“evidence from the motions of old stars that the galaxy ...etolstoy/gfe09/patrick.pdf · older...

Eggen, LyndenBell, Sandage (1962)

“Evidence from the motions of old stars that the galaxy collapsed”

Top-down model of the formation of the Milky Way using evidence from stellar kinematics

Patrick Bos

March 5, 2009 Eggen, Lynden-Bell, Sandage (1962) 2

My twenty minutes● Collapse in a nutshell● Stellar kinematics & age estimation● Kinematics in a collapsing (proto)galaxy● Correlations

– Age & eccentricity

– Age & angular momentum

– Age & vertical velocity

● Spatial- and timescales


Collapse in a nutshell● 1010 yr ago

● tcollapse

~ 108 yr

● Scale of collapse:

– Rnow

/ Rproto

~ 1/10

– znow

/ zproto

~ 1/25

● Protogalaxy with angular momentum

● Rotating disk


How to collect the evidence


Stellar kinematics● Data: 3D velocities of 221 stars

● Solar neighbourhood, R = Rsun

● Model galaxy (N.B.: galactic plane only)

– Axial symmetry, conserves ER and h

– Potential

● Integrate orbits● Derive ‘eccentricities’

= GM

bb2R2

e=Rapo−R periRapoR peri


Age estimation● Data: U and B photometry● UV excess: ● Metals absorb UV in stellar atmospheres● Younger stars, higher Z, lower ● Older stars, lower Z, higher

U−B=U−B−⟨U−B ⟩

U−B

U−B


Kinematics during collapse● Assume:

– ψ axially symmetric at all times (but MW is barred!)

– masses whose h differ significantly don’t exchange h

● Then h conserved for each element of matter● Eccentricity:

– slow collapse: e constant

– fast collapse: e larger


Quick overview● Eccentricities e from velocities + model:

– Constant for slow collapse

– Larger for fast collapse

● UV excess from photometry: age approximation● Protogalaxy: rings of gas with h/m, so stars

formed from same ring all have same h today


The actual evidence (pictures!)


Eccentricity vs UV excess

circular straight line

Average U-B(no excess)

Eccentricitycorrelates with age!


Angular momentum vs UV excess

R in plane vs h (circular) in model

Protogalaxy: rings of constant h

Formedduring collapse!


Vertical speed vs UV excess● Mean z

max correlates

with excess (age)

● Ez does not grow

● Old stars formed at high z, new ones within 1 kpc (disk)

● Scale: 10 kpc/400 pc-> z

now / z

proto ~ 1/25


Other spatial/timescales 1● Apogalactica R

apo; up to ~50 kpc

● Model: R(h) (now) ~ 5 kpc

● Assume eccentric stars formed at ~Rapo

● Radial scale of collapse: Rnow

/ Rproto

~ 1/10


● Suppose tcollapse

>> trot

~ 2*108 yr

● Then vR,gas

<< vφ,gas so for formed stars as well

● Slow collapse: estar

constant (collapsing model); orbits stay circular

● Data inconsistent, so tcollapse

~ 108 yr (fast)

Other spatial/timescales 2


Conclusion● Age ~ eccentricity ~ apogalacticum ~

galactocentric distance at time of formation● Old stars: h like in center; central stars

belonged to same h ring in protogalaxy● Oldest stars must have been formed during

collapse of h rings● Milky Way disk formed through collapse of

rotating protogalactic gas clouds


Fin

Questions?



We want more!


Biases


Apogalacticum vs angular momentum

1


Eggen, LyndenBell, Sandage (1962)

“Evidence from the motions of old stars that the galaxy collapsed”

Top-down model of the formation of the Milky Way using evidence from stellar kinematics

Patrick Bos

2


My twenty minutes● Collapse in a nutshell● Stellar kinematics & age estimation● Kinematics in a collapsing (proto)galaxy● Correlations

– Age & eccentricity– Age & angular momentum– Age & vertical velocity

● Spatial- and timescales

3


Collapse in a nutshell● 1010 yr ago

● tcollapse

~ 108 yr

● Scale of collapse:

– Rnow

/ Rproto

~ 1/10

– znow

/ zproto

~ 1/25

● Protogalaxy with angular momentum

● Rotating disk

The scenario that is scetched in this paper is the following. About 10^10 yrs ago a big cloud of gas called our protogalaxy started collapsing. This collapse took place in about 10^8 yrs and it shrunk radially (in cylindrical coordinates) by a factor of about 10 and vertically, towards the disk, by a factor of about 25. It fell into a disk because the protogalaxy must have already had angular momentum, so because of rotation the radial collapse is smaller than the vertical collapse.

All this they derived on the basis of their data.

[[angular momentum: already there or from couple from nearby clouds]]

4


How to collect the evidence

So how did they come to this conclusion? They used basically two types of observations of 221 dwarf stars (subsolar mass) in the solar neighbourhood (within 100 pc).

5


Stellar kinematics● Data: 3D velocities of 221 stars

● Solar neighbourhood, R = Rsun

● Model galaxy (N.B.: galactic plane only)

– Axial symmetry, conserves ER and h

– Potential

● Integrate orbits● Derive ‘eccentricities’

= GM

bb2R2

e=Rapo−R periRapoR peri

First, 3D velocity measurements were collected for the dwarf stars, which are all in the solar neighbourhood (~10 kpc). We then take a model of the galaxy (in the galactic plane only!) for which we assume axial symmetry. This means that the radial kinetic energy and the angular momentum h are conserved. The most general potential that satisfies these criteria is given here. We can then use this and our initial values of the velocity and the position (the same position as the sun) to integrate orbits, of which two are plotted here. From these orbits we can measure all kinds of parameters, like the energy, the ang mom and the eccentricity. We define it using the apo- and perigalacticum, the farthest and closest points. This is not a strict eccentricity because the orbit precesses.

6


Age estimation● Data: U and B photometry● UV excess: ● Metals absorb UV in stellar atmospheres● Younger stars, higher Z, lower ● Older stars, lower Z, higher

U−B=U−B−⟨U−B ⟩

U−B

U−B

The second type of data they used are U and B photometry. These we use to derive the UV excess, which is the U-B color difference with an average value. The higher the UV excess, the more UV it has w.r.t. average.

Metals in stellar atmospheres absorb UV radiation and because metallicity Z changes due to enrichment of the gas clouds by the first generation of stars, younger stars will have more metals and thus more UV absorption and thus a lower UV excess, whereas older stars, which were formed when there were less metals, have higher UV excess.

The UV excess can therefore be used as an age estimator.

7


Kinematics during collapse● Assume:

– ψ axially symmetric at all times (but MW is barred!)– masses whose h differ significantly don’t exchange h

● Then h conserved for each element of matter● Eccentricity:

– slow collapse: e constant– fast collapse: e larger

Now there's one more thing we need to consider before we look at the data. We need to find out how stellar orbits react to collapse.

ELS first assume that the potential is axially symmetric at all times. We now know that this is wrong though, because the MW is a barred spiral! I don't know what the implications of this might be on this theory.

Next they assume that masses whose angular momenta differ significantly don't exchange angmom.

These together mean that h will be conserved for each element of matter.

For the eccentricity there are two possible situations: if the collapse is slow w.r.t. the rotation time e will be constant, but if it is fast e will become larger. Compare to a planet around a star: if the star would suddenly become twice as massive, the planet would suddenly fall towards the star and thus its orbit would become eccentric.

8


Quick overview● Eccentricities e from velocities + model:

– Constant for slow collapse– Larger for fast collapse

● UV excess from photometry: age approximation● Protogalaxy: rings of gas with h/m, so stars

formed from same ring all have same h today

So a quick overview of what we now have:1) We have eccentricities and these will be constant if

collapse was slow and larger if collapse was fast2) We have UV excess which gives an age approx3) We can see the protogalaxy as rings of gas clouds,

rotating with the same angular momentum per unit mass, because only clouds with similar ang mom will exchange ang mom and thus become equal. The stars that form from one ring will then have the same ang mom and because that is constant after collapse they can always be identified as belonging to the same protogalactic ring.

9


The actual evidence (pictures!)

So with that behind us we can get to the actual results.

10


Eccentricity vs UV excess

circular straight line

Average U-B(no excess)


First we have this plot of eccentricity (horiz) versus UV excess (vert). E = 0 circular, E = 1 straight line. Even though these are magnitudes, the UV excess simply goes up like 'this' (upward), so higher is more UV.

So as we can clearly see eccentricity is correlated with UV excess and because higher UV excess means older, *CLICK* we have the remarkable result that eccentricity correlates with age!

How can we explain this?

11


Angular momentum vs UV excess

R in plane vs h (circular) in model

Protogalaxy: rings of constant h

Formedduring collapse!

Let's look at this plot of angular momentum versus UV excess and therefore age. This plot shows UV excess horiz and ang mom vertically. We see a very similar correlation, but what does this mean?

We see that the older stars have lower ang mom. *CLICK* Let’s take h = 12 as our average and compare this to the current circular ang. mom. as function of galactic radius. We then see that h = 12 corresponds to a radius of ~5 kpc. However, they are now in the solar neighbourhood, so at about 10 kpc. Their ang momenta tell us that they once belonged to the same ring of mass. *CLICK* Therefore, the older stars must have formed during collapse, when the ring was still at a higher distance from the center! This explains the high eccentricity, because when they were formed, the galaxy was collapsing quickly, so their orbits would naturally become elliptical.

12


Vertical speed vs UV excess● Mean z

max correlates

with excess (age)

● Ez does not grow

● Old stars formed at high z, new ones within 1 kpc (disk)

● Scale: 10 kpc/400 pc-> z

now / z

proto ~ 1/25

Another piece of evidence is in this plot of vertical speed, i.e. speed in the z direction, parallel to the axis of rotation, against UV excess, age. You can use this speed to calculate approximately the maximum height above or below the plane the star will reach.

Let’s see what this tells us. First: *CLICK* the average z_max correlates with age. Because the vertical energy is not expected to change much (some exotic energy source would be needed) this means that these older stars could have formed at all z’s, while younger stars were all formed near the plane. Which is in accordance with the previous conclusions.

We can also use this plot to estimate the scale of collapse in the vertical direction by taking the maximum heights, which are maximum heights of formation *CLICK*; this gives us about 10 kpc over 400 pc, 1/25

13


Other spatial/timescales 1● Apogalactica R

apo; up to ~50 kpc

● Model: R(h) (now) ~ 5 kpc

● Assume eccentric stars formed at ~Rapo

● Radial scale of collapse: Rnow

/ Rproto

~ 1/10

Another spatial scale can be estimated as follows. We have integrated the orbits and have the apogalactica, the points of greatest distance from the center. These run up to about 50 kpc. As we saw before these oldest stars have the same angular momenta as stars in circular orbits at about 5 kpc. So if we assume that the farthest stars were formed at the apogalactica, we have a radial collapse scale of 1/10. Of course this needed to be smaller than the vertical scale, otherwise we wouldn’t be living in a disk galaxy.

14


● Suppose tcollapse

>> trot

~ 2*108 yr

● Then vR,gas

<< vφ,gas so for formed stars as well

● Slow collapse: estar

constant (collapsing model); orbits stay circular

● Data inconsistent, so tcollapse

~ 108 yr (fast)

Other spatial/timescales 2

Then finally they reason their way to a timescale of collapse. Suppose first that collapse time is far greater than one period of revolution, which is about 2 times 10 to the eighth years. Then the radial velocity due to collapse will be much smaller than the circular velocity due to rotation, for the gas, so for the stars formed in the gas as well. We saw earlier however that for slow collapse we have that the eccentricity of a star is constant in a collapsing galaxy. This would mean that the orbits nowadays should still be circular, but this is not what we have seen. So the timescale of collapse must be comparable to the timescale of revolution, so on the order of 10^8 years. This means fast collapse so the eccentricities can be explained.

15


Conclusion● Age ~ eccentricity ~ apogalacticum ~

galactocentric distance at time of formation● Old stars: h like in center; central stars

belonged to same h ring in protogalaxy● Oldest stars must have been formed during

collapse of h rings● Milky Way disk formed through collapse of

rotating protogalactic gas clouds

So to conclude, what have we found?First age correlates with eccentricity, correlates with

apogalacticum, correlates with maximum distance from the galactic center at the time of creation.

We combine that with the idea that because of the rings of constant ang mom in the protogalaxy, the old stars must have belonged to the same ring as the ones closer to the center nowadays.

This leads us to the conclusion that these old eccentric stars must have formed during the collapse of these rings of angular momentum.

The Milky Way disk then seems to have been formed through the collapse of rotating protogalactic gas clouds.

16


Fin

Questions?


17


We want more!

18


Biases

Upper left: 1) UV excess increases with total space velocity (other paper). 2) Observations of weak nearby stars have usually been confined to those with appreciable proper motion. This means that there is some bias against weak stars in circular motion, thus at the left in general. 3) However, there is no special bias for UV excess. 4) All stars in circular orbits that were found have low UV excess.

Bottom right: majority of high-velocity stars were discovered before UV photometry was available, so no bias there as well.

19


Apogalacticum vs angular momentum

“evidence from the motions of old stars that the galaxy ...etolstoy/gfe09/patrick.pdf · older...

Documents