Determining the Scale Height of FeIII in the Milky Way

by Matt Miller

UW REU Summer 2009

Advisor: Dr. Bart Wakker

Overview• General background

• ISM phases

• Scale height

• Techniques for finding the column density

• Apparent optical depth method

• Linear conversion method

• Curve of growth method

• Data reduction/analysis

• Introduce the patchiness parameter

• χ2 minimization procedure

• Results

• Comparison with previous estimates

Phases of the ISM

* Indicates values taken from Savage & Wakker, 2009

+ Indicates values taken from Reynolds, 1989

Hot Ionized Medium (HIM)

Warm Ionized Medium (WIM)

Warm Neutral Medium (WNM)

Cold Neutral Medium (CNM)

Component

~106

8000 – 12000

6000 – 12000

50 – 100

Temperature (K)

~3.6 x 10-5*

0.025+

~0.3*

~0.3*

Midplane Density no (cm-3)

2.6* ± .5

~ 1.5+

0.24* ± .06

0.24* ± .06

Accepted Scale Height H (kpc)

> 3 x 1018

1 x 1020

2.2 x 1020

2.2 x 1020

Total Column Density (noH)

What is a Scale Height?

• Assuming ISM has (volume) density that decreases exponentially from the galactic plane

• Obviously ISM does not exhibit this distribution perfectly

• Scale height is height off of galactic plane at which the density drops off by a factor of e

n(z) = no exp(-z /H)

Photo of NGC5775 courtesy of Rand 2000

Why FeIII?

• Traces the warm ionized medium (WIM)

• Many ions have an ionization potential greater than that of hydrogen, and thus could trace the WIM, but FeIII has several appealing characteristics

1. Enough abundance to be easily observed

2. FeIII is not contaminated by molecular hydrogen absorption lines

3. 1122Å line is in the UV, along with several FeII lines to facilitate the curve of growth method

4. Absorption is not too strong either

• Other candidates could work (such as AlIII, SIII, CIII etc.) but have various issues

Where the Data Came From

Image Courtesy of NASA and STScI

• Used data from the Far Ultraviolet Spectroscopic Explorer (FUSE)

• Designed to analyze Far Ultraviolet part of the spectrum

• 4 mirrors, 2 coated with lithium fluoride (LiF) and 2 with silicon carbide (SiC)

• LiF channel used above 1100Å and is more sensitive between 1000 and 1100Å

• Data has been analyzed for other ions, (primarily OVI) but FeIII and FeII lines have not been rigorously analyzed

Techniques for finding the Column Density

• Apparent optical depth technique

• Linear conversion of equivalent width

• Curve of growth method

The column density (N) is simply the volume density integrated along the line of sight of the target

N(FeIII) =

N(FeIII)sin(b) = noH(1 – exp(-z /H))

z

dzbzn0

)csc()(=d

drrn0

)(

Apparent Optical Depth Method

• Most straightforward approach to derive column densities

• Optical depth is a measure of the strength of the observed absorption line

• The apparent optical depth is what is actually observed (not necessarily the true optical depth)

• There exists a straightforward relationship between the apparent optical depth and the column density along a line of sight

• This can be integrated as a function of wavelength or velocity

I(λ) = Ioexp(-τ(λ))

τa(v) = mc

ef λo Na(v)

2

Linear Conversion Method

• Makes the assumption that the FeIII absorption line is on the linear portion of the curve of growth (not quite true)

• Only used on FeIII

• Leads to a lower estimate to the column density due to the shape of a curve of growth

Non-linearLinear

Curve of Growth Method

• Used to estimate both FeII and FeIII column densities

• Analyzed FeII absorption lines at 1144, 1063, 1096, 1121, 1143, 1125, 1055, 1112, 1133, 1142, 1062, 1127, and 1106Å

• Equivalent width values for FeII lines can be fitted to a best-fit curve of growth that is determined by using different FWHM and column density values

• When analyzing FeIII, one has to make/validate the assumption that the FeII and FeIII gas are in the same region

• With the measured equivalent width for FeIII and the best FWHM for FeII, the FeIII column density can be derived from a curve of growth applicable to FeIII

Data Reduction of FeIII

• Primary absorption line lies at 1122 Å

• The apparent optical depth method involved only a straightforward calculation, and was overall the most reliable

• The curve of growth approximation consistently led to a higher estimate for the column density

• Comparing the two FeIII column densities is useful since it provides information on how much the absorption line is smeared by instrumental effects

Data Analysis

• Two straightforward unknown parameters

• Midplane Density (no)

• Scale Height (H)

• Determination of the scale height requires not only finding column densities for targets in the Milky Way, but extragalactic targets as well

• Column densities and distances to stellar targets are used to derive no

• Column densities to extragalactic targets combined with no then determine H

• Also important to account for HII regions along the line of sight

Photo of NGC 5806 & NGC 5750 courtesy of SDSS

Patchiness Parameter

• The ISM in general is not neatly distributed

• It becomes necessary to introduce an extra parameter that represents the patchiness of how the ISM is distributed

• This factor is added into the total error of each data point

σ2 = σN2 + σd

2+ σp2

Photo courtesy of NASA APOD

Minimization Procedureχ2

• Applied in log[N(FeIII) sin(b)] – log(z) space

• Varied the three parameters over different ranges to create different predicted curves

• σp from 0.01 – 0.25 in steps of 0.01

• H from 0.50 – 2.5 (kpc) in steps of 0.05

• log(no) from -9.0 - -6.0 ( cm-3 ) in steps of 0.01

• Allowed these to vary until we found combinations that gave a reduced χ2 of 1

Previous Results

• The accepted value of the scale height of the WIM is from Reynolds (1989) using pulsar dispersion measures

• The scale height for free electrons is derived as H ≈ 1.5 kpc

• Also using the pulsar dispersion measures, Gaensler et al. (2008) derived a scale height for free electrons of H = 1.83 +0.12 kpc

• However their technique did not allow for a patchiness parameter (σp)

• Both of these techniques suffer from the fact that pulsar distances are difficult to determine

-0.25

• Savage & Wakker also estimate the scale height of the WIM from AlIII

• Their estimate for the scale height (of the WIM) is H = 0.9 + 0.6 -0.3kpc

• However this estimate does not include extragalactic sightlines

Acknowledgements

If you are still interested, visit my website at www.astro.wisc.edu/~mmiller

Special thanks to…

• My advisor Dr. Bart Wakker

• Dr. Ed Mierkiewicz for directing the REU program

• UW Astronomy & Physics Departments as well as the NSF for making this program possible