The Fascinating Yolk of the Rotten Egg Nebula

QX Pup: The Fascinating Yolk of the Rotten Egg Nebula

by Kristin L. Berry

Submitted to the Department of Department of Earth, Atmospheric and Planetary Sciences in partial fulfillment of the requirements for the degree of

Bachelor of Science in Earth, Atmospheric and Planetary Sciences

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

June 2013

redacted Author Signature Department of Department of Earth, Atmospheric and Planetary Sciences May 22, 2013 Certified by Signature redacted Richard P. Binzel Professor of Planetary Sciences Sg atuahesis rere Supervisor Certified by. L Amanda S. Bosh Lecturer Thesis Supervisor Signature redacted Accepted by.. Richard P. Binzel Chair, Committee on Undergraduate Program

SEp 28 7017 LIBRARIES ARCH[VES Contents

Acknowledgments ...... 5

A bstract ...... 6

Introduction ...... 7

Background and Previous Work ...... 7

Mira Variables ...... 7

QXPup ...... 9

Planetary Nebulae ...... 10

Rotten Egg Nebula ...... 10

Nebular Light Echoes ...... 11

M ethods ...... 11

Data and Instrumentation ...... 11

R esu lts ...... 20

A n alysis ...... 21

D iscussion ...... 24

Conclusions and Further Work ...... 26

Appendix ...... 28

C od es ...... 28

Bibliography ...... 31

1 List of Figures

1 Light curve for LX Cyg, a typical Mira. These data are from the AAVSO [15].

Note the approximately year-length period and large amplitude of variation,

as well as the approximately sinusoidal shape of the light curve, with a slightly

steeper rising branch than falling branch. [15] ...... 8

2 Image of the Rotten Egg Nebula taken in JHK by Arne Henden at the 1m

telescope at the US Naval Observatory in Flagstaff, AZ ...... 10

3 Observations in B, V, R, I over time. Data in B are blue, V are green, R are

red, and I are black. The vertical bar indicates when telescopes and CCDs

were switched on April 20, 2009...... 13

4 This is a small subsection of a data frame centered around the Rotten Egg

Nebula, which is enclosed in a trapezoid defined by the four visible points.

Note that this clearly includes two neighboring stars. The circled stars sur-

rounding QX Pup were used as comparison stars. The'apertures shown have

a radius of 6.5 pixels...... 14

5 The flux of all comparison stars used are plotted here, separated by filter (I,

R, B, V from top to bottom.) Note the coincidence of abnormalities across all

filters at several moments in time. This indicates that some sort of irregularity

exists on those nights which is being reflected by the comparison stars. . . . 17

2 6 Light curves for each filter. Note the characteristic Mira shape clearly exhib-

ited by the light curve in I, and a prevalent vertical scatter across all filters

in several locations. Data plotted in black are in I, red in R, blue in B, and

green in V ...... 18

7 Light curves for each filter plotted on separate y-axes of flux, but a common

x-axis of time. Outliers (> 3a) have already been removed...... 19

8 Phase-folded plot of I data. The blue circles are from the first cycle, the

green x's are from the second cycle, and the red asterisks are from the third

observed cycle of variation in this star. Note the steeper rise and more gradual

fall typical of Mira variables, and that the first cycle seems to have the highest

peak and the last cycle the lowest ...... 21

9 Phase-folded plots of the R and B data folded around the period calculated

in I of 535.4 days. Note the steeper rise and more gradual fall from maximum

typical of Mira variables, and the large scatter in the data...... 22

10 Phase-folded plots of V data folded around the period calculated in I of 535.4

days. While there is a slight maximum visible, it's important to note the large

scatter in the data. The fit plotted over the data has an R2 value of 0.067. 23

3 List of Tables

1 QX Pup Essential Information ...... 10

2 Number of images per CCD, filter...... 12

3 Description of Telescopes and CCDs ...... 12

4 Images omitted from analysis...... 14

5 Comparison stars for photometry generated by the AAVSO...... 16

6 Fit Param eters by Filter ...... 20

4 Acknowledgments

This thesis would never have been possible without Dr. Amanda Bosh who helped me

get back into astronomy after a long absence, and then continued to provide much needed

guidance and support again and again. Thanks to Professor Richard Binzel for extremely

helpful feedback and for being the most awesomely enthusiastic professor I had during my

time at MIT. Thanks to Jane Conner for never-ending encouragement, enthusiasm, and advice.

This work would not be possible without the data taken by John Gross at Sonoita Re- search Observatory, and offered generously to me for analysis by Arne Henden. Neither of these would have been possible without the support of the AAVSO (American Association of Variable Star Observers.)

5 QX Pup: The Fascinating Yolk of the Rotten Egg Nebula

Kristin L. Berry

Submitted to the Department of Department of Earth, Atmospheric and Planetary Sciences on May 22, 2013, in partial fulfillment of the requirements for the degree of Bachelor of Science in Earth, Atmospheric and Planetary Sciences

Abstract

QX Pup is a known Mira variable at the core of the Rotten Egg Nebula that has not been studied in detail since its discovery in 1983. In this study, four years of photometric data in V and I and two years of photometric data in R and B are analyzed. A period of T = 535.4 8 days, and a magnitude drop of Am, = 2.2 0.69 are measured in I, and and phase shifts between the the other three filters and I are determined to be #R = 6 40 days, OB = 66 64 days, #, = 16 86 days. These results are used to speculate about the possibility of a light-echo off the Rotten Egg Nebula and the conditions on Earth-like planets around Mira variables.

Thesis Supervisor: Richard P. Binzel Title: Professor of Planetary Sciences

Thesis Supervisor: Amanda S. Bosh Title: Lecturer Introduction

The Rotten Egg Nebula is a very well-studied pre-planetary nebula (pPNe,) with a compar-

atively neglected, infrared-discovered [6], Mira variable at its core. This study first reviews

what is currently known about this Mira, QX Pup, and the Rotten Egg Nebula, and then

moves on to analyze QX Pup using four years worth of data in V and I, and two years worth

of data in R and B, taken at Sonoita Research Observatory, part of the AAVSO's worldwide

network of robotic telescopes. The aim of this study is to look for any changes in this variable

star during the four-year observation period by performing photometry on the nebula it lies

within, and determining any phase shifts between the light curves in different filters.

Background and Previous Work

Mira Variables

It was said by Robert F. Wing in the 1970's that "... observers can derive a lot of pleasure from the study of Miras, and ... theoreticians, for the most part, can not." [18] This was because a while Mira's variation of flux with time is dramatic and easy to measure, a link between these dramatic flux variations and any physical model of the stars themselves was fleeting. While we do know today that there is a relationship between the Mira's period and its luminosity, metallicity, and rate of mass loss, the exact relationships, and reasons behind them, remain largely unknown.

Mira variables are cool red giants with temperatures around 3000 K, radii around 200

1 2 - 300 r8 en, and luminosities of 3000 - 4000 L,,, . They are post-main sequence stars that lie on the asymptotic giant branch (ABG,) and experience characteristic changes in flux.

These flux variations are caused by changes in opacity of their atmosphere and temperature, pressure, and density changes which occur in the H ++ H+ and He ++ He+ zones that cause physical pulsations in the star's radius. The opacity changes are a result of varying

'The radius of the sun: r,,, = 6.96 x 108 m 2 The luminosity of the sun:Lun = 3.85 x 1026 W

7 amounts of heavy metals like TiO in the star's atmospheres over their periods [17]. Miras

are classified as long period variable stars (LPVs,) with periods of T = 150 - 1000 days and

magnitude changes of at least 2.5 magnitudes in V over a period [13]. Neither the periods,

nor the magnitude changes are constant cycle-to-cycle, and in fact, many show dramatic

differences [13]. Miras lose about 10-6Msoar/yr and many produce planetary nebulae (PNe)

on their way to becoming a white dwarves. A plot of LX Cyg, a typical Mira variable, is

shown in Figure 1. Note the long period, and general sinusoidal shape, and large magnitude

drop of 4 magnitudes-all typical of Mira lightcurves.

LX Cyg

9 - 10 *

12 - -

16I 16 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Year

Figure 1: Light curve for LX Cyg, a typical Mira. These data are from the AAVSO [15]. Note the approximately year-length period and large amplitude of variation, as well as the approximately sinusoidal shape of the light curve, with a slightly steeper rising branch than falling branch. [15]

Like other Long Period Variable (LPV) stars, a period-luminosity relationship (PL relationship) has been determined for Miras by studying Miras in clusters of known distances like the LMC (Large Magellanic Cloud.) Miras are important as distance indicators for old and intermediate-aged stellar populations. Unfortunately, the only PL relationship known for Miras is in the near infrared K filter (Mk = p[logP - 2.38] + 6, p = -3.51 + 0.20,

J = -7.15 + 0.06 for oxygen-rich Miras,) in which we don't have any recent data for QX Pup [16].

Only 30% of Miras have light curve shapes that differ significantly from a sinusoidal fit. [12] After all, most Miras are fundamental-mode radial pulsators, though some do show various overtones [12]. Miras often exhibit a clear asymmetry between the rising and falling

8 branches of the light curve, and OH emission seems to be linked to the steepness of the rising

branch of the light curve. Again, Mira pulsations are not strictly periodic. [12] Miras with

periods < 200 days tend to have symmetrical light curves and small amplitudes, whereas

Miras with periods more than 200 days tend to have larger amplitudes and steeper rising

branches in the light curve, and are more likely to exhibit period variations [13]. Miras with

periods greater than 300 days are also likely to have bumps in the light curve, particularly

in the rising branch [13]. One can quantify the shape of the light curve using the visual light

asymmetry factor, f = tge, where tise is the rise time, and Tdays Tda ys is the period of the Mira

in days. 80% of Miras lie within an f range of 0.4 - 0.5 [12] Since QX Pup is an M-type star, we expect to see approximately sinusoidal variation.

While the Mira classification is a broad one, many Miras do evolve out of it. For example,

Miras which begin to behave too erratically to remain classified as a Mira are often re- classified as SRb (Semi-Regular type b.) While a definitive link has not been established,

RV Tauri stars are thought to be the next evolutionary stage low-mass, low-luminosity, low-metallacity Miras evolve into before producing planetary nebulae [17].

QX Pup

Feast's 1983 study of QX Pup [6] classified it as a Mira variable, calculated a period of

T = 648 days, and a Am = 1 mag in K [6, 11]. This was in the infrared, where the star's light is largely unimpeded by the nebular dust. The star is not directly visible in optical wavelengths because it is obscured by dust [5]. Its light is, however; reflected by the nebula in visual wavelengths. The light reflected by the nebula is expected to have a phase shift from the light emitted directly by the variable, but the period of the pulsations should be the same. If the phase difference between the Mira variable and the light reflected by the nebula can be determined, it may be possible to use this information to determine the physical dimensions of the nebula [3,7].

9 QX Pup Summary Alternative Designations OH 231.8+4.2 000-BFC-998 (AAVSO UID) RA (J2000) 07 42 16.83 (hh mm ss) DEC (J2000) -14 42 52.1 Galactic Coord 231.836 +4.220 Spectral Type M911I Variable Type Designation 'M' (Ceti-type Mira) J 8.310 mag 9.470 mag B 8.31 mag V 9.47 mag

Table 1: QX Pup Essential Information

Figure 2: Image of the Rotten Egg Nebula taken in JHK by Arne Henden at the 1m telescope at the US Naval Observatory in Flagstaff, AZ

Pre-Planetary Nebulae

Rotten Egg Nebula

The Rotten Egg Nebula is an asymmetrical, bipolar pre-planetary nebula which lies in front

of the open cluster M46. Pre-planetary nebulae bridge the evolutionary gap between the

Asymptotic Giant Branch and the planetary nebula stage in the standard evolutionary sequence of mid-mass (0.5 - 10 solar mass) stars [11]. This stage in development is not well understood, making the Rotten Egg Nebula an interesting object for study. Figure 2 shows

10 an image of the Rotten Egg Nebula in JHK taken by Arne Henden at the 1m USNO in

Flagstaff, AZ. [1,5]

Nebular Light Echoes

Light echo astronomy is a relatively new technique for studying the structure and composition of circumstellar and interstellar media. This is a potentially valuable technique, as given a distance and a light echo, one can find the actual three-dimensional structure of the surrounding dust. (The distance to structures with known dust-shell geometry can also be found, but this is a less common situation.) The morphology of a light echo is dependent on both the three-dimensional distribution of the dust and the location of the observer. The wavefronts propagate outwards from the central star in a very elongated ellipsoid [10], and scattered-light echos can be observed, provided that the light is sufficiently luminous and the reflecting dust is sufficiently dense. Sugerman [14] found that Miras with high mass-loss rates can produce observable echoes within their circumstellar envelopes.

While no Miras have yet been studied in detail in this manner, a Cepheid variable RS Pup, which lies inside of a reflection nebula, has been extensively studied using light echoes [9].

The large angular extent of the nebula, approximately 2.5 arcminutes, made it possible to isolate several distinct nebular features which could be resolved and analyzed separately [9]. With the addition of polarimetry data [2], it became possible to reconstruct a rough three- dimenosional outline of the nebula's likely structure.

Methods

Data and Instrumentation

This dataset was taken from January 15, 2008 to December 16, 2011 by a robotic telescope at Sonoita Research Observatory (SRO) in Sonoita, AZ 3. From 01-15-2008 to 04-20-2009, 3 Part of the AAVSO's network of robotic telescopes, managed by John Gross

11 images were taken automatically with a 35 cm telescope and a 1024 x 1024 CCD. In April

2009, this was replaced by a 50 cm, f/4 Newtonian Reflector with a SBIG STL6303E 3072 x

2048 CCD. For details about these detectors, please see Table 3.

Images were taken every 1-3 nights when QX Pup was visible. Before the switch to the

larger telescope, data were taken in B, V, R, and I. After the switch to the larger telescope, only images in I and V were taken. On a normal observation night during the latter half

of data acquisition, eight images: four in I and four in V, were taken. A graph of the data

coverage by filter vs. time is shown in Figure 3. Images in I had an exposure time of 63.4

seconds, V had an exposure time of 47.5 seconds, R had an exposure time of 31.7 seconds,

and B had an exposure time of 15.85 seconds. The basic characteristics of the data are summarized in Table 2. The data were received already dark-subtracted and flattened from

Arne Henden. 4

small CCD large CCD totals 1587 1477 exp times B 193 0 15.85s V 603 739 47.5s R 192 1 31.7s I 599 737 63.4s

Table 2: Number of images per CCD, filter.

4 Much of the information about preliminary data analysis is taken from the author's unpublished Field Report for 12.411, dated 01/27/12

Telescope SRO 35cm SRO 50 cm F-number f/4 CCD Model SBIG STL1001E SBIG STL6303E Pixel Res. 1024x1024 3072x2048 Detector Size 24.6 x24.6mm 27.5x18.4mm Read Noise 15 e- RMS 15 e- RMS Gain 2.2 e-/ADU RMS 2.3 e-/ADU FOV - 1.83x1.23 arcminutes

Table 3: Description of Telescopes and CCDs

12 _ _ _QX Pup Data 5

4 Mxx00100C

1~ Qi d-I

2 mxxnmo:x

Fe 2008 Aug 2008 Feb 2009 Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 Observation Date

Figure 3: Observations in B, V, R, I over time. Data in B are blue, V are green, R are red, and I are black. The vertical bar indicates when telescopes and CCDs were switched on April 20, 2009.

Pre-photometry Preparation

Before performing photometry, the images were registered, which is this process of aligning images so that the same pixel coordinates on each image correspond to the same physical coordinates on the sky. All but 113 of the 3064 total images had World Coordinate System

(WCS,) a system for attaching physical (world) coordinates to each pixel of an image, information embedded in their FITS headers. As only approximately 3.7% of the data lacked

WCS information, they were simply omitted from further analysis. (See Table 4.) The iraf command wregister was used to register all images to a good standard reference image. Suc- cessful registration was confirmed by creating animated gifs from the output FITS files and viewing them carefully by eye.

13 Due to low signal in bluer wavelengths, images in V and B were stacked nightly using the

iraf command imcombine with combine= "sum", so that the stacked and unstacked images

were available, in V and B, for later photometry.

Number Reason 1 Actually RY Lep 113 No WCS information

Table 4: Images omitted from analysis.

Relative Photometry

QX Pup's field is very crowded-in fact, it lies in front of the open cluster M46 [7]. An

example image of average seeing, taken in I, is shown in Figure 4. Note that the nebula

overlaps two nearby, unrelated stars. When the seeing is poor, this problem is exasperated.

Figure 4: This is a small subsection of a data frame centered around the Rotten Egg Nebula, which is enclosed in a trapezoid defined by the four visible points. Note that this clearly includes two neighboring stars. The circled stars surrounding QX Pup were used as comparison stars. The apertures shown have a radius of 6.5 pixels.

14 Relative photometry was performed in each filter by using the iraf command phot, a pho-

tometry routine which uses circular apertures, for each of 19 comparison stars and five 'sky

circles' around the nebula and polyphot, a photometry routine which allows the specification of arbitrary polygonal apertures, with a trapezoidal aperture for the nebula. A selection of these apertures are shown in Figure 4.

Nineteen comparison stars were selected for this field using the AAVSO's Variable Star

Plotter '. For the comparison stars, an inner circular aperture with a 6.5 pixel radius was used for the signal counts and a sky annulus between radii of 6.5 and 11.5 pixels was used for the sky value. By visually inspecting several images, it was determined that for most comparison stars on most nights, only a radius of 5-13 pixels around each relatively free from overlap with other stars, due to the crowded nature of the field. Photometry was performed using each combination of inner and outer apertures at 0.5 pixel intervals. These results were then plotted, and the combination which resulted in the least scatter in the data was selected: 6.5 pixels for an inner aperture and 11.5 pixels for an outer aperture. The same apertures were used for each comparison star and for every night. This is not a perfect solution and results in several comparison stars being clipped or including more sky signal, and therefore noise, than would otherwise result. A selection of comparison stars, with the inner aperture of 6.5 pixels is shown in Figure 4.

The trapezoidal aperture shown in Figure 4 was used for the nebula's signal. Due to its proximity to nearby stars, rather than using a sky annulus, five circular areas around the nebula were averaged to obtain a sky value for the nebula.

Data frames with pixels values not between 0 and 66535 (all possible values which may be taken by the detector) were flagged as 'BadPixels' by IRAF and were filtered out from any further analysis, as this indicates they did not record valid data. After filtering out these bad data, the relative flux from the nebula was calculated in the normal way, by subtracting off the sky flux for the nebula estimated from the 'sky circles,' and then dividing by the sum

5 http://www.aavso.org/vsp

15 AUID RA Dec Label U B V B-V Rc Ic J H K Comments 000-BBN-545 7:41:22.91 -14:49:11.1 87 - 8.786 8.667 0.119 8.416 8.327 8.157 8.113 8.051 000-BBN-561 7:41:51.56 -14:59:30.8 94 - 9.422 9.403 0.019 - - 9.278 9.299 9.250 000-BBN-542 7:41:19.43 -14:48:47.5 103 - 11.360 10.259 1.101 9.672 9.243 8.135 7.604 7.443 000-BFS-959 7:42:05.93 -14:44:33.5 106 - 10.702 10.571 0.131 10.488 10.379 - - - 000-BBN-578 7:42:17.59 -14:56:09.8 110 - 11.095 10.977 0.118 10.901 10.796 10.585 10.522 10.527 000-BFS-960 7:41:45.41 -14:46:21.5 111 - 11.626 11.062 0.564 10.730 10.398 - - - 000-BBN-593 7:42:46.55 -15:00:13 111 - 12.561 11.083 1.478 - - 6.567 5.557 5.217 000-BFS-961 7:42:10.39 -14:46:18.2 114 - 11.933 11.354 0.579 11.021 10.689 -- - 000-BFS-962 7:42:20.15 -14:38:29.6 117 - 12.201 11.706 0.495 11.413 11.111 -- - 000-BFS-963 7:42:07.28 -14:46:00.2 120 - 12.160 11.966 0.194 11.851 11.706 -- - 000-BFS-964 7:42:12.22 -14:47:22.3 122 - 12.294 12.176 0.118 12.117 12.042 -- - 000-BFS-967 7:42:40.80 -14:42:53.9 132 - 13.693 13.161 0.532 12.848 12.527 - - - 000-BFS-968 7:42:32.98 -14:38:31.5 136 - 14.309 13.587 0.722 13.147 12.692 - - - 000-BFS-969 7:42:02.00 -14:40:28.5 137 - 14.481 13.663 0.818 13.204 12.759 -- - 000-BFS-970 7:42:03.93 -14:41:25.9 138 - 14.246 13.805 0.441 13.539 13.265 -- - 000-BFS-971 7:42:13.85 -14:44:39.9 139 - 14.436 13.909 0.527 13.580 13.256 - - - 000-BFS-972 7:42:11.41 -14:46:42.2 142 - 14.602 14.191 0.411 13.903 13.663 -- - 000-BFS-973 7:42:13.51 -14:46:20.5 144 - 14.828 14.371 0.457 14.075 13.795 -- - 000-BFS-974 7:42:35.61 -14:45:09.2 147 - 15.504 14.740 0.764 14.318 13.884 -- - 000-BFS-975 7:42:27.22 -14:43:34.7 148 - 15.464 14.817 0.647 14.430 14.047 -- - 000-BFS-976 7:42:28.78 -14:43:18.6 150 - 15.500 14.984 0.516 14.632 14.324 - - - 000-BFS-977 7:42:12.54 -14:43:54.1 152 - 15.816 15.223 0.593 14.862 14.506 -- - 000-BFS-978 7:42:20.44 -14:43:49.9 154 - 15.999 15.434 0.565 15.024 14.664 -- - 000-BFS-979 7:42:33.76 -14:39:13.3 156 - 16.082 15.589 0.493 15.262 14.935 -- -

Table 5: Comparison stars for photometry generated by the AAVSO. CD

350000 All Comparison Stars Vs. Time 300000 250000 x 200000 150000 ix 100000 L (D~ 0 50000 0 -0 4b2008 Aug 2008 Feb 2009 AI4IE~aT~parisoft5t~owWs. TlIM(ug 2010 350000 r Feb 2011 Aug 2011 300000 (DD 250000 o e-m x 200000 WcE I ,N ii wt 0 150000 x tw x p 100000 50000 0 -500 b 2008 Aug 2008 Feb 2009 Autl I M parso"&I PV/s. Tlme'ug 2010 Feb 2011 C 600000 Aug 2011 500000 400000 (. + x 300000 U 200000 (.D 100000 0C+ 0 IWW -100QL b 2008 Aug 2008 Feb 2009 AuAIWgrparisoneL- 600000 M7WVs. Timekug 2010 Feb 2011 Aug 2011 500000 CD 0 400000

0 -1000?S )2008 Aug 2008 Feb ( D 2009 Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 cc~ of the fluxes of the comparison stars.

The resulting light curves, with V and B unstacked are shown overlaid in Figure 6. Outlier > 3o- away from the local average were discarded. For a better sense of how they vary individually, they are shown on a combined graph with their own y-axis for flux, but

common x-axes in Figure 7. Note the clearly Mira-characteristic nearly sinusoidal variation in I, and the similar variation in R and B. No clear variation is visible in V, likely due to the very low SNR in V.

QX Pup Relative Flux

1.0 I-

S0.5

10WV'W 0.0 iE00 Low~~h *4pI~mgp

Febs 2008 Aug 2008 Feb 2009 Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 Date

Figure 6: Light curves for each filter. Note the characteristic Mira shape clearly exhibited by the light curve in I, and a prevalent vertical scatter across all filters in several locations. Data plotted in black are in I, red in R, blue in B, and green in V.

18 c q

71 1.0 0.8 -% I v 0.6 cj: 0.4 0.2 0.0 (D Fet 2008 CDc Aug 2008 Feb 2009 Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 0.10 0.08 0.06 v - 0.04 -. - Q 0 0.02 PDD ~ 0.00 reb 2uuoD Aug 2008 Feb 2009 Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 CD ' 0.10 0.08- 0.06 - 0.04 * e 0.02 a.. 3';* h. 4 0 C 0.*00 .4 * S....

Feb 2008 Aug 2008 Feb 2009 Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 0.10 0.08- . S . . 0.06 S CD 0.04r . 0.02 dA 0.00. * S S S Mar 2008 * S Sep 2008 Mar 2009 Sep 2009 Mar 2010 Sep 2010 Mar 2011 Sep 2011 Results

As discussed earlier, Mira variables typically have sinusoidal light curves, and sinusoidal

forms are usually used to fit them [12]. A two-term Fourier series was used to fit the I data

and a one-term Fourier series was used to fit the R and B data, which only exist for slightly

more than a third of the time we were taking data, to avoid over-fitting. The V data were

fit using a one-term Fourier series, constrained to have a period between 400 and 575 days

(approximately the highest and lowest of the periods found for R, B, and I,) due to noisiness in the V data.

Using these models, in I, a magnitude drop of 2.2 t 0.69 was found, and the period was determined to be 535.4 8 days. In R, a magnitude drop of 0.97 0.73 was found, and the period was determined to be 421 115.8 days. In B, a magnitude drop of 1.14 1.5 was found, and a period of 404 141 days was calculated. In V, a magnitude drop of 0.33

0.87 was found, and a period of 570 186 days was determined. The period found in the

I filter, 535.4 days, was taken as the calculated period for the system, since Miras do not usually have periods which vary by filter, and the highest SNR data available were taken in

I. The smaller periods calculated for the R and B filter data-sets are probably an artifact of the smaller set of data (notably less than 500 days) available in these filters.

There were notable time-shifts between the time of maximum in each filter. I was taken as the zero-point, and the shifts from it in each filter were calculated. R's offset from I was 6

40 days; B's offset was 66 64 days days; and V's offset was 16 86 days. These results are summarized in Table 6.

Filter Am Period Time Offset I 2.2 + 0.69 535.4 8 days 0 days R 0.97 0.73 421 115.8 days 6 t 40 days B 1.14 1.5 404 141 days 66 64 days V 0.33 0.87 570 186 days 16 86 days Table 6: Fit Parameters by Filter

20 Analysis

To gain further insight into the system, the data were phase-folded with period of T 535.4

days, the period calculated in the I filter, around their maxima (with maxima at # = 0.)

Plots for each filter were generated. I is shown in Figure 8, R and B are plotted together in Figure 9, and V is plotted in 10.

Phase-folded lightcurve in I 1.4

I~Cycis2I 1.2 [~e~j

1 0 Of%# 0.81- X x H 2 .8 8 0 :3 LL 0.6 X X 0 40D 00 W X 0 X0 0 X X 0 T; M OA XX 0 0 10,41 00 OP) X110 x a &; 0 pis I*-ift low * V1x N # X 0.2 r. - *M X x ox N x 0 0

-0.2 -

-0. I I I I I I I I I -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 04 0.5 Phase

Figure 8: Phase-folded plot of I data. The blue circles are from the first cycle, the green x's are from the second cycle, and the red asterisks are from the third observed cycle of variation in this star. Note the steeper rise and more gradual fall typical of Mira variables, and that the first cycle seems to have the highest peak and the last cycle the lowest.

21 Phase-folded light curves in R and B 0.14 0 Data in R 0 0.12 0 0 Data in B

0.1 - 0- 0 0 X 0.06 - r_ 0- 0 0 6 0 , 0 U 0.06

+U) 0.04 0~ 0c 0 0c N;i t 0 & O 0 oo 0 0.02 0 S 0 000008%

K 0 C 0 0 -0.02 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Phase

Figure 9: Phase-folded plots of the R and B data folded around the period calculated in I of 535.4 days. Note the steeper rise and more gradual fall from maximum typical of Mira variables, and the large scatter in the data.

22 Phase-folded lightcurve in V 0.07 fitdcurve 0 0.06 - o08 0 0I - 0 0 0 00 8 0C-0 0 0000 0.. o0 0.05 00 0 0 0 0 -00 0 0 c 0 g% 0 0.04 0 1 0 0 00 00 N2 - 0- 0.03 0 0 0 0 0~ 0@ *13 00 c% 00 0.02

00 0 - c&OD0 0.01

0 0 0 0 0 0

- I I - -n ni -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 X

Figure 10: Phase-folded plots of V data folded around the period calculated in I of 535.4 days. While there is a slight maximum visible, it's important to note the large scatter in the data. The fit plotted over the data has an R2 value of 0.067.

23 The steeper rise and more gradual fall clearly visible in the phase-folded plot of I, Figure 8,

is very typical of Mira variables. Note also that each cycle of the Mira has a slightly different

amplitude in I, with the first cycle (blue markers) having the largest and the last (red

markers) having the smallest amplitude in I. Secular amplitude variation of this sort is very common in Miras. Since the comparison stars don't show any evidence of a slope, it is likely that this effect is real. The same general pattern of a roughly sinusoidal maximum is more subtly visible in the plot of phase-folded data in R, B, and V. In V, a very slight maximum is visible. A sinusoidal fit is overlaid, but it's important to note that the R2 value of the fit is only 0.067.

Discussion

The calculated magnitude drop of Am, ~ 2.2 is very typical for a Mira variable, as is the general shape of the light curve in I. While the magnitude drops in R and B are also typical, the magnitude drop in V of only Amt ~ 0.33 is smaller than usual, likely due to scattering occurring within the Rotten Egg Nebula. The period calculated in this study of T = 535.4 days is significantly shorter than the period of T = 648 days calculated by Feast in 1983 from data taken in L and K [6]. This sort of secular variation in period is common in Mira variables, and it is likely that the measured change in period is real.

The phase shifts from the I filter of R = 6 40 days, qB = 66 64 days, and v

16 86 days are interesting, but cannot be interpreted further without better SNR. If physical, the differences in phase probably indicate that light in different wavelengths is being emitted from, or reflected off of different areas of the star or surrounding environment.

Miras have both thick atmospheres, deep circumstellar envelopes, and this Mira, QX Pup, also lies inside of a pre-planetary nebula. Without higher SNR data, any further analysis would be speculation. Further, polarimetry data, which could be used to determine the angle at which light scattered off of the dust, would be required to even more accurately assign a

24 physical meaning to these phase differences.

There are some interesting parallels that can be drawn between the QX Pup system and the future of our solar system and other planetary systems, whose central stars may eventually evolve into Mira variables. The absolute luminosity of QX Pup is not known, so here we will talk about 0 Ceti, the original Mira variable, instead. If 0 Ceti were in the same location as as the Sun in our current solar system, the solar constant (flux from the star at 1

AU) would on average be 1.207 x 107W/m 2 and would vary between 1.126 x 10 7 W/m 2 and

1.225 x 107 W/m 2 , over the Mira's period of approximately 332 days or about 7.6%/year.

For comparison, the current luminosity of the Sun has a variability of 0.1% over our 11-year solar cycle, or just 0.09%/year.

Earth's current globally-integrated average temperature is 287 K. A simple one-dimensional atmospheric model (Equation (1)) can reproduce this to 256 K. Using this model, the equi- librium temperature of the Earth, with 0 Ceti replacing Sol, during minimum and maximum output of 0 Ceti would be 2482 K and 2495 K, respectively. Even though this is an unrea- sonable baseline, just the temperature change would make it very difficult for life to survive.

The habitable zone around a star is the area in which it could theoretically support life.

While there are different definitions of the habitable zone, the most common is to just take it as the area within which an earth-like planet could have liquid water given the appropriate atmospheric conditions. The inner bound of this habitable zone is defined by breakdown of water via photolysis and the outer edge of the habitable zone is bounded by conditions which cause C02 clouds to form, which initiates runaway glaciation [8]. Using an estimate of Ti =

269 K for the first condition, To = 169 K for the outer condition, and an albedo of a = 0.3, we can use the same simple atmospheric model used earlier (Equation (1)) to calculate the inner and outer bounds of the habitable zone during the minimum and maximum luminosity output from the Mira, by solving for d. [4]

T =((1 - a)Lstar)$ (1) TP= 167ro-d2 )()

25 At its minimum luminosity of 8400 Lso0ar, 0 Ceti's habitable zone would extend from

82.3 - 208.5 AU. At its maximum luminosity of 9360 Lsoiar its habitable zone would extend from 86.86 - 220.1 AU. While there is a surprising amount of overlap between these two calculated habitable zones, it is important to note that the habitable zone defines an area where a planet could exist with the atmospheric conditions to support liquid water on its surface. An individual planet's liquid water is unlikely to survive such a large luminosity increase.

From looking at the consequences for surface temperature and some quick estimates of shift in habitable zone, it is clear that variable star systems are bad for developing and sustaining planetary life. As all stars will experience some significant amount of variation in luminosity as they age off of the main sequence, an understanding of variable stars can give us some insight as to the timescale on which life can develop in planetary systems.

Conclusions and Further Work

A period of T, = 535.4 8 days, a magnitude drop of Am, = 2.2, and a time of minimum at was calculated in the I filter for QX Pup. R, B, and V were fit to sinusoids of this period and exhibited phase shifts from the I filter light curve of OR = 6 40 days, OB 66 64 days,

, = 16 86 days. As mentioned earlier, interpretation of these phase shifts is difficult, due to lack of high SNR data. The phase shifts could could be due to light in different filters scattering off of different layers in the star's atmosphere, its extended circumstellar shell, or the Rotten Egg Nebula that surrounds it.

There are two further steps which could be taken from here. The first and most important is to improve the quality of the period and phase-shifts measured by taking data with a larger telescope with a higher SNR.

The next step is to make an attempt to actually detect the light echo directly. As mentioned earlier, this is an ambitious task, and likely will require both the acquisition of

26 polarimetry data so that the scattering angle can be used in the calculation of distance and potentially an attempt at isis-style image subtraction to try to detect the subtle nebular light echo directly.

27 Appendix

Codes

Data Processing Pipeline

Here is a small section of my data processing pipeline. It was written using pyraf, a package

which allows IRAF utilities to be called from within a python script.

#####################################

# SRO QX PUP PHOTOMETRY PIPELINE

import sys,os from pyraf import iraf import pylab import datetime import numpy from scipy.stats import nanmedian, nanmean iraf.digiphot(_doprint=O) iraf.apphot(_doprint=O)

#########################io#############

# PHOTOMETRY RUNS

#######################io############### def run-phot(plypref ix, image.dir):

photgons = ['nebula-sky-centers.reg', 'comp-stars-centers.reg',\ 'comp-sky-centers.reg'] polygons = ['nebula.reg']

for photgon in photgons:

poly-file = '/home/kree/Desktop/THESIS/data/'+ photgon ply-dir = './' + ply-prefix + '_ + photgon[O:-4]

print " ... RUNNING PHOT

28 print " --- ON " + photgon + " --- "

iraf.phot.setParam('coords', poly-file) iraf.phot.setParam('image', image-dir) iraf.phot.setParam('output','default')

if photgon == 'comp-stars-centers.reg': iraf.phot.setParam('aperture', 6.5) else: iraf.phot.setParam('aperture', 11.5)

iraf.phot.setParam('verify','yes') iraf.phot.setParam('interactive', 'no') iraf.phot.setParam('datamin', 5) iraf.phot.setParam('datamax', 65535) iraf.phot.setParam('calgorithm', 'none') iraf.phot.setParam('salgorithm', 'centroid') iraf.phot.setParam('annulus', 6.5) iraf.phot.setParam('dannulus', 3) iraf.phot() #this generates all the plys

print " .. .CLEANING UP... " rmcommand = 'rm ' + ply-dir + '/' + '*' #ply_dir + '_sum' os.system(rm-command)

print " ... MOVING MAGS ...

mkdir-command = 'mkdir ' + ply-dir movecommand = 'my *.mag.1 ' + ply-dir

os.system(mkdir-command) os.system(move-command) os.system('cd ' + plydir)

print "... TXDUMPING ... "

iraf.txdump(ply-dir + '/*.mag.1', 'AREA,SUM,PERROR', \ 'yes', Stdout= ply.dir + '/' + ply-dir + 'output') print ply-dir + '/*.mag.1', 'AREA,SUM,PERROR', 'yes'

print "... DONE WITH TEST FOR " + photgon + " ... " for polygon in polygons:

29 poly-file = '/home/kree/Desktop/THESIS/data/'+ polygon ply-dir = './' + ply-prefix + '_' + polygon[0:-41

print " ... RUNNING POLYPHOT print "--- ON " + polygon + "

iraf.polyphot.setParam('image', imagedir) iraf .polyphot.getParam( 'output','') #default is fine iraf.polyphot.getParam('sigma','') #default is fine iraf.phot.setParam('verify','yes') iraf.polyphot.setParam('interactive', 'no') iraf.polyphot.setParam('polygons', poly-file) iraf.polyphot.setParam('datamin', 5) iraf.polyphot.setParam('datamax', 65535) iraf.polyphot.setParam('calgorithm', 'none') iraf.polyphot.setParam('salgorithm', 'centroid') iraf.polyphot.setParam('annulus', 10) iraf.polyphot.setParam('dannulus', 10)

iraf.polyphot() #this generates all the plys

print " ...CLEANING UP... " rmcommand = 'rm ' + plydir + '/* os.system(rm-command)

print " ... MOVING PLYS ...

mkdircommand = 'mkdir ' + ply.dir movecommand = 'my *.ply.1' + plydir

os.system(mkdir-command) os.system(move-command) os.system('cd ' + ply.dir)

print "... TXDUMPING ... "

iraf.txdump(ply-dir + '/*.ply.1', 'AREA,SUM,PERROR', \ 'yes', Stdout= ply-dir + '/' + ply-dir + '_output') print plydir + '/*.ply.1' + 'AREA,SUM,PERROR', 'yes'

print "... DONE WITH TEST FOR " + polygon + " ... print "DONE WITH TESTS"

30 Bibliography

[1] Javier Alcolea. Oh 231.8+4.2 : What lurks inside. Asymmetric Planetary Nebulae III, 313, 2004.

[2] H. E. Bond and W. B. Sparks. On geometric distance determination to the Cepheid RS

Puppis from its light echoes. aap, 495:371-377, February 2009.

[3] M. Cohen. Studies of bipolar nebulae. VII - The exciting star of OH 0739-14 /equals

OH 231.8 plus 4.2/. pasp, 93:288-290, June 1981.

[4] W. C. Danchi and B. Lopez. Effect of Metallicity on the Evolution of the Habitable

Zone from the Pre-main Sequence to the Asymptotic Giant Branch and the Search for

Life. ApJ, 769:27, May 2013.

[5] JOEL H. KASTNER et al. Direct detection of the mira at the heart of oh 231.8. The

Astronomical Journal, 116, 1998.

[6] M. W. Feast et al. The infrared variability of oh0739-14. MNRAS, 203, 1983.

[7] Arne Henden. Qx pup. http://www.aavso. org/qx-pup.

[8] J. F. Kasting, D. P. Whitmire, and R. T. Reynolds. Habitable Zones around Main

Sequence Stars. icarus, 101:108-128, January 1993.

31 [9] P. Kervella, A. Merand, L. Szabados, P. Fouqu6, D. Bersier, E. Pompei, and G. Perrin.

The long-period Galactic Cepheid RS Puppis. I. A geometric distance from its light

echoes. aap, 480:167-178, March 2008.

[10] P. Kervella, A. M6rand, L. Szabados, W. B. Sparks, A. Gallenne, R. J. Havlen, H. E.

Bond, E. Pompei, P. Fouqu6, D. Bersier, and M. Cracraft. RS Puppis: A Unique

Cepheid Embedded in an Interstellar Dust Cloud. The Messenger, 150:46-48, December

2012.

[11] Leal-Ferreira, M. L., Vlemmings, W. H. T., Diamond, P. J., Kemball, A., Amiri, N.,

and Desmurs, J.-F. Rotten egg nebula: the magnetic field of a binary evolved star.

A &A, 540:A42, 2012.

[12] T. Lebzelter. The shapes of light curves of Mira-type variables. Astronomische

Nachrichten, 332:140, February 2011.

[13] J. A. Mattei. Introducing Mira Variables. Journal of the American Association of

Variable Star Observers (JAAVSO), 25:57-62, 1997.

[14] B. E. K. Sugerman. Observability of Scattered-Light Echoes around Variable Stars and

Cataclysmic Events. aj, 126:1939-1959, October 2003.

[15] Matthew Tempelton. Mira variables with period changes. http://www.aavso.org/

qx-pup, 2012.

[16] P. A. Whitelock, M. W. Feast, and F. van Leeuwen. AGB variables and the Mira

period-luminosity relation. mnras, 386:313-323, May 2008.

[17] Lee Anne Wilson and Massimo Marengo. Miras. JAAVSO, 40, 2012.

[18] Robert F. Wing. Mira variables: An informal review. Contributions from the Perkins

Observatory, 1974.