Edwin Powell Hubble in 1929 studied distant galaxies and found that they were moving away from us. Hubble calculated what has become known as the Hubble's constant H0 - defining the relationship between a galaxy's speed and its distance. Hubble's original value for H₀ was 550 kilometres per second per megaparsec (km/s/Mpc).

Hubble's successor Allan Sandage in the early 1960's was accumulating data to so show how more rapidly the universe was expanding - he measured at redshifts z greater than 0.5 by choosing the brightest members of rich galaxy clusters (a collection of galaxies) as "standard candles". Alan Dressler says this premise "all but collapsed" when Beatrice challenged Sandage's premise that the brightest galaxy in every cluster has about the same true luminosity.

Robert C. Kennicutt Jr. describes Beatrice methods as developing, "virtually from scratch". Virginia Trimble, covering all her bases, uses the phrase "she created, as nearly single-handedly as anything in modern astrophysics can be single-handed, the discipline of modeling the evolution of galaxies to account for their chemical compositions, luminosities, colours, and gas contents as a function of time and applied those models to fundamental astronomical problems, including that of determining the age and geometry of the universe as a whole".

Beatrice's thesis was the first detailed study of how galaxies change in brightness (magnitudes) and color (temperature - blue stars are hotter than red stars, also blue galaxies have younger stars) as their compositions and star-formation rates changed. She combined a number of streams of astronomical disciplines- stellar evolution and atmospheres, stellar and interstellar (the interstellar medium) abundances of metals (i.e. the elements other than Hydrogen and Helium), observed magnitudes and colours of stars and galaxies (i.e. photometric observations), galaxies, and computer programming. These fields of expertise had not been previously combined. Kennicutt describes the paper as "one of the most interdisciplinary works of its day, and certainly one of the boldest graduate thesis projects ever undertaken."

Beatrice's mathematical model would introduce or refine methods that are still used today to model the chemical evolution of galaxies, gas contents, and apply those to stellar statistics and evolution of the Hubble sequence. Her model would show how her mathematical solutions could be compared to the observations at that time of redshifts z and apparent magnitudes of galaxies. She computed the evolution history of galaxies from Population I stars, with stars forming in discrete steps of 10⁹ years. For each of these steps, she calculated the number of stars, with 13 different masses, born in the previous interval. The stars according to mass and age where then plotted a Hertzsprung-Russell Diagram. She varied a number of parameters - integrated photometric properties, gas contents, and metal abundances and the evolution of this with time - in her models.

At that time, observations were using the magnitude-redshift (m-z) relation for the brightest elliptical galaxies in clusters to measure the deacceleration parameter q0. Beatrice's inspiration was to use all range of galaxy types, not just ellipticals. The importance of this paper is that galaxies fade rapidly so that corrections are required when using the concept of 'standard candles'. Also that the colours of galaxies of all Hubble types (the Hubble sequence) can be explained as a result of different histories of star formation without assuming different ages. But she concluded that the different galaxy types have not been found to have an evolutionary sequence as assumed by Hubble, e.g. irregulars do not evolve through spirals into ellipticals.

Sandra Faber describes another important aspect of Beatrice's work. "she was the best critic of my own papers, and she did the favor for many others. In consequence, she became a clearinghouse for new results, playing the vital role of coordinator and communicator in a field where many different inputs had to be evaluated and synthesized. Beatrice won the reputation as the "Whole Earth Catalog" of galactic studies. She knew who was doing what and could put you in contact with just the person you needed to talk to. No one before or since has played this role to such perfection, and the communications gap left by her passing is as much missed, I believe as the cessation of her scientific output." This was written five years after Beatrice died.

Refer Appendix A The Published Works of Beatrice Tinsley and Appendix B. Publications of Beatrice Tinsley.

1. Star Formation Rates In Normal And Peculiar Galaxies

In 1978 with co-author Richard Larson, Beatrice produced the paper "Star formation rates in normal and peculiar galaxies" (1978ApJ...219...46L). This paper compared the broad band (UVB) colours of the mostly normal galaxies to Peculiar, collisional galaxies. The irregular galaxies were bluer in colour. They used computer simulation of color evolution models with the parts: an old stellar population with a declining Stellar Formation Rate (SFR) , and a relatively young population formed in a "burst" of short duration. Most of the normal galaxies could be accounted by models with a little burst component, but a modest range of timescales and a declining SFR. For the color range in the irregular galaxies, a substantial burst component was needed, as well as a range of times since the burst.

The importance of this paper is that the average stellar age of a galaxy where normal smooth-arm spiral galaxies have low star-formation rates and hence an older average stellar age compared to an irregular galaxy with higher present-day star formation rates.

Kennicutt makes reference to this paper as one which he could have easily nominated as one of the most important papers in the last 100 years. The conclusions of the paper is still controversial but consistent with available data. This is Beatrice's most cited paper.

2. Open vs. Closed Universe

Beatrice writing to her father, says "it may be bad science, as you say 'bad science' to like the universe being open because it feels better, but there is in me a strong delight in that possibility. I think I am tied to the idea of expanding for ever - like life in a sense - more than spatial infinity. In fact more complicated theories are possible, in which the universe is closed spatially, so finite in extent, but will expand for ever. Eddington was wedded philosophically to that model. Currently James Gunn and I are working on the possibility that a model like this really fits the observations best. I'm afraid it's so complicated to get good enough data and bright enough ideas, that we may never feel sure. It amuses me the way scientists' philosophical prejudices colour their arguments. Our friend Jerry Ostriker and I continually accuse each other of making biased scientific arguments because he says I really want the universe to be open, and I say he really wants it to be closed. Gets us nowhere but makes good parties. "

1. Beatrice on Publicity and Controversy

Beatrice describes "a spate of notoriety.. besieged by phone calls etc. including yesterday a telephone interview with the Canadian Broadcasting Company. Funnily it's by no means the most significant work I've done, but it captures the public imagination more than most things. Fun being famous for a little while! Sometimes I remember in a rather startled way how I used to read the encyclopedia as a kid and wish I could understand and contribute to cosmology".

This was her paper, Unbound Universe, with James E. Gunn ApJ 194 543-553, submitted 28 June 1974.

There were newspaper reports on a talk that Beatrice and James E. Gunn had given at the December 1974 Texas Symposia in Dallas conference. Her reaction to this publicity was "It's fun being spectacular sometimes but we've all got mountains of crank mail from the exposure - what happens when you start blowing up the universe."

Also from this meeting there was publicity in The New York Times, and Der Spiegel which prompted Scientific American to ask for an article, "by far the best generalists' science publication there is" - "chance to teach our stuff to the public." Beatrice edited the final version published in January 1976.

Of her colleagues, Beatrice wrote "I don't see as it is a weakness to be motivated by emotions. What else is the driving force, or the inspiration to think of useful theories? Only if emotional attachment to one's own theory makes one blind to alternatives is it bad. But on the whole I find controversies that I get involved in are stimulating to think the next way to return to the ball, and we all learn what are useful ideas or otherwise as we go."

3. Annual Review Of Astronomy And Astrophysics 1976

Beatrice was given the prestige with her French colleague, Jean Adouze, to write this review titled "Chemical evolution of galaxies" 1976ARA&A..14...43A This paper has 154 citations. This allowed Beatrice to discuss the theories of nucleosyntheses, origin and evolution of stellar populations. "A state of the Universe" address.

This included a flowchart which clearly shows a picture of all the processes that affect galactic evolution.

4. Galaxy Counts

Counts provide information as to the structure of the universe and how galaxies formed and changed with time - whether galaxies are scattered uniformly through space and whether ancient collisions and mergers of galaxies have affected the numbers of galaxies. Edwin Hubble counted galaxies in the 1930s. Although Hubble detected galaxies as faint as magnitude 20, he did not draw any conclusions.

Beatrice resurrected the counting of faint galaxies. The farther away the galaxy is, the longer ago its light must have left to reach us. So we have look back in time as we look at distant galaxies. Because of this look-back time, a count of all galaxies mixes up the effects of galactic changes with time and the distribution of galaxies at different distances. To help separate these two effects, astronomers count down to the same limiting magnitude in each area of sky.

This paper was "Galaxy counts as a cosmological test" 1974ApJ...194..555B. Astronomers look for evolution by comparing the numbers of galaxies as the limiting magnitude grows fainter. Because galaxies are uniformly scattered, they should appear at the same rate as fainter, and therefore more-distant, galaxies are counted. A change in the number implies that galaxies have somehow changed. Her conclusion is that the differences between observations are as sensitive as the cosmological models being tested.

5. Red Shift Surveys

Faint redshift surveys were originally motivated by Beatrice's suggestion that the faint blue galaxies that had been observed were, in fact, high redshift young ellipticals. However, it soon became clear that from the redshift-dependent field galaxy luminosity function that galaxy evolution up to redshift of 1 is rather complex. There is a rapid decline in the number of small irregular blue galaxies whereas the massive regular systems evolve more slowly. Today, this is still the significance of these redshift surveys. The Hubble Space telescope (HST) may have confirmed this with the these photos Faint Blue Sub-Galactic Clumps may be Galaxies Under Construction.

Beatrice overcame her isolation from her peers when she was working from home by attending and giving lectures all over the world, as well as writing many letters and making phone calls. What postage and telephone bills she must have had. This hectic lifestyle even continued once she was a faculty member at Yale University in 1975. She gave lectures in England, Italy, Switzerland, and France. Beatrice attended many International Astronomical Union (IAU) (symposia, and colloquia meetings) and AAS conferences. For example, in August 1976, she spent a month in Britain to complete her Annual Review Of Astronomy And Astrophysics then went onto Grenoble and Paris .

In 1978 there were conferences at University of Maryland, University of California (Santa Cruz), and Princeton. In August 1978, Amsterdam for one day.

Refer Appendix C The Schedule of Beatrice Tinsley.

We know from Beatrice's correspondence that one of her heroes was William Alfred (Fred) Hoyle. This did not stop her from writing a critical paper on Hoyle. She writes of the reaction to her paper - "Well received", "I feel specially gratified about my own one I think it was the best work I've done and a significant discovery - others think so to -. The paper is about Hoyle's theory was also accepted by all but Fred, though nobody took his line of defence seriously. I had a very good conversation with him about it, and we basically agreed that Barnothy and I showed very serious difficulties for his theory though not insuperable ones. The paper was "A critique of Hoyle and Narkilav's New Cosmology" 1973ApJ...182..343B. The Hoyle paper concluded that the gravitational constant G affects only stellar temperatures and luminosity. She thought that Hoyle's conclusions were 'implausible.' She argued that these predictions would mean much brighter and bluer (hotter) than observations show.

Despite her criticism of Hoyle's work earlier, Beatrice was invited to speak at a conference in Venice 1974 celebrating Hoyle's 60th Birthday. Her reaction to the invitation - "very moved to be giving a review of cosmology at Hoyle's sixtieth birthday, since it was his books that I read at high school that introduced me to the subject." Her argument at that time was that the effect of the aging of stars in bright, massive objects is to make them grow significantly fainter with time. This is still true today for isolated galaxies - with more gas providing the fuel, more stars will form and hence the more luminosity. Over time, the gas fuel supply is expended, so less stars are formed and hence luminosity diminishes. The opposing view to Beatrice's then was held by Ostriker and Tremaine who argued that galaxies will eat up the fuel from nearby galaxies - hence with a new source of fuel, this will increase the star formation rate, so making them grow brighter with time. The Ostriker and Tremaine view is true for colliding galaxies. The arguments depend upon the type of galaxy and the bandpass (i.e. blue vs red vs infrared) in question.

Some of her students are now professors. One is Professor Simon White who sent me the following email "I knew Beatrice Tinsley while a graduate student and interacted with her on many topics in astronomy. I remember particularly well one evening when I was visiting Yale (as a graduate student) and she took me out to dinner in a restaurant there. The conversation ranged over many topics in astronomy, but she also told me about her battle with cancer which was to claim her life a year later. I was deeply impressed by her matter-of-fact attitude towards the illness and the fact that she remained optimistic and dedicated to astronomy in the face of it. Beatrice was, I think, the most original and impressive of all the women astronomers I have known. "

Another former student is Dr. Curt Struck who is a Professor of Astrophysics in the Department of Physics and Astronomy at Iowa State University. Dr. Struck received his Ph.D. at Yale University under Beatrice and Richard Larson.

1. Do Important Papers Produce High Citation Counts?

This was a question asked by Dr. Helmut. A. Abt at the 195th AAS Meeting, in January 2000. "We found that the important papers averaged 6.7 times as many citations as the controls. Ninety-four percent of the important papers produced more citations than the average for the controls. Thus important papers almost invariably produce high citation counts. We also found that the lifetimes of the important papers were 2.5 times longer on the average than for the controls."

I was only able to obtain the abstract of this paper. I do not know if this paper gave an actual number for citations.

2. Long Term Histories of Astronomical Papers

H.A. Abt in 1981 said that citations reached a maximum five years after publication. The citation counts for Beatrice's top two cited papers, numbered 1 and 2, from the year of publication until 1999 are in the table below. The citation counts for these two papers reveal a very different story to Abt's comments. Across the bottom row is the year in which the paper was cited e.g. 78 is 1978.

Table 1 Number of Citations By Year

1	8	22	24	25	23	30	29	24	27	31	19	24	28	22	23	25	27	33	28	26	17	16
2	-	-	2	10	10	14	16	21	20	19	18	24	26	25	24	27	28	28	23	33	21	23
yr	78	79	80	81	82	83	84	85	86	87	88	89	90	91	92	93	94	95	96	97	98	99

Paper 1. 1978ApJ…219…46L "Star formation rates in normal and peculiar galaxies" This paper has had 533 citations. Beatrice was the co-author with Richard B. Larson. This paper had acceptance only after its second year of publication in 1978 - and the citation counts were still climbing eighteen years its after publication.

Paper 2. 1980FCPh….5..287T "Evolution of the Stars and Gas in Galaxies" This chapter was part of the "Fundamentals Of Cosmic Physics" published in 1980 has had 415 citations. This work where Beatrice is the sole author, took five years to reach 20 citation counts, but this was not the maximum citations reached - this was seventeen years after its publication.

3. When Do Astronomers Write Their Best Papers?

Abt, H.A. in 1983 in his paper "At What Ages Did Outstanding American Astronomers Publish Their Most-Cited Papers" concluded that astronomers typically write their best papers between the ages of 40 and 50. Unfortunately we did not have the good fortune of Beatrice surviving very long after her 40th birthday.

4. Citation Counts For Papers By Women Astronomers

Trimble in her introduction to Payne-Gaposchkin's autobiography states that women astronomers average 32 citations per year. From the chart below, Papers and Citations By Year, the citations that Beatrice received very quickly jumped to over 50 per year from 1974. For the next 23 years, the citation counts were in excess of 100 per year reaching a maximum of 208 in 1985. Even in 1999 the citation count is over 50.

As of the end of March 2000, her work is still being cited, nearly 20 years after her death. A lasting legacy.

5. Self-Citation Rates.

Trimble states that of the 496 astronomical papers published in 1983, 15.1% were self-citations. Of all the papers authored or co-authored by Tinsley there were 3873 citations. Of these, there were 253 citations where Tinsley was self-citing which is 6.53%. Of Beatrice's top 10 papers, by number of citations, there were 1949 citations. Of these there were only 56 self-citations, which is 2.9%. Beatrice's citation count is far from inflated by self-citation.

6. Funding

H. A. Abt in his 1984 paper "Citations to Federally-Funded and Unfunded Research" states that "Sloan Fellows and university authors receiving most funds of auxiliary outside funding (NASA, NSF) produce higher-cited papers than papers without such funding."

Of Beatrice's top 10 papers, by number of citations, (refer Table 3 Top 10 Cited Papers) eight had this type of funding. But Beatrice was a peculiar circumstance of having only "Soft money". It was only because of funding provided by these agencies that Beatrice had any funds at all to publish her papers.

7. Citations to Single and Multiauthored Papers

H. A. Abt in his 1984 paper concluded that the "Number of citations increases linearly with the number of authors". Just examining the top 10 cited papers this is not an easy assumption to confirm. With Beatrice's top cited paper, she is co-author with Richard B. Larson, her next cited paper she is the sole author. Beatrice is the sole author in two of her top 10 cited papers.

8. Discrepancies

ADS Database Citation gives the following warning "The Citation database in the ADS is NOT complete. Please keep this in mind when using the ADS Citation lists."

Caution: If you use the ADS Custom Query Search Page and enter the author of 'Tinsley, B.M.' you will see a count of 112 papers. This filter also gives the papers of her husband Brian, Tinsley, B.A. from Appendix A. The Published Works of Beatrice M. Tinsley there are 101 papers.

Trimble produced the following table comparing astronomers who had died before 1985 with a living (control) astronomer to conclude that in a wake of a death - a brief period of memory and sympathy followed by forgetfulness, citation rates decrease. From the chart above of Papers and Citations By Year this is not the case for Beatrice.

Table 2 Number of Citations to Papers by Index (Deceased) and Control (Living)

Date of Death	Index/Control	First/ Last Paper	1965-69	1970-74	1975-79	1984
May 1981	Beatrice Tinsley	1967	11 (2*)	86 (104*)	465 (783*)	69 (175*)
	Virginia Trimble	1981	28	187	311	66

Source: Table 1 Number of Citations to Papers by Index (Deceased) and Control (Living) Astronomers 1965-79 and 1984

Note. The citation counts obtained using the ADS database (*) and that given by Trimble.

Kennicutt gives of number of papers that Beatrice wrote for the ApJ as being 43 papers, I had the number as 37 (refer Appendix B Publications of Beatrice Tinsley).

Trimble gives the number of papers that Beatrice wrote in her 14 years as 114. I have 101 papers. (refer Appendix A The Published Works of Beatrice M. Tinsley).

9. Beatrice M. Tinsley - Top 10 Cited Papers