星空可否不要老？－歲差

58落曦

相信有不少讀者都聽過黃道十二宮，即使對天文不太熟悉的讀者亦可能對占星學中的十二個星宮和相應的生日日期，甚至星座性格、運程等略有耳聞；熟悉天文的更會糾正我說現在國際天文聯會（IAU）已確認了蛇夫座為第十三個黃道星座。但大家可知道今天的黃道星座跟二千多年前希臘天文學家所觀察的有甚麼分別？

春分點和星座的變化

答案是太陽經過各個星座的時間不同了。 在觀星時，我們假定地球為宇宙中心，地球本身不會動，而星星一直在一個很大的天球上運動。在此模型上，太陽一直相對於背景星空運行，並於每年春分（現時公歷為3月20-22日其中一日）時自南向北穿過天赤道，這時候，黃道與天球赤道的相交點就被稱為春分點（First Point of Aries），相應地，在秋分時太陽由北向南穿過天赤道時，黃道與天球赤道的相交點就被稱為秋分點（First Point of Libra）。根據IAU，現時春分點位於雙魚座，即在春分當日太陽在天球上的位置位處於雙魚座。細心的讀者可能會發現春分點的英文名譯作中文有白羊座第一點的意思，為什麼太陽於春分時位於雙魚座，卻被命名為「白羊座第一點」？

圖一：春分點與天球模型

為什麼春分點（First point of Aries）會在雙魚座（Pisces）？答案其實頗為簡單：在公元前130年古希臘天文學家喜帕恰斯（Hipparchus，190-120 BC）為春分點命名時，太陽於春分經過的確實是白羊座。只不過隨著歲月流逝，地球的自轉軸因為重力作用而漸漸改變指向，這種變化亦被稱為歲差。歲差的出現令地球經過兩次春分點的時間略少於太陽在黃道環繞一周的時間。在這現象的影響下，春分點日漸向西移，並在公元前100年進入了雙魚座。大約於公元2700年左右，春分點就會由雙魚座移至寶瓶座。

所以現在每年星座出現在夜空的日子大約比二千多年前遲了一個月，例如當時的白羊座會在九月中的半夜經過中天，現在就要等到十月尾了。另一個更具體的例子是夏季大三角的牛郎、織女。相信大家都聽說過牛郎織女相會於雀橋的故事吧，牛郎星和織女星之間隔着銀河，在每年七夕，兩顆星之間的距離會是一年之中最接近的，所以就有牛郎織女七夕相會的傳說中。由於歲差影響，他們相會的時間會愈來愈遲，七夕有一天會變成「八夕」甚至「九夕」、「十夕」，並一直推遲，直至回歸七夕。所以，如果大家拿着我們學會福利包中的星圖，回到二千年前的香港使用的話，恐怕有認錯星座的風險呢！

不過，占星學中的黃道十二宮並不會受歲差影響。占星學中定義了春分點為白羊座的開始，並以十二個中氣點（亦即是二十四節氣中每月的第二個節氣）作為星座的間隔，與星座、天球運動、黃道等等全部無關。所以，不論將蛇夫座加入黃道星座，還是春分點快要從雙魚座移至寶瓶座都影響不了占星學的分類。占星學利用天體的運動和相對位置來占卜，但黃道十二宮卻不受歲差所影響是其中一個科學家視占星學為偽科學的原因。

歲差的成因

歲差的主因太陽及月球的引力對地球不同部分有不同的影響。由於地球並不是圓的，它其實是一個中間稍寬的扁球體，赤道的直徑比南北極之間長了約43公里，就像一個大陀螺一般。這個陀螺的轉軸一直與黃道面保持大約23.5度的交角，並同時被太陽和月球的引力所球的引力所拉扯(如下圖)，兩者對地球產生了力矩（Torque），大家可以幻想成在垂直於地球自轉軌道的平面將地球逆時針轉的拉力，使自轉軸的指向往順時針方向轉移。

圖二：地球自轉軸轉動

歲差的發現

托勒密（Claudius Ptolemy，90-168 AD，羅馬帝國時期的希臘天文學家，著有《天文學大成》等對後世科學發展影響極大的巨著）在《天文學大成》中指出喜帕恰斯量度了角宿一和其他亮星的位置，並將觀察所得的數據與提默洽里斯（Timocharis，320-260 BC）和阿里斯基爾 （Aristillus，fl.ca. 261 BC）所觀察的數據作比較，並得出角宿一在二百年內相對於秋分點移動了兩度的結論，於是推斷出分點於黃道上向西移，並稱之為分點歲差。正如同上文舉的例子一樣，當一顆星相對秋分點移動的話，我們在地球上觀察到它的時間就會愈來愈遲。可是喜帕恰斯的所有紀錄經已隨歲月失落了，天文學家們目前對他的研究的理解都是基於托勒密的轉述。

歲差的影響

回歸年與恆星年

托勒密亦指出喜帕恰斯發現了回歸年與恆星年之間的分別。

回歸年是由地球上觀察，太陽在黃道上運行一周所需的時間，例如由春分點環繞黃道一周所需時間就稱之為春分點年。現在的歷法普遍基於平回歸年（黃道上所有點的平均值）制定，平回歸年大約等於365.2422日，而在計算閏年後，格里曆（即現時我們使用的公歷）平均每年有365.2425日，所以大約每3,333年，格里歷就會相對於平回歸年有一天的誤差。

而恆星年指的則是太陽在天球運動中回到相同赤經的時間，每一恆星年是地球圍繞太陽公轉三百六十度的真正時間，恆星年比回歸年長大約20分鐘24秒 ，所以每隔26,000恆星年，回歸年就會跟恆星年相差一年左右。恆星年並不會隨分點的移動而變化，所以以恆星年作為基礎的歷法將會漸漸與季節不同步，大約每71年就會有一日的偏差。測量恆星年的其中一個方法是以兩次在黎明之際觀察到同一粒星的昇起作為一年。

北極星的轉變

歲差的另一個影響就是北極星的改變。辨認北極星是觀星愛好者其中一個必修的課題，透過它，我們可以在沒有工具的情況下辨別出北方，並且作為尋找其他星座的參考。一般而言，最接近天球北極（即地球的自轉軸延伸後和天球在北方的相交點）的亮星會被定義為北極星，而現時的北極星是勾陳一，又被稱為小熊座α。它的視星等達到1.97，並且極為接近天球北極（現時離天球北極只有約0.75°），可以算是一粒頗為稱職的北極星。基於歲差的關係，勾陳一在2100年最接近天球北極（離天球北極只有約0.45°），並在之後漸漸遠離。之後我們熟悉的織女會於公元13,700年成為北極星，而這稱號會在約8000年後交給天龍座 α（右樞），再過5000年左右後，北極星的稱號便會歸還給勾陳一，並一直循環。不過北極星並沒有一個明確的定義，有很多恆星亦被認為在過去或將來適合作為北極星，例如夏季大三角中的天津四（它在大約公元一萬年至公元一萬一千五百年是最接近天球北極的亮星）和小熊座的北極二（即中國的「帝星」，它在大約公元前一千五百年至公元元年是最接近天球北極的亮星）。而勾陳一－織女－天龍座α的循環只是其中一個較為簡單和廣泛傳播的說法。 基於地球的自轉軸傾斜的週期為約26,000年，北極星轉變的循環同樣是約26,000年。

四季交替

在天文之外，歲差的發現亦有助我們了解我們的家：地球。

在北半球，秋季和冬季較接近近日點，所以地球從春分點移動至秋分點遠比由秋分點去春分點遠。因此，春季和夏季在現時比秋冬季長，而這關係隨着地球的轉軸的轉動和分點的移動，會一直改變。如下圖所示，現在是春夏較長而秋冬較短，五千年多後就變成夏天和秋天較長了，每一個季節都有大約一萬年時間會相對較長，之後一萬年較短。大家可能會奇怪：為什麼這次的週期不是26,000年？答案是有另外兩個天體跟太陽一樣用引力影響了地球的公轉軌道，使相對於近日點的週期由26,000年縮短至約21,500年。猜猜是哪兩個？（提示：太陽系中除太陽外還有哪些天體有足夠質量去影響地球的轉軸？可以反白看答案。）答案：木星和土星

圖三：歲差對氣候的影響

當再有人告訴你他／她是在甚麼星座出生時，記得提醒他／她要考慮到歲差並推前一至兩宮，並將身上的幸運石、顏色甚麼的全部更換。相信他／她的表情一定相當精彩。

資料來源：

Benson, G. (2007). Global Warming, Ice Ages, and Sea Level Changes: Something new or an astronomical phenomenon occurring in present day? Retrieved from http://web.archive.org/web/20080304224356/members.aol.com/gregbenson/iceage.htm

Kaler, J.B. (2002). The ever-changing sky: a guide to the celestial sphere. Cambridge University Press.

My Dark Sky. (2008). The Earth’s Wobble – Precession. Retrieved from https://mydarksky.org/2008/10/14/the-earths-wobble-precession/

Neuhäuser, R.; et al. (2007). "Direct detection of exoplanet host star companion γ Cep B and revised masses for both stars and the sub-stellar object". Astronomy and Astrophysics. 462 (2): 777–780.

Western Washington University Planetarium. (2008). Astro 101 - Precession of the Equinox. Retrieved from http://www.wwu.edu/depts/skywise/a101_precession.html.

How were the earliest black hole formed?

58 Wood Villager

Introduction

A black hole is a region in the universe where gravity pulls so much that even light cannot get out. Since light cannot get out of a black hole, we cannot observe and detect it easily. As a consequence, what’s inside a black hole is still a mystery in our universe. We are now knowing more about black holes, such as their formation process and development, but still there is an interesting field of study.

What types of black holes are there?

There are three types of black hole – primordial black holes, stellar black hole and supermassive black hole, which are classified depending on their mass and they are formed in different ways. Primordial black hole is the black hole born in early universe. It is formed by compressing matter with extremely high density, existing in the early expansion of the universe so it is the smallest in mass. Another type is stellar black hole. A stellar black hole is formed by the collapse of a massive star, which has a mass 8 times the mass of our Sun. The star then explodes and the mass remaining in the core is a stellar black hole. This process is called hypernova explosion. The third type of black hole is supermassive black hole. They possess the highest mass among the three types of black hole and they can be found in almost all currently known massive galaxies.

How does a black hole develop?

It is well-known that a black hole will go through the process of accretion to become more massive. For instance, a primordial black hole, which is just born with low density, enlarges by pulling in materials like gases from its surroundings. A black hole may be merged with another black hole nearby due to their gravitational attraction between them to form a more massive black hole.

Is it possible to have a black hole during the early stages of the universe?

Some scientists believe that black holes existed in the universe as early as about one billion years after the Big Bang, as they hold an idea that quasars, which are billions of light years away from us, with their brightness (radiation) 10-100000 times that of the Milky Way, should have been powered by a supermassive black hole in it. Discoveries of big black holes in tiny galaxies show us that big black holes should have formed in the early universe before galaxy collisions, and thus supporting the theory of the early formation of a black hole.

Now the question is, how can a “mature” black hole be formed by accretion given that there were inadequate gases during the early stages of the universe? If a black hole developed through the conventional development process, the formation of quasars would be too slow as the gases required were not abundant at that early time.

“Direct collapse” black hole

To explain the existence of black holes in the early stage of the universe, “direct collapse” black hole was made a hypothesis in the 2000s. “Direct collapse” black hole hypothesis suggests that the primordial gas, i.e. primordial cloud of hydrogen and helium, would undergo direct collapse to form a black hole. In the process, the primordial gas flows along the dark matter filaments, forming a cosmic web that could connect the structures in the early universe (dark matter is an unidentified type of matter that makes up considerable part of the universe). The gas was kept hot due to the presence of a sea of ultraviolet photons, thus any star formation is suppressed. There will be intersections between these dark matter filaments, leading to the formation of the first group of galaxies. The process of direct collapse repeated throughout the early stage of the universe, and more and more galaxies were formed. Thus, even though the density of gas was not high at the time, black holes can still develop quickly, producing a large amount of quasars.

Here is a simulation image of the cosmic web structure based on a supercomputer:

(Credit: Aaron Smith/TACC/UT-Austin.)

Study of the early universe

In order to understand more about the early universe, astronomers have been studying old stars. Through these studies, not only can they know more about the structure of the young universe, but also prove the existence of direct collapse black holes.

CR7 (Cosmos Redshift 7), one of the brightest existing stars from the early universe, was identified in a Hubble Space Telescope investigation called COSMOS. The star is formed soon after the Big Bang. Astronomers deemed this particular star as an ideal sample for studying early stars and investigating early black holes. From the studies of CR7’s electromagnetic spectrum, it was discovered that certain hydrogen line known as “Lyman-alpha”, was several times brighter than expected in the spectrum. Furthermore, its electromagnetic spectrum also revealed several unusual features, including an unusual bright helium line, and absence of lines from other element heavier than helium. These findings give evidence to the existence of direct collapse black hole, providing us with a more comprehensive view of early black holes.

Besides CR7, NASA recently announces the discovery of two other “direct collapse” black hole candidates based on its observation with the Chandra X-ray Observatory. This further supports the hypothesis of direct-collapse black holes.

As scientists successfully identify the existence of early black holes and obtain more information of their formation, we are indeed getting closer to solving the mysteries of black holes, as well as understanding the origin of our universe.

Reference

1. Johnson, R. (2016). Astronomers find evidence for ‘direct collapse’ black hole. Retrieved from:

https://www.ras.org.uk/news-and-press/2887-astronomers-find-evidence-for-direct-collapse-black-hole

2. Smith, A., Bromm, V. and Loeb, A. (2016). “Evidence for a direct collapse black hole in the Lyman α source CR7”. Monthly Notices. Volume 460. Issue 3.

3. May, S. (2008). “What is Black Hole?”. NASA Knows. (Grades K-4). Retrieved from:

http://www.nasa.gov/audience/forstudents/k-4/stories/nasa-knows/what-is-a-black-hole-k4.html