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The Proper Motion (Orbit) of M31
3 papers by groups led by people at STSCI
(see my JournalClub site for links)
Paper 1: Sohn et al, astro-ph May 2012
Paper 2: van der Marel et al
Paper 3: van der Marel et al
Journal Club website is
adansonia.as.arizona.edu/~edo/JournalClub
Why do we care about parallaxes and proper motions?
(a very short, woefully incomplete list)
1) How else do we know the brightnesses of stars?
(how bright is a Cepheid, tests of stellar evolution code,
distance to LMC, distance ladder…)
2) We’d like a volume limited sample of stars (in the largest possible
volume (Sun’s nearest neighbors are well hidden, bright stars are rare).
3) Structure and evolution of Milky Way, for instance (how was
the halo put together, how was Milky Way assembled).
4) We’d like to know all phase space dimensions:
radial velocity
proper motion in x direction
proper motion in y direction
xyz positions (distances)
5) We can derive the potential of the Milky Way from moving groups
of stars (star streams… run time backwards in correct potential).
6. We can derive some distances independent of some of the steps
on the distance ladder, for instance, using water maser P.M.’s
What can we do from the ground and space before
GAIA?
Ground-based parallaxes of 1mas, or, with more epochs, 0.3 mas
or so. To V= 13-20 or so.
Hipparcos parallaxes ~1mas to V=8, except for some unfortunate
places on the sky (Pleiades); re-reductions give 0.6 mas or so.
So far, the ground wins?
Ground-based proper motions (perhaps with long time baselines)
give proper motions of 1mas/y. Perhaps tied to QSOs or galaxies
Or really faint stars.
Hipparcos proper motions were 1mas/y for bright stars,
now degraded to >15 mas/y because of unknown proper motions
of the reference stars. It is tied to egal by a coord rotation.
So why was Hipparcos a triumph?
Hipparcos catalog--118,218 stars with 1 mas astrometry.
Tycho catalog--106 stars with 20-30 mas astrometry
and 2-color photometry.
Tycho-2 catalog– 2.5 million stars. 99% of all stars to V=11.
Distances determined to better than 10%- - 21k stars
Distances to better than 20%-- 50k stars
Two examples of ground all-sky: USNO-B, which you should
know and love… 1 billion stars to V=21, 20mas accuracy in astrometry.
UCAC (USNO CCD Astrometric catalog): UCAC-4 about 20mas
So the all-sky nature of Hipparcos to levels that match
dedicated (not all sky) ground-based surveys is one reason
we remember Hipparcos. And its success led to GAIA
which should be 1000x better.
GAIA will be launched in late 2013
It uses the same ideas as Hipparcos, two telescopes separated
by ~100 degrees on the sky,
putting images on the same detector, so small and large
angles can be measured at same time. But it uses CCDs
so crowded fields can be measured and you aren’t restricted to
one star at a time, as was Hipparcos, which used a photomultiplier
with translucent bands at regular spacings.
Estimated full-mission (6 year) results:
Note that the units are MICRO-arcsec or MICRO-arcsec-y
Parallax
V=6-13 8 micro-arcsec
14 13
15 21
16 34
17 55
18 90
19 155 (that’s 0.1 mas)
20 275
So at the faint end, it’s about the same as the ground-based
Except that it does every star in the sky.
Parallax Horizon
(no extinction)
1% error 5% 10% 20%
The Sun
0.8kpc 1.8 2.5 3.5
K5 giant
1.3
4 7.5 11
10d Cepheid 1.2
6 12 22
So for parallaxes alone, you survey a fair fraction
of the MW for supergiants, a modest fraction for giants,
a smaller fraction of late type dwarfs.
Proper Motions
(in mid-experiment things will be about 1.5 times worse)
V=6-13 5 micro-arcse/y
14 7
15 11
16 18
17 30
18 50
19 80
20 145
There are LMC and M31 stars in these magnitude ranges.
For reference, at 50 kpc, 100 micro-arcsec/y = 24 km/s
so we can measure individual stars in LMC to 24 km/s.
We can measure the halo (and couple it with radial vels)
to discover fossil stream that tell us MW accretion history.
Now what about HST
It turns out that HST is a great proper motion machine
(I won’t discuss parallaxes with FGS here).
Ivan King and Jay Anderson and others pioneered this.
It has been used for relative proper motions in globular
clusters (membership, high-vel stars, white-dwarf sequences etc).
It has been used for absolute (tied to QSO reference frame) proper
motions of dwarf galaxies (Piatek, Pryor, Olszewski).
You can get proper motions in only a couple of years.
We can get systemic motions in dSph good to 30-50 kms
(and down to 10 km/s if a third epoch is ever granted).
So we know the orbit shapes.
Proper motion of LMC has even been measured by
Kalivayalil et al and remeasured (same data) by us. QSO’s
in every field.
This HST measurement changed LMC studies because it’s seen that
LMC is falling in for the first time. And it only took a couple of years
between epochs.
In passing, what we gain is the superb precision. The good
measurement is only different from the ground-based by 1.5x the
error in the ground-based (errors in ground-based are large,
too large).
Well, wouldn’t it be nice to know the space motion of M31?
But M31 is 10-15x as far away as LMC.
Do we have to wait 20 years? What about systematics?
What do we use for a reference frame? Galaxies?
But there are problems and solutions:
1) Gaia will be linked to a QSO frame. It’s in space
so the fact that QSOs have weird SEDs doesn’t so
much matter.
2) HST has good resolution, makes all galaxies have different
shapes. This is bad. But see the papers I’m reviewing.
3) Both HST and GAIA have CCDs that are (will be) suffering
from CTE degradation from “cosmic rays”. With HST you
can post-flash the detector, expose longer, or inject charge.
With GAIA you extensively model, with real data with the real CCDs,
the degradation by exposing the CCDs to high cosray fluxes
in the lab. You find which model best fits the data and that tells
you your corrections.
Right now with WF3, which seemingly flew yesterday, investigators
are being asked which options to take to deal with CTE degradation.
With GAIA, uncorrected, faint stars’ centroids move by something like
10x the needed centroiding precision.
If you want 500 pages about Hipparcos (it’s fascinating reading
actually, see
www.rssd.esa.int/index.php?project=HIPPARCOS&page=Overview
and click on “Overview of the catalogs”
Check out the 1998 ARAA
Some good links for GAIA are (this is only a start)
sci.esa.int/science-ewww/area/index.cfm?fareid=26
link.springer.com/article/10.1007/s10686-012-9310-5/fulltext.html#Sec1
adsabs.harvard.edu/full2005ESASP.576..729D
Before these papers, what’s an example of reducing HST astrometry,
based on the work by Piatek et al (there are other techniques as well,
by Jay Anderson and collaborators).
I. Identify QSOs using any technique you can.
II. Approximately center the QSO, expose deeply enough to NOT
overexpose QSO while getting good exposures on dSph stars.
Dither as many times as you can.
Get at least one exposure in another color to be able to make a CMD.
III. Calculate the PSF at every position. Use one PDF per epoch.
IV. Remove distortions and mitigate distortions by returning to approx
same pixel at each epoch.
V. Fit PSF to data. Recalculate centroids and photometry till
convergence.
VI. Measure the motion of the QSO against member stars,
multiply by -1.0
VII. Convert to reference frame of choice from xy.
What do they do in these papers, and what’s different?
Differences: first, they have hundreds of stars to use to determine
PSF of stars and distortions of camera that aren’t properly solved for.
This allows the frame-to-frame and epoch-to-epoch distortions to
be known better.
Second: They have hundreds of galaxies versus 1 QSO. We have to
do a global solution, they can measure the motion of each star locally.
Why don’t we do this? Why doesn’t everyone?
First epoch M31 is from some of the “deepest-ever” images: 100 ksec=
28 hours per filter. Those images were also dithered.
You probably need a few orbits per first-epoch in nearby objects, more
than one field per object, and dithering (though you can relax any
of those constraints as desperation sets in.
WFPC2 probably never good enough. And nearby objects are big on sky.
So what did they do?
I. Deep stacked image
II. Star/gal lists, CMD to ID M31 stars.
III. Template fitting of each star (as we did)
AND each galaxy (all galaxies have different shapes).
IV. Positions- corrected for distortions and CTE degradation.
V. Iterate.
VI. Transform epoch 2 onto epoch 1.
VII. Local motion of M31 stars wrt galaxies.
VIII. Transform xy to coord system of choice.
VIII. Average the 3 fields together (paper I) or correct
for the fact that M31 has substantial expected motions
from field to field (perhaps larger than the tangential motion
of the galaxy as a whole).
IX. Correct for solar motion as best as is possible.
Example of the reconstruction of 3 galaxies and one star.
Left: original. Middle: reconstruction. Right: residuals.
Note bottom row if WF3, rotated 35 degrees from ACS.
Heliocentric proper
motions in km/s
for all 3 fields. Errorweighted mean in black.
It’s consistent with
water maser PM
for M33… M31
water masers are
being measured now
What did they get?
They measure a heliocentric proper motion of
about -0.0422 +-0.0123, -0.0309 +-0.0117 mas/y.
This differs from 0.0 at 4.3σ.
The two velocity components of proper motion are
-125+-31, -74+-28.4 km/s
After correcting for Solar Motion by subtracting a big
number , they get a tangential velocity of center-of-mass of M31
relative to center-of-mass of Milky Way of 17 km/s +- 17.
Using the new value of LSR motion and solar peculiar
vel, they convert heliocentric RV to -109.2+-4.4 km/s.
This implies a virtually radial orbit.
Using timing arguments and cosmological simulations, they
calculate mass of MW and M31, getting slightly lower numbers
because of solar motion and other assumptions.
Given the proper motion of M33 from water maser VLBI
indicates that M33 and M31 are a bound pair.
Implications (paper 3):
Now that you know Vtan and errors, RV and errors, masses of
M31 and MW and errors you can run many models and derive
the odds of M31 hitting the Milky Way, etc.
Odds of a direct hit (peri passage <25kpc) 40%.
Most likely outcome: MW and M31 merge, M33 orbits them
and may merge later.
9% chance M33 merges with MW BEFORE M31 does.
7% chance M33 gets ejected from Local Group.
85% chance Sun ends up much farther out than 8.5 kpc.
10% chance it ends up farther than 50 kpv from center
of the extended Andromedamilk.
20% chance Sun will travel through M33 while being bound
to Andromedaway.
Black:M33-MW
Red: M31-MW
Green: M31-M31
M33 blue: past orbit
Tidal radius: black circ
COM of MWM31: +
M31MW not
relaxed yet
Let me end by showing an old Mathias Steinmetz video: