SPECTRAL CHANGES INAT MICROSCOPII

ATTRIBUTED TO FLARINGAdam Clarke

2011

Abstract

Spectroscopic analysis of AT Microscopii has been conducted during a periodof flaring with estimated magnitude increase of three. The spectrum is shown toundergo considerable changes including doppler broadening, area increase and somepotential pattern in peak value which require further analysis to confirm. Delayedchanges in the full width at half maximum compared with the continuum is linked toflare activity triggered by single magnetic loop formation. A decrease in peak wave-length of approximately six angstroms has been detected and cannot be determinedto be either physical or erroneous in nature without further analysis and observation.The FWHM is converted to a velocity change of ∆VH gamma = (92.100±5.700)kms−1

and ∆VH delta = (122.000±24.000)kms−1 from quiescent level to the maximum valueduring the flare outburst.

1

Contents

1 Introduction 31.1 What is a dMe Type Star? . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Rise Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Decay Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.3 Decay Time Constant . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 AT Mic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4.1 Debiasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.2 Flat Fielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.3 Other Reduction Techniques . . . . . . . . . . . . . . . . . . . . . 5

2 Methodology 52.1 IRAF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Image Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Spectra Extraction using IRAF . . . . . . . . . . . . . . . . . . . . 62.1.3 Wavelength Calibration Using IRAF . . . . . . . . . . . . . . . . . 7

2.2 IDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 Reading in the Calibrated Files . . . . . . . . . . . . . . . . . . . . 102.2.2 Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Wrapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Results 12

4 Analysis 15

5 Discussion 19

6 Conclusion 20

7 Acknowledgements 21

A IDL Functions and Procedures 23A.1 Averaging FITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23A.2 Line Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24A.3 Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25A.4 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26A.5 Wrapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A.6 Multiple Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2

1 Introduction

In this paper observations of dMe type star AT Microscopii (AT Mic) are consideredduring periods of flaring, in particular with a flare of estimated magnitude increase ofthree. Comparison with quiescent period spectroscopy to the period of flaring, wasconducted to determine any changes attributed. During the period of flaring DopplerShifting or broadening is expected which would indicate matter being accreted eithertoward or away from the line of observation, or in the case of broadening could indicateatmospheric turbulence. The change in magnitude and the ratios between quiescent andoutburst levels are also considered to determine trends between the two.

1.1 What is a dMe Type Star?

Stars are classified dependant on their spectral type and the Harvard system, foundedby Cannon and Pickering [1912], which lists them in order of atmospheric temperature.An “M” type star on its main sequence, like AT Mic, typically has a temperature of ≤3,700K and is red in visual colour. The preceding “d” marks it as a dwarf star and thesucceeding “e” specifies that the star has emission lines.

1.2 Flares

Stellar activity is based upon the rotation of stars. Rapidly rotating stars seem tooffer more activity than those with longer rotational periods due to a magnetic dynamotype effect. One type of activity associated with rotation is flaring. Flares occur whenmagnetic energy in the stellar atmosphere is suddenly released, relating to a suddenincrease in brightness of the star. Flares have many features associated with them;

1.2.1 Rise Time

The rise time of a flare is defined as the time taken for the intensity of the star to beenhanced from the quiescent level to its maximum intensity. Because of the naturalvariation in some stars a flare is defined as the scenario where at least two consecutiveobservation points lie 3σ above the average quiescent intensity, where σ is the standarddeviation of the quiescent stars level, taken during the same observations.

1.2.2 Decay Time

The decay time is the time taken between the peak of the flare period intensity andthe end of the flare, located when the intensity returns to the quiescent intensity. Dueto the nature of flares, the decay time is much longer than the Rise Time which leads

3

to difficulty in estimation, since stars observed can often have set before the star hasreturned to quiescent levels.

1.2.3 Decay Time Constant

Hence it is much preferable to ascertain the decay time constant, which is defined as thetime taken for the flare to decrease in intensity by a factor of (1/e) This is fitting sincethe flare decay often fits an exponential decay. Whilst the scope of this experiment isnot to determine the values of this constant, its exponential nature will help confirmthat the observations are of a flare event.

1.3 AT Mic

AT Mic is a visual binary system both of which are of the type dMe. Table 1 specifies itssignificant properties necessary for observation. This particular star was observed by ateam consisting of myself and four colleagues, using the 1.9m Grubb-Parsons telescope,situated at the South African Astronomical Observatory as part of a UCLan fundedstudent experience. Time-sampling intervals of 1000 seconds were taken, until flaringwas detected using a secondary 0.5m telescope conducting real time photometry. Upondetection of flaring the time-sampling period was reduced to a period of 500 seconds forapproximately 2.5 hours, which should cover the flare and the stars return to quiescentlevel.

AT Mic was not being observed at the onset of flare, instead once a flare was detectedusing the smaller photometric telescope the larger telescope had to be manoeuvred to theflaring target. This meant that the spectroscopic data will not show the two consecutivepoints at 3σ, however since the photometric data does show this, we can say withcertainty that a flare is being observed.

Table 1: Observational Data for AT Mic

Name AT Mic

RA 20 41 51.1586

Dec -32 26 06.830

Visual Magnitude 10.25

Spec Type. M4Ve

4

1.4 Data Reduction

The spectroscopic data from the telescope needed to be reduced to remove additiveeffects such as background noise and differences in pixel sensitivity. For the SAAO datagathered this comprised of debiasing and flat-fielding.

1.4.1 Debiasing

The bias level is an offset added to the signal readout of the CCD which makes surethe input value to the Analogue-to-Digital converter is always positive [Kilkenny andWorters, 2010]. It is an intrinsic noise which must be subtracted from all output CCDimages. This is done by taking bias-frames, 0 second exposure readouts, averaging theseand subtracting it from the objective CCD images.

1.4.2 Flat Fielding

CCD response varies across the instrument, resulting in individual pixels have differingsensitivities. To overcome this, flat fields are taken during observations of photomet-rically flat source. In the case of the data gathered at SAAO, the 1.9m telescope waspositioned targeting a white section of the dome, which was illuminated uniformly. Onceseveral flat field images are found, an average is taken, and then all objective CCD framesare divided through resulting in a constant level of sensitivity across the images.

1.4.3 Other Reduction Techniques

Dependant on the instrument used, there is sometimes a requirement for Dark framesto be taken. However due to the nature of the SAAO CCD used and its cooling levels,this is not a necessity for the data gathered. The SITe CCD used had a dark count ofa few counts per pixel per hour and so this can be ignored.There was also a slight issuewith the spectrograph becoming slanted during observations, for some unknown reason,which needed to be extracted with care to avoid loss of data.

2 Methodology

2.1 IRAF

2.1.1 Image Reduction

As described earlier, the first part of the project involved taking raw telescope data andcorrecting the CCD frames for additive effects. Many modern computing programs are

5

available across differing platforms, one of the more widely available being the ImageReduction and Analysis Facility (IRAF) created by the National Optical AstronomyObservatories (NOAO). This is free-ware and is renowned for its cross-platform compat-ibility. IRAF is no longer supported by an official funded team, and as such technicalsupport is given by volunteers. Since the program was not available on the universitynetwork, it had to be installed on a personal laptop. Problems with the downloadedbinaries and the installation script, coupled with volunteer based support created un-foreseen delays in the beginning of the data analysis, although the problems that arosegave good experience of the issues astronomers can have to deal with, when installingolder programs that have passed out of funded service and maintenance.

IRAF is set up to work for certain CCD types “out of the box” however parameters hadto be refined to work with the header information set by the SAAO telescopes. Thismainly comprised of editing translation tables so that IRAF could understand the SAAOspecific header information. This was needed for specific packages, for example allowingthe program to determine the difference between flat, image and bias frames.

Over the period of the observing week bias frames were taken which needed to be com-bined to form a master bias. This was done using the zerocombine procedure within thenoao, imred, ccdred package. Similarly the flat fields were combined to form a masterflat, using the flatcombine procedure within the same package. As previously mentionedthe CCD is of high enough quality that the dark count can be assumed negligible.

Now all the master correction files had been created, they were applied to the objectframes. This was done by running the ccdproc procedure. In short this takes eachobject frame, subtracts the master bias and then divides through by the master flat.The output is then a object file which has negligible additive effects which can now beused for scientific purposes which overwrites the original files. Therefore care must betaken at this stage to have a backup of the raw telescope data in case of error.

2.1.2 Spectra Extraction using IRAF

At this stage however the images are still CCD exposures with the spectral dispersionbeing along the horizontal pixel direction, and the spectrum being located approximatelyin the middle of the CCD. It was necessary to extract the spectrum, although this wascomplicated by the aforementioned slanting of the spectra. Consider first the idealsituation of a spectra dispersed horizontally over 5 pixels across the middle of the CCD.IRAF can be made to simply define an aperture, in this case one would pick six pixeldiameter to lower any data loss, and specify the centre pixel of the spectrum. Theprocedure built into the program would then start at one end of the CCD, and movethe aperture across whilst reading the counts, producing a spectrum.

However the inclusion of a slant meant that this simple method would not prove success-ful without dramatic loss of data. Instead, once the aperture had been defined, it wasnecessary to form a trace profile to track the dispersion through the slant. Essentially

6

the trace determines the shape and behaviour of the aperture as it moves along the dis-persion axis. Once the aperture has been defined, using IRAF’s interactive cursor mode,the trace is generated, and is shown in Figure 1. This shows a slant of approximately4 pixels across the whole CCD, and shows the user defined fitting line. The aperturediameter is set to allow for all points which are within one pixel of the fitted line. Thisthen means the extracted spectra will have the maximum possible data retention. Be-cause the slant changed over the observing periods, this trace had to be checked for eachexposure to make sure all the data was being extracted, reducing any automation theprogram could have achieved if the spectra were not slanted. The output once the traceis completed is a one dimensional fits file.

Figure 1: IRAF Trace showing slanted spectra and fitted extraction line.

2.1.3 Wavelength Calibration Using IRAF

The final part of the preliminary data reduction is to calibrate the wavelength scale,the flux scale being left uncalibrated since this project is mainly interested in relativechanges between the ratio’s of the levels between quiescent and activity periods. Usuallyone would take a catalogue spectra of the arc lamp used for the arc exposures and lookfor patterns in the spacings of the lines (the relative heights being variant betweendifferent lamps). However the spectrum in this wavelength region of the CuAr arc isvery cluttered and because of this, it is rather difficult to identify lines.

7

Instead a logical system was implemented to try and conceive a wavelength calibration.It is known the that Balmer lines will be broadened during the period of flaring. There-fore inspecting a flare spectrum should easily show at a glance which lines are Balmerin origin. An example flare spectrum is shown in Figure 2 with the pixel values ofthe Doppler broadened lines marked. The differences between the pixel counts of thebroadened lines was determined and this is summarised in Table 2.

Table 2: Pixel Differences for Flare Spectra

Line Pixel Location (Pixel) Differences (Pixels) Ratio

1 649470

1.82872 1119257

3 1376

Then catalogue values for the Balmer series were compared with the values in Table2 with the principle being that one ratio would coincide with the ratio 1.8287. Thecatalogue values are shown in Table 3.

Table 3: Wavelength Differences for Comparison Spectra

Line Wavelength (A) Differences (A) Ratio

Hβ 4861520

2.1757Hγ 4340239

1.8244Hδ 4101131

Hε 3970

8

Figure 2: Example Flare Spectra with Pixel Counts shown for Broadened Balmer Lines.

Knowing the wavelengths of the three lines, hydrogen delta, gamma and epsilon, allowthe spectra to be wavelength calibrated. This is done by opening any spectrum in IRAFand identifying the wavelengths of two or more lines using the interactive cursor mode.IRAF then iterates and finds the best fit for the data. The more line values the useradds, the more accurate the iteration should be. Once the lines are identified, IRAFcreates a file which can then be applied to all the other frames. This calibrates them tothe defined scale, and also changes it so that, as is more traditional, the x-axis increaseswith wavelength. An example of a calibrated, quiescent spectrum is shown in Figure3.

9

Figure 3: Calibrated Quiescent Spectrum

2.2 IDL

At this stage, since all of the reduction and calibration had been completed, IRAF wasno longer sufficient to continue with the data extraction and processing. As such theInteractive Data Language (IDL) package was utilised, and this was readily availableon the university starlink network. This distribution also includes the Solar Softwarepackages (SSWIDL) which have many pre-defined, user created procedures and functionsfor dealing with astronomical file formats.

2.2.1 Reading in the Calibrated Files

The first requirement for IDL was to be able to read in the FITS files from IRAF. Thetechnicality behind this, was that the files output are only one-dimensional counts. Usingthe READFITS function in the SSWIDL libraries imported the spectrum as expected,but the wavelength scale was reverted back to a channel count number. Further in-spection of the files and IRAF documentation showed that the wavelength calibration isstored under two additions to the header, CRVAL1 and CDELT1, being the wavelengthcoordinate of the first pixel and the wavelength interval per pixel respectively.

10

Furthermore, an average quiescent spectrum was required and as such it was necessaryto write a function. IDL is a command line programming language, and it is possibleto write instructions manually, but the creation of procedures and functions help toautomate the process, which saves time for tasks which are to be repeated on multipledata sets as well as allowing for better debugging of errors. The function written can befound in A.1 and the code itself has been commented to guide the reader through thecommands.

In short, the user to specifies a file or files to be read in and the function reads in the dataand averages across all files if multiple were specified. Naturally the code also performsthe average if single files are specified, though this has no effect on the spectrum since itdivides by unity. This makes the procedure more generic. The header is then inspectedto extract the wavelength scale and exposure time, so the spectrum can be normalised,removing any effect of differing exposure times. Finally the spectrum is plotted so theuser can check for consistency, i.e. null input data or the presence of a cosmic ray.

Because the function has been written in a way where most of the required data is takenfrom the header, this function should be readily available for use with other CCD’s fromdiffering observatories with little or no adaptation.

2.2.2 Curve Fitting

Now IDL has extracted both the counts, and the wavelength value for each pixel, mea-surements can be made on the data. For the spectral analysis it was useful to considerthe full width at half maximum (FWHM), area, peak and continuum level. The easiestway for IDL to ascertain these values is to fit a gaussian to the spectral lines. SSWIDLlibraries contain many functions already written that allow the fitting of data, the mostdocumented and reliable being MPCURVEFIT. This requires multiple inputs, the usermust specify their own gaussian description function, weights for each point and initialguesses which the procedure uses to iterate from. Danielle Bewsher provided a gaussiandescription function which has been tested thoroughly. The weights for each point inthis scenario are all equal and so an array must be created with the same number ofelements as the FITS file, with all the values being equal to one.

A function was written to automate the creation of initial guesses, and running the curvefitting, then outputting the final results for peak, centre, width and background as wellas statistical uncertainties in the values. This can be found in A.2 and once again, thefunction has been commented to guide the reader through the code.

2.2.3 Area

Finding the area under the peaks gives an indication of the energy contained within theline, which during a flare would be expected to increase overall. This is as simple as

11

creating a function which loops over the whole histogram of the peak, summing the valuemultiplied by the change in wavelength. It should be noted that this area also includesthe continuum area, and for a more detailed analysis this would have to be removed,which will be discussed later. The function written to calculate the area can be foundin A.3.

2.3 Time

Since the overall aim of this project was to compare and contrast the spectral linecharacteristics over the period of the flare and prior to activity the values attained sofar are going to be compared as a function of time. Therefore it was necessary to createa function that inspected the headers of the FITS files and extracted the date in MJDat the start of the exposure. It was not necessary to extract the value for exposure time,since at this stage all the exposures had been normalised to one second. The function isgiven in A.4.

2.4 Wrapper

At this point considerable processing time was saved by the creation of a wrappingfunction as given in A.5. This in principle calls on all aforementioned functions andprocedures, and allows batch processing of all the steps for a specific data set.

3 Results

Two lines were analysed, the Hydrogen Gamma line, which is the most intensive in thespectrum and the Hydrogen Delta line. The results gathered are given below”

12

Tim

ePeak

Peak

Error

Centre

CentreError

Wid

thW

idth

Error

Background

Background

Error

Area

(MJD-55405)

(Counts)

(Angstroms)

(Angstroms)

(Counts)

(Unca

librated)

0.00000

65.9750

1.19132

4342.37

0.0090943

0.507870

0.0119825

10.5193

0.244756

233.665

0.01902

99.1422

1.00568

4334.57

0.0107200

0.945285

0.0116443

39.4404

0.248224

1119.94

0.03019

99.4371

0.99713

4334.61

0.0107784

0.961084

0.0117063

21.7919

0.248828

728.547

0.03716

116.821

1.13019

4334.61

0.0083571

0.826668

0.0101856

21.7206

0.244991

729.456

0.04583

116.036

1.19009

4334.55

0.0082184

0.776586

0.0101933

19.2494

0.243236

657.800

0.05436

100.698

1.54816

4334.55

0.0092599

0.676312

0.0137288

17.7749

0.240970

569.472

0.06234

97.3072

1.71757

4334.59

0.0091721

0.668407

0.0157123

17.5286

0.241585

556.233

0.06868

121.563

1.35980

4334.56

0.0075666

0.720398

0.0106230

19.0467

0.242132

646.856

0.07654

140.278

3.05950

4334.61

0.0066448

0.596644

0.0159092

18.4038

0.241050

621.960

0.08354

125.988

4.18765

4334.61

0.0081034

0.569322

0.0216112

19.7592

0.240813

621.983

0.09164

176.757

10.6384

4284.92

0.0778760

0.343223

0.0298459

15.7776

0.235702

541.115

0.09792

135.645

2.72083

4334.58

0.0075414

0.598402

0.0148441

19.9679

0.240200

650.865

0.10580

98.9482

1.28786

4334.46

0.0100712

0.686891

0.0112810

19.2934

0.239714

603.270

0.11206

110.776

3.60427

4334.55

0.0150232

0.559717

0.0209129

19.0071

0.238811

580.995

0.12001

129.640

51.6369

4334.59

0.0560858

0.431252

0.1164850

19.4602

0.237880

567.549

Tab

le4:

Res

ult

sfo

rth

eH

yd

roge

nG

amm

aS

pec

tral

Lin

e

13

Tim

ePeak

Peak

Error

Centre

CentreError

Wid

thW

idth

Error

Background

Background

Error

Area

(MJD-55405)

(Counts)

(Angstroms)

(Angstroms)

(Counts)

(Unca

librated)

0.00000

22.4077

0.91598

4111.51

0.0328961

0.71074

0.0348377

3.79184

0.254648

93.8737

0.01902

34.4160

0.84011

4105.89

0.0370475

1.34835

0.09384381

8.6695

0.264533

535.251

0.03019

31.1404

0.74119

4105.70

0.0470379

1.77976

0.0524443

8.53741

0.286952

330.496

0.03716

43.1374

0.84422

4105.75

0.0294021

1.33418

0.0315867

5.03591

0.263882

324.661

0.04583

43.0164

0.89751

4105.87

0.0276248

1.17164

0.0293768

7.59553

0.256772

296.765

0.05436

34.5024

0.95206

4105.89

0.0324287

1.04052

0.0345150

6.70499

0.251582

240.439

0.06234

40.1008

0.94126

4105.87

0.0282142

1.06299

0.0299498

5.02212

0.252411

219.534

0.06868

47.9352

0.98582

4105.83

0.0225333

0.97054

0.0239820

6.34508

0.248898

258.987

0.07654

51.3498

0.95769

4105.76

0.0216116

1.02131

0.0227381

5.17923

0.250649

247.668

0.08354

41.9027

0.98138

4105.78

0.0258423

0.97285

0.0272078

5.80263

0.248828

232.383

0.09164

43.5402

1.01916

4105.81

0.0240369

0.91230

0.0257207

5.66479

0.246787

226.674

0.09792

46.5618

0.99355

4105.77

0.0229665

0.94821

0.0241367

6.10838

0.247885

247.729

0.10580

37.0770

1.03177

4105.77

0.0278355

0.87968

0.0291975

5.78931

0.245376

211.658

0.11206

32.0121

0.97354

4105.68

0.0339869

0.977872

0.0351451

5.67614

0.248757

205.832

0.12001

31.3904

1.01675

4105.69

0.0330864

0.879101

0.0331768

5.28109

0.244884

187.672

0.12872

29.8891

1.03065

4105.79

0.346208

0.888243

0.0367469

4.20949

0.245815

161.001

Tab

le5:

Res

ult

sfo

rth

eH

yd

roge

nD

elta

Sp

ectr

alL

ine

14

4 Analysis

The first thing to note is that the width given in the results tables is in fact the gaussianwidth and not the FWHM. In one dimension, a Gaussian is the probability densityfunction of a distribution given by:

f(x) =1

σ√

2πe−(x−µ)2/2σ2

(1)

The FWHM is found by considering the points at half maximum value. The scalingfactor preceding the exponent can be ignored and thus we need to solve:

e−(xo−µ)2/(2σ2) =1

2f(xmax) (2)

But f(xmax) occurs at xmax = µ thus:

e−(xo−µ)2/(2σ2) =1

2f(µ) =

1

2(3)

Solving:

e−(xo−µ)2/(2σ2) = 2−1 (4)

−(xo − µ)2

2σ2= − ln 2 (5)

∴ xo = ±√

2 ln 2 + µ (6)

Thus FWHM ≡ x+− x− = 2√

2 ln 2σ. Further analysis was achieved simply by plottingthese values as a function of time to try and determine if there are any recurring patternsbetween the two lines. With the need to incorporate the above mathematical conversionfrom gaussian width to FWHM it was once again simpler to automate the process ofplotting the graphs using a procedure. This is given in A.6 and the graphical outputsare given below:

15

Figure 4: Hydrogen Gamma Properties as a function of Time

16

Figure 5: Hydrogen Delta Properties as a function of Time

17

Figure 6: Hydrogen Gamma Area as a function of Time

Figure 7: Hydrogen Delta Area as a function of Time

The errors on the area graphs are comparable with the data point sizes. All errorsshows are systematic errors outputted from MPCURVEFIT. It should also be noted

18

that there will be some error attributed to the fitting procedure itself, however this isnot quantifiable and therefore is not shown. This error arises from an issue where thespectral lines analysed are only a few angstroms in width and with a spectral resolutionof approximately one angstrom/pixel leads to a problem where each spectral line iscomposed of only three-four points and thus the iterative process of MPCURVEFITleads to uncertainty in the location and characteristics of the fitted gaussian. Simplyput the more points per spectral line present in the data, the better the gaussian fit,thus the higher the spectral resolution the more reliable the results will be.

It is possible to convert the FWHM values in to a velocity thus comparing the differencein atmospheric velocities of the lines. Consider the following equations:

(FWHM)star =√

(FWHM)2observed star

− (FWHM)2instrumental width

(7)

FWHM = 2√

2 ln 2σ (8)

∆λ

λo=v

c(9)

Combining Equations 7, 8 and 9 gives the following relation, assuming that the instru-mental width is a gaussian of width one angstrom:

v =∆λ

λoc =

√(2√

2 ln 2σ)2 − 1

λoc (10)

This equation is then used to calculate the velocities of the quiescent line profile andthe highest flare width profile, thus giving rise to the maximum change in velocity (thiscorresponds to the first two data points in both line profiles). This leads to ∆VH gamma =(92.100± 5.700)kms−1 and ∆VH delta = (122.000± 24.000)kms−1

5 Discussion

The centre of both the hydrogen gamma and delta lines appears to be reduced by sixangstroms once the flare begins. Whilst this seems unphysical at first and could possiblybe attributed to inaccurate wavelength correction, the fact it appears in both of the linesprofiles seems to indicate a real phenomenon. However without further investigation itwould not be possible to determine this any certainty. The hydrogen gamma line appearsto have a sudden drop at t = (0.09164) MDJ-55405. Closer inspection of the same pointsin the peak, FWHM and Continuum plots also show points which appear to be lowerthan the trends. Therefore it would be sensible to regard this as an erroneous data

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point, possibly as a feature of incorrect gaussian fitting which was not spotted in theverification stages of the automated procedures or an issue with that specific spectrum’swavelength calibration.

Whilst at first the peak plots appear to show some pattern, considering the extra un-plotted error arising from the uncertainty in fitting the gaussian to so few points, theapparent distribution cannot really be separated from the systematic error and thereforewithout further investigation it would be unconvincing to state that there is any changein either the hydrogen gamma or delta line peak values during a period of flaring.

For both the hydrogen gamma and delta profiles the FWHM and continuum levelsfollow a sensible predicted trend. The lines show clear broadening at the onset of theflare with gradual decrease as time continues. The graphs appear to have similaritiesto the exponential decay time as described earlier on. It is important to note thatdifferent levels correspond to different temperatures and thus different regions of thestellar atmosphere. It is clear from the hydrogen delta data that the continuum showsa rise due to the flare sooner than the FWHM and it appears to reduce back to the pre-flare level sooner. It is possible then to conclude that the continuum and the FWHMare attributed to different parts of the atmosphere.

This is explained by Pallavicini and Priest [1991] who explain the creation of a magneticloop in which the ionised particles are constrained. As these particles move through theloop they eventually come in contact with the photosphere or chromosphere (dependanton the nature of the magnetic loop). When this occurs it triggers a flare event, resultingin the continuum level showing changes earlier than the FWHM.

The area under the spectral lines gives an view of the energy involved. It would beexpected that during a flare the area should increase dramatically and then exponentiallydecrease as via the decay time. This is shown in both lines, with the hydrogen gammaand delta lines showing an approximate increase of five and six times the quiescent levelrespectively.

6 Conclusion

In conclusion it has been found that AT Mic’s spectrum undergoes considerable changesupon flare outburst. Firstly the lines are doppler broadened, showing an increase inenergy of the system. No pattern has be found for the peak levels of the lines, butit should be noted that for this uncalibrated flux scale little meaning could have beendeduced from any result in this area. Delayed changes in the FWHM compared with thecontinuum has been linked to flare activity triggered by single magnetic loop formation asdetailed by Pallavicini and Priest [1991]. An approximate shift in line centre wavelengthof six angstroms has been detected however without further analysis this cannot thoughtof as a physical phenomenon rather than either an instrumental error, or an issue withthe wavelength calibration.

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Given more time on the project it would have been interesting to make further analysis ofthis shift in wavelength, by taking a higher resolution spectrum of more peaks and seeingif this occurs in all lines, or if indeed it is an error in data processing. To further analysethe trend in peak level changes a flux calibration would have to be applied to the data.This would allow a more mathematical treatment of errors and would determine whetherthe changes seen in figures 4 and 5 are real phenomenon or statistical noise. This wouldrequire the observation of a standard star at the observatory and thus was unobtainablein the confines of this project. Furthermore it would have been interesting to writeanother IDL procedure which could calculate the effective area, the area relation betweenthe continuum area and the area under the peak. This would allow direct comparison ofchanges between the differing lines which may produce some more patterns for analysis.Finally, time permitting it would have been useful to analyse more of the lines found inthis region of the spectrum. The hydrogen epsilon line at 3934 angstroms was attemptedbut is in fact blended with ionised Calcium which in low resolution spectroscopy cannotbe separated [Phillips et al., 2008], once again repeating the observations with higherresolution would help, providing much more workable data.

Finally using the equation for the Doppler/Velocity relation, and assuming that theinstrumental width also follows that of a gaussian function the changes in velocitywere calculated to be ∆VH gamma = (92.100 ± 5.700)kms−1 and ∆VH delta = (122.000 ±24.000)kms−1 from quiescent level to the maximum value during the flare outburst.

In terms of personal gain this project has given me the opportunity to gain valuable skillsin observational astronomy, using multiple programs both in and out of service, scriptingand automating data processing for considerable time saving as well as learning to writein LATEX, which is used by many professional physicists to write academic papers andtheses. Again given more time on the project it would have been more effective to createfunctions in IDL which can perform the data reduction stages, thus removing the useof IRAF, cross program file compatibility issues and problems experienced in installingand operating a system that is only given support by volunteers.

7 Acknowledgements

The Author wishes to thank:

• Prof. G.E. Bromage, for patient support, supervision, ideas, confidence and feed-back

• Dr. H. Worters, for IRAF parameter help, and supervision observing at SAAOand

• Dr. D. Bewsher, for IDL guidance and general removal of dead ends.

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References

A. J. Cannon and E. C. Pickering. Classification of 1,688 southern stars by means oftheir spectra. Annals of Harvard College Observatory, 56:115–164, 1912.

Dave Kilkenny and Hannah Worters. The SAAO 1.9-m Telescope and Grating Spectro-graph, 2010.

R. Pallavicini and E. R. Priest. The role of magnetic loops in solar flares [and discussion].Philosophical Transactions: Physical Sciences and Engineering, 336(1643):pp. 389–400, 1991. ISSN 09628428. URL http://www.jstor.org/stable/53825.

Kenneth. Phillips, Uri Feldman, and Enrico Landi. Ultraviolet and X-ray Spectroscopyof the Solar Atmosphere, volume 44 of Cambridge Astrophysics Series. CambridgeUniversity Press, 2008.

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A IDL Functions and Procedures

A.1 Averaging FITS

FUNCTION ave_fits,file,wav=wav,dl=dl,exptime=exptime

;DESCRIPTION: This procedure reads in a number of fits files,

;sums them and divides through by the number of files inputted.

;Used to create master quiescent files, or read in single files, since

;the division will have no effect on single files. The wavelength

;calibration is extracted from the header using the values specified

;from IRAF. Finally the function also divides each file by the

;exposure time before summing to remove any issues with differing

;integration lengths

;WRITTEN: Adam Clarke 7th March 2011 - BSc Project work

;USAGE: output=ave_fits(’input file’)

nf = n_elements(file) ;finds number of files

dl = fltarr(nf) ;set up array for delta lambda

exptime = fltarr(nf) ;set up array for exposure time

tdata=fltarr(1749) ;creates array for data

;for loop reading in fits

for i=0,nf-1 do begin

;read fits, storing header in index

data = readfits(file(i),index)

;save exposure time to array

exptime(i) = float(strmid(index(23),20,10))

;save delta lamba to array

dl(i) = float(strmid(index(45),14,16))

tdata = tdata + (data/exptime(i)) ;sum fits

endfor ;end for loop

;divide data creating the average file

mdata = tdata/float(nf)

;Need to take the specific section of the string value, using

;strmid(index(line number),start character,character length) and then

;put floats around it to convert it so that it can be used to plot the

;spectrum with the wavelength calibration

;extract pixel 1 wavelength value

crval1 = float(strmid(index(43),15,16))

;extract wavelength change per pixel

cdelt1 = float(strmid(index(45),14,16))

;create wavelength scale using aove values

wav = findgen(1749)*cdelt1+crval1

plot,wav,mdata, title=’AT Mic, average quiescent spectrum’,

xtitle=’wavelength (angstroms)’,ytitle=’counts (uncalibrated)’

return,mdata

end

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A.2 Line Fitting

FUNCTION line_fitting,tmp_data,tmp_wav,ig=ig

; PURPOSE: Procedure for running MPCURVEFIT with data

;

; USAGE: line_fitting

;

; REQUIRED KEYWORDS: N/A

;

; OPTIONAL KEYWORDS: N/A

;

; NOTES: This procedure runs MPCURVEFIT with the data in tmp_data and

;tmp_wav. It limits the width from ebing negative, to prevent

;MPCURVEFIT iterating the wrong way. MPCURVEFIT outputs the results in

;a table as well as statistical errors, sigma. The function creates

;its own initial guesses by finding the maximum value in the

;wavelength range and attributing the same values central wavelength.

;

; HISTORY: Written 22/03/11 Adam Clarke

nn = n_elements(tmp_data)

ww = findgen(nn)*0.+1.

lc = where(tmp_data eq max(tmp_data))

peak = max(tmp_data)

ig = [peak,tmp_wav(lc),1.,min(tmp_data)]

;This prevents the width from being a negative value.

parinfo = replicate(value:0.,limited:[0,0],

$ limits:[0.D,0.D],parname:’’,4)

;names of parameters

parinfo[*].parname=[’Amplitude’,’Line centre’,’FWHM’,’Background’]

;width contrained to be positive

parinfo[2].limited(0) = 1

parinfo[2].limits(0) = 0.0

;starting parameters

parinfo[*].value = ig

yfit = mpcurvefit(tmp_wav,tmp_data,ww,ig,

$ sigma,function_name=’fgauss’,parinfo=parinfo,/quiet)

print, " Peak, Centre, Width, Background:"

print, ig

print, sigma

return,yfit

END

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A.3 Area

FUNCTION calc_area,tmp_wav,yfit, dl

;DESCRIPTION: A FUNCTION FOR CALCULATING THE AREA OF THE FITTED

;GUASSIAN DATA.

;WRITTEN: ADAM CLARKE - 28TH MARCH 2011

;USEAGE: area=calc_area(tmp_wav,yfit,dl)

;Set number of elements equivelent to the number of values in tmp_wav

nn = n_elements(tmp_wav)

;Initialise area at zero

area = 0.

;Loop for summing each value of yfit

FOR i=0,nn-1 DO BEGIN

;Take initial value of area, and add

;the value of yfit multiplied by

;change in wavelength

area = area+(yfit(i)*dl(0))

ENDFOR

;Return area for use later

return,area

END

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A.4 Time

FUNCTION ajc_time,file,ref=ref

;DESCRIPTION: This function extracts the MJD from the header of a

;file. Because of restrictions in IDL for the length of floating point

;values, the loop is created to find the lowest MJD in the files

;specified and uses this as a reference to subtract, thus changing the

;number to a length that IDL can sucessfully handle.

;

;WRITTEN: 4/4/11

;

;ADAM CLARKE

;Find the number of elements in ’file’

nf = n_elements(file)

;set mjd as an array with nf number of elements

mjd = dblarr(nf)

for i=0,nf-1 do begin ;for loop reading in fits

data = readfits(file(i),index) ;read fits

;Set reference from lowest value of MJD

IF (i eq 0) THEN ref = floor(float(strmid(index(22),19,11)))

;Subtract ref fromt the MJD and return this as a new value

mjd(i) = double(strmid(index(22),19,11))-ref

endfor

print, mjd ;print time in MJD

END

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A.5 Wrapper

PRO wrapper,file,ss,ee

;WRITTEN: Adam Clarke - 21st March 2011

;UPDATED: 4/04/2011

;DESCRIPTION: This procedure brings together the other procedures

;written and allows for batch processing without the need to type many

;commands

;USEAGE: wrapper, file, ss, ee

;where file=input file location (can be multiple since the wrapper

;uses the average function) and lower and upper are the wavelengths

;the peak is located between

;Read in the file and call it data, take header information

;inc. Exposure time etc and average it.

data = ave_fits(file,wav=wav,dl=dl,exptime=exptime)

;Set number of points.

npts = 10

;Set initial guesses, ii=Maximum peak between values of ss and ee then

;extract npts number of points around this, to get the

;tmp_data and tmp_wav of the peak for analysis.

kk = where(wav lt ss,nkk)

ss2 = kk(nkk-1)

jj = where(wav gt ee,njj)

ee2 = jj(0)

ii = where(data(ss2:ee2) eq max(data(ss2:ee2)))

tmp_data = data(ss2+ii-npts:ss2+ii+npts)

tmp_wav = wav(ss2+ii-npts:ss2+ii+npts)

stop ;allows for checking of imported spectrum plot

;Run line_fitting procedure on tmp_data, and tmp_wav, with initial

;guesses ig

yfit = line_fitting(tmp_data, tmp_wav,ig=ig)

;Calculate Area and print

area=calc_area(tmp_wav,yfit,dl)

print,area

;Stop to allow further use of tmp_data, tmp_wav, sigma, and ig to

;check for clarity

stop

END

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A.6 Multiple Plots

PRO multi, time,peak,peak_err,cen,cen_err,wid, wid_err,bgrnd, bgrnd_err

;This creates a page with four plot spaces on it

;Written: Adam Clarke

;16th May 2011

;Custom string to get the angstrom symbol

angstrom = ’!6!sA!r!u!9%!6!n’

;Set plotting device to Postscript:

SET_plot, ’ps’

;Set the filename

DEVICE, FILENAME=’graphs.ps’,xsize=’10’, ysize=’7’, /inches,/HELVETICA, set_character_size=[140,180]

;Make IDL’s plotting routine fit four plots to a page with two

;columns and two rows

!P.MULTI=[0,2,2]

;Plot #1 - Centre with Error (Top Left)

ploterror, time, cen,cen_err, title=’Centre’, xtitle=’MJD-55405’, ytitle=’Centre (’+angstrom+’ )’,

$ xtickinterval=0.04

;Plot #2 - Peak with Error (Top Right)

ploterror, time, peak, peak_err, title=’Peak’, xtitle=’MJD-55405’, ytitle=’Counts’,

$ xtickinterval=0.04

;Plot #3 - Gauss width with Error (Bottom Left) - uses conversion factor from width to FWHM

FWHM=2*SQRT(2*ALOG(2))*WID

FWHM_ERR=2*SQRT(2*ALOG(2))*WID_ERR

ploterror, time, fwhm, fwhm_err, title=’FWHM’, xtitle=’MJD-55405’, ytitle=’FWHM (’+angstrom+’ )’,

$ xtickinterval=’0.04’

;Plot #4 - Background Value with Error (Bottom Right)

ploterror, time, bgrnd, bgrnd_err, title=’Continuum’, xtitle=’MJD-55405’,

$ ytitle=’Counts’, xtickinterval=0.04

;Close the file

DEVICE, /CLOSE

;Return plotting to Windows

SET_PLOT, ’x’

;Reset plotting to one plot per Window

!P.MULTI=0

END

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