The Formation of the First Stars Massimo Stiavelli STScI - PowerPoint PPT Presentation

The Formation of the First Stars Massimo Stiavelli STScI Baltimore (MD, USA)

Plan of the Lectures 1. Physical Conditions after Recombination, Cooling, Density Perturbations 2. Formation of the First Stars, Properties of the First Stars, Death of the First Stars 3. Feedback and Self-Regulation, the First Star Clusters, First Quasars 4. Photometric redshifts: methods and limitations

Multiplicity • So far we have considered the case of a single star forming in each halo. This is accurate for low mass halos but is no longer correct for the more massive halos that we are now considering. • We can repeat the analysis on the minimum mass for the onset of the Jeans instability in order to derive a condition for multiplicity.

Multiplicity • The analysis is valid only for those massive 10 halos that did not have 14 progenitors forming 18 Population III stars. In the absence of a UV background this is essentially impossible. • The figure shows the most likely redshift when a 10 8 M  halo had a progenitor with mass 10 6 M  .

Multiplicity • We saw that the Jeans mass is given by: • The total gass mass is only M gas = 0.173M so that requiring M J to be equal to M gas gives us a condition for the change in temperature. • We find that the required T/T 0 ~ 7.

Multiplicity • Thus, the onset of the Jeans instability requires a temperature: • We can compute the cooling timescale at this temperature as:

Multiplicity • The collapse timescale is given by: • Requiring the two timescales to be identical gives us a condition on the required molecular hydrogen fraction. Requiring that this fraction be smaller than the maximum fraction derived previously gives us a condition on the mass:

Multiplicity • Halos that are more massive than the fragmentation mass will have a collapse timescale slower than the cooling time scale. • This means that they will continue cooling before collapsing. • By cooling further the Jeans mass will decrease even further and when cooling is finally halted at 120K the Jeans mass will be only a fraction of the total gas mass enabling simultaneous Jeans instabilities with the resulting fragmentation and formation of multiple stars.

Multiplicity • We can derive the maximum number of stars that can form in a halo of a given mass (the multiplicity) by requiring the Jeans mass M J to be equal to 0.173 M/N s where N s is the stellar multiplicity. • Using the expression for the Jeans mass we find that the maximum multiplicity of an halo above the minimum fragmentation mass is:

Multiplicity • This result relies on the fact that molecular hydrogen cooling becomes ineffective below 120K. • Considering the cooling function in the presence of metals we find that for Z > 5 10 -6 Z  metal cooling becomes more effective than molecular hydrogen cooling. • Thus, for Z > 5 10 -6 Z  we should expect halos to fragment much more efficiently and form lower mass stars.

Feedback • Population III stars are very luminous and they will affect their environment. • We will focus on the Lyman-Werner continuum, i.e. on photons with energy between 11.18 and 13.6 eV which are able to photo-dissociate H 2 (through the Solomon process) without any shielding by neutral Hydrogen.

Feedback • A background in the Lyman-Werner bands is important because by dissociating H 2 can prevent the formation of other Population III stars. • Before this is possible, sufficient Lyman-Werner photons must be produced to dissociate cosmic H 2 which would otherwise shield other halos.

Feedback • Adopting for a Population III star a 10 5 K black body we find that during its lifetime a star emits of the order of 1.7 × 10 63 LW photons. • Absorbing a LW photon dissociates H 2 with probability of 15% so a star destroys 2.5 × 10 62 H 2 molecules. This is all H 2 contained in a volume of 17 Mpc 3 . • Thus cosmic H 2 will be dissociated when the cumulative Pop III density reaches 0.06 Mpc -3 with a corresponding background J LW = 1.6 × 10 -24 erg s -1 cm -2 Hz -1 sr -1 .

Feedback • For higher backgrounds H 2 forming inside collapsing halos will begin to dissociate. • We can compute this effect by requiring the dissociation timescale τ diss and the formation timescale τ form to be equal. τ diss = 1/(4 π 1.1 × 10 8 J LW ) s. τ form =3.23 × 10 13 s (M/10 6 M  ) -2.22 [(1+z)/31] -7.83 . • Where we have derived τ form from the formation rate k m multiplied by the electron density n e = x n HI . • From τ diss = τ form we find: • Where J 21 = J LW *10 21 .

Feedback • We can obtain the cumulative number of Population III stars ignoring feedback simply by using the dark halos statistics. • Feedback can be incorporated considering that each star will produce a given number of LW photons, by computing at each redshift the buildup of J LW and the minimum critical mass. • Only halos more massive than M C will contribute to the mass at any z.

Feedback • The figure shows the Pop III cumulative density per comoving Mpc 3 without (dashed) or with (solid red) LW feedback. • At later redshift also chemical feedback will become important.

Feedback • A more complete treatment will include a delay in the formation of a star and consider the probability that halos can be pre-enriched by previous generations of stars so that they can no longer form Population III stars. • The plot on the right includes radiative and chemical feedback but doesn’t include winds.

Contribution to Reionization • Population III stars will contribute to reionization. However, this contribution is modest because of the negative LW feedback. • A crucial factor in deriving the contribution to reionization is the estimation of the escape fraction of UV photons. The plot on the right gives the escape fraction including multiple stars per halo. The upper lines are for 300 M  , the lower ones for 150 M  . The dotted lines are for the case without multiplicity.

Contribution to Reionization • Population III stars can partially ionize the Universe to an ionized fraction x ≤ 0.1. The precise details depend on the model but the contribution generally remains minor.

Local Feedback • The ionizing radiation from a Population III star includes photons with energy significantly higher than the ionization energy of Hydrogen. This excess energy is available for heating up the HII region. • Let’s compute the excess energy assuming that all ionizing photons are absorbed:

Local Feedback • If the column density of Hydrogen is lower and some of the photons escape because their ionization cross section is lower a more relevant quantity is the weighted excess energy which accounts for the ionization cross section: • In practice the relevant number will be somewhere these two values.

Local Feedback • Let’s compute the value of the excess energy as a function of temperature: • At increasing temperature the difference between these two values increases.

Local Feedback • The more interesting quantity is the equilibrium temperature of the HII region. This is found by requiring that the heating term (from the excess energy) is equal to the cooling mechanisms: recombination cooling, breemstrahlung, collisional excitation cooling, collisional ionization cooling, and inverse Compton cooling (the latter relevant only for z>50). • The equilibrium temperature is:

Local Feedback • The ultraviolet continuum of a Population III star ionizes the neighborhood of the object. • We can compute the total gas mass contained within the radius of the Stroemgren sphere and obtain the halo mass by dividing by 0.173. This gives the maximum halo mass that can be ionized completely: • Population III stars with mass below 130Ms are unable to fully ionize a halo with mass of 10 6 M  . • Comparing the thermal velocity of the ionized gas to the escape velocity of the halo shows that the ionized gas is too hot to be confined by the halo and all gas is lost to the IGM.

Local Feedback • The halo mass able to contain all gas ionized by a 300 M  Population III star can be computed by deriving the equilibrium temperature of the gas and comparing it to the escape velocity.

Local Feedback • Local ionization may actually provide positive feedback because the complete destruction of molecular M =2.5 10 5 M  hydrogen is compensated by the increase in the density of free electrons that catalyze Isolated halo the formation of molecular hydrogen. Pre-ionized halo

Local Feedback • A calculation of the gas escape for the case of a Pair instability supernova shows that much more significant halo masses are needed to contain the gas heated by the supernova: • The gas in such halo is enriched to 1.5 10 -4 Z  . Subsequent generations of stars may have a mass function extending to lower masses because this content of metals is sufficient to make cooling effective below the 120 K limit of molecular hydrogen which sets the maximum multiplicity of halos.

The First QSOs • The known QSOs at redshift 6 are extremely rare with a density of about 0.5 Gpc 3 and they must be powered by black holes of large mass (few 10 9 M  ). • This is estimated requiring the observed luminosity to be lower than the Eddington luminosity: • Explaining how such massive black holes can grow in less than 1 Gyr is non-trivial.