to early-type spirals
• Star formation in spiral galaxies is concentrated in the spiral arms, where gas density is higher and triggered by density waves
• The SFR in spiral galaxies is sustained by ongoing gas accretion and recycling from stellar evolution

Irregular galaxies

• Irregular galaxies often have high SFRs relative to their mass, due to their gas-rich nature and turbulent environments
• Starburst galaxies, a subset of irregular galaxies, experience intense episodes of star formation triggered by galaxy interactions or mergers
• The high SFRs in irregular galaxies can be short-lived, as the available gas is rapidly consumed or expelled by feedback processes

Star formation rate vs redshift

• The cosmic star formation history describes the evolution of the global SFR density over cosmic time, peaking at redshifts $z \approx 1-3$

Low redshift galaxies

• In the local universe ($z < 0.5$), SFRs are generally lower compared to the cosmic peak, with a mix of quiescent and star-forming galaxies
• Low redshift star-forming galaxies are typically less massive, less luminous, and have lower gas fractions than their high-redshift counterparts

High redshift galaxies

• At high redshifts ($z > 1$), SFRs are significantly higher, with a larger fraction of galaxies experiencing intense star formation
• High-redshift galaxies are more gas-rich, compact, and turbulent, leading to enhanced star formation activity
• The peak of cosmic star formation at $z \approx 2$ corresponds to the era of maximum galaxy growth and assembly

Cosmic star formation history

• The cosmic star formation history traces the evolution of the global SFR density over cosmic time
• It shows a rapid rise from early times, peaking at $z \approx 2$, followed by a decline towards the present day
• The shape of the cosmic star formation history is shaped by the interplay of gas accretion, feedback processes, and the evolving galaxy population

Star formation rate indicators

• Different observational tracers are used to estimate SFRs, each with its own strengths, limitations, and assumptions

Ultraviolet continuum

• UV continuum emission (1250-2500 Å) directly traces the photospheric emission from young, massive stars (O and B stars)
• UV-based SFRs probe recent star formation on timescales of $\sim$100 Myr, but are sensitive to dust extinction
• Dust corrections are necessary to account for the attenuation of UV light, especially in dusty, star-forming galaxies

Recombination lines

• Recombination lines, such as H$\alpha$ (6563 Å), arise from the ionized gas surrounding massive stars in H II regions
• H$\alpha$ emission provides a nearly instantaneous measure of the SFR, tracing stars with ages $<10$ Myr
• Recombination lines are less affected by dust than UV emission but still require extinction corrections

Infrared emission

• Dust heated by young, massive stars emits thermal radiation in the infrared (IR) wavelengths (8-1000 $\mu$m)
• IR emission traces dust-obscured star formation, capturing the SFR missed by UV and optical indicators
• Total IR luminosity is often used as an SFR indicator, assuming a constant dust heating efficiency and initial mass function

Radio emission

• Radio continuum emission at 1.4 GHz is a tracer of SFR, arising from synchrotron radiation from relativistic electrons and free-free emission from H II regions
• Radio SFR indicators are unaffected by dust attenuation, making them valuable for dusty, star-forming galaxies
• The radio-SFR relation is based on the tight correlation between radio and far-infrared emission, known as the radio-FIR correlation

Star formation laws and models

• Star formation laws and models aim to describe the relationship between gas density and SFR, providing insights into the physical processes regulating star formation

Schmidt-Kennicutt law

• The Schmidt-Kennicutt (SK) law is an empirical relation between the surface density of gas ($\Sigma_{gas}$) and the surface density of star formation ($\Sigma_{SFR}$)
• The SK law is typically expressed as a power law: $\Sigma_{SFR} \propto \Sigma_{gas}^N$, with $N \approx 1.4$
• The SK law holds on global scales for disk galaxies, but breaks down on smaller scales and in extreme environments

Gas density and star formation

• Gas density is a key factor in regulating star formation, as higher densities lead to increased gravitational instability and collapse
• The critical gas density for star formation depends on the balance between gravity and turbulent support
• Molecular gas (H$_2$) is more directly related to star formation than atomic hydrogen (H I), as it traces the dense, star-forming regions

Turbulence and star formation

• Turbulence in the interstellar medium plays a dual role in star formation, both triggering and suppressing it
• Turbulence can create local overdensities and compress gas, leading to gravitational collapse and star formation
• However, turbulence can also provide support against collapse, increasing the critical gas density for star formation

Feedback effects on star formation

• Stellar feedback processes, such as stellar winds, supernovae, and radiation, can significantly impact star formation
• Feedback can heat and expel gas from star-forming regions, reducing the efficiency of star formation and regulating the global SFR
• Positive feedback can also occur, where compression from shocks and turbulence triggered by feedback leads to enhanced star formation

Environmental effects on star formation

• The environment in which galaxies reside can strongly influence their star formation properties

Galaxy mergers and interactions

• Galaxy mergers and interactions can trigger intense starbursts by funneling gas into the central regions and inducing gravitational instabilities
• The enhanced SFRs in merging systems can be an order of magnitude higher than in isolated galaxies
• The merger-induced star formation depends on the mass ratio, gas content, and orbital parameters of the interacting galaxies

Tidal effects and star formation

• Tidal interactions between galaxies can lead to the formation of tidal tails, bridges, and shells, which can host star-forming regions
• Tidal compression and shocks can trigger star formation in the outskirts of interacting galaxies
• However, tidal stripping can also remove gas from galaxies, reducing their potential for future star formation

Starburst galaxies and star formation

• Starburst galaxies experience exceptionally high SFRs, often triggered by mergers or interactions
• The intense star formation in starbursts can deplete the gas reservoir on short timescales ($<100$ Myr), leading to a rapid decline in SFR
• Feedback from the starburst can drive powerful outflows, expelling gas and regulating the star formation efficiency

Stellar initial mass function

• The stellar initial mass function (IMF) describes the distribution of initial masses for a population of stars formed in a single star formation event

IMF variations across galaxies

• The shape of the IMF can vary across different galaxies and star-forming environments
• Some studies suggest a top-heavy IMF in starburst galaxies, with a higher fraction of massive stars compared to the Milky Way IMF
• Variations in the IMF can impact the derived SFRs, as different indicators trace different stellar mass ranges

IMF impact on star formation rates

• The choice of IMF affects the conversion factors used to derive SFRs from observational tracers
• A top-heavy IMF implies a higher proportion of massive stars, leading to higher luminosities and ionizing photon rates per unit mass of stars formed
• Uncertainties in the IMF can introduce systematic uncertainties in the derived SFRs and the cosmic star formation history

Star formation and galaxy evolution

• Star formation plays a crucial role in the evolution of galaxies, shaping their properties and chemical composition

Stellar population synthesis models

• Stellar population synthesis models are used to interpret the observed properties of galaxies in terms of their star formation histories
• These models combine stellar evolutionary tracks, stellar atmospheres, and an assumed IMF to predict the spectral energy distribution of a galaxy
• By fitting observed galaxy spectra with these models, the star formation history and stellar populations of galaxies can be inferred

Chemical enrichment from star formation

• Star formation drives the chemical evolution of galaxies through the production of heavy elements in stellar nucleosynthesis
• Massive stars (>8 $M_{\odot}$) contribute to the rapid enrichment of the interstellar medium through their stellar winds and supernova explosions
• The chemical abundance patterns in galaxies provide insights into their star formation histories and the efficiency of galactic outflows

Star formation and galaxy mass assembly

• Star formation is a key process in the growth and assembly of galaxies over cosmic time
• The stellar mass of a galaxy is built up through a combination of in-situ star formation and galaxy mergers
• The relative importance of these two channels depends on the galaxy mass, redshift, and environment
• Feedback from star formation can regulate the gas supply and limit the maximum stellar mass of galaxies