[MUSIC] 音乐。
Good morning, good afternoon, good evening, whatever time, 早上好，中午好，晚上好，啥时候都好吧，
your enthusiasm for exoplanets is bringing you back, welcome. 你对外星的热爱又把你带到这里，欢迎。
In this week, during this week, we will continue the description 在本周的时间里，我们会继续说明
of the properties of the exoplanetary system that have been detected. 已经探测到的外星系统的性质。
Of course the idea is, always to bring constraints for planet formations, making 意思是，要一直考虑外星形态存在的限制，
the link between initial conditions and the 在初始条件和观察到的
observed end state of the formation process. 经过演化进程的状态间寻找联系。
Now we start with the properties of the central mass in the system. 我们先从系统中的中心质量开始。
What do we expect? 我们希望什么？
We assume that protoplanetary discs have masses that 我们假设初始的时候圆盘形状态是有质量的，
are scaling with the mass of the central star. 并且用中央的恒星作度量。
So you form bigger stars in bigger discs. 所以可以认为越大的恒星，周围的圆盘物质越大。
Makes sense and as at least from the core operation scenario you need more 这可以说的过去，并且至少需要更多物质去构建核心，
solid material to build up the core and then gather an equation of the core. 以聚合成相等的核心？
it seems that you should be able to do it more efficiently in a big disk. 看起来似乎圆盘越大，构建核心效率越高。
So for more massive planets in more massive discs, 同样盘子越大，行星也越大，
so have more massive planets around more massive stars. 同样盘子越大，行星也越大，
And actually, that's the same for the gravitational instability approach. 事实上，这和重力不稳定性接近是一样的。
Because to get instability, you need a massive disc. 因为要变得不稳定，就需要一个巨大的盘子。
So you will, with this process, form massive planets. 所以，照着这个进程，形成巨大的行星。
It's even probably impossible to form 重力不稳定的圆型尘埃中形成小质量行星几乎
small mass planets with gravitational instability. 是不可能的。
So, the prediction we can make is that more 因此，我们可以预言，越大质量的恒星附近更有可能找到大质量行星
massive planets are probably found around more massive stars. 越大质量的恒星附近更有可能找到大质量行星
So, what do we know from the observational point of view. 如此，我们根据观察都发现了哪些观点。
There have been several projects targeting low mass 目前已经有一些项目把小质量恒星
stars and high mass stars to search for planet and try to answer this question. 和大质量恒星作为研究目标，以尝试回答这些问题。
And maybe the first one to mention is the one around low mass stars and dwarfs. 首先被提及的会是在低质量恒星和矮星附近的目标。
And I will start with [INAUDIBLE] velocities that's programmed here, 我将会从径向速度法开始，
that is described that has been conducted by Xavier [UNKNOWN] 描述的是由Xavier指导的
from The [INAUDIBLE] Observatory in collaboration with our team in 来自于位于Geneva的合作的天文台，
Geneva and we have fellow [INAUDIBLE] M dwarfs from the sun. 我们跟踪M矮星
And from these observations, we could infer frequencies 并且由这些观察，我们可以推断在那些恒星附近
of planets of different types around those stars. 不同类型行星出现的频数。
For example, we have seen that giant planets are very rare at the level 例如，我们发现巨大行星在1%~2%等级里是非常罕见的，
of a percent or 2 if we go out to hundred day period. 如果周期大于100Days。
So big planets are rare around M dwarfs from the radial velocity survey. 从径向速度法获取结果说明大行星在M矮星附近是很稀有的。
On the contrary, super Earths and Neptune are very 相反，超级地球和海王星却很多，
numerous, at the level of 50%, plus minus 20. 在50%±20%的水平，
So that's the same type of numbers 这和我们寻找类太阳的恒星，
than what we find for solar type stars. 相比也是有同样的数量级。
So it's easy to form small mass planets around small star. 所以，更容易在小质量恒星附近形成行星。
These findings can be compared with 这些发现可以和开普勒卫星
the results obtained with the Kepler satellite. 为所公认的结果相比较。
In the Kepler field, we have something like 在开普勒的领域，
4,000 stars with a temperature smaller than 4000 degrees. 像小于4000°的恒星有4000个。
And those are defining our low mass stars. 并且那些都被定义为小质量恒星。
Courtney Dressing and David Charbonneau from The Center for Astrophysics in Boston 天文物理学的两个波士顿的科学家，
had a look at the sample of M stars in Kepler and derived the fraction of 在M恒星发现了一个例子，由此推断平均每个恒星有小部分行星
planet per star on average around M dwarfs in the Kepler sample. 附近有M矮星。
The results, well one of the interesting results is that there is 关于结果，其中一个有趣的结果是，
almost no giant planet transit in front of M dwarfs. 几乎没有巨大行星在M矮星前发生凌日现象。
There is only one case known and 已知只有一个案例并且
that has confirmed by ground-based radial velocities. 通过了基于地面的径向速度法确认。
But most of the planets are of small size because from the 但是，大部分行星都很小，
transit, from the Kepler data, we measure the size of the planet. 因为，通过凌日，通过开普勒的数据，我们可以测量行星的大小。
And so the findings of Dressing and Charbonneau is that if we restrict the 所以D和C的发现
sample of planets to be smaller than 4 earth's radii, so 如果我们限制为小于4倍地球半径，
smaller than Neptune basically, then there is an average of .9 planet 那么经本上小于海王星，那么平均每个M矮星会有一个0.9个行星。
per M dwarf in the sample and if we only consider even smaller planets, 如果我们只考虑更小的行星，
earth size planet still within the 50 day period, then 像地球大小的行星周期仍然小于50Days，
we have an average of .5 planet per star [INAUDIBLE] M dwarf. 那么平均一个M矮星会有0.5个行星。
So very clearly the the formation 因此，很明显，
of planet around M dwarfs is favoring the M矮星附近，
low size planets. 更容易形成小行星。
Now if we have a look at the other side of the spectrum of the sun trial star mass, 现在，如果我们看一下太阳频谱的另外一边，
we need to go to stars with 2-3 solar 我们需要到2到3倍质量的恒星，
masses to see the difference with the solar type stars. 才能看到与类太阳恒星的区别。
And so on the main sequence, we go up to the AB dwarfs, 所以按照主星序，我们看看AB矮星，
but those are hot, high-rotation stars for which the spectral 但是那些外星很热，转速很高，对于那些光谱很
lines are very broadened and so it's very difficult to detect planet around those. 宽，并且很难在他们周围探测到行星。
So a better approach is to look at G, 所以，更好的方法是观察巨大的，
giants, that are evolved version of these A-type star. 那些是进化了的A型恒星。
And here in the diagram obtained from the Exoplanet Encyclopedia in Paris, 在这里图表中，可以从外星百科全书中得到，
it's just a number of planet in function of
the mass of the central star, and we see that for high masses,
2-3 solar masses, there are detection, there are several tens of them.
So, we do find planets around giant stars.
If we look at the same sample, but now in a diagram showing the planet
mass versus the star mass, we see that most of them are massive planets.
Of course, there is a detection bias
here because for giant stars, because of intrinsic
variation of the star, it's very difficult
with radial velocities to detect small mass planets.
So there is a bias, but we clearly see
that there are a lot fo massive planets around giants.
So how now, can we compare?
Because we are completely biased for these
giant stars, we have no small planet detections.
So we cannot compare directly the frequencies with other type of stars.
So what we can do is to consider the total mass on the, the form of planets,
the normal planetary mass in the system normalized by the number of stars
that is in the given bin of star mass.
So, we can roughly make 3 big bins.
We have the small mass stars, the M dwarfs.
We have the solar type stars, and we have
the more massive stars, the evolved stars, the giants.
And in each bin, we put the total mass of the
planets and we normalize by the number of stars in each bin.
And you obtain this figure that was made
by my colleague [UNKNOWN], a few years back.
And that very clearly shows how the content under the form of planet, the, the
material under the form of planet is
increasing with the mass of the primary star.
So the mass of planetary material scales with the mass of the star.
And again, if we come back as you already have seen this slide
before in the course, that's the detection of very massive
planet in the outer regions of systems of massive stars.
They are A Stars and the detection have been made by direct imaging.
Of course if they are massive and far from
the star, it's easier to detect the planet through imaging.
But if those planets would exist around smaller mass stars, it
would even be easier to detect them and we do not.
So it seems that these massive stars have, are
favorable place for the formation of these big planets outside.
And there is even another case where the central star is a B9,
it's compound [INAUDIBLE], and that there is a companion of the level of
12-13 Jupiter masses at 55 AU from the central star.
So, are those system very common or not?
That's a very important question because planet formation scenario
based on the core [UNKNOWN] have difficulties to form them.
So, you can form maybe the planet in the inner region of the
system and have the planet move
outside by migration, by planet-planet interaction, all,
all type of processes that can happened, but if most of those stars
have these planets, then it's starting to be difficult to explain it this way.
So, the statistics about the massive planet in the outer region
of massive stars will be an interesting question to be addressed by the
new generation of planet imager that are being installed these days on the
large telescope G pie on Gemini, and a sphere on the VAT.
And maybe in the next version of the book, we will have results on these aspects.
Thank you.
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