DIFFERENTIAL PHOTOMETRY OF COMETS

T. Scarmato¹

1 – Toni Scarmato’s Observatory, San Costantino di Briatico, Calabria, Italy

ABSTRACT

Here we present the results obtained with three comets 73P/Schwassmann-Wachmann B the component B, 6P/d’Arrest and C/2008 J1 (Boattini). Comet 73P was observed in April 2006 with a CCD camera Starlight Express SXL8 attached to direct heat of a Newton telescope 250 mm, focal length 1200 mm, while the 6P and C/2008 J1 were ever observed by telescope Newtonian but with a CCD camera Atik 16IC to direct heat. CCD room was added a filter photometric Rc (Schuler). For the 6P has been used a defocus of 14 pixels, meaning that the central nucleus of Counterfeiting has defocused a FWHM of 14 pixels. The technical data of the tools used are shown in Tables 1 and 2.

INTRODUCTION

Over the past 10 years the survey conducted on Earth by comets is that space has revealed that these vagabonds of the area have unique characteristics and not all behave the same way and not all have the same composition. It 'been discovered that in addition to the "classical" code of Ions and dust, comets may produce code of sodium and lately has been observed in comet C/2006 P1 an IRON NEUTRAL TAIL.

(Fulle et al. 2007; See the link http://digilander.libero.it/infosis/homepage/astronomia/c2006p1.htm)
One of the ways, and the scope of instruments amateur, to observe comets is the visual observations. Depending on the brightness of the comet (magnitude) just a simple binoculars to be able to admire the comets. Until a few years ago the dedicated amateur astronomers are so profitable enough to estimate the magnitude of visual comets, which can be done based on certain methods. One of these, described simply, is to defocus the coma of the comet to make the surface uniform brightness and then if in the instrument field there are some stars brighter and fainter since the comet, comparing the brightness of the comet with that of the stars defocused that you know the magnitude and then make an estimate of the apparent magnitude of the comet. (See ICQ - http://www.cfa.harvard.edu/icq/icq.html for more informations). These estimates and allow themselves to still provide the photometric evolution of the comet, even though the reserve of comets with beautiful surprises "outburst" (increases brightness) that evolve both short and medium and long term. This suggests that comets are bodies active AND RETAIN and probably even when they seem really quiet in the area continues to issue material in the coma, which then expands into space, ALSO AT GREAT DISTANCE FROM SUN. One of the most interesting is that of a comet 29P a periodic comet showing a very interesting activities for more than 6 U. A. from the Sun with outburst that could be periodic. Again, however, the mechanism underlying its behaviour has not been explained satisfactorily and scientifically certified.
The issuance of this material change continuously over time in terms of foliage and thus its brightness. We can ask; It can observe the changes in brightness of foliage even when they are small? And what is the accuracy of the measures that need to be able to have a meeting in observation of hours detect variations in brightness? It is possible with amateur instruments to reach levels of accuracy in measuring the magnitude and possibly other parameters to monitor in the short to medium term evolution of photometric hair of a comet or, if this is far from the sun and "apparently" inactive, the brightness variation of the "core"?
To answer these questions may come to the aid PHOTOMETRY DIFFERENTIAL.
The differential photometry, applied to the transit of extrasolar planets, has shown that with amateur instruments can reach accuracies thousandths of magnitude. There are many transits observed with this technique and a very difficult transit was discovered by amateur instruments. This is HD 17156b (Barbieri et al. 2007), whose brightness variation is only magnitudes 0.005. (In Fig. 1 you can see the change in the brightness of a star that is suspect the existence of a planet transit).

Fig. 1: The peak negative visible in the figure shows the change in magnitude of a star probably

due to the transit of a planet in front of the star.

The depth is about 8 thousandths of magnitude with an rms of 0.005 magnitudes.
The shots were made with a Newton aperture 250 mm, focal length 1200 mm, Atik 16IC CCD camera

and filter Rc photometric (for characteristics see table 2).

To make differential photometry is necessary to collect as many photons from the sources and then compare the resulting figures. As the number of photons that gather for a given source crucially depends on its brightness, if a source emits a steady stream, the number of photons that arrive at our detector will be settled within experimental error due to various causes, such as variation environmental conditions, temperature, etc ... velature
If instead a source does not emit a steady stream, the number of photons that arrive will vary over time. If the change is small, for example in the order of thousandths of magnitude, then it can detect it is necessary to compare the flow of variable source with the stable flow of sources. Let us therefore refer to a simple formula which calculates the relationship between the flow of the star in question and the total flow of other reference sources said. (See next par.)

Tab.1: CCD camera’s characteristics

Parameters	STARLIGHT EXPRESS SXL8	ATIK 16IC
Area in Pixel array	512X512 (262.144 pixels squares)	659X494 (325,546 pixels squares)
Pixel size	15x15 micron	7.4x7.4 micron
Full well depth	150.000e	40.000e
Dark current	1e per second a -30°C	<1e per second at -25°C
Peak spectral response	530nM, 50% a 400 nM e 650 nM	500 nM
Quantum efficiency	30% a 530 nM	>50% a 500 nM
A-D converter	12 bits	16 bits
Readout noise	< 20e	7e
Anti-blooming	Yes	yes
Cooling	Yes	yes
CCD Type	Philips FT12	Sony ICX-424AL
CCD size (area sensitive)	7.8x7.8 mm	4,8x3,7 mm

Tab.2: Characteristics of the Telescope and Filter

Parameters	Telescope	Parameters	Filter Rc
Aperture	250 mm	Productor	Schuler
Focal Lenght	1200	Band	Larga
Scale with SXL8	2.57 arcsec/pixel	Lambada peak	5978 A
Scale with Atik16IC	1.26 arcsec/pixel	FWHM	1297 A
Optic	Newton
Type	Reflector
Fov with SXL8	22’x22’
Fov with Atik16IC	14’x11’

When calculating the scale relate to the formulas:

, ,

Where dim is the effective size of the chip of CCD camera.

PURPOSE OF RESEARCH

As we have said before in recent times has been demonstrated that even an amateur can achieve scientifically significant photometric astronomical objects and in particular in the detection of transits of extrasolar planets.
The technique is to resume telescope with CCD + filter R the star under investigation and field around it and then applying the differential photometry noted the decrease of magnitude of the star caused by the passage of the planet in front of it along the line of sight observers .
In order to apply the differential photometry is necessary to have other stars in possibly the same brightness as that under consideration concerned. When the series of images, as long as possible, at least 3 or April 4 hours, the images are reduced by the calibration files, dark, flat and if necessary the bias. The images are then calibrated with a small program (IRIS) to measure the number of ADU of the stars in the field. When the measure for all the stars considered good according to their individual flows, the formula

This formula gives a relationship between the flow of the star under investigation and the total flow of the stars of reference. To normalize the values obtained, it is estimated the median and the relationship

It then constructs the graph using a linear function that provides the best fit for the data obtained.
If the star is magnitude <11, has been shown that the blurring of the telescope can increase the accuracy if the flow is sufficiently high crop that is at least equal to 70% of the dynamics of the CCD and less than 90%. The blur is a method that allows you to collect the same number of photons but spread over an area greater than the CCD camera. In this way you have a question on homogeneous flow and shrinking the scintillation which increases the error on the measure. The bigger the brightness of the star must be greater focus to get more precise. See results with transits.
For comets is not yet clear whether or not blur improves the accuracy of the measure. We will see a further example periodic comet on 6P who provided interesting results, however. Moreover, it is not a linear function used to rent the data, but is compared only flow from the comet with one of the stars of reference. For this we must choose the right time of exposure. In general, the exposure time must take into account the number of photons collected during a single exposure. For comets is not yet possible to establish a formula that allows them to calculate with good precision, and then takes into account that the higher the ratio S/N (Signal to Noise), is the best measure of the flow from the comet. The aim is to apply this technique to the study of comets photometric to show if you can reach the same levels of accuracy that are obtained in observing the transit and then see if the results are in agreement with those obtained using scientifically tested and accepted as valid. We then compared the results with comets of varying magnitude shoot with and / or without blurring. This will enable us to understand if you should decide whether or not the blur on objects comet or whether it is better to opt for shooting without blur.

METHODOLOGY

The methodology is to compare the flow of the object under investigation with the flow of objects that are in the same field. Shooting as we said earlier should be made preferably with the filter for photometric R Johnson Cousin or, for that comets can isolate the issue in the band in which the dust that can be found in the hair of the comet transmit light coming from the Sun. The series should be longer possible, at least two hours and exposure times to have an S / N highest possible but taking into account that the comet has moved in the individual recovery. If the telescope on equatorial mount must be well aligned with the pole and must be minimized problems bending and tracing. We stress however that the images with objects can be moved measured as the total flow is always captured by the pixels of the room. It 'important not include windows opening to be such as to contain the flow but not too large to incorporate any background stars near the source.
The images will then be calibrated with the dark, the flat and if necessary by the bias. If it is possible we must maintain stable temperature of the room by at least 0.5 degrees. If you are unsure of what is most important series of darks during the shooting in order to mediate all the images and obtain a master dark refers to all possible temperatures occurred throughout the recovery.
Depending on the brightness of the comet, the 'quantum efficiency of the room and taking into account that the R photometric filter reduces the total quantity of photons arriving in the CCD compared to shoot without a filter, unless you have a formula to get the appropriate time optimum exposure, is bypassing the problem of doing tests with increasing exposure times from at least 60 seconds.
When the counting of ADU is equal to 70% of the level of saturation of the room then you can already proceed to capture the full range of images. If you want a better S / N must be taken into account both its motion of the comet that does not exceed 90% of the level of saturation of the room.
Once the images are made to their development, first of all calibrating them then with a program that can measure the ADU of individual items automatically, you get the count for each image. In our case was used IRIS. The program, once measured the individual sources in the individual images, providing an output file with dates in JD - ADU and the values of the objects for each image records in chronological order. (see Table 3)

Tab. 3: sample records with the data, measure,

in the first column is the Julian Date observation on each image, in subsequent

columns are the counts the object that you want the photometry of stars and reference

JD	FLUSSOJ1	REF1	REF2
2454718.3129500	21304	510508	44780
2454718.3136991	22548	521433	45027
2454718.3144502	22145	518231	39568
2454718.3152014	23422	515335	42985
2454718.3159549	22926	509435	42423
2454718.3167083	22180	512611	37962
2454718.3174618	25370	503666	43654
2454718.3182141	25005	512055	37463
2454718.3189653	21340	504458	38060
2454718.3197176	24238	499754	41179
2454718.3204699	23582	513459	46686
2454718.3212222	23654	510294	39781
2454718.3219745	21456	502620	38062
2454718.3227269	25412	507747	38987
2454718.3234792	23214	499630	35155
2454718.3242315	20154	498266	38123
2454718.3249838	20619	510332	37554
2454718.3257361	24418	493006	38936
2454718.3264884	22754	496654	40879
2454718.3272407	21454	493840	37073

Since the program can do so automatically photometry on only 5 items at a time, if you need more than 5 photometric objects, you get more than one file with the data of individual objects. To put them together you can use Excel and then create a single file type. Txt to be able to develop a program of analysis of the curves of light. In our case was used GNUPlot. It then proceeds with the comparison between the flow of the object under investigation and the flow of the other items measured in the field. The formula described above

permit to obtain the values that are fitted by a linear function that determines the best performance of our points of the curve of light. The sum in the denominator to obtain a theoretical star whose flow is equal to the sum of the flows of individual stars. In this way you can build a chart that if precision is desired, highlights the brightness variations that appear as positive or negative peaks in the curve of light. (see first results).
As for the comets is not yet clear whether or not blur helps to increase the accuracy of the measures also bright comet, so this research will tell us what are the limits of the method of photometry differential applies to comets.
We will see in the next paragraph the results and then we will draw conclusions based upon qualitative and quantitative them.

FIRST RESULTS

Photometry of the Comet 73P/Schwassmann-Wachmann B

Here are the orbital elements of the component b of the comet 73/P.

Epoch 2006 May 25.0 TT = JDT 2453880.5

T 2006 June 7.92466 TT MPC

q 0.9390718 (2000.0) P Q

n 0.18394396 Peri. 198.80779 -0,02873648 +0.98221260

a 3.0620506 Node 69.88766 -0,88989677 +0.05940885

e 0.6933193 Incl. 11.39726 -0,45525592 -0,17812634

P 5.36

Comet 73/P is a periodical that has fragmented several times in its repeated passes at perihelion. The various pieces are away from each other because of the initial thrust due to the process of fragmentation that still has not been explained fully.
The components brighter, the c and b, during the last passage to perihelion showed strong activity with further fragmentation and an interesting photometric evolution.

Fig.2: Comet 73/Pb resumed the evening of April 22, 2006

In the first decade of April the comet 73/P-b had an outburst resulting in fragmentation of the nucleus. In the evenings from April 20-24 was possible to see the piece that was seconded by the core and is slowly away towards South-West. (see Fig.2)
The repeated outburst and fragmentation have been registered by many observers.

(See link http://digilander.libero.it/infosis/homepage/astronomia/73p.htm)

For our analysis we chose the images of 28 April 2006 as b component was apparently quiet after a strong outburst occurred in the previous week. The series of images covering a time interval of about 2 hours.

Fig. 3: The comet 73/Pb resumed the evening of 28 April 2006.

On the left image was obtained with mediating

Astroart 150 frames for 30 sec each, and aligning on the photometric center of the comet.

On the right the same images have been mediated by aligning on the center of photometric stars.

The error of alignment is 1-2 pixels. Note that near the comet there are stars

in the field who do not have permission to use openings

more than 9 pixels as the counts were altered as a result of their presence.

The comet was at 0.147 U. A. from Earth and the heliocentric distance was 1104 U. A. Because of its proximity to Earth on its own motion of the comet was high, you could appreciate in a few minutes observing with a 7x50 binoculars. For this reason, the exposures were only 30 seconds each. The shots were made Newtonian telescope with a 250 mm aperture, focal length 1200 mm, with a CCD camera Starlight Express SXL8 Rc filter and direct fire. (for the complete system see Tables 1 and 2). As we said in the introduction, for our purposes it is necessary that the comet is that the stars of reference remain the same field throughout the recovery. Consequently only two stars were adapted from a photometric to perform with good precision photometry of the comet(see Table 4)

Star/Catalog	mag. - USNO B1	mag. - TYCHO 2	mag. - SDSS
T 2574:136:1 (Ref1)	R1=8.95 – R2=8.89	Bt=10.946 – Vt=10,629	R=9.340
T 2574:578:1 (Ref2)	R1=9.77 – R2=9.69	Bt=12.147 – Vt=10,629	R=10.119

Tab. 4: photometric parameters of the stars of reference derived from catalogs

on-line using the Aladin, after calibrated astrometry the image aligned on the stars of the previous figure.

The photometric results obtained can be seen in the figures below.

	Km/UA	In Meter
Rho (Coma Radius)	2500	2500000
D (Earth-Comet)	0,1470	22050000000
R (Sun-Comet)	1,1040

Aperture 9 pixels, Resolution 2.57 arcsec/pixel

25 cm Telescope Newton f/4.8 + CCD Starlight Express SXL8 + Rc

Fig. 4: The graphs show the flux of the comet 73/P component b compared with the flux

of the stars of reference (see Table 4 for the characteristics of the stars).

The rms respectively 0.027 for comet and 0.026 for the two stars of reference.

You can notice a decrease in the flux of the comet after JD = 0.33.

Fig. 5: The graph of the magnitude of the comet 73/P with the flux converted into magnitudes,

showing an “increase” after JD = 0.33, about 0.1 magnitudes with an rms of 0.026.

Table 5 contains all of the counts of comet and star of reference for the complete set of images.

Tab. 5: stream of comet 73/P and stars measured in reference ADU.

2453854.2948300	43122	77148	42716	7462
2453854.2952639	43263	77186	42118	7466
2453854.2956910	41906	77440	42334	8245
2453854.2961181	43726	77987	44574	7256
2453854.2965451	43511	77571	42832	7124
2453854.2969722	42395	80968	42784	7360
2453854.2974051	46635	81939	44015	6851
2453854.2978368	44829	79937	42819	7766
2453854.2982697	42082	79934	44021	6835
2453854.2987014	42543	79241	42499	6581
2453854.2991285	39404	75079	40089	6559
2453854.2995556	41024	70964	39651	6960
2453854.2999826	42848	77175	42878	6795
2453854.3004178	44315	80350	44099	7523
2453854.3008507	41299	75986	40397	5986
2453854.3012836	41706	73070	39240	7017
2453854.3017153	37008	71079	36351	5587
2453854.3021516	32503	62588	33743	5797
2453854.3025845	32622	61504	33217	4651
2453854.3030116	29289	55679	29462	3622
2453854.3034387	34160	61201	34083	5869
2453854.3038646	32757	62828	32372	5725
2453854.3047188	38450	69845	38685	6905
2453854.3051458	38795	73453	40774	6460
2453854.3055729	41520	74084	39418	6367
2453854.3060012	42677	76695	42539	6723
2453854.3064294	44801	79864	44848	7553
2453854.3068565	44750	81793	43188	7384
2453854.3072824	46080	83451	45802	8598
2453854.3112338	42389	77093	41590	7351
2453854.3116586	44796	82719	44337	7018
2453854.3120868	43952	79834	44569	6690
2453854.3125127	39393	75638	40026	6990
2453854.3129387	39414	71519	38906	7971
2453854.3133692	37629	72553	40967	5745
2453854.3137951	48091	87991	47044	7859
2453854.3142211	38100	70384	38582	7344
2453854.3146539	34730	64462	34974	5771
2453854.3150810	32800	60279	32529	5181
2453854.3155093	28434	56282	28488	4946
2453854.3159363	20492	38034	21139	3135
2453854.3163634	38112	68684	38106	6860
2453854.3167894	41049	73896	40353	5826
2453854.3172164	41467	76812	43358	6273
2453854.3176447	48147	89003	47486	7535
2453854.3180718	48149	85850	44553	8509
2453854.3232025	42562	75731	42256	7224
2453854.3236319	45075	81118	43025	7709
2453854.3260428	49174	88664	47766	8202
2453854.3264699	50100	90785	49995	9423
2453854.3268981	52865	92734	50150	8794
2453854.3273229	49881	90974	48768	8567
2453854.3277500	48863	92440	48795	9181
2453854.3281748	47856	85336	45869	7236
2453854.3286019	45779	85540	48769	6927
2453854.3290289	48186	89477	48941	8705
2453854.3294560	48403	87292	47545	8631
2453854.3298831	47652	89083	49035	8768
2453854.3303102	48495	89567	47982	6933
2453854.3307373	47780	88657	48642	7512
2453854.3311632	49677	94014	49555	8356
2453854.3315891	48846	91980	50490	7354
2453854.3320174	48170	91270	49957	8058
2453854.3324444	48760	93201	50053	7784
2453854.3328727	49710	93820	51172	8330
2453854.3333009	49407	93070	48513	7796
2453854.3337269	36239	67466	34721	6233
2453854.3341516	47106	85642	46316	8508
2453854.3345764	50107	94855	49986	7660
2453854.3350023	47526	90568	46456	7834
2453854.3354271	43731	80639	44166	6850
2453854.3358542	45258	87600	47171	7502
2453854.3362813	45449	81987	45485	8433
2453854.3367083	48856	90578	49431	7848
2453854.3371331	48748	88361	49286	8700
2453854.3375602	47910	85082	48206	8212
2453854.3384132	51688	95900	52899	9387
2453854.3414873	51208	99782	52024	8618
2453854.3419167	52320	101028	54772	8960
2453854.3423437	52349	100523	54490	9896
2453854.3427708	53073	100132	53709	9007
2453854.3431991	53526	98937	53319	7907
2453854.3436273	53347	98506	54782	8884
2453854.3440556	53216	99591	53443	9803
2453854.3449109	52374	100087	53787	9624
2453854.3453368	52767	99574	54305	8875
2453854.3457616	51486	99416	53650	8925
2453854.3461898	54220	97200	53627	10159
2453854.3466169	53521	98869	53360	9400
2453854.3470440	50826	98262	53814	7222
2453854.3474711	52060	98320	50659	10029
2453854.3478981	51398	100018	52322	9785
2453854.3483229	51111	98508	54326	8762
2453854.3487488	53656	98440	51956	9259
2453854.3491759	52244	98781	53077	8182
2453854.3496030	51213	101466	53432	8231
2453854.3500301	50098	89265	51892	8906
2453854.3508843	51537	97129	55581	8439
2453854.3513113	50280	95883	53773	9410
2453854.3517373	53831	101658	54352	8641
2453854.3521678	53745	100975	52800	8076
2453854.3525984	50911	100137	52666	9049
2453854.3530255	51764	98159	53469	7809
2453854.3534525	52435	101186	53714	8057
2453854.3538785	52690	99882	52924	9468

Using formulas, magstar = - 2.5 * LOG ((1 + (aduref2 + aduref3) / aduref1)) + magref1, where magref1 R is the magnitude of the star brighter used as a reference, obtained from USNOB1 catalog, (see Table 4), you get the magnitude of the star theoretical reference.

Through the formula magcomet = - 2.5 * LOG (aducomet/(aduref1 + aduref2 + aduref3)) + magstar you have the magnitude of the comet. The median values derived with the flux of Table 5 are: magstar = 8.378 (+/-0.012), magcomet=9.581(+/-0.029).

Photometry of the Comet C/2008 J1 (Boattini)
Here are the the orbital elements of the comet C/2008 J1

 
C/2008 J1 (Boattini)
Epoch 2008 Nov. 30.0 TT = JDT 2454800.5
T 2008 July 13.2757 TT MPC
q 1.724289 (2000.0) P Q
z +0.006102 Peri. 68.1304 +0.4602796 +0.1204894
+/- 0.000017 Node 273.4188 -0.6424076 +0.7290203
e 0.989478 Incl. 61.7787 +0.6127440 +0.6738039

Comet C/2008 J1 discovery a few months ago from the Italian astronomer A. Boattini, had a seemingly stable photometric performance but showed a very peculiar shape-behaviour. (See fig. 6)

Fig. 6: Comet C/2008 J1 taken on 4 September 2008

with a Newton Telescope 250 mm, focal length 1200 mm CCD camera and filter Rc.

As you can see the coma is very asymmetrical with a part that stretches to the north-east and the other almost in opposition in south-west. This form has remained stable throughout the period of our observations. The series of images for our research were obtained on the evening on 4 September 2008, when the comet was in position circumpolar. There were obtained 120 images from 30 seconds each with a telescope Newton 250 mm aperture, focal length 1200 mm, Atik CCD filter and 16IC Rc direct fire. (for the complete system see Tables 1 and 2). The pursuit of hype was not optimal for different images are moved, but were the same used for granting the photometry. The stars photometric shown good are 4 and listed in Table 6.

Fig. 7: Comet C/2008 J1 observed the evening on 4 September 2008.

On the left image was obtained with mediating Astroart

120 frames for 30 sec each, and aligning on the photometric center of the comet.

On the right the same images have been mediated by aligning on the center

of photometric stars. The error of alignment is 2-3 pixels

with the stars moved because of bad pursuit.

Stella/Catalogo	mag. - USNO B1	mag. - TYCHO 2	mag. – GSC 2.2
T 4637:1159:1 (Ref1)	R1=11.27– R2=11.23	Bt=12.349 – Vt=11.682
T 4637:617:1(Ref2)	R1=11.13 – R2=11.06	Bt=13.956 – Vt=12.105
GSC1393 (Ref3)	R1=11.32 - R2=11.15		R=11.63
GSC1353 (Ref4)	R1=11.32 - R2=11.38		R=11.88

Tab. 6: photometric parameters of the stars of reference derived

from catalogs on-line using Aladin, after calibrated

astrometry the image aligned on the stars of the previous figure.

The photometric results obtained can be seen in the figures below.

Comet aperture 9 pixels - Resolution 1.26 arcsec / pixels - 25 cm Ttelescope Newton f / 4.8 + CCD Atik 16IC + Rc

	Km/UA	In Meter
Rho (Coma Radius)	8086	8086000
D (Earth-Comet)	1,7480	2,622E+11
R (Sun-Comet)	1,8590

Fig. 8: The graphs show the flux of Comet C/2008 J1 compared with the flux of the stars of reference

(see table 6 to the characteristics of the stars). The rms respectively 0.033 for the comet and 0.015,

0.016, 0.014 and 0.019 for the four stars of reference. In this case you can see a steady flux to the comet

Fig. 9: The graph of the magnitude of Comet C/2008 J1 with the flux converted into magnitudes.

Table 7 contains all of the counts of comet and star of reference for the complete set of images.

Tab. 7: flux of Comet C/2008 j1 and reference stars measured in ADU.

JD	FLUX J1	REF1	REF2	REF3	REF4
2454714.3031400	18874	245875	222713	212977	173819
2454714.3038912	18420	253472	218828	212601	176458
2454714.3046435	18142	245895	224638	208284	173900
2454714.3053958	18133	242647	223286	213281	179610
2454714.3099109	17733	244434	216729	203897	178731
2454714.3106632	17668	240236	219056	204217	177629
2454714.3114155	18245	240671	216362	204213	169502
2454714.3121678	18669	244127	221165	207542	173659
2454714.3144248	18442	235001	218930	209665	170851
2454714.3174317	18405	245570	214685	203178	168355
2454714.3181840	17489	242733	218669	206881	169021
2454714.3189363	17133	238523	213165	210145	171222
2454714.3196887	18018	239488	208716	204651	173325
2454714.3204410	17084	241981	212967	208017	170167
2454714.3211933	18301	240135	217480	201351	171155
2454714.3219456	17821	242549	219252	206058	179801
2454714.3226979	18059	237805	216615	203213	171788
2454714.3234502	17410	244399	213869	201020	173868
2454714.3242025	17933	239360	218067	207680	172780
2454714.3249537	18619	242001	220301	206994	174190
2454714.3272060	17375	241884	223142	208855	171438
2454714.3302141	18157	241299	215738	209070	169150
2454714.3317164	18689	242728	217818	205311	173234
2454714.3324688	18278	244125	219442	206704	168348
2454714.3332199	17000	238077	217973	209619	167213
2454714.3339722	18904	242767	217060	206526	176056
2454714.3347222	17479	234015	215369	205403	174140
2454714.3354745	17880	236483	219168	203051	169807
2454714.3362269	17294	233079	213202	208774	168975
2454714.3369792	16814	238769	214999	201713	171643
2454714.3377303	17553	233497	212183	203835	168614
2454714.3392338	17482	238611	217952	199011	164718
2454714.3399861	17598	234458	213103	201071	167594
2454714.3407373	16847	232583	214739	206655	171227
2454714.3422407	16874	234063	211729	203823	168908
2454714.3429919	18457	237978	208213	200498	170823
2454714.3437442	18464	236291	214609	203953	168025
2454714.3452477	17493	235147	218660	206231	166720
2454714.3460000	18119	239310	215962	202415	164812
2454714.3467546	17875	232375	219524	202079	167912
2454714.3475069	18659	239577	213984	206503	167367
2454714.3482593	17267	233063	219596	208560	175925
2454714.3497627	17171	236689	213270	200364	172910
2454714.3505139	17285	237687	214304	197557	167595
2454714.3512662	16870	231404	213348	198920	167256
2454714.3520440	16721	229285	210145	201836	166196
2454714.3535463	16252	230441	208440	201572	164855
2454714.3542986	16436	232161	215050	201111	165823
2454714.3550509	17394	230301	212043	199631	172361
2454714.3558032	18354	236899	212054	201038	167810
2454714.3565544	16942	237107	219957	203007	171447
2454714.3573067	17700	234630	218623	204776	171500
2454714.3588102	17339	242049	211012	209180	173012
2454714.3603137	18890	237448	215079	209571	174886
2454714.3610648	18269	238738	219464	204326	169609
2454714.3618171	17571	239704	215044	209232	173936
2454714.3625694	17439	237467	214809	203765	164596
2454714.3633206	17779	239445	214869	207153	169952
2454714.3640718	17362	243125	218798	207177	161879
2454714.3648241	17622	241400	215737	211213	172211
2454714.3670787	16919	239450	218923	208054	172940
2454714.3678287	18955	239932	221623	212892	171010
2454714.3685810	18255	244619	217409	205596	175083
2454714.3693333	18072	240864	220085	204083	168337
2454714.3700845	18257	241872	226881	210498	170606
2454714.3708356	18525	238506	221179	207278	172561
2454714.3715880	18640	246568	221219	211742	170405
2454714.3723391	18594	243821	215176	204609	168390
2454714.3730914	18377	239463	223369	212002	167849
2454714.3745949	18127	236085	217971	205026	174093
2454714.3753484	19155	236740	219834	206834	173195
2454714.3760995	18429	233979	212231	208493	174678
2454714.3776030	17626	243636	217492	206478	170289
2454714.3783542	16972	241982	216403	207006	172598
2454714.3791053	17726	243870	214632	206912	170358
2454714.3798576	18090	241292	219561	204245	167541
2454714.3806088	17750	236792	217340	203519	169424
2454714.3813611	18682	236327	219197	203524	168310
2454714.3828646	17944	239353	212514	201802	173039
2454714.3843692	16800	235332	213562	203659	167766
2454714.3851215	18727	237857	215517	199941	170392
2454714.3858727	18076	228357	209310	201855	169326
2454714.3866250	17576	234272	216829	203240	166036
2454714.3873762	16704	235636	218036	203021	172795
2454714.3888796	17942	235660	218047	198438	166511
2454714.3903831	17678	235787	212758	201402	165550
2454714.3918866	17043	236001	216339	201378	168996
2454714.3926377	16564	238188	211582	203442	168518

Using the formula, magstar=-2.5*LOG((1+(aduref2+aduref3+aduref4)/aduref1))+magref1, where magref1 R is the magnitude of the star brighter used as a reference, obtained from USNO catalog B1, (see Table 6), you get the magnitude of the star magstar theoretical reference. Through the formula, magcomet=-2.5*LOG(aducometa/(aduref1+aduref2+aduref3+aduref4))+magstella. The median values derived with the flux of Table 7 are The following: magstar=9.895(+/-0.012), magcomet=14.068 (+/-0.036)

Photometry of the Comet 6P/d’Arrest

Here are the the orbital elements of the comet 6P

6P/d'Arrest
Epoch 2008 Aug. 2.0 TT = JDT 2454680.5
T 2008 Aug. 14.9589 TT MPC
q 1.353507 (2000.0) P Q
n 0.1507993 Peri. 178.1196 +0.7332504 +0.6435761
a 3.495718 Node 138.9358 -0.6281291 +0.7646977
e 0.612810 Incl. 19.5148 -0.2603801 -0.0323621
P 6.54

The periodic 6P, with a period of 6.54 years, has repeatedly made the halfway point and has been studied in depth. The last step to the minimum distance from the sun happened on 2 August 2008 and was seen almost daily for a discrete period of time. It was then pointed out the possible outburst of small claims that first had not been observed. (See link ... ... ...)

Fig. 10: Comet 6P observed on 25 August 2008

with a Newton Telescope 250 mm,
1200 mm focal length CCD camera and filter Rc

The increase in brightness was quite sudden, but apparently in agreement with his approach to our star, in August, reaching an apparent visual magnitude around 9. The survey CCD instead showed that there were signs of outburst that were not observed visually.
The series of images for our research were obtained on the evening of 25 August 2008, when the comet was 18 degrees over the location for our, DECL. = -26 45 10 south in the constellation of Capricorn. There were obtained 120 images from 30 seconds each with a telescope Newton 250 mm aperture, focal length 1200 mm, Atik CCD filter and 16IC Rc direct focus. (for the complete system see Tables 1 and 2).
The pursuit of hype was not optimal for different images are moved, but were the same used for granting the photometry. The inner part of the hair including false nucleus has been defocused to a FWHM of 14 pixels. (See fig. 11)

Fig. 11: Window aperture of 14 pixels for the inner side of the coma of the comet.

Even the stars in the field are therefore defocused. Those found to have good photometric are 5 and the listed in Table 8.

Fig. 12: Comet 6P observed the evening of 25 August 2008.

On the left image was obtained with mediating Astroart 120 frames for 30 sec each, and aligning on the photometric center of the comet.

On the right the same images have been mediated by aligning on the center of photometric stars. The error of alignment is 1-2 pixels.

Stella/Catalogo	mag. - USNO B1	mag. - TYCHO 2	mag. – GSC 2.2
T 6916:1257:1(Ref1)	R1=10.53– R2=10.50	Bt=11.223 – Vt=10.788
GSC 6916:1515 (Ref2)	R1=12.77 – R2=12.28		R=11.89
GSC 6916:1396 (Ref3)	R1=12.88 - R2=12.61		R=12.19
GSC 6916:1522 (Ref4)	R1=13.33 - R2=13.04		R=12.69
GSC 6916:1391 (Ref5)	R1=13.46 – R2=12.93		R=14.41

Tab. 8: photometric parameters of the stars of reference derived from catalogs on-line using the Aladin,

after calibrated astrometry the image aligned on the stars of the previous figure.

Photometric results obtained can be seen in the figures below.

Aperture 18 pixels - Resolution 1.26 arcsec / pixels - 25 cm telescope Newton f / 4.8 + CCD Atik 16IC + Rc

	Km/UA	In Meter
Rho(Coma radius)	3556	3556000
D(Earth-Comet)	0,384000	57600000000
R(Sun-Comet)	1,359300	2,03895E+11

Fig. 13: The graphs show the flow of comet 6P compared with the flow of the stars of reference

(see Table 8 for the characteristics of the stars).

The rms respectively 0.070 for the comet and 0.066, 0.117, 0.085, 0.100 and 0.156 for the five stars of reference.

Fig. 14: The graph of the magnitude of the comet 6P with the flux converted into magnitudes.

Table 9 contains all of the counts of comet and star of reference for the complete set of images.

Tab. 9: flux of comet 6P and reference stars measured in ADU.

JD	FLUX6P	REF1	REF2	REF3	REF4	REF5
2454704.3083700	37867	224178	47183	38927	20148	14576
2454704.3109861	42824	223268	45818	31885	23986	17024
2454704.3113912	39180	224716	46784	37926	21857	20870
2454704.3117951	39002	227117	48248	35008	20863	21727
2454704.3122002	40843	226255	48009	40420	27079	26528
2454704.3126042	45915	231501	49080	33373	25076	20758
2454704.3130104	40377	230241	47846	36436	28258	23665
2454704.3134155	41071	229023	48297	40692	20405	20019
2454704.3138194	46246	233043	46849	31612	20765	20386
2454704.3142257	43130	229366	52568	35948	25029	21327
2454704.3146308	38978	229414	53867	41207	22496	16884
2454704.3150359	39156	230281	51956	39110	24439	19139
2454704.3154410	42554	232979	46456	39065	23859	24958
2454704.3158472	41442	229932	43404	35045	24199	20071
2454704.3162836	37332	233405	52041	34386	26034	17982
2454704.3166875	46279	228677	54908	37957	18589	23658
2454704.3170914	42250	228710	52010	36268	21542	15776
2454704.3174965	41567	231089	49512	35910	22145	17856
2454704.3179005	39710	212056	42193	31064	23542	17604
2454704.3187095	39995	228884	49485	40509	23891	20922
2454704.3191134	45640	231753	51540	32687	30443	18268
2454704.3195185	41316	222134	47725	32381	24972	21428
2454704.3199236	36875	228439	56454	36080	19940	22840
2454704.3203287	40365	230221	45685	32720	23733	23736
2454704.3207338	43772	231807	47436	37165	22160	25331
2454704.3211389	43600	228490	50170	36296	20841	20299
2454704.3219491	38244	228196	50395	41505	24331	22020
2454704.3223553	46129	229800	51281	36517	24871	16364
2454704.3227604	40185	243119	51397	36123	27038	24729
2454704.3231644	43824	237051	55095	46937	29188	21709
2454704.3235694	45036	233168	48929	35965	22597	19059
2454704.3243773	41870	232529	50224	40205	26059	19267
2454704.3247789	44571	237753	50540	39775	24050	17214
2454704.3251840	42006	234547	49770	39477	24108	16752
2454704.3255880	48215	246234	53023	41294	25611	26804
2454704.3259931	40094	237541	56203	34457	24437	19020
2454704.3263970	45747	232447	55212	36998	23827	18972
2454704.3268021	37021	229948	53939	39498	26476	23454
2454704.3276111	44084	237780	54585	36361	22018	17655
2454704.3280162	47151	236811	52473	40086	28361	26275
2454704.3284201	39204	237875	54199	40514	28482	23081
2454704.3292303	39980	236834	52838	42414	29297	22900
2454704.3296354	43274	234596	53848	39957	23576	20152
2454704.3300405	37443	243613	52748	41703	26235	21922
2454704.3304456	44254	244385	50139	40886	23394	24578
2454704.3308495	42377	243936	51130	39786	20902	16257
2454704.3312546	46943	231648	55593	35349	23199	22439
2454704.3320648	42695	242374	50438	40231	22914	22850
2454704.3324699	42816	245335	51396	37125	31012	23130
2454704.3332801	42389	237410	55330	42015	24349	18268
2454704.3336863	46439	237130	53607	34724	26854	24042
2454704.3340914	44372	246804	55613	30492	28332	20285
2454704.3344977	43895	244160	50004	34655	26424	22092
2454704.3349016	44738	237793	56328	43824	25043	21970
2454704.3353067	43563	241437	51260	39982	25582	24261
2454704.3357106	49113	241942	51663	37861	24389	23251
2454704.3361157	43782	243737	47455	40399	21849	22947
2454704.3365197	46067	237199	51358	41909	28308	20642
2454704.3369236	44631	240665	49711	38341	27084	20433
2454704.3381366	45260	241711	55006	40648	22410	16245
2454704.3397558	43172	245454	49875	42573	29218	18015
2454704.3401609	40415	237169	49326	42724	24539	19745
2454704.3405660	44761	238140	49681	38713	26481	22555
2454704.3409711	41853	236062	51351	39448	24890	16242
2454704.3413762	44323	243477	51445	38304	25997	17168
2454704.3417801	45337	238029	49023	39085	26613	17749
2454704.3421852	43278	233822	55607	38472	25389	18162
2454704.3429954	39533	241041	49570	38782	22750	17855
2454704.3438067	47807	245839	47268	37791	26391	20100
2454704.3454271	43857	242345	52525	39372	24995	15223
2454704.3458310	49617	254965	51602	38497	24204	21322
2454704.3462361	46831	287115	51169	42109	26491	21288
2454704.3466400	40746	256219	51052	31434	26603	22317
2454704.3470451	46335	252329	50579	37702	26808	16425
2454704.3474537	47700	237153	49662	39809	27608	18685
2454704.3482616	43618	240948	44360	39867	24539	13244
2454704.3490683	46483	239310	47070	40047	25990	15664
2454704.3498715	39114	239155	50893	43584	24719	18817
2454704.3506782	43561	239541	50671	41086	25429	20481
2454704.3510833	43571	243364	45814	41517	28270	19256
2454704.3514873	44280	243450	52107	39636	27828	15329
2454704.3518924	44370	239198	53437	36852	29624	21106
2454704.3522975	41430	311198	51473	44277	28552	17169
2454704.3527025	42537	284545	50191	35616	27059	19081
2454704.3531065	45634	268876	52894	36145	26812	15087
2454704.3535116	41079	233942	48088	38004	28196	17865
2454704.3539167	41866	241125	47377	38085	27682	19558
2454704.3543218	43037	242980	45975	36784	28496	18200
2454704.3555359	41752	245819	44444	35270	26091	19685
2454704.3563449	40016	240343	46839	42883	24396	20637

Using the formula, magstar =-2.5 * LOG ((1+(aduref2+aduref3+aduref4+aduref5)/aduref1))+magref1, where magref1 R is the magnitude of the star brighter used as a reference, obtained from USNO catalog USNO B1, (see Table 8), you get the magnitude of the star magstar theoretical reference. Through the formula, magcomet=-2.5*LOG(aducometa /( aduref1+aduref2+aduref3+aduref4+aduref5))+ magstar The median values derived with the flux of table 9 are as follows: magstar = 10,029 (+ / -0.024), magcometa = 12,370 (+ / -0.077)