Aurora Kesseli
Colby College

REU program-Summer 2011
Univ. of Wisconsin - Madison
Madison, WI 53706

akesseli at

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I have been working this summer with Barbara Whitney on explaining multi-wavelength variability in Young Stellar Objects(YSOs) in the Orion Nebula. We have been modeling YSOs with a variety of different properties like hotspots, warps in the accretion disk, and spiral arms. The code that creates these models is a radiative transfer and was written by Barbara Whitney. Our models are attempting to explain the data collected by the Spitzer/Infrared Array Camera(IRAC), which is analyzed by M. Morales-Calderon et al. in her papers, Mid-Infrared Variability of Protostars in IC1396A(2009), and YSOVAR: The First Sensitive, Wide-Area, Mid-Infrared Photometric Monitoring of the Orion Nebula Cluster(2011).

Out of all of the YSOs that were surveyed over half of them showed some form of vairability. Variability comes in a few different forms as observed by M.Morales-Calderon et al.:

Our models

Barbara Whitney's HOCHUNK codes is able to then create light curves, polarization plots, and spectral energy distributions(SEDs) for each of the models. We will use our models in order to explain the different forms of periodic variations that are mentioned above.

I will not discuss the polarization plots or Spectral Energy Distributions but you can see the images of all of the polarization plots and SEDs here: Polarization plots and SEDs

Periodic Variability
Semi-Periodic Variability
Other Models

Periodic Variation

Fig. 1. Snapshots of YSO as we move around the star every 20 degrees from 0 to 360 with 2 hotspots and a warp in the disk seen at a 65 degree viewing angle

From the light curve we can see that it exhibits a periodic variability.

Triangle: V Band (0.55 microns)
Plus Signs: I Band (0.8 microns)
Asterix: J Band (1.23 microns)
Filled Circle: IRAC band 1 (3.6 microns)
Circle: IRAC band 2 (4.5 microns)

Fig.2. Light curve shown at a viewing angle of 60 degrees using the fiducial model of two hotspots and a warp.

In order to explain this light curve we can use what is known about the effects of hotspots and warps and apply it to what can be seen in the movie (fig.1). The difference between the hotspot and the rest of the star is greatest in the V-Band since it has the shortest wavelength, therefore the V band is affected mostly by the hotspot. As the wavelength increases the influence of the hotspot becomes less prominent and the light is more stongly affected by the disk. This is because the dust in the disk absorbs optical radiation and in turn emits infrared radiation, and the temperature of the inner wall of the disk emits most of its radiation in IRAC wavelengths. A blackbody radiation curve can demonstrate this easily.

Fig. 3. Planck function where the highest curve is at a temperature of 10000, the next is 5000, then finally 2000.

Looking at the radiation curves, we can see that the higher the temperature the shorter the peak wavelength. Therefore as the temperature decreases as we move further from the star the peak wavelength increases. At the disk radius the peak wavelength is in the IRAC wavelength.The video below shows the progression of wavelength from shortest to longest using the fiducial model.

Fig. 4. Fiducial model seen at a rotational angle of 20 degrees and a viewing angle of 65 degrees, where the wavelength cycles in increasing wavelength from V-Band(0.55 microns), R(0.67), I(0.8), J(1.23), H(1.66), K(2.16), IRAC Band 1(3.55), 2(4.50), 3(5.73), 4(7.87), M1(23.68), M2(71.42).

As we cycle through the wavelengths the spot becomes less prominent and the disk becomes more prominent. Using this we can explain the behavior of the light curve nicely. When the spot is in view at 0 degrees and 360 degrees the V band is at its highest point, and as the spot moves around the star the V-Band magnitude decreases. There is a second small peak at 180 degrees because the second hotspot briefly comes into view. This is only the case at a large viewing angle, because at a viewing angle of less than around 50 degrees the second spot does not come into view and we can see a more normal periodic pattern.

Fig. 5. Fiducial model shown at 4 different viewing angles (20, 40, 60, 80) where 0 degrees in pole on and we are moving towards the center of the star.

At 80 degrees when we are looking at the star we are looking almost directly through the disk which creates the chaotic pattern that is seen. There is not that much variation because not as much light is making it through the disk.

Semi-Periodic Variation

We created an upward and downward trended periodic variation in a few different ways. The radius or temperature was increased as the star turned thus increasing the luminosity since they exhibit a direct relationship in the luminosity equation: . We also increased the accretion rate to increase the magnitude of the star. The more infalling material onto the star the brighter it will be.

Fig. 6. Movie of the variable accretion model over 720 degrees seen at a viewing angle of 60 degrees.

In the movie we see that the radius of the disk increases as the accretion rate increases also. This is because the infalling material is heating up the star. The dust gets destroyed around 1600 degrees and as the star heats up the radius where the temperature is 1600 degrees increases and moves further away from the star. Therefore, the disk radius increases as the dust destruction radius also increases.

Fig. 7. Variable accretion model where the amount of infalling material was increased slightly every 20 degrees. The model has a viewing angle of 60 degrees.

Fig. 8. Light curve where the radius of the star was increased at every 20 degrees. This model was also seen at a viewing angle of 60 degrees.

Fig. 9. Light curve where the temperature of the star was increased at every 20 degrees (60 degree viewing angle).


Fig. 6. YSO with no hot spots and a bigger warp seen at a 65 degree viewing angle.
The dippers are the light curves where there is a smooth or periodic pattern followed by a short dip in the flux.

Fig. 7. Light curve of a model with no hotspots and a big, wide warp, viewed at 65 degrees.

A dip can be explained by the warp obsuring part of the star at that viewing angle.This dip occurs at 0 degrees, and from the movie we can see that the image at 0 degrees has the bottom and top of the star being covered by the warp in the disk. The V-Band, I-Band, and J-band exhibit very little variability besides the dip because there is no hotspot to cause the periodic variations. Also it is only the V, I, and J bands that experience the large dip because that is the light that is coming from the star and the IRAC is coming from the disk and just exhibits a normal periodic curve because of the warp like we saw in all of the other models.

In the fiducial model, seen at a viewing angle of 75 degrees we see a dip in the IRAC bands this time instead of the optical bands.

Fig. 8. Fiducial model seen at a viewing angle of 75 degrees in the IRAC 1 band with a wavelength of 3.55 microns.

Fig. 8. Light curve of the fiducial model at a viewing angle of 75 degrees.

This can be explained as the same phenomenon as the previous model except here since we are at such a high angle of inclination the hotspots are probably completely obscured by the disk so the optical light is pretty much constant. The IRAC bands now show the dip because of the warp also. We believe this is because the IRAC radiation is mostly coming from the disk and at 0 degrees the warp in the front of the disk obscures the back of the disk blocking the radiation from being seen and thus creating a dip in the light curve.

Other Models

We created many other types of models some of them like the one below that has spiral arms.

Fig. 9. YSO with two spiral arm and 2 hotspots seen at a viewing angle of 65 degrees.

An image of the light curves of all of our different models can be found here.

Useful links

The following links are very useful for looking up info on UNIX, web page making, and astrophysical data and journals.

SIMBAD (Stellar/Galactic database)

NED (Extragalactic database)

UNIX tutorial

Web page basics

NASA Astrophysics Data Service