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- [Jacob] And yeah,
thank you for having me

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and giving me the
opportunity to talk today.

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My name is Jacob Luhn and
I'm a graduate student

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at Penn State University

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where I've just finished up my fifth year

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and today I'm gonna be talking

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about some recently published results

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as well as some upcoming results

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relating to stellar RV jitter,

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with the goal of building up

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an astrophysical motivated predictor

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of stellar RV jitter.

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Hey, there we go.

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So despite the fact
that most of our planets

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are now discovered
through transit surveys,

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radial velocity observations
are still as important as ever.

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They are used to confirm
or reject planet candidates

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as well as measure masses,

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and so that we can eventually

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get planet densities.

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But with this added role
of transit follow up,

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comes additional strain
on our RV resources,

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and especially considering the
number of observations needed

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for precise mass measurements
of earth like planets

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around some like stars,
this is a real problem.

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And it becomes important
to select and prioritize

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our targets so that we can
maximize our science returns.

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And to do this, we can use
the fact that some stars

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are simply better suited for
radial velocity measurements

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than others because of stellar
radial velocity jitter.

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So RV variability astrophysically,

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comes from various sources.

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I've listed a few of the major
ones here and divided them

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by those that are driven
by magnetic activity,

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and those that are driven by convection.

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And so we know that RV jitter
increases with both activity

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as well as with convection.

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But we wanted to better
understand the role

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that both of these plays in an RV jitter.

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And so I individually measured the masses

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of 600 California planets of stars

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to investigate trends
with stellar properties

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and I'm showing the results here.

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RV jitter as a function
of surface gravity,

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color coded by activity S-index.

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And to guide you, I've
broken it up roughly

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into main sequence, sub
giants and giant regimes.

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The first feature that we notice here,

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is this overall L shape.

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With the active stars piling up,

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at high surface gravity's near
the zero age main sequence,

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and then a horizontal
floor of inactive stars

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that show a gradual
increase with evolution.

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And so what we've identified
here are empirically

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the activity dominated and the
convection dominated stars.

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You might also notice a number

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of high points here, and
these are simply most of these

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are due to non subtractive planets

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that we weren't fully able to constrain.

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And so, what we're
getting from this picture,

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then is the idea that RV jitter
tracks stellar evolution.

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And so what that means
is that the star is born,

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and it's rotating rapidly
and so it's very active

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and therefore jittery,

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it loses angular momentum
on the main sequence

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from stellar winds and
decreases in both activity

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and jitter, continues to do so until

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it falls to some jitter
minimum where it transitions

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from activity dominated
to convection dominated

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and undergoes a gradual
increase from convection

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as it evolves into the subgiant,
and later giant regimes.

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But this isn't the whole story.

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We know that stellar
evolution depends heavily

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on stellar mass.

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And so we expect the same
to be true for the evolution

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of stellar RV jitter.

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And we find that when we break

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our sample up by mass, that
that is indeed the case.

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And then we find that more massive stars

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reached their jitter minimum
at later evolutionary stages.

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This is because more massive
stars evolve more quickly

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and so they are moving to the right

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on this plot more rapidly.

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In addition, most of the
massive stars in the sample,

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are above this Kraft break,

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and so they undergo a delayed

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spin down and it's not
until the subgiant regime

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that they are able to begin spinning down.

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While we're on the subject
of more massive stars,

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one of the other interesting
results of this from the sample

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of RV jitter came from the presence

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of low jitter "F" stars.

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Now, "F" stars are typically
avoided in RV surveys

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because of their expected high RV jitter.

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And so we wanted to determine
a way to distinguish the high

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from the low jitter "F" stars,

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and the insight there was
that the high jitter stars

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will either be active or evolved.

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And so we created this jitter metric

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where it includes an
activity time log(R'HK),

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and then also the absolute
magnitude in the Gaia G-band

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as a proxy for evolution.

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And when we plot our
RV jitter as a function

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of this jitter metric, we
see that it does a good job

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of distinguishing or separating
the high jitter stars

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from the low jitter stars
and if we were to only

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use an activity term, you can see

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that it's not quite as clean.

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And so again, this is
used to separate high

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and low jitter "F" stars,
but what we find is that

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this actually works quite
well for all of the stars

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in our sample and not just to separate

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high and low jitter stars,

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but actually has some good
predictive value as well.

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And so here I'm showing
the same plot RV jitter

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as a function of this jitter
metric for all of the stars

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in our sample, and just doing
a simple linear fit here

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for stars with this
jitter metric below 1.5.

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And with that, we're able to
predict the jitter for those

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stars with a median
percent error of about 27%,

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which is significantly better than

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similar empirical predictors
of RV jitter for instance,

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Wright 2005 which is good

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to about a factor of two.

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So this is a great first
simple jitter predictor.

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But we want to go a step
further and build something

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a little more astrophysically motivated,

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that can incorporate the
different individual components

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of RV jitter.

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And so to do that, oh,

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and here's what this would look like

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if we only used an activity term again.

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But this more astrophysically
motivated jitter predictor,

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we're developing this model,
where jitter is the sum

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of a budgeter of four
components, an activity component

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that depends on log (R'HK)
and the mass, granulation,

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and an oscillation
component that both depend

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on the effective temperature
of the surface gravity

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and the radius, but with
different exponents,

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and then an overall
instrumental component.

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That's the same for the
whole sample from Keck HIRES.

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So to ensure that we're actually

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fitting astrophysical components,

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we can use the fact that
granulation and oscillations

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we have theoretical
expectations for those scaling

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relations, so rather than
using uniform priors for those

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hyper parameters for the
granulation and oscillations,

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we can use Gaussian priors

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centered on those values

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from the relations shown there.

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And just to demonstrate
that those showed good

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agreement with our, with our data,

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I'm showing here one individual
star with cleanly resolved

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stellar p mode oscillations.

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This is not your typical planet RV curve,

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but this is p mode oscillations.

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And the expected amplitude for the,

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radial velocities matches
almost exactly what we see.

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So, just a demonstration of this,

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these scaling relations.

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The other benefit from this
model comes from our ability

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to easily incorporate the stellar
uncertainties into the fit

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so we allow our model to fit
the true stellar parameters,

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given the uncertainties,
input in the fit gives us

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a probabilistic relation

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rather than a deterministic one.

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Final piece to this jitter
predictor comes from our decision

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to fit the jitter floor.

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So, as I mentioned, any
unsubtracted planets,

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introduces scatter above the floor

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and so we use, reintroduce
a scatter term "S"

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that's drawn from a gamma
distribution to account for this.

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Such that the true stellar jitter is just

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"S" plus one times the
calculated jitter floor

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and the exact shape and size
of this gamma distribution,

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which are set by alpha and beta
are left as free parameters

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in our fitting as well.

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And what this looks like,
then I'm showing the posterior

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for that distribution, with
each individual sample from

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our posterior in gray, and
then the median in orange.

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And I find it a little easier to think.

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of this as showing the
distribution of the,

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again quote unquote,
true jitter in the units

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of the jitter floor.

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So now that we have the
whole model built up.

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Let's take a look at some of the results.

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So, on the left, I'm showing
the data this RV jitter.

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(background noises)

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as a function of....

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(noises continue)

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as a function of....

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(mumbling)

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- [Moderator] Can you
pause Jacob and(mumbles)

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- [Jacob] Yeah, okay, all right,

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RV jitter as a function here
of log (R'HK), activity,

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and then color coded by mass.

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And then on the right showing
our ability to fit that data

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with this model, and you can
see that it does rather well.

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But just the caveat that
this is our ability to fit

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the data with the model and
as I mentioned, it's allowed

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to fits the true cellar
parameters and it also has

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flexibility in this upward scatter term.

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And so what we want is we
want to be able to predict

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the jitter, our priori.

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And so to do that, we have
to take our best fit model

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and sample from the posterior
of the hyper parameters

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from the left, as well as
the input stellar parameters

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to predict RV jitter.

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And this gives us a probabilistic

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RV jitter that has uncertainty
coming from the hyper

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parameter uncertainties, the
stellar parameter uncertainties

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in that upward scatter term.

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So once we do all that,
then here's our ability

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to predict RV jitter.

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And so I'm just showing
one posterior sample

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now on the right.

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From the posterior of
our predicted jitter.

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So you can see that we
still do rather well

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and to see exactly how well we can do,

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I'm showing us a summary
plot here of the absolute

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fractional error as a
function of stellar mass.

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And for stars below 1.2

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solar masses, which is
about 70% of our sample,

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we can predict with a median percent error

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of about 20 to 25%.

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If you're comparing that to the number

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I quoted earlier, for the
simple jitter predictor of 27%,

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it might not sound like
much of an improvement.

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But there are a few
things to remember one,

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that simple jitter
predictor did a good job,

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but it was only for the low

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jitter metric stars whereas
this model uses all of the stars

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in our sample and so can be
fit for a wider range of stars.

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Additionally, the major motivation here

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was to get an astrophysical based model

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and so this, if you'll remember,

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models the individual
components of RV jitter.

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And so one of the natural
data products of this model,

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is the individual expected jitter

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for activity granulation and oscillations.

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And so I'm working on
putting all of this together

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into a publicly available
Python package to be used

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by the exoplanet community

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that I'm tentatively calling JITTTER,

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because JITTTER is the
tool to estimate RV jitter.

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And this is as I said, this
will be a publicly available

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Python package will allow
users to predict RV jitter

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not just for the overall
astrophysical floor,

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but also for individual components.

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- [Moderator] A couple
minutes left, Jacob.

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- [Jacob] Okay, great, thank you.

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I'm just wrapping up.

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And also allow users to
input their own distribution

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of stellar parameters so it
can properly sample those.

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And additionally, I didn't
talk too much about this,

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but because we modeled the
instrumental uncertainty

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for Keck HIRES, this allows
users to take that out

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or swap it for other instruments,

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if they want to predict jitter
for a specific instrument.

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So yeah, and I'm alluding to this is still

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under development, I'm
working on putting together

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the user interface.

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And so I'd love to hear
feedback from the community

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on special use cases or
features that we maybe

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haven't thought of yet.

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So feel free to reach out to
me, I'd be happy to chat more.

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And so just to wrap up, then,

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I want to quickly go
through my conclusions

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and say that RV jitter evolves
from activity dominated

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to convection dominated,

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with more massive stars
reaching their jitter minimum

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at later evolutionary stages.

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Low jitter "F" stars exist
and can be distinguished

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with this jitter metric.

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And that same jitter metric works

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for other stellar types as well.

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And we're putting together
a tool to predict RV jitter

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for a wide range of stars

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that can model individual
components of RV jitter

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which will inform our target selection

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as well as prioritization and also inform

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our observation strategy so
that we can custom tailor them

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to mitigate individual
components of RV jitter.

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So with that, I will end
and take any questions.

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- [Moderator] Thank you very much, Jacob.

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And the questions are coming in.

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First off, do you expect
this tool would work as well

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for lower mass stars
"K" or perhaps even "M"?

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- [Jacob] Yeah, that's a
question I've gotten a lot.

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I think, in general, it would,

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although because we don't
have any stars in our sample.

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Probably down to "M" might
be a little ambitious,

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but certainly, I would think
to lower mass "K" stars.

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So I think our sample went down to

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about point seven solar masses.

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So I would say tentatively, yes.

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But it's not something that I've yet

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looked into a whole deal.

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- [Moderator] Okay, and the next question,

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Is all of the larger
fractional error for stars

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greater than 1.2 solar masses explained

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by the low number of samples?

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Or could it be that the hyper
parameters of your model

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might be different for more massive stars

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than for less massive stars?

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- [Jacob] Yes, that's a great question

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and something that we're
still looking into.

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Yeah, I think a large part of it is

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because we have so few stars out there.

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Yeah, 70% of our stars are below 1.2

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solar masses, so I think
that is a large part of it.

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But I think there could
also be a difference

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in the the hyper parameters as well

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and I've tried different methods

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fitting just the low mass stars

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and then fitting the high
mass stars separately.

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And there hasn't been a huge difference.

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And I think we've opted to stay,

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with this kind of bulked model.

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And just keep in mind that it's not

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as effective for the higher mass stars.

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But I think those in general
have larger scatter as well.

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And so they're just not fit as well.

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- [Moderator] Finally,
can you talk more about,

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how photometric time series can be used,

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to better constrain the jitter prediction,

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in particular, in combination with v Sin i

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and inclination estimates,

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given that the oscillation
granulation signatures

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or inclination depend?

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- [Jacob] Yeah, that's a good question.

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So yeah, I haven't thought too much yet,

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about how we can incorporate,

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photometry into this.

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So yeah, I don't have a
great answer for that,

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at the moment,

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so one of the things,
actually that I left out,

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is this model does incorporate

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a v Sin i in the activity term.

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And I just chose to leave that off

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for simplicity in this talk.

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So we do incorporate that.

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But yeah, I think building something

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that incorporates the photometry,

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would also be very useful.

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I'll keep looking into that.