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
• nly for those massive

halos that did not have progenitors forming Population III stars. In the absence of a UV background this is essentially impossible.

• The figure shows the

most likely redshift when a 108 M halo had a progenitor with mass 106 M.

10 14 18

Multiplicity

• We saw that the Jeans mass is given by:
• The total gass mass is only Mgas = 0.173M so that requiring MJ

to be equal to Mgas gives us a condition for the change in temperature.

• We find that the required T/T0 ~ 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

• f 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 MJ to be equal to 0.173 M/Ns where Ns 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 H2 (through the Solomon process) without any shielding by neutral Hydrogen.

Feedback

• A background in the Lyman-Werner

bands is important because by dissociating H2 can prevent the formation of other Population III stars.

• Before this is possible, sufficient

Lyman-Werner photons must be produced to dissociate cosmic H2 which would otherwise shield other halos.

Feedback

• Adopting for a Population III star a 105 K black body

we find that during its lifetime a star emits of the order

• f 1.7 ×1063 LW photons.
• Absorbing a LW photon dissociates H2 with

probability of 15% so a star destroys 2.5 ×1062 H2

• molecules. This is all H2 contained in a volume of 17

Mpc3.

• Thus cosmic H2 will be dissociated when the

cumulative Pop III density reaches 0.06 Mpc-3 with a corresponding background JLW = 1.6 ×10-24 erg s-1 cm-2 Hz-1 sr-1.

Feedback

• For higher backgrounds H2 forming inside collapsing halos will begin to

dissociate.

• We can compute this effect by requiring the dissociation timescale τdiss

and the formation timescale τform to be equal. τdiss= 1/(4π 1.1×108 JLW) s. τform=3.23 × 1013 s (M/106 M)-2.22 [(1+z)/31]-7.83.

• Where we have derived τform from the formation rate km multiplied by the

electron density ne = x nHI.

• From τdiss= τform we find:
• Where J21 = JLW*1021.

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 JLW and the minimum critical mass.

• Only halos more massive than MC will contribute to

the mass at any z.

Feedback

• The figure shows the Pop III

cumulative density per comoving Mpc3 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 106 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 hydrogen is compensated by the increase in the density of free electrons that catalyze the formation of molecular hydrogen.

Isolated halo Pre-ionized halo

M =2.5 105 M

• 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
• f 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

• f halos.

Local Feedback

The First QSOs

• The known QSOs at redshift 6 are extremely rare with a density
• f about 0.5 Gpc3 and they must be powered by black holes of

large mass (few 109 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.

The First QSOs

• The standard paradigm for black hole growth (in the absence of

mergers) is that of Eddington-limited accretion with dMBH/dt = ξLEdd/c2 where the parameter ξ is connected to the accretion efficiency ε as follows:

• The luminosity is related to the accretion flow : L = ε dM/dt c2. The

mass not converted to energy is accreted by the BH so that dMBH/dt = (1- ε) dM/dt. This gives us ξ= (1- ε) / ε. Generally one takes ε = 0.1.

• Since Ledd is proportional to M the equation for the BH mass is an

exponential growth with time constant, called Salpeter time, given by:

The First QSOs

• With ε=0.1 the Salpeter time is about 45 Myrs.

Growing from, ~5 M to 3×109 M requires 20 e- folding times, i.e. 900 Myrs, which implies that the BH would have to grow at the Eddington rate throughout all the time from very high redshift down to z=6.

• Population III stars leave a few 100 M BH at z=50

reducing the growth need 16-17 e-folding times.

• However, extended Eddington accretion is

considered unlikely because of the role of mergers and of the fuel supply.

The First QSOs

• When halos with black holes merge the black

hole may be ejected. Ejected black holes will stop accretion. Even without ejection the accretion disk will be disrupted.

Most black holes may be unable to survive merger events

The First QSOs

• Even if mergers were not a threat, being able

to accrete at the Eddington rate for a long time requires a very steady fuel supply that is not distrupted by infalling gas, supernovae, etc.

• Most seed black holes will not be capable of

accreting at this rate.

The First QSOs

• In the volume of a z=6 QSO there are thousands of

Population III stars at z=45-50 so it is easy to postulate that one of them will be in an environment suitable for such growth.

• Only those in the most favorable conditions will be

able to accrete at the Eddington rate. The fact that this is a rare event is needed to avoid overproducing bright QSOs.

• Mergers are less important when the BH masses are
• unequal. Thus, in one BH manages to grow

significantly before the first merger it will be able to continue doing so.

The First QSOs - Another model

• Because of the problems of accretion from a single stellar mass

seed another model has been proposed where a black hole of 104 M forms from direct collapse of a primordial composition neutral hydrogen cloud in a 108 M halo (Begelman, Volonteri, Rees).

• The cloud needs to be primordial in composition because in the

presence of metals it would cool and fragment into stars.

• However, in order to remain primordial the formation of Pop III

stars in 106 M progenitor halos needs to be suppressed. This is possible only if the halo collapses after the Lyman-Werner background is in place.

The First QSOs - Another model

• Even with primordial metallicity, collapse to a BH instead of

formation of stars requires somewhat special initial conditions to avoid fragmentation.

• More detailed modelling shows that these late forming halos live

preferentially in voids.

• Thus, one would predict early QSOs to be anti-biased which is

not observed.

• Both models for early QSO formation have some difficulties. My

personal preference is for the one where formation is started from a stellar seeds (since they will likely exist).

Bibliography

• Stiavelli, First stars and reionization, Wiley
• Peebles, Principles of physical cosmology, Princeton
• Peacock, Cosmological Physics, Cambridge
• Bromm & Larson, 2004, ARAA, 42, 79
• MANY papers: Galli&Palla, Abel, Oshea&Bryan.