第23章恒星の死The Death of Stars

Arrange the following stars in order of their evolution:

次の星を、進化の順に並べよう。

Would you expect to find any white dwarfs in the Orion Nebula? (See The Birth of Stars and the Discovery of Planets outside the Solar System to remind yourself of its characteristics.) Why or why not?

オリオン大星雲で白色矮星が見つかると予想するだろうか。その理由は何か。「星の誕生と太陽系外惑星の発見」で、この星雲の特徴を振り返ろう。

Suppose no stars more massive than about 2 M_Sun had ever formed. Would life as we know it have been able to develop? Why or why not?

約2 M_Sunより重い星が、これまで一度も生まれなかったとする。私たちの知るような生命は、発達できただろうか。その理由は何か。

Would you be more likely to observe a type II supernova (the explosion of a massive star) in a globular cluster or in an open cluster? Why?

II型超新星〈大質量星の爆発〉は、球状星団と散開星団のどちらで観測される可能性が高いだろうか。それはなぜか。

Astronomers believe there are something like 100 million neutron stars in the Galaxy, yet we have only found about 2000 pulsars in the Milky Way. Give several reasons these numbers are so different. Explain each reason.

天文学者は銀河に約1億個の中性子星があると考えているが、天の川銀河で見つかったパルサーは約2000個にすぎない。この数が大きく異なる理由をいくつか挙げ、それぞれ説明しよう。

Would you expect to observe every supernova in our own Galaxy? Why or why not?

私たちの銀河で起きる超新星を、すべて観測できると予想するだろうか。その理由は何か。

The Large Magellanic Cloud has about one-tenth the number of stars found in our own Galaxy. Suppose the mix of high- and low-mass stars is exactly the same in both galaxies. Approximately how often does a supernova occur in the Large Magellanic Cloud?

大マゼラン雲の恒星数は、私たちの銀河の約10分の1である。大質量星と低質量星の割合が、両銀河でまったく同じだとする。大マゼラン雲では、およそどのくらいの頻度で超新星が起こるか。

Look at the list of the nearest stars in Appendix I. Would you expect any of these to become supernovae? Why or why not?

付録Iの近隣の恒星の一覧を見よう。超新星になるものがあると予想するだろうか。その理由は何か。

If most stars become white dwarfs at the ends of their lives and the formation of white dwarfs is accompanied by the production of a planetary nebula, why are there more white dwarfs than planetary nebulae in the Galaxy?

星の大半が最期に白色矮星になり、その形成に惑星状星雲が伴うなら、銀河に惑星状星雲より白色矮星が多いのはなぜか。

If a 3 and 8 M_Sun star formed together in a binary system, which star would:

3太陽質量と8 M_Sunの星が、連星系で一緒に生まれたとする。次のそれぞれに当たるのは、どちらの星か。

You have discovered two star clusters. The first cluster contains mainly main-sequence stars, along with some red giant stars and a few white dwarfs. The second cluster also contains mainly main-sequence stars, along with some red giant stars, and a few neutron stars—but no white dwarf stars. What are the relative ages of the clusters? How did you determine your answer?

二つの星団を発見した。第一の星団には主に主系列星があり、それに加えて赤色巨星がいくつかと、少数の白色矮星がある。第二の星団にも主に主系列星があり、赤色巨星がいくつかと、少数の中性子星があるが、白色矮星はない。どちらの星団がより古いか。どのように判断したか。

A supernova remnant was recently discovered and found to be approximately 150 years old. Provide possible reasons that this supernova explosion escaped detection.

最近発見された超新星残骸が、約150年前のものとわかった。その超新星爆発が検出されなかった理由として、何が考えられるか。

Based upon the evolution of stars, place the following elements in order of least to most common in the Galaxy: gold, carbon, neon. What aspects of stellar evolution formed the basis for how you ordered the elements?

恒星の進化に基づき、金、炭素、ネオンを、銀河で少ないものから多いものへ並べよう。進化のどの側面を根拠に、その順序を決めたか。

What observations or types of telescopes would you use to distinguish a binary system that includes a main-sequence star and a white dwarf star from one containing a main-sequence star and a neutron star?

主系列星と白色矮星を含む連星系と、主系列星と中性子星を含む連星系を区別するために、どのような観測や望遠鏡を使うか。

How would the spectra of a type II supernova be different from a type Ia supernova? Hint: Consider the characteristics of the objects that are their source.

II型超新星のスペクトルは、Ia型超新星のものとどう違うだろうか。ヒント：それぞれの発生源となる天体の特徴を考えよう。

The ring around SN 1987A (Figure 23.12) initially became illuminated when energetic photons from the supernova interacted with the material in the ring. The radius of the ring is approximately 0.75 light-year from the supernova location. How long after the supernova did the ring become illuminated?

SN 1987Aを囲む輪（図23.12）が初めて光ったのは、超新星からの高エネルギー光子が、輪の物質と相互作用したときだった。輪の半径は、超新星の位置から約0.75光年である。超新星が起きてから、どれほど後に輪は光り始めたか。

What is the acceleration of gravity (g) at the surface of the Sun? (See Appendix E for the Sun’s key characteristics.) How much greater is this than g at the surface of Earth? Calculate what you would weigh on the surface of the Sun. Your weight would be your Earth weight multiplied by the ratio of the acceleration of gravity on the Sun to the acceleration of gravity on Earth. (Okay, we know that the Sun does not have a solid surface to stand on and that you would be vaporized if you were at the Sun’s photosphere. Humor us for the sake of doing these calculations.)

太陽の表面の重力加速度gはいくらか。主な性質は付録Eを参照しよう。地表のgの何倍か。太陽の表面での自分の重さを計算しよう。地球での重さに、太陽と地球の重力加速度の比を掛ければよい。もちろん、太陽には立てる固体の表面はなく、光球にいれば蒸発してしまうことは承知している。計算のため、この仮定に付き合ってほしい。

What is the escape velocity from the Sun? How much greater is it than the escape velocity from Earth?

太陽からの脱出速度はいくらか。地球からの脱出速度の何倍か。

What is the average density of the Sun? How does it compare to the average density of Earth?

太陽の平均密度はいくらか。地球の平均密度と比べてどうか。

Say that a particular white dwarf has the mass of the Sun but the radius of Earth. What is the acceleration of gravity at the surface of the white dwarf? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the white dwarf (again granting us the dubious notion that you could survive there)?

ある白色矮星が太陽の質量と地球の半径を持つとする。表面の重力加速度はいくらか。地表のgの何倍か。その表面での自分の重さはいくらになるか。ここでも、生き延びられるという怪しげな想定を認めてほしい。

What is the escape velocity from the white dwarf in Question 36? How much greater is it than the escape velocity from Earth?

問題36の白色矮星からの脱出速度はいくらか。地球からの脱出速度の何倍か。

What is the average density of the white dwarf in Question 36? How does it compare to the average density of Earth?

問題36の白色矮星の平均密度はいくらか。地球の平均密度と比べてどうか。

Now take a neutron star that has twice the mass of the Sun but a radius of 10 km. What is the acceleration of gravity at the surface of the neutron star? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the neutron star (provided you could somehow not become a puddle of protoplasm)?

今度は、太陽の2倍の質量と10 kmの半径を持つ中性子星を考えよう。その表面の重力加速度はいくらか。地表のgの何倍か。何とか原形質の水たまりになるのを免れられるとすれば、そこでの自分の重さはいくらになるか。

What is the escape velocity from the neutron star in Question 39? How much greater is it than the escape velocity from Earth?

問題39の中性子星からの脱出速度はいくらか。地球からの脱出速度の何倍か。

What is the average density of the neutron star in Question 39? How does it compare to the average density of Earth?

問題39の中性子星の平均密度はいくらか。地球の平均密度と比べてどうか。

One way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?

恒星の半径を求める一つの方法は、ほぼ黒体のように放射すると仮定し、光度と温度を使うことである。惑星状星雲の中心星の測定から、典型的な中心星は太陽の16倍明るく、20倍高温〈約11万K〉だとわかった。半径を太陽の半径の何倍かで求めよう。典型的な白色矮星の半径と比べてどうか。

According to a model described in the text, a neutron star has a radius of about 10 km. Assume that the pulses occur once per rotation. According to Einstein’s theory of relatively, nothing can move faster than the speed of light. Check to make sure that this pulsar model does not violate relativity. Calculate the rotation speed of the Crab Nebula pulsar at its equator, given its period of 0.033 s. (Remember that distance equals velocity × time and that the circumference of a circle is given by 2πR).

本文のモデルでは、中性子星の半径は約10 kmである。1回転につきパルスが一つ起きると仮定する。アインシュタインの相対性理論によれば、何も光速より速くは動けない。このパルサーモデルが相対性理論に反しないことを確かめよう。周期0.033秒のかに星雲のパルサーについて、赤道での回転速度を計算しよう。距離＝速度×時間、円周＝2πRであることを思い出そう。

Do the same calculations as in Question 43 but for a pulsar that rotates 1000 times per second.

毎秒1000回転するパルサーについて、問題43と同じ計算をしよう。

If the Sun were replaced by a white dwarf with a surface temperature of 10,000 K and a radius equal to Earth’s, how would its luminosity compare to that of the Sun?

太陽が、表面温度1万K、半径が地球と同じ白色矮星に置き換わったら、その光度は太陽と比べてどうなるか。

A supernova can eject material at a velocity of 10,000 km/s. How long would it take a supernova remnant to expand to a radius of 1 AU? How long would it take to expand to a radius of 1 light-years? Assume that the expansion velocity remains constant and use the relationship: $\text{expansion time}=\frac{\text{distance}}{\text{expansion velocity}}.$

超新星は毎秒1万kmで物質を放出し得る。残骸が半径1 AUまで広がるには、どのくらいかかるか。半径1光年までならどうか。膨張速度は一定とし、次の関係を使おう。$\text{膨張時間}=\frac{\text{距離}}{\text{膨張速度}}.$

A supernova remnant was observed in 2007 to be expanding at a velocity of 14,000 km/s and had a radius of 6.5 light-years. Assuming a constant expansion velocity, in what year did this supernova occur?

2007年、ある超新星残骸が毎秒1万4000kmで膨張し、半径は6.5光年と観測された。膨張速度を一定と仮定すると、超新星が起きたのは何年か。

The ring around SN 1987A (Figure 23.12) started interacting with material propelled by the shockwave from the supernova beginning in 1997 (10 years after the explosion). The radius of the ring is approximately 0.75 light-year from the supernova location. How fast is the supernova material moving, assume a constant rate of motion in km/s?

SN 1987Aを囲む輪（図23.12）は、爆発の10年後の1997年から、超新星の衝撃波で押し出された物質と相互作用し始めた。輪の半径は、超新星の位置から約0.75光年である。一定速度と仮定し、超新星の物質の速さをkm/sで求めよう。

Before the star that became SN 1987A exploded, it evolved from a red supergiant to a blue supergiant while remaining at the same luminosity. As a red supergiant, its surface temperature would have been approximately 4000 K, while as a blue supergiant, its surface temperature was 16,000 K. How much did the radius change as it evolved from a red to a blue supergiant?

SN 1987Aになった星は、爆発前に、同じ光度を保ちながら赤色超巨星から青色超巨星へ進化した。赤色超巨星のときの表面温度は約4000 K、青色超巨星のときは1万6000 Kだった。この変化で、半径はどれほど変わったか。

What is the radius of the progenitor star that became SN 1987A? Its luminosity was 100,000 times that of the Sun, and it had a surface temperature of 16,000 K.

SN 1987Aのもとの星の半径はいくらか。光度は太陽の10万倍、表面温度は1万6000 Kだった。

What is the acceleration of gravity at the surface of the star that became SN 1987A? How does this g compare to that at the surface of Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.

SN 1987Aになった星の表面の重力加速度はいくらか。地表のgと比べてどうか。質量は太陽の20倍、半径は太陽の41倍だった。

What was the escape velocity from the surface of the SN 1987A progenitor star? How much greater is it than the escape velocity from Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.

SN 1987Aのもとの星の表面からの脱出速度はいくらだったか。地球からの脱出速度の何倍か。質量は太陽の20倍、半径は太陽の41倍だった。

What was the average density of the star that became SN 1987A? How does it compare to the average density of Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.

SN 1987Aになった星の平均密度はいくらだったか。地球の平均密度と比べてどうか。質量は太陽の20倍、半径は太陽の41倍だった。

If the pulsar shown in Figure 23.16 is rotating 100 times per second, how many pulses would be detected in one minute? The two beams are located along the pulsar’s equator, which is aligned with Earth.

図23.16のパルサーが毎秒100回転しているなら、1分間に何個のパルスが検出されるか。二つのビームはパルサーの赤道に沿い、その赤道は地球の方向と揃っているとする。