AST4320 - Cosmology and extragalactic astronomy Lecture 19 Let there be light! Stars... 1
GMCs are `supersonically turbulent. Turbulence: Starformation Inside GMCs.
GMCs are `supersonically turbulent. Starformation Inside GMCs. Observations indicate that observed absorption lines in GMCs have a finite width of ~ 6 km/s, indicative of the rms turbulent velocity of gas in the GMC. This `turbulent velocity is a factor of ~ 15-30 times higher than thermal motion associated with inferred T of ~10 K. In turbulent media, the Jeans mass changes to where sigmaturb denotes the rms turbulent velocity of the gas. In turbulent media, the Jeans mass changes to
GMCs are `supersonically turbulent. Starformation Inside GMCs. A crucial aspect of turbulence is that the RMS velocity is scale-dependent that depends on properties of the turbulence. For supersonic turbulence: Interestingly, observed line widths in GMCs also scale as Delta v ~ R 1/2, providing further support for supersonic turbulence in clouds. Importantly, sigmaturb is largest on the largest scales in the GMC, and smallest on the smallest scales.
GMCs are `supersonically turbulent. Starformation Inside GMCs. A crucial aspect of turbulence is that the RMS velocity is scale-dependent that depends on properties of the turbulence. For supersonic turbulence: Interestingly, observed line widths in GMCs also scale as Delta v ~ R 1/2, providing further support for supersonic turbulence in clouds. Importantly, sigmaturb is largest on the largest scales in the GMC, and smallest on the smallest scales. Also note, turbulent compression enhances density by where M denotes the Mach number of the turbulence (M=sigmaturb/cs)
Starformation Inside GMCs.
Recall Challenges Challenges: 1. GMCs rotate. Need to loose angular momentum, otherwise stars would rotate very fast. 2. Gravitational binding energy must be radiated away, but cores are opaque to most radiation. Partial Solutions (Qualitative): 1. GMCs as a whole are stabilized against gravitational collapse. Turbulent compression cause small parts of GMC to collapse. 2. Because only a small fraction of GMC collapses, less binding energy needs to be radiated away. Cores in GCMs remain opaque, but less so than the GMC as whole would have been.
Origin of the Supersonic Turbulence If supersonic turbulence regulates star formation, then we need to understand origin of this turbulence. Turbulence generally exists if there is something perturbing (`stirring up ) the system. Possible mechanisms include 1.Galaxy formation: accretion of new gas, (tidal) interactions with nearby galaxies, mergers 2. Supernova explosions outside the GMC 3. Spiral structure in galaxies 4. Protostellar outflows 5. Stellar winds. 6. Ionizing radiation
What Masses Will the Stars Have? Supersonic turbulence gives rise to following mass-dependence of the number of compressed `fragments : For comparison, the massive end of the Initial Mass Function (IMF, number of stars that form as a function of mass) has been inferred to be Provides further support for the idea that supersonic turbulence is driving star formation.
Summary Supersonically Driven Star Formation Starformation represents a key process in galaxy formation. The typical overdensity of a star compared to the background density today is ~ delta~10 31, and thus requires collapse over ~ 10 orders of magnitude in spatial scales. Once gas has assembled into a galaxy, instabilities (gravitational, thermal) can create significantly overdense `giant molecular clouds (GMCs) inside this gas. Supersonic turbulence inside GMCs then prevents the GMC from collapsing as a whole, while allowing smaller scale fragments -formed via turbulent compressionto collapse under gravity. The mass function of fragments formed in this picture resembles the massive end of the inferred stellar `initial mass function.
Lecture 19: Let there be light! Basic properties of stars from hydrostatic equilibrium & virial theorem Radiation from stars UV & IR emission is tracers of ongoing star formation. Star formation history of the entire Universe. A few `cool star formation tracers: X-ray binaries; gamma-ray bursts 12
Starformation Inside GMCs.
What is a Star, Wikipedia? `A star is a massive, luminous sphere of plasma held together by its own gravity... For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and then radiates into outer space.
Stars The structure of stars is regulated by hydrostatic equilibrium. From lecture 2. Here p(r) denotes the gas pressure, rho denotes the gas density, and phi denotes the total gravitational potential. In equilibrium, the (`total ) time-derivative vanishes d/dt=0, and This is the equation of hydrostatic equilibrium. Key properties of stars can be obtained from this equation, and the virial theorem
Central Pressure In Stars Hydrostatic equilibrium implies that the central pressure of a star is Plugging in solar radius + solar mass we get For comparison P=nkT; for n=1e24/cc, this would require T~5e7 K.
Central Temperature In Stars We will show that the virial theorem implies an average -which should be considered a lower limit - temperature of Plugging in solar radius + solar mass we get a lower limit of Hydrostatic equilibrium + virial theorem give approximate values for central pressure and T of the sun of & Actual values are Tc=1.6x10 7 K, Pc=2.4x10 17 dyn/cm 2.
Mass/Radius Relation The virial theorem again implies a relation between the mass and radius of a star. empirical relation between Tc and M: Simple virial theorem + empirical relation between Tc and M quite nicely capture inferred mass-radius relation of stars.
Mass/Luminosity Relation Assuming - which is ok - that stars radiate black body spectra, then Use relations for T vs M and R vs M to see following scaling relation Stellar luminosity expected to be strong function of mass.
Mass/Luminosity Relation Assuming - which is ok - that stars radiate black body spectra, then Use mass-radius relation to eliminate R-dependence Use virial theorem eliminate T-dependence. Stellar luminosity expected to be strong function of mass. Previous assumes uniform T. In reality there is a T-gradient across star: hot in interior, cooler on surface. Once this T-gradient is taken into account
Mass/Luminosity Relation Simple virial theorem also nicely capture inferred luminosity-radius relation of stars.
Nuclear Reactions Nuclear fusion can occur inside stars when Tc >10 7 K. We found that and that which used where I `renormalized by substituting the real central T of the sun. Nuclear reactions require M >~ 0.1 Msun [real value ~0.07 Msun]. Objects below this mass thresholds are known as `brown dwarfs.
Brown Dwarfs Discovered only almost exactly 21 years ago!
Mass Range of Stars Lower limit on stellar mass of Mlow=0.07 Msun is set by nuclear fusion requirement. For M >~ 50-100 Msun the high luminosity of the stars translates to a large radiation pressure. Photons can `push out atmospheres. This sets an upper limit at Mhigh~100 Msun. Massive stars have indeed been observed to have prominent stellar winds because of their large radiation pressure. Nice illustration of instability of massive stars are Wolf-Rayet stars.
Wolf-Rayet Stars Wolf-Rayet star: massive star (M > 20 Msun) that is blowing out gas at velocities of thousands of km/s.
Life Time & Luminosity-Temperature Relation of Stars With nuclear fusion powering stars, the life-time of stars is That is the highest mass stars live shortest. Substituting some numerical values: the sun lives for ~ 10 Gyr. Then, a 30 solar mass star would live for ~ 10 Myr. Also recall that,, This implies that
Summary of Stellar Properties I Hydrostatic equilibrium + the virial theorem gives the central density + temperature of stars to about an order of magnitude The virial theorem + empirical relation between Tc and M implies a relation between the mass and radius of a star, which is in good agreement with observations. Simple virial theorem also nicely capture inferred luminosity-radius relation of stars.
Summary of Stellar Properties II Stellar masses lie in range M=0.07-100 Msun brown dwarf limit radiation pressure limit Massive stars live shortest Massive (and luminous) stars are the hottest. Basic properties of stars can be understood with simple physics.
Hertzsprung-Russel Diagram Basic properties of stars can be understood with this simple physics. Luminous Faint Hot Cold
Hertzsprung-Russel Diagram Basic properties of stars can be understood with this simple physics. Luminous M=60 Msun Stellar masses lie in range M=0.07-100 Msun M=0.1 Msun Faint Hot Cold
Hertzsprung-Russel Diagram Basic properties of stars can be understood with this simple physics. Luminous M~20 Msun t~10 Myr M~0.3 Msun t~100 Gyr Faint Hot Cold
Animated Hertzsprung-Russel Diagram Visual illustration of life-time of stars. Symbol color indicates T, symbol size R
With basic radiation properties of stars understood, we can connect to real observables.
What Masses Will the Stars Have? Supersonic turbulence gives rise to following mass-dependence of the number of compressed `fragments : For comparison, the massive end of the Initial Mass Function (IMF, number of stars that form as a function of mass) has been inferred to be Provides further support for the idea that supersonic turbulence is driving star formation.
The Initial Mass Function (IMF) Inferring the initial mass function from observations is challenging, because observations measure the present day mass function (PDMF). PDMF can be obtained by counting stars of a given M within a given volume V. However, massive stars with t < 10 Gyr (age of Milky Way) have moved off main sequence, and are not represented in PDMF. PDMF IMF 1. Must correct for earlier generation of `lost high-mass stars, which requires on star formation history + assumptions on IMF as a function of time. 2. To constrain high-mass end requires large volumes, and hence assumptions on whether the IMF changes with location.
The Initial Mass Function (IMF) Must correct for earlier generation of `lost high-mass stars, which requires on star formation history + assumptions on IMF as a function of time It is somewhat disconcerting that the break from the Salpeter law identified in many IMF studies needs to be invoked near the place where the correction becomes important (around one solar mass) Bastian et al. 2010, ARAA.
Functional Forms of the IMF Functional form of IMF is still debated.
Universality of the IMF? Studies [...] suggest that the vast majority were drawn from a universal system IMF: a power law of Salpeter index (Γ = 1.35) above a few solar masses, and a log normal or shallower power law (Γ 0-0.25) for lower mass stars... Observations of resolved stellar populations and the integrated properties of most galaxies are also consistent with a universal IMF, suggesting no gross variations over much of cosmic time. A Universal Stellar Initial Mass Function? A Critical Look at Variations Bastian, Nate; Covey, Kevin R.; Meyer, Michael R., 2010, Annual Review of Astronomy and Astrophysics
Towards Integrated Spectra of Stellar Populations Suppose a GMC turns some gas into stars at time t=0. If we... 1. specify the initial mass function N(M) 2. use our understanding of stellar evolution which give us the luminosity L(M), the temperature T(M) [or better the full spectrum], and age t(m) Then we can predict how much radiation the star forming regions emits as a function of time.
Integrated Spectra of Stellar Populations UV Optical Leitherer et al. 1999 Infrared 2 Myr 10 Myr As time passes, the more massive, luminous, hotter stars disappear. These stars are luminous in the UV.
Integrated Spectra of Stellar Populations UV Optical Leitherer et al. 1999 Infrared 2 Myr 10 Myr The UV flux is more `sensitive to the presence of young stars, i.e. star formation activity.
Star Formation Indicators: UV Flux The integrated UV flux has been demonstrated to be a good tracer of SFR (e.g. Kennicutt 1998, Annual Reviews of Astronomy & Astrophysics.) Many other tracers exist which we can understand qualitatively: 1. Recombination lines such as Balmer-alpha 2. IR emission.
Integrated Spectra of Stellar Populations UV Optical Leitherer et al. 1999 Infrared Ionizing flux very sensitive to young stars & ongoing star formation. Ionizing flux is easily absorbed by HI gas inside galaxy, which creates electrons + protons. These recombine into e.g. Balmer series photons such as Balmer-alpha H-ionizing non-ionizing
Star Formation Indicators: UV Flux The integrated UV flux has been demonstrated to be a good tracer of SFR (e.g. Kennicutt 1998, Annual Reviews of Astronomy & Astrophysics.) Many other tracers exist which we can understand qualitatively: 1. Recombination lines such as Balmer-alpha 2. IR emission.
Star Formation Indicators: IR Flux Recall that star formation occurs inside the densest cores inside GMCs. Nearest GMC: the Orion nebula. Cores contain molecules (+`dust ) which are opaque to visible and UV But...absorbed UV and optical emission is reemitted in IR. Joint IR and UV measurements provide a powerful way of probing star formation.
Insight Into Star Formation: Largest Scales We have good measurements of the number of star forming galaxies as a function of UV-luminosity (i.e. SFR) and cosmic time. Number density described well by Schechter function UV-bright UV-faint UV-luminosity
Insight Into Star Formation: Largest Scales We have good measurements of the number of star forming galaxies as a function of UV-luminosity (i.e. SFR) and cosmic time. Luminosity density (total UV-luminosity per unit volume) is given by We can measure UV-luminosity density! UV-bright UV-faint UV-luminosity
Insight Into Star Formation: Largest Scales We have good measurements of the number of star forming galaxies as a function of UV-luminosity (i.e. SFR) and cosmic time. Luminosity density (total UV-luminosity per unit volume) is given by We can measure UV-luminosity density! UV-bright UV-faint and infer star formation rate density [rate at which stars form per unit vol.] UV-luminosity
`Lilly-Madau -Diagram The star formation rate density as a function of age of the Universe. Star formation rate density reached a peak at z=2-3 (this is also where quasar activity is maximal). Things are much `calmer again.
`Lilly-Madau -Diagram Compare with cosmological gas accretion rates onto galaxies. Star formation rate density reached a peak at z=2-3 (this is also where quasar activity is maximal). Things are much `calmer again.
`Lilly-Madau -Diagram Compare with cosmological gas accretion rates onto galaxies. Note how relative contribution of cold and hot model accretion differs per simulation (which reflects the current uncertainty)! Gas accretion in both hot and cold modes is decreasing rapidly at z<2, likely responsible for decline in SFR density.
Insight Into Star Formation: Smaller Scales Another important observed correlation related to star formation in galaxies is the Kennicutt-Schmidt Law. gas (HI +H2)mass per unit area star formation rate per unit area Important,it has been shown observationally that these laws do not apply when applied to one local patch inside one galaxy.
Other `Cool Tracers of Star Formation High-Mass X-Ray Binaries (HMXBs) compact object (NS,BH) Hot `accretion disk (next lecture) emits X-rays donor HMXB: `high mass donor> 5-10 solar masses.
Other `Cool Tracers of Star Formation High-Mass X-Ray Binaries (HMXBs) compact object (NS,BH) Hot `accretion disk (next lecture) emits X-rays donor HMXBs again requires presence of massive, i.e. young stars!. X-rays coming from accretion disks may provide measure of ongoing star formation.
Recall: X-rays do not come from Ordinary Stars X-rays UV Optical Leitherer et al. 1999 Infrared 2 Myr 10 Myr
Other `Cool Tracers of Star Formation High-Mass X-Ray Binaries (HMXBs) Mineo+2010, Gilfanov+2004. Text relation holds over ~ 4 orders of magnitude. scatter ~ 0.4 dex L X =2.5 10 39 SFR M yr 1 erg s 1
Other Cool Star Formation Indicators Gamma-Ray Bursts (GRBs) `Gamma-ray bursts (GRBs) are flashes of gamma rays associated with extremely energetic explosions that have been observed in distant galaxies. They are the brightest electromagnetic events known to occur in the universe. MV ~ -36 Text GRBs can easily be detected out to the largest cosmological distances.
Other Cool Star Formation Indicators GRBs narrow beam of intense radiation released during a supernova or hypernova as a rapidly rotating, high-mass star [M>20 Msun] collapses to form a neutron star, quark star, or black hole Text GRBs associated with high-mass star [M>20 Msun] --> tracers of star formation?
Other Cool Star Formation Indicators GRBs associated with high-mass star [M>20 Msun] --> tracers of star formation? Text Why cool?: We can detect GRBs irrespective of luminosity of galaxy in which it went off.
Other Cool Star Formation Indicators GRBs associated with high-mass star [M>20 Msun] --> tracers of star formation? Text Why cool?: We can detect GRBs irrespective of luminosity of galaxy in which it went off. If faint end slope of the UV -luminosity function is steep [alpha < -2], then luminosity density - and SFR density - dominated by low-luminosity galaxy, we would not be able to detect. However, we could detect GRBs going off in them!
Other Cool Star Formation Indicators GRBs associated with high-mass star [M>20 Msun] --> tracers of star formation? Text Additional contribution from galaxies too faint to be detected directly? or...imf...metallicity effects Why cool?: We can detect GRBs irrespective of luminosity of galaxy in which it went off. If faint end slope of the UV -luminosity function is steep [alpha < -2], then luminosity density - and SFR density - dominated by low-luminosity galaxy, we would not be able to detect. However, we could detect GRBs going off in them!
Summary We can understand basic properties of stars from hydrostatic equilibrium & virial theorem mass-radius; mass luminosity; temperature-luminosity; mass range If gas is turned into stars, then the initial mass function (IMF) describes the number of stars as a function of stellar mass M. Inferring IMF is challenging. Most data consistent with universal IMF. At M > Msun Text UV [& IR] emission is tracer of ongoing star formation. Universe most actively transforms gas into stars at z=2-3. Present-day activity is much reduced. Likely related to reduced gas accretion rates onto galaxies