物理學 1912

小麥哲倫雲中 25 顆變星的週期

亨麗埃塔·斯旺·勒維特

一顆星脈動的快慢，透露出它真正有多亮——於是一隻碼錶，就能丈量宇宙。

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In depth · the introduction

有些星像心臟一樣搏動，以穩定的節律一脹一暗。一位失聰的女性，在玻璃底片上一顆顆數著它們，注意到：搏得最慢的，正是最亮的星——並把這一點，變成了一把丈量宇宙的尺。

核心想法

有一類星，叫造父變星，會以幾天到幾週的規則節律變亮、變暗。亨麗埃塔·勒維特在它們身上發現了一條乾淨的規則：一顆造父變星完成一次脈動用的時間越長，它真正放出的光就越多。那次脈動，就像印在星上的一張標籤，寫著它究竟有多亮。

這就解開了天文學最古老的難題。一顆暗淡的星，可能是近處一盞昏燈，也可能是遠方一盞明燈，你通常分不清是哪一種。可一旦星的脈動告訴了你它真實的亮度，再把它和「它看上去有多暗」一比，就知道它必定在多遠。勒維特，造出了第一把丈量宇宙的尺。

它是如何誕生的

勒維特在哈佛天文台工作，是「計算員」中的一員——一支受僱查看天空照相底片的女性團隊，活兒極費心力，薪水卻很低。她被分去做變星，而且做得極好，最終編錄了一千多顆。為了讓比較公平，她專挑小麥哲倫雲裡的星——那是南天的一團光斑，裡面的星離我們大致等遠——於是亮度上的任何差別，都必定是真實的。

1908 年，她近乎順帶地記下：越亮的，週期越長。到 1912 年，憑 25 顆仔細測過的造父變星，那點端倪已成了一條定律：圖上的一條直線。這份三頁的通告，以她主管的名義發出，只有一句話把這項工作歸給「勒維特小姐」。

它為何重要

在勒維特之前，對於離我們最近的近鄰之外的任何東西，沒人能可靠地說出它有多遠。她的定律，成了一架距離測量階梯最底下的一級，而這架階梯一路伸向整個可觀測宇宙。不到十年，埃德溫·哈伯就用造父變星證明了那些旋渦「星雲」其實是遠在銀河系之外的一個個完整星系，進而證明它們正彼此飛離——宇宙在膨脹。這一切，沒有一把丈量宇宙距離的尺都到不了，而勒維特，給出了第一把。

一個可以想像的畫面

想像一群人舉著一模一樣的燈籠，每盞的亮度都由一條簡單的規則定死——閃得慢，說明這盞燈籠亮；閃得快，說明它暗。你站在夜裡的曠野上，沒法直接量出哪盞燈籠離你多遠。可你盯著一盞看它怎麼閃，規則就告訴了你它真正燒得多亮；再拿它和「從你站的地方看上去有多暗」一比，你就能一步步量出那段距離。造父變星就是那些燈籠，它們的脈動，就是那閃爍。

它的位置

幾個世紀以來，天文學裡的距離只能伸到視差——近處恆星那極微小的擺動——所能承載的盡頭，至多幾百光年。勒維特定律打破了這層天花板，把埃德溫·哈伯（1929，也在本館）所需要的工具遞到了他手裡，讓他得以丈量星系、發現宇宙膨脹，進而鋪就了勒梅特與大霹靂宇宙學。直到今天，造父變星仍在幹著這份活，正處在那場尚未了結的「哈伯張力」——關於宇宙究竟膨脹得多快——的正中心。

The original document

Original source text

H. S. Leavitt (signed by E. C. Pickering) · Harvard College Observatory Circular 173 (1912): 1–3

Whose work this is

The following statement regarding the periods of 25 variable stars in the Small Magellanic Cloud has been prepared by Miss Leavitt.

The Circular carries the director Edward C. Pickering's signature, but its opening sentence is unusually frank about authorship: the science is Leavitt's. She had measured these stars on photographic glass plates of the southern sky exposed at Harvard's station in Arequipa, Peru.

The straight line

A straight line can be readily drawn among each of the two series of points corresponding to maxima and minima, thus showing that there is a simple relation between the brightness of the variables and their periods.

Leavitt plotted each star's brightness — once at its brightest, once at its faintest — against its period. Against the period itself the points curve; against the logarithm of the period they fall on two clean parallel straight lines. That is the period–luminosity relation, now called Leavitt's law.

Why the trick works

Since the variables are probably at nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness.

This single sentence is the whole idea. A star looks fainter both when it is dimmer and when it is farther away, and normally you cannot tell which. But all 25 stars sit together in the Small Magellanic Cloud, at one common distance — so the distance cancels, and the differences in brightness must be real differences in how much light the stars pour out. Period, something easy to measure, became a proxy for true luminosity.

Foreshadowed four years earlier

In her 1908 catalogue "1777 Variables in the Magellanic Clouds" (Annals of Harvard College Observatory 60: 87), Leavitt had already noticed the pattern in a single line:

It is worthy of notice that the brighter variables have the longer periods.

[ … ]

[Editorial] The Circular closes by noting that the relation should let astronomers determine distances once the line is calibrated against a few Cepheids of known parallax — a calibration Leavitt herself was never assigned to do. The full three-page scan, with her table and the two-line graph, is at the source below.

Harvard College Observatory · March 3, 1912