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C:/comets/C2011L4/SLC L4+S1/v4/130619

Submitted for publication to

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY

“The location of Oort Cloud Comets

C/2011 L4 Panstarrs and C/2012 S1 ISON,

on a Comets´ Evolutionary Diagram”

Ignacio Ferrín, Institute of Physics,

Faculty of Exact and Natural Sciences, University of Antioquia,

Medellín, Colombia, 05001000 ferrin@fisica.udea.edu.co

Number of pages 51

Number of Figures 22

Number of Tables 4

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Abstract The scientific results found in this investigation are:

(1) We reduced 9615 photometric observations of comets C/2011 L4 Panstarrs, C/2012 S1 ISON, C/1973 E1 Kohoutek, C/2002 O4 Hönig and 1P/Halley, and we present their secular light curves (SLCs). (2) We measured the Slowdown Event (SDE) of C/2011 L4 Panstarrs (Figure 1). This is the distance at which the brightness increase rate slows down to a more relaxed pace. We find R(SDE) = -4.97±0.03 AU (or t(SDE)= 2012 04 14±3 d). (3) We derive the absolute magnitude of C/2011 L4 Panstarrs and the power laws that define its brightness behavior. The absolute magnitude is m(-1,1)= +5.6. After passing the SDE, the comet is increasing its brightness with a shallow power law R+2.24. The magnitude at perihelion can be measured from the SLC and we find m(1,q)= -1.2±0.2 giving it entrance to the Great Comet Cathegory (those comets with negative magnitudes at perihelion). Additionally the comet exhibited a perihelion surge (Figure 12). (4) Comet C/2012 S1 ISON is at the present time (June 2013) approaching

perihelion (Tq =2013 Nov. 28th). Thus the information contained in this report, is preliminary. We measured the SDE of C/2012 S1 ISON, finding R(SDE)=-5.07 ±0.03 AU (which corresponds to 2013 01 17±3 d). Notice the coincidence in value with C/2011 L4 Panstarrs. For the absolute magnitude we find m(-1,1)= +12.7±0.1. Clearly this is an intrinsically faint comet (Figure 13). (5) Technically speaking, since January 17th±3 d, 2013, comet ISON has been

on a stanstill for more than ~132 d, within the same magnitude ±0.2 mag, a rather puzzling feat (Figure 8). Since the nucleus brightens like R+2, the comet is actually dimming. We will present the SLC of comet C/2002 O4 Hönig who also presented a flat light curve and who desintegrated. At perihelion the orbit of ISON enters the Roche Limit of the Sun, and the calculated temperature is 2919 K. There is a significant probability that the comet may turn off as comet C/2002 Hönig did, or alternatively, it may desintegrate at perihelion. The future of this comet does not look bright. (6) A comparison of two estimates of water production rate by Schleicher (2013) with a calibration by Jorda, Crovisier & Green (2008), reveals that comet ISON is depleted in water content by a factor of 9.2, aproximatelly (Figure 20). (7) An estimate of the water budget of these two comets allows the calculation

of the water-budget age, WB-AGE, and of their Remaining Returns, RR (Figure 21). The comets lie in the RR versus mass-loss age, ML-AGE, diagram, in the region of the Oort Cloud comets (the left part of the diagram). To cover the whole range of possibilities for comet ISON, we show the result for two WBs (4.2E09 to 6.3E09 kg), two radii (0.335 to 2.0 km), and one δ (dust to gas mass ratio) (δ =0.5). It is found that the location on the diagram does not change by much. The diagram is forgiving, and the results are robust. (8) For comparison we present the SLC of comet C/1973 E1 Kohoutek, the

famous comet that fizzled, and show reasons to conclude that it didn’t. We also show the SLC of comet C/2002 O4 Hönig, a comet with a leveled off light curve that desintegrated. (9) If the SDE represents the change over from CO2 to H2O controlling

substance, then there should be a corresponding SDE for the change over CO

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to CO2 controlling substance. We would expect this change to take place far away from the Sun (R<-10AU). (10) Table 2 and Figure 16 allow us to define the Jupiter Family Interval of Comets, as 1.24<R(SDE)<2.09 AU. This is a narrow Interval in which 5 comets from the Oort Cloud and 6 comets from the JF, have their SDEs, for reasons unknown. (11) Figure 22 allows the determination of the Death Ages of several comets,

assuming they will continue evolving along an isoline. We have measured DA(KO)=1.7E06 cy, DA(V1)=1.4E05, DA(L4)= 36000cy, DA(Hö)=6 cy. (12) Since suffocating comets move upward in the RR versus ML-AGE diagram, and sublimating comets move downward, there must be an intermediate value where motion must be horizontal, a suffocation-sublimation-border. We estimate the border at RR(SB)=(6±5) 104 . At the present moment the border is so wide, that we do not know on what side of the border comet Hale-Bopp is. (13) The Desert of Comets is the right hand, lower part of the diagram were we

should expect to find few or none comets. We measure a theoretically value for the start of this region at 3.9 109cy<Desert. However, observationally, the Desert is starting much before, maybe as low as 1000 cy, thus we have a huge discrepancy. Additional observations are needed. (14) There are many questions to be answered that have to deal with the RRversusML-AGE evolutionary diagram. However, one single question may be representative: Is it possible to calculate an evolutionary model containing all important physical phenomena, capable of predicting the long term motion of comets in the diagram? In particular, why is comet 103P moving in that particular direction, 60º to the isolines? Key words: comets: general, asteroids: general, 1P/Halley, C/1995 O1 Hale-Bopp

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1. INTRODUCTION For a quick introduction to the scientific issues considered in this work,

skip to the Figures. In particular, Figures 21 and 22 sumarize our investigation.

2013 offered the opportunity to observe two new comets coming from the

Oort cloud, C/2011 L4 Panstarrs and C/2012 S1 ISON. Both have orbits with

excentricity e ~ 1.0.

In June 6th, 2011, astronomers at the Institute of Astronomy of the

University of Hawaii, discovered a comet designed C/2011 L4 Panstarrs

(Wainscoat and Micheli, 2011). We will show that when the comet reached to

R= -4.95 AU (the minus sign indicates pre-perihelion location), the brightness

law slowed down. We call this the Slowdown Event, SDE. This is not

surprising. 12 other comets, including comet 1P/Halley, have exhibited such

SDEs (Ferrín, 2010, Paper II; Ferrín 2013c) and they are listed in Table 2.

In September 21st of 2012, Nensky and Novichonok (2012) discovered

comet C/2012 S1 ISON at the notable distance of -6.3 AU. The object is

coming from the Oort cloud with an excentricity of 1.0000013, esentially

parabolic. It has been increasing in brightness at a rate R+5.60 and if it were

to continue at this rate, it would certainly attain a magnitude much brighter than

the full moon. However we will show that the comet had a SDE event on

January 17th±3, 2013 (Figures 4-8).

For comet ISON, we will show that the comet has been in an almost

perfect standstill for ~132 d, within ±0.2 mag. We will show that this comet lies

in the Remaining Returns, RR, versus Mass-Loss Age, ML-AGE, diagram in the

region of Oort Cloud comets (Figure 21) and it is the oldest of the group.

The fate of this comet is uncertain. The standstill suggests that the

comet may turn off completely, or activity may pick up, although less likely.

The object is entering the solar glare (Figure 4), and we will not know its

fate until observations are attempted betwen October 11th and November 4th ,

when the comet will be briefly above 50 degrees of solar elongation in difficult

observational conditions.

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2. DATA SETS

The data sets to create the secular light curves are available in the

internet:

(1) The Cometary Science Archive http://www.csc.eps.harvard.edu/index.html

is a site to visit because it contains useful scientific information of current

and past comets, and it is mantained by Daniel Green.

(2) Another usefull site is the Minor Planet Center repository of astrometric

observations, http://www.minorplanetcenter.net/db_search . Daniel Green

is the Director of the Center.

(3) Seiichi Yoshida’s web place http://www.aerith.net contains many raw light

curves and has access to oriental sites difficult to translate.

(4) The Yahoo site http://tech.groups.yahoo.com/group/CometObs/ contains up

to date observations by many observers for many comets.

(5) The spanish group measures magnitudes with several CCD apertures:

http://www.astrosurf.com/cometas-obs. It is managed by Julio Castellanos,

Esteban Reina and Ramon Naves.

(6) The site http://www.observatorij.org/cobs/ contains many observations in

the ICQ format, as well as news concerning comets, and it is mantained

by the Crni Observatory with Jure Zakrajsek as curator.

(7) The german comet group publishes their observations at

http://kometen.fg-vds.de/fgk_hpe.htm . The editor is Uwe Pilz.

(8) Observers from south america collect their observations here:

http://rastreadoresdecometas.wordpress.com/ This is the web site of

LIADA. The site is managed by Luis Mansilla.

(9) The site http://www.shopplaza.nl/astro/cometobs.htm contains observations

of many comets and it is taken care off by Reinder J. Bouma and Edwin

van Dijk.

In this work calendar dates will be expressed YYYYMMDD. Althought

not cotinuous, this is a monotonously increasing number.

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3. SECULAR LIGHT CURVES, SLCs

3.1 INTRODUCTION

The SLCs give an unprecedent amount of information on the photometric

behaviour of comets, with more than 30 parameters measured from the plots

(Ferrín 2005a=Paper I, 2005b, 2006, 2007, 2008, 2010=Paper II, 2012, 2013a,

2013b, 2013c).

The elaboration of the Secular Light Curves (SLCs) follows closely the

procedures described in the Atlas of Secular Light Curves of Comets (Paper II).

The preferred phase space to describe the luminous behaviour is the m(1,R) =

m( Δ ,R) – 5 log Δ versus Log R plane, where Δ is the Sun-Earth distance and

R the heliocentric distance. In the m(1,R) versus Log R diagram, powers of R,

R+n, plot as straight lines of slope 2.5 n. The R+n behavior is easy to spot and

measure. At the bottom of the plot, the nucleus appears as straight lines in the

form of a pyramid, with a power law R+2.0.

To carry out this investigation we reduced 9615 photometric observations

of 5 comets: C/2011 L4 Panstarrs, C/2012 S1 ISON, C/1973 E1 Kohoutek,

C/2002 O4 Hönig and 1P/Halley . Except for the SLC of comet 1P/Halley that

was presented previously in the Atlas, all the other SLCs are new.

Except when it is otherwise stated, in this work we adopted the envelope

of the data set as the correct interpretation of the observed brightness. There

are many physical effects that affect comet observations like twilight, moon

light, haze, cirrus clouds, dirty optics, lack of dark adaptation, excess

magnification, and in the case of CCDs, sky background too bright, insufficient

time exposure, insufficient CCD aperture error, and too large a scale. All these

effects diminish the captured photons comming from the comet, and the

observer makes an error downward, toward fainter magnitudes. There are no

corresponding physical effects that could increase the perceived brightness of a

comet. Thus the envelope is the correct interpretation of the data. In fact the

envelope is rather sharp, while the anti-envelope is diffuse and irregular.

A key to the photometric parameters measured in the SLCs is given in

Paper II. However a short description is given next.

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(1) The magnitude at , R, , is denoted by V( , R, ), where is the comet-

Earth distance, R is the Sun-comet distance, and is the phase angle. (2) q,

the perihelion distance, is given in AU. (3) Q, the aphelion distance, also in AU.

(4) The turn on point RON. (5) The turn off point ROFF. (6) The sum of these

two values RSUM = -RON +ROFF. (7) The asymmetry parameter ROFF/RON. (8)

The magnitude at turn on VON(1,R,0). (9) The magnitude at turn off VOFF(1,R,0).

(10) The absolute magnitude before perihelion m(Δ,R)=m(-1,1). (11) The

absolute magnitude after perihelion m(+1,1). (12) The mean value of both

<m(1,1)>. (13) The absolute nuclear magnitude VNUC(1,1,0). (14) The

amplitude of the secular light curve

ASEC(-1,1) = VNUC(1,1,0) - m(-1,1), (1)

Asec measures the difference between the nuclear absolute magnitude and the

total absolute magnitude. ASEC(-1,1) can be considered a measure of activity of

a comet, and thus a proxy for age. (15) The effective diameter D. (16) The

photometric age P-AGE(-1,1) in comet years (cy), defined below. (17) In the

top line of the plot, right hand side, JF16/1 means that this is a Jupiter family

comet of 16 comet years of age 1 km in diameter. (18) V.year is the version of

the plot. (19) Epoch, indicates the years of the observations that were used to

define the envelope of the light curve. Additionally for a RON and ROFF there is a

corresponding TON, TOFF, the times at which the comet turns on and off.

In this work we will be concerned only with the following parameters:

RON, ROFF, m(-1,1), V(1,1,0) and Asec(-1,1), that will be used to calculate the

photometric age, P-AGE, the diameter D, and TON, TOFF, needed as limits to

integrate the water production rate to get the water budget (Section 8).

3.2 PHOTOMETRIC AGE, P-AGE

The photometric age defined in Paper II is an attempt to define the age of

a comet using activity as a proxy:

P-AGE (-1,1) = 1440 / [ ASEC (-1,1) . RSUM ] comet years (cy) (2)

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where ASEC= mplitude of the secular light curve = V(-1,1,0) – m(-1,1), and RSUM

is the sum of the turn on, -RON, and turn off, ROFF, distances of the comet.

P-AGE is measured in comet years to be sure that they are not confused with

current years. The constant is chosen so that comet 29P/Neujmin 1 has a

P-AGE = 100 cy. The minus sign in Δ, indicates observations pre-perihelion.

3.3 CALCULATION OF THE DIAMETER, D

The absolute nuclear magnitude in the visual, VNUC(1,1,0), is related to

the diameter, D, by a compact and amicable formula derived in Paper II:

Log [ pV D2EFFE / 4 ] = 5.654 - 0.4 VNUC(1,1,0) (3)

where pV is the geometric albedo in the visual. For comets for which the

geometric albedo has not been measured, it is common to adopt pV = 0.04.

Thus the previous equation can be simplified even further:

Log [ D2EFFE ] = 7.654 - 0.4 VNUC(1,1,0) (4)

which is easy to remember.

3.4 A LOWER LIMIT TO THE NUCLEAR DIAMETER

(Ferrín 2013b) has shown that there is a maximum value to Asec,

Asec(Limit)=11.6±0.1. A practical consequence is that we can set a lower limit

to the diameter of any comet if the absolute magnitude, m(-1,1), is known, and

this is the case for most comets. Thus

VNUC(1,1,0) < m(-1,1) + 11.6 (5)

Comets with Asec=11.6 are so active, that they must be sublimating from

100% of their surface area.

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4. SLC OF C/2011 L4 PANSTARRS

Figure 1 shows that C/2011 L4 Panstarrs turned on much before comet

Halley (at RON= -6.15±0.19 AU) (Paper I). Since water can not sublimate at

distances beyond -6 AU, the comet must be composed of something more

volatile than water, probably CO or CO2. Spectroscopy could tell.

Then, at R(SDE)= -4.97±0.03 AU, which corresponds to 20120414±3 d,

the comet had a SDE versus a SDE for 1P/Halley R(SDE)= -1.7±0.1 AU.

Before the SDE, the power law was R+8.67 and after it was R+2.24 (Table 3).

Ferrín (2013b) has shown that there is a maximum value to ASEC,

Asec(Limit)=11.6±0.1. Since we know m(-1,1) from the visual SLC in Figure 2

(m(-1,1)= 5.6±0.1), we can calculate V(1,1,0)= 17.2±0.2 using Equation 5.

With a geometric albedo pV= 0.04 and Equation 4, we get a lower limit to the

diameter of D> 2.4±0.3 km.

To calculate P-AGE we assume that the turn off point is equal to the

turn on point. Then we find P=AGE>2.8 cy which indicates that this is a young

comet. Combining this information with an eccentricity e=1.000028 (Table 2),

we conclude that this is a fresh, active new comet coming from the Oort Cloud,

and thus it is reasonable to assume that it is sublimating from 100% of its

surface area, consistent with Asec=11.6. Thus D=2.4 km is a good first

approximation to the diameter until a better values comes in. We will use this

information to plot the comet in the RR versus ML-AGE diagram (Figure 21), but

since the diagram is logarithmic, it is very forgiving. We could have a diameter

twice that value, that the location in the diagram will not change by much.

In Figure 2, we see the difference MPCOBS versus Visual. The plot

shows that caution has to be exercised when using this data, since the CCD

and visual observations differ by a large amount. For example, it is the absolute

magnitude from visual data that has to be used when calibrating the water

production rate, not the magnitude from the CCD data. Additionally, it is the

visual absolute magnitude that has to be used to calculate a lower limit to the

diameter, with Asec(Limit) in Equation 5.

The observed difference is CCD (MPCOBS, mostly red magnitudes) -

VISUAL. To convert from CCDR to visual we have to add a color index R-

V=0.48 mag (Paper I). Then the difference V(CCD)-VISUAL is even larger and

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pre-perihelion reaches to 1.7 mag. The comet abandons the power law and

exhibits a brightness surge, near perihelion. The comet passed the m(1,q)=0

line and reached to m(1,q)= -1.2, sufficient to place it into the Great Comet

Cathegory (those with negative m(1,q)).

Figure 3 compares visual and CCD data. Observations still show a

significant difference, smaller than with the MPCOBS data. This data also

shows the SDE, but due to scatter, it is not possible to derive a precise date for

the event.

5. SLC OF C/2012 S1 ISON

Figure 4 shows the number of observations of this comet, versus the

elongation angle from the Sun. It can be seen that some observers make an

effort to go down to 50º elongation, difficult conditions to observe a faint comet.

The Figure also shows that the data gathering on this comet is complete, since

there are no additional observations below 45 degree elongation.

The next observing window will take place from 20131007 to 20131104

when the comet will be above 50º elongation, in the morning sky, for a brief

period of time. Observations in this short window are crucial to clarify in what

direction this puzzling comet is going, and if it has survived up to that point.

Figure 5 show the light curve of the comet, unreduced magnitude, versus

time, for CCD observation. The slowdown event is clearly seen. The upper

plato has a value R(Δ,R)=15.2±0.1. The SDE measured from this plot is

t(SDE)=20130112±3d.

Figure 6 shows the data of the spanish group cometas-obs. Contrary to

our policy of showing only the envelope of the observations, this plot shows the

daily means of CCD observations. The SDE is clearly seen at t(SDE)=

20130108±3 d.

Figure 7 shows the visual observations. Only 9 visual observations are

available, due to the faintness of the comet and the fact that it transversed a

field congested with stars. This plot shows the inner sanctum, the region of

visual observations with magnitudes around and fainter than 15th. Currently the

inner sanctum is visited by 6 deep sky comet observers.

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Figure 8 shows the MPCOBS data base, plotted as a function of time.

The SDE is clearly seen at t(SDE)=2013 01 09±3 d. Notice that after the

event, the comet remained with its magnitude virtually unchanged for ~132 d.

The stanstill of the comet can only imply that the nucleus is depleted in

water. There could due be rock, dust or debris under the surface, but water

seems to be scarce.

Figure 9 shows the same MPCOBS data base, but this time plotted as a

function of Log R. This is the right plot to derive tendencies, since power laws,

R+n, plot as straight lines. From this Figure the location of the SDE can be

measured on 2013 01 17±3 d. Notice the lack of brightness increase after the

event.

Figures 5 to 9 show evidence that this comet had a Slowdown Event at a

distance R(SDE)= -5.07±0.03 AU. Table 1 compiles some statistics derived

from the different data sets.

Ferrin et al. (2013a) have made a new calibration of the T versus R

temperature. Using T=325º/SQRT(R) we find T(SDE) = 143±5 K. We do not

find any significance attached to this number.

Figure 10 shows comet C/2012 S1 ISON in full scale. The data points

cover a small space of the plot and so predictions are difficult and risky. There

is still a long way to go to reach perihelion, and the comet could pick up on

brightness or turn off completelly like in the case of comet C/2002 O4 Hönig

(Sekanina, 2002), that desintegrated while approaching perihelion. There is an

upper limit to the diameter of the comet of 4.0 km due to Li et al. (2013), that

also sets an upper limit to the photometric age, P-AGE<10 cy. Thus this is a

young comet. If we assume that Asec(Limit)=11.6, then we can set a lower

limit V(1,1,0)=23.8 that corresponds to D=0.12 km. However with this limit the

comet is younger (P-AGE=1.3 cy), than comet Hale-Bopp (2.3±0.2 cy), which is

improbable because this comet is not so bright. Thus this lower limit is too low,

and it is not applied.

If we impose the condition that the turn on point can not be farther away

than the turn on point of comet Hale-Bopp (RON= -16.8 AU) then we can set a

lower limit to the diameter of the nucleus of this comet, V(1,1,0)=20.0, that

corresponds to a nucleus of D=0.67 km, and a P-AGE=3.4 cy, older than comet

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HB. Using the upper and medium limits, the turn on point is restricted to -16.8

<RON< -13.5 AU, the amplitude restricted to 5.5<Asec(-1,1)<8.1, and the

photometric age restricted to 3.4<P-AGE<6 cy. However these numbers are

valid only if it continues behaving as predicted, which is doubfull.

For comparison we will show next the SLCs of comets C/2002 Hönig and

C/1973 E1 Kohoutek, the famous comet that fizzled.

6. SLCs OF COMETS C/2002 HÖNIG AND C/1973 E1 KOHOUTEK

Comet C/2002 Hönig (Figure 11) is particularly relevant to this

investigation because it desintegrated (Sekanina 2002). The SLC shows a SDE

at R(SDE)= -1.26±0.06 AU. It held its brightness constant for about 50 days,

and then turned off near perihelion.

Figure 12 shows the SLC of comet C/1973 E1 Kohoutek, the famous

comet that fizzled. This is a misname. After the SDE the comet continued

brightening at a healthy rate, exhibiting a brightness surge at perihelion,

reaching to m(1,q) = -2.0, and thus into the Great Comet Cathegory (comets

with a negative magnitude at perihelion). So it did not really fizzled.

If there are comets that fizled, that description should be applied to

comets Hönig and ISON.

In Figure 13, the SLCs of comets C/2012 S1 ISON, 1P/Halley and

C/2002 O4 Hönig are compared. A number of features can be discerned. The

turn on distance of C/2012 S1 is much farther away than that of 1P. All three

comets exhibit SDEs. Predicting the future light curve of ISON is difficult.

There is a chance that this comet may turn off completely, like comet Hönig did.

It is possible to calculate the Roche Limit of the Sun, using a density of 1

gm/cm3 for the comet, that of water. We find R(Roche)= 1.92 106 km. While

the comet reaches perihelion at q=0.012472 AU=1.87 106 km. Thus the comet

enters the Roche Limit of the Sun and it may desintegrate. The future of this

comet does not look bright.

6. WHY SHOULD THERE BE A SDE?

When a comet from the Oort Cloud (e=1.0) falls into the Sun, the upper

layer of the nucleus contains fresh volatiles like CO, CO2 an H2O. As the

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comet approaches, temperature increases, and the first one to sublimate is CO.

Next sublimates CO2 and finally H2O. This is due to their different vapor

pressures. Sublimating CO or CO2, the light curve far from the Sun is a

straight line with a power law ~ R+9.1±2.0 (Table 2). The H2O does not have

sufficient temperature to sublimate and thus CO or CO2 control the surface

sublimation and the light curve. The sublimation rate increases as the comet

approaches the Sun, and at a given temperature, H2O overpowers CO or CO2,

and H2O now controls the surface sublimation. The brightness increase

decreases its rate according to the new sublimation rules. This is a

hypothetical mechanism behind the SDE. However, there have been no

numerical or theoretical models to explain this discontinuity, and thus the

hypothesis remains unconfirmed. The dispersion of R(SDE) values (Table

2), seems to be real and not due to observational error. m(SDE) would seem

to be related to the ratio CO/H2O or CO2/H2O. It is expected that

espectroscopic and compositional estudies of C/2011 L4 Panstarrs and C/2012

S1, would reveal differences that can be correlated to the list of SDE’s

properties compiled in Tables 1 to 4.

In fact, if the SDE represents the change over from CO2 to H2O

controlling substance, then there should be a corresponding SDE for the

change CO to CO2 controlling substance. We would expect this change to

take place far away from the Sun (R<-10AU). Thus we predict the existence of

another SDE, but this time due to the CO/CO2 change over.

7. THREE DIAGRAMS Figure 14 shows the m(1,1) versus n in Rn diagram. The values

measured in Table 3 are plotted here. They separate Pre and Post-SDE

events, and Oort Cloud Comets from Jupiter Family comets into 4 distinct

regions. In particular the Pre-Post SDE of Oort Cloud comets are clearly

separated.

Another way to separate the comets from different reservoirs is to plot

the Pre-SDE versus Post-SDE slopes of the power law like in Figure 15, taken

from Table 3. In this plot the Pre-SDE n is compared with the Post-SDE n. The

two groups, Oort Cloud comets and Jupiter Family comets, are clearly

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separated. Oort Cloud comets have n-post-SDEs smaller thant JF comets,

while the n-pre-SDE values are about the same.

The m(SDE) versus R(SDE) Diagram is shown in Figure 16 and it is

based on the data presented in Table 2. It shows 10 comets closely located in

a narrow interval of this phase space, and three comets beyond this interval.

Most of these comets are members of the Jupiter family but notice that 5

members of the Oort Cloud are located inside the Jupiter Family Interval.

Maybe these Oort Cloud comets are old and have exhausted their CO and CO2

layers. Or maybe there is a different reason. It remains unexplained why this

change takes place preferentially at 1.24<R<2.09 AU from the Sun pre-

perihelion (Figure 16).

8. MASS-LOSS BUDGET AND MASS-LOSS AGE

8.1 INTRODUCTION

One way to assign an age to a comet is using the amount of mass loss

by the object per orbit, as a proxy for age. It is to be expected that older objects

are less active than younger objects. This mass loss (ML) may be composed

of water, CO, CO2 or pure dust (like in the case of 3200 Phaethon), or a

combination of them. The objects come from three repositories: the Oort

Cloud, the Jupiter Family, and the asteroidal belt. However all produce water

in large amounts. To calculate the water budget, WB, we will make use of

water production rates Q, measured with a variety of techniques, from ultraviolet

to radio.

In this work we will assume that the envelope of the water production rate

observations is the correct interpretation of the water data. The situation is not

different to the situation we found in the visual and CCD photometry of comets

(Section 3.1 and Paper II).

With water measurements we have a simmilar situation. It is difficult to

capture the whole flux of the object and thus errors are downward. A number of

effects conspire to lower the water flux. For example a half power beam width

smaller than the water coma size, or insufficient integration time, or insufficient

CCD aperture error, or small instrument. Combi et al. (2013) report water

production rate measurements versus aperture size for comet C/2009 P1

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Garradd at 2 AU from the Sun. The plot (Figure 17), show an exponential

increase with an asymptotic value. This is one reasons why it is advisable to

adopt the envelope of the water production rate measurements, as the correct

interpretation of the data.

We define the water budget, WB, as the total amount of water expent by

the comet in a single orbit. The same way for the mass-loss, the dust-loss or

the CO-loss budgets.

The water budget in kg is given by sum of the daily production rate

values, from TON to TOFF :

TOFF

WB = QH2O(t) Δt (6)

TON

The sum goes from TON to TOFF and this information is taken from the

SLC plots. Let us define new ages, the water-budget age, WB-AGE, and the

mass-loss age, ML-AGE thus

WB-AGE [cy] = 3.58 10+11 / WB (7)

The equation for the mass-loss age, ML-AGE, is the same:

ML-AGE [cy] = 3.58 10+11 / ML (8)

In Equations (9) and (10) we have chosen the constant so that comet

28P/Neujmin 1 has a WB-AGE, or ML-AGE=100 cy. The WB-AGE is calculated

for several comets in Table 4.

8.2 Mass Loss, ML, and Remaining Returns, RR

We have seen how to determine the comet water loss per apparition in

kg. However we are interested in the total mass loss. To calculate it we need

the dust to gas mass ratio, δ.

16

Using a model, de Almeida et al. (2009) have derived production rates of

gas and dust for several comets. Their results for comets 1P, 46P, 67P, and

C/1996 B2, are particularly relevant to this investigation. Figure 18 shows that

the dust to gas mass ratio is constrained to 0.1<δ<1.0, and that δ=0.5 is a

mean value that fits the general distribution quite well, over a range of several

orders of magnitudes. Thus we will adopt δ=0.5 in this investigation, with a

range of values 0.1<δ<1.0 . However the RR versus ML-AGE diagram (Figure

21) will show that the location of a comet on the diagram is not sensitive to the δ

value.

With this information it is possible to calculate the thickness of the layer

lost per apparition using the formula

Δr = ( δ + 1 ) WB / 4 π rNUC2 ρ (9)

where rNUC is the radius of the nucleus and ρ its density. This equation can be

derived from the density, given by ρ= ΔM/ΔV, the volume removed given by

ΔV= 4πrNUC2Δr, and ΔM, the mass removed given by ΔMH2O + ΔMDUST +

ΔMOTHER = WB [ 1 + ( ΔMDUST+ ΔMOTHER)/WB). We may take the contribution

of other ices as MOTHER /ΔMH2O =0.05 aproximatelly. For the density we are

going to take a value of 530 kg/m3 which is the mean of many determinations

compiled in Paper I. Then

RR = rNUC/Δr (10)

The resulting values of Δr and RR are compiled in Table 4 for 27 comets.

For example we see that comet 45P lost 9.7 m in radius. Since the radius of

this comet is only 430 m, the ratio rNUC/Δr = 46. This calculation implies that the

comet will sublimate away in only 46 additional returns, if the mass loss rate

continues at the present rate.

8.3 Comet C/2011 L4 Panstarrs

Figure 19 shows the water calibration of this comet, used to calculate the

water budget. There are only two water measurements available in the

literature, Biver et al. (2012) and Opitom et al. (2013). They coincide quite well

17

with the Jorda, Crovisier & Green (2008) calibration, if the line is displaced

downward by a factor of 6.2x. Using this information a water budget is

calculated in Table 4, and adopting D=2.4 km as a first approximation to the

diameter, from Section 4, it is possible to plot this comet in Figure 21. The

object lies in the Oort Cloud region, as expected.

8.4 Comet C/2012 S1 ISON

For comet ISON there are also only two measurements of the water

production rate. Schleicher has published a value 3 10+26 mol/s, but with a

viable range from 1 10+26 to 1 10+27 on 13th March 2013 (Schleicher 2013a), and

6 10+26 mol/s but with a viable range from 2 10+26 to 2 10+27 on May 4 2013

(Schleicher 2013b). These values are plotted in Figure 20 along with the

Jorda, Crovisier & Green (2008) water calibration. It can be ascertained that

comet ISON is a factor of 9.2 below this calibration, suggesting that this comet

is depleted in water. Additionally the power law after the SDE is very shallow or

null. Using the calibration by Jorda, Crovisier & Green (2008) downsized by a

factor of 9.2, we estimate a mass loss compiled in Table 4. Using an upper

limit of the diameter, 4 km, and a lower limit D=0.67 km from Figure 10, we can

place the comet in the RR versus ML-AGE diagram of Figure 21. Comet ISON

is found in the region of Oort Cloud comets, even considering a wide range of

parameters. This seems to be the oldest comet we have from the Oort cloud,

based on its location on the diagram.

8.1 Comet C/2002 O4 Hönig

This is an Oort Cloud comet as can be deduced from the eccentricity of

the orbit, e=1.00076, slightly hyperbolic. In fact this is the most hyperbolic

comet of the list, what prompts us to question if the extraordinary nature of this

object, may be related to it eccentricity, and if this could be a true hyperbolic

comet.

The desintegration of this object was registered by many observers and

was analized in detail by Sekanina (2002), who concluded that the total amount

of dust expent was 1 to 2 1010 kg. For our work will adopt 1.5 1010 kg of dust.

He also assigns a probable diameter of 0.7 km, if the object is made of CO.

18

If we adopt δ=1, then the mass of gas was identical and ML=3 1010 kg,

ML-AGE=24 cy, and RR=13. However if we adopt δ=0.1, then the mass of gas

is 10 times the mass of dust, and we get ML = 1.65 1011 kg, ML-AGE = 2.4 cy

and RR=1.7 . Since the comet desintegrated (Sekanina 2002), we select this

last option as the one that better describes the observations.

With this information the object takes a location in the RR versus ML-

AGE diagram near the RR=1 desintegration limit (Figures 21, 22).

9. THE REMAINING RETURNS VERSUS MASS-LOSS AGE DIAGRAM The Remaining Returns versus Mass-Loss Age diagram (Ferrín et al,

2012; 2013), is an evolutionary diagram that makes use of the water budget

(the amount of gas and dust expent by the comet per orbit), and the diameter of

the comet. These two parameters have to be known in order to plot any comet

on the diagram.

Additional comets have been added to the original RR versus ML-AGE

diagram (Ferrín et al. 2012; 2013b; 2013c). These objects illustrate the

complexity of the diagram. The complete description of the diagram has been

moved to the Caption of Figure 21.

For a sublimating away comet, the thickness of the layer removed by

appartion should remain constant as a function of time, as can be seen from the

following argument. The energy captured from the Sun depends on the cross

section of the nucleus, π rN2 , on the Bond Albedo, AB, and on the solar

constant, S. A constant fraction of this energy is used to sublimate a volume of

the comet K 4 π rN2 ΔrN . Equating both energies we find that ΔrN should be a

constant:

(1- AB) S π rN2 = K 4 π rN

2 ΔrN (11)

ΔrN = (1- AB ) S / 4 K

and r/Δr would tend to zero as the comet sublimates away. However if the

comet contained much dust, part of it would remain on the surface, Δr would

tend to zero due to soffocation and r/Δr would tend to infinity. Thus,

sublimating away comets tend to zero. Soffocating comets tend to infinity

(confirmation Figure 21, 22).

19

10. EVOLUTIONARY LINES

Comets move on the RR versus ML AGE diagram. It is a work beyond

the scope of this paper, to calculate trayectories on the plot. Models could

show rather complicated behaviour and nonlinear motion, if for example the

pole orientation is changed by jets, as has been seen to take place.

However, it is possible to get a preliminary idea of what this motion might

be, by considering a very simple model of a sublimating comet. The more

complex problem of a suffocating comet, is once again, beyond the scope of

this work.

In Section 9 we have shown that in the case of a surface sublimating with

no dust left on the surface, the surface layer removed should be a constant as a

function of time. Then if we start with a given radius, it is possible to calculate

RR and ML-AGE as a fuction of time, and plot the result in Figure 22. We found

that trayectories are straight lines with negative slope. Suffocating comets have

positive slopes. If the slope is negative, then there will be a time when the

evolutionary line will intersect the RR=1 line, the desintegration line. The

intersection ML-AGE is the Death Age, DA.

In this fashion we find DA(Kohoutek)=1.7E06 cy, DA(NEAT)=1.4E05,

DA(Panstarrs)= 36000cy, DA(Hönig)=6 cy.

One puzzling aspect of this calculation is that comet Hönig reached its

RR=1 line at the early age of DA=6 cy (Figure 22). The youngness of the

comet is confirmed by its eccentricity, e=1.00078, the largest of the whole group

in Table 2, and by the fifth position in Table 4 of a total of 27 comet, in terms of

production rate,.

Sekanina (2002) favors a CO composition, and calculates that the comet

expelled one third of its mass in the event, which in our notation means RR=3.

He concludes: “....the massive outburst of comet Hönig can be explained if the

entire nucleus is assumed to have been engulfed in an explosion caused by a

suddently exposed reservoir of highly unstable ices, typified by carbon

monoxide”. And adds: “The proposed scenario, which of course is ony one of

20

many, envisages that the comet was discovered while in a major persevering

outburst”.

In view of the present investigation, another hypothesis comes forward.

Comet Hönig may have been a very young (pristine) fragment of a hyperbolic

comet coming from or beyond the Oort Cloud, made mostly of CO ice, that

sublimated away as a consequence of its approach to the Sun. This

hypothesis explains a number of features, better than the former one.

10.1 THE SUFFOCATION-SUBLIMATION-BORDER, SSB

Since suffocating comets move upward in the RR versus ML-AGE

diagram, and sublimating comets move downward, there must be an

intermediate value where motion must be horizontal, a suffocation-sublimation-

border. We estimate the border at RR(SB)=(6±5) 104 . Notice the large error.

At the present moment the border is so wide, that for example we do not know

on what side of the border, comet Hale-Bopp is.

10.2 CONVERSION FROM COMET YEARS TO EARTH YEARS

It is easy to convert from comet years to Earth years. For example in the

vertical axis the remaining returns of comet 1P/Halley are RR(1P)= 1158. We

know the orbital period of this comet is 76 years. Thus, assuming the comet

follows the isoline, the extinction date will be 88008 Earth’s years. On the

horizontal axis of the diagram, the isoline intercepts the RR=1 line at

DA(1P)=1.1 106 comet years. Thus the conversion for comet 1P/Halley is 12.5

cy/y.

For comet C/1996 B2 Hyakutake, a=951 AU, PORBITAL= 29300 y. From

Figure 22, the vertical axis tells us that this comet has 272 returns left. That is

8.0 106 Earth’s years. On the other hand the horizontal axis of Figure 22,

tells us that the Death Age is DA(HY)=1.1 105 cy. Thus for this comet the

conversion is 72.5 cy/y.

Once again it must be emphasized, that these calculations are valid only

if comets follow the isolines, which has not yet been demonstrated. For

example comet 2P/Encke does seems to be following an isoline, but comet

103P/Hartley 2, clearly is not (Figure 22).

21

Now we see the advantage of using comet years. Comet years are the

same for all comets, while Earth’ years are not.

10.3 THE DESERT

Figure 22 also clarifies the concept of desert. Observationally, we do

not have any comet plotted in the lower right hand side of the diagram. We

would expect sublimating comets to sublimate away in a time scale much

shorter than for suffocating comets to suffocate.

Theoretically (Figure 22), the suffocation-sublimation border line, will set

a remaining returns value, RR(SSB). This value in turn fixes an isoline, of

several mega-comet years. This line intercepts the RR=1 line at the Dead Age

of that several mega-comet years. This is the lower limit of the desert. There

are not objects above this one, by definition.

At the present moment the comet that sets the limit is 2P/Encke, with a

death age DA= 3.9 109 cy, that is 3.9 109cy<Desert.

However, observationally, the Desert is starting much before, maybe as

low as 1000 cy, thus we have a huge discrepancy. We are not going to

advance any hypothesis to resolve it. One way to resolve the discrepancy is

having more observations.

Clearly, this evolutionary model is simple, incomplete, sketchy and

imperfect. But it shows the virtue of defining DA, and that is an interesting

accomplishment.

Much theoretical work remains to be done, to ellucidate the full meaning

and the limitations, of the RR versus ML-AGE diagram.

11. CONCLUSIONS

The scientific results found in this investigation are:

(1) We reduced 9615 photometric observations of comets C/2011 L4 Panstarrs,

C/2012 S1 ISON, C/1973 E1 Kohoutek, C/2002 O4 Hönig and 1P/Halley, and

we present their secular light curves (SLCs). The first two comets turned on

beyond -10 AU from the Sun. For comparison comet 1P/Halley turned on at R=

-6.2±0.1 AU. Since water ice can not sublimate at distances R<-6 AU, these

22

comets have to contain substances more volatile than water, like CO or CO2.

Spectroscopy could tell.

(2) We measured the Slowdown Event (SDE) of C/2011 L4 Panstarrs (Figure

1). This is the distance at which the brightness increase rate slows down to a

more relaxed pace and it is reminiscent of the same process for comet

1P/Halley and 11 other comets listed in Table 1. We find R(SDE) = -4.97±0.03

AU (or t(SDE)= 2012 04 14±3 d). For comet 1P/Halley R(SDE) = -1.7±0.1 AU.

(3) We derive the absolute magnitude of C/2011 L4 Panstarrs and the power

laws that define its brightness behavior. The absolute magnitude is m(-1,1)=

+5.6 compared with m(-1,1)= +3.7±0.1 for comet 1P/Halley. After passing the

SDE, the comet is increasing its brightness with a shallow power law R+2.24.

The magnitude at perihelion can be measured from the SLC and we find

m(1,q)= -1.2±0.2 giving it entrance to the Great Comet Cathegory (those

comets with negative magnitudes at perihelion). Additionally the comet

exhibited a perihelion surge (Figure 12).

(4) We measured the SDE of C/2012 S1 ISON. We find R(SDE) = -5.07±0.03

AU (which corresponds to 2013 01 17±3 d). Notice the coincidence in value

with C/2011 L4 Panstarrs. We also measure the absolute magnitude. We find

m(-1,1)= +12.7±0.1. Clearly this is an intrinsically faint comet (Figure 13).

(5) Technically speaking, since January 17th±3 d, 2013, comet ISON has been

on a stanstill for more than 132 d, within the same magnitude ±0.2 mag, a

rather puzzling feat (Figure 8). We will present the SLC of comet C/2002 O4

Hönig who also presented a flat light curve and who desintegrated. At

perihelion the orbit enters the Roche Limit of the Sun, and the calculated

temperature is 2919 K. There is a significant probability that comet C/2012 S1

ISON may turn off as comet C/2002 Hönig did, or alternatively, the comet may

desintegrate at perihelion. The future of this comet does not look bright.

(6) A comparison of two estimates of water production rate by Schleicher (2013)

with a calibration by Jorda, Crovisier & Green (2008), reveals that comet ISON

is depleted in water content by a factor of 9.2, aproximatelly (Figure 20).

(7) An estimate of the water budget of these two comets allows the calculation

of the water-budget age, WB-AGE, and of their Remaining Returns, RR (Figure

21). The comets lie in the RR versus mass-loss age, ML-AGE, diagram, in the

23

region of the Oort Cloud comets (the left part of the diagram). To cover the

whole range of possibilities for comet ISON, we show the result for two WBs

(4.2E09 to 6.3E09 kg), two radii (0.335 to 2.0 km), and one δ (dust to gas mass

ratio) (δ =0.5). It is found that the location on the diagram does not change by

much. The diagram is forgiving, and the results are robust.

(8) For comparison we present the SLC of comet C/1973 E1 Kohoutek, the

famous comet that fizzled, and show reasons to conclude that it didn’t. We also

show the SLC of comet C/2002 O4 Hönig, a comet with a leveled off light curve

that desintegrated.

(9) If the SDE represents the change over from CO2 to H2O controlling

substance, then there should be a corresponding SDE for the change over CO

to CO2 controlling substance. We would expect this change to take place far

away from the Sun (R<-10AU). Thus we predict the existence of another SDE,

but this time due to the CO/CO2 transition.

(10) Table 1 and Figure 16 allow us to define the Jupiter Family Interval of

Comets, as 1.24<R(SDE)<2.09 AU. This is a narrow Interval in which 5

comets from the Oort Cloud and 6 comets from the JF, have their SDEs, for

reasons unknown.

(11) Figure 22 allows the determination of the Death Ages of several comets,

assuming they will continue evolving along an isoline. We have measured

DA(KO)=1.7E06 cy, DA(V1)=1.4E05, DA(L4)= 36000cy, DA(Hö)=6 cy.

(12) Since suffocating comets move upward in the RR versus ML-AGE diagram,

and sublimating comets move downward, there must be an intermediate value

where motion must be horizontal, a suffocation-sublimation-border. We

estimate the border at RR(SB)=(6±5) 104 . At the present moment the border

is so wide, that for example, we do not know on what side of the border, comet

Hale-Bopp is.

(13) The Desert of Comets is the right hand, lower part of the diagram were we

should expect to find few or none comets. We measure a theoretically value for

the start of this region at 3.9 109cy<Desert. However, observationally, the

Desert is starting much before, maybe as low as 1000 cy, thus we have a

discrepancy. Clearly more observations are needed.

24

(14) There are many questions to be answered that have to deal with the RR

versus ML-AGE diagram. However, one single question may be representative:

Is it possible to calculate an evolutionary model containing all important physical

phenomena, capable of predicting the long term motion of comets in the

diagram? In particular, why is comet 103P moving in that particular direction,

60º to the isolines?

ACKNOWLEDGEMENTS

Thanks to hundreds of observers (impossible to acknowledge all of them

here), seeking faint specs of diffuse light, at odd hours of the night. We thank

CODI of the University of Antioquia for their support through project E01592.

25

REFERENCES

Biver, N., Bockele-Morvan, D., Moreno, R., Crovisier, J., Hartough, P., de Val Borro, M., Kidger, M., Kueppers, M., Szutowicz, S., Lis, D.C., Blake, G.A., 2012. CBET 3230. Combi, M.R., Makinen,J.T.T., Bertaux, J.L., Quemerais, E., Ferron, S., Fougere, N., 2013. Icarus, in press. de Almeida, A.A., Trevisan Sanzovo, D., Sanzovo, G.C., Boczko, R., Miguel Torres, R., 2009. Advances in Space Research, 43, 1993-2000. Ferrín, I., 2005a, Paper I. Icarus 178, 493-516. Ferrín, I., 2005b. ICQ 27, 249-255. Ferrín, I., 2006. Icarus, 185, 523-543. Ferrín, I., 2007. Icarus, 187, 326-331. Ferrín, I. 2008. Icarus, 197, 169-182. Ferrín, I., 2010, Paper II. PSS, 58, 365-391.

http://arxiv.org/ftp/arxiv/papers/0909/0909.3498.pdf Ferrín, I., 2010. PSS, 58, 1868-1879. Ferrín, I., Hamanova, Hiromi, Hamanova, Hiroko, Hernandez, J., Sira, E., Sanchez, A., Zhao, H., Miles, R., 2012. PSS, 70, 59-72. Ferrín, I., Zuluaga, J., Cuartas, P., 2013a. MNRAS, in press. Ferrín, I., 2013b. Submitted for publication. Ferrín, I., 2013c. Submitted for publication. Green, D.W., 2013. Cometary Science Archive.

http://www.csc.eps.harvard.edu/index.html . Jorda L., Crovisier J., Green D.W.E., 2008. Paper presented at the Asteroids, Comets, Meteors Conference, (ACM), 8046.pdf. Nevsky, V., Novichonok, A., 2012. CBET 3228. Opitom, C., Jehin, E., Manfroid, J., Gillon, M., 2013. CBET 3444. Sekanina, Z., 2002. ICQ, 24, 223-236. Schleicher, D., 2013a. CIAU 9254. Schleicher, D., 2013b. CIAU 9254. Wainscoat, R., Micheli, M., 2011. IAUC 9215.

26

Figure 1. The secular light curve (SLC) of comet C/2011 L4, log plot, MPCOBS data. The data shows a clear SDE at R(SDE)= -4.97±0.03 AU, which corresponds to 20120414±3 d. The slopes before and after SDE are measured. The nuclear line is calculated assuming Asec(Limit)= 11.6 (Ferrín 2013), and sets a lower limit to the diameter of the nucleus, D>2.4 km. Since the photometric age is small (P-AGE>2.8 cy), it is reasonable to assume that it is sublimating from 100% of its surface area. Thus D>2.4 km is a good lower limit to the diameter.

27

Figure 2. SLC of C/2011 L4 Panstarrs, Log plot, CCD compared to visual

data. The plot shows that the difference MPCOBS/CCD/R-VISUAL is different

before than after perihelion. This is clear evidence of the insufficient CCD

aperture error (Paper II). The difference is larger after perihelion because the

comet was larger in size and thus the whole flux could not be captured by CCD

observations. Data bases like MPCOBS contain measurements that are a

byproduct of astrometry. Photometric measurements are encapsulated in the

software, using fixed and small apertures that do not capture the whole flux.

28

Figure 3. SLC of C/2011 L4 Panstarrs, Log plot, Visual compared to CCD

data. CCD observations still show a significant difference with visual data.

The differece, however, is smaller than with the MPCOBS data. This data also

shows the SDE, but due to scatter, it is not possible to derive a precise date for

the event.

29

Figure 4. Number of observations of comet C/2012 S1 ISON versus Elongation angle, E. The data comes from the MPCOBS database. The number of observations decreases as the comet gets nearer to the Sun, and observing conditions become more difficult. This is the reason to believe that the photometric data sets used in this work, are essentially complete.

30

Figure 5. Comet C/2012 S1 ISON, CCD uncorrected data versus time. The slowdown event is clearly seen. The upper plato has a value R(Δ,R)=15.2±0.1. The SDE measured from this plot is t(SDE)=2013 01 12±3 d.

31

Figure 6. Comet C/2012 S1 ISON, cometas-obs CCD data, averaged daily.

This data set shows an increase in brigthness at the end of the period. This is

not confirmed by the other data sets that show a leveled off activity. The slight

increase may be an effect due to the diminishig elongation and solar

background contamination, instead of a real effect. It seems as if the comet

may have overshoot its activit, at the SDE, t(SDE)= 2013 01 08±3 d.

32

Figure 7. Comet C/2012 S1 ISON, visual data. Only 9 visual observations

are available, due to the faintness of the comet and the fact that after it

transversed a field congested with star, it moved into the Sun’s glare. This plot

shows the inner sanctum, the region of visual observations with magnitudes

around and fainter than 15th. The inner sanctum was visited by 6 deep sky

comet observers.

33

Figure 8. Comet C/2012 S1 ISON, MPCOBS data in time format. The SDE

is clearly detected on 2013 01 09±1 d. Notice that after the event, the comet

remained with its magnitude virtually unchanged for 128 d, with no suggestion

of changing within ±0.2 mag. Before the SDE, sublimation was controlled by

CO2. At SDE, water took over and now controlls sublimation. The standstill of

the comet can only imply that the nucleus is depleted in water. It could be rock,

dust or debris under the surface, but with little or no water.

34

Figure 9. Comet C/2012 S1 ISON, MPCOBS data in log format. From this

Figure the location of the SDE can be measured and the power laws calibrated.

SDE took place on 2013 01 17±3 d. Notice the shallow brightness increase (or

no increase) after the event. Actually it is a decrease in brightness, since the

power law is less than +2.0.

35

Figure 10. Comet C/2012 S1 ISON, full scale. The data points cover a small space of the plot and so predictions are difficult and risky. There is still a long way to go to reach perihelion, and the comet could pick up on brightness. O the other hand, it could also turn off completelly like in the case of comet C/2002 O4 Hönig (Sekanina, 2002), that desintegrated in view of observers, while reaching to perihelion. There is an upper limit to the diameter of the comet due to Li et al. (2013) of 4.0 km that also sets an upper limit to the photometric age, P-AGE<10 cy, a young comet. If we assume that Asec(Limit)=11.6, then we can set a lower limit V(1,1,0)=23.8 that corresponds to D=0.12 km. However with this limit the comet is younger (P-AGE=1.3 cy) than comet Hale-Bopp (2.3±0.2 cy), which is improbable since this comet is not so bright. Thus this lower limit it too low and it is not applied. If we impose the condition that the turn on point can not be farther away than the turn on point of comet Hale-Bopp (Ron= -16.8 AU) then we can set a lower limit to the diameter of the nucleus of this comet, V(1,1,0)=20.0, that corresponds to a nucleus of D=0.67 km, and a P-AGE=3.4 cy, older than comet HB. Using the upper and medium limits, the turn on point is restricted to -16.8<Ron<-13.5AU, the amplitude restricted to 5.5<Asec(-1,1) <8.1, and the photometric age is restricted to 3.4<P-AGE<6 cy. However these numbers are valid only if it continues behaving as predicted, which is doubfull.

36

Figure 11. The SLC of comet C/2002 O4 Hönig, log plot. The comet has a SDE at R(SDE)= -1.26±0.06 AU, m(SDE)=7.9±0.1 with m(-1,1)= +7.8±0.1. The horizontal line shows that the comet desintegrated in a time span of 50 d.

37

Figure 12. The SLC of comet C/1973 E1 Kohoutek, the famous comet that

fizzled. The comet was discovered with a power law R+5.78 which would have

produced a bright comet at perihelion, were not for the SDE at R(SDE)= -1.95

±0.05 AU, m(SD)= +6.5±0.1. Even so the comet reached magnitude m(1,q) =

-2.0 at perihelion, giving it entrance to the Great Comet Cathegory (comets with

negative magnitude at perihelion). So it did not really fizzled. The nucleus line

in the form of a pyramid has been drawn assuming that Asec=11.6, a maximum

limit found for other comets (Ferrín, 2013).

38

Figure 13. The secular light curve of comet C/2012 S1 compared with that

of comet 1P/Halley and comet C/2002 O4 Hönig. A number of features can

be discerned. The turn on distance of C/2012 S1 is much farther away than

that of 1P. All three comets exhibit SDEs. This diagram shows clearly that

predicting the future light curve of ISON is difficult, because the comet still has a

long way to go, and additionally, it has remained at a standstill for ~132 d since

January17th±3 d, 2013 up to June 19th, 2013, a four month interval. The

perihelion distance is q=0.124 AU and the perihelion time 131128.

39

Figure 14. A m(1,1) versus n Diagram for Comets. Or the Pre-SDE versus

Post-SDE versus Oort Cloud versus JF comets diagram. The values measured

in Table 3 are plotted here. They separate Pre and Post-SDE events, and Oort

Cloud Comets versus Jupiter Family comets into 4 regions. In particular the

Pre-Post SDE of Oort Cloud comets, are clearly separated.

40

Figure 15. Another way to analyze the Pre-SDE and Post-SDE slopes of the power law. In this plot the Pre-SDE n is compared with the Post-SDE n. The two groups, Oort Cloud comets and Jupiter Family comets, are clearly separated. Oort Cloud comets have n-post-SDEs smaller thant JF comets, while the n-pre-SDE values are about the same. The data comes from Table 3.

41

Figura 16. The Slowdown Magnitudes of 14 comets are plotted versus

their slowdown distances from Table 2. 11 of 14 (79%) lie in a narrow

vertical interval centered at R(Interval)= -1.68±0.07 AU. Two comets (C/2011

L4 Panstarrs and C/2012 S1 ISON) lie in the middle of the diagram, and

another (C/1995 O1 Hale-Bopp) lies to the extreme left. This Figure and Table

1 allow us to define the Jupiter Family Interval of Comets, as

1.24<R(SDE)<2.09 AU. Inside this Interval there are 5 Oort Cloud comets and

6 JF comets. The interval has a width of 0.85 AU, while typical measuring

errors are ±0.07 AU. Thus individual differences appear significant. The

Interval may represent the changeover from CO2 to H2O controlling of the

surface sublimation. It is not yet clear if the other three comets represent the

CO to CO2 change over.

42

Figure 17. The water production rate in comet C/2009 P1 Garradd is shown

near 2 AU pre-perihelion, as a function of aperture size (data from Combi et al.,

2013). The flux increases asymptotically as aperture increases, allowing the

definition of infinite aperture water production rates. This is one reasons why it

is advisable to adopt the envelope of the water production rate measurements,

as the correct interpretation of the data. See text for additional reasons.

43

Figure 18. The Dust to Gas Mass Ratio, δ. The data for 4 comets (1P, 46P,

67P, and C/1996 B2), from de Almeida et al. (2009), shows that the dust to gas

mass ratio, δ, is constrained to 0.1<δ<1.0. The ratio δ = 0.5, describes quite

well the general tendency over 5 orders of magnitude, and it is adopted in this

work. However, Figure 21 will show that the location of a comet in the RR

versus ML-AGE diagram, is insensitive to the δ ratio.

44

Figure 19. Water calibration of comet C/2011 L4 Panstarrs. Only two data

points are available, however they agree quite well. The water production rate

by Jorda, Crovisier & Green (2008) has been scaled down, but the slope has

been preserved.

45

Figure 20. Water calibration of comet C/2012 S1 ISON. The two data points are due to Schleicher (2013), while the solid line is the calibration by Jorda, Crovisier & Green (2008). This plot suggests that comet C/2012 S1 is depleted in water with respect to other comets by a factor of 9.2. We adopt the slope of Jorda, Crovisier & Green (2008) but move the production rate down by that amount.

46

Figure 21. Remaining Returns versus Mass-Loss Age diagram. Nomenclature: 1P=1P/Halley. KO=C/1973 E1 Kohoutek. P1=C/2009 P1 Garradd. V1=C/2002 V1 NEAT. HB=C/1995 O1 Hale=Bopp. L4=C/2011 L4 Panstarrs. HY=C/1996 B1 Hyakutake. Hö=C/2002 O4 Hönig. (1) The diagram covers a large area: 8 orders of magnitudes in the vertical, 6 in the horizontal axis. (2) If the comet were made of pure ice, the layer removed by apparition would remain approximatelly constant (see demonstration in the text, Section 9), and r/Δr would tend to zero as the comet sublimates away. If the comet contained much dust, part of it would remain on the surface, Δr would tend to zero and r/Δr would tend to infinity. Thus sublimating away comets move down, suffocating comets move up. (3) The location of a comet is not sensitive to the dust to gas mass ratio, δ. The error bars represent the limits 0.1< δ<1.0. (4) Four comets are being suffocated: 107P, 133P, 3200 and 2006 VW139. (5) 2006 VW139 is the most extreme object in the upper right hand corner. (6) Five comets belong to the graveyard in this definition (1000 cy < P-AGE), 107P, 133P, D/1891W1 Blanpain, 2006 VW139 and 3200 Phaeton. The location of 3200 is plotted for three diameters of the dust particles, 1.0 mm, 0.1 m and 0.01 mm. It is not surprising that ABCs occupy the upper right hand corner of the diagram. This is expected on physical grounds. The diagram says that they are old (large ML-AGE) and that they have a substantial dust or crust layer (large r/Δr ). (7) The diagram separates comets into classes: Oort Cloud comets on the left, Jupiter Family comets in the middle and asteroidal belt comets, ABCs, above right.

47

(8) Comet 2P/Encke shows evolution of the parameters between the 1858 and the 2003 apparitions. Comet 103P shows evolution between the 1991 and the 2010-11 apparitions (Ferrín et al., 2012). Comet 39P jumped in position due to an orbital change. Comets evolve from the left side toward the right side as they age. If they move up they are choked by a dust crust. If they move down they sublimate away. If they move toward the left, they rejuvenate. If they are in the graveyard and move toward the left, they become Lazarus Comets (Ferrin et al. 2013a). If they approach RR=1, they desintegrate. If they are scattered, they jump. Thus RR versus ML-AGE, is an evolutionary diagram. (9) The 39P jump. Comet 39P had a close encounter with Jupiter in 1963 and the orbit changed substantially. Fortunatelly we know the SLC quite well (Paper II), and not only it is possible to estimate the old mass loss but also estimate the future mass loss. The comet jumps in the diagram due to the orbital change. (10) There should be a comet desert in the lower right hand side of the diagram. We expect comets to sublimate away in a time scale much shorter than would take for a comet to suffocate, thus we do not expect to find comets sublimating away in that region. No objects are found plotted in that area. (11) Since the diagram is log-log and covers 8 and 6 orders of magnitude in the Y and X axis, the diagram is very forgiving. A factor of 2 error in any of the two variables changes the location of the data point by less than an order of magnitude. (12) RR=1 is the desintegration limit. The comet nearer the desintegration limit is C/2002 O1 Hönig, which in fact desintegrated (Sekanina, 2002). (13) For comet ISON we show the results for two WBs (6.8E06 to 1.07E07 kg), two radii (0.34 to 1.0 km), and one δ (δ=0.5). The comet is the oldest of the Oort Cloud group.

48

Figure 22. Evolutionary Paths. In this simple model, the layer removed from the cometary nucleus is constant as a function of time (Section 9). Then the evolutionary lines are straight lines of negative slope. These lines will intercept the RR=1 line, the desintegration line, at the Death Age, DA. The death ages of several comets have been measured. We find, DA(KO)=1.7E06 cy, DA(V1)=1.4E05, DA(L4)= 36000cy, DA(Hö)=6 cy. Comet 2P/Encke is following an isoline, but comet 103P/Hartley 2, is not. The model predicts DAs in the graveyard region. Since not objects have been found in this region up to now (0/27 or <3.6%), the question is if this is an observational bias, or if there is a mechanism that derails the isoline. The location of the suffocation-sublimation-border (SSB), is estimated at RR(SSB)=(6±5) 104. It is not known on what side of the border comet Hale-Bopp is.

49

Table 1. Slowdown Event of comet C/2012 S1 ISON,

measured from different data bases.

DATABASE->

PARAMETER

CCD MPCOBS-

CCD-TIME

MPCOBS-

CCD-LOG

VISUAL COMETAS-

OBS-CCD

T(SDE) 2013 01 12 2013 01 09 2013 01 17 <2013 01 12 2013 01 08

Δt (SDE)= t - Tq -320±1 -323±1 -312±1 <-320 -324±1

R(SDE)(AU) -5.15±0.03 -5.18±0.03 -5.07±0.03 ----------- -5.19±0.03

R(Δ,R)(SDE) 15.2±0.1 15.4±0.1 ------------ ----------- 15.7±0.1

m(1,R)(SDE) 12.3±0.1 12.5±0.1 12.4±0.1 ----------- 12.8±0.1

V(Δ,R)(SDE) ------------ -------------- ------------- 15.1±0.1 -----------

Table 2. Distances, magnitudes at Slowdown,q,e,i,Tiss. ----------------------------------------------------------------

R(SDE) m(SDE) q e i Tiss Comet

-1.26 8.0 0.776 1.000795 73.1 0.31 C/2002 O4 Hönig

-1.8 8.9 0.316 1.000240 119.9 0.00 C/1956 R1 Arend-Roland

-4.97 10.6 0.302 1.000028 84.3 0.00 C/2011 L4 Panstarrs

-1.56 7.55 0.171 1.000018 77.1 0.00 C/2006 P1 McNaught

-1.96 6.4 0.142 1.000008 14.3 0.00 C/1973 E1 Kohoutek

-5.08 12.5 0.012 1.000004 62.1 0.00 C/2012 S1 ISON

-1.39 7.6 0.099 0.999903 81.7 0.06 C/2002 V1 NEAT

-1.7 6.73 0.230 0.999758 124.9 -0.33 C/1996 B2 Hyakutake

-6.29 4.82 0.914 0.994929 89.4 0.04 C/1995 O1 Hale-Bopp

-1.68 5.55 0.586 0.967813 162.3 -0.61 1P/Halley

----------------------------------------------------------------

-1.57 10.6 1.031 0.707045 31.9 2.46 21P/Giacobinni-Zinner

-1.24 9.38 1.059 0.694533 13.6 2.64 103P/Hartley 2

-1.8 16.3 1.057 0.659295 11.7 2.81 46P/Wirtanen

-1.9 10.0 1.598 0.537385 3.2 2.88 81P/Wild 2

-2.09 13.81 1.509 0.516946 20.5 2.90 9P/Tempel 1

----------------------------------------------------------------

* JF-Box,-1.24<R(SDE)<-2.09 AU or <R>= -1.70±0.08 AU, N=12

50

Table 3. Absolute magnitudes, P-AGEs and power laws

-------------------------------------------------------

Comet P-AGE3 m(-1,1) n in R^n

(cy) PreSDE PostSDE

-------------------------------------------------------

Oort Cloud

-------------------------------------------------------

C/2002 O4 Hönig +7.9±0.5 13.7 +3.28

C/1956 R1 AR +6.3±0.1 +7.2 +4.0

C/2011 L4 Pan +6.7±0.1 +8.7 +2.24

C/2006 P1 McN 11< +5.2±0.1 +10.6 +1.55

P/1973 E1 Koho +5.6±0.1 +5.8 +2.49

C/2012 S1 ISON +12.7±0.1 +5.6 +0.172

C/2002 V1 NEAT 15< +6.7±0.1 +13.0 +3.37

C/1996 B2 Hyak 18 +4.8±0.1 +11.6 +2.33

C/1995 O1 HB 2.4 -0.6±0.1 +10.7 +2.58

1P/Halley 7.1 +3.9±0.1 +8.9 +3.35

-------------------------------------------------------

Jupiter Family

-------------------------------------------------------

21P 22 +8.0±0.1 +9.1 +5.16

103P 14 +8.3±0.1 +9.5 +5.55

46P 15 +7.6±0.1 +5.2 +7.20

81P 13 +5.8±0.2 +9.3 +7.03

9P 22 +6.4±0.2 +7.7 +6.50

-------------------------------------------------------

1 Comet C/2011 L4 has the smallest Post SDE n value

of the whole sample.

2 C/2012 S1 has the smallest rate of increase Post SDE

of the whole sample.

3 It is evident from column P-AGE that comets with

SDE have P-AGE<25 cy.

51

Table 4. Water budget, WB, water budget age, WBAGE, Remaining

Returns, RR=rN/ΔrN,δ=M(dust)/M(gas).WB-AGE[cy]=3.58E+11/WB

[kg], WB/WB(1P)=WB/4.51E11 kg

Comet

WB [kg]

WB-

AGE

[cy]

WB

----- %

WB(HB)

rN [km]

ΔrN[m]

δ=0.5

RR

δ=0.1

RR

δ=1

RR

δ=0.5

C/1995O1 Hale-Bopp 2.67E+12 0.13 100 27 0.82 44600 24550 32732

29P/SW 1 5.60E+11 0.63 20.9 15.4 0.53 3.9E4 2.2E4 2.9E4

29P/SW 1 5.60E+11 0.63 20.9 27.7 0.16 2.3E5 1.3E5 1.7E5

1P/Halley 4.51E+11 0.79 8.4 4.9 4.2 1580 868 1158

C/1996B2 Hyakutake 2.25E+11 1.6 8.4 2.4 8.8 370 204 272

C/2002 O4 Hönig4

1.50E+11 2.2 6.2 0.35 303 1.7 10 6

C/2002 O4 Hönig4

1.50E+10 24 3.3 0.35 27.6 17 10 12

C/2009 P1 Garradd 1.42E+11 2.5 5.3 8.9 0.40 3.0E4 1.7E4 2.2E4

109P/Swift-Tuttle 1.29E+11 2.8 4.8 13.5 0.15 115500 63500 84685

C/2002 V1 NEAT 1.10E+11 3.3 4.1 1.7 8.6 247 135 198

C/2011L4 Panstarrs 7.60E+10 4.7 2.8 1.2 11.9 138 75 101

C/1973E1 Kohoutek 5.50E+10 6.5 2.1 1.9 3.4 755 415 553

65P/Churyumov-Gera 3.06E+10 12 1.1 3.7 0.50 10020 5500 7349

19P/Borrelly 2.17E+10 16 0.81 2.25 0.96 3178 1748 2330

81P/Wild 2 2.09E+10 17 0.78 1.97 1.2 2200 1200 1624

103P/Hartley2

19911

1.41E+10 25 0.52 0.57 7.4

δ=0.135

85

δ=0.02

70

δ=0.25

77

δ=0.135

103P/Hartley2

2010-20111

2.24E+09 160 0.084 0.57 1.2

δ=0.135

539

δ=0.02

440

δ=0.25

485

2P/Encke 2003 8.58E+09 42 0.32 2.55 0.30 11700 6436 8580

2P/Encke 1858 1.28E+10 28 0.47 3.20 0.28 15500 8525 11367

9P/Tempel 1 1.27E+10 28 0.47 2.75 0.38 9900 5450 7270

45P/H-M-P 7.95E+09 45 0.30 0.43 9.7 60 33 44

96P/Machholz 6.55E+09 55 0.25 3.2 0.14 3.0E4 1.7E4 2.2E4

46P/Wirtanen 4.01E+09 90 0.15 0.60 2.5 327 180 239

28P/Neujmin 1 3.58E+09 100 0.14 11.5 0.006 2.6E06 1.4E06 1.9E6

26P/Grigg-Skejelle 1.64E+09 218 0.061 1.47 0.017 11700 6450 8600

133P/Elst-Pizarro 1.81E+08 1978 6.8E-3 2.3 0.007 4.0E05 2.2E05 2.9E5

107P/Wilson-Harrin 2.03E+07 1.7E4 6.8E-4 1.65 0.0017 1.3E6 7E5 9.8E5

D/1819W1 Blanpain 1.40E+07 2.6E4 5.1E-4 0.16 0.0012 1770 970 1300

2006 VW139 4.00E+06 8.9E4 1.5E-4 1.8 2.8E-4 8.8E6 4.9E6 6.5E6

C/2012S1ISON3 6.30E+09 57 0.24 2.0 0.35 7688 4228 5638

C/2012S1ISON 4.21E+09 85 0.16 2.0 6.0E-4 11532 6343 8457

C/2012S1ISON 6.30E+06 57 0.24 0.34 12.3 37 21 27

C/2012S1ISON 4.21E+09 85 0.16 0.34 8.2 56 31 41

3200Phaeton2(dust) 4.00E+08

895 0.015 2.5 1.4E-2 ----- 2.6E5 1.7E5

3200Phaeton2(dust) 4.00E+07 8950 0.0015 2.5 1.4E-3 ----- 2.6E6 1.7E6

3200Phaeton2(dust) 4.00E+06 89500 0.00015 2.5 1.4E-4 ----- 2.6E7 1.7E7

0. N(comets)= 27.

1. For comet 103P Sanzovo et al. (2010) found 0.02 < δ < 0.25

2. For comet 3200 Phaeton, Li and Jewitt (2013) find only a dust

ejection. For this comet we do not calculate a water-budget age

but a mass-loss age.

3. For comet ISON we show the results for two WBs (6.8E06 to

1.07E07 kg), and two radii (0.335 and 1.0 km).

See text.

4. Since comet C/2002 O4 Hönig actually desintegrated (Sekanina, 2002)

we picked the lowest value, RR=1.7.