elements of observational cosmology 14.05.2009 cosmic star formation history: evolution of galaxies ...
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Elements of observational cosmology
14.05.2009 Cosmic star formation history: evolution of galaxies general framework modelling
Cosmic star formation history Galaxies contain:
stars gas dust dark matter
The physics of galaxy formation deals with:
the dynamics of stars (gravitational interactions),
thermodynamics of gas energy production of stars. Stars form from gas clouds,
but new stars heat these clouds, which dissipates them and stops the formation of other stars.
Cosmic star formation history: protogalaxies
After recombination, the overdensities in the Universe started to grow.
The first pieces of matter that broke free of the Universe's expansion consisted mostly of dark matter + some neutral hydrogen with a tiny amount of helium.
Credit: James Schombert, University of Oregon
Cosmic star formation history: protogalaxies
Once such an object begins to collapse under its own gravity, it is called a protogalaxy.
Credit: James Schombert, University of Oregon
Cosmic star formation history: protogalaxies
Dark matter and ordinary matter (i.e. hydrogen and helium gas) separated at this time.
It is because gas can dissipate its energy through collisions. The atoms in the gas collide and heat up, the heat is radiated in the infrared light. The result is the gas loses energy, moves slowly and collapses to the center.
Dark matter does not interact this way and continues to orbit in the halo.
Credit: James Schombert, University of Oregon
Cosmic star formation history: protogalaxies
Even though there are no stars yet, protogalaxies should be detectable by their infrared or submm emission (i.e. their heat). However, they are very faint and very far away, so we have not been successful in discovering them at that early stage (before star forming) yet.
Credit: James Schombert, University of Oregon
Cosmic star formation history: star formation in protogalaxies
As the gas in the protogalaxy loses energy, its density goes up. Gas clouds form and move around in the protogalaxy on orbits. When two clouds collide, the gas is compressed into a shock front.
Credit: James Schombert, University of Oregon
Cosmic star formation history: star formation in protogalaxies
The first stars in a galaxy form and start production of the first photons by thermonuclear fusion. The galaxy becomes a primeval galaxy (but still often called a protogalaxy in the period of its first “virgin” starburst).
Credit: James Schombert, University of Oregon
Cosmic star formation history: protogalaxies
Deep observations by the Spitzer Space Telescope in IR: a diffuse glow, possibly from first generation stars (hundreds of times more massive than Sun). The infrared background light shows bright patches that might have originated from clusters of these first objects. Gray areas depict places where nearby foreground stars from our Milky Way Galaxy were digitally removed.
Spitzer, Kashlinsky et al. 2007
Cosmic star formation history: star formation in protogalaxies
Star formation sites in primeval galaxies are similar to star forming regions in present-day galaxies, like Milky Way: a group of young stars embedded in a cloud of heated gas. The gas will eventually be pushed away from the stars to leave a star cluster. Star Forming Region NGC 3582
Credit & Copyright: T. A. Rector (U. Alaska), T. Abbott, NOAO, AURA, NSFredit: James Schombert, University of Oregon
Cosmic star formation history: star formation in protogalaxies
The first stars in our Galaxy are the globular star clusters orbiting in the halo, outside the stellar disk with the spiral arms. Most galaxies with current star formation now have an underlying distribution of old stars from the earlier epochs of star formation.
Credit: SAO
Cosmic star formation history: protogalaxies and the
beginnings of globular clusters Today's globular
clusters: have a form very close
to a sphere Contain ~ 100 000
stars Located in the galaxy
halo and very seldom in the disc
Globular Cluster M13Credit: ESO
Globular clusters as the birth places of the first stars in the
Universe: H-R diagram
Globular Cluster 47 Tucanae: much more “evolved”, mainly old stars of the II population
Open Cluster NGC 7789
Cosmic star formation history: protogalaxies and the
beginnings of globular clusters Today's globular
clusters: contain much less
metals than younger objects which confirms they formed from a primeval gas not yet enriched by supernovae
Parmentier & Gilmore 2001
Cosmic star formation history: death of the first stars
The most massive stars end their lives as supernovae. The first stars, built only from hydrogen, we more massive than today's newly born stars and ended their lives soon in supernovae explosions.
This shell of enriched gas is ejected into the galaxy's gas supply. Thus, the older a galaxy, the more rich its gas is in heavy elements, a process called chemical evolution.
Cosmic star formation history: death of the first stars and enrichment of the
interstellar medium
This shell of enriched gas is ejected into the galaxy's gas supply. Thus, the older a galaxy, the more rich its gas is in heavy elements, a process called chemical evolution.
Credit: M. Rawlinson
Galaxy evolution: nature or nurture
In other words, is the fact that we observe elliptical and disc galaxies related to their initial properties or rather to their surroundings?
There is no simple answer to that.
Galaxy evolution: nature
If “nature”: the present appearance of a galaxy could be related to the dynamic of the gas infal in the very beginnging, hence its initial halo mass
Galaxy evolution: nurture
However, galaxies do not live separated from the others: there are many processes that can occur between them and cause a different evolution of galaxies in denser environments: mergers, stripping, harassment...
The global SFH
Is traced by the chemical evolution of galaxies, i.e. the history of the metal production in galaxies.
Also the rest-frame UV luminosity of galaxies is supposed to trace well their metal production rate, because both are produced primarily by massive stars. In practice the conversion from a UV luminosity density to an actual cosmic star formation rate is not straightforward, since it involves a knowledge of the Initial Mass Function (what was the N(M) vs M of stars in a galaxy/galaxies in the beginning?). And also not sufficient since a large part of the UV light is “eaten” by the dust.
The global SFH
Early estimates of the metal production rate as a function of redshift (based on the redshift and data from QSO absorption line systems) indicated a monotonic increase in the metal production rate from z = 0 to z ~ 1 (with the rate at z ~ 1 about 10x higher than now).
The global SFH: the Madau plot (Madau et al. 1996) from HDF-N
Element and star formation history of the universe. The data from various surveys (metal lines + UV rest frame luminosity) provided a measurement or a lower limit to the universal metal ejection density, dot(ρ
Z), as a function of
redshift. Translation it into into a total star formation density, ρ , depends on the Initial ∗Mass Function. For example for a Salpeter mass function of 42 should be applied.
The global SFH: the Madau plot (Madau et al. 1996)
K Triangle: Gallego et al. (1995). Filled dots: Lilly et al. (1996). Diagonal cross: lower limit from Steidel et al. (1996a). Filled squares: lower limits from the Hubble Deep Field images. The dashed line depicts the fiducial
rate, ΣZ , given by the mass
density of metals observed today divided by the present age of the universe (see text for details). A flat cosmology with
q0 = 0.5 and H
0 = 50 km s−1
Mpc−1 has been assumed.
The global SFH: the Madau plot In this original diagram, no
corrections were made, for either dust extinction or for surface brightness effects. Consequently, the results were presented as lower limits.
Both in the original work and in some of the subsequent works (e.g. including partially the effects of dust extinction), it was found that the star formation rate peaks at a redshift of z ~ 1-2 and decreases or stays nearly constant at higher redshifts
Ferguson, Dickinson & Williams 2000
The global SFH: the Madau plot
We clearly observe the rise in the star formation rate in the past until z~2.
Most of the investigations until now concluded that the star formation rate rises from the present to z ~ 1-2 and then stays approximately flat to z ~ 5.
However, is it a real decrease of the star formation rate for z>2? Possible problems: dust extinction (still poorly understood) selection effects cosmological surface brightness dimming.
Another approach: the evolution of stellar masses
Another way to address the question of the history of mass assembly in galaxies is to try to measure the actual stellar masses of galaxies (as opposed to the rates of star formation): how the amount of stellar mass in galaxies changes with cosmic time?
Pozzetti et al. 2007
108 M ≤M* ≤ 10⊙ 13 M ⊙
Another approach: the evolution of stellar masses
By z ~ 1, about 50-75% of the present-day stellar mass density had already formed, but at z~2.5 it was significantly lower from today's. However, difficult to say how much - from 4.5 to 17 times (depending on the survey).
Pozzetti et al. 2007
108 M ≤M* ≤ 10⊙ 13 M ⊙
When we try to model it precisely, galaxy evolution is
traced by: Stellar evolution:
As we have seen, galaxies evolve in various senses. Among others, the most prominent aspect of galaxy evolution is that of stellar population and resulting change of metallicity, appearing in their colors and spectral features (lines, breaks, etc.). This is the key factor of galaxy evolution.
Chemical evolution In general, we use evolutionary synthesis models of
galaxies
Evolution of Stars
The life of stars is determined by their initial mass.
Light stars live long, end with a moderate ejection of gas and subsequent cooling.
Heavy stars live short, end with violent explosions and mass ejections.
Stellar evolution: the Hertzsprung-Russel (HR) diagram
(Schaller 1992)
This (theoretical) HR diagram represents a relationship between the effective temperature and luminosity of stars.
Stellar evolution: the Hertzsprung-Russel (HR) diagram
(Schaller 1992)
Timescales:Main sequence lifetimes1.0 Msun: 9.0×109 yr2.2 Msun: 5.0×108 yr15 Msun: 1.0×107 yr
Giant branch lifetimes1.0 Msun: 1.0×109 yr2.2 Msun: 3.8×107 yr15 Msun: 1.5×106 yr
Observed HR diagram
Messier 3 (M3): a globular cluster
Life of stars and their nucleosynthesis
Stars produce heavy elements by the nuclear reaction, and how far the reaction goes depends on the mass of stars.
Lighter than the Sun
Heavier than the Sun
Core temperature
107 K 108 K 3 * 108 K 109 K 5 * 109 K
Birth H-burning He-burning C, O-burning Si-burning
Supply of metals to the intergalactic space occurs
mainly by: Stellar winds Matter ejections in the final stages of life of
(more or less massive) stars
Supply of metals to the interstellar space I: stellar wind
Some of very massive stars expel their outer hydrogen layer by radiation pressure: stellar winds. This occurs for almost all stars, but is especially efficient for OB and Wolf-Rayet stars.
This is often observed with a specific spectral feature: P-Cygni profile.
Supply of metals to the interstellar space I: stellar wind
WR124
Stars with masses similar to the Sun run out the hydrogen in the core, change their equilibrium structure and expand, and become cool huge stars (red giant branch stars: RGBs).
After the RGB phase, these stars become unstable and repeat expansion and contraction (thermal pulse asymptotic giant branch stars: TPAGB). Because of this pulsation, the outer layer of a star is expelled into the interstellar space and forms a gas nebula, called planetary nebula (PN). The nebulae expand into the space and mix with the interstellar medium (ISM), and provide heavy elements contained in the gas.
The death of light stars : planetary nebulae (PNe)
Supply of metals to the interstellar space II: final life stages of stars
M57 (Ring Nebula)
NGC6543 (Cat’s Eye Nebula)
Menzel 3 (Ant Nebula)
PK285
Then, finally they end their life with a very energetic explosion (supernova: SN). The ejected gas from a star forms a nebula, called a supernova remnant (SNR). This also provides the ISM with heavy elements.
The death of heavy stars : supernovae explosions
Stars several times heavier than the Sun repeat expansion and contraction, and change their internal structure a few times depending on the mass.
Heavy elements supplied by SN II
M1 (Crab Nebula)
Supernova II remnant
Supernova II remnant
N132D (LMC SNR)
Blue: [OI]Green: [OIII]Red: [SII]
A significant fraction of stars are born as binaries. The last stage of such stars are different from that of single stars because of mass exchange between them.
The death of binary stars : Type Ia supernova (SN Ia)
Supply of metals to the interstellar space II: final stage of stars
Stars with M < 8Msun end as white dwarfs. WDs in a binary system can often accrete gas from a close companion star. Then, it finally exceeds a critical mass and collapses, resulting in a runaway fusion reaction: Type Ia supernova (SN Ia). Each SN Ia produces Fe of 0.3-1.3 Msun, i.e., SN Ia is the most important source of iron in a galaxy.
Type Ia supernova: the Roche robe
The mass transfer is determined by the Roche potential:
where is the rotation period and s is the distance to the rotation axis.
The equipotential surface enclosing both stars and passing the Lagrange point L1 is called the Roche robe.
Type Ia supernova: schematic picture of binary mass transfer
Type Ia supernova: binary evolution
Heavy elements supplied by SN Ia
Tycho’s SNR
Supernova Ia remnant
Chandra images
Chemical Evolution of GalaxiesChemical Evolution of Galaxies
The ISM of galaxies is compressed and cooled by various mechanisms, and form dense gas clouds. At the center of these clouds, nuclear reactions begin and the clouds become stars.
Stars produce heavy elements and returns them back to the ISM. Gas mixed with the heavy elements form stars more easily than pristine gas because they can cool by various line radiation processes, and accelerate subsequent star formation of the galaxy in which they reside.
However, less massive stars live long and hardly return gas into the ISM. Hence, the rest of gas reduces and finally runs out. This is the end of the star formation of a galaxy.
The star formation revives when gas is newly provided, e.g., via merging or infall of other galaxies.
ISM
Star formation
Stellar evolution
Stellar death
Mass ejection
Mass ejection
Stellar winds PNe
SNRs
Supply of heavy elements
Heavy element production
Star formation in galaxies is affected by the amount of heavy elements which galaxies ever produced.
The history of the amount of stars formed in galaxies is called the star formation history (SFH). This is what we really see in the Madau plot.
Heavy element production
Heavy element production
Chemical evolution of galaxies
Chemical evolution of galaxiesChemical evolution of galaxies
The produced heavy elements are not always in a gas state: indeed, more than a half of the heavy elements form tiny solid grains, called dust. Dust grains are usually suspended within the ISM in galaxies.
Star formation activity is closely related to heavy element production. This therefore mean that the star formation is also connected to the production of dust.
Hence, intense star formation always accompanies active dust production. On the other hand, dust grains also accelerate the efficiency of star formation. The interplay between the star formation and dust is very complex and nonlinear.
ISM
Star formation
Stellar evolution
Stellar death
Mass ejection
Mass ejection
Stellar winds PNe
SNRs
Supply of heavy elements
Heavy element production
Heavy element production
Heavy element production
Chemical evolution of galaxies: metal and dust
Chemical ingredients: where they are produced and how they are inserted into the ISM
ISM
Star formation
Stellar evolution
Stellar death
Mass ejection
Mass ejection
Stellar winds PNe
SNRs
Heavy element production
Heavy element production
Dust destruction
DustDust
Dust production
SNRs
Heavy element production
Protoplanetary disk
Dust production
Cool star atmosphere PNe
Dust production
Blast wave by SNe
Supply of heavy elements
Chemical evolution of galaxies: metal and dust
Estimating the SFR from observations is then usually more Estimating the SFR from observations is then usually more complicated than just measuring the UV light of galaxiescomplicated than just measuring the UV light of galaxiesBy using a mass distribution function of stars in their birth (initial mass function: IMF), we can convert the number of massive stars (current “massive SFR”) to the total number of newly born stars, i.e., the total SFR. Since massive stars are what we mainly see, the understanding of the IMF may be the key ingredient.
Some examples of the IMF estimated from observations. The IMF is often approximated by a power-law form with reasonable lower and upper masses.
(Kroupa 2002)
Initial mass function: examples
Salpeter (1955) IMF:
Miller & Scalo (1955) IMF:
Initial mass function: examples
(Pagel 1997)
FUVFIR
Dust
Short-wavelength photons like UV are easily scattered and absorbed by small solid grains like dust (extinction), and re-emitted in the far-infrared (FIR).
Obviously the amount of UV light obscured by dust is only measured at FIR wavelengths. Otherwise this leads us to a serious underestimation of the SFR.
Problem in the Estimation of SFR from UV: dustProblem in the Estimation of SFR from UV: dust
BC93 Fig. 4a BC93 Fig. 4d
Evolutionary synthesis of galaxy spectra: how to use all the ingredients to model the galaxy evolution
(Bruzual & Charlot 1993)
The effect of star formation history
Synthesizing isochrones can convolve with arbitrary star formation history (Green’s function):
with fλ an instantaneous-burst SED, Fλ the spectrum of a population with arbitrary SFR Ψ(t).
(N.B. this assumes time-invariant IMF.)
Commonly used is exponentially decaying SFR:
Evolutionary synthesis of galaxy spectra
Note that emission lines will never be fit (BC93 models only include stars)
Overprediction of flux at blue end, because of internal extinction due to dust
(Bruzual & Charlot 1993)
Evolutionary synthesis of galaxy spectra
Application to irregulars
(Bruzual & Charlot 1993)
Evolutionary synthesis of galaxy spectra
Application to spirals
AGB stars dominate the light of intermediate-age stellar populations
Main Sequence +
He-burning stars dominate the light of young stellar populations
RGB stars dominate the light of old stellar populations
Evolutionary synthesis of galaxy spectra: recent development
Including the late-stage evolution of stars
(Maraston 2005)
The effect of TPAGB stars
(Maraston 2005)
The effect of TPAGB stars
Star formation history of present day galaxies as the key
to the SFR history of the Universe
Local galaxies can be used to study the SFR history of the Universe in two ways: Investigating the SFH of a given galaxy (like
Milky Way) we can assume that all the galaxies of a similar size and conditions (environment, dark halo mass) should have a similar history. E.g. we determine IMF from the MW stars.
But, if the structure formation in the Universe has been hierarchical, it means that the big structures formed first and small structures later (or still forming)
Star formation history of present day galaxies as the key
to the SFR history of the Universe This means, that
some local dwarf galaxies may be exact counterparts of first galaxies which appeared in the Universe
-> Search for local, dwarf, low-metallicity galaxies which have just recently started their stellar production
NGC 1705
Dwarf galaxies
• In number, most of galaxies are dwarfs, though giant galaxies dominates in luminosity.
• Dwarfs are considered to be similar to galaxies in very early Universe in many senses: small size, active star formation, sensitive to feedback effect, etc.
• They have been dismissed for a long time because their small size and luminosity.
Schematic view of the star formation and metallicity history
(Grebel 1998)
SF boxes:
Grebel 1998
SF boxes in dSph’s: Grebel 1998
Physical reason of the structure of dwarfs
1. Low surface brightness2. Low luminosity3. Lack of gas for non-star forming dwarfs
Shallow gravitational potential of dwarf galaxies is the origin of these features:
Once first generation of stars are born, subsequent supernova explosions cause a galaxy-wide stellar wind: galactic wind.If mass of a galaxy is small, gas is accelerated easily and velocity exceeds the escape velocity of the galaxy (we will revisit this issue later).
Binding energy of baryons in the dark halo potential well is
where s: fraction of stellar mass to total baryon mass, M: halo mass, b: mass ratio of baryon to M, and R: galaxy size.We assume that the mass density is the same for all over the galaxy, then we have
Energy input on ISM by SNe
Number of SNe ever occurred
Mass of stars ever formed
∝ ∝
R
M
s
Ms
R
MbME bind
3535bind
sME s
Galactic wind scenario of Dekel & Silk (1986)
Critical value so that the energy of SNe exceed the binding energy of the ISM and the gas is expelled out of the galaxy
N.B. Star formation does not occur when Ms is small
Surface brightness
Ms is small surface brightness and luminosity become ⇒small
3535 sMME ssSN52
sMs
532ss MRMI
Galactic wind scenario of Dekel & Silk (1986)
Additional material: element production
Chemical evolution model: basic equations
(baryon)
Total gas ejection rate of stars is expressed as
(1)
where
mt: turnoff mass at time t = lowest mass of stars dying at time t
m – wm: ejected mass
t-m(m)(m): birth rate at t-m= death rate at time t
m: main sequence lifetime for a star with mass m
Remnant mass:
(2)
Chemical evolution model: basic equations
Evolution of the metal abundance Z is written as
(3)
where
EZ: ejection rate of metal(s) from stars (main sequence stars, Wolf-Rayet stars, SNe, etc.)
Zf: infalling metals per time
ZMg: mass of metal(s) in the gas.
Chemical evolution model: basic equations
Ejection rate of metals reads
(4)
where
(m – wm )Zt-m(m) : mass of metal(s) which was locked in a star of mass m at time t - m(m) and is now ejected at time t,
mpZm: new metal(s) produced by a star of mass m with originally formed from gas with metallicity Z.
N.B. Ansatz in eqs.(3) and (4): instantaneous mixing of produced metal(s) with the ISM.
Chemical evolution model: basic equations
Chemical evolution model: basic equations
Returned mass per mass of stars formed is
(5)
This is independent of star formation rate, thus only valid for a single generation of stars.
Mass of produced metal(s) per remaining stellar mass (including stellar remnant) is called yield. This is expressed as
(6)
Chemical evolution model: instantaneous recycling
As a first order approximation, the instantaneous recycling approximation is often adopted:
1.massive stars die immediately after their birth and less massive stars live forever,
2.produced elements are instantaneously mixed with the ISM, is used.
N.B. This is only valid if the SFR is almost constant over a timescale of 107 yr for lighter elements like O, C, N, Mg, etc.(SN II origin), and of 108-9 yr for heavier elements like Fe (SN Ia origin).
Chemical evolution model: instantaneous recycling
If the instantaneous recycling applies, using R and y and assuming the IMF is constant with time (meaning R = const.), we obtain
(7)
(8)
Inserting eq.(8) into eq.(4), we have
(9)
thus
(10)
Chemical evolution model: instantaneous recycling
As for stellar mass, with eq.(7),
(11)
and for gas mass,
(12)
Then, we have
(13)
These equations are the framework under the instantaneous recycling.
Chemical evolution model: analytic solution for a simple case
Closed-box model
Assume we have a closed system containing only gas with zero metallicity (not essential) and no stars.
Since f = e = 0, Mg(t = 0) = M, Ms(t = 0) = 0,
(14)
(15)
which lead
(16)
or equivalently
(17)
The metallicity of the gas is
(18)
N.B., Z(t) depends only on Mg(t)/M, thus not explicitly on t.
For a simple estimate, we can use
(19)
Chemical evolution model: analytic solution for a simple case
The metallicity of stars can also be obtained as follows.
Under a closed-box assumption, the stars and the gas altogether must contain all elements ever produced. Hence
(20)
1: average metallicity of stars (without metals in remnant)
2: metallicity of gas
3: mass of all metals ejected into the ISM
4: average values with assumption:
Chemical evolution model: analytic solution for a simple case
Thus, we have
(21)
Integrating eq.(11) leads to
(22)
Combining the above, we have
(23)
Finally, we obtain an important result:
(24)
i.e., the average stellar metallicity cannot exceed the average yield.
Chemical evolution model: analytic solution for a simple case