2013年4月21日

Dark Matter - Fate of Our Universe

Author: Angus 

Is dark matter really a matter in dark? I will say no but nearly.

Matter that doesn’t emit (or emits very little) nor absorb electromagnetic radiation (or absorbs very little) can be considered as dark matter. The term of dark matter is brought up into the world of astronomy by scientists Jan Oort and Fritz Zwicky in early the 20th century to account for the missing part of the total mass in the universe.

Mass-to-light ratio
is used to express the relation between mass and light output of the mass using (of sun) as reference. So mass-to-light ratio of sun is 1. Scientists found out the light emitted from a galaxy multiplying with the average mass-to-light ratio, the mass of the galaxy comes out , followed by division by the volume that the galaxy occupied, we can find out the average density for luminous matter . If we compare the result to the critical density (the density that makes the universe flat, which mentioned in the last part), the density of luminous matter is only 0.5% of critical density. (Iain Nicolson (2007) “Dark Side of the Universe Dark Matter, Dark Energy, and the Fate if the Cosmos” page34)


1. How we discover 



►The figure shows the relationship between angular velocity of stars orbiting the center of the spiral galaxy and the distance of stars away from the center of the spiral galaxy. Line A is the expected Keplerian result which the stars follow Kepler’s laws (square of orbital speed of star is proportional to cube of distance from the semi-major axis, distance between center and the star). Line B is the actual result observed by advanced telescopes. (Picture from Wikipedia) 



►The picture shows how stars distributed in a spiral galaxy


By Newton’s law of universal gravitation 
 and centripetal force , we get the equation . Assuming the disk part is a perfect circle, and the density of matter is even distributed in the disk, we get mass  for disk part. The larger r (distance between center and star) the smaller w (angular speed) we get, but the reality isn’t. What makes the two lines different? The secret lies under dark matter. 

To remain the angular velocity being the same value when distance increases, extra mass must be added, so a large portion of mass without shining also should be taken into account, those are dark matter.

Also, phenomena of gravitational lens can help scientists to find out dark matter. With the assistance of general relativity, mass distorts the nearby spacetime and bends the light when light travels across. The image of background source may be magnified and distorted because of lensing effect. So if unreasonably distorted of images of stars with no shining massive matter stays in front of it may illustrate the presence of dark matter. 



►The image show the lensing effect (Picture from Wikipedia)



2. Types of dark matter

There are two types of dark matter, one is baryonic dark matter and the second is non-baryonic dark matter.

2.1 Baryonic dark matter

Baryonic matter is a matter that made up by three quarks or antiquarks (not to mention any anti-matter in this article), involving into four fundamental force (strong nuclear force, weak nuclear force, electromagnetic force and gravitational force), simply to say, baryon is everything we see, we touch, we lived with.

Baryonic dark matter is talking about the massive astrophysical compact halo object (MACHO), which is present around our galaxy. It can be black holes, neutron stars and dwarfs (white, brown and red one). Black hole with escape speed equaling to speed of light attracts everything nearby, even light (See more detail in previous article by Wayne Chan). But that doesn’t mean black hole wouldn’t emit electromagnetic wave near event horizon. The wave emitted called Hawking Radiation with interesting characteristic, faster emission rate with smaller black hole. Neutron star is a super dense remnant from massive star during a supernova after throwing off most of its surface layer. The materials in the star are supported by the neutron degeneracy pressure (no two neutron can occupy same quantum state). The mass limit is between 1.4 and around 3.2 (the upper limit of neutron star is still not very sure nowadays) solar mass.

White dwarf is the dense remnant of star after the life of main sequence star ends. The material is supported by electron degeneracy pressure, which is similar to the neutron star’s one, with a 1.4 solar mass upper limit according to Chandrasekhar limit. White dwarfs emit its remaining thermal energy stored and no nuclear fusion takes place, with time flies, the white dwarfs will turn into black dwarf after emitting all its remaining light.

Red dwarf is a main sequence star but with upper limit around 0.35 solar mass, it has much less luminosity and the mass isn’t large enough for helium flash. It only fueled by p-p chain, the nuclear fusion with four protons into helium nucleus.

Brown dwarf with an upper limit around 75 Jupiter mass can’t fuse hydrogen into helium, is considered as fail star.

2.2 Non-baryonic dark matter

Non-baryonic matter is a matter not formed from atoms and quarks. The matter only involve in weak nuclear force and gravitation, which is completely different from baryonic matter. But that “ghost” like particle how can we distinguish between the baryonic dark matter and non-baryonic dark matter?

In the first few moments of our early universe, everything is fixed, including the baryon-photon ratio. During the time, the Big Bang nucleo-synthesis took place, of which only atoms like hydrogen, deuterium (heavy hydrogen), helium-3 (light helium), helium and lithium exist. The portion of different types of atoms depends on the baryon-photon ratio, so too many baryon (>8% of total density) on the early universe causes more helium (larger portion in baryon) that we observed today, and too less baryon (<2% of total density) causes much less helium (lower portion in baryon). In the present moment, the baryon mostly composed of 74% of hydrogen and 26% of helium by mass. Then we can conclude that the baryon abundance lie between 2% and 8% of total density required turning our universe into flat (although our universe isn’t flat but nearly) (Adams Laughlin (1999) “The Five Ages Of The Universe” chapter1). So the other ingredients to fill up the universe are around 23% of dark matter and around 70% for dark energy, only 4.6% from atoms.

Non-baryonic dark matter is divided into three types, Hot Dark Matter (speed comparable with speed of light, neutrino is an example), Warm Dark Matter and Cold Dark Matter, in term of their mass and velocity, of which massive matter means lower speed, so mass and velocity are the same things.

3. Fate of our universe

As the previous paragraph mentioned the term “critical density”, but, how critical density relates to our future?

Our universe is under a battle between the gravitation and the force to expand (dark energy). If the mean density of total matter and radiation exactly equal to the critical density, the universe will expand forever but tends to zero when time travels and Euclidean geometry apply (for example, the triangle is 180 degree). If the mean density is below the critical density, the universe is open and the expansion is kept forever but the rate slows down because of gravity. The curvature of the universe would be negative with saddle-shaped surface (triangle is less than 180 degree). If the mean density is above the critical density, the universe is said to be positive curved with spherical surface (triangle is large than 180 degree), of which the universe is limited space but without boundary. The expansion of the universe will be stopped in someday and start shrinking into a “Big Crunch”.


▲Picture from The University of Hong Kong Department of Physics

The situation mentioned above is all about the possible situation without dark energy. Taking account of dark energy makes the situation more complex.

So, scientists certainly find that the mean density of our universe is lie between 0.1 and 10 where 1 equals to critical density. With the Hubble’s law, the redshift (speed of receding) of other galaxies is proportional to the distance between our Earth and galaxies, which shows the universe is expanding.


But no one knows whether the matter is laid in or out of threshold of critical mass and how our universe will evolve into, maybe only time can tell.

To find more about the topic, related stuff or astronomy magazines, please get more detail in our counter and use Astronomy Library service. WE ARE WAITING FOR YOUR ENQUIRY!!!!!!

2013年4月17日

[天文週] 天文雙週 - 2013彗星年[Astronomy Weeks]


2013年被譽為「彗星年」,今年先後會有兩顆較明亮的彗星於香港上空出現,亮度足以用肉眼觀測得到,他們分別是「泛星」彗星(C/2011 L4 Pan-STARRS) 以及「光科網」彗星(C/2012 S1 ISON)。自問不是很清楚甚麼是彗星,或者對彗星只是有基本的了解,參與我們天文雙週吧,你將會從中學懂更多。這次天文雙週內有一連串多元化的活動,除了觀星外,還有紀錄片觀賞、講座、展出及售賣天文書籍、儀器及精品,以及香港太空館導賞。有興趣的你必定要密切留意啦!

活動詳情:

活動名稱: 天文雙週 - 2013彗星年

日期: 4月23日 (星期二)

時間: 18:00 – 21:30

地點: 香港太空館

活動內容: 太空館導賞



日期: 4月25日 (星期四)

時間: 19:00 – 20:30

地點: MB201

活動內容: 天文紀錄片觀賞



日期: 4月26日 (星期五)

時間: 19:00 – 20:30

地點: MB201

活動內容: 天文講座 「彗星:來去匆匆的訪客」

講者: 香港大學物理系助理教授 吳志勇博士



日期: 4月15至19日 (星期一至五),4月22至26日 (星期一至五)

時間: 11:00 - 19:00

地點: 邵逸夫樓平台 (Subway旁),學生會大樓地下 (Starbucks對出)

活動內容: 展出及售賣天文書籍、儀器及精品



日期: 4月15至19日 (星期一至五),4月22日 (星期一),4月24至26

日 (星期三至五)

時間: 20:30 - 22:00

地點: 鈕魯詩樓天台

活動內容: 觀星



查詢: Cherry (6485 2100),Iris (9062 4738)


報名方法:
1) 到天文學會COUNTER
(開放時間: 11am – 7pm)
我們的counter將會在以下地方擺放:

15-19/4 邵逸夫樓平台 (Subway旁)

22-26/4 學生會大樓地下 (Starbucks對出)


2) 將以下資料電郵至 suastro@hku.hk
姓名(中文):
姓名(英文):
性別:
UID:
就讀科目:
就讀年級:
聯絡電話:
電郵地址:



活動已開始接受報名,所有活動費用全免,歡迎各位同學於以上時間到我們的counter留位及查詢。同學亦可以回覆此電郵,留下上述資料留位。如有任何查詢, 歡迎致電Cherry (6485 2100), Iris (9062 4738)或電郵至suastro@hku.hk查詢。



香港大學學生會天文學會

2013-2014年度

電郵: suastro@hku.hk
網址: http://www.hku.hk/suastro
Astro-blog: http://hkusuastro.blogspot.hk
Facebook: https://www.facebook.com/hkusuastroclub


2013 is called the “Year of Comets”. Two comets could be observed with naked eyes in Hong Kong if you are lucky enough. They are Pan-STARRS(C/2011 L4) and ISON(C/2012 S1). You can learn more about comets by joining activities during the Astronomy Weeks, which includes exhibition and sale of astronomy books, equipment and some other products, film appreciation, talk, stargazing and visiting the Hong Kong Space Museum. If you are interested, you must not miss any of these activities! See you there!!!



Details of the activity:

Name of function: Astronomy Weeks – 2013 “Year of Comets”



Date: 15-19 April 2013 (Mon-Fri), 22-26 April 2013 (Mon-Fri)

Time: 1100-1900

Venue: Run Run Shaw Podium (next next to subway), SU Building G/F (opposite to

Starbucks)

Activity: Exhibition and sale of astronomy books, equipment and some other products



Date: 23 April 2013 (Tue)

Time: 1800-2130

Venue: Hong Kong Space Museum

Activity: Visiting the Space Museum


Date: 25 April 2013 (Thu)

Time: 1900-2030

Venue: MB201

Activity: Film appreciation



Date: 26 April 2013 (Fri)

Time: 1900-2030

Venue: MB201

Activity: Astronomy talk - Comets: Visitors from Space



Date: 15-19 April 2013 (Mon-Fri), 22 April 2013(Mon), 24-26 April 2013 (Wed-Fri)

Time: 2030-2200

Venue: Roof of Knowles Building

Activity: Stargazing



Enquiries: Cherry (6485 2100) or Iris (9062 4738)



Application method:

1) Come to our counter:

(Opening hours: 11 am. – 7p.m.)

Our counter will be set up at:

15-19/4 Run Run Shaw Podium

22-26/4 SU Building G/F (opposite to Starbucks)



2) Apply through email by attaching following information:
Name (Chinese):
Name (English):
Gender:
UID:
Degree Curriculum:
Year:
Contact no.:
Email address:



The application period has been started. All activities are free of charge. Don’t hesitate and join us by visiting our counter and reserve for your place! Should you have any enquiries, please feel free to contact us via suastro@hku.hk or Cherry at 6485 2100 or Iris at 9062 4738.



Astronomy Club, HKUSU

Session 2013-2014

Email: suastro@hku.hk
Website: http://www.hku.hk/suastro
Astro-blog: http://hkusuastro.blogspot.hk
Facebook: https://www.facebook.com/hkusuastroclub

2013年4月10日

萬物終結者之謎—黑洞

By 井口的一隻小歪

  在香港城市裡頭,抬頭仰望夜空,看得見的星星扳扳手指頭就數得完,說真,只是「齋」看實在是沒有甚麼趣味。無邊無際的天空正正是代表了自由,正如一隻井中的青蛙,牠未必有足夠力量跳出井口,未必能夠清楚井外的世界,但至少若牠能夠在腦海中恣意地想像井口,牠絕不會苦悶。這道理也正正和我想說的一樣。而這次我要說的,正是所有人到現刻也看不見的東西-黑洞。

  黑洞……就是黑色的大洞嗎?人們總覺得她的名字很吸引。聽說黑洞的重力很強,一旦被吸了進去就再也不能回來。這是真的嗎? 要了解之前,不如先先看看不同的黑洞照片。

(National Geographic)




形成黑洞的選拔賽
究竟天體要成為黑洞要有甚麼條件呢?除了在宇宙一開始就存在的黑洞以外,其實天體要通過一個「黑洞選拔賽」,其條件就是質量要大約有太陽的25倍或以上。也就是說,在這場黑洞的選拔賽上,及格與不及格,幾乎是從一出生起就注定好了。為甚麼說是「幾乎」呢?其實在一次審核之後,還有一個復活賽。當質量僅差一點就能達到大約太陽質量的25倍時,若附近還有其他恆星,又能從對方那裡吸收氣體,又達到足以成為黑洞的應有質量時,就能成為黑洞。宇宙當中存在許多2至3個星星一組、互相繞著對方公轉的「聯星」。正因如此,只差臨門一腳的時候,便可以奪取鄰近星星的力量。

圖1: 質量達太陽 10 倍的黑洞之電腦模擬圖
從恆星成為黑洞

那麼接下來,我們來看看恆星是怎樣進化成黑洞吧。

恆星不可能自出生就永遠地綻放光芒。即使是星星,也有所謂的壽命。

另外,恆星不可能一生都維持同一個模樣,星星也會變老的。質量愈小的恆星愈長壽,質量愈大的恆星,老化的速度則愈快。這是由於大質量恆星的核心較熱和密度較高,它們燃燒氫氣的速度更高,所以生命反而較短。這是因為黑洞,正是較重恆星的壽命到達盡頭的時候最終的模樣。在黑洞選拔大賽的勝利者,起初也和太陽一樣,因核聚變而綻放出耀眼的光芒。但是時間久了,便會耗盡反應的物質。

當中心物質因核聚變而變成鐵後, 由於繼續燃燒鐵的核反應需要吸收能量才能運行 ,所以恆星核心產生能量的能力就會馬上停止,核心的壓力驟降。當核心積聚了足夠的鐵後﹐在百分一秒之內, 核心會猛烈地收縮,同時把核心的溫度提高。所有尚未使用的燃料會迅速核聚變成鐵或變成鎳,核心的外殼會塌縮在核心上,形成既小又密度高的核心。外側則由既冷又輕的氫氣體包圍,演變成雙層結構的天體。由其核心會不斷收縮,原子核的天然密度會成為巨大的阻力,防止核心進一步收縮,這時核心便會猛烈反彈,產生強烈的衝擊波,並把恆星外殼炸毀。這就是「超新星爆炸」。

超新星爆炸之後,其中心已經變成黑洞了,爆炸後所剩下的質量太陽只有太陽的三倍。

一但成為了黑洞,就再也不能回復以往的模樣,也再沒有下一個階段。這就是太陽質量25倍以上恆星最後的姿態。
圖2: 可以看見星星的一生
source: http://www.lcsd.gov.hk/CE/Museum/Space/EducationResource/Universe/framed_c/lecture.html 
HK Space museum 

就連宇宙最快的「光」也逃不掉

只要進入黑洞所在的一定範圍以內,所有物質都會被它的重力所補獲,再也回不來。一旦進入這個範圍,無論是多麼快的事物,都無法再次逃出黑洞,除非有東西能夠超越光速,否則即使是全字宙最快的「光」,有高達3x108 m/s的速度,也逃不掉黑洞的引力。

由於光無法離開黑洞,所以我們也無法直接觀察黑洞本身。也是因為如此,美國物理學家(John Archibald Wheeler, 1911-2008)才命其為 “black hole” ,中文直譯為「黑洞」。
圖3: 黑洞的引力 
Source: http://www.welchco.com/02/14/01/60/04/03/1207.HTM
黑洞的城牆在何處?

黑洞的城牆其實就是事件穹界,事件穹界的意思便是事件在內不能為人所探知。在事件穹界之內的一切皆不能逃離,所以在這個城牆以內發生的一切,將永遠不能為人所知,事件穹界的半徑稱為史瓦西半徑(rs) ,數值的大小只取決於黑洞的質量。



G是萬有引力常數,c是光速,M為質量。



圖4: 史瓦西半俓 
Source: http://www.lcsd.gov.hk/CE/Museum/Space/EducationResource/Universe/framed_c/lecture.html 
HK Space museum
一般而言,是將史瓦西半俓直至內部的範圍定義為黑洞,而位在史瓦西半俓中心,便是所有質量皆壓縮成一點的地方,也就是「奇點」(Singularity)。
圖5: 奇點所在之處http://www.lcsd.gov.hk/CE/Museum/Space/EducationResource/Universe/framed_c/lecture.html 
HK Space museum
奇點十分不可思議,因為它聚集了黑洞所有質量。很多人以為奇點是一個半徑等於零、但密度無限大的地方。其實,比較正確的說法是我們根本不知道那裡是甚麼一回事,因為我們所知的一切物理定律根本不適用於情況如此極端的地方。
圖6:只要進入了這個半俓的範圍內,無論是誰也沒法走出來的。廣義相對論的中心思想是質量會扭曲其附近的時空,質量越大,影響越明顯。同樣道理,光線在通過大質量物質附近時,亦不會以直線運行。
source: astronomy.swin.edu.au
身體會否會變成麪條?

有很多人會說「只要我們進入了黑洞的範圍,就會變成麪條」,事實上是否這樣呢?

我們會從黑洞邊界接收到一股潮汐力。潮汐力是萬有引力的效果,它使得潮汐發生。它源於一個星體的直徑上各點的引力場的不相等。就例如地球上所發生的潮汐現象,就是因為這股力量。而這股力量是月球的引力影響了地球所產生的。
圖7: 潮汐力的影響 
Source: http://163.20.160.24/~star/modules/myalbum/photo.php?lid=1205
即是當人類先踏出腳尖接近黑洞,但頭部還在外側時,因施加在身體頂端「頭部」和尾端「腳尖」的重力不同,便會受到潮汐力的影響。當施加在頭部和腳尖的重力相差過大時,人類的身體就會被拉得細長。

但若果我們是身處在星系中心的超巨大黑洞時,所接收到的潮汐力(如銀河系)只有0.016 m/s2.

若果是一個小型黑洞(質量很小),其潮汐力是非常巨大的。頭部和腳尖的重力加速度相差約160萬m/s2。 亦即是約地球加速度的16萬倍。那就像你站在地面上被2000架飛船拉扯。

但即使在這個情況下,只要我們的身高愈矮,我們所接收到的潮汐力就會愈小。

在以上的相同條件下,體長只有1mm的跳蚤從恆星黑洞接收到的潮汐力,僅有105地球引力左右。換言之,接收到潮汐力的物質長度愈大,所承受的潮汐力也就愈大。因此月球對整個地球的引力影響,對於地球來說便會有「潮漲潮退」的明顯現象,但我們人在地球卻不會被拉長。

要了解黑洞真正面目,仍然有很多事物需要我們去探討。有機會的話我可以帶你去遊覽黑洞-沒有回程的旅行,你敢來嗎?請繼續留意ASTRO blog的更新。下期將會介紹另一黑-黑暗物質。

Sources:
Nature of universe, Physics Department, HKU(http://www.physics.hku.hk/~nature/notes/index.html)
Black Hole Physics: Basic Concepts and New Developments
Springer by V. Frolov (Author), I. Novikov (Author)
Photo Gallery, National Geographic
(http://science.nationalgeographic.com/science/photos/black-holes-gallery/

Author: Wayne Chan (CY)

2013年4月7日

[活動預告] 與天同行—古今星中外





有些時候…你抬頭看看天空,你可以看到一彎新月。

有些時候…你到郊外夜遊,你可以看到漫天星空。

這就是天文嗎?你有沒有曾經想過以前的人怎樣看天?

究竟東方和西方對天的態度有甚麼分別呢?



即使你對天文沒有基本的認識,也可以透過這個活動去了解一下天文的發展過程:

究竟古人如何看天上的星星?究竟如何觀察天空上的事物?古人如何利用天上的運

動去了解天氣的變化?這四個講座會令你學得更多。


活動詳情:

活動名稱: 與天同行—古今星中外

日期: 4月9日 (星期二)

地點: MB201

時間: 19:00 - 21:00

活動內容: 講座~遠古天文觀

講座~歐洲古天文

名額: 50 (歡迎walk-in)




日期: 4月12日 (星期五)

地點: MB201

時間: 19:00 – 22:45

活動內容: 講座~中國古天文

講座~現代對天的看法

觀星環節

名額: 50 (歡迎walk-in)


查詢: CY (6331 8961)