I give permission for public access to my thesis and …...Thesis submitted for review by the faculty of the Five-College Astronomy Department and the Mount Holyoke Physics Department

I give permission for public access to my thesis and for any copying to be done at the discretion of the archives librarian and/or the College

librarian.

Abigail Daane

BBRRIIGGHHTTNNEESSSS AANNDD CCOOLLOORR VVAARRIIAATTIIOONNSS IINN TTHHEE HHOOTT PPUULLSSAATTIINNGG HHOORRIIZZOONNTTAALL BBRRAANNCCHH SSTTAARR

PPGG11662277++001177

Abigail Ruby Daane Mount Holyoke College

Advisors: Professor M. Darby Dyar

Department of Astronomy, Mount Holyoke College &

Professor Suzan Edwards Department of Astronomy, Smith College

& Professor Don Terndrup

Department of Astronomy, Ohio State University

Thesis submitted for review by the faculty of the Five-College Astronomy Department

and the Mount Holyoke Physics Department in partial fulfillment of the degree of

Bachelor of Arts with Honor

May 2004

ii

AACCKKNNOOWWLLEEDDGGEEMMEENNTTSS

I wish to thank my family, Mom, Dad, Heather, and Drew for encouraging me

to always be true to myself and give life and learning my all.

A hearty thanks to my advisors: Darby – for taking on an advisee from a different field and providing

motivation, correction, friendship, help, laughter, and determination. Suzan – for knowing about stars and having an incredible readiness to

provide truly selfless help. Don – wow – for teaching me all about observing, sharing enthusiasm, and

251 pages of data!

Thanks to NSF and Ohio State University – for the opportunity to participate in the REU Program during the summer of 2003.

To the committee – thank you for agreeing to read about my pulsating star!

Mark Peterson and Douglas Leonard – Although you did not have direct contact with my thesis, I feel I should thank you for the incredible amount I learned this year and the new *positive* working habits I acquired from you both.

Mount Holyoke Dance Dept. – I owe you my sanity. I wish to give a special thanks to Rose Flachs and her positive teaching style.

Phil Yecko – for introducing me to variable stars and all their enigmas.

Erica – for putting up with my crazy kooky ways at the observatory!

Cindy Morrell – Talk about the organizing queen! I really appreciated your patience and uncanny knack for finding solutions.

Mount Holyoke Geo Lab (and Darby) – yippee for the great computers and working space!

iii

Thanks to the Mount Holyoke Physics and Astronomy gals: Maria, Krysta,

Evelyn, Emily, and Katie Peek for smiles and cheer.

Jesse – You are amazing for listening to long rants over the phone, reminding me of my love of learning, and the unfailing, unfaltering support you have provided me over the past year.

Janey and Erin – Without you I would not be me. For help with Excel, wheelie chairs, for hugs, deep breathing, and thoughts outside of science, thank you so very much.

Finally, I owe an inexpressible thanks to my Grandma Helen, who always encouraged me to follow my dreams.

iv

AABBSSTTRRAACCTT

Stars that exist on the Extreme Horizontal Branch like the subdwarf B

star PG1627+017 have recently been found to have small variations in

magnitude. The quasi-periodic changes in magnitude are believed to be

caused by pulsations in the interior of the star that change the star’s luminosity

and temperature. This paper focuses on measuring the variations in

brightness of the hot pulsating variable star PG1627+017 in the ultraviolet

light, U at λ= 0.37 µm or 3700 Å, and red light, R at λ= 0.66 µm or 6600 Å.

Pulsation theory for low order gravitational mode pulsations predicts

temperature changes from 32,000 to 35, 000 K. The corresponding changes in

magnitude will not be achromatic and larger amplitudes are expected at

shorter wavelengths.

Mean brightness from night to night changes by 0.089 in U, and 0.04

in R. Changes during a single night are smaller in amplitude, with U

variations typically 1.4 times greater than the R variations. The star’s changes

in brightness do not follow a clear trend and are more complicated than

originally expected. Nevertheless, all nights show the furthest values from the

mean magnitude to be in the ultraviolet light. These shorter wavelengths are

v

seen to vary approximately twice as much as the longer red wavelengths, 0.04

vs. 0.02 magnitudes. This implies that subdwarf B star is not acting in an

achromatic manner and is therefore experiencing changes in temperature on

the surface of the star. These are the results of the first extensive observations

of a hot subdwarf B star in the ultraviolet and red wavelength simultaneously.

TTAABBLLEE OOFF CCOONNTTEENNTTSS CChhaapptteerr TTiittllee PPaaggee Acknowledgements ii Abstract iv Table of Figures vii Chapter 1 Introduction – Stellar Properties and Stellar Evolution 1 Chapter 2 Overview of Subdwarf B Stars 9 Chapter 3 Background – Stellar Pulsation 14 Chapter 4 Data Collection and Reduction of a Subdwarf B Pulsator 21 Chapter 5 Results and Analysis of Data 33 Appendix A Graphs 46 References 61

vii

IINNDDEEXX OOFF FFIIGGUURREESS AANNDD TTAABBLLEESS NNuummbbeerr PPaaggee NNuummbbeerr PPaaggee Figure 1.1 4 Figure 4.3 27 Figure 1.2 6 Figure 4.4 28 Figure 1.3 7 Figure 4.5 29 Figure 2.1 12 Table 5.1 35 Figure 3.1 14 Table 5.2 36 Figure 3.2 15 Table 5.3 38 Figure 3.3 18 Figure 5.1 46 Figure 3.4 19 Figure 5.2 49 Table 4.1 22 Figure 5.3 37 Table 4.2 30 Figure 5.4 52 Figure 4.1 25 Figure 5.5 55 Figure 4.2 26 Figure 5.6 58

1

CCHHAAPPTTEERR 11 IINNTTRROODDUUCCTTIIOONN -- SStteellllaarr PPrrooppeerrttiieess aanndd SStteellllaarr EEvvoolluuttiioonn

Astronomy is a field that exists in constant flux. New discoveries are

continually made, causing old theories to be discarded or changed to fit the newly

analyzed data. Only a few years after printing, textbooks are most assuredly

incomplete and in many cases incorrect. New articles and papers are published

daily. In January of 2003, a paper was published that shared the discovery and

classification of a new type of star that is the subject of this thesis.

This variable star has been classified in the subdwarf B category and its

existence was discovered in 2002 by Elizabeth Green. It lies on the Extreme

Horizontal Branch and is believed to pulsate because of low-order gravity mode

pulsations. In an effort to explain this new star and its believed stage of life, a

brief summary of the processes by which information is obtained about the

evolution of a star is given below.

1a. Basic Stellar Properties

Measurement of distance is the biggest challenge faced by astronomers as

they strive to discover the true nature of stars. Much information is easy to obtain

by simply using the naked eye to observe the night sky, such as the brightness of a

2

star and its temperature. It is immediately obvious that some stars are

significantly brighter than others. This observation is known as the apparent

brightness or apparent magnitude, which is the amount of radiation per unit area

or in other words, the flux of light we see here on Earth. The apparent brightness

is defined as a function of the star’s luminosity and its distance from us.

24Lfdπ

= [1.1]

where f is apparent brightness, L is luminosity, and d is the distance between the

observer and the star. Because the apparent brightness is light per unit area, it

follows that luminosity is the total power of a star’s radiation. Distance can be

determined by using parallax, and thus, luminosity can be found. Likewise, if the

distance to a certain galaxy or cluster is known, the luminosity can easily be

found. Depending on the light radiated from a given star, we can find its

chemical composition and its stage in life. Luminosity is the first of two vital

pieces of information that give us clues about the interiors of stars.

The second observable fact that provides copious amounts of information

can be seen with the naked eye on a clear night: temperature. The classifications

are more precise than a hotter “blue” star or a cool “red” star and follow in this

order: OBAFGKML from hottest to coolest. In turn, each of these letters has

subcategories; for instance, A0, A1…A9. Our Sun is classified as a G2 star.

Surface temperature is measured by spectroscopy, or the study of spectral

lines. It has been observed in laboratories on Earth that different atoms and

molecules will absorb and emit light at extremely specific wavelengths when

3

excited to certain states. Depending on those absorption and emission lines, we

can determine chemical makeup and temperature of the star with impressive

accuracy.

When both luminosity and temperature are known, the radius of the star

can be found by this equation:

2 44L R Tπσ= . [1.2]

where L is luminosity, R is the radius, and T is the surface temperature of any

given star. Once luminosity, temperature, and radius are known, a wealth of

information can be gathered.

The mass is the most informative characteristic; however, it is not easy to

measure. From nearby binary systems, the gravitational attraction between stars

can be calculated and related to their masses by Kepler’s third law:

( )2 2 31 24P a M Mπ= + . [1.3]

where P is the period of orbit, a is the semi-major axis and M1, M2 are the masses.

Unfortunately, mass is more difficult to observe than luminosity or temperature.

A useful way of representing the lives and stages of all stars was devised

in the early twentieth century by astronomers Ejnar Hertzsprung and Henry Norris

Russell. They created a single diagram where stars of all temperatures and

luminosities, as well as masses and radii, can be plotted and compared. This is

officially called the Hertzsprung-Russell (H-R) diagram (Figure 1) and is now

used throughout stellar astronomy. The H-R diagram is a plot of temperature

4

against luminosity that produces a distinct and informative blueprint for all stars’

lives.

The most visibly striking feature on the H-R diagram is the apparent

superhighway of stars running from the cool, dim stars (red dwarfs) in the right

lower corner, to the hot, bright stars (blue giants) in the upper left. This is known

as the main sequence. Red giants and super giants are large, luminous cooler stars

in the top right corner, and hot, dim stars called white dwarfs are located in the

lower left corner.

Figure 1.1 The HR Diagram shows the Temperature vs. Luminosity graph for stars of different ages and masses. Figure taken from S. Edwards, Smith College.

5

1b. Stellar Evolution

The main sequence is not a line of progression in the life of a star.

Instead, depending on the luminosity and temperature of a particular star, they

spend much of their lives on the main sequence in a single position. A star’s mass

ultimately determines where it resides on the main sequence. It follows that the

larger masses are hotter and more luminous. These high mass stars, such as O

stars, have a short stay on the main sequence, typically a few million years. This

is an incredibly short amount of time compared to the hundreds of billions of

years an M star will typically reside there!

In the main sequence, stars burn hydrogen into helium within their cores.

This process takes up most of the typical stars’ life and thus, the bulk of stars

“loiter” in this stage of fusion. As helium gradually increases in the core, the

hydrogen from the surrounding shells begin fusing and the core steadily increases.

When the shell narrows because of this fusion of hydrogen, the energy released

increases rapidly. This forces the outer layers to expand and absorb much of the

energy before it reaches the surface. During this stage of expansion, the star

leaves the main sequence, and heads towards the upper right corner of the H-R

diagram, evolving into a cooler red giant (Figure 1.2).

Red giants are rightly named because they are both cool and large when

compared to their previous and future states, and indeed are the largest of stars!

Their cooler temperature is caused by the lower density of the outer layers, yet

they are still very luminous because of their size expansion. Within this

6

expanding core of the main sequence star, pressure increases as the hydrogen

shell around the helium burning core contracts. For red giants whose mass is

greater than two solar masses, helium fusion (the act of helium fusing into heavier

Figure 1.2 shows the possible evolutionary tracks of a Sun-like star. The usual path for stars is to follow the dotted line around the top of the diagram, however, subdwarf B stars avoid the AGB Region and scoot over to the EHB (here shown as Ex. H. B. stars). Figure taken from S. Edwards, Smith College. elements) can occur. The pressure increases more rapidly as the hydrogen shell

expands, and eventually the pressure reaches a point where the atoms are so close

that their electrons become degenerate.

The electron degeneracy pressure induces a helium flash, where energy

explodes out of the core. In a few seconds, massive amounts of helium and

7

energy are produced. The release of so much energy allows for various levels of

mass loss and the possibility for the outer envelopes to be discarded. The star’s

radius shrinks and its temperature increases. At the same time, fusion of the

newly formed helium is converted to carbon inside the core by means of a triple-

alpha process.

[1.4]

The next stage of a star depends particularly on how much mass loss

occurs during the helium flash. If there is a significant loss like that shown in

Figure 1.3 shows an example of a star in the Red Giant phase on the left, the inert helium core too cool to begin fusion. Next, after the helium flash and extreme mass loss, EHB stars are left with only a helium burning core and a hydrogen burning shell. http://www-astronomy.mps.ohio-state.edu/~pogge/ Ast162/Unit2/lowmass.html

Figure 1.3, the star moves to the Horizontal Branch (HB) on the H-R Diagram

and is called a subdwarf star. The time spent here is quite short, only hundreds of

8

thousands of years. If stars of a few solar masses experience a severe mass loss,

they end up on the Extended or Extreme Horizontal Branch (EHB), located in the

upper middle part of Figure 1.2. This stage of evolution is where the star studied

in this paper exists.

9

CCHHAAPPTTEERR 22 OOVVEERRVVIIEEWW OOFF SSUUBBDDWWAARRFF BB SSTTAARRSS

When a star ends up on the Extreme Horizontal Branch, it appears as a hot

(22,000-40,000 K), pulsating subdwarf B (sdB) star. The term subdwarf refers to

stars existing below the main sequence on the HR Diagram. Because of their

mass loss, the sdB stars sometimes become extremely unstable. The hydrostatic

equilibrium, or the balance existing between the electron degeneracy pressure

outwards and the gravitational pull inwards, is lost. A fluctuation between these

two forces ensues as they struggle to find that equilibrium again. When the

electrons become degenerate, the power of the electrons’ repulsion kicks in and

the gravitational force is overthrown, pushing the star’s layers radially, (or in the

case of the star studied in this paper, often non-radially) outwards. As the

expansion occurs, the outer layers of the star are spread thin. The electrons push

each other apart until the force of the pressure cannot withstand the gravitational

pull, and the contraction occurs again. This process repeats itself again and again

until the equilibrium is established once more. The stars whose mass losses are

not devastatingly extreme grow into giants again on the Asymptotic Giant Branch

and eventually end in explosive, fascinating deaths. However, because of the lack

of hydrogen surrounding the core, stars on the EHB do not have enough hydrogen

fuel to drive into the giant phase again. Thus, the sdB star discussed in this paper

10

does not follow the evolutionary track to the Asymptotic Giant Branch. Instead,

they find their equilibrium once more as even hotter subdwarf O stars with their

temperature, Teff 45,000 K. In their own good time, they fade into white dwarfs.

A more complete explanation about the properties of these stars is given in

Fontaine et al. (2003).

The star in this paper has a temperature near 30,000K, which is on the

cooler end of the pulsating sdB stars. SdB stars that have lost almost all of their

outer envelopes end up with only a core of helium (less than 0.5 of the Sun’s

mass) and a thin shell of hydrogen (less than 0.2 of the Sun’s mass) covering it.

This is significant because the star’s mass was originally at least that of the mass

of the Sun, if not a couple times greater (Green et al. 2003). These stars are

commonly found in the disk of our Galaxy and in some star clusters (Liebert et al.

1994).

SdB stars are of particular interest to astroseismology because of their

intricate pulsations. Astroseismology, the study of oscillations in a star that

pulsates in numerous excited normal modes simultaneously, provides information

about the inner structure of these stars. Just as the use of seismology has greatly

increased knowledge of the interior of the Earth, astroseismology too is enabling

grand discoveries, without the help of any seismographs! Depending on the

chemical makeup of the layers within the star, the different oscillations will dive

to different depths of the interior and be bent in ways specific to the material

through which they are passing. Because stars on the EHB are essentially the

11

same as the cores of red giants, astroseismological studies may also help reveal

the details of the interior structure of these stars.

Theorists have looked into various explanations for these variations.

1. Rotation of the star is not an option because there are more than two

periods in the light curve, which implies a more complicated behavior than

mere rotation.

2. Orbital motion cannot account for these pulsations as well because the

periods of both p-mode and g-mode oscillations are too short for the

spectrally identified sdB stars.

3. Cataclysmic variables cannot explain pulsations because these multimode

periods are not equally spaced like those we observe from CVs.

4. It was thought for a time that pulsations could only be present in binary

systems, however O’Donoghue et al. (1998) found that this was not the

case.

5. It has therefore been assumed that the most viable option is that the stellar

pulsation comes from within the star itself (Kilkenny et al. 1997).

With light curves from two wavelengths, these pulsations can be observed

and tested for color changes. A comparison can be made between their

amplitudes to check for similar or varying changes in temperature. For example,

Figure 2.1 shows three computer models (the solid lines) of spectrum of a

subdwarf B star. The larger image deals with the longer wavelengths and how a

cool companion star, such as an M dwarf with a temperature of T2, would

12

influence them. These data correspond to a different paper (O’Donoghue et al.

1998). The R1 is related to the sdB star and the 0.15 times the radius of the Sun

corresponds to a size very near Jupiter. The real importance for the color

brightness variation existing in this paper is shown in the enlarged portion of the

graph showing the three computer models of the sdB star, each with a different

temperature: 35000, 33000, and 32000 K.

Figure 2.1 is taken from O’Donoghue et al. (1998) and shows a plot of computer models (solid lines) in Log (Wavelength) vs. Log (Flux). The letters correspond to what light is found at those wavelengths, i.e., U stands for ultraviolet. T2 in the large image corresponds to the effects a cool companion star, such as an M dwarf, would have in the JHK region. http://www.obs-nice.fr/grec/astrosismologie.html

13

The overall spectral energy distribution of a hot star will be much brighter

at U than at R. In the spectrum in Figure 2.1 showing a model sdB star with a

temperature of 35,000K, the U/R flux ratio is about 2.4, which would translate

into a U-R color index on the standard magnitude system of about -1.8, which

corresponds to a very blue star. The effect on star colors for varying temperatures

is shown in the inset, where the largest changes are seen in the U band and the

smallest changes occur in the V band. Changes would be even less at R.

The models of g-mode pulsations for sdB star predict very small

wavelength dependent variations, with an amplitude ratio of 1.09 for B/V (blue

light/visible light) and 1.38 for U/V (ultraviolet light/ visible light) (Green et al.

2003). It follows that the variation with respect to R would be even more

apparent. The amplitude ratio of U/R is what this paper tries to measure.

Even with the U and R filters at a larger distance, the U is seen in the

computer models to vary only slightly more than the R. Yet, the value of U/R

should be greater than both the B/V and U/V and therefore more easily measured.

The light curve data must be extremely accurate to be able to compare these small

changes in flux (in units of erg s-1 cm-2 Hz-1) that make a difference in the

modeling of sdB stars. To test for this modeled change in magnitude (and

temperature), a technique will be used to measure the relative change in U

wavelengths, or the proportional variation, when compared to R wavelengths.

14

CCHHAAPPTTEERR 33 BBAACCKKGGRROOUUNNDD –– SStteellllaarr PPuullssaattiioonn

Although astroseismology is relatively new, helioseismology, or the study

of the Sun’s pulsation, has existed for more than 30 years. Through these studies,

modes have been defined to describe

the various types of pulsation which

each occur for a different reason.

Most prominent in the Sun are the

pressure-mode pulsations, or p-mode

pulsations, and these were the first

type of pulsation to be found in sdB

stars. P-modes are believed to be

caused by an iron opacity κ (kappa)

mechanism in the thin, outer diffusion-

dominated envelopes. This essentially

means that the iron abundance is elevated above the normal composition within

the atmosphere of the star. This radiation pressure provides an outward force on

atoms (like iron) that have high opacities. (Charpinet et al. 1996)

P-mode pulsation can be thought of as an assortment of sound waves that

are more influential in the outer layers and surface of the star as the Figure 3.1

Figure 3.1 Variety of P-mode pulsations, more abundant on the surface layers and infrequent inside. http://science.msfc.nasa.gov/ssl/pad /solar/p_modes.htm

15

shows. Just as the different layers inside the Earth bend waves because of their

different densities, so do the layers in a star. Imagine a bell just after it has been

sounded. That vibration is

similar to the effect that the p-

mode pulsations have on the

surface of stars. On the Sun, it

is possible to observe how

these p-modes affect its

radiation in the radio waves

because the surface of the Sun

can be resolved on today’s

telescopes. This is observed by

finding the change in Doppler

(or red) shift in the

wavelengths of light as it arrives from the Sun. These shifts appear as peaks and

troughs on the Sun’s surface in those wavelengths as shown with exaggeration in

Figure 3.2.

Currently, approximately 10 million different pulsation modes have been

observed from the Sun. Each mode is believed to be driven by pressure and can

described in an equation using both radial and spherical harmonics. P-mode

pulsation can be described in this manner:

Figure 3.2 P-mode pulsation in 3-D. The values for n, m, and l are exaggerated over 1000 times to show the vibrations. http://odin.math.nau.edu/~jws/dpgraph/Yellm.html

16

tilmn

lmneYrtr ,,),()(),,,(.,ωφθξφθξ −= [2.1]

The ξ is the scalar displacement caused by the mode, using spherical

polar coordinates (r,θ,φ) and time (t) to describe the perturbation. The angular

frequency (ω) is used to describe mode frequencies by theorists, and experimental

observers have typically substituted circular frequency v = ω/2π.

With all pulsations, there exist corresponding n, l, and m quantum

numbers. The “radial order” of a mode is labeled as n, and describes the total

number of nodes present. This would be fairly simple to acquire in 2-D but when

observing a star, the nodes in the interior of the star must be taken into account as

well. Of course, these cannot be observed directly, so theorists use computer

models and knowledge of the outer layer to predict what is occurring inside. The

l, or “angular degree” is used to describe the product of the stellar radius and the

horizontal wavenumber. It is typically less than the radial order and represents

the colatitude pulsation. Directly dependent on l is the “azimuthal order” labeled

as m, which is the longitudinal response to the angular degree. Its value must be

less than or equal to l’s number. For p-mode pulsations, a possibility exists that

l=0, and the pulses are completely radial. However, this is a special case and does

not apply for the target star, PG1627+017 where buoyancy forces are present.

Other types of pulsations exist in stars as well. These include f-modes, r-

modes, and g-modes. F-modes are surface gravitational modes that depend on the

fundamental fluids (hence the name) outside the core, just like the pressure

17

modes. R-modes are due to rotational effects and are particularly seen when

observing pulsars and neutron stars. F and r-modes have not been observed in

pulsating sdB stars. The same was true for p-modes, although they have been

observed in the Sun since the 1970’s.

The discovery of the p-mode pulsation occurred only recently in sdB stars

(Kilkenny et al. 1997). Unofficially known as EC14026 stars, these variables

vibrate with periods from 80-600 seconds. The longer periods of pulsation

systematically indicate cooler stars while still remaining within the sdB category.

Recently Green et al. (2003) found another group of sdB stars whose

pulsation periods are a few hours instead of a few hundred seconds and are at

least a factor of ten too long to be a result of p-mode waves. Instead, a

gravitational restoration force, whose mechanism to excite the modes is currently

thought to be the same iron opacity mechanism causing p-mode pulsation

(Fontaine et al. 2003), must cause the driving of these deeper pulsations, their

strength lying in the inner layers of the star. These low-amplitude gravity mode

(g-mode) pulsations are found to occur in ~75% of sdB stars cooler than 30,000 K

or 25%-30% of all sdB stars (Green et al. 2003).

G-modes have been observed only in hot stars, and thus are not observed

from the Sun. G-mode pulsation, to the first order of oscillation, can be thought

of as water waves propagating over the surface, moving the star through large,

sloshing bulbous shapes. It can be mapped by following the changing patterns,

much like weather fronts are mapped across the globe.

18

The lower the l and m numbers for g-modes, the deeper the pulsation

occurs within the star. For example, consider that a given g-mode oscillator has

been thrown out of equilibrium to have the following parameters associated with

it: l=1, m=0. This straightforward oscillator would then be moving such a way

that it could be represented by a filled water balloon. By squeezing the “equator”

or middle of the

balloon, the top and

bottom would be

pushed outward, but the

thin balloon surface

would still be on the

entire outside as Figure

3.3 shows. Then as the

squeezing pressure is released, the gravitational restoration force would pull the

top and bottom back in momentum. As the quantum numbers increase, the shape

of this greatly simplified star becomes more elaborate (and realistic).

Figure 3.4 shows various possibilities for low-order pulsations. Stars do

not have only one of these pulsation modes, as the figure shows. Instead, on a

given star, many of different modes of pulsation add to and cancel out other’s

peaks and troughs to create the measured luminosity.

Figure 3.3 An example of the g-mode pulsation that would occur if the n=1, l=1 and the m=0.

19

0,0 1,0 1,1

2,1 3,0 3,1

The intricacy of the star’s movement develops quickly. However, in

general theorists believe that g-mode pulsation is dominant only in the low-orders

in sdB stars. Fontaine et al. (2003) have determined a viable theory where these

pulsations can be explained by using l=3 and 4 modes, instead of the l=1 and 2

that were originally supposed. This complicates the modeling but is the closest

theorists have come thus far to matching a model with the observed variations in

luminosity. For more information about the modeling see Fontaine et al. (2003).

The only guideline for modeling is to make the model fit the observations

of the light curves and this is a newly unlocked field of work. The goal of this

paper is to obtain clear light curves that have accurate information about a sdB

star in two different wavelengths simultaneously. This will increase knowledge

of the actual oscillations in luminosity, as well as help indicate the reasons behind

these oscillations. The current theorists are trying to combine these p and g-

modes to produce models that match up with what we know about the physical

Figure 3.4 shows a few examples of the low-order g-mode pulsations that appear for specific l and m values. The numbers to the right of the images correspond to l,m.

20

periods, and what makes sense in terms of the physics and chemistry known

today.

“Most exciting is the fact that …despite its relative simplicity and the

richness of the parameters available, the failure of this model suggests that

standard stellar evolution theory does not fully explain the evolution of sdB stars

and or the nature of pulsations within them. We have something new to learn.”

(Reed et al. 2004)

21

CCHHAAPPTTEERR 44 DDAATTAA CCOOLLLLEECCTTIIOONN aanndd RREEDDUUCCTTIIOONN ooff aa SSddBB PPuullssaattoorr 4a. Data Collection

Testing for achromatic behavior, or lack thereof, involves data collection

from a single star in two different wavelengths. Recall from Equation 1.2 that

luminosity is proportional to the square of the radius, and if the radius is the only

variable, no color variation should be observed from the star. In other words, all

light emitted would vary the same amount relative to the other wavelengths. This

achromatic variation (constant temperature) is sometimes observed in p-mode

pulsators. However, theorists predict that g-mode pulsation must be caused by

changes in temperature as well as the rise and fall of the photosphere (the point at

which light can escape from a star). Although the star is not in hydrostatic

equilibrium, its layers do essentially stay in a specific arrangement, i.e. hydrogen

on the outside, helium held inside that layer. Restated, the star is not so disturbed

as to be churning up the core onto the surface.

It is predicted that different emission wavelengths will produce light

curves showing variations in their amplitudes. This implies that the surface is

changing temperature with time as well as changing in radius. The wave modes

cause these pulsations by creating a pattern of higher radius and cooler

temperature over the surface that propagates around the star. When computer

22

models use g-mode pulsations (to account for the changes in temperature), the

observed light curves can be made (Fontaine et al. 2003). Models indicate that

the variations in the relative amounts of ultraviolet and red light depend on the l

number of the principle modes. Odd numbered modes have been found to have a

larger variation in models (Randall, private communication).

The g-mode pulsating star PG1627+017 was chosen for observation

because of its previously established pulsation period of a few hours and the

adequate number of comparison stars nearby with similar magnitudes. A nearby,

slightly redder star, PG1432+004, was observed at various times each night to

help calibrate images for PG1627.

STAR Name Right Ascension (hr, min, sec)

Declination (deg,arcmin, arcsec) Epoch

PG1627+017 16h 29m 34s +0°01’38.2” J2000.0

PG1432+004 14:35:20.00 +0°13’48.0” J2000.0

Table 4.1 defines the coordinates of the two stars that were observed. The epoch corresponds to the positions occurring on the Julian day 2451545 at 12:00 (Universal Time) i.e. January 1, 2000.

All time-series photometry was gathered on July 1-6, 2003 at the MDM

Observatory on Kitt Peak, Arizona by Donald Terndrup and Abigail Daane. The

2.4 m Hiltner Telescope and CCD (Charged Couple Device) camera with 9.4

arcminute FOV@ 0.28 arcseconds/pixel were used for all data collection. The

CCD camera was 2048 x 2048 pixels. The images were taken while binned 2 x 2

pixels for speed.

23

Nights one, two, and four went very smoothly with almost photometric

skies and relatively good seeing (measuring the turbulence in the atmosphere),

less than two arcseconds for most of the observing. None of the nights was

photometric (ideal seeing) and nights three, five, and six had sections of poor

seeing but were for the most part good sources of data. The end of night three

does not have a clear light curve, and has been omitted from the data compilation

because of cloud coverage. Clouds also became a problem on night five; during

the middle hours the sky became completely opaque. Night six had clear skies

off and on during the night, but was never completely cloudy. There were wisps

and several moments where the guiding star was lost. In total, the observing run

was successful and the data acquired for our purposes were more than sufficiently

informative.

The process of gathering accurate data begins with taking bias and flat

exposures. To calibrate the images of the star, it is necessary to eliminate

electronic bias and pixel sensitivity effects. Bias/zero exposures are taken to

remove the internal dc offset, or the electronic offset from the camera, and do not

open the shutter for any light to be recorded. Biases can be taken before the Sun

has set, as the uniqueness of the camera is the subject of interest.

At sunset, the “flat” exposures are taken. Flats correct for the fact that

some pixels are more sensitive to photons than others. They also account for the

manner in which the shutter opens, which can influence the intake of light. As the

shutter opens, the middle of the exposure is exposed before the edges and

24

consequently receives more light. Flats take images of a uniformly illuminated

source of light, such as a white spot on the wall or the sky just after the Sun sets

when the stars are not yet visible. Because two different filters are used, one flat

must be taken for ultraviolet (U) light (λ=0.37 µm) and one for red (R) light (λ=

0.66 µm). Flats for the shorter wavelength filters are acquired first when it is still

relatively light, with the longer wavelengths following. It takes a longer time to

gather the shorter wavelengths, i.e. ultraviolet, because the light is more scattered.

Ideally, the pixel count should be somewhere around 20-30 thousand. This

ensures that the flat is not over-exposed and still has enough photons gathered to

give adequate information.

When the sky is completely dark, actual data acquisition can begin! The

telescope is first slewed to a random bright star near the zenith to confirm that its

coordinates are concurrent with the computer. This is also where the focus is

measured by taking several exposures, changing the focus and measuring for the

smallest value of the FWHM (full-width, half-max) in the stellar images.

In order to measure the pulsations of a star, the variance of light must be

compared with that of other, non-varying objects (stars) with similar magnitudes

in the same CCD frame. PG1627 is in a stellar field whose location fits well for

this differential photometry because several other stars of similar magnitudes are

present. Initially 10 stars were used for the R filtered images, and 7 stars for the

U filtered images. However, one of the comparison stars (star number six) for the

R filter has been identified as a variable star as well, so it has been deleted from

25

the star average. Examples of the corrected images of the field of view in the R

and U filter are shown in Figures 4.1 and 4.2. The relevant stars are indicated by

the red line and corresponding number.

Figure 4.1 shows a typical image from night four, image number 48 (n4048) in the R filter. The comparison stars are labeled with numbers, and PG1627 is labeled with the boxed number five. The color is inverted in order to see the contrast more easily.

The images of the stars are then collected through the ultraviolet (U) filter

at λ=0.37 µm and the red (R) filter, at λ= 0.66 µm. Exposure times ranged from

6-15 seconds for the R filter and 30-75 seconds for the U filter, the range due to

the airmass.

26

Figure 4.2 shows a typical image from night four, image number 49 (n4049) in the U filter. The comparison stars are labeled with numbers, and PG1627 is labeled with the boxed number four. The color is inverted in order to see the contrast more easily.

As the airmass increases because of atmospheric extinction, the star’s

magnitude decreases. This is corrected automatically by using the comparison

stars. Extinction corrections are also dependent on the color of the star, although

these effects are much smaller than the overall dimming with airmass. However,

by taking exposures of a similarly hot, non-variable star PG1432, adjustments can

be made to compensate for the change in color. Returning to this comparison star

field at subsequent intervals during the night, the slight changes due to airmass are

27

measured. The subsequent fall of PG1432 in instrumental magnitude due to

atmospheric extinction can be applied to the subject of interest, PG1627.

Figure 4.3 demonstrates the process of the changing slope occurring in the

data for night two. The data points are from star PG1432 that should be observed

to have a constant magnitude, neglecting the affect of atmospheric extinction.

Therefore, discovering the influence of the night’s change in atmosphere is easily

accomplished by taking the observed negative slope and correcting it to have no

slope. When this slope correction is applied to PG1627, the magnitudes become

more accurate.

Figure 4.3 shows two sets of data of PG1432 from night two. The top trend line represents the slope that has been corrected for change in airmass from the original trend line (bottom).

28

Figures 4.4 and 4.5 show all nights where the airmass value was

recorded for PG1432. As each night progresses and the star moves towards the

horizon, its magnitudes fall with a different slope. In comparison to Figure 4.4, it

is evident in Figure 4.5 that the descent of light collected is more of a factor for

the ultraviolet light. Thus, the red light drops close to 0.02 magnitudes during one

night, whereas the U light drops roughly twice as much, 0.04 magnitudes per

night. It is therefore imperative that airmass be taken into account as this study is

measuring variance in magnitude. Some of the nights do not fall in a linear

fashion and this has an effect on the light curves. A linear fit for this color change

was applied to the light curves for this paper, however, further study should look

into this data correction.

Figure 4.4 shows the fall of U differential magnitude with respect to its airmass.

29

Figure 4.5 plots the R differential magnitude with respect to the airmass. The R falls with the increase in airmass, but the decrease in U is more significant.

Each night’s magnitudes are found using the corresponding measured

airmass for that specific night. Table 4.2 is a list of all slopes applied to the data.

Unfortunately, night five did not have sufficient data to make a slope of the

changing airmass because of lack of data. Instead, a substitution of an average

number of the other slopes was used.

3.b Image Reduction

Image processing takes the raw images that are straight from the camera

and applies all of the standard corrections to those images. For this processing, a

program from Unix machines called IRAF (Image Reduction and Analysis

Facility) is used. Within IRAF is a wealth of commands to calibrate images from

30

CCD cameras. The first step is to perform the functions of overscan and trim.

The overscan defines the dark current that is measured at the edge of each image.

This applies the

information about

the thermal noise

in the image and

then the trim

command literally

cuts off the

overscan region on

the image. Subsequently, the zeros and flats are applied to each image.

The next step is to align all images to the same coordinate system so that

the stars positions are clearly identified. From image to image, the stars are

shown in a slightly different place so that the centers of the stars are shifted within

the coordinate system. In order to compare each star’s image with the next, a set

of coordinates must be defined for each star. Conveniently, this can also be done

in IRAF. A list is made of the approximate centers of stars and a command called

wphot sweeps out a small radius around each given coordinate set to find largest

pixel count where the actual center of the star is located. As long as the images

are similarly aligned, this process runs smoothly. A different list must be made

for each night and the wphot process must be checked to make sure the positions

have not significantly moved during the night. If they have moved, INDEF or

Night R Airmass Slope (magnitude/airmass)

U Airmass Slope (magnitude/airmass)

1 0.0069 0.0411 2 0.0092 0.0202

3 0.0146 0.0711

4 0.0053 -0.0012

5 0.0050 0.0500

6 -0.0044 0.0035

Table 4.2 shows the slopes of magnitude versus airmass that were applied to the data sets to correct for atmospheric extinction.

31

tiny magnitudes (too small to be a star’s center) will appear in an output file

instead of the correct information. In this case, a new list of points must be made

and the coordinates readjusted.

After the coordinates of the star’s centers have been established, aperture

photometry is done with the local sky estimator. This is a process that defines the

total area of the star in the image, counts the photons within that area, and

subtracts the sky background noise from the measured pixel count.

Now the images are actually ready to be properly viewed and cleaned!

The first step is to clean the cosmic rays on the image, which requires the

examination of each star whose data will be used. Having already clearly defined

and labeled the stars, the “imexamine” command in IRAF is used to look at the

radial plot of each one. This command finds the maximum pixel count (the center

of the star) and plots the light distribution radially outwards. With this tool, it is

easy to pick out the pixels with an abnormally large number of photons collected,

indicating that a cosmic ray is present. Cosmic rays are high-energy particles that

are hurtling into our atmosphere from anywhere outside the Earth.

Using a device in IRAF under digiphot/apphot called imedit, the cosmic

rays can be deleted and replaced with values that are taken from an average of

adjacent pixels surrounding them. This is a smooth process, provided that the

cosmic rays are sufficiently distant from the star on the image, so as not to affect

its pixel count. It also provides a check to see if all of the images have been

32

correctly reduced, are not overexposed, and have good focus. All blurry or

overexposed images are noted and recorded for the next processes.

Finally, a file is made with information about each star such as the image

name, magnitude, Heliocentric Julian date, exposure time, airmass, and

coordinates. These files are then copied into Excel spreadsheets where they are

ready for general analysis. An example set of these files is in the following

chapter.

33

PG1627+017 Night 4 Data orig obs id xcoord ycoord xerr yerr mag merr sky serr air exp HJD 363 1 641.4 905.4 -1.6 1.38 15.635 0.004 63.7 5.1 1.165 7 825.6996140 364 2 596.3 633.5 -2.7 1.47 16.922 0.008 63.6 4.8 1.165 7 825.6996140 365 3 615.3 757.6 -1.69 1.63 17.103 0.010 63.1 4.8 1.165 7 825.6996140 366 4 538.3 899.5 -2.66 1.46 14.625 0.002 64.8 5.1 1.165 7 825.6996140 367 5 454.6 694.7 -2.43 0.74 14.179 0.002 65.8 5.2 1.165 7 825.6996140 368 6 415.6 697.1 -1.38 1.08 17.159 0.010 63.1 4.9 1.165 7 825.6996140 369 7 447.7 985.8 -1.29 1.77 15.280 0.003 64 5 1.165 7 825.6996140 370 8 342.4 582.5 -2.61 2.52 16.338 0.006 63.3 4.8 1.165 7 825.6996140 371 9 141.8 642.6 -3.22 0.63 15.760 0.004 63.3 4.9 1.165 7 825.6996140 372 10 165.8 872.4 -3.25 2.36 16.225 0.005 63 5 1.165 7 825.6996140 373 11 138.6 708.1 -2.36 0.1 15.191 0.003 63.9 4.9 1.165 7 825.6996140 374 1 536.7 900.3 -0.31 -1.69 18.882 0.008 39.2 4.1 1.164 42 825.7004994 375 2 639.3 568.4 0.26 -0.57 17.075 0.003 41.6 4.4 1.164 42 825.7004994 376 3 446.4 986.6 0.36 -1.44 19.249 0.010 38.8 4 1.164 42 825.7004994 377 4 453.4 695.6 0.35 -1.43 15.377 0.001 45.9 6.4 1.164 42 825.7004994 378 5 164.4 873.4 -0.64 -0.65 19.548 0.013 37.8 4.1 1.164 42 825.7004994 379 6 137.2 708.8 0.19 -1.2 19.369 0.011 38 3.8 1.164 42 825.7004994 380 7 212.5 440.1 0.5 -0.92 18.945 0.008 40.5 4.1 1.164 42 825.7004994 381 8 140.4 643.5 0.39 -0.54 19.051 0.009 38.5 4.2 1.164 42 825.7004994

Table 4.1 shows an example data set from the fourth night. An explanation of the column headings is found within the chapter. The table is continued on the following page. The column obs is repeated for continuity between pages.

34

mod R R R R

obs HJD filt image coordfile w w*val <comp> dmag corr sca 363 825.6998050 R n4048 n4R1627.xy 1 15.635 15.898 -1.719 -1.719 -0.002 364 825.6998050 R n4048 n4R1627.xy 1 16.922 365 825.6998050 R n4048 n4R1627.xy 1 17.103 366 825.6998050 R n4048 n4R1627.xy 1 14.625 367 825.6998050 R n4048 n4R1627.xy 1 14.179 368 825.6998050 R n4048 n4R1627.xy 0 0 369 825.6998050 R n4048 n4R1627.xy 1 15.28 370 825.6998050 R n4048 n4R1627.xy 1 16.338 371 825.6998050 R n4048 n4R1627.xy 1 15.76 372 825.6998050 R n4048 n4R1627.xy 1 16.225 U U U U 373 825.6998050 R n4048 n4R1627.xy 1 15.191 <comp> dmag corr sca 374 825.7008929 U n4049 n4U1627_2.xy 1 18.882 18.874 -3.497 -3.496 -0.003 375 825.7008929 U n4049 n4U1627_2.xy 1 17.075 376 825.7008929 U n4049 n4U1627_2.xy 1 19.249 377 825.7008929 U n4049 n4U1627_2.xy 1 15.377 378 825.7008929 U n4049 n4U1627_2.xy 1 19.548 379 825.7008929 U n4049 n4U1627_2.xy 1 19.369 380 825.7008929 U n4049 n4U1627_2.xy 1 18.945 381 825.7008929 U n4049 n4U1627_2.xy 1 19.051

Table 4.1 continued.

35

CHAPTER 5 RESULTS and ANALYSIS of DATA 5a. Results

The goal of this project is to test the achromaticity of light curves in

different wavelengths. It is theorized that in subdwarf B pulsators, the ultraviolet

light actually varies more in relative amplitude than its cooler counterpart, red

light. Therefore, a comparison of the differential magnitudes of the wavelengths

on both the U and R light curves is of great interest.

The process of determining the light curves involves many steps, as is

obvious by the extremely large set of data gathered. Table 5.1 shows two

examples of the sets of data gathered, one each from the U and R filters. The data

from all of the stars observed were assembled into Excel spreadsheets and the

bolded titles of the columns are defined in the following paragraphs.

The first column labeled obs is the observation number, id is the number

given to each star on the image, and the next two columns, xcoord and ycoord,

give the coordinates for that star on that particular image in pixels. The next

column is the shift those coordinate values have compared to the (somewhat

arbitrary) finder chart values. Mag is the instrumental magnitude measured for

each star; found by this equation:

36

Mag = -2.5log(count) + constant

where the count is the total number of photons collected for the star and the

constant is added to make the value positive. The Mag’s error is next, followed

by the sky value and its error. The sky value is the count per pixel assigned to the

supposedly “dark” sky. Air stands for the value of the airmass when the image

was taken and exp is the exposure time in seconds. Original HJD stands for the

original Heliocentric Julian Date and the Modified HJD is the middle of the

actual exposure, taking into account the fact that the original HJD is recorded 13

seconds before the exposure. Filt is the filter used; image represents the name of

the image, and coordfile is the coordinate file used to define the middle of the

stars as well as the previous columns for x and y values. Next the w and w*val

give an option to weight some values of magnitude more heavily, or not at all.

With all of this critical information, the standard with which our variable

is compared can be found. This value is called the U and R <comp> and is the

calculated average magnitude of all comparison stars. Having that standard

established, the next columns of values calculated are the U and R ‘differences in

magnitude,’ shortened to dmag, i.e., the brightness relative to the collection of

comparison stars. Dmag was found by taking the difference between the <comp>

and our star’s magnitude for the same exposure.

Taking the slopes of these curves to be falling in a linear fashion, this

extinction is corrected using this equation:

U = Udmag – slope*air

37

R = Rdmag – slope*air

where U and R are the corrected differential magnitude with respect to the color

correction from airmass specific to the particular picture. The slope is measured

in relative magnitudes per airmass and those values were previously shown in

Table 4.2. Recall that the thicker the airmass, the more effective the second term

becomes in increasing the negative value (in astronomy negative values are

brighter), and lifts the later data on the graph as the night goes on.

The U and R values for all six nights of U and R (corrected differential

magnitudes) are plotted against the modified HJD in Figures 5.1 and 5.2

(Appendix A). The more negative the magnitude value, the brighter the star.

Thus the y-axis is aligned in such a way that the peaks of the curve are the

brighter points of PG1627 (although their values are more negative). Values for

the U graphs axes range from –3.4 to –3.65 differential magnitudes and –1.65 to –

1.9 differential magnitudes for the R graphs. The x-axis uses an identical time

scale for every graph, 0.25 of the HJD, showing that the time-series photometry

took place for a different length each night. A close inspection of both the U and

R light curves reveals that on a given night the U magnitude varied around 0.04

mags, and the R varied around 0.02 mags. A 0.02 magnitude change is a 2%

change in brightness. Extreme precision in data collection is mandatory to detect

these small changes.

Each night produced a different light curve that varied in both oscillation

patterns and in mean value. The fundamental mode is believed to be caused by

38

the radial motion and appears as the main rise and fall of the light curve but it is

obvious that this is not the only factor involved. The oscillation pattern for

PG1627 is not a standard curve like a Cepheid variable’s curve, but rises and falls

at different rates and to different amplitudes each time. For example, in the

beginning of night two’s light curve for the U wavelength, the curve looks almost

cycloidic. Compare this to night six, where many smaller changes in amplitude

are added to the fundamental mode’s curve. Both of these curves are different

from each other, as well as differing within their own curve from the beginning

and ending of the night. Night four has a potentially linear rise in the beginning

of the curve and a quick drop from the maximum brightness that is unseen in any

of the other nights. This intricate and complicated pattern is not easy to reproduce

in a model, especially when these curves are only about one fourth of the entire

curve for a day.

The mean value of

the star also varies, again

nearly two times more (0.040

vs. 0.089 mags) in the U than

in the R wavelengths. These

values are plotted in Figure

5.3 and listed in Table 5.2.

This graph of the average

values of U and R for each

Night <R Magnitude>

1 -3.542 -1.716 2 -3.510 -1.717

3 -3.570 -1.720

4 -3.493 -1.736

5 -3.527 -1.696

6 -3.481 -1.696

Table 5.2 shows the average differential magnitudes over all of the nights in the U and R light curves. The R light varies in mean by a total of 0.04 differential magnitudes, and the U light varies with a 0.089 value.

39

night does not show an obvious correlation between nights. However, this does

effectively show that the U average value varies by almost a tenth of a magnitude!

The value of 0.089 for the change in magnitude corresponds to an 8.5% increase

in brightness!

Mean Values of U and R

-3.6

-3.58

-3.56

-3.54

-3.52

-3.5

-3.48

-3.46

-1.8 -1.78-1.76-1.74-1.72-1.7-1.68 -1.66 <R>



Figure 5.3 shows a plot of the mean values of U vs. R. Each point represents a single night. The values of the points are given in Table 5.2.

Before further analysis, a plot of the U and R data in tandem on a single,

scaled graph can help to confirm that the oscillations are indeed comparable and

correlated. This is accomplished by taking the dispersion from the mean values of

both wavelengths and weighting the values of one set of data (or both sets) to

make their light curves coincide.

40

Table 5.3 shows the scale factors applied to the Rdisp values each night.

Scaled graphs, (Figure 5.4 in Appendix A), are used to ascertain whether

the reduction processes were relatively accurate and to see if an eyeball estimate

approach will show a larger dispersion from the U mean value. Udisp and Rdisp

stand for the dispersion from the mean values of the U and R. These are found by

the following equations:

Udisp = U - 

Rdisp = (R - <R>)

Rscaled = Rdisp*scale

where and <R> are the averages of all corrected differential magnitudes for

a particular night and scale is the scaling factor required to match the smaller

values of R with the larger values of U. The scale values used

for each graph are found in Table 5.3.

From night to night there is quite a range of scale

factors. The average scale of all but night two is 1.41, which

requires an increase of the dispersion of R values. The graph

of night two shows magnitudes in the R that follow the U’s

curve, but the R values in the last peak are so much larger than

in the beginning of the night that the scale value of 0.8

only accounts for the end of the night. This means that

one scale value cannot account for this night’s more

complicated behavior. Night four has a similar trend that shows the scaled value

of R only matches up with one half of the night. This is also true for night six to a

Night scale

1 1.5

2 0.8

3 1.2

4 1.6

5 1.45

6 1.3

41

lesser degree. They are indeed the same stellar oscillations appearing through

both the U and R filters, however their color variation changes during those

nights. It seems that two different kinds of patterns have surfaced. Some nights

(one, three, five) have specific constants that can be applied to match up the data,

and other nights display a more intricate set of oscillations.

5b. Analysis

The data collected are now in the form of several light curves. Some of

the nights had larger errors in the color correction from airmass than others.

Those errors are probably the cause of the variations in the mean magnitude as

well as in the scaled graphs. In future research, these data should be taken more

frequently to enable greater accuracy for the color correction. However, given the

corrections available, it is still possible to compare the ultraviolet and red light

curves.

One way of looking for a larger range in the ultraviolet light is by showing

a set of histograms that plot the U and R dispersion from the mean magnitude

(Figure 5.5 in Appendix A). The individual dispersion from the mean varied

from night to night in both the U and R, but the U wavelengths were always larger

and the red light is always more concentrated around the mean value.

When looking at the histograms from nights one and five, it seems that the

U has a much larger dispersion and the R values are more closely situated around

the mean. However, this trend does not carry through all of the nights.

42

Distinctively different is night three, showing no outer extremes in the U and

fairly equal dispersion for both wavelengths. Had all of the graphs been like night

three, it would have appeared that the data were telling a story of achromatic

behavior. Nights two, four, and six do have the bulk of the U values in these

graphs fairly matched with the R values like night three. However, they all show

extremities represented fully in the U magnitude. From six nights of data, the

dispersion of the U magnitudes is more commonly spread out than the R

magnitudes but significant exceptions exist. PG1627 cannot therefore be defined

as achromatic and is quite complicated in its respective variations.

The final manner in which these data are presented is the plot of the

change in U versus the change in R magnitudes (Figure 5.6 in Appendix A). The

U and R values in all of these graphs are selected for pairing from images that are

always sequential. The paired images are taken within two minutes of the end of

the first exposure to the beginning of the next exposure. The stalled time in

between exposures is required to find the pixel count and clear the CCD for the

next image. On average about 5% of the data per night is thrown out from the

original data set because the time in between exposures is recorded as longer than

2 minutes. The dotted line is the slope of y=x for comparison. The best-fit solid

line is the slope of the data in these graphs and an indicator of the overall

dispersion. If the slope is greater than one, then the U wavelength on average

makes a larger change than the R wavelength.

43

These plots are extremely interesting because they are clearly not always

oscillating in the same manner. They also do not indicate that a larger variance is

primarily found in the U magnitudes. The best-fit lines from Excel suggest that

the U’s dispersion is approximately equal to the R’s dispersion. These lines split

the data exactly in half. However, nights one, four, and five all seem to show a

different trend line that is steeper than the Excel best-fit line. The graph from

night six may have two different trend lines showing on one night! On the whole,

the data sets tend to loosely associate with two types of graphs. Out of the six

nights of data, the graphs of night two and night four seem not to show any real

trend with slopes of U/R = 0.59 and 1.09. They have a few extreme points where

the U varies a great deal more than the R, but these seem to be overall oddities

within the night. On night two, the slope is less than one, but it is clear that the

change in U has a range that is much larger. Nights one, five, and six however,

show that there is a larger dispersion in the U, with values of U/R = 1.2, 1.13,

1.14, respectively. The slope of night three is nearly one, U/R = 1.02, and is

therefore in the middle of these two groups. Night three has no extrema, and

shows no signs of U having a larger dispersion. The dynamics of the star on this

night seem to have paused and it is actually showing achromatic behavior!

5c. CONCLUSIONS

PG1627+017 is the first pulsating sdB star to be observed in the U and R

wavelengths simultaneously. In this preliminary analysis, it has been found that

44

this sdB star existing on the EHB seems to be experiencing different kinds of

observable variations. It follows the patterns of a star whose brightness changes

in the U are typically larger than those at R. On timescales of days, the mean

brightness changes in the U are typically 0.09 mag, and are about half that amount

at R with mean brightness changes of about 0.04 magnitudes. On timescales of

hours, the amplitude of U and R variations is smaller and exhibits complex

relations, but again the variations at U are greater than at R.

The dispersion around the mean during one night in the U light is on the

order of 0.04 magnitudes, which is approximately twice that of the R light with its

variations of 0.02 magnitudes. The scale factor between the light curves shows

that the dispersion from the mean value in U is on average 1.4 times larger than in

R, restated: U ≈ 1.4R. In addition to these observations, histograms of the spread

of data from the mean show that the extreme values on all nights are represented

in the U wavelength. These observations validate the theory of temperature

changes because the U values are shown to vary more, both by the dispersion

around the mean and by normalizing and scaling the R data to fit the U data.

The values of the slope on the (R -<R>) vs. (U -) graph also followed

the theoretical prediction of U/R being greater than one, but only very slightly,

with the slope value around 1.1. This information will help to provide more

insight as to how the g-mode pulsation influences the luminosity, as it is obvious

that something other than radial motion is taking place on the surface of this star.

45

In the future, it would be beneficial to repeat this time-series photometry

with several sdB stars for longer periods of time. Plans are currently in progress

to use a worldwide observing run to track a subdwarf B star for several sets of

periods. This would enable study of the changing mean value in greater detail. It

would also increase the completeness of the oscillations patterns and thus make it

easier for theorists to match these curves. Further analysis is needed and expected

in the near future. As techniques in astroseismology improve and our knowledge

of this type of recently discovered star grows daily, the true variations of sdB stars

and their angular modes of pulsation are soon to be revealed.

46

AAPPPPEENNDDIIXX AA Figure 5.1

Night 1 Modified HJD vs U Magnitude

-3.65

-3.60

-3.55

-3.50

-3.45

-3.40822.70 822.75 822.80 822.85 822.90 822.95

Modified HJD

U D

iffer

entia

l Mag

nitu

de


-3.65

-3.60

-3.55

-3.50

-3.45

-3.40823.67 823.72 823.77 823.82 823.87 823.92

Modified HJD

U D

iffer

entia

l Mag

nitu

de

47

Figure 5.1 continued.


-3.650

-3.600

-3.550

-3.500

-3.450

-3.400824.65 824.70 824.75 824.80 824.85 824.90

Modified HJD

U D

iffer

entia

l Mag

nitu

de


-3.650

-3.600

-3.550

-3.500

-3.450

-3.400825.65 825.70 825.75 825.80 825.85 825.90

Modified HJD

U D

iffer

entia

l Mag

nitu

de

48



-3.65

-3.60

-3.55

-3.50

-3.45

-3.40826.65 826.70 826.75 826.80 826.85 826.90

Modified HJD

U D

iffer

entia

l Mag

nitu

de


-3.65

-3.6

-3.55

-3.5

-3.45

-3.4827.65 827.70 827.75 827.80 827.85 827.90

Modified HJD

U D

iffer

entia

l Mag

nitu

de

49

Figure 5.2

Night 1 Modified HJD vs R Magnitude-1.85

-1.80

-1.75

-1.70

-1.65

-1.60822.65 822.70 822.75 822.80 822.85 822.90 822.95

Modified HJD

R D

iffer

entia

l Mag

nitu

de


-1.80

-1.75

-1.70

-1.65

-1.60823.65 823.70 823.75 823.80 823.85 823.90 823.95

Modified HJD

R D

iffer

entia

l Mag

nitu

de

50



-1.8

-1.75

-1.7

-1.65

-1.6824.65 824.70 824.75 824.80 824.85 824.90 824.95

Modified HJD

R D

iffer

entia

l Mag

nitu

de

Night 4 Modified HJD vs R Magnitude -1.85

-1.8

-1.75

-1.7

-1.65

-1.6825.65 825.70 825.75 825.80 825.85 825.90 825.95

Modified HJD

R D

iffer

entia

l Mag

nitu

de

51


Night 5 Modified HJD vs R Magnitude

-1.85

-1.80

-1.75

-1.70

-1.65

-1.60826.65 826.70 826.75 826.80 826.85 826.90 826.95

Modified HJD

R D

iffer

entia

l Mag

nitu

de

Night 6 Modified HJD vs R Magnitude

-1.85

-1.8

-1.75

-1.7

-1.65

-1.6827.65 827.70 827.75 827.80 827.85 827.90 827.95

Modified HJD

R D

iffer

entia

l Mag

nitu

de

52

Figure 5.4

Night 1 Modified HJD vs U and Scaled R Magnitudes

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08822.70 822.75 822.80 822.85 822.90 822.95

Modified HJD

Dis

pers

ion

from

Mea

n M

agni

tude

U MagnitudeR Magnitude


-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.080823.65 823.70 823.75 823.80 823.85 823.90 823.95

Modified HJD

Dis

pers

ion

from

Mea

n M

agni

tude


53



-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.080824.65 824.70 824.75 824.80 824.85 824.90

Modified HJD

Dis

pers

ion

from

Mea

n M

agni

tude



-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.080825.65 825.70 825.75 825.80 825.85 825.90

Modified HJD

Dis

pers

ion

from

Mea

n M

agni

tude

U Magnitude

R Magnitude

54



-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08826.65 826.70 826.75 826.80 826.85 826.90

Modified HJD

Dis

pers

ion

from

Mea

n M

agni

tude



-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08827.65 827.70 827.75 827.80 827.85 827.90

Modified HJD

Dis

pers

ion

from

Mea

n M

agni

tude


55

Figure 5.5

Night 1 Frequency of Dispersion from Mean U and R Values

0

2

4

6

8

10

12

-0.05 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Dispersion from Mean Values

Freq

uenc

y

U ValueR Value


0

5

10

15

20

25

30

35

-0.05 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045


Freq

uenc

y

U ValueR Value

56



0

3

6

9

12

15

18

21

-0.05 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045


Freq

uenc

y

R ValueU Value


0

5

10

15

20

25

30

-0.05 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045


Freq

uenc

y

U ValueR Value

57



0

2

4

6

8

10

12

14

-0.05 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045


Freq

uenc

y

U ValueR Value


0

3

6

9

12

15

18

-0.05 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045


Freq

uenc

y

U ValueR Value

58

Figure 5.6

Night 1 Change in R vs Change in U

y = 1.2133x

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.05 -0.03 -0.01 0.01 0.03 0.05

R - <R>

U -




y = 0.5911x

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.05 -0.03 -0.01 0.01 0.03 0.05

R - <R>

U -



59



y = 1.02x

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.05 -0.03 -0.01 0.01 0.03 0.05

R - <R>

U -




y = 1.09x

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.05 -0.03 -0.01 0.01 0.03 0.05

R -<R>

U - 

60



y = 1.13x

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.05 -0.03 -0.01 0.01 0.03 0.05

R - <R>

U -




y = 1.14x

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.05 -0.03 -0.01 0.01 0.03 0.05

R - <R>

U -



61

REFERENCES Bennett, J., Donahue, M., Schneider, N., Voit, M., The Cosmic Perspective, 2nd Edition, Addison Wesley 2002 Carroll, B. W., Ostlie, D. A., An Introduction to Modern Astrophysics. Addison-Wesley 1996 Charpinet, S., Fontaine, G., Brassard, P., & Dorman, B. A driving mechanism for the newly discovered class of pulsating subdwarf B stars. 1996, ApJ, 471, L103 Greene E. M., Fontaine, G., Reed, M. D., Callerame K., Seitenzahl I. R., White, B. A., Hyde, E. A., Oestensen, R., Cordes, O., Brassard, P., Falter, S., Jeffery, E. J., Dreizler, S., Schuh, S. L., Giovanni, M., Edelmann, H., Rigby, J., Bronowska, A., Discovery of A New Class of Pulsating Stars: Gravity-mode Pulsators among Subdwarf B Stars Astrophys.J. 583 (2003) L31-L34 Fontaine G., Brassard P., Charpinet S., Green E.M., Chayer P., Billeres M., Randall S.K. A driving mechanism for the newly discovered long-period pulsating subdwarf B stars. 2003 ApJ 597..518F - Astrophys. J., 597, 518-534 (2003) Kilkenny, D., Koen, C., O’Donoghue, D., Stobie, R. S. A new type of rapidly pulsating star – I. EC14026 – 2647, the class prototype Mon. Not. R. Astron. Soc. 285, 640-644 (1997) Liebert J., Saffer, R. A., Green, E. M. The evolved hot stars of the old, metal-rich galactic cluster NGC 6791. 1994, Astron. J. 107, (4), 1408 O’Donoghue, D., Koen, C., Lynas-Gray, A. E., Kilkenny, D., Wyk, F. van, The EC14026 stars – VI. PG 1047 +003 Mon. Not. R. Astron. Soc. 296, 306-316 (1998) Randall, S., U. Montreal, private communication Reed, M. D., Kawaler, S. D., the Whole Earth Telescope Xcov 17 / 21 / 23 teams Observations of the pulsating subdwarf B star Feige 48: Constraints on evolution and companions. Mon.Not.Roy.Astron.Soc. 348 (2004) 1164

62

Terndrup, D., Ohio State University, private communication Info on Helioseismology: http://128.32.135.2/~stark/Seminars/Aaas/helio.htm For where Subdwarf B came from: http://www.astro.uni-bonn.de/~webstw/science/stwsdb.html Help on AGB: http://www.noao.edu/outreach/press/pr03/sb0307.html For other modes and such: http://www.maths.soton.ac.uk/~na/MATH6107/lecture9.pdf For really awesome movies of models: http://www.ap.stmarys.ca/~guenther/seismology/seismology.html

Documents

I give permission for public access to my thesis and …...Thesis submitted for review by the faculty of the Five-College Astronomy Department and the Mount Holyoke Physics Department