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大爆炸 --- 宇宙的起源. 『 從原子到宇宙 』 課程 第十六週 胡維平 國立中正大學化學暨生物化學系 12/22/2011. Static Universe?. Edwin P. Hubble 1889-1953 Discover other galaxies in 1923 Discovery the expansion of the Universe in 1929 Observation support for the Big Bang Theory. Mount Wilson Observatory in California.

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Edwin P. Hubble


Discover other galaxies in 1923

Discovery the expansion of the Universe in 1929

Observation support for the Big Bang Theory

Mount Wilson Observatory in California

The 100-inch (2.5 m) Hooker telescope at Mount Wilson Observatory that Hubble used to measure galaxy distances and a value for the rate of expansion of the universe.


Henrietta Swan Leavitt


Discover the period-luminosity relationship of Cepheid variable stars in 1912



H = 500 km/s/Mpc

T = 1/H = 20億年?

1 pc = 3.26 ly


The factor H0, now called the Hubble constant, is the expansion rate at the present epoch. Hubble's measurements of H0 began at 550 km s-1 Mpc-1; a number of systematic errors were identified, and by the 1960s H0 had dropped to 100 km s-1 Mpc-1. Over the last two decades controversy surrounded H0, with measurements clustered around 50 km s-1 Mpc-1 and 90 km s-1 Mpc-1. There is now a general consensus that H0 = 70.8 (km/s)/Mpc. The inverse of the Hubble constant - the Hubble time - sets a timescale for the age of the Universe: 1/H0 = 13.8 Gyr.

big bang theory
Big Bang Theory

In 1927, Georges Lemaître, a Belgian physicist and Roman Catholic priest, proposed that the inferred recession of the nebulae was due to the expansion of the Universe. In 1931 Lemaître suggested that the evident expansion of the universe, if projected back in time, meant that the further in the past the smaller the universe was, until at some finite time in the past all the mass of the Universe was concentrated into a single point, a "primeval atom" where and when the fabric of time and space came into existence.

Lemaître's Big Bang theory was advocated and developed by George Gamow, who introduced big bang nucleosynthesis (BBN) and whose associates, Ralph Alpher and Robert Herman, predicted the cosmic microwave background radiation (CMB).


Cosmic Microwave Background

The cosmic microwave background (CMB) radiation is an emission of uniform, black body thermal energy coming from all parts of the sky. The radiation is isotropic to roughly one part in 100,000. As the universe expanded, adiabatic cooling caused the plasma to lose energy until it became favorable for electrons to combine with protons, forming hydrogen atoms. This recombination event happened when the temperature was around 3000 K or when the universe was approximately 379,000 years old. At this point, the photons no longer interacted with the now electrically neutral atoms and began to travel freely through space, resulting in the decoupling of matter and radiation.The color temperature of the decoupled photons has continued to diminish ever since; now down to 2.725 K, their temperature will continue to drop as the universe expands.

too smooth?


WMAP data reveals that its contents include 4.6% atoms, the building blocks of stars and planets. Dark matter comprises 23% of the universe. This matter, different from atoms, does not emit or absorb light. It has only been detected indirectly by its gravity. 72% of the universe, is composed of "dark energy", that acts as a sort of an anti-gravity. This energy, distinct from dark matter, is responsible for the present-day acceleration of the universal expansion. WMAP data is accurate to two digits, so the total of these numbers is not 100%. This reflects the current limits of WMAP's ability to define Dark Matter and Dark Energy.


Inflation Theory

Inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part of the electroweak epoch following the grand unification epoch. It lasted from 10−36 seconds after the Big Bang to sometime between 10−33 and 10−32 seconds. Following the inflationary period, the universe continues to expand. The inflationary hypothesis was originally proposed in 1980 by American physicist Alan Guthin 1980.


一般相信在大爆炸之後約 0.0001 秒左右溫度降至 1012K,此時宇宙中的質子與中子脫離與輻射線的平衡而成型。到了大約在大爆炸之後四秒左右溫度降至低於 1010 K,此時宇宙中的電子也脫離與輻射線的平衡而成型。至此,構成原子的基本粒子都已經出現,但由於溫度仍然太高,宇宙中尚無重於氫的穩定原子核,此時宇宙中充斥著高速運動的質子、中子、與電子以及非常高能量的輻射線。


Big Bang Nucleosynthesis

Where did all the atoms come from?

在大爆炸後約三分鐘,質子與中子開始可以結合而成重氫的原子核而不立刻被光子所分解。接下來一連串的核反應將絕大部分的重氫很快的轉變成包含二個質子及二個中子的穩定氦 (He) 原子核。然而,比氦更重的原子核此時不易形成因為自然定律中不容許有原子量為五或八的穩定原子核存在;而缺乏這些作為橋樑的原子核,更重的原子核不易快速的被製造出來,而宇宙仍持續的膨脹、冷卻。在大約宇宙生成 30 分鐘後,大爆炸所產生的核反應完全停止進行。此時,宇宙中的物質以質量而言約含 75% 的質子、25%的氦原子核、大量很輕的電子、以及非常微量的重氫及鋰原子核。


Formation of atoms and the last scattering

此時的宇宙溫度仍然非常高 (108 K 左右),強大的輻射線使電子無法停留在固定的原子核上,物質主要以單原子離子狀態存在。由於自由運動的電子很容易散射光線,此時宇宙是處於名符其實的混沌狀態;光子無法自由穿越,輻射場與物質間不斷的進行能量交換。這種情況一直持續到了大約四十萬年後,當宇宙的溫度降到了約一萬度以下,電子才開始能與原子核結合型成中性的原子,宇宙也在此時變成透明,輻射場與物質間的作用大幅降低,而重力的作用正開始逐漸朔造新的宇宙結構。


First Stars

Formed 200-400 million years after Big Bang

Mass: 100-300 solar mass

Lifetime = a few million years

Became Black holes, Supernovaes

Simulated image of the first stars, 400 million years after the Big Bang.


Proton-Proton (PP) Chain in the Sun

T > 10 Million K

Inside the Sun, about 655 million tons of hydrogen are converted into 650 million tons of helium every second. In stars heavier than about 2 solar masses, in which the core temperature is more than about 18 million K, the dominant process in which energy is produced by the fusion of hydrogen into helium is a different reaction chain known as the carbon-nitrogen cycle.

the cno cycle
The CNO Cycle

The carbon-nitrogen-oxygen cycle, a cycle of six consecutive nuclear reactions resulting in the formation of a helium nucleus from four protons. The carbon nuclei with which the cycle starts are effectively reformed at the end and therefore act as a catalyst. This is believed to be the predominant energy-producing mechanism in stars with a core temperature exceeding about 18 million K.


The triple alpha process

When the star starts to run out of hydrogen to fuse, the core of the star begins to collapse until the central temperature rises to ~100×106 K. At this point helium nuclei are fusing together at a rate high enough to rival the rate at which their product, beryllium-8, decays back into two helium nuclei. This means that there are always a few beryllium-8 nuclei in the core, which can fuse with yet another helium nucleus to form carbon-12, which is stable

4He + 12C  16O (a process)

Ordinarily, the probability of the triple alpha process would be extremely small. However, the beryllium-8 ground state has almost exactly the energy of two alpha particles. In the second step, 8Be + 4He has almost exactly the energy of an excited state of 12C. These resonances greatly increase the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted by Fred Hoyle before its actual observation, based on the physical necessity for it to exist, in order for carbon to be formed in star.


Carbon Burning

The carbon-burning process is a set of nuclear fusion reactions that take place in massive stars (at least 8 solar mass at birth) that have used up the lighter elements in their cores. It requires high temperatures (> 5×108 K) and densities (> 3×109 kg/m3)

Oxygen Burning

The oxygen-burning process is a set of nuclear fusion reactions that take place in massive stars that have used up the lighter elements in their cores. It occurs at temperatures around 1.5×109 K and densities of 1010 kg/m3.


Silicon Burning to Iron

After high-mass stars have nothing but sulfur and silicon in their cores, they further contract until their cores reach temperatures in the range of 2.7–3.5 GK; silicon burning starts at this point. Silicon burning entails the alpha process which creates new elements by adding the equivalent of one helium nucleus (two protons plus two neutrons) per step in the following sequence: (to Fe and Ni)


For a star with 15 solar mass:

Less and less energy is produced per nuclear reaction in the nucleosynthesis of these high mass elements. So each burning phase lasts a shorter and shorter amount of time.



The r-process is a nucleosynthesis process, likely occurring in core-collapse supernovae (see also supernova nucleosynthesis) responsible for the creation of approximately half of the neutron-rich atomic nuclei that are heavier than iron. The process entails a succession of rapid neutron captures (hence the name r-process) on seed nuclei, typically Ni-56.


Neutron Stars

A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II supernova event. Such stars are composed almost entirely of neutrons. A typical neutron star has a mass between 1.35 and about 2.0 solar masses, with a corresponding radius of about 12 km

In general, compact stars of less than 1.44 solar masses – the Chandrasekhar limit – are white dwarfs, and above 2 to 3 solar masses, a quark star might be created; Gravitational collapse will usually occur on any compact star between 10 and 25 solar masses and produce a black hole.

D = 5×1017 kg/m3 = 5×108 ton/cm3


Circumstellar rings around SN 1987A, with the ejecta from the supernova explosion at the center of the inner ring


Black Hole

If the mass of the remnant exceeds about 3–4 solar masses (the Tolman–Oppenheimer–Volkoff limit)—either because the original star was very heavy or because the remnant collected additional mass through accretion of matter—even the degeneracy pressure of neutrons is insufficient to stop the collapse. No known mechanism (except possibly quark degeneracy pressure, see quark star) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.

escape velocity > speed of light


Supermassive Black Hole

A supermassive black hole is the largest type of black hole in a galaxy, on the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.