The Radcliffe Wave in Stars ?

This started out as a post eDR3 exercise trying to compare the (updated) OBA stars map in the 5kpc around us (Zari+20), with (low-mass) YSO maps extending to 3kpc.

To do the YSOs, I essentially used W1-W2>0.2, absmag(W1)<3.5 parallax>0.3 (and G<17 and parallax_error<0.12) and G-band variability > 0.02mag (all Gaia from eDR3).

The resulting sample (in translucent red; initially without the absW2<3.5-cut) gets some further CMD cuts to eliminate evolved giants, M-dwarfs etc.. as illustrated here:

There is a long dense-gas feature in the Galactic solar neighbourhood, called the Radcliff Wave

This results in the following map:

which meshes nicely with the OBA star map:

Note the distinct differences, which must be related to a) age and b) high-mass/low-mass SFR differences.

The map seems to show the Radcliffe Wave in YSOs extending over ~4 kpc, with also a coherent Z-structure.

HWR is excited about this, as this may offer the possibility to get the full kinematics (at least the vertical ones) of the Radcliffe wave. HWR has not kept up whether recent papers have done similar things.

The Origin of the Small-Scale Stellar Orbit(-Phase) Substructure in the Milky Way's Disk

Practical Context

These are some notes on a sequence of possible projects that should on-board Verena Fürnkranz to her thesis project, provide a first sketch of her foreseen thesis project & mesh this with the wrap-up projects of Johanna Coronado. Broadly speaking, the goal of the research line is to

• characterize the "orbit substructure of the Galactic disk"
• develop and apply tools that tell us what caused that substructure (birth memory or resonances)
• ask (and answer) what this tells us about the transition to "field stars" and the role of resonances in creating the orbit distribution on the Galactic Solar neighbourhood.

Observed orbit(&phase) sub-structure in the Galactic Disk

It is easily said, and partially true, that the orbits of stars - when combined with their ages and abundances - encode much about the formation history of the Milky Way. It is true that the distribution p(age, abundance, orbit) of stars is the dominant observational foundation of learning about the particular formation history of our Galaxy.

And it is also true that with the advent of Gaia and spectroscopic surveys we can construct  and approximate version of p(age, abundance, orbit) over a sizeable portion of the Galactic disk (<2 kpc around the Sun).

At face value, the kinematics of a star are described by (x,v). Given a gravitational potential, Φ (x,t), this determines an orbit. If the gravitational potential is nearly symmetric, say axisymmetric, and nearly time-independent, then an orbit can be described by a set of orbit numbers (integrals-of-motions or actions), which are time-independent, and orbital phases.

In particular, then transformation to action-angle variables,

(x,v) + Φ (x) --> (J,θ) proves useful, as the actions J are constant and "adiabatic invariants"; and the angles, θ, just increase linearly with time. Transforming the 6D (x,v) to 3 actions (constants along the orbits) and 3 angles (effectively orbital phases) is maybe the most elegant coordinates to use. J_phi is the angular momentum, J_R quantifies the orbit's radial oscillation, and J_z its up-and-down motion.

If one then looks at the distribution of orbits in this space, one finds it to be "clumpy", both in orbit-space (J only) and orbit&phase-space, (J,θ); this is especially true for stars of the same abundance [Fe/H], i.e. the same birth-material composition. Some of these clumps reflect clusters, others not. This is a main results of Johanna Coronado's thesis. Others have found related results: in particular, Pisc-Eri !!

Now, there is no simple model for a 'clumpy distribution', which raises the question what we can learn. One way to look at a clumpy distribution is to consider high density regions to be distinct sub-structures, sitting on top of a smooth background. This is an excellent starting point, but has the drawbacks of some arbitrary decisions:

-- where to cut off membership in a given structure?

-- deciding when a density lump is significant enough to warrant its consideration as distinct structure. 

Possible origins of the sub-structure

There are at least two distinct origins of clumps on orbit&phase space:

• the stress were born on nearly the same orbits, and are still clumped; this leads to a set of questions:
• How close are they in phase, θ?
• Is there evidence that they are dispersing?  In that case we would expect Δθ~ΔJ
• What can we learn about the cluster/association --> field transition?
• stars, possibly born on quite different orbits, are being "herded" onto particular orbits (or orbit&phase) by quasi-periodic perturbations of the potential's symmetry (== resonances).
• What does that teach about resonances, and the features (spirals, bar) that may create them?

Goal of the project(s)

The overall goal would be to develop a comprehensive understanding of the small-scale orbit sub-substructure of stars in the Galactic Solar neighbourhood, in order to

• see which substructures reflect birth-memory
• see which substructures reflect resonances
• see what can be learned about clusters star formation and the role of resonances in either case.

Project Steps and Issues

Finding and Characterizing Orbit Clumps

This entails several steps:

• How to best find them; Johanna's approach can be a very good baseline for now?
• calculate action-angle variables
• use friends-of-friends algorithm (FoF) to cluster them.
• How to decide what to include in a clump (Johanna's linking length)?
• How to quantify the clump-aground contrast? [Johanna has not yet done that]

Basic Data Sets

We need 6D phase space coordinates, which means in practice (alpha, delta,D,mu_alpha,mu_delta,v_los); in the longer run getting abundances would be good, too.

But to start, we will take Gaia DR2 and eDR3, specifically the subset of objects that has RV, to get 6D.

Note that at the moment, only stars with 4300K < T < 7500K are included in the Gaia RV catalog. For populations <400Myrs, the "turn-off" stars (that can tell us the age of the population) are too hot to be included in the RC sample.

Diagnostic tools for the origin of clumps

• are clumps birth remnants of clusters and associations? Then they should be nearly co-eval; and they should be young (< t_dyn ~ 250 Myrs). This can be done by drawing up a CMD, and seeing whether it looks like a mono-age "cluster".
• are they a consequence of resonances? In that case we would expect a wide spread of ages. And we would expect that stars have a streak-like morphology in, e.g., the J_phi - J_R diagram (see Trick et al 2018). And we should expect gradual changes with position in the (R,phi) Galactic plane.
• are they dispersing? If so, there should be a correlation Δθ~ΔJ , where the slope is given by dΩ/dJ * t_age

Next Steps

Let's look at Pisc-Eri in action-angle space as well as we can. If Johanna can Walk Verena through all the steps:

• calculate actions and angles with galley
• run FoF on them, and identify Pisc-Eri in (J,θ) space (with Johanna's software)
• vary the linking length to see what works best.
• project (J,θ) into (x,mu_alpha,mu_delta)-space, and find members without RV. This is the first step of really new terrain.

Cosmology in a nutshell

 Minimalist "Cosmology in a Nutshell"

Things "every astronomer should kind-of know"; HWR - very undigested list

Space and the overall evolution of the Universe is described by a metric

• it's the Robertson-Walker metric; cosmological principle puts all interesting stuff into a(t)
• a(t) depends on mass-energy-density of the Universe; and an expansion scale factor H(t); (1+z)~1/a
• a(t), which depends on O_M, O_L, O_R, determines the dependence of fluxes and sizes on redshift, which in turn constrains the "Omegas"

An expanding Universe goes through distinct thermal phases: T ~ 1/a

• there are 10^9x more photons in the Universe, but rho_phot ~ a^-4; while rho_mass~a^-3; the two are equal at z~15.000
• after three minutes, kT ~ DeltaE (proton - neutron) --> He forms
• at z~1300 T~4000K recombination P+e- --> H
• "surprising" in light of 13.6EV <--> 20.000K
• scattering off free electrons (Thompson) disappears --> long-mean-free path
• ==> CMB: photons from "surface of last scattering" elsewhere, reaching us now
• CMB bizarrely uniform on large scales
• small-scale temperature fluctuations (10^-4.5) reflect initial density fluctuations (in complex ways)
• at z~9, discrete UV light sources (hot stars, accretion disks) re-ionize the Universe
• making it (partially) transparent in UV

Structure grows, eventually forming galaxies, etc..

• initial fluctuations seeds in inflationary epoch (frozen quantum fluctuations)
• grow happens in competition between gravitational instability and expansion never faster than linear delta ~ a. <-- therefore structure growth depends on (and constrains) the Omegas
• eventually some fluctuations become no-linear --> gran. collapse --> halos

We now know the Omegas and Ho at the % level

• from all the above

thoughts on new, but potentially misclassified, classical Cepheids (I20+ sample)

On simple lightcurve classification to for classical Cepheids in the context of the Inno+20 draft

Starting point:

We have ~800(?) new classical Cepheid candidates from I+20. A good number of them have been recognized as variables in other surveys, but classified as different sources. The main other classifications are:

a) eclipsing binaries (EB)

HWR's 'by-eye' distillation of lightcurve characteristics that look non-Cepheid-like:

• rise and fall are symmetric; i.e. flipping the time axis would leave the light curve invariant
• the downward deviations (from the median) are larger than the upward deviations

b) W Vir (CWA & CWB)

HWR's 'by-eye' distillation of lightcurve characteristics that look non-Cepheid-like:

• rise-time longer than fall-time (only CWA's); opposite to DCeph
• have not discerned lightcurve characteristics in CWB that look different from DCeph

c) rotators (ROT)

HWR's 'by-eye' distillation of lightcurve characteristics that look non-Cepheid-like:

• Fourier decomposition "wiggly", i.e. much power in the 4th - 7th order components
• scatter of individual points from Fourier fit large, compared to Fourier amplitude; i.e. basic periodicity + much "noise"

HWR's Basic Impression

• Indeed, many of the "new candidates" are different types of variables.
• There should be a few simple lightcurve criteria to add/modify that should greatly reduce the contamination. These are spelled out below.

Possible steps to implement:

Diagnosis:

•  let's re-check whether the 'contaminants' do not lie in funny corners of our current lightcurve-shape space (A21,A31,phi21,phi31) that can be cut at little loss to the DCeph completeness.
• the plot below is from an OGLE paper, and sats e.g. that really most CWA's should lie elsewhere in Period phi21,phi31 space

• Can you make plots a la Figure 3 in the draft, with all the externally confirmed DCeph as pale grey points, and the location of the "new candidates" that are classified as "others" by others as coloreds points (as separate colors, or in separate plots for EB, ROT, CWA & CWB).

Possible simple new light curve criteria

Here is a proposal how to use the 7th-order Fourier representation of the light curve to calculate a few other statistics that may be very effective at weeding out contaminants (at little completeness loss).

Let's call that function F7(p), where p=phase within [0,1].

Let me suggest to calculate from the analytic form F7(p) the following quantities:

• mM: the median magnitude,  so that 50% of the period the source is brighter than mM, according to F7(p)
• sig-mM: the variance < (F7(p)-mM)^2 > calculated over the part of the light curve where F7(p) is fainter than mM; and 
• sig+mM: the variance < (F7(p)-mM)^2 > calculated over the part of the light curve where F7(p) is brighter than mM. [I think in all cases a "primitive" splitting of the period in say 1000 bins, and doing all of this brute force, should be fine.]
• f-mM: the fraction of the period (according to F7(p)) where the magnitude is fainter than mM
• f+mM: the fraction of the period (according to F7(p)) where the magnitude is fainter than mM
• f_rise: that is the fraction of the period in which (according to F7(p)) the light curve rises; and 
• f_fall: .. where it falls
• scatter: the rms of the deviation of the data points from F7(p) (in mag), normalized by the rms of F7(p) itself.
• n_max: the number of maxima that F7(p) has within a period: this should be 1 for smple light curves, but 3-5 for wiggly ones. 

So, that seems like a lot; but let's just explore them right now.

I think this is better than "machine learning" classification, because it depends less on the "data quality" the sampling rate etc..

Here's my propsal what to look for in diagnostic plots:

• weeding out EBs:  plot  ( sig-mM / sig+mM ) vs f-mM, for verified Cepheids and verified (or externally classified) EBs. I would suspect that for EB's ( sig-mM / sig+mM )  is greater than for DCeph, and f-mM is smaller; this does not yet capture the time-symmetry of EB lightcurves
• weeding out rotators:   plot scatter vs n_max (as defined above); I would suspect that for rotators scatter and n_max are larger (for DCeph vs ROT)
• weeding out CWA: plot f_rise vs phi21  for DCEPH vs CWA/CWB

Stellar Astrophysics from TESS Lighcurves of Eclipsing OBA stars?

OBA Stars physics from eclipsing light-curves?

Background and Goal

Massive stars, according to conventional wisdom, frequently are in close binaries, of comparable mass (size). First strand: massive star physics is not well constrained, and massive binary structure/evolution physics rests on small samples (10's).  Second strand: detailed lightcurve modelling of eclipsing binary systems (given TESS-like quality) can yield very detailed information 

about Mass (ratios), radius (ratios), Temperature (ratios), etc..

Starting Point and Sample

Eleonora Zari devised a large (500k) sample of plausible OBA stars candidates (G < 16), for spectroscopic follow-up with SDSS-V. Multi-epoch BOSS spectra. The stars were selected to have (intrinsically) blue colors, albeit possibly subject to dramatic reddening, and a likely M_K < 0.

But their variability can be assessed with the usual trick of backing the rms lightcurve variability pout of the GDR2 "errors" (in G, BP and RP).

OBA star candidates in the variability vs color-variability plane. Among blue, luminous stars there are essentially two categories of variables (rms G-band > 0.05): pulsators (RRL & Cepheids), with BP/RP variability ~1.6, and (presumed) eclipsing binaries (with BP/RP~1). The latter are the objects of desire here, and selected as in the Figure below.

The rms of the light curve for eclipsing systems is a funny thing: it dramatically favours systems where the eclipses are both deep and occupy a substantive fraction of the orbital period: very close, equal mass/radius binaries are the posterchildren..


Their sky distribution suggests that they are young (massive?) stars:

mostly in the Milky Way, but also in the LMC; the sample if candidate close-eclipsing-binaries contains 1350 targets.

Lightcurve analysis

Their apparent magnitude distribution suggest that > 500 of them should be in the TESS lightcurve 'comfort range'.

But their sky distribution implies crowding that might affect the light curve quality.

Does it makes sense to check for how many of them TESS light curves are available? And then fit them?

pseudo-wide-area-IFU: slit-less bright stellar spectroscopy

Mapping stellar pops/kinematicss with slit-less spectroscopy?

Science goal:

There are parts of the sky that are quite 'crowded' in stars, where we would like to get some basic spectroscopic information for all (bright enough) stars: velocity, Teff, (logg), and [Fe/H] (other elements, too?).

The prime example (accessible to optical observations) in our Milky Way may be Baade's window; and parts closer to the Galactic center, for near-IR observations.

This would lead to orbit-abundance-age(?) information for vast sets of stars, as a basis for dynamics,

and for formation studies based on the structure of the abundance-orbit distribution.

Effective ways of getting such information:

The "obvious" straightforward approach may be to do vast bona-fide IFU mosaics. But this approach is likely to hit its limits (sociological, time-allocation?) at 100-200 pointings? At any rate, e.g. Baade's window is 1000's [TBC] of squarearcmin (or MUSE FOV's).

Slit-less spectroscopy as an alternative?

The basic set-up envisioned is a follows: consider a classic long-slit spectrograph, where usually a slit selects a tiny fraction of the focal plane for subsequent dispersal by a grating/grism/prism; often a pass-band filter in the optical path limits the spectral extent.

Now, envision that same set-up, but with the aperture (slit) plate removed. Let's consider the regime of a single bright star in the field: the detector then will show a simple spectrum of this star; as the star is a point-source, the slit mainly served to eliminate much of the sky background. So, one will have a spectrum of a star (limited by, say, a narrow-ish passband filter of, say 200A), but with "200A's worth of sky", not the "2A's worth of sky" (for a slit).  Note, that to good approximation, the stellar spectrum depends on 5 numbers, (x,y)_pos, flux, Teff, v_los, [Fe/H]   (where logg and flux are degenerate at a known distance).  If you wanted to get (Teff, v_los, [Fe/H]) for that star, you'd fit model spectra, given (x,y)_pos, flux. These 6 pieces of information are to be compared to photometry, which yields three pieces of information: (x,y)_pos, flux.

Now, imagine the field being full of bright stars, and slit-less spectroscopy. It will look the same as before, just like a seemingly (!) crowded mess with 100s (1000s) of star spectral streaks, many of them overlapping. But -- and this is the core conjecture of this approach -- when it comes to information content, this image is not much more crowded. Let's presume that we have photometry, which makes (x,y)_pos, flux_normalization a "given". Then we have to solve for 

p( { Teff, v_los, [Fe/H]}_(all_stars_in_field) | {(x,y)_pos, flux}__(all_stars_in_field) ).

As long as the signal detection is linear, this is just the linear superposition of the problem above.

And, if observations at different angles are obtained (2-3), then degeneracies of directly overlapping

stars could be mitigated [HWR's view: that's almost unneeded: the famous SB2 binaries show that

separation in velocity space suffices..]

The bain is possibly: how narrow to choose the passband filter., not to get killed by sky; but still have enough spectral coverage to get stellar parameters.