Background Starlight Polarimetry in the Age of SOFIA and Gaia Dan - PowerPoint PPT Presentation

Background Starlight Polarimetry in the Age of SOFIA and Gaia Dan Clemens (Boston University) NSF/AST 14 ‐ 12269 & 18 ‐ 14531 , USRA SOF_4 ‐ 0026, & NASA NNX15AE51G gratefully acknowledged 1

Findings First, Talk Second 1. The combination of Gaia DR2 with near ‐ infrared (NIR) Background Starlight Polarimetry (BSP) is transformative – Distances to dark clouds to <3% uncertainty – Can classify stars as foreground, embedded, background, and deep background – Better star cluster stellar memberships Proper motions are better than distances • 2. The HAWC+ far ‐ infrared (FIR) imaging polarimeter on SOFIA is fabulous – Sensitive tool for performing FIR thermal emission polarimetry (TEP) – Combined with NIR BSP ‐ > B ‐ field characterized over wide range of scale sizes 3. B ‐ field strengths from Davis ‐ Chandrasekhar ‐ Fermi (DCF) method ‐ > too low – Forward modeling of cluster star Position Angle dispersions (  PA ) reveals BSP noise bias – Bayesian posteriors for � ( B ) also favor lower  PA , higher B strengths – Foregrounds and deep backgrounds both contribute  PA noise, masking target cloud value 2

BSP Review (Unpolarized Light*) Background Stars Observer Sees: Molecular (or atomic) Starlight with impressed cloud or zone with B ‐ field Linear polarization signal B Plane of Sky aligned dust grains Andersson+’13 (P || B POS ) ∆ � Estimate B ‐ field Strength as � � � 4� � ∆ �� (Davis, Chandrasekhar & Fermi) 3

We use Mimir – NIR Imaging Polarimeter for BSP FOV = 10x10 arcmin at 1. Galactic Plane survey • 1024x1024 pixels at 0.6”/pixel on (GPIPS) of 3,237 10x10’ the 1.8m Perkins telescope in FOVs like this one Flagstaff, AZ 2. Individual Dark Clouds H (1.6  m) and K (2.2  m) stellar located off the Galactic • polarimetry. plane, like L1544 3. Outer Galaxy fields towards Perseus Spiral Arm with 4 open stellar clusters

Cluster Stars = Ideal, Same ‐ Distance, Multiple BSP Probes Target Cloud Observer Star Cluster Background Foreground Stars Stars Must isolate cluster stars from field (fore + background) in the FOV m H • Past techniques: spatial over ‐ density +/ ‐ Color ‐ Magnitude Diagram • placements – Select “members” based on probability of being in the over ‐ density and falling into the Giant or Main Sequence branches (Mercer+’05) (J ‐ K) – Fit colors for age, metallicity, distance, reddening (Hoq & Clemens ’15) CMD of NGC663 – Not very robust, nor accurate if Giant branch is poorly populated, esp when using NIR colors in JHK with best ‐ fit Isochrone (H&C ’15) 5

Then came Gaia DR2 in April 2018… Parallax, proper motions, optical g ‐ band magnitudes • – to > 10 kpc, m g < 20 mag We fetched Gaia data for 30+ open cluster fields in Perseus • – Test B ‐ field changes from Perseus Spiral arm to interarm regions – Clusters selected to be in front of, within, and behind Perseus Arm Matched Gaia stars to Mimir ‐ observed NIR polarimetry stars (simple 1.5” cone) • – Incredible match rate On average, ~925 Mimir polarization ‐ measured stars per FOV  900 ( 97% ) matched to Gaia stars • More than half of the cluster FOVs had < 10 stars that did not match. • Reiterate: Nearly every star with measured polarization now has a distance measure, also • Created Bayesian Markov Chain Monte Carlo (MCMC) code to separate cluster • members from field stars Each star has likelihood of being drawn from the cluster or the field; greatest one kept – Cluster likelihood based on gaussians in 3 ‐ D of parallax, proper motion in RA, pm in Dec 6 –

Cluster Parameters Were Recovered Stunningly Well For FOV containing cluster NGC 1245: S/N ~ 80 ‐ 380 (left) Stars across FOV (right) parallax vs proper motion 100 pc 1 kpc 10 kpc 100 kpc Field Stars 7

Cluster Parameters Were Recovered Stunningly Well For FOV containing cluster NGC 1245: S/N ~ 80 ‐ 380 (left) Stars across FOV (right) parallax vs proper motion 100 pc 1 kpc 10 kpc 100 kpc Cluster Member Stars Field Stars 8

MCMC Cluster Separation Recovers the Color ‐ Mag. Diagram • Color (J ‐ K) – magnitude (H) diagram for one cluster – Cluster member stars populate Giant and Main Sequence Branches well – Field stars look like, well, field stars – Polarization fraction uncertainty  P below 5 ˚ to H=15.5 9

Gaia Parallaxes + NIR BSP – Cloud, Cluster Distances Classically, cloud distance methods plot • E(B ‐ V) or A V vs stellar distance – Looking for a jump associated with the cloud – Difficult, if A V varies across the face of the cloud (which it does) – Polarization percentage, P , often has the same problem Try using Pol. PA as the changing property • – Versus Gaia DR2 distances (w/ uncertainties) GF9 ‐ 2 distance of 270  10 pc Better, use Stokes U and Q simultaneously • from PA jump with parallax. – Look for jumps at the same distance(s) in Fit using MCMC (Clemens+’18) both 10

Gaia Parallaxes + NIR BSP – Cloud, Cluster Distances Classically, cloud distance methods plot • E(B ‐ V) or A V vs stellar distance – Looking for a jump associated with the cloud – Difficult, if A V varies across the face of the cloud (which it does) – Polarization percentage, P , often has the same problem Try using Pol. PA as the changing property • – Versus Gaia DR2 distances (w/ uncertainties) GF9 ‐ 2 distance of 270  10 pc Better, use Stokes U and Q simultaneously • from PA jump with parallax. – Look for jumps at the same distance(s) in Fit using MCMC (Clemens+’18) both 11

Gaia, NIR Polarimetry, and Stokes U, Q steps Used MCMC to find • number(s), location(s) of jumps in Stokes U, Q in open cluster FOVs Field stars in blue • Cluster members in red • NGC 2262 located at • about 4.74  0.1 kpc Behind two distinct – foreground layers One with no P , one with – significant P 12

Gaia, NIR Polarimetry, and Stokes U, Q steps Used MCMC to find • number(s), location(s) of jumps in Stokes U, Q in open cluster FOVs Field stars in blue • Cluster members in red • NGC 2262 located at • about 4.74  0.1 kpc Behind two distinct – foreground layers One with no P , one with – significant P 13

B ‐ field strengths – Davis ‐ Chandrasekhar ‐ Fermi method ∆ � • � � � 4� � ∆ �� ; where  V is gas velocity dispersion,  is gas mass density, and  PA is BSP PA dispersion.  PA can be found many ways • Unweighted frequentist dispersion – Weighted frequentist dispersion – Boostrap with resampling – Gaussian fitting of PA distributions –  PA can be corrected for observational uncertainty, if uniform in the sample • � ���������� � � ��� and � �� is the same for each pixel Works for TEP; ∆ �� ������ � ∆ �� – Not so for BSP because of the wide range of stellar brightnesses ‐ > range of � �� • Forward ‐ model from observations to uncover ∆ �� ������ for BSP – 14

Forward ‐ Modeling : Cluster Fields ‐ >  PA vs m H ; Cluster N(m H ) Thousand(s) of stars per Mimir FOV • – 16 HWP angles ‐ > 4 U, Q sets and robust  PA – Fit run of  PA vs m H for each FOV Predictive noise function for model stars • Each cluster ‐ > apparent magnitude • function – Binned by magnitude – Can fit, but that misses Giant vs Main Sequence numbers too much – Keep averages in bins for modeling Poisson draws, using these means • 15

Forward Modeling Flow of Computation 1. Establish Cluster 2. Create apparent Membership with 3. For the FOV, characterize polarization magnitude bins uncertainty as function of apparent brightness Gaia + MCMC 5. Form model Stokes 4. Draw Poisson ‐ based U, Q for each mock numbers of stars for each star. Use <U>, <Q> mag bin to create mock from real cluster plus cluster with same  PA (m H ) from fit. magnitude distribution 16

Compute  PA for model cluster stars • – “model output  PA ” (I use bootstrap)  PA (true) – Find it is <  PA (observed) for the real cluster Whoops! Forgot to include  PA (true) • – The “astrophysical” dispersion ‐ > DCF Method – Include a synthetic version of this dispersion Implemented as draws from a gaussian distribution of • PAs with  G =  PA (true) (model output) Future ‐ > based on 2nd Order Structure Function? • Sweep of  PA (true) steps from 0 to 40 ˚ by 0.5 ˚ • (Re)Compute model output  PA • Do for 50,000 mock clusters for each  PA (true) • – Generates distribution functions of model output  PA Each cluster shows different relation between •  PA (true) and  PA (model output) – Reflects S/N of observations; stellar brightnesses 17

Compare Cluster  PA (obs.) to Infer Mock Cluster  PA (true)  PA (obs.) values select a range • of likely  PA (true) values – True values < observed values 4 ˚ Convolve  PA (true) • distributions with gaussian modeled  PA (obs.) 7 ˚ Result is a posterior • (true) distribution � (  PA (true)) – Very gaussian looking NGC 869 Orange = Convolved Values Blue = Gaussian Fit 18