Older ResearchMy Thesis Research
Correlated NoiseAs part of my work on SHARP, I have found the proper way to computed the weighted average from correlated data (i.e. covariance is non-zero). This topic isn't really discussed in the standard astronomy statistics books. The technique is useful for extinction mapping as well as treating correlated noise in SHARP. A memo describing the results is here.
Caltech Submillimeter Observatory/SHARP
Alignment of Magnetic Fields in Cores
The relative importance of magnetic fields compared to turbulence in star-formation is still an open question. For the past several years I have been using SHARP, a polarimeter on the CSO to observe sub-millimeter polarized dust emission. The dust grains preferentially align with their long axis perpendicular to the local magnetic field direction. These grains will then emit polarized light, which we can observe and thus infer the local magnetic field direction.
I am part of a collaboration that is observing the magnetic field geometry in a sample of about one dozen low-mass cores. Because these cores are isolated, nearby, and with simple geometries that can be directly compared to theoretical models of magnetically regulated star formation. The first paper on this survey was published in 2011 (Davidson et al. 2011). A second paper was published in 2013 (Chapman et al. 2013).
Below is a figure showing the results for one core, L483. The inferred magnetic field vectors are plotted in red and blue to distinguish if they come from high- or low-flux regions. In the left-hand panel the lengths of the vectors are proportional to the percentage polarization. The grayscale picture shows a 4.5 micron map of L483. The contours are the 350 micron emission measured by SHARP. The right-hand panel plots the vectors on one possible model from Allen, Li, & Shu (2003). The dashed circle denotes the infall radius for this source, which is needed to scale the vectors onto the theoretical model.
Magnetically regulated star-formation models predict that the magnetic field should align with the axis of the outflow from the young star and that it should have a pinch or hourglass morphology as gravity drags the field lines inward. In L483, the mean magnetic field direction is plotted as a gray vector, and it is offset by only 12 degrees from the axis of the outflow (shown as a black vector). Because we measure the plane-of-sky projection of the magnetic field and outflow directions, this difference in angle is the projected separation, φ.
This projected separation between any two vectors, φ, varies with the intrinsic separation angle, α, and the inclination angle, i, of the outflow (where i=90° is an outflow pointing along the line of sight). Because the red vector in the cartoon below traces a circle around the blue vector, a range of φ values are possible for each inclination.
The figure below shows the results from the seven sources observed to date. The projected separation between the outflow axis and magnetic field axis for each source is plotted as a red circle on top of the density function resulting from the above cartoon. Three different values of the intrinsic misalignment angle, α, are shown. By fitting our data to the density distribution, we obtain a best-fit value for α of 35°. With Monte Carlo simulations, we estimated the probability of obtaining an alignment of 35° or less by pure chance to be about 5%. In other words, with 95% confidence we have found a real correlated between the magnetic field direction and the outflow axis in low-mass cores.
Lastly, to improve our signal-to-noise, we rotated, scaled, and combined the individual maps of our cores to create a source-average map. The below figure shows the inferred magnetic field vectors from the source-average map overlaid on the theoretical model of Allen, Li, Shu (2003). The magnetic field appears to have a pinch, as predicted by the model. Furthermore, the field is well aligned with the outflow axis, and the flattened infall envelope (also known as a pseudodisk).
Magnetic Fields and Filaments
Magnetic fields may also be important in the formation of filaments. The interstellar medium is partially ionized and this ionized material is collisionally coupled with the neutral gas and dust. Because the ionized gas cannot move across magnetic field lines, the gas and dust are constrained to gravitationally collapse along magnetic field lines. If the magnetic field is ordered, this could lead to the formation of filaments
The filament OMC3, in Orion, is a prime example of a filament that appears to have formed from gravitational collapse along the field lines. The above figure shows the electric field (E-field polarization (the magnetic field would be perpendicular to the displayed vectors). Notice that the angles of the E-field polarization vectors align extremely well with the overall filament direction. This implies that material has gravitationally collapsed along the magnetic field lines, rather than across the field lines.
Comparison of Cloud and Core Magnetic Fields
Another way to test magnetic star formation theory is to compare the magnetic field direction in the cloud with that in the core. If the two directions are similar, it suggests the cores formed from the cloud under the influence of the magnetic field. However, if the directions are random, then turbulence is most likely more important in forming cores.
I am in the early planning stages of obtaining near-infrared polarimetry for each core from the above sample. The near-infrared will come from Mimir, an instrument I have used previously. Below is a picture I obtained on one source. The red vectors are of L1448-IRS2 obtained with SHARP while the black vectors are from Mimir. The grayscale and contours are CO emission from the COMPLETE survey. The mean directions of the near-infrared and sub-millimeter polarization appear similar, suggesting that magnetic fields may have some influence on the star formation process. As more data are taken, I will be able to draw more conclusions.
High-Mass Star Formation
There are two main theories for the formation of high-mass stars: competitive accretion and merging among lower-mass stars versus monolithic collapse. In an attempt to test these two theories, I observed two quiescent high-mass cores in Orion with CARMA. Based on previous data it was believed that both cores were starless. Therefore, they were enticing objects for study to learn about the initial conditions of high-mass star formation. The masses of the cores are 12 solar masses (ORI2_6) and 46 solar masses (ORI8NW_2). These cores are plotted in the figure below.
N2H+ 1-0 is shown as black contours and HCO+ is shown as white contours. The contours are overlaid on a color map of the 350 micron continuum emission. The two cores appear to exhibit different modes of star formation. The more massive core (ORI8NW_2) appears to have fragmented into about six+ clumps while the less massive core has not fragmented. In a turbulent medium fragmentation is predicted to form clumps with masses resembling the stellar initial mass function (IMF). Under the competitive accretion model the observed fragments in ORI8NW_2 may eventually merge to form a massive star.
The location of the molecules also hints at star formation in both cores. N2H+ does not peak at the location of the continuum, while HCO+ does. This behavior could be explained if the N2H+ was being destroyed via reaction with CO that had returned to the gas phase due to heating from one or more central protostars:
In fact, when we compared our CARMA data to Spitzer data (T. Megeath, private comm.), we found that both cores do contain protostars. See the figure below, where the moleculare emission is now plotted in red and green. ORI8NW_2 appears to contain multiple protostars while ORI2_6 only contains one. Again, this may point to turbulent fragmentation in the higher mass core.
To better understand the masses and dynamics of these two cores more data are needed. ORI8NW_2 in particular shows evidence of significant missing flux due to the interferometer. We need single dish data to fill in the missing flux and obtain a complete picture. I have begun a collaboration to obtain single dish N2H+ data for ORI2_6 and ORI8NW_2. We are currently awaiting the results of IRAM 30m and NRO 40m proposals.
HAWC+ (PI Darren Dowell) is an instrument being built for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is a 2.5m telescope mounted on an airplane. By flying at 40,000 ft, SOFIA is above much of the atmosphere and polarization measurements from 50-200 microns are possible. These wavelengths are inaccessible from the ground due to atmospheric absorption. I will be working on writing the data analysis pipeline. HAWC+ is scheduled for first light in 2015, and will be available to the entire astronomy community.
A topic that interests me is the variation in the percentage polarization with wavelength. The exact shape of this polarization spectrum reveals details about the physics that aligns dust grains with the magnetic field. The figure below compiles most of the current observations on the polarization spectrum. The general dip and then rise in the spectrum neccesitates at two emission components. 50-200 micron data are nessary to distinguish between dust models.
Nicholas L. Chapman 2013-September-27