3.4 宇宙距离梯子
Section outline
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From Parallaxes to Hubble's Law
::从帕拉克斯到哈勃法How do we know distances to objects in space? No method for determining distances works at all scales. The analogy with a is that we have different steps that allow us to bridge one method for measuring distances to the next one . First we find distances to the closest objects. Then we use information about those nearby objects to infer distances to more distant objects.
::我们如何知道空间物体的距离?没有确定距离的方法在所有尺度上都是有效的。比方是,我们有不同的步骤可以连接测量距离的方法。首先,我们找到距离最接近的物体。然后,我们使用关于附近物体的信息将距离推至更远的物体。-
For the closest objects, the moon or Venus, we can use radar ranging. This allowed scientists to figure out the distance to the Sun. Once we know the distance to the Sun, we can figure out how much energy is being emitted each second (i.e., the "luminosity") in the following way: the Sun emits equal amounts of energy in all directions. We can use a photon counter to determine how much light is being emitted at various wavelengths. Each photon has an energy:
and luminosity,
, is the total energy per wavelength per second. Next, we have to determine what fraction of energy is intercepted by the photon counter; this will scale as the area of a spherical shell centered on the Sun with a radius equal to the Earth-Sun distance:
-
::L收集器4R2采集器 -
where
is the luminosity of the Sun
::在那里,L是太阳的光辉 -
is the energy per second intercepted by the photon collector
::回收器是光子采集器每秒截获的能量 -
is the distance from the Sun to the collector (on Earth)
::R是从太阳到收藏家(在地球)的距离
::对于最接近的天体, 月球或金星, 我们可以使用雷达测距。 这样可以让科学家了解太阳的距离。 一旦我们知道太阳的距离, 我们就可以以以下方式知道每秒排放多少能量( 光度 ) : 太阳向各个方向排放等量的能量。 我们可以使用光子计数器来确定不同波长的光量。 每个光子都有能量: E=hVV和光度, L是每秒每波长的总能量。 下一步, 我们必须确定光子反射器截获的能量的分数; 这将以球壳在太阳上的核心区域, 半径相当于地球- 太阳距离 。 L是太阳光度的光度, R是光子采集器每秒截获的能量, 从太阳到采集器的距离( 地球 ) 。 -
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For stars in
our
part
of the Milky Way galaxy, we can use trigonometric parallax measurements to determine distances. Once we know the distance, we can measure the energy per second with a photon counting device and use this to calculate the luminosity of the stars. This helped us to understand that stars with different types of spectra have different luminosities. As soon as that correlation was established we could turn this around to take the next step on the distance ladder.
::对于银河系中我们部分的恒星来说,我们可以使用三角对准光蜡测量来确定距离。一旦我们知道距离,我们就可以用光子计数设备来测量每秒的能量,然后用光子计数设备来计算恒星的光度。这有助于我们理解,不同频谱的恒星有不同的光度。一旦建立了这种关联,我们就可以转过身,在距离梯子上迈出下一步。 -
For stars that are farther away in
our
galaxy, we can obtain spectra
to
derive spectral
types and luminosity classes. O
nce we have the spectral type, we also know the true luminosity of the star
,
,
from our work on the previous rung of the distance ladder. Now, we measure the apparent brightness with our photon-counter and flip the equation above
and use
to calculate R (distance).
The apparent brightness will be fainter
when
the object is farther away.
This is an example of a
standard candle
- we know the intrinsic brightness of an object (a star in this case) and use
the difference between the intrinsic brightness and the apparent brightness to
estimate
the distance.
::对于银河系中距离较远的恒星,我们可以获得光谱以得出光谱类型和光度等级。 一旦我们有了光谱类型, 我们也可以从我们先前在距离梯子上运行的工作中知道恒星的真正的光度, L*。 现在我们用光子反射器测量表面亮度, 并翻转上面的方程。 当天体距离更远时, 亮度会更暗。 这是标准蜡烛的一个例子, 我们知道一个天体的内在亮度( 此处是一颗恒星) , 并且使用内在亮度和表面亮度的区别来估计距离 。 -
Cepheid variables: Henrietta Leavitt discovered a relationship between periodicity in the brightness variations of Cepheid stars and their true luminosity (described in Chapter 1.1). Cepheids are another example of a
standard candle
that allowed us to derive distances to nearby galaxies.
::Cepheid变量:Henrietta Leavitt发现了Cepheid恒星亮度变化周期与其真正光度之间的关系(见第一章第1.1节)。 -
The Tully-Fisher relation found that the faster a galaxy is spinning, the brighter it is. Like the Faber-Jackson relation for estimating distances to galaxies, the technique allows astronomers to relate an observation (here, the spin rate of a galaxy) that is reasonably easy to make to the distance to that object.
::Tully-Fisher关系发现,星系旋转的速度越快,越亮。 与估计星系距离的Faber-Jackson关系一样,该技术让天文学家可以将观测(这里是星系的旋转速率)与相对容易到达该天体距离的观测(这里是星系的旋转速率)联系起来。 -
A Type Ia supernovae
is a
carefully regulated process - mass from
an
evolving binary companion is funneled onto
a
white dwarf. When the white dwarf accretes enough mass to hits the
Chandrasekhar
limit of about 1.4 M
sun
,
a
Type 1a supernova occurs and the white dwarf evolves into a neutron star. A Type Ia supernova is always the same physical process, so it is always the same brightness. Type 1a supernovae are lucky events
that provide
very bright standard candles.
::Ia 型超新星是一个精心监管的过程 — 进化中的二进制伴侣的质量被渗入白矮星。 当白矮星的重量达到Chandraskhar 1.4 Mmun的极限时, 会出现1型超新星, 白矮星演变成中子星。 Ia 型超新星总是同一个物理过程, 所以总是同样的亮度。 1型超新星是幸运的事件, 提供了非常亮的标准蜡烛 。 -
Redshift - Hubble found a relation between the redshift of a galaxy and its distance.
In this case, a spectrum is obtained and the measured shift of spectral lines is the redshift that reveals the velocity of a galaxy. If spectral lines are shifted toward redder wavelengths, the galaxy is moving away from us; if spectral lines are shifted toward bluer wavelengths, the galaxy has a component of radial velocity that is coming toward us.
The precision of redshift measurements has been improved (e.g., by Freedman et al.) and shown to be a reliable distance indicator at the largest scales in our universe.
::红色移位 - 哈勃发现一个星系的红色移位与其距离之间的关系。 在这种情况下, 获得了一个频谱, 测量到的光谱线的移动是显示一个星系速度的红色移位。 如果光谱线向红波长移位, 星系将远离我们; 如果光谱线向蓝色波长移位, 星系将具有射线速度的成分, 它会向我们飞来。 红移测量的精确度已经提高( 例如, Freedman 等人 ) , 并显示它是我们宇宙最大尺度的可靠距离指标 。
The cosmic distance ladder - different techniques are used to determine distances at different scales. By cross-checking distances between rungs of the distance ladder, we can reliably establish distances to galaxies out to the edge of the observable universe. Which method is well-suited for measuring distances to nearby galaxies? To nearby stars?
::宇宙距离梯子 - 使用不同的技术来决定不同尺度的距离。 通过交叉校验距离梯子之间的距离, 我们可以可靠地确定星系与可观测宇宙边缘的距离。 哪种方法适合测量距离到附近星系的距离? 对附近的恒星来说 ? -
For the closest objects, the moon or Venus, we can use radar ranging. This allowed scientists to figure out the distance to the Sun. Once we know the distance to the Sun, we can figure out how much energy is being emitted each second (i.e., the "luminosity") in the following way: the Sun emits equal amounts of energy in all directions. We can use a photon counter to determine how much light is being emitted at various wavelengths. Each photon has an energy:
and luminosity,
, is the total energy per wavelength per second. Next, we have to determine what fraction of energy is intercepted by the photon counter; this will scale as the area of a spherical shell centered on the Sun with a radius equal to the Earth-Sun distance:
