(intro music)
It's a great privilege to
have the Bok Prize ceremony that we give every year from the Astronomy Department and
before we get to the talk itself, that they will accompany the ceremony, I wanted to mention a few words of background.
First, we have the privilege and
pleasure to host
the grand-
Great-grand.
-great-granddaughter
of Bart Bok,
Abigail, and her mother Gay, right? And, and, at dinner we will have also the father Alexander, right?
So a few words about the Bok family.
As you may have heard, the,
Bart Bok is, was, a
Dutch-American astronomer; he worked mostly on the structure and evolution of the Milky Way.
In particular, he discovered the Bok globules that
looked very strange at the time - they looked like
the, the cocoons of
insects on the sky, and it wasn't clear what, what is inside, and
he conjectured that these might be sort of like a womb that that makes new stars in it.
And it was a conjecture because you couldn't see through them, they were opague. 
And then later when infrared astronomy developed,
people could tell that indeed stars are being made in these globules. And so that was a very important discovery about the way that
nature makes stars. We see stars. We didn't know where they come from,
so that was an important aspect of figuring it out.
And then I should mention that he married the
fellow astronomer that was actually- who was senior then he was at the time
Priscilla Fairfield in 1929.
And
he passed away, Bart Bok, in 1983, but, but before that he, he, was named an asteroid after him and,
and, his wife, Priscilla, and he thanked the International Astronomical Union for giving him a little plot of land
that he, where he can retire and live on so that was his -
(audience laughter)
Just a few words about his background: he was born in a small Dutch town of Hoorn,
north of Amsterdam,
and then
Priscilla was an associate professor in astronomy, and
the young Bart Bok was assigned to her reception committee. He was a graduate student 10 years younger than she is
and fell in love with her.
And the rest is history.
And,
the following year, he
broke off his thesis studies at Groningen and moved across the Atlantic to Cambridge, Massachusetts, where we are,
on the invitation of Harlow Shapley, the director of the Harvard College Observatory at the time. And
a couple of days after moving to the US, on September 9th,
1929, so
91 years ago.
Two days after moving to the US,
they were married here; so this caused
an unusual circumstances here
in a way, but both of them continued to work together, and they remained at Harvard University for 30 years from
 1929 to 1957.
And they had two children: a son, John Fairfield, and a daughter, Joyce Annette.
So here we are looking at -
John, John's children.
-exactly.
Okay, so that's history,  and
I just wanted to mention a few words about this
year's recipient, Jack Steiner, sitting over there. You don't need to stand up yet.
So Jack actually did his PhD in the Astronomy Department at Harvard,
finished - they graduated in
2012, right, worked primarily with Ramesh and
McClintock, Jeff McClintock, but with both of you, I guess. Yeah, you will tell.
Primarily with with Jeff. And then,
he was a postdoc at the University of Cambridge - the other Cambridge, the original Cambridge - 
in 2012, and then
came as the Hubble Fellow to the Center for Astrophysics in 2012 for three years, and then
went to Paris, right?
You were there. Yeah, but you decided to come back to MIT,
and
he was an Einstein postdoc fellow at MIT, and then,
most recently he became an astrophysicist at the Chandra X-ray Center here at the Center for Astrophysics. And
Jack, and Jack, has a lot of important
scientific results to his credit that, over the years, earned him
many awards in addition to this one:
he received the Harvard, the Merit Fellowship in 2010, the Fireman Prize
in 2012, just to show that Astronomy Department does
appreciate talent that later
matures and becomes ever more prominent.
And,
obviously, he also received prize fellowships like the Hubble Fellowship, Einstein Fellowship, and so forth.
And then,
I wanted to ask Abigail to help me with the award -
so just a few words about Abigail: she works as a grant writing manager
At Root Capital, and 
earlier, she pursued the graduate degree at the University of Oxford, and
she has a lot of talents based on what I read, but I don't want to embarrass her by spelling all of them out.
 (audience laughter)
But I would like to ask Abigail to say a few words first, and then we move on.
Thank you. It's a pleasure to be here with you all today.
I'm representing my family. 
We are not astronomers, anymore, which I think is sad, but it's exciting to be here, and
one of the kind of legends of Bart Bok that I've been taught my whole life was how he had such a passion for
sharing astronomy with the public and with communicating and
really promoting science
as much as he could to people who are
total lay people. And I find this sort of beautiful poetry in the fact that I, a
 perfect lay person, am being welcomed by you all at this amazing event.
And I really think that it makes me feel
very proud to know that Bart's legacy and Priscilla's legacy is still
very much alive here today. So thank you.
 (audience applause)
All we can say is that you carry his biological DNA,
we are trying to carry his academic DNA, here.
And, every year we try to reward the previous
graduate student of ours that did very well later on,
recognize the important work that was done. So maybe we should ask Jack to come over, and...
I am pleased to present the Bok Prize.
Thank you very much.
Thanks!
Congratulations!
(audience applause)
And this is to you.
Thank you.
So Jack will speak today about measuring spins of stellar-mass black holes - a very timely subject -
and he's doing it with X-ray spectroscopy.
Well, I first want to begin by saying
thank you so much to the Bok family
for this honor, thank you to the department for this honor, and
I'm very excited to be able to share to you- share with you
what for me has been the most exciting and rewarding of
scientific
adventures to embark on, which is delving into the spins of stellar-mass black hole systems. 
And for me this is a very-
it's, it's not only a scientifically fulfilling subject, but at this moment has a very deep personal connection to me.
Jeff McClintock was my advisor for my, my thesis work that I'm-
the basis for what I'm gonna be telling you today. Jeff died just a little over two years ago, and
for those of us here who knew him, he was the paragon of
what we look for in a scientist, he was
someone who
had such passion and such joy in
the sense of discovery - more so than anyone I can think of - and Jeff loved data with just
an incandescent
fury that was just - it was so much fun to to dive into problems with him.
So this is of course a picture from Jeff later in his career.
I'm showing you a picture of Jeff early in his career, here, where he was
in...
off the coast of Africa at the launch of Uhuru, a telescope that he helped
build, design, and was a part of all the way through.
And
it was one of my joys to be able to share with Jeff
my experience of being involved in the launch of NICER and the adventure of sort of a new instrument making discoveries on the sky
shortly before he died. So I wanted to
share this picture with you, as well as to say that I first encountered Jeff in 2006,
starting off as a fledgling grad student in this department.
And the way I encountered him was Jeff was giving the colloquium here, where I'm standing now,
telling us about a new enterprise he was starting to work on, and he was looking for new graduate students.
He had made some of the first measurements of black hole spin, and he was presenting work on GRS 1915, which is a source
I mentioned earlier today in my lunch talk, a very
exciting and dramatic black hole system.
And he was introduced by Ramesh, who
called Jeff "Mister Black Hole", which is a fantastic superhero name;
and, and that is really Jeff to a tee. But, but his superpower was not about black holes,
it was actually - his superpower was the ability to inspire in others his intense joy for science.
And he would be delighted to be here today and I,
except for maybe this description of him, I'm sure he would have been embarrassed, but I
am sharing with you all of these results that he nurtured and,
and had such joy and passion for, and at the end of this
I hope you'll come away with a bit of a sense of what Jeff viewed as the capstone on his wonderful career.
So, uh,
while I have control of my emotions,
let me dig into the science of this - which is, first I want to tell you a little bit about X-ray binary systems, which are
the environments in which these black holes
that I'm going to tell you about live. We only know about them, but we think there are many
tens, hundreds of millions of black holes roaming around our galaxy, but unless they're interacting with some close neighbor/companion,
they're completely invisible to us.
So, these X-ray binary systems are our window into the behavior of black holes in our galaxy.
And I'll tell you about how we go about measuring their mass as a quick
primer, and then onto how we go about measuring their spin.
So a typical X-ray binary system schematically looks something like this, where there's a companion star, which may be overflowing
its, its Roche lobe,
giving a stream of gas that feeds onto the black hole
through an accretion disk. Now, typical size scales here are that
the accretion disk and the companion star separation from the black hole will be a few solar radii -
so these are really generally quite compact systems, closer in than,
than the Earth is to the Sun.
And all of the X-ray emission that comes from these systems comes from something like a hundred miles,
within a hundred miles, from the very center of the singularity that is the black hole.
So this is a very compact systems that emit enormously, these
prodigious black hole systems can outshine the Sun by a factor of a million in X-rays.
At all in X-rays. So these are tremendously bright, tremendously compact,
and they are some of the most mysterious objects in our universe,
the subject of scrutiny by not only astronomers, but by fundamental physicists, in science fiction and literature,
and
in philosophy.
So these black holes are born in the supernova deaths of some of the most massive stars that are formed in these sorts of
beautiful OB associations, where the most massive stars are born, live for several million years, and then go supernova.
And the most massive of these systems, we think, produce black holes as remnants from their dense cores.
We know of something like 50 black hole candidates in our galaxy that we've discovered over time since the dawn of X-ray astronomy in the
late 1960s, and this is showing you a compilation of a subset of these: this is, this plot is now somewhat out of date,
this was made by a collaborator, Jerry Orosz, need to ask him to
update this with a few new add-ons,
but this is showing you a subset of those 50 that are the dynamically confirmed black hole candidates -
so that is, these are systems for which we have made a
lower limit estimate of the mass of the compact primary, and we know it's above the threshold for a neutron star,
so it is a black hole. And you see that these are roughly divided into two camps: up here, there are these very large
companion star wind fed, massive
systems, and down here
there are systems for which the companion star is generally redder, smaller, and the disk of the black hole is oftentimes larger than,
than the companion star.
These are all Roche lobe filling, and
they're transient, so they go off for about a year and then are in deep quiescence for decades, maybe centuries.
These are all persistent systems, fueled by the wind of the close companion star. And when we observe these systems,
as we have for
over 16 years with the great Rossi X-ray Timing Explorer instrument, we see that the
variety of behavior that black holes exhibit is enormously rich. So this is something like a Hertzsprung-Russell diagram
for black hole systems in the X-rays - this is showing you the hardness on this axis and the
intensity on this axis. So this is in detector units,
so every one of these points would be modulated in principle by the the distance to the black hole.
But this is showing you some 30 black holes
superimposed, all of their behavior over RXTE's 16 year history.
And, and this is comprised of many Q-shaped curves, where an individual black hole went into an individual outburst,
rose in a hard state, transitioned to a soft state, declined, and came back to quiescence.
I've -
I'm showing you not just the behavior of these systems, but also encoding in a rainbow of color here.
This, this color is telling you something about the flicker noise of these black hole systems -
so this is how noisy the accretion flow is when we observe it in X-rays. And this, this is telling us something, that
the states and patterns of behavior
we observe are not just modulated by hardness, but there's some intrinsic noise in that as well,
there's a timing process at play that changes in lockstep with the, the hardness changes;
so this is going to be sort of critical to
our understanding the rich phenomenology of these intricate black hole systems.
But in juxtaposition to this rich pattern of behavior I'm showing you here,
black holes are astonishingly simple.
They're the simplest objects in the universe.
They are described entirely, the No-Hair Theorem tells us, by just their mass and
their spin. All the information, all of the
molecular bonds, all of the complex
information that was a part of everything that went into the, the star and fell into the black hole after it was formed,
is radiated away; and all you're left with is two numbers that tell you everything there is to know about a black hole -
this is so remarkable, I'll give you a better
quote than, than I could provide myself in a few slides here.
But this is really something fundamental, something bizarre, and something remarkable that the universe has to offer us.
And the story I want to tell you today is that Jeff dedicated his career in
the early days to measuring mass for the first time, providing the first dynamical evidence that there was
a black hole system - there was a real black hole
in the universe, in our galaxy, before this was widely accepted.
And then, the work that I participated in
for my thesis and in Jeff's later career to measure the spins, which he referred to as the most
fulfilling part of a very
fulfilling career.
So, how is it that we go about finding black holes in the first place?
Well, unfortunately, we haven't come up with anything better than waiting around for them to go bang.
So right now, all we can do is sit around
with
X-ray detectors that are looking at all parts of the sky, or monitoring as
many patches of the sky as regularly as possible, and wait for something new to show up. That -
we don't have a better system yet devised to detect black holes than that.
But fortunately for us, any new black hole in our galaxy that goes off,
it gets so bright that we are certain to detect it.
And roughly, this is a cadence of a couple per year, thereabouts,
but it's, it's both frustrating and challenging to think about how we can do better than this and discover systems
that are not
enormously bright in active outburst; but presently that's that's where we're mostly stuck. So we wait for something to go up into outburst,
we identify its optical counterpart, and then we wait for it to get quiet in the X-rays - for the outburst of this
very bright avalanche of gas in the accretion disk to fade and diminish until the system becomes quiet once more; and when it's quiet,
we can go about measuring the dynamics of the system. And just to illustrate this for you in a concrete way,
this is showing you GX 339-4, which is sort of the canonical
prototype of
black hole X-ray binary systems. This is showing you
several outbursts of GX 339 actually, but this is showing you how it rises in a hard state, transitions across
to a soft state - this is all in a matter of several weeks -
it typically spends several months declining in a soft state, and then over a period of a few more weeks
will go back into a hard state and fade into quiescence.
So this is the typical behavior.
GX 339 is one of the few that's had recurrent outbursts, so
every five or so years, you get another bright outburst and it goes through the same pattern again. But when it's in this quiescent phase,
we're able to do some
fantastic complementary science,
but as we go about measuring the dynamics of the system - and this was how Jeff was a part of
identifying the first concrete black hole system: this is A0620-00,
identified by Jeff McClintock and
Ron Remillard as a black hole
for the first time in 1986. This was the thing that
proved to the community that black holes were bonafide real
systems. And
this is now a much richer data set by Joey Nielsen from a little over ten years ago showing you a beautiful
sinusoidal curve, this is the radial velocity of the companion star orbiting around the black hole.
So we're seeing it, the Doppler shift as it moves away from us and towards us, and by tracing out
the simple period and semi-amplitude of the system, you end up with a very lovely
relationship here that defines a mass function, that is in fact a lower limit on the mass of the compact object.
The thing that Jeff and Ron found was that this
mass, this, this lower limit on the mass, was above three solar masses - known to be above the highest possible mass for a neutron star: 
it had to be a black hole.
This is in a little more detail, showing you that this quantity is related to the compact object's mass,
modulated by the sine cubed of the inclination with respect to the line-of-sight, and
'q' here is the mass ratio of the companion star to the, to the black hole.
So we in fact have techniques that we've developed for measuring 'i' and 'q'.
Using the fact that these companion stars are tidally locked,
so that one orbital rotation corresponds to one rotation of the star itself, that allows us to by- to devise
q sin(i)
through a relationship called the Eggleton relationship.
The punchline being that if you can measure how broad your lines are, you can determine
v sin(i). And then inclination itself we measure by looking at this double
ellipsoidal modulation as a function - and this is a light curve of the system, as it's orbiting around it gets
brighter twice and fainter twice each time it orbits around because of this
cool and faint tip on the front of the star, and
this large area that you see when you get the full teardrop shape of the tidally distorted
companion. So,
these observables let us cleanly get a dynamical mass for a black hole, again
this was done for the first time in 1986 by Jeff and Ron,
and, with that, I've told you half there is to know about a black hole.
But that was the simple half, and the less exciting half, frankly.
So I'd like to move on to telling you about spin.
And as I said, to really impart the,
the wonder and the shockingness of the existence of black holes that are
describable by just mass and spin, I
want to give you a quote better than what I could provide on my own.
This is the great Subrahmanyan Chandrasekhar, who Chandra is named after,
who said "In my entire scientific life,"
and again, this is *the* Chandrasekar, "the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity,
discovered by Roy Kerr, provides- provides the absolutely exact representation of untold numbers of massive black holes to populate the universe".
That is, that black holes are real objects described by only mass and spin: that was,
to Chandrasekar, the most shocking thing in his scientific career. He gets poetic after that statement.
Ok. And
what are the sorts of things that we hope to learn by going about making these spin measurements?
Well, there are some really fundamental questions to both physics and astronomy that we're
in the process of being able to assess with these measurements. For one thing,
we're learning whether or not relativistic jets,
which are ubiquitous in black hole systems, whether or not these jets are powered by the spin of the black hole or by an accretion process.
This is, a, 
still a forefront subject,
and the spin measurements I'll be telling you about have been
integral in making some of these assessments.
We're learning something very fundamental about how black holes are formed, and what the supernova explosion
process is that that gives us a black hole: is the spin imparted at birth? Is the spin something that's accreted? This is something
we're in the process of learning.
And turning to systems other than the stellar mass: how is it that super massive black holes grow over cosmic history? And of course
where - as you, as you see from gravitational wave measurements, and, and -
we're in a new era where we're able to start using the kinds of techniques to tell us about
the black hole's properties, mass and spin, to assess something about whether or not
GR is correct. So something about fundamental physics itself.
I would say we're not here yet for these kinds of techniques,
but we're laying the groundwork to do those sorts of things in the electromagnetic spectrum.
But the basics for how we go about measuring spin are
wonderfully quite simple.
So it so happens in that if you take a particle, put it in orbit around a black hole in general relativity,
there's a very important orbit
that is the inner most stable circular orbit, or ISCO, and if you put a gas particle in orbit at the ISCO and you
flick it with your finger,
it will either go further out into the disk and be fine or it will plummet in a dynamical time into the horizon,
never to be heard from again. So this special radius, the ISCO,
we think truncates the accretion flow
so that there is a hole around the black hole at the ISCO that is outside of the horizon.
And the location of that ISCO, importantly, changes monotonically as you change the spin of the black hole - so that is if you take
here a 10 solar mass black hole, it has an ISCO out in GR units at 6M
for, or 90 kilometers for those of us who like to get anchored in some, some numbers,
and if you have its cousin who is the same mass,
but now maximally rotating so that it's dimensionless spin parameter is one,
that ISCO creeps all the way into 1M, so it's essentially the same value as the horizon.
And these two extrema, a difference of a factor of six in radius, have enormously different observable
results - and that,
inferring the the location of the ISCO, is really what we're measuring and allowing us to measure spin itself.
This is just showing you a plot of that relationship,
maximally rotating at one, non-rotating at zero, and, in fact, retrograde spins are allowed, in which
the disk is rotating in the counter sense to the angular momentum of the black hole.
There are two techniques in the X-rays that are currently being used to measure spin:
there's a continuum fitting technique, and that's going to be mostly what I tell you about today,
and there's also an iron line technique, which is most commonly called the reflection method.
The continuum technique uses broadband
thermal emission from the accretion disk to tell us the location of that ISCO radius;
the reflection method tells us, uh- uses
relativistically broadened line profiles to tell us about how close in that emission is to the black hole itself,
telling us the location of the ISCO from the
red wing of that iron line.
There are other methods, of course, that exist.
I'll tell you a little bit more about QPOs, quasi-periodic oscillations, that are a very tantalizing
prospect for making the most precise measurements of spin, and of course, as we all know, gravitational waves are
revolutionizing our understanding of black hole systems - of course,
this is a very different population of black holes not located in our galaxy, but located out in the cosmological flow.
And there's,
there's going to be a new technique that will be on the sky in the next couple of years,
actually polarimetry has promise for measuring black hole spins as well, and
we will have an X-ray polarimeter within the next two years
if all goes according to plan.
So first, continuum fitting.
Continuum fitting is
very simple and elegant.
So when I first was discussing
spin measurements with Jeff and Ramesh, I could tell Jeff loved this but Ramesh loves
simplicity in theory, and this -
I think it was Ramesh who in fact came up with this slide and made this point so well that, you know, any undergraduate
can walk away with I think a good sense of how we're doing things.
So, the way that we go about measuring the radius of a star that we can't resolve on the sky is
we plop down a spectrograph,
we determine a temperature. We know that a star emits roughly like a blackbody, and
so that means that if we can measure a temperature and
we have some measure of the total flux of the system, then we can determine a solid angle on the sky. So two observables,
total flux and temperature, tells us a solid angle. And if we also know the distance from, for instance, Gaia parallax,
then that turns into a radius. So this is, this is how we go about
measuring the radius of stars and how this has been done for decades,
oversimplified, certainly.
But by analogy, what we're doing now is changing from a spherical geometry to a cylindrical one.
So we have one broken symmetry,
we need now to know the projection inclination axis. And it turns out that, of course, the disk is not a single-temperature blackbody,
but it has a temperature profile. So we need some
model to tell us what the flux profile looks like, but essentially the, the core physics is the same:
we're using blackbody emission with a simple temperature measurement and flux measurement, which we can get from a single X-ray
observation, if we know distance and now inclination, we can determine the radius of the ISCO.
Now, to go to the true holy grail here, spin - dimensionless spin parameter -
we also need to know mass, mass is the scale parameter.
So if we can get mass, inclination, and distance, we've measured spin from a single X-ray observation.
Now to summarize that,
some of the logistics from the observable end,
we really want to have spectra where
you're dominated by the component of interest, that is the thermal emission from the accretion disk.
Again, we need theory to provide for us a model for the disk flux, fortunately
this was done rigorously back in the 1970s by Navikov and Thorne and then Page and Thorne with a small correction a year later.
This is showing you the
emission as a function of radius for different
spins. And you see that as you march along upwards in spin for a fixed mass accretion rate, you're getting more emission
it's- so it's getting brighter, and it's coming from closer and closer in: so it's getting hotter and it's getting brighter, and there's a dramatic
change, you'll note, between non-spinning and something close to maximally rotating. This is what we're measuring.
And lastly, I don't have time to go into detail on this talk,
but I encourage anyone who's curious to ask me,
we often have to make the assumption that the black hole binary spin axis is aligned with the orbital,
orbital ax- the rotation axis. So there's good reasons to believe in this, and we've done one important test of this,
please ask me if you want to hear more.
Ok, so let me give you a concrete example,
this is showing you a typical soft thermal state for the black hole LMC X-3.
And what we're seeing here is a very bright accretion disk that's peaked at roughly 1keV.
So this thermal disk emission is what we're interested in modeling,
this, we measure the temperature and we measure how much flux we're getting, this is gonna let us measure spin.
There's also always this pesky non-thermal component - now, for many folks
the non-thermal piece is their bread and butter, but here, thermal continuum fitting,
we want to know what is that disk temperature and what is its flux.
And we can do that very reliably, you can see how much signal there is in this observation.
Now in practice, this turns out to work incredibly well very reliably, and the best
test of this was something I did as part of my thesis work, where we looked at LMC X-3,
which is one of the handful of persistently bright sources that's also very
highly variable - so we can explore a range of luminosity, it's been observed with many different instruments separated by many years.
This is showing you a light curve of LMC X-3 going back into the 1980s,
you'll recognize a suite of your favorite X-ray detectors,
the Greatest Hits going back decades now,
who have all looked at LMC X-3, and we have, in total, around 750 observations of LMC X-3 that we used.
For some detailed
reasons related to where are- where we believe our model is reliable, we exclude both the very brightest end and the faintest end of,
of this,
of this range. I'm happy to say more if anyone is curious, but with 450 data points here,
what we do is we look at how consistently can we measure the inner radius with each of these observations,
again, some 400 plus observations, and we find consistency among an array of very different detectors
over decades to within about 5%,
including all
differences. So this is a remarkable validation of the idea that there is
notionally a constant inner radius in these systems that, that is the ISCO, and that this is eminently measurable
by continuum fitting itself. So this is
proof that there's a constant inner radius, but this is not actually proof that that inner radius matches the ISCO.
And some of our colleagues working in
GRMHD, the magneto-hydrodynamics,
question this assumption.
And so this is showing you work from
Bob Penna when he was a graduate student here, just a simulation that Bob ran of an accretion flow onto a black hole where I've,
where I've marked the ISCO -
sorry -
with this black vertical line. And so you see there's gas flowing into the ISCO, it looks like there's gas flowing out,
that's actually just patterns, so just a barber pole effect,
but you're seeing an accretion flow here plummeting onto the black hole, and what we can do is take Bob's simulation,
with all the state-of-the-art
MHD code at the time, and
we can make a simulated observation of that to test our assumption that that inner radius was in fact the ISCO and not some other location.
And what we find is that
in fact we were a bit wrong.
We're not actually at the ISCO, which would be, which would be the case if this dashed line matched the solid line.
but we're within such a small epsilon that this is
negligible compared to our observable uncertainties and mass inclination and distance.
So, the punchline is this continuum fitting method is very strongly underpinned,
and, in fact, the enterprise of measuring black hole spin is most strongly underpinned by the state of the art in theory and the state
of the art in,
in data, which is LMC X-3 itself. So we went ahead,
we've measured the mass of LMC X-3, we measured its inclination in its distance, and
this is showing you the final result we have for its spin. So this is showing you really the measurement units up top,
that is the- the location of that ISCO radius is this top axis and how that maps into spin is
here on the bottom axis. There, there's a quite nonlinear relationship between the two, so this is the quantity
we actually measure, this is the quantity of interest. And it turns out that the spin is about 0.25,
it's a low spin source,
and this is the most precise measurement
of this inner radius that we've been able to do to date, and this is incorporating all of the-
not only all of our
statistical errors, but all the
systematics that we could explore.
So that's continuum fitting in a nutshell, and I want to also touch upon the other major technique by which
spin measurements are made - this is the so-called reflection or iron line method of measuring spin.
So continuum fitting - this is now a,
not a very elegant cartoon
I'm afraid, but this is a cartoon showing you a black hole with an accretion disk, and some nebula around it. Now this nebula is
a corona of hot electrons,
by analogy to the corona of hot electrons we see around the Sun. Now, we don't know much about the shape of this
corona or, uh - and we have now some constraints on where it is located in some circumstances -
but generally, this corona is more mysterious than it is constrained.
This is responsible for that non-thermal blue piece I showed you in the spectrum earlier; and
the cause of that non-thermal emission is the compton scattering of
emission from the- thermal emission from the accretion disk,
where a photon- an X-ray photon runs into a hotter electron and gets up scattered in
the corona, and some of that emission it turns out will
scatter backwards and illuminate the accretion disk.
When that happens, a reflection component is produced - this induces
fluorescent emission and a continuum of emission, and this so-called reflection spectrum here is shown in blue in the rest
wavelength- or in the, the rest frame of the gas, and in red, I'm showing you what the observer sees
when this is convolved with all relativistic effects around the black hole that broadens
these features appreciably.
And just to walk you through this a little more,
piecemeal, this is showing you now a marching in of line emission
from far out in the disk to close in in the disk. So this is emission
now coming out from far away, where relativistic effects are quite minor, at 400 rg, and you see the classic double horn line profile, and
as you go in, you see that you start to get Doppler boosting -
so special relativistic effects start to take hold - you're boosted on one end, de-boosted on the other,
but then as we go further in you'll see that there's a net redshift as well as the gravitational redshift becomes important.
So this is all the
emission losing energy on its way out of the potential of the black hole. And when you put that together,
integrating what line profile you expect to see from a black hole
that's emitting iron everywhere in its disk, you see a canonical
profile like this, peaked at something like six and a half keV,
with emission that extends down to a few keV - this very extreme broad red, red wing is the hallmark of
reflection emission, and,
and, the extent of the reddening of that wing is what we use to tell us about the spin of the black hole.
So you can see here, comparing the same non-spinning black hole to its maximally rotating cousin,
we see that there's an extreme red wing on the tail of the
extreme spin case that is not present for the non-rotating black hole.
So it is by modeling this signature that we go about measuring spin, and, and this is showing you now the highest signal
reflection spectrum that had ever been obtained at the time,
this is really fantastic work by Javier Garcia, taking the entire RXTE archive of
observations of GX 339, that same canonical black hole I showed you earlier,
and putting together a 44 million count spectrum that shows this broad iron line here,
and the associated, this is the the Compton hump that has really been used extensively now in the age of NuSTAR as a
further anchor for reflection modeling and measuring spin. So this is showing you those lines and the performance of Javier's leading
reflection model relxill - what you see does a quite good job measuring the spin of this black hole.
So that's the techniques in a nutshell, and
I would like now just to say a few more words about how it is that in practice we go about
taking these measurements and put these in some context. So
this is again showing GX 339 as it goes through its, its outbursts, as seen with RXTE.
The places that we go to measure
thermal continuum fitting spin are over here where the disk dominates in soft states, and you can see that these soft states are typified by
very low rms noise. So that is, it's not flickering, it's very stable, and
almost all the emission is coming from an accretion disk.
By contrast, when we want to make the reflection measurements
we're specifically looking for times where the non-thermal piece is quite prominent,
so actually out here, in these bright and intermediate phases
of hard- either hard states or intermediate states - that's where we tend to go about measuring spin with
reflection techniques. So it is the case that we generally cannot get the same-
take one data set and extract two spin measurements at the same time,
simply because one method is optimized when the other one is
hampered, but it is the case that we can take one source and wait for it to evolve over a timescale of weeks or months,
from one state to another, and use the aggregate of those data to make our spin measurements.
And with that in hand, let me now show you the census of black hole spin measurements that we have now as a community
over the last,
roughly 15 years that this has been a serious enterprise of making these spin measurements;
so I've ordered this list roughly by spin, with high spins up top, low spins at the bottom, and you'll see that we have a, a
wide range of spins produced by nature going from essentially non-spinning to maximally rotating - that didn't have to be the case,
but that is what nature affords us. And you see that
there are a handful of systems where we have measurements with both
continuum fitting and iron K, and to save your eyes a little bit of trouble arranging things, I've highlighted in,
in yellow here cases where we're in very good agreement between the two methods and in blue a couple of cases where we have
significant tension between the two methods, roughly at a level of, I would say, two sigma kind of disagreement.
Over the last few years, we've tried to examine these two sources to see if we can understand the nature of why
there's
discrepancy here, and there hasn't been clear resolution yet.
But this is it, this is roughly two dozen black hole systems for which we've gone about measuring,
measuring their spins - and again, nature provides the full range of possibilities.
I'd like to just put up a quick comparison,
I'm not going to spend too much time on this, but I just want to highlight that
both methods are
determining spin by measuring that ISCO radius,
they're using different features, of course, and they're measuring in different states,
but I want to mention that the continuum fitting technique is really tuned for stellar mass black holes.
We would love to take this to AGN systems,
in fact, I've been in discussion with some some folks here about how we might do that,
but it turns out it's significantly more challenging for a number of reasons -
this is really mostly and best suited to steller mass black hole.
The reflection method by contrast is our avenue into the spins of AGN, so already this has been done
for many dozens of systems, and Laura Brenneman here is
one of the very leading experts on that, and anyone who's interested in that should- I encourage you to talk to Laura.
The great advantage to the continuum fitting approach is
that the model complexity is very low. It's about as simple a model as you could ever hope for.
By contrast, the reflection method
has a rather high complexity to it,
it depends on having some understanding of the coronal geometry, or at least a prescription for that geometry,
and one often has to make some simplifying assumptions about the disk atmosphere structure, how the ionization and density profiles go,
so that's that's a significant challenge.
The continuum fitting challenge is really going about measuring mass, inclination, and distance, and bringing that externally to the X-ray data. That's why
in this table,
excuse me, we don't have a fuller census of the continuum fitting spin measurements.
So we're going about making
these mass/inclination/dis- distance measurements from the ground, and we'll fill in that table as we go.
So, um, with that as sort of the census of the state of the art, I'd like to turn to:
what does the future hold for our approach to interrogate spin and measure this fundamental of black holes?
So the first thing I wanted to mention to you all is that there is this very tantalizing, exciting
possibility for,
for spin measurements that has been known for, for
well over a decade now. That is we find that at some very
isolated moments in time - so the
black holes produce these high frequency QPOs, and
they produce them in a very specific three-to-two resonance. So this is showing you here a census of some of these measurements for
various black holes, if you have a favorite telephone number check for it here;
but you'll notice that the same source here, 1550, has
frequencies in one observation
184/276 and the later observation 184/276.
So these are three-to-two ratio QPOs that are stable in time,
stable frequencies for the, the- for a given source, so it's repeatable,
and we find that this is
mostly
manifest only when the system is about to produce a strong ballistic jet, and then it goes away.
So we've been looking for more and more of these systems that we only have a handful, and,
frustratingly, we only have a handful, in fact four,
where we have both high-frequency QPOs and spin data. So what's special about these resonant frequencies and these
these QPOs? Well, this,
this kind of frequency range is exactly matched to the dynamics at the ISCO,
so this is where you would say the Keplerian frequency is at at the ISCO,
this is that same ballpark. The fact that they're stable makes us think that they're from a fixed structure in the system,
most obviously would be the ISCO, and the fact that
they've been observed only
infrequently
makes us try to rise to the challenge to get more measurements of this phenomenon.
So right now, we're trying very hard with NICER and ASTROSAT to hunt for more of these.
So with only a few measurements, right now
we're in a situation where we have many more models than we do data points, and it's not clear which is correct.
That's not a position you want to be in.
What's encouraging is that all of these models are capable of making very precise measurements of spin, so in fact
these are an order of magnitude or more more precise than we can do with either continuum fitting or reflection.
But again, we have too many models and we haven't been able to calibrate what the correct model is yet,
so this is to be determined, but
X-ray timing missions like NICER and ASTROSAT are where our hopes are to make this critical headway,
and if we can crack this egg,
then we will be in tremendous shape to really propel the state-of-the-art in spin measurement to a new generation.
And so this is low frequency data,
these are not high frequency QPOs,
but I just wanted to, for eye candy and somewhat out of a frustration of not having Q-
high frequency QPOs to show you, just give you a sense of what it is that we're looking for, what this would look like.
So these again are low frequency QPOs
observed with NICER for a black hole MAXI 1535-57,
so these are at a few Hertz, about 2 and 5 Hz,
what we're looking for is these kinds of features,
roughly this strength, but up here in
the hundreds of Hertz range. So we are still waiting for a new black hole to show us,
show us these features, we can measure it's spin, and try to get this calibrated.
But what I'd like to also turn to is what we can hope for in the near-term in the future.
So, what's quite exciting - and we heard a little bit at lunch about this - is a domain where we're interested- where we're entering
surveys with large datasets from the ground in the optical, and of course in the X-ray we have new
large area detectors coming online. I certainly-
well, Athena certainly, and then we're all hoping for Lynx as well,
and a probe class mission is proposed
called STROBE-X, which would be sort of a generational successor to NICER, which I spoke about this afternoon.
And I just want to highlight that
one of the things I showed in my lunch talk is that NICER is capable of getting roughly a 10%
disk radius measurement every second for a bright black hole. So this is reaching the viscous timescale for the first time. This is tremendous.
But what's astonishing to me is that with STROBE-X or something of its scale, where we're talking about 10
meters squared or thereabouts effective area wise,
you can get a 10% disk radius every
10 milliseconds; that's
approaching the orbital timescale at the inner disk, this is getting to a dynamical time scale range. This would be transformative.
In particular, this would enable us to do things like phase resolved spectroscopy of high frequency QPOs,
if we can get some good high frequency QPO data,
and allow us to go a step further, like map disk structure at the viscous timescale.
This is just a highlight for you, to convince you that this is actually not a total pipe dream. This is showing you what a
3 Crab source would look like with 15,000 counts in just a hundredth of a second with STROBE-X,
simulation, of course.
And it's not only a matter of our
ability to probe the black holes that we know about and can detect in our, in our own galaxy in new ways,
but our ability to take what we've been able to do in our galaxy and extend it to the full domain of the local group.
This is showing you that same map by Jerry Orosz, but now
extended to show you what we might see if we could look at the full
local group using Athena, and in some cases using STROBE-X.
In particular, if we can probe out to cosmological scales, which is something really
not, not so much in the domain of a STROBE-X instrument,
which is not imaging, but something with Athena, you can start to see, uh,
X-ray binaries and systems that, you know, 4, 10 megaparsecs away, really opening up our volume that we can
access X-ray binary systems - so this is showing
NGC 1313, which is home to
one of the favorite ULX systems that that is regularly studied, and this is showing how well you can isolate a
given X-ray source from the confusion of its neighbors with a couple of different apertures.
So with that,
I'd like to leave you with
the main takeaways here:
so there are two primary spectroscopic techniques that we're using in X-rays to go about measuring the spins of stellar-mass black holes,
there's continuum fitting and reflection.
We see that the two methods themselves have delivered little more than a dozen measurements a piece,
and, so in total, we have roughly two dozen spin measurements with about two sigma consistency between one another.
X-ray timing is a very promising avenue, if we can get it calibrated to measure spin it will give us the most precise measurements.
And, while I didn't have time to adequately talk about it here,
the growing results from gravitational wave measurements are just such an exciting complement to these techniques that we can do in our own galaxy.
So this has been a very exciting time.
The foundation for the spectroscopic techniques is
empirically anchored in the existence of a constant inner radius. This is most,
most strongly demonstrated in the system LMC X-3, for which we see that stability
anchored for us.
So again, we have roughly two dozen measurements at present, and I think it's reasonable to expect that in the near future
we can at least double that population and start to extend our view out from our galaxy to the local group, and
maybe even start to go extragalactic. Right now, we're working very hard to improve our precision,
and, again, calibrate this X-ray timing technique.
But I would like to end for you with a note just showing a highlight of
the capstone of Jeff's career.
So Jeff himself was instrumental in measuring
masses and spins
of these ten systems.
So this,
this
tremendous legacy is complete knowledge of these ten black holes, and I
am enormously amazed by Jeff and his perseverance, and I'm enormously excited that
this was
something that he achieved in his career and that I got to be a part of such a tremendous legacy. Thank you.
(audience applause)
It's also important to mention that the- one of the greatest
satisfaction that a mentor like Jeff could have had is to have a student of you. So-
 Thank you.
I couldn't avoid thinking that the window that you described to black holes is a traditional window
that was extremely successful, the only game in town for decades,
but now there are two contenders,
you know, on the block that could potentially- so one of them is obviously gravitational waves, you know,
LIGO and future extensions of it,
there is another one that, you know, might actually be quite useful, and that's Gaia in finding binaries that have
a dark companion that is very massive.
But, just speaking about the gravitational waves, which already give us some statistics,
it seems like there is a clear discrepancy between the results that they provide and those results in the sense that,
you know, most of their black holes are much more massive than most of your black holes. What do you make of it?
This is, this is true, and it's been-
sorry, close your eyes while I flip through here to,
to this line. Yeah, this is showing
with- the size of each of these dots match to the,
the mass of the black hole. This is showing that- they call it the X-ray measurement,
so these are the X-ray binary systems that we've measured the masses for in
comparison to the gravitational-
the merging- these are the progenitor
black hole systems in green, and you notice that these are- are much larger on the whole, and so I think
what this is telling us is that we're probing two different populations. And the reason for it,
I don't have- I- I'm not authoritative enough to give you a firm answer, but I will tell you my speculation,
which is that I think
in both cases, we're looking at binary systems that are relatively compact, but I think it's quite likely that,
while the black holes that we observe in our galaxy, which are none of them
in globular clusters,
may- some of them may have originated there. I
speculatively will suggest that it's possible that these
larger, more massive black holes formed in dense environments and had
supernova explosions of a different character, where they may not have received a kick that ejected them from the cluster, and if so
they're in this very dense
environment, where most massive objects would tend to sink to the center,
potentially being able to merge through three-body interactions, which would give you a different character than we have from the population
we observe in our galaxy. But I think,
to me, this is just enormously exciting, and it's illustrative of why it's important to make these kinds of measurements with different techniques because I think,
you know, beforehand - actually, the original
gravitational wave event was essentially off the charts in mass for them. They weren't looking in that window,
that was that was at the very corner of what, what was being searched for.
So this is, you know, who would have thought, this is really-
There's another complication, because they were, the, say, college of the LIGO collaboration for decades was to build up a library of templates,
because the signal will- they expected the signal to be just a little bit above the noise,
so they would fish out the signal with a template, the library-
once they saw the first event, it was clear that they can see it with their own eyes, you know,
so nature was very kind to us,
in a way, compared to what the expectations that were based on your, your data.
Yeah. Absolutely.
Yeah, questions
Yeah, I do have a question, but I just wanted to say
that way I got to know Jeff was because he was here every Saturday.
So, this persistence of, you know, working hard - and this was really around the time before the spin -
but, you know, working on the math and establishing that there's a population of black holes
in the galaxy, he was on the job all the time.
Yes.
So, that said, now I'm going to ask you a question, which actually may be related to Avi's question,
because one of the things that leaks out when you look at the Orosz diagrams that you showed,
is that for the wing systems, none of those stars, and that is drawn to scale, if I remember correctly- 
Yes.
-none of those stars are large giants.
They may be evolved stars, but they are not on the large end, none of them has a
radius close to an AU, for example.
This is true.
When we look at other galaxies, and we look at some of the very luminous
X-ray sources, some of which are thought to be black holes, some of which are neutron stars,
but these are the most luminous ones, occasionally thought to be candidates for more massive black holes -
some of them seem to have supergiant companions.
And, so, I've been looking at this a little myself lately, and I'd like to ask now the expert,
do you have an idea as to why the set of donors that you see in a diagram like this
doesn't extend to much larger stars?
I know time scale is part of the answer, but beyond that.
I, I think that's a great question. I,
I don't have a good answer, I- and I just, speculatively, I wonder if,
you know, if you form- if
you're in a position where you have such a large binary, if that might lend itself to sort of a common envelope scenario,
which would essentially drag the black hole in and eject a lot of that envelope and leave you with just a core to accrete from.
I think it's- that's again just
speculation - I think that's enormously interested- interesting, and I,
yeah, I haven't thought a lot about it.
To grow the big black holes-
Yeah
-we know-
By the way, one anecdote is the black holes that the LIGO detects
could merge within a Hubble time only if they start with a separation that is less than a few times their progenitor size.
Unless you have mass transfer from a third star.
Yes, that's a caveat.
Yes.
So looking at the distribution of spins that you bring in from Jeff's,
it seems like the wind feds were obviously much, much faster, and the transients had a wide range-
Yes.
-you care to comment on... What sets the distribution of those spins?
Yeah, well that, so that's a very, that's
a great question, and I would say it's
small enough number, number of statistics that I shouldn't-
Ok.
-it would be dangerous to overspeculate. Let me try to- 
Speculate ahead!
-flip to that - but,
you know, I think it's an indication-
let me say, Tassos Fragos did some really excellent work
trying to just ask the question of is
there enough time to accrete the spins for all of these black hole systems; and the answer for the most massive
companion star systems, you won't be surprised, is that no,
they're high spin and they have high mass companions that are ticking time bombs that detonate before...
actually, yeah, I think, I think that one will be more clear.
So, so yeah, the time scale is just not sufficient to accrete for these, um,
these wind fed binaries here,
where you see the,
well, big, er- black hole masses are larger,
but especially the spins are larger and the companion masses are also sort of tens of solar masses.
Down here the- where the spins are sort of widely distributed from zero to maximal,
Tassos found that there was sufficient time to accrete the spin for every system, except
GRS 1915, which breaks all molds, was a little too extreme for him to be able to accommodate. But the story that works for Tasos
and his picture of binary evolution was that you could form a binary
with essentially lower mass and zero natal spin, and spin all of these things up
via accretion of the, of the donor star; and all these systems had to be formed with very high spin at birth.
So this would again be pointing to two different
supernova processes, these I will note all have higher mass than
these guys here, with the exception of GRS 1915.
But that's a consistent story. 
Make them with very high spin at birth,
you need to make them from a disk in the core of the star. So there needs to be some disk there as well.
Well, I mean if you take the, if you were to take the Sun and trap its anchor momentum into,
into a black hole,
I forget the precise number, but you would have something like
2,000 times the maximal angular momentum of a black hole. So it's, there's enormous amount of angular momentum in even something
slow, spun down like our Sun
to support that. Now if you- but you do have to transfer that to a core, it is true,
but the angular momentum reservoir is there for all of these systems.
Um, let's start with Carl, then Ramesh.
(unintelligible) has always just wondered, but what happens if the spin is misaligned from the, um, from the disk?
Wonderful, that's great. So,
there are a lot of interesting things that may happen -
so one of the explanations for why we get QPO features in black holes, a
popular model is that that's caused by a warp in the disk because it's misaligned with the binary plane,
and so you see that as a QPO. But as a result of this warp,
you also induce a torque on the black hole that will cause it to align with the binary, uh,
orbital plane. And if you,
asks- well, what is the relative angular momentum between, you know,
this massive, maximally rotating black hole and some wimpy star that's orbiting around it at a solar radius or two.
Well it turns out that that wimpy star has about a hundred times more angular momentum than your black hole, and then something like
10^7 years of accretion, you've
torqued it into alignment.
But that's, uh,
but that's assuming some degree of efficiency, so
depending on models for this, you expect something in the neighborhood of 1% to 10% of
black hole systems,
just by random draw, would be...
would be misaligned now, if they all formed with, sort of, random orientation its, um, early phase.
Now,
I'll just skip ahead to say there- one of the frustrating things is there's very few instances where we can actually test this.
For this one lovely system, XTE J1550,
we were able to take advantage of these X-ray jets that were detected at large scales years after outburst and radio data,
and just, uh,
adopt a
blast wave model for the propagation of these jets to place a constraint on the inclination of the system,
of the jet from the system, and compare that to the binary orbital
angle. And what we find is that it has to be relatively close to a line - this is showing you,
now, the plane of the sky, where this band shows the
orbital angular momentum, which could be-
which we don't know the position angle for, and this is showing you the results from the jet, which have a very
fine position angle and,
and inclination
determination. And so it has to be within about 12 degrees, at least,
projected along our inclination. So this is one case where we could test it and it looks aligned,
we would love to have more instances, instances where we can test the
theoretical expectation that they should be aligned, but we just don't have those in practice.
We're running a little overtime, but last question to Ramesh.
Um, yeah. So, (sneeze) back you described two methods,
the reflection method and continuum fitting method,
both of them assume that the disk comes down to the ISCO-
That's right.
-right?
And, what's assured us that the two methods actually use different spectral shticks?-
Yes.
-Which are mutually exclusive?
And at least there's a law,
which, to tell the truth, Jeff and I are responsible for,
the law says that in the soft state, fine, the disk comes down to the ISCO.
Yeah.
But these other states, the disk probably does not come down to the ISCO. 
It's truncated at some larger radius, okay?
Yeah, yeah.
We thought there was a fair amount of evidence for that. 
But now, if both methods give the same correct spin, it means that in both of these states, the disk really is coming down to the ISCO.
Th-
Is that a valid conclusion?
I would say that's,
that's at least a reasonable conclusion yes, though with the caution that
many of the measurements are being done when the system isn't in a faint hard state, where we expect things are more truncated;
but even there,
recent studies with NuSTAR that is giving us sort of the the best view into,
the, I guess, the, the best reflection data, the best vision of the hard state,
many of those are showing that the truncation is sort of
five to ten times the ISCO when you're in these very faint hard states here, so it's not
great truncation - we think that, so that indications are that that must happen somewhere down here is it's really fading into a deep quiescence.
But measurements that are taken up here,
it's true you you could take the conservative
vantage point that those are just lower limits, but typically they're rather high, so it's still quite high lower limit
you would establish if it is in fact truncated a little bit away from the ISCO.
So I would say that's at least a reasonable way to look at it,
but it does appear that when you're up in this horizontal branch here, if there is truncation,
it's just sort of a mild degree of truncation, it's not
large-scale.
So Ramesh, that shows a lot of scientific integrity on your side.
Well-
Basically bringing up the point that you're- the law that you developed with Jeff appears not to be supported-
Jeff got it wrong!
(audience laughter)
But let's- 
I egged him on.
-but Jack got it right-
We'll see.
-so let's thank Jack again!
(audience applause)
(outro music)
(outro music)
