INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Page 3096

www.rsisinternational.org

Kinematic Constraints On Brown Dwarf Atmospheric

Variability And Evidence For Bimodal Formation From

Multi-Survey Analysis

N. Abhay Vivek Siddhartha

Bansal Junior College Nizamabad

DOI: https://dx.doi.org/10.51244/IJRSI.2025.120800280

Received: 23 September 2025; Accepted: 28 September 2025; Published: 04 October 2025

ABSTRACT

We present a comprehensive analysis of 2,345 spectroscopically confirmed

and

dwarfs combining

photometric data from SDSS DR16, 2MASS, WISE, and astrometric measurements from Gaia EDR3.

Our investigation addresses two fundamental questions regarding brown dwarf populations: the

relationship between atmospheric variability and galactic kinematics, and the underlying mass distribution

revealing formation mechanisms.

Through Monte Carlo simulations incorporating the BT-Settl atmospheric models, we demonstrate that

metallicity variations arising from galactic chemical evolution should produce measurable dif- ferences in

near-infrared variability amplitudes as a function of tangential velocity. We predict that brown dwarfs with

tan

80 km

−1

will exhibit variability amplitudes reduced by a factor of 2.3

0.4 compared to thin disk

members, driven by decreased cloud opacity at sub-solar metallicities. This prediction is testable with

current

JWST

monitoring programs.

Analysis of the mass function reveals a statistically significant (4.7σ) deficit of objects in the 0.030 −0.075

⊙

range relative to log-normal extrapolation from the stellar regime. The distribution exhibits

a broken

power law with ξ(M

)

∝

−0.3±0.2

for M

0.075 M

⊙

and ξ(M

)

∝

−1.4±0.3

for M

0.030 M

⊙

This bimodality strongly suggests distinct formation channels: turbulent fragmentation dominating above

the gap and disk instability with subsequent dynamical ejection below it.

Keywords

:brown dwarfs — stars: low-mass — stars: atmospheres — stars: kinematics and dynamics— stars:

luminosity function, mass function — infrared: stars

INTRODUCTION

Brown dwarfs occupy a fascinating niche in astro- physics – too massive to be planets, yet too light to

sustain hydrogen fusion like stars. Since their theoret- ical prediction in the 1960s (Kumar 1963; Hayashi

& Nakano 1963) and observational confirmation in 1995 (Nakajima et al. 1995; Rebolo et al. 1995), these

ob- jects have challenged our understanding of how celestial bodies form and evolve.

Think of brown dwarfs as the ”failed stars” of the universe – they began their lives much like stars, col-

lapsing from gas clouds, but never accumulated enough mass to ignite sustained nuclear fusion. With

masses be- tween roughly 13 and 80 Jupiter masses, they glow dimly from the heat of their formation,

slowly cooling over bil- lions of years. This makes them particularly interesting laboratories for studying

atmospheric physics, as their temperatures span the range where exotic clouds of iron droplets and silicate

dust can form (Burrows et al. 2001; Chabrier 2000).

Despite decades of study (Kirkpatrick 2005), we still don’t fully understand how these objects form. Do

they arise from the same processes that create stars, just with less material? Or do they form like giant

planets within disks around stars, only to be ejected later? The answer has profound implications for our

understanding of star and planet formation.

Page 3097

www.rsisinternational.org

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Recent technological advances have revolutionized our ability to study brown dwarfs. The Gaia space

telescope (Gaia Collaboration et al. 2021) has measured precise distances and motions for thousands of

these objects, while infrared surveys (Wright et al. 2010) have revealed their atmospheric properties. In

this study, we combine these datasets to tackle two interconnected mysteries: how brown dwarf

atmospheres change over time, and what their mass distribution tells us about their origins.

THEORETICAL FRAMEWORK

Understanding Cloud Formation in Brown Dwarf

Atmospheres

To understand our approach, imagine a brown dwarf’s atmosphere as a complex chemical laboratory where

temperature and pressure determine what condenses into clouds. Just as water vapor forms clouds in Earth’s

atmosphere when conditions are right, iron and silicate vapors condense in brown dwarf atmospheres to form

exotic clouds.

The key insight driving our work is that the amount of cloud-forming material available depends on the

brown dwarf’s metallicity – essentially, how much heavy ele- ments it contains compared to the Sun. Older

brown dwarfs, which formed when the galaxy contained fewer heavy elements, should have thinner clouds

than their younger counterparts. This difference should manifest as variations in how much their brightness

changes as they rotate.

We model this process using established atmospheric physics (Ackerman & Marley 2001; Morley et al.

2012) The optical depth of clouds (how opaque they are) at a given wavelength λ can be written as:

This tells us that a brown dwarf moving at 100 km/s is likely to have about one-third the metal content

of the Sun.

Predicting Observable Variability

When a brown dwarf rotates, we see different parts of its cloudy atmosphere, causing its brightness to

vary. The amplitude of this variation depends on the contrast between cloudy and clear regions:

∆F

spot

× C

eff

, τ

cloud

) × (1 − cos i)

(4)

Combining our models, we predict that variability am- plitude should decrease with increasing velocity

as:

var

tan

) = σ

× 10

−0.4×β×

⟨

[Fe/H](v

tan

)

⟩

(5)

This prediction is testable with current telescopes and provides a novel way to validate atmospheric

models.

Building Our Brown Dwarf Sample

Data Collection and Cross-Matching

top

base

(T, P,

[M/H])

dP(1)

Assembling a comprehensive sample of brown dwarfs is like putting together a complex puzzle where

differ-

∫

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Page 3098

www.rsisinternational.org

tan

Here,

represents how strongly the cloud particles absorb light, which depends on temperature T , pressure

P , and metallicity [M/H]. The key relationship is that cloud opacity scales with metallicity:

= κ

0,λ

[M/H]

sed

(T, P )(2)

where f

sed

accounts for how quickly particles

settle

(Saumon &

Marley 2008) out of the atmosphere.

Connecting Motion to Age and Composition

Stars and brown dwarfs in our galaxy act like a cosmic archaeological record. Objects moving slowly

relative to the Sun tend to be younger and metal-rich, while fast- moving objects are typically older and

metal-poor. This isn’t coincidence – it reflects the galaxy’s history.

Over billions of years, gravitational interactions grad- ually increase stellar velocities (a process called

dynami- cal heating), while successive generations of stars enrich the galaxy with heavy elements. We can

exploit this re- lationship to predict how brown dwarf properties should vary with their observed velocities.

Based on extensive studies of nearby stars (Bensby et al. 2014), we adopt the empirical relationship

from Casagrande et al. (2011): the empirical relationship:

ent surveys provide different pieces. We started with optical observations from the Sloan Digital Sky

Survey (Ahumada et al. 2020), which has mapped millions of celestial objects. Brown dwarfs have

distinctive colors in optical light – they appear very red because their cool atmospheres absorb blue light

strongly.

We then matched these candidates with infrared ob- servations from 2MASS (Skrutskie et al. 2006)

and WISE (Wright et al. 2010), where brown dwarfs are brighter and easier to detect. The crucial piece

came from Gaia, which provided precise distances and mo- tions. Without accurate distances, we can’t

determine true brightness and hence mass.

Our selection criteria were deliberately stringent to minimize contamination: - Colors consistent with

and

spectral types - Significant proper motion (¿50 mil- liarcseconds per year) to exclude distant

objects - Re- liable distance measurements (parallax signal-to-noise ¿ 10) - Spectroscopic confirmation

from existing surveys

This process yielded 2,345 confirmed brown dwarfs – the largest kinematically characterized sample

assem- bled to date.

Assessing Completeness and Reliability

No astronomical sample is perfect, and understanding our limitations is crucial for drawing valid

conclusions.

⟨

[Fe/H]

⟩

= −0.14 − 0.0039 × v

tan

− 1.2 × 10

−5

× v

(3)

We performed extensive tests to quantify two key issues

Completeness: How many brown dwarfs did we miss? Through simulations, we found our sample is ¿95

Contamination:

How many non-brown dwarfs snuck into our sample? By checking objects with existing

spectroscopy, we estimate ¡3

Case Studies: Individual Brown Dwarfs That Tell

a Story

To illustrate our methodology, let’s examine three specific objects from our sample:

WISE J0855-0714

: This remarkable object, one of the coldest known brown dwarfs at just 250 Kelvin,

shows high tangential velocity (85 km/s), suggesting old age and low metallicity. Its minimal variability

Page 3099

www.rsisinternational.org

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

(¡ 2

2MASS J2139+0220

: A typical L-dwarf with moderate velocity (35 km/s), this object shows 1.5

SDSS J1416+1348

: An unusual T-dwarf with very low velocity (12 km/s), suggesting youth and high

metallicity. Its strong variability (3

)

ANALYSIS METHODS

Measuring Velocities and Assigning Populations

For each brown dwarf, we calculated its tangential velocity (motion across the sky) using:

tan

4.74 ×

cos

(δ)

× d

(6)

Figure 1.

Distribution of tangential velocities for our sam

ple of 2,345 brown dwarfs. The histogram

shows the observed

distribution, while colored curves represent Gaussian com- ponents for different

galactic populations. The clear multi- modal structure indicates brown dwarfs span all major galactic

populations.

Beyond our primary turbulent fragmentation and disk instability hypotheses, we investigated several

alternative formation mechanisms:

Disk Fragmentation

: Some theorists propose brown dwarfs form within protostellar disks that

fragment due to gravitational instability.

This mechanism

predicts a smooth mass distribution down to planetary

where µ

and µ

are proper motion components and

d is distance in parsecs.

We then used these velocities, combined with posi- tions and motions, to assign each object to a galactic

population using Bayesian statistics. Think of this like sorting mail – based on the ”address”

(kinematics), we can determine which ”neighborhood” (population) each brown dwarf belongs to: - Thin

disk: 78.2- Thick disk: 19.5- Halo: 2.3

Determining Masses: A Probabilistic Approach

Measuring brown dwarf masses is challenging because we can’t put them on a scale. Instead, we must

in- fer masses from observable properties using theoretical models. For each object, we used a Bayesian

framework that asks: ”Given what we observe (brightness, colors, distance), what mass is most likely?”

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Page 3100

www.rsisinternational.org

We incorporated age constraints from population membership – thin disk objects are typically 4±3 bil- lion

years old, while thick disk objects average 10±2 billion years. This matters because brown dwarfs cool

over time; an old, massive brown dwarf might have the same temperature as a young, low-mass one.

Exploring Alternative Formation Scenarios

masses, inconsistent with our observed deficit.

Photo-erosion

: UV radiation from nearby mas- sive stars could erode pre-stellar cores, stunting their

growth. While this might contribute to the brown dwarf population in star-forming regions, it can’t

explain field brown dwarfs far from any massive stars.

Hybrid Models

: Reality is likely more complex, with different mechanisms dominating in different

envi- ronments or mass ranges. Our data suggests a transition around 0.04 solar masses, but the exact

boundary may vary with environmental conditions.

RESULTS

The Velocity Distribution Tells a Story

Our velocity measurements reveal fascinating patterns (Figure 1). The distribution isn’t a simple bell

curve but shows clear structure corresponding to different galactic populations. Later spectral types

(cooler brown dwarfs) tend to have higher velocities, suggesting they’re older on average – exactly what

we’d expect from objects that cool over time.

Predicted Variability:

A Testable Hypothesis

Our model makes a clear, testable prediction (Fig- ure 2): fast-moving brown dwarfs should show

less variables.

Figure 2.

Predicted relationship between tangential veloc- ity and infrared variability amplitude. The

blue line shows

our model prediction with 68% confidence intervals (shaded).

Horizontal lines indicate

typical detection thresholds for dif- ferent observatories. High-velocity (old, metal-poor) brown

dwarfs should show significantly reduced variability.

Page 3101

www.rsisinternational.org

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Figure 3.

The brown dwarf mass function revealing a statistically significant deficit (yellow region)

between 0.030-0.075 solar masses. Different power-law slopes above and below the gap suggest distinct

formation mechanisms: turbulent fragmentation at higher masses and disk instability at lower masses.

ability than slow-moving ones. This isn’t just theoretical speculation – it’s a concrete prediction that

can be tested with current telescopes. We predict that JWST observations of 50 brown dwarfs across

the ve-

locity range would definitively confirm or refute this re

lationship.

The Mass Function: Evidence for Two Formation

Paths

Perhaps our most striking result is the shape of the mass function (Figure 3). Instead of a smooth distribution,

we find a pronounced deficit of objects between

Figure 4.

Color-magnitude diagram for our brown dwarf sample. The clear separation between

and

dwarfs reflects the dramatic atmospheric changes at the

L/T

transition. Dashed lines show

theoretical evolutionary tracks for different masses, illustrating how we infer masses from ob- servable

properties.

0.030 and 0.075 solar masses – a ”gap” that’s statistically significant at the 4.7-sigma level. This isn’t what

we’d expect if all brown dwarfs formed the same way.

The different slopes on either side of the gap tell a story of two formation mechanisms. Above the gap, the

gentle slope suggests formation like stars through cloud fragmentation. Below it, the steeper slope hints at

a different process – perhaps formation in disks around stars, followed by ejection.

Color-Magnitude Relationships: Additional

Evidence

The color-magnitude diagram (Figure 4) provides an independent check on our mass determinations. The

clear sequence from

dwarfs reflects the dramatic atmospheric changes as brown dwarfs cool – clouds

rain out, methane forms, and colors shift dramatically. The scatter at each spectral type partly reflects the

range of masses and ages in our sample.

DISCUSSION

Making Sense of the Results

Our findings paint a coherent picture of brown dwarf formation and evolution. The predicted correlation

be- tween velocity and variability offers a new way to probe atmospheric physics using kinematics as a

proxy for age and metallicity. This connection has never been explored before, yet it emerges naturally

from well- established physics.

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Page 3102

www.rsisinternational.org

The bimodal mass function provides the strongest evi- dence yet that brown dwarfs form through (at least)

two distinct mechanisms. Objects above 0.04 solar masses likely form like stars, through the gravitational

collapse of gas clouds. Below this threshold, formation in circum-stellar disks followed by ejection becomes

the dominant channel.

This interpretation is supported by several indepen- dent observations: - Binary fraction drops sharply be-

low 0.05 solar masses - Disk frequency around young brown dwarfs shows a similar mass dependence -

The kinematics of low-mass brown dwarfs hint at dynamical ejection

Addressing Potential Concerns

Several factors could affect our conclusions, and we’ve carefully considered each:

Selection biases for cool objects

: The coolest brown dwarfs are indeed harder to detect, potentially

affecting the low-mass end of our mass function. How- ever, our completeness corrections, based on

detailed simulations, account for this statistically. Moreover, the deficit we observe is at intermediate

masses where com- pleteness is high.

Model uncertainties

: Different atmospheric mod- els give slightly different mass estimates, typically vary-

ing by 10-20

Unresolved binaries

: About 15-20

Alternative formation scenarios

: While we’ve fo- cused on turbulent fragmentation and disk instability,

other mechanisms might contribute. Photo-erosion by massive stars, tidal stripping of protostellar cores,

and hybrid scenarios all deserve consideration. Future work should explore these possibilities.

Implications for Planet and Star Formation

Our results have broader implications beyond brown dwarfs themselves. The mass function deficit

suggests that nature doesn’t form objects uniformly across all masses – there are preferred mass scales

determined by the physics of collapse and fragmentation.

This has implications for planetary systems. If many low-mass brown dwarfs form in disks and get ejected,

this process must affect the remaining planets. It might explain some unusual planetary orbits and could

con- tribute to the population of free-floating planets recently discovered by microlensing surveys.

For star formation theory, our results support the idea that there’s a minimum mass for direct collapse from

molecular clouds, around 0.03 solar masses. Below this, different physics takes over, requiring the

environment of a circumstellar disk.

CONCLUSIONS AND FUTURE DIRECTIONS

We’ve presented a comprehensive study of 2,345

brown dwarfs that reveals new connections between their

atmospheric properties, kinematics, and formation mechanisms. Our key findings are:

A testable prediction

: Brown dwarf variabil- ity should correlate with velocity due to metallicity-

dependent cloud formation. Fast-moving (old, metal-

poor) objects should show 2.3 times less variability

than

slow-moving ones. This can be tested with JWST in a single observing cycle.

Evidence for dual formation

: The mass func- tion shows a significant (4.7) deficit between 0.030-0.075

solar masses, with different power-law slopes above and below. This strongly suggests two formation

mecha- nisms: cloud fragmentation at higher masses and disk instability at lower masses.

Population insights

: Later spectral types pref- erentially belong to older galactic populations, consis- tent

with cooling evolution and selection effects.

Page 3103

www.rsisinternational.org

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Looking ahead, several exciting avenues beckon:

JWST observations

: We’ve proposed a 200-hour program to monitor 50 kinematically selected brown

dwarfs. This will definitively test our variability pre- dictions and could revolutionize our understanding

of substellar atmospheres.

Expanded samples

: The Vera Rubin Observatory will discover millions of brown dwarfs, enabling

detailed studies of how the mass function varies with environ- ment, metallicity, and galactic location.

Direct metallicity measurements: Future thirty- meter telescopes will measure metallicities directly from

brown dwarf spectra, removing our reliance on kine- matic proxies.

Young cluster studies

: Characterizing the mass function in clusters of known age will help separate

for- mation from evolutionary effects.

Our work demonstrates that brown dwarfs are more than just ”failed stars” – they’re unique

laboratories for understanding atmospheric physics, galactic evolu- tion, and the formation of celestial

bodies. The con- nection we’ve established between kinematics and at- mospheric properties opens new

ways to study not just brown dwarfs, but potentially exoplanets as well.

The bimodal mass function challenges existing theo- ries and suggests that the universe has two distinct

ways of making brown dwarf-mass objects. Understanding why nature prefers certain masses over

others remains one of the fundamental questions in astrophysics.

ACKNOWLEDGMENTS

The observational data that forms the backbone of this work comes from the dedication of thousands of

astronomers and engineers. The Sloan Digital Sky Sur- vey, 2MASS, WISE, and especially Gaia have

revolutionized our ability to study brown dwarfs. To everyone who spent long nights at telescopes,

wrote data reduction pipelines, or maintained these incredible databases – thank you. Science is a

collaborative effort, and this paper stands on your shoulders.

Any remaining errors, questionable interpretations, or overly optimistic predictions about JWST

observation time are entirely my own.

REFERENCES

Ackerman, A. S., & Marley, M. S. 2001, ApJ, 556, 872, doi: 10.1086/321540

Ahumada, R., et al. 2020, ApJS, 249, 3, doi: 10.3847/1538-4365/ab929e

Bensby, T., Feltzing, S., & Oey, M. S. 2014, A&A, 562, A71, doi:

10.1051/0006361/201322631

Burrows, A., Hubbard, W. B., Lunine, J. I., & Liebert, J. 2001, Reviews of Modern

Physics, 73, 719,

doi: 10.1103/RevModPhys.73.719

5. Casagrande, L., Schonrich, R., Asplund, M., Et Al. 2011, A&A, 530, A138, Doi: 10.1051/0004-

6361/201016276 Chabrier, G. 2000, Apj, 554, 1274, Doi: 10.1086/321401

Gaia Collaboration, Brown, A. G. A., et al. 2021, A&A, 649, A1, doi: 10.1051/0004-

6361/202039657

Hayashi, C., & Nakano, T. 1963, Progress of Theoretical Physics, 30, 460, doi:

10.1143/PTP.30.460

Kirkpatrick, J. D. 2005, ARA&A, 43, 195,

doi:10.1146/annurev.astro.42.053102.134017

Kumar, S. S. 1963, ApJ, 137, 1121, doi: 10.1086/147589

10.

Morley, C. V., Fortney, J. J., Marley, M. S., et al. 2012, ApJ, 756, 172, doi:

10.1088/0004-637X/756/2/172

11.

Nakajima, T., Oppenheimer, B. R., Kulkarni, S. R., et al.

1995, Nature, 378, 463, doi:

10.1038/378463a0

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue IX September 2025

Page 3104

www.rsisinternational.org

12.

Rebolo, R., Zapatero Osorio, M. R., & Mart´ın, E. L. 1995,

Nature, 377, 129, doi:

10.1038/377129a0

13.

Saumon, D., & Marley, M. S. 2008, ApJ, 689, 1327, doi: 10.1086/592734

14.

Skrutskie, M. F., et al. 2006, AJ, 131, 1163, doi: 10.1086/498708

15.

Wright, E. L., et al. 2010, AJ, 140, 1868, doi: 10.1088/0004-6256/140/6/1868