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in the last ten years the existence of supermassive black holes in the central part of an increasing number of galaxies has become a stronger and stronger evidence . in order to understand the formation process and the evolution of those black holes , it is important to relate them to the properties of the host galaxy .
it was shown that the existence of a central smbh affects the dynamics not only in the core of the host galaxy but even in a region far from the hole .
several relationships have been recently proposed between the mass of a central smbh and the velocity dispersion @xcite , the bulge luminosity or mass @xcite or the dark matter halo @xcite , of the corresponding galaxy . among them , the relationship with the smallest scatter is @xmath4 where @xmath5 .
the different values of @xmath6 , found by several authors using different samples and different fitting methods , are well discussed in the paper of tremaine et al .
@xcite that obtain @xmath7 where ( and also afterwards in the rest of our paper ) @xmath8 is expressed in solar masses , @xmath9 in @xmath10 and logarithms are base 10 .
from the theoretical point of view there are still different interpretations of these results @xcite and in order to give a contribution to this open debate , in a previous paper @xcite , we proposed to study a relationship between the kinetic energy of random motions of elliptical galaxies and the rest energy of their central supermassive black hole .
we used a sample formed by the intersection between the set of galaxies studied by tremaine et al . @xcite and the kinematical data extracted by @xcite that refer to the effective semimajor axis of each galaxy @xmath11 ( related to the effective radius @xmath12 by the formula @xmath13 where @xmath14 is the ellipticity ) .
the model used to compute the kinematical parameters is very simple .
busarello , longo and feoli @xcite assumed that an elliptical galaxy    1 .   has a spheroidal symmetry , 2 .
follows the de vaucouleurs @xmath15 law , 3 .
its rotation axis is perpendicular to the line of sight , 4 .
its stars have a rotation velocity with cylindrical symmetry and 5 .
its velocity dispersion tensor is isotropic and has spherical symmetry .
the details of the procedure used to compute velocity dispersions , rotation velocities and the masses of the 13 elliptical galaxies included in the so called sample a ( see table 1 ) were fully explained in @xcite and summarized in our previous paper @xcite ( hereafter afdm ) .
our first results were very encouraging because we found , taking into account errors in both variables and using an iterative procedure due to orear @xcite : @xmath16 with ( see appendix for definitions ) @xmath17 and with a linear correlation coefficient @xmath18 .
if the akritas and bershadi method @xcite is used , the slope of the relationship is even closer to unity : @xmath19 with @xmath20 .
even better results can be obtained using a reduced sample ( hereafter sample b ) of galaxies if we eliminate the two ellipticals with the largest residuals n821 and n4697 .
the relationships obtained applying the fitting procedure to the remaining 11 galaxies are listed in afdm .
the satisfying results are the increase of the correlation coefficient , the decrease of @xmath21 , and a slope closer to unity .    in order to understand better the origin of this relationship
, we have performed in this paper four new tests :    1 .
we used the well known iterative procedure of fitexy routine ( we had never used before ) to analyze again the same samples a and b of the previous paper afdm in the case of errors in both variables ; 2 .
the simplest hypothesis of a linear relationship was tested using the exact `` least - squares '' fitting method ; 3 .
the kinematical data used in the previous paper were extracted by old sources so we have performed a check of the relationship using the data recently published by hring and rix @xcite .
4 .   in afdm
we have considered only elliptical galaxies . in this paper
we tested the robustness of the relationship , including in the statistical analysis also the lenticular and spiral galaxies of the sample published by hring and rix @xcite .
there is another remarkable novelty contained in this paper .
actually in afdm we found a very poor correlation between the mass of the galaxy and its velocity dispersion . on the contrary with the sample of hring and rix @xcite
this relationship is stronger and we will show that if @xmath22 and @xmath23 then ( as we expected ) a relation @xmath24 is such that @xmath25 furthermore , using the new data , we will show that the equation ( 7 ) has a @xmath21 smaller than the relation ( 6 ) .
.we list in column ( 1 ) the name of the galaxy , in column ( 2 ) the black hole masses taken from tremaine et al .
the velocity dispersions ( column 3 ) and the rotation velocities ( column 4 ) are taken from busarello , feoli and longo @xcite , the masses in column ( 5 ) from curir et al.@xcite and the corresponding relative errors in column ( 6 ) from busarello and longo @xcite .
the sources of the experimental data for each galaxy are listed in the above mentioned papers . [ cols="^,^,^,^,^,^ " , ]     the results are listed in table 5 and we argue that for the sample b the hypothesis is certainly right , and for the samples a and @xmath26 it can be acceptable . only the samples @xmath27 and c have a too high @xmath21 .
the linear fit of sample c is shown in fig .
1 with a dashed line and involves @xmath28 .
the fourth test for our relationship is the inclusion of lenticular and spiral galaxies in the statistical analysis .
our sample d is now composed by all the 29 galaxies listed in table 2 . in fig .
3 we show with a dashed line the best fit ( 11 ) for the 18 ellipticals ( denoted with boxes ) , with the dot - dashed line the best fit for the remaining 11 galaxies ( denoted with circles ) : @xmath29 and with a solid line the best fit for the whole sample d @xmath30 we argue that the contribution of lenticular and spiral galaxies increases the slope that becomes closer to unity .
from the first samples of data ( a and b ) we were induced in a previous paper @xcite to consider a relationship between the masses of smbhs and the kinetic energy of random motions in elliptical galaxies . this suggestion
is now confirmed first by reanalyzing the old data using the fitexy routine and then comparing the results with the corresponding fit of a new set of kinematical data extracted from the paper of hring and rix @xcite . in the light of fig .
3 we show that the relationship works well also for lenticular and spiral galaxies .
the remarkable result is that the relationship we proposed ( 7 ) , has now a smaller scatter with respect to the old equation ( 6 ) and the @xmath8 vs @xmath31 law .
furthermore we have shown that , using the new data , all these relationships can be strictly connected because ( unlike afdm ) the mass of the galaxy strongly depends on the velocity dispersion : the linear correlation coefficient of this relationship ( 8) is very high and the @xmath21 very low .
finally our result ( 14 ) with @xmath32 is surprisingly smaller than the ones expected of @xmath33 or @xmath34 .    for the sample
a and b , given the assumptions of the model of busarello , longo and feoli @xcite , it is clear that triaxiality , anisotropy of the velocity field , inclination , deviations from the @xmath15 law , are all sources of possible errors that could affect the derived kinematical parameters . for the remaining samples we must consider that the masses are not computed with the same method and
often refer to a bulge region that ends to @xmath35 . at the same time
all the velocity dispersions are no longer averaged until the effective semimajor axis of each galaxy .
so the nonhomogeneity of the measurements and the differences in the part of the galaxy that each single measure now considers , can affect also the results obtained with the new set of data .
of course a rigorous analysis will be possible only when the observational uncertainties in all quantities are reduced and the sample is further extended .
however , though with the caution due to all these possible error sources , the study of the relationship we propose between the rest energy of a smbh and the kinetic energy of random motions of the host galaxy appears to be very useful for a more complete understanding of the formation and evolution of smbh not only in elliptical galaxies .
we are grateful to gaetano scarpetta , antonio donofrio and nicola de cesare for useful comments and franco caprio for helpful suggestions about computer programs . the research was partially supported by far fund of the university of sannio .
l. ferrarese and d. merritt , _ astrophysical journal _ * 539 * , l9 ( 2000 ) .
k. gebhardt et al .
, _ astrophysical journal letter _ * 539 * , 13 ( 2000 ) .
s. tremaine et al .
, _ astrophysical journal _ * 574 * , 740 ( 2002 ) .
j. kormendy and d. richstone _ annual review of astronomy and astrophysics_*33 * , 581 ( 1995 ) ; j. magorrian et al . ,
_ astronomical journal _ * 115 * , 2285 ( 1998 ) ; a. marconi et al . , in iau symp .
205 , _ galaxies and their constituents at the highest angular resolutions _ , ed .
r. t. schilizzi , s. vogel , f. paresce and m. elvis , ( s.francisco : astronomical society of the pacific . ) , 58 , ( 2001 ) d. merritt and l. ferrarese , in aps conf .
249 , _ the central kpc of starbursts and agn _ , ed . j. h. knapen , j.e .
beckman , i. shlosman and t.j .
mahoney , ( san francisco : astronomical society of the pacific ) , 335 , ( 2001 ) n. hring and h. rix , _ astrophysical journal letter _
, * 604 * , l89 , ( 2004 ) d. richstone et al . ,
_ nature _ , * 395 * , a14 , ( 1998 ) r. p. van der marel , in iau symp .
186 , _ galaxy interactions at low and high redshift _ , ed .
d. b. sanders and j. barnes , ( dordrecht : kluwer academic publishers ) , ( 2002 ) l. ferrarese , _ astrophysical journal _ , * 578 * , 90 , ( 2002 ) a. burkert and j. silk , _ astrophysical journal _ , * 554 * , l151 , ( 2001 ) v. i. dokuchaev and yu .
n. eroshenko , preprint ( astro - ph/0209324 ) , ( 2002 ) m. g. haehnelt and g. kauffmann , _ monthly notices of the royal astronomical society _ , * 318 * , l35 , ( 2000 ) f. c. adams , d. s. graff and d. o. richstone , _ astrophysical journal _ , * 551 * , l31 , ( 2000 ) a. feoli and d. mele , _ international journal of moden physics d _ , * 14 * , 1861 , ( 2005 ) g. busarello , g. longo and a. feoli , _ astronomy and astrophys . _ , * 262 * , 52 , ( 1992 ) g. busarello and g. longo , _ morphological and physical classification of galaxies _ , eds . g. longo et al .
( dordrecht : kluwer academic publishers ) , 423 , ( 1992 ) a. curir , f. de felice , g. busarello and g. longo , _ astrophys .
letter commun .
_ , * 28 * , 323 , ( 1993 ) orear , j. 1982 , _ american journal of physics _ ,
* 50 * , 912 , ( 1982 ) m. g. akritas and m. a. bershadi , _ astrophysical journal _ , * 470 * , 706 , ( 1996 ) g. de vaucouleurs et al .
, _ third reference catalogue of bright galaxies _ , ( berlin heidelberg new york : springer - verlag ) , ( 1991 ) r. l. davies , g. efstathiou , m. fall , g. illingworth and r. l. schechter , _ astronomical journal _ , * 266 * , 41 , ( 1983 ) a. matkovi and r. guzmn , _ monthly notices of the royal astronomical society _ , * 362 * , 289 , ( 2005 ) and references therein .
we have tried to maximize the errors so we have always chosen in the table 1 of tremaine et al.@xcite the maximal difference between the measure of the black hole mass and its high or low values in parenthesis .
so , for example , for ngc 3379 the measure @xmath36 becomes in our statistical elaboration ( see column 2 of table 2 ) @xmath37 .
accordingly , the formula used in this paper to estimate all the maximal errors in the functions f of the parameters @xmath38 is @xmath39 furthermore the reduced @xmath21 is defined as : @xmath40 for a relation of the form @xmath41 .
we support , with new fitting instruments and the analysis of more recent experimental data , the proposal of a relationship between the mass of a supermassive black hole ( smbh ) and the kinetic energy of random motions in the host elliptical galaxy . 
 the first results obtained in a previous paper with 13 elliptical galaxies are now confirmed by the new data and an enlarged sample . 
 we find @xmath0 with @xmath1 depending on the different fitting methods and samples used . 
 the meaningful case @xmath2 is carefully analyzed . 
 furthermore , we test the robustness of our relationship including in the sample also lenticular and spiral galaxies and we show that the result does not change . finally we find a stronger correlation between the mass of the galaxy and the corresponding velocity dispersion that allows to connect our relationship to the @xmath3 law . with respect to this law , our relationship has the advantage to have a smaller scatter .    
 keywords : black hole physics  
 galaxies : kinematics and dynamics