We can move on to our third presentation
for the afternoon that's actually
third and final presentation.
Monica Valluri from astronomy.
Let me see here. So we see you Monica,
I guess we need to see your slides,
so while she pulling it up,
the title of the project is
"Probing the Nature of Dark Matter
"by Modeling The Milky Way" and
this time Monica's project is also
one of the most recent, part of the
most recent cohort of
MICDE Catalyst grants
and there are number of Co-PIs.
And, oh yes however I
leave that to Monica to
talk about it. Yep, I
see her more up there.
Okay, Monica with the other--
- [Monica] Can you see me?
- [Krishna] Yeah, I'll give you all,
I'll give you all a heads up in
about 20 minutes into your talk.
(mumbles)
- Okay.
Okay, so.
Thank you for
inviting me to give this talk.
It's a pleasure to be able to
describe some of the work that
has been going on in my group.
I'm trying to probe
the nature of dark matter
by modeling The Milky Way.
And there's a fairly large number of
collaborators on this project,
I will mention the ones that are
more actively involved as we go along.
So, to just give you some sense of context
with every galaxy, including The Milky Way
is embedded in a dark matter halo
and within that dark matter halo
comprises between 80 and 90 percent
of the total gravitating
mass in the galaxy.
Its presence is inferred purely
from its gravitational influence
on visible matter like stars and
hydrogen gas.
And today despite several decades,
couple of decades of
particle physics experiments
trying to detect the dark matter,
the dark matter particle has
so far not been discovered.
And so astrophysics,
astrophysical constrains
on dark matter tend to, are considered
likely to be extremely
useful for identifying
the nature of the dark matter particle,
in particular whether
is relativistic or not
and what kind of interactions
dark matter particle might
have amongst themselves.
Some of the things that we do know about
dark matter comes from
cosmological simulations
and these simulations predict
some very specific things.
First they predict that
the dark matter halo
of galaxies like The Milky Way should be
not spherical but triaxial, that is
they have three unequal symmetry axis.
A small radial they're
likely to be flattened
but they become more
triaxial at large radial.
Other predictions include that
the density profile at the center
should be fairly cuspy, that is
its density is rising steeply
and are power losses at the center.
And that there are a large number of small
satellites, the little
things that you can see,
fuzzy balls, that you can see around
around the galaxy,
many of which might have
been disrupted by tidal field
from The Milky Way.
So, our goal in this project is
to test some of these predictions
by modeling stars in The Milky Way halo.
In particular we don't know whether
The Milky Way's disk, how it is oriented
relative to the dark matter halo,
it could be aligned with its
the rotation axis
parallel to the short axes or it could be
a lined in the other direction.
The data that we are gonna use
for this modeling, it comes from
a map which was made by
satellite called Gaia
and this map is presented here,
it's not a photograph, is actually a map
which consists of a
billion individual stars
whose brightness and position have been
accurately
obtained and then plotted on this map.
That at the center, shows
the center of our galaxy,
there's a couple of
satellites, the large and small
Magellanic clouds, the dark area shows
dusk in the galaxy and as I said
this map was obtained the Gaia satellite,
which is an European
space agency satellite,
which was launched on 2013.
The first data release was obtained
in September of 2016,
the second data release
which was obtained in 2018 is the one
that we have been using the data from
and future data releases are
expected in the coming years.
So, the satellite obtains what is called
parallax that is it obtains the
geometric distances to stars and
proper-motions
that is the motion across
the plane of the sky,
and it does this for a billion stars.
It also obtains the Doppler velocities
for about a 100,000 stars,
the brightest of these billion stars.
And there are also
ground-based spectroscopic
surveys which give additional
Doppler velocities.
So, our goal is to model something like
several million of these stars
which lay within about 30 or
40 kiloparsec on the center,
a kiloparsec, a parsec being
about 10th to the 16th meters.
So the way we are going to do this
is by what is called
distribution function fitting,
where we assumed that the function,
the distribution function
which describes the stars
that is, it gives you,
the density of stars per unit volume,
per unit physical
volume, per unit velocity
volume and velocity space.
That is an unknown quantity
and we also don't know
what the dark matter
distribution is, that's the
second unknown quantity.
And of course we know
what the normal matter is
where it that is distributed, that's what
we called the Baryonic distribution,
we see that from observations,
so the dark matter in the Baryons
together constitute the
gravitational potential
and it is in this potential
that the stars are orbiting
and so the distribution
function, that we can compute,
has to be taught consistence with this
with this gravitational potential.
So, we use a variety of different data
from Gaia that is the,
in some cases we have six dimensional data
but for the most part because
the majority of the stars that are only
proper motion we don't
have regular velocity
we only get five dimensional data
and then we construct the Bayesian model
to inform the properties
of the model that is
the properties of the
distribution function,
the properties of dark
matter halo by matching
individual, properties
of individual stars,
taking account the fact that you don't
that there is a certain selection function
you don't see everything
and the errors on the data.
So to just give you a sense
of what action modeling is
orbits in galactic potentials admit
three isolating integrals of motion.
And a well-know theorem called the
Jeans Theorem argues that
the phase space distribution
functions of stars and galaxy
of galaxies should be a function
of this integrals of motion.
So you can, in practice you can use
any integrals but these actions are
specific, are particularly useful
and therefore it is actually very
important to be able to evaluate actions
from the phase space coordinates,
and the action is defined as
by this equation
where p is the canonicaly
conjugate momentum
for each of the coordinates.
So in this graph, for instance, you see
a typical rosetta orbit, which
you would see in spherical potential
and it is, it has
some of the actions that conserves
at the angular momentum
energy and the third action
which in this case is
the total angular momentum.
So it had been lots of classical methods
for evaluating actions,
these are well-known
from classical mechanics.
In flattened systems,
it is possible to make
something called the
epicyclic approximation and then calculate
the actions in that manner.
Until recently it has not been possible
to compute actions for general potentials
similar to
those that we see in galaxies.
In 2012,
professor James Binnie
from University of Oxford, came up
with what is called the Stackel fudge,
where he argued that if you
since most general form of potential
that can, for which
you can compute actions
is a separable Stackel potential,
which is given by this expression five
in a coordinate system which is
confocal, ellipsoidal coordinate system,
you can calculate the motions
in two direction lamda and nu
with a canonical conjugate momentum
p lamda and p nu
by two separate equations
and the actions are then
j lamda and j nu
are easily computed
using integrals over,
which can be computed
by numerical quadrature.
So, Binney showed that
this Stackle fudge even though most
galaxies do not have Stackle potential
if you pick a
Stackle potential,
which is approximately equal to
a Stackle potential, you
can get accurate actions
to within one percent
for most disk orbits.
So the red points in this graph show
a previous kind of approximation called
the Adiabatic approximation.
Whereas the Stackle fudge shows the
the black triangles
shows the Stackle fudge
and what we want to see is that
this is computed as an orbit
evolves over 700 dynamical times
and since actions are meant to be conserve
you see that the Stackle fudge
gives you almost constant values
varying by one percent.
Whereas the previous
approximation gives a much wider,
much greater variation.
So, although the Binney's
method works well
is not extremely efficient for
general potentials and so my collaborator
Eugene Vasiliev whose post
is currently at Cambridge,
developed a flexible code called
flexible package called AGAMA,
which computes
actions in general potentials for much
orbits so this is just a
two dimensional projection
of an orbit
and is ten times faster than
say the Stackle fudge.
It does fail in some places
but it has been
remarkably powerful and AGAMA
the power of AGAMA and
the fact that it has been
so powerful, is illustrated in the fact
that this package has been used in
over 40 publications in
the last year and a half.
So, some of the limitation
of AGAMA as it stands now are
that is still only works for
axis and metric potentials
and it is not
so it doesn't work for the
kind of triaxial potential
we think that exits in galaxies
and the speed of the
computation of the potential
is extremely critical to
having fast action computation.
So, one of the goals of this project was
to try and convert the action finder
to such that it could run on a GPU
and Alexander Gaenko from CSCAR so
the MICDE Grants allowed us
to hire
Dr. Gaenko who's an
expert on GPU programming
and other things and other
computational aspects
to help us transforming this AGAMA code
such that it would work on actions
and this plus give you basically
an analysis of the performance
so the code,
of course, improves
with multiple threads, this is for
test with over 2,000 stars
and it runs quad
the time for a star is
quadratic for star
because of various
because of the accuracy requirements.
So, one of the things
that has been done so far
is that Alexander Gaenko has identifed
the parts of the AGAMA code which are
bottle type performance, bottle-necks
and in particular there are
axisymmetric action integrators
so he has been testing and
he has been showing that
two things which take up
a significant proportion
of the time are
can be adapted and he's done
some test with proxy codes
for these root finders which are used
in the action finders and finds
a seven times speed up,
is possible
and so we think that
in over a fairly short time scale,
by the end
of this year we should be able
to have a version of AGAMA
which works on GPU
and will allow us
to do the kind of analysis
we need for the stars
with the sample sizes we have.
So,
AGAMA is c++ code but it is
there's a Python interface
and so the code that
we are actually using for
the modeling of the galaxy
is called iGalapagos
and it's a Python code.
Some of the results that
we have from that so far
are a modeling of The Milky Way halo,
a sample of stars called RR LYRAE stars
which comes from the Gaia satellite,
and this analysis, this
is just a distribution
in what is called galactic coordinates, L
being the
what we call longitude and
B being latitude, galactic longitude
and galactic latitude at the center
of the galaxy is at zero zero.
And this analysis has been running
has been done by Kohei Hattori
On high performance computing networks,
Kohei was here as a post opp but has
has recently move to Carnegie Melon
where still he is running this code,
320 cores where it takes
a week of wall time.
Right now, we're only
running with 4,000 stars
but we have
16,700 RR LYRAE stars
and in the future data releases
will give us up to a 100,000 stars.
So, the analysis that he has done so far
includes some validation test
which shows that you can
fit the rotation curve
that's a circular velocity curve of
The Milky Way to get the dark matter
and the model for the barions,
and also the acceleration of the star
is above and below the disk.
And most impressively,
in these two panels on the right:
one panel shows the
data for RR LYRAE stars
and the panel on the extreme right shows
the model and one of the things
some of the things you can see
there's a quadruple axisymmetry here
which our model picks up
there's a certain
and this is joint correlation
between two proper motion components
this is showing the dispersion and
the proper motion in
the latitude direction
and so the distribution
these plots on the right tell us
that the distribution function
that off the actual stars
is being well-recovered
and the shape of the dark matter halo
the rotation, other data being well-fitted
and this modeling tell
us that the rotational
the halo shape within 20 kiloparsec
is almost spherical, is
almost nearly spherical
and this is encouraging but
one of the things that we
said before was that
this is not based on a
triaxial model yet, because,
and the goal has been
to improve our modeling so we can get
to the triaxial models.
Another test that we are doing
is being done by Pablo Fernandez de Salas
whose a postdoc in
Stockholm working with me
and Katie Freeze,
and he is applying the
same code iGalapagos
to set a simulations,
a cosmological simulations
called the Latte simulations
from Andrew Bessel who was the
speaker in one the MICDE
colloquial this past year.
This simulation has satellites,
has screens, modules
and are very representative of
The Milky Way, and one of the simulations,
one of the assumptions
we made in our modeling
is that The Milky Way is in equilibrium
which it is not, and so one of the test
we are doing is to see how badly our
models work if we make the assumption
of dynamical equilibrium.
So, this is the model
for the Latte galaxy, this is the
shows its flattening, it's quite a
flattened halo and unlike
the real Milky Way,
and has an axis ratio
within 20 kiloparsec of above .6
so it's quite flat like a pancake.
So our goal is to test
how the measurement of
the shape is affected by this equilibrium.
So our preliminary test have been done
by generating a whole sample of
mock halo stars from the
cosmological simulation
from the Latte simulation,
we have three different
simulations and are
making mock data in three
different positions in the
galaxy because we don't know
the sun is in some arbitrary position
and our ability to observe the galaxy
can only give us a limited view of
the stars and the galaxy.
And iGalapagos has been
drawn on this mock data
and so far
we get, so if the red curve here shows
the potential, the true potential and
the blue curve shows the
best fit potential from
stars, dark matter and gas.
And the shape that is obtained here
is .7
and I said that the true data
and the data used currently
are only within 25 kiloparsec,
I said that the true shape
is actually something like
.66, so this is not bad
it's definitely, good and
better than ten percent
but if we are going to do
more test to understand how
sensitive this is
to various,
to the kind of non-equilibrium
effects from satellites.
As I said earlier,
The Milky Way is not
in equilibrium and in fact
that are many satellites
which are currently
being tightly disrupted
by the galaxy. One of which is
the Sagittarius stream
and Sagittarius is
shown in this image here,
a graduate student who is working with us,
Youja Wu, from the Physics department,
has been looking at using actions of these
stars in the halo
to try and find modular events,
which you don't see any longer
in terms of these streams.
So, the idea is that in
an adiabatically varying
gravitational potential
the actions of trajectories
are approximately conserved.
So even if the tidal disruption
of a satellite by the potential spread
the debris across the entire sky
making it hard to detect
if you find the
if you have six dimensional
phase space data
that is three position
and three velocities
and a knowledge of the potential
which we will obtain for say iGalapagos
you can then hunt for previously
accreted satellites using
clustering in action space.
So, the question that we
hope to answer with this are
since the potential is not
really adiabatically invariant
I mean it is, it is somewhat
adiabatically invariant
but no exactly, how
massive does the satellite
need to be to be
detectable and how recently
should it have to been
accreted to still be detectable
in action space?
So, and the other question
which is relevant to our
understanding of dark matter is that
much of some this debris,
not necessarily all
of it but some of this
debris is likely to be
near to the position of the sun
and so if we can
tell that there are correlations
between dark matter,
debris, and stellar
debris from satellites we
might be able to use this to detect
over-densities in dark matter,
which could be helpful for
direct detection experiments.
So, the work that has been done by Youja
is in collaboration
with Robin Sanderson and
Andrew Wetzel at UC Davis.
And they gave us
data on the infalling and satellites
to some of these galaxies
that's plotted here in action space,
so each color represents one of these
16 different satellites which
came into this galaxy and
whose action at the present
time are computed in
the potential and plotted in action space.
So, without actually
knowing this information
about the actual satellites Youja applied
a clustering algorithm to the actions
using two different kind
of clustering algorithms.
One was called StarGO which
uses a self-organizing
map and the other is
something called EnLink
which is a density-based clustering.
In multidimensional space
this plot shows the clusters in
action space as identified by this
software called EnLink.
And this is, you know
there is a good amount
of correspondence between these two,
we use a couple of different metrics,
one is called purity and
one is called recovery,
which tells us what fraction of
a particular object was actually in fell,
is fell in, is recovered
by one of the clusters
in action space, how much contamination
so that's what's called recovery
and the second quantity purity tells us
how much contamination there
is from other satellites.
And so this shows the total mass of
all of the satellites that fell in
versus the time at which they fell in,
and the shapes tells us whether the purity
and the recovery match each other,
so if the purity and the
recovery are both high then
they're represented by
a triangle but if one is
purity is high but the recovery is not
it's represented by a circle.
So we see that
only satellites
with masses of about of
a billion solar masses,
which fell in less than seven
gigayears or seven and a half gigayears
bout half the age of the universe.
So, the top left hand corner gives us the
gives an understanding of what
satellites we can currently recover
in a simulation like Latte.
So,
I don't know how much time I have left.
- [Krishna] About, you
are about 25 minutes.
- Okay, in that case I
think I'm going to stop.
I mean there's another
project that we're doing
which has to do with
with identifying streams in the halo
also using actions but I will skip that
because it was not part of our original
project description.
So, I will just summary
conclude by saying that we are
we have adopted this
multi-pronged computational
effort to try and constrain
the properties of dark matter
using observations of The
Milky Way stellar halo.
One of the things we have
done so far has to apply
our action based on distribution
function fitting code
to our (mumbles) data which have told us
have been useful for measuring
the shape of the halo,
we are testing assumption
of dynamical equilibrium,
we are also using this
action computation to
identify previously accreted satellited
to understand the decreation
history of the halo
and detect maybe local dark matter.
And we are also doing a bunch of N-body
simulation which I didn't describe
to try and constrain the properties of the
central density profile
of dark matter halos
and so
some of the successes are
that I want to thank
MICDE for this funding
which has enabled a lot of
this research especially
the GPU acceleration that is being done by
Alex Gaenko and the
work that is being done
by Youja Wu,
and I also want to say that the process of
you know, the robust process
of proposal evaluation
and feedback, extremely helpful feedback
from the MICDE Grants cycle
enables us to get a NASA grant
we applied for it in July
we got notified that it
was awarded in November
so this research will be
will continue to be funded by NASA.
So, I'll stop there
and take questions.
- [Krishna] Okay, thanks Monica.
also thanks for bringing up
that little mention
of the extra success that
this sort of program promotes.
As before,
attendees put
post your questions in the chat box
will pick them up, maybe I can start out
I have a couple of questions
and the first is related to.
Just trying to get
an outsider's understanding of the halo
though when you said that the halo
appears differently at smaller radii
how does one understands that because
if one just looks at it
as a three dimensional
ellipsoid sitting around the galaxy
what is the difference,
is it the density distribution
that appears different
at smaller radials? If you just look at
the high density near the small
at the smaller radii,
that region of high
density is flattened out?
Or--
- [Monica] Yes.
So if you measure the shape,
so if you take the shape of the density
you look at the moment of
inertia denser, for instance
if you take that mass
as a function of radius
you calculate the moment
of inertia denser,
you'll find that a small radii
sort of the Eigenvectors will be octagonal
and of course their eigenvalues
of the three components
of the moments of inertia denser
will be equal, approximately equal or
at least two of them will be equal,
one of them will be flattened,
but as you go out those eigenvalues,
of the moment of inertia
denser, as you go out
and radius will become
more and more different,
and so that's why we call
it triaxial by radii.
Sort of axisymmetric
or at least we seem to find
that is almost spherical at small radii.
- [Krishna] So okay,
very naive this is some
sort of a mass effect
that the main body of
the galaxy is pulling
in the dark matter as well?
But the dark matter is much denser I mean
there's much more of the dark matter,
that's why should it.
- [Monica] So a small radii,
within the solar,
sorry not within the solar of course
within the solar radius but also
within The Milky Way
the disk region of the galaxy,
which is such a very, there's less than an
inner one third of the dark matter halo
the mass of
The Milky Way stars and gas dominates.
So, you'll think that the potential
should be much flatter but the process
by which
the halo has been built up has led to,
repeated episodes of
feedback from cloud formation
and others things which have sort of
puffed up the entire potential
and made it significantly rounder.
We would not predict, we would not
I would say that most of the simulations
don't predict the spherical
halo at small radii,
they predict a quite flattened halo
but which seems like our calculations are
showing that it is,
it is probably close to spherical.
I mean this method is not the
only one that has found this
I mean the same data,
same kind of data applied
using a different method called
the Jean's equation method
found essentially the same results.
So we think that is a robust result
and we'll have to understand it better
I mean it could be telling
us about something about
the nature of dark matter.
So, there are certain types of
dark matter models, one
some of which are called
specifically self-interacting dark matter
does tend to dissipate more a minute
the particles interact, a
small region of high density
causing the potential
to become more spherical
at small radii
So I think it's to early to say that it's
one versus the other but
there are other kinds of
dark matter species which
explain this kind of round shape.
- [Krishna] And actually that
leads to my other question
that I also wanted ask, which is that
now with your Bayesion approach
what aspects of the model are you
refining, I guess you have some priors
for certain parameters in the model--
- [Monica] Yeah, so there are
So there's actually
something like 16 parameters
in the model there are several parameters
which describes the density
distribution of the dark matter
so there's a central slow,
central density
cast,
it's a profile, I mean
in log space it's add
the power of some alpha
where, you know, that's a key parameter
it's sort of turns over
in radius, at some radius
so that's another free parameter
the absolute density at the center
of the third free parameter,
the Doppler mass, the
flattening is another parameter.
And then there are
parameters which describe.
Although we know something
about the overall
mass distribution of the Baryons
we are not assuming
directly, we are assuming
a certain profile, a density
profile for the stars,
density profile for the gas and so
all of those are free
parameters, there's a certain
ranges of which
we are assuming
in most cases flat trials.
So, or uniform trials,
so there are few systems
few parameter over we need to
apply slightly different trials.
The distribution function also
has some parallel forms so there are
certain priors on that as well.
Certain parameters from that as well
but yeah, 16 different parameters
goes into this modeling.
- [Krishna] And how are
you doing samplings?
- [Monica] I think is just, yeah
one the standards maybe there are ways to
make it go faster but is a
something called MCENCE which is
quite common to use in astronomy.
- [Krishna] I don't
know, Mariana, you seeing
any other question in the Q&A chat?
- [Mariana] No, there's
no questions in the Q&A.
- [Krishna] Okay, there
aren't any other questions or
nothing else from the moderators.
Thank you Monica and thanks
to everybody who participated
on this second session,
Stephen,
Xun,
and Monica and of course all your Co-PIs,
attendees and everybody.
As you heard before this is
supposed to be part of the
MICDE symposium, we managed to
intended to do the part that we though was
more critical to MICDE functioning and
part of the, and has a role in
the rest of our program,
so the Catalyst Grant
process is on the way
and we do have
other, the symposium itself will occur,
for now it is planned for September 29th.
The plan is to have it in person
if that is allowed, by then.
But before that,
next Friday on the 17th
we have a webinar by Marisa Eisenberg
from School of Public Health,
Marisa's been working directly
with the State in modeling and advising
and modeling the progression of COVID-19,
in Michigan, she's been very
busy with that actually.
It's taking a while to set it up
so that she can put herself
away from all of that
very important work, and will give us
this webinar that is
time for the three pm,
on April 17th, using most
likely the same format
so we hope many of you will
be able to attend that.
Otherwise thanks everybody
and we will
I guess see you all around in our
various video chats,
And webinars and so well, so forth,
otherwise, as is common
stay well and stay safe.
